Class _ir3.53_ GopyiightN^ uo CDEmiGifr o£Po&m ADVANCED SHOP DRAWING !% QrawMlBook (h 7m PUBLISHERS OF bOOKS F O Fl.^ Coal Age ^ Electric Railway Journal Electrical World ^ Engineering News -Record American Machinist v Ingenieria Intemacional Engineering 8 Mining Journal ^ Power Chemical d> Metallurgical Engineering Electrical Merchandising ENGINEERING EDUCATION SERIES ADVANCED SHOP DRAWING PREPARED IX THE EXTENSION DIVISION OF THE UNIYEESITY OF WISCONSIN BY VIXCEXT C. GEORGE, B. S. IXSTRUCTOR IX MECHANICAL ENGINEERING THE UXn'ERSlTY OF WISCONSIN First Edition McGRAW-HILL BOOK COMPANY, Ixc. NEW YORK: 370 SEVENTH AVENUE LONDON: 6 & 8 BOUVERIE ST., E. C. 4 1920 s'^ Copyright, 1920, by the McGraw-Hill Book Company, Inc. THK MAPLE PRESS YORK PA QEC -8 ld20 ©Ci.AG04509 PREFACE The contents of this book have been laid out with the ob- ject in view of enabhng any one who has had some prehminary training in Mechanical Drawing and in the use of drawing in- struments, to gain a practical knowledge of drafting as applied to various lines of engineering. The text material and problems have been so arranged that they should not be difficult for the student who has had sufficient practice in drawing to have become familiar with the principles of orthographic projection and the use of drawing instruments. Emphasis has been laid on drafting as applied to such special subjects as Pictorial Representation, Patent Office Drawings, Electrical Drawing, Piping Layouts, Structural Drawing, and Sheet Metal Work. These chapters are not elaborate but are designed to give the draftsman a working knowledge of these lines. The author wishes to express his appreciation to Professor Ben G. Elliott of the Department of Mechanical Engineering of the Extension Division, University of Wisconsin, for his many helpful suggestions and criticisms given during the preparation of this book, and to Professor H. D. Orth, Department of En- gineering Drawing, University of Wisconsin, for his helpful criti- cism of the completed manuscript. Acknowledgment is due also to the C. F. Pease Company of Chicago, for the use of some of their cuts of blue printing machines. . V. C. George. The University of Wisconsin, Madison, Wisconsin. October 1, 1920. CONTENTS CHAPTER I WoRKii<0 (0(0(0 < z .si si^ ..1 -y i:5i....iB|- ■iiiii-" 2 -Nio'*intt)h-«)(no- I- 1 k~ ft «l 1 ^ ^^^^^.^^ -i ^^^ ^ "O -- -----^ — s — crJr i^.„^.~:^ ^ T5 ^ 7 '^lir^i - J ii I o 2 8 ADVANCED SHOP DRAWING In assembling this end, the boxes are placed over the crank pin, the strap placed around the boxes, and the wedge secured in position by means of the cap screws. The stub end is next moved into position between the jaws of the strap, and is secured by the bolts. On account of the heavy service for which the rod is designed, there is no allowance made for play between the boxes. The boxes are made of cast iron, babbitted, with flanges to prevent lateral movement. The babbitt, which forms the rubbing sur- face, is an anti-friction metal, sufficiently fusible to be melted in a common ladle. Its use is very desirable because of its prop- erty of forming a perfect bearing easily without the necessity of reboring. The boxes are held in position by a wedge which is raised and lowered by means of two cap screws passing through the strap and tapped into the wedge. 3. Scale. — It is generally necessary to make mechanical draw- ings to some convenient scale. The scales to which the several details are drawn should be so chosen that the space allotted to each detail will bear some reasonable proportion to the space allotted to the other details. In other words, a comparatively small and insignificant part should not be drawn to a large scale and a larger and much more important part to a much reduced scale. If, however, a certain small part is highly important and intricate in design, it may be advisable to draw it to a large scale in order to show it clearly and to emphasize the fact that it should be accurately made. The space given to each detail should he in proportion to its importance and size, thus giving the plate a proper balance. 4. Legend. — Beneath each detail there should appear a title or ''legend. " This legend gives the name of the part, the number required for one machine, the material of which it is to be made, and whatever finish, if any, is required. A legend may appear something like this: Face Plate 1 — Required Cast Iron Scale ?," = V or Stuffing Box Gland 2 — Required Brass Scale 6'' = 1' WORKING DRAWINGS 9 FIRST USED ON. MATERIAL MAT SPEC. HEAT TREAT.. HARDNESS FINISH ALLOWABLE VARIATION ON PIMENStONS LOCATING FINISHED SURFACES IS PLUS OR MINUS X>05 UNLESJ OTHCKWISE SPtCIFIED. r^£^ DOME ST fc £f/a//ve£^/A(e coAfPAAfr BAYTON -PtLCQUfittT- OHIO. DATE DRAWN BY TRACED BY. SCALE. NO. Complete Wiring Diagram Of COHNECTICUT AUTOMATIC IgNITER System TVpe 'GO" or^' OmeWire System " Connecticut Ifictric Company, Inc. MeniDCN, CONN SCALE .c^?!^!^n?rr;?r. oatc .m ^r .«?.^ '-^'-^ ■ OH.BYrrfliy...... .TR.8Y'?;.a:^' ... etc. •Y./vP..a/Tffec/ )^ro/7f /O" J- 2-/ 7^ J'*-f7 ^ 2 CAR B -7-30-/4 C>£ TA //- Fig. 7. — Record strip title. company. This gives a standard title. A space is left for the name of the drawing, to be lettered in by the draftsman. The draftsman's name should appear in writing in the corner of every plate. The name should not be lettered in. In Fig. 7 is shown a record strip title. The spaces in the center are left for records of changes which may be made from time to time on the original tracing. Spaces are left in each case for the particular informa- WORKING DRAWINGS 11 tion needed by the company. If a bill of material is to be added, it is usually placed just above the title corner or in the upper right-hand corner as shown in Fig. 8. /V/^/?/r DfSCRlPT/O^ MATER/AL R£Q RtMAR/<5 M/NO S/ZE BAS£ c./. J PATT /VO. /7 @ JOOPf/AL SOX " 2 •• ^4- ^ 5/i>iFT STE£L /fo/4. / ® LE.VEH tv./. fi^j" 2 ® LE.VER " " 2 ® HA NO LEVER " i'-H" / ® L////K •' i"-^f 5 2 LE/VGTH5 ® P/A/ STEfL //>//». 4- 3 @ SEPARA rOH " 3 z r///CK/ifess£5 @ A£y l^i- 3 E lE/VGT/YS s/>ifr p/A/ " f^'i 8 SETSCREW " r-i" 3 Sro'O BOLT " 1"-^" 4 THREAD ^" The. P£e/rl£55 Eng/neer/ng Co. DETA/LS OF 3H/FTER ^c^ /2" FHICT/ON CLUTC/i 3CAIE, 3"=/ FT. o/d//Vi5 7, /.a/T! Droivn £>y ................ TracBc/ by.. Approved: ea e>y C/j/ef £^g''' Fig. 8.— Title with bill of material. 6. Tracing.— The usual order of procedure in tracing is as follows : 1. Center lines. 2. Small circles and arcs of circles. 3. Large circles. 4. Straight object lines. 5. Extension and dimension lines. Two guide lines should be drawn in light pencil for lettering. These should be erased after the tracing is finished. Tracing cloth has a dull side and a glossy side. Either side may be used to work on, but most draftsmen prefer the dull side as it will take a pencil mark. Before any lines are inked in, the cloth should be dusted with chalk dust or talcum powder to 12 ADVANCED SHOP DRAWING remove the oily preservative which covers the surface. This oil, if allowed to remain on the cloth, will prevent the cloth from taking the ink properly and ragged lines will result. Some drafting offices use tracing paper instead of cloth because it is less expen- sive. It is not so durable, however. Sometimes pencil draw- ings are made on transparent paper and blue prints made directly from these, thus saving the expense of tracing. This is usually done when a blue print is needed in less time than the slower process of tracing permits. These drawings must be made with a soft pencil to insure heavy black lines. If the lines are not fairly heavy, the resulting blue print will appear weak. 7. Blue Printing. — Blue printing is done on sensitized paper by exposing it either to sunlight or to artificial light. Before the paper is exposed it has a yellow color. On exposure to light the paper turns blue with a bronze tint. When blue prints are made, the light is allowed to shine through the tracing on to the paper. Since the paper is sensitized only on one side, care must be taken to expose the yellow side to the light. The inked lines on the tracing do not allow the light to pass through and thus the drawing is printed. When the paper has been properly exposed, it is removed from the printing frame and washed in clean water. The water ''fixes" the print and brings out the details clearly. Wherever the light strikes, the paper turns blue, but where the lines on the tracing protect it, the paper remains as it was. Some experience is necessary in order to expose the paper properly. Usually the paper is tested by exposing several small pieces until the proper degree of exposure is determined. This saves wasting several full-sized prints. In case the paper is under-exposed, the print is ruined, but if it is over-exposed it may be placed in a water bath which contains a solution of bichro- mate of potassium. This will intensify the blue, leaving the white lines more distinct. The print should be thoroughly washed in clear water after intensifying. Blue print clotL is used in some cases where a durable print is desired. There are several machines on the market for making blue prints. Figure 9 shows an upright electric machine. An electric arc lamp furnishes the light. The tracing is placed on the glass cylinder with the paper next to the tracing. The canvas roll holds the tracing andfthe paper securely in place while the printing is being done. The electric arc travels from the top to the bottom of the machine at a rate of speed which may be Fig. 9. — Upright electric blue print machine. {Facing page 12.) Fig. 10. — Sunlight blue print machine. Fig. 11. — C. F. Pease continuous blue print machine. WORKING DRAWINGS 13 varied, depending on how long the operator wishes to expose the print. A sunhght machine is shown in Fig. 10. This machine works on a frame which is usually attached to a window sill. After the paper and tracings have been adjusted, the frame is placed outside the window in the sunlight. The advantage of this machine is the low first cost and small running expense. The disadvantage is that it is absolutely dependent on sunshine. The intensity of the light varies so much throughout the day and from day to day that it is difficult to know how to expose the paper properly. Some electric machines work continuously. Such a machine is shown in Fig. 11. It is so arranged that the paper is fed in from a roll. The paper passes slowly through the machine and directly through the special washing and drying device which is attached. Such machines are used in large offices where great quantities of prints are turned out each day. Black Prints. — Black prints are similar to blue prints except that black lines are produced on a white background. This paper is not used to the extent that blue print paper is used. Mounting Prints. — -Prints used in the shops are necessarily handled a great deal and unless they are protected will soon become spoiled. They may be protected by mounting them on cardboard or, as is done in some cases, on sheet iron. When mounted, they are usually covered with a coat of shellac which prevents them from becoming dirty and unreadable. They may be rendered waterproof by treating them with a solution of one part paraffin and three parts gasoline. They should be allowed to remain in this solution for a few minutes and then be wiped off. If the solution dries on them, they will be covered with paraffin. The paper will soak up enough paraffin to make it waterproof. 8. Vandykes. — In printing from a tracing, only one print can be made at a time. It is sometimes necessary on large orders to make several prints at the same time. , In such cases instead of making more than one tracing, which is expensive, Vandyke copies are made. Vandyke paper or cloth is so treated that on exposure to light it turns dark and becomes opaque. Wherever the light does not strike, it becomes transparent. The same tracing may be used to print several Vandykes. After Vandykes are printed, they are washed in clear water and then placed in a fixing solution which renders them impervious to light. The 14 ADVANCED SHOP DRAWING fixing solution is made up from the fixing salt which is usually sent with each roll of Vandyke paper. Full directions for making the solution accompany each package of salt. After fixing, the Vandykes are washed again and allowed to dry. These Vandykes are used instead of tracings for making prints. Before printing, the Vandykes are usually wiped with a cloth dampened in a mixture of gasoline and white oil. This makes them clearer and more transparent, and also removes any dirt which may have collected on them. The prints obtained are white prints, however, since only the lines of the drawing are transparent. On white prints, the lines are blue on a white background. Problem 1 Make an assemblj^ drawing of the crank end details shown in Fig. 5. Use a 12" X 18" sheet with the 18" dimension horizontal. The drawing should be made to a 3" scale (3" = 1')- Draw the views and sections indicated in the small sketch. Problem 2 Make full size detail drawings of the clamp bolt, clamj) bolt nut, clamp bolt washer, adjusting screws, and binder stiids for the 12" lathe tailstock shown in Fig. 3. Use the standard 12" X 18" sheet of drawing paper placed horizontally on the drawing board for these details. The legend for each part should be put under the drawing of it, as explained in Article 4. In the plate title in the lower right-hand corner put Details of 12" Tailstock together with the scale, date, etc. Problem 3 Make a full size detail drawing of the binder plugs, binder washer, binder handle, spindle crank, and spindle crank handle of the 12" tailstock. The directions given previously should be followed. Problem 4 Make a full size drawing of the spindle, spindle screw, spindle screw nut, spindle screw washer, center, and feather key of the 12" tailstock shown in Fig. 3. Decide which size drawing paper to use and arrange the parts on the sheet so that they will be well balanced. Problem 5 Make a half size drawing of the base and clamp of the 12" tailstock, showing enough views to make them entirely clear. Problem 6 Make a half size drawing of the tailstock body and cap of the 12" tail- stock, showing enough views and sections to make them entirely clear. CHAPTER II GEARING 9. Spur Gears. — Spur gears are the most common type of gears and are used for power transmission between parallel shafts. The gears of Fig. 12 would be called a pair of spur gears, or a spur gear and pinion, the smaller one being the pinion. Figure 13 shows the names of the different parts of a gear. Figure 14 shows two cylinders rolling together without slipping. In order to transmit more power than can be transmitted by the Fig. 12. — Spur gear and pinion. smooth surfaces, projections may be put on B parallel to the axis, and corresponding recesses on^. If, now, it is considered that A is provided with similar projections and B with similar recesses, one can see clearly the direct transition from the rolling cyHnders of Fig. 14 to the toothed cylinders of Fig. 15 and then to the spur gears of Fig. 12. 10. Pitch Circles. — -The pitch circles of spur gears are the same as the circumferences of the imaginary contact cylinders such as shown in Fig. 15. It is from these pitch circles that all gearing calculations are made. 15 16 ADVANCED SHOP DRAWING ROOT CIRCLE DEDENOUM CIRCLE PITCH CIRCLE ADDENDUM CIRCLE Fig. 13. — Gear parts. Fig. 14. — Friction cylinders. Fig. 15. — Toothed cylinders. GEARING 17 11. Pitch Diameter. — The pitch diameter of a gear is the diameter of its pitch circle. This is the diameter used in nearly all gear calculations. 12. Pitch. — Pitch is a word used to designate the size of teeth on a gear. There are two kinds of pitch, diametral and circular. The diametral pitch system is the one generally used. 13. Diametral Pitch. — ^Diametral pitch is the number of teeth on a gear for each inch of diameter of its pitch circle. If there are 32 teeth on a gear, and the diameter of its pitch circle is 4'', there are ^% or 8 teeth per inch of diameter of the p'itch circle. The diametral pitch is, consequently, 8. To Find the Pitch Diameter. — Having given the number of teeth and the diametral pitch, divide the number of teeth by the diametral pitch. Example. — What is the pitch diameter of a gear having 66 teeth and of 12 diametral pitch? Let P = diametral pitch. Then D = pitch diameter N = number of teeth D = N P 66 i) = j^ or 5M" (1) To Find the Diametral Pitch. — Having given the pitch diameter and the number of teeth, divide the number of teeth by the pitch diameter. Example. — What is the diametral pitch of a gear having 48 teeth and a pitch diameter of 6''? P = ^ D 48 P = ^ or 8 (2) To Find the Number of Teeth. — Having given the diametral pitch and the pitch diameter, multiply the pitch diameter by the dia- metral pitch. Example. — How many teeth in a gear of 4^^" pitch diameter and 8 pitch? N = P X D iV = 4M X 8 or 37 (3) 18 ADVANCED SHOP DRAWING Consequently, it is seen that, having given any two of the three terms — pitch diameter, diametral pitch and number of teeth, — the third can be readily found. 14. Circular Pitch. — Circular pitch is the distance between similar points of adjoining teeth measured on the pitch circle as indicated in Fig. 13. It is the distance from the center of one tooth to the center of the next, or from the side of one tooth to the corresponding side of the next, the distance in both cases being measured around on the arc of the pitch circle, as in Fig. 13, and not straight across on the chord. In solving for the pitch diameter, circular pitch, or number of teeth, by the circular pitch system, it is necessary to make use of the constant 3.1416. This constant is designated by the Greek letter w (pronounced as if spelled "pie ") . The pitch diam- eter, the circular pitch, or the number of teeth can be found if two of these are known. To Find the Pitch Diameter. — Having given the number of teeth and the circular pitch, multiply the circular pitch by the number of teeth and divide by tt. Example. — What is the pitch diameter of a gear which has 48 teeth and ^" circular pitch? Let P' = circular pitch D = pitch diameter N = number of teeth 7r= 3.1416 ^ ^ P' XN To Find the Circular Pitch. — Having given the pitch diameter and the number of teeth, multiply the pitch diameter by r (which gives the circumference of the pitch circle), and divide this cir- cumference by the number of teeth. Example. — What is the circular pitch of a gear having 36 teeth and a pitch diameter of d"? N P' = ^iMl|->l^ or 0.4363" (5) 36 GEARING 19 To Find the Number of Teeth. — Having given the circular pitch and the pitch diameter, multiply the pitch diameter by w and divide by the circular pitch. Example. — What is the number of teeth in a gear having a circular pitch of 1}^'' and a pitch diameter of 7J-^''? N = Zi?^|:AM6 ^^. ^g 22 teeth (6) 1.25 Since there cannot be a fractional part of a tooth, it will be necessary to change either the pitch diameter or the pitch so as to have a whole number of teeth. The number of teeth may be assumed to be 18 and the circular pitch IJi". The pitch diameter to correspond may be found by Formula (4) : j^ 1.25 X 18 The circular pitch system has the disadvantage that either the pitch diameter or the circular pitch will always be an inconvenient fraction, due to the fact that tt (3.1416) is always used in making the calculations. It is rapidly becoming obsolete. It is used, however, by pattern makers in spacing the teeth on patterns for cast gears. There is a definite relation between circular pitch and diam- etral pitch. Having given the circular pitch, one can find the equivalent diametral pitch, or having given the diametral pitch, one can find the equivalent circular pitch. ttD N = P XD or ~ PXD = P = ttD P' TT P XP'= TT This means that diametral pitch X circular pitch = tt Also P' ='^ 15. Addendum Circle. — The addendum circle is the circle bounding the ends of the teeth. By referring to Table 1, Col- 20 ADVANCED SHOP DRAWING umn 4, it will be seen that, for length of standard teeth, the radius of the addendum circle is greater than that of the pitch circle by an amount „, so that its diameter is greater than that of the 2 pitch circle by an amount of p. Hence, to find the outside Table 1. — Gear Wheels Table of Tooth Parts — ^Diametral Pitch in First Column Diam- etral pitch P Circular pitch P" Thickness of tooth on pitch line t Addendum or 1" s Working depth of tooth D" Depth of space below pitch line s+f Whole depth of tooth D" +f K 6.2832 3.1416 2.0000 4.0000 2.3142 4.3142 M 4.1888 2.0944 1.3333 2.6666 1 . 5428 2.8761 1 3.1416 1 . 5708 1 . 0000 2.0000 1.1571 2.1571 IK 2.5133 1.2566 . 8000 1 . 6000 0.9257 1.7257 13-^ 2 . 0944 1 . 0472 0.6666 1.3333 0.7714 1.4381 m 1 . 7952 0.8976 0.5714 1.1429 0.6612 1.2326 2 1 . 5708 0.7854 0.5000 1.0000 0.5785 1.0785 2H 1 . 3963 0.6981 •0.4444 0.8888 0.5143 0.9587 2>i 1.2566 0.6283 . 4000 0.8000 0.4628 0.8628 2H 1 . 1424 0.5712 0.3636 0.7273 0.4208 0.7844 3 1.0472 0.5236 0.3333 0.6666 0.3857 0.7190 3>^ 0.8976 0.4488 0.2857 0.5714 0.3306 0.6163 4 0.7854 0.3927 0.2500 . 5000 0.2893 0.5393 5 0.6283 0.3142 0.2000 0.4000 0.2314 0.4314 6 0.5236 0.2618 0.1666 0.3333 0.1928 0.3595 7 0.4488 0.2244 0.1429 0.2857 0.1653 0.3081 8 0.3927 0.1963 0.1250 0.2500 0.1446 0.2696 9 0.3491 0.1745 0.1111 0.2222 0.1286 0.2397 10 0.3142 0.1571 . 1000 . 2000 0.1157 0.2157 11 0.2856 0.1428 0.0909 0.1818 0.1052 0.1961 12 0.2618 0.1309 0.0833 0.1666 . 0964 0.1798 13 0.2417 0.1208 0.0769 0.1538 . 0890 0.1659 14 0.2244 0.1122 0.0714 0.1429 0.0826 0.1541 15 . 2094 0.1047 0.0666 0.1333 0.0771 0.1438 16 0.1963 0.0982 0.0625 0.1250 0.0723 0.1348 17 0.1848 . 0924 0.0588 0.1176 0.0681 0.1269 18 0.1745 0.0873 0.0555 0.1111 0.0643 0.1198 19 0.1653 0.0827 0.0526 0.1053 . 0609 0.1135 20 0.1571 0.0785 . 0500 0.1000 0.0579 0.1079 22 0.1428 0.0714 0.0455 . 0909 0.0526 0.0980 24 0.1309 0.0654 0.0417 0.0833 0.0482 0.0898 26 0.1208 . 0604 0.0385 0.0769 0.0445 . 0829 28 0.1122 0.0561 0.0357 0.0714 0.0413 0.0770 30 0.1047 0.0524 . 0333 0.0666 0.0386 0.0719 GEARING 21 diameter, that is, the diameter to which a blank must be turned before the teeth are cut, 2 must be added to the number of teeth in the gear and the sum divided by the diametral pitch. Thus outside diameter = — p — (7) Example. — What is the outside diameter of a gear having 40 teeth and 4" pitch diameter? P = P = ^ or 10 Outside diameter (0. D.) = N D 40 4 ^^ N + 2 P 40 + 2 = 4.2' 10 16. Dedendum Circle. — The dedendum circle is the circle limiting the working depth of the teeth. Its radius is greater than that of the root circle by an amount equal to the clearance. It indicates the depth to which the teeth of the other gear fit into the spaces. Therefore, for standard teeth, the dedendum circle is the same distance inside the pitch circle that the adden- dum circle is outside the pitch circle. Consequently, the diam- . N - 2 eter of the dedendum circle for standard teeth is — p — . 17. Root or Clearance Circle. — A certain amount of clearance is usually cut at the bottom of the spaces between teeth to allow dirt and other foreign matter to work out of the gears without breaking the teeth. The amount of this clearance below the dedendum or working depth circle is left to the judgment of the designer, but it is customary to make it one-tenth of the thickness of the tooth. If P is the diametral pitch, the thickness of the 1.57 tooth will be half the corresponding circular pitch, or — ^• .157 Hence, the clearance will be ^-p- • Since the depth of the stand- ard tooth is equal to the sum of the addendum, the dedendum, and the clearance, and since the addendum and dedendum are each 1 • 1 1 equal to pf the total depth to which the teeth are cut is p + p + 0.157 2.157 — 7T— or -^F, — 22 ADVANCED SHOP DRAWING 18. Tables of Tooth Parts.— In Table 1 the items in the differ- ent columns are as follows: Column 1. Diametral pitch. Column 2. Circular pitch. Column 3. Thickness of tooth on pitch line. It will be noticed that the figures in this column are one-half of the corresponding figures in Column 2. This means that the thickness of the tooth is usually one-half of the circular pitch. Column 4. Addendum, or face of tooth. See Fig. 13. Table 2. — Gear Wheels Table of Tooth jParts — Circular Pitch in First Column Circular pitch P' Threads of teeth per inch linear 1" Diametral pitch Thickness of tooth on pitch line t Addendum or 1" P Working depth of tooth D" Depth of space below pitch line s +/ Whole depth of tooth D" +f 2 H IH Hs IH f^i IH Hs IM y^ iKe ^y2z IH Hx IH y^. iHs i^^i IH yf> iHe 1^9 iVs % iKe ^yii 1 1 1^6 iKs Va IM ^Ke l^fs H l>i H Wz iMe \yix H IM H 1% H IH ^ m Ke iH H 2 ^ 2>i Ke 2H M 2H H 2M H 2H Hi 2H H 3 H6 3K Ho 3H H 3M 1.57D8 1.6753 1.7952 1.9333 2.0944 2.1855 2.2848 2.3562 2.3936 2.5133 [2.6456 ,2.7925 2.9568 3.1416 3.3510 [3.5904 .8666 .9270 1888 ,5696 4.7124 5.0265 5.2360 5.4978 5.5851 6.2632 7.0685 7.1808 7.3304 7.8540 8.3776 8 . 6394 9.4248 10.0531 10.4719 10.9955 1.0000 0.9375 0.8740 0.8150 . 7500 0.7187 0.6875 0.6666 0.6562 0.6250 0.5937 0.5625 0.5312 . 5000 0.4687 0.4375 0.4062 0.4000 0.3750 0.3437 0.3333 0.3125 0.3000 0.2857 0.2812 0.2500 0.2222 0.2187 0.2143 0.2000 0.1875 0.1818 0.1666 0.1562 0.1500 . 1429 0.6366 0.5968 0.5570 0.5173 0.4775 0.4576 0.4377 0.4244 0.4178 0.3979 0.3780 0.3581 0.3382 0.3183 0.2984 0.2785 0.2586 0.2546 0.2387 0.2189 0.2122 0.1989 0.1910 0.1819 . 1790 0.1592 0.1415 0.1393 0.1364 0.1273 0.1194 0.1158 0.1061 0.0995 0.0955 0.0909 1.2782 1.1937 1.1141 1.0345 0.9549 0.9151 0.8754 . 8488 0.8356 0.7958 0.7560 0.7162 0.6764 0.6366 0.5968 0.5570 0.5173 0.5092 0.4775 0.4377 0.4244 0.3979 0.3820 0.3638 0.3581 0.3183 0.2830 0.2785 0.2728 0.2546 0.2387 0.2316 0.2122 . 1989 0.1910 0.1819 0.7366 . 6906 0.6445 0.5985 0.5525 . 5294 0.5064 0.4910 0.4834 0.4604 0.4374 0.4143 0.3913 0.3683 0.3453 0.3223 0.2993 0.2946 0.2762 0.2532 0.2455 0.2301 0.2210 0.2105 0.2071 0.1842 0.1637 0.1611 . 1578 . 1473 0.1381 0.1340 0.1228 0.1151 0.1105 0.1052 1.3732 1.2874 1.2016 1.1158 1.0299 0.9870 0.9441 0.9154 0.9012 0.8583 0.8156 0.7724 0.7295 . 6866 0.6437 . 6007 0.5579 0.5492 0.5150 0.4720 0.4577 0.4291 0.4120 0.3923 0.3862 0.3433 0.3052 0.3093 0.2943 0.2743 0.2575 0.2496 0.2239 0.2146 0.2060 0.1962 GEARING 23 Column 5. Working depth of tooth = Addendum + Deden- dum. Since the Addendum equals the Dedendum, the figures in this column are twice those of Column 4. Column 6. Depth of space below pitch line, ov flank of tooth. The figures in this column are greater than those in Column 5 by the amount of '^f,^^ which is the clearance; that is, the point of the mating tooth does not go below the working depth circle (or Dedendum Circle) as shown in Fig. 13. Column 7. Whole depth of tooth. Table 2 is similar to Table 1 except that the circular pitches instead of the diametral pitches are given in the first column. 19. Velocity Ratio. — By velocity ratio is meant the number of revolutions, or the part of a revolution, that the driven gear makes for each revolution of the driving gear. Two gears in mesh are usually denoted as ''driver" and "driven," their desig- nation being self -apparent. Since the pitch circles are tangent in two gears that are in mesh, their velocity ratio may be cal- culated as if they were two rolls rolling together without slipping as in Fig. 14. If A and B were the same size and A the driver, then for each revolution of .4, B would also make one revolution. If B were twice the diameter oi A, it would take two revolutions of A to cause B to revolve once. This relation may be expressed in the form of an equation as follows : Revolutions of B Pitch diameter of A Revolutions of A Pitch diameter of B or ■D ] f i R — (P^^ch diameter oi A) X (Revolutions of A) Pitch diameter of B Example. — ^If gear A with a pitch diameter of 4^' makes 10 r.p.m., how many will gear B, with a pitch diameter of 8'', make? Let pitch diameter oi A = 4" Let pitch diameter oi B = 8'' Let revolutions per minute (r.p.m.) of A = 10 To find r.p.m. of B 4 X 10 . , ^ — Q = 5 r.p.m. for B o If the number of teeth in each of the gears is given, instead of the pitch diameters, the r.p.m. of B may be found in the same way. 24 ADVANCED SHOP DRAWING Example. — Thus, if A has 48 teeth and makes 30 r.p.m., what will be the r.p.m. of B having 20 teeth? 48 X 30 20 = 72 r.p.m. for B If the revolutions of each of the gears and the number of teeth in one of them are known, the number of teeth in the other may be found as follows : rrt xu • D (Teeth in A) X (Revolutions of A) ieetn m n = ^^ , — —. ^r^^^ Revolutions of B Example.- — If A with 48 teeth makes 30 r.p.m., how many teeth has B if it makes 72 r.p.m? 48 X 30 72 = 20 teeth for B If the number of revolutions of each gear and the pitch diam- eter of one are given, the distance between centers may be found by first determining the pitch diameter of the other gear and taking one-half the sum of the two pitch diameters. Fig. 16. — Annular or Internal gearing. Example. — If A with a pitch diameter of 8" makes 25 r.p.m. and B makes 100 r.p.m., what is the distance between centers? Let revolutions of il =25 Let revolutions of 5 = 100 Let pitch diameter of A = 8'' The pitch diameter of B will be 8 X 25 100 = 2' GEARING 25 The distance between centers will be H(8 + 2) = 5" In the case of spur gears, the distance between the centers of the gears is the sum of their radii, but in the case of annular or internal gears, Fig. 16, the distance between centers is the difference of their radii. The simplest form of the general equation regarding the veloc- ity ratios of gears is: (Pitch diameter of ^) X (Revolutions of ^) = (Pitch diameter of B) X (Revolutions of B) In this equation, the number of teeth may be used instead of the pitch diameters. 20. Special Gears. — Rack and Pinion. — If the diameter of one of the gears of Fig. 12 is imagined to be increased until it becomes infinite, it will then become a straight bar with teeth cut in its side meshing with a gear as in Fig. 17. Such a combi- FiG. 17. — Rack and pinion. nation is called a rack and pinion. The number of revolutions that the gear can make in one direction depends upon the length of the rack. Annular Gears. — An annular or internal gear is one in which the teeth are cut internally on the pitch circle, the rim being outside of the pitch circle. Figure 16 shoWs an annular gear and pinion in mesh. 21. Gear Drawings. — Working Drawing of a Spur Gear. — In making a working dra>wing of a spur gear, complete data are usually not given. The draftsman must supply much that is necessary to make a complete shop drawing. In order to do 26 ADVANCED SHOP DRAWING this, it is necessary to know what the proportions of the various parts should be, to understand what the different dimensions are for and what is meant by the terms used. It is not necessary to show all the tooth outlines, although a few conventional teeth are generally drawn. Example. — Make a shop drawing of a 28 tooth, 4 diametral pitch spur gear; face 2'^; diameter of shaft l/iie"; length of hub 2M'' projection on one side; 4 arms or spokes. Pitch Diameter. — The pitch diameter is 2% or 7". On a drawing, the pitch diameter of a gear should always be noted ^ 2" J ^^ 28 T., 4. P., Spc»r Gear. |- Wanted Cast Iron. Fig. 18. — Working drawing of spur gear, either ''Pitch Dia." or ''P. D." as it is the most important di- mension. The conventional line for the pitch circle is a dash and two dot line as shown in Fig. 18. Outside Diameter. — From Table 1, the addendum of a 4 pitch 1" gear tooth is p-= li" or .25''. The pitch diameter plus twice the addendum [7'' + (2 X .25'')] gives 7^" as the outside diameter. This may be drawn as in Fig. 18. Root Diameter.- — The root diameter is found by subtracting twice the sum of the addendum and the clearance; [2 (s +/)] from the pitch diameter: 7" - 2(.2893") = 6.421" +• This root diameter should be shown, although it is the practice in some shops to show rather the whole depth of tooth. If the gear were GEARING 27 to be cast, it would then be necessary for the drawing to show the root diameter so the pattern maker would know what diameter to turn the blank upon which to fasten the teeth. Thickness of Rim.- — If the thickness of the rim is made }'2 of the circular pitch, it will be strong enough. From Table 1 the circu- lar pitch corresponding to 4 diametral pitch is .7854''. ^^ — ^r— = .3927, thickness of rim Then Inside diameter of rim = (pitch diameter) — 2[(s + /) + rim thickness] Inside diameter of rim =7-2 (.2893 + .3927) Inside diameter of rim = 7 — 1.364 Inside diameter of rim = 5.636'', say 5%" Choosing an approximate final dimension like this, it is better to choose the dimension that gives the greatest strength. . Diameter of Hub. — If the diameter of the hub is made 2 times the diameter of the shaft, it will be thick enough. Wi^" X2 = 2%", diameter of hub Length of Huh. — In this case the length of hub is given as 23-^". If it were not given, however, it should be at least equal in length to the diameter of the shaft, and is usually made greater. The specifications state that the hub shall project on one side, evidently to give clearance between the rim and a surface through which the gear shaft may project. Consequently, Fig. 18 shows the hub projecting 3^^" on one end, which is sufficient ' r a gear this size. Width of Arms. — The arms should be drawn of such ?ldth at the hub, that, if extended, they would be tangent to the shaft. At the outer end or near the rim they should be approximately J^o of the width at the hub. In this case the width of arm would be 13^^" at the hub and %" at the rim. These figures are for heavy transmission and can be reduced somewhat for light work. The arms are often made with a taper of 3^^" per foot. The sec- tion of the arms must be indicated. This can best be done by making a small revolved section on the arm as was done in Fig. 18. Thickness of Arms. — If the thickness of the arm at each end is made equal to .4 of the width at each end, it will be strong enough. This gives approximately 3^^" and %", respectively. Where 28 ADVANCED SHOP DRAWING the gear is small, it is often made with a sohd web instead of p utting hjarms. Width of Face. — In this case the width of the face is given as 2''. It should always be equal to at least 2 or 3 times the circular pitch. This is determined by the designer according to the load that the gear teeth must carry. Tooth Outlines. — The lines and dimensions shown in Fig. 18 are all th.it are necessary for the gear to be made in the shop. Sometimes, however, a few teeth are shown in approximate out- line. If this is desired, they can be drawn as follows: Draw a radius of the pitch circle as in Fig. 19. On this radius draw a semi-circle with center at A . Bisect AB Sit C. With B Fig. 19. — Layout of tooth outline. as a ceiP^r and a radius BC, draw an arc intersecting the semi- circle ODB at D. With as a center and a radius OD, draw an arc EDF. Space out a few teeth on the pitch circle, as a, b, c, etc. With a radius DB and centers on arc EDF, draw arcs through the points a, h, c, etc. on the pitch circle, from the arc EDF out to the addendum circle. The part of the tooth between the arc EDF and the dedendum circle is drawn radial. To do this draw a straight line toward the center of the gear from the point where the tooth arc intersects the arc EDF. A small fillet, or arc, rounds the tooth outline from the dedendum circle into the root circle. Keys and Keyways. — The sizes of keys for use on shafts of vari- ous diameters are shown in Table 3. The width of the keyway in the shaft and in the hub is the same. Half the thickness of GEARING 29 the key way is cut in the shaft and half in the hub. In the case of armed wheels, the keyway should always be put in line with one of the arms. In this position, the keyway will weaken the Fig. 20. — Method of dimensioning keyways. hub less than if it were placed between two arms. Special short hubs sometimes have more than one key. Figure 20 shows a new method of dimensioning keyways in shafts and hubs. DIMENSIONING OF DIMENSIONING OF KEYWAY IN SHAFT KEYWAY IN HUB DIMENSIONS OF KEYS. DIAMETER 0F5HAFT5 WIDTH THICKNESS INCHES INCHES INCHES 1 -° 're 3 16 3 16 \ -k TO 1 — 5 J. '8 16 16 4- ',-6 ^0 ''i 3 a 5 16 1 — TO 2 ^ ' 16 "-' '^ 16 1 2 3 8 2il TO 2\i 1 i 2ll TO 3| 1 16 ^Te TO 3;i i 1 3|i TO 4| II 16 ^S TO A^e , j- '8 3 4- 4j TO 5 1 1 15 16 5i TO 6| 1 ' 2 1 6^ TO 7| .3 '4- '§ Table 3. This method has come into practice in late years and is desirable because it permits the mechanic to make a better fit between the key and keyway than is possible under the old method shown in Fig. 18. 30 ADVANCED SHOP DRAWING Problem 7 (a) In a gear having 48 teeth and 1" circular pitch, what is the pitch diameter? (6) A gear with 4" pitch diameter has 80 teeth; what is the pitch? (c) Two gears are in mesh. The driver makes 20 revolutions and the driven makes 15. The driver has 72 teeth and its diametral pitch is 8. How many teeth in the driven, and what is the distance between the centers? (d) In an annular gear and pinion, the pinion makes 3 revolutions while the annular gear makes 1 revolution. The pitch diameter of the pinion is 4". What is the distance between the centers of the two gears? (e) In two spur gears that are in mesh, the distance between their centers is 15". If the driver makes 50 revolutions, while the driven makes 30, what are their pitch diameters, and how many teeth in each, if their diamet- ral pitch is 8? Problem 8 Make a full size drawing of a spur gear of 36 teeth, 6 pitch; shaft diam- eter 1"; width of face l}i"; length of hub 2" with projection on one side; 4 arms. Draw the same views as shown n Fig. 18. CHAPTER III GEARING (Bevel, Worm and Special Gears) 22. Bevel Gears. — Bevel gears are gears used to connect shafts that intersect. Shafts meeting at any angle may be connected by bevel gears, though the great majority of bevel gears are found on shafts meeting at 90°. Figure 21 shows a pair of bevel gears, the axes of which intersect at an angle of 90°. ''Miter gears" is a special name sometimes given to two bevel gears of the same size connecting shafts at 90°. In the case of the spur gear, it was imagined that the teeth were developed on a rolhng cyhnder. In the bevel gear, the teeth are Fig. 21. — Bevel gearing. developed on a cone called the pitch cone, so that all dimensions of the teeth diminish toward the apex of the cone as can be seen in Fig. 21. Bevel gears are generally laid out in pairs, since one bevel gear will mesh properly only with its mate, and not with any other gear even of the same pitch. All calculations for bevel gears are made in exactly the same way as for spur gears. The pitch diameter of a bevel gear is the diameter of the base of its pitch cone. 23. Bevel Gear Layout. — A drawing for bevel gears is not quite so simple as that for spur gears. A complete drawing of the gears, as 'shown in Fig. 21, is not necessary, however; a sec- tion through the axes generally being sufficient. Figure 22 shows 31 32 ADVANCED SHOP DRAWING a drawing of a set of bevel gears with the angles and dimensions which are necessary for the shopman. Figure 23 is an enlarged partial view of the 32 tooth gear of Fig. 22. Example. — Make a drawing of a pair of bevel gears having 56 and 32 teeth respectively, 8 pitch, shaft angle 90°. Pitch Diameter. — Referring to Fig. 22, pitch diameter of large gear = ^% or 7''. The axis of this gear is OB. Fig. 22. — Shop drawing of bevel gears. Pitch diameter of small gear = 32^or4". The axis of this gear is OA . Since the gears are to connect shafts at right angles, the lines OA and OB should be laid out for Y = 90°. On the hne OA lay out Oa = 3J^", the pitch radius of the large gear; on the line OB lay out Oh = 2", the pitch radius of the small gear. Through GEARING 33 a and perpendicular to Oa draw MD. Through h and perpen- dicular to Oh draw CD. The point D where these lines intersect will be the ''pitch point/' the point where the pitch circles are tangent. Make Ma = Da and Cb = Db. From M, D, and C draw light lines to 0, dash and two dot lines as was done in Fig. 18. These lines then form the sides of cones, the bases of which are MD and DC. These cones are called the ''pitch cones" and in bevel gears correspond to the pitch cylinders of spur gears. The angles X and X' formed by the sides of the pitch cones are called the "pitch angles." Through M draw MA perpendicular to OM; through D draw AB perpendicular to OD) and through C draw CB perpendicular to CO. The pro- jections of these three lines beyond the rims of the gears may later be erased from the finished drawing. Addendum. — On the three perpendiculars just drawn, MA, yl5, and5C, lay out from the three points M, D, and C the ad- dendum as taken from Table 1. For 8 pitch the addendum is .1250''. The new points just located represent the tops of the teeth at the outer surfaces of the gears. Depth of Teeth.— For 8 pitch the depth of tooth is 0.2696'', or the depth of space below pitch Hne is 0.2696 - 0.1250 = 0.1446". Laying off this distance in the other direction from C, D, and M gives the bottoms of the teeth at the outer extremities of the gears. Thickness of Rim. — The thickness of rim K is made approxi- mately equal to one-half the circular pitch, as in the case of spur gears. Backing. — The dimensions / and /' of the hubs are called the "backing" and are important dimensions. On account of the inclination of the teeth of a bevel gear, there is a pressure tend- ing to force the gears apart. Bevel gears must, therefore, be rigid and have hberal backing on the hubs. Each gear should have a shaft bearing and a thrust bearing as close as possible. If the drawing is laid out accurately, the outside diameters can sometimes be scaled with sufficient accuracy, the dimensions being given to the nearest hundredth inch. When this method is not considered accurate enough, the dimensions can be calcu- lated to thousandths or ten-thousandths of an inch. Some of the calculations given below are worked out very closely. It is necessary for the draftsman to have some knowledge of trigo- nometry in order to make these calculations. 34 ADVANCED SHOP DRAWING Pitch Angle. — By referring to Fig. 23, X', the pitch angle, can be found as follows : Oa = Zy^' = 3.5'' Ma = 2" (Angle MaO is a right angle) Mn 9 Tan Z' = ^ = Tf^ or 0.5714" Oa 3.5 X' = 29° 45' Fig. 23. — Enlarged view of bevel gear tooth. Outside Diameter. — ^The triangles MOa and eMd, Fig. 23, are similar, since their sides are perpendicular and each contains a right angle. Therefore, angle X' = angle eMd or 29° 45'. The side Md = 0.1250" for an 8 pitch gear as taken from Table 1. eM Cos eMd = dM Therefore, eM = dM cos eMd. By substitution 0.1250 X 0.8682 = 0.10852". The Outside Diameter (O.D.) = Pitch Diameter (P.D.) + 2 eM. Therefore, the O.D. = 4" + 0.217" = 4.217". Face Angles. — Drawing lines from the tops of the teeth to the center gives the angles W and W , Fig. 22, which are called the '^face angles." These lines represent the tops of the teeth and are the lines to which the gear blanks must be turned. To get the face angle, TF', the angle R of Fig. 23 must be added to the angle X'. First the length of the side OM must be found. Oa Cos X' = OM GEARING 35 Therefore, Tan/e = By substitution OM = -^% or .r4L = 4.031'' cosX' Md OM 0.125 0.8682 = 0.03101 4.031 R = 1° 47', nearly. The face angle W = X' + R (29° 450 + (1°470 - 31° 32' Cutting Angles.- — The angles U and U\ Fig. 22, formed at by drawing lines from the bottoms of the teeth to are called the '^ cutting angles." The cutting angle, U', Fig. 23, is less than the pitch angle, X', by the amount of the angle S. Mc Tan *S = OM Therefore, Mc = 0.1446 " (From Table 1) ^ 0.1446 ^^o-o^ tan S = ^^TTT^ = 0.03o87 4.031 >S = 2° 3', nearly The cutting angle U' = X' - S = (29° 45') - (2° 3') = 27° 42'. Fig. 2i. — Section view of bevel gear. Edge Angles. — The angles Z and Z', Fig. 22, at the backs or outer edges of the gears are called the "edge angles." The edge angle Z' = the pitch angle X'. The equations used above can be used only when the gear shafts make an angle of 90°, though the procedure for other shaft angles is similar. Most of the other dimensions are similar to those of spur gears. 36 ADVANCED SHOP DRAWING Figure 24 shows a bevel gear with the names of the various angles and parts. These are the dimensions and angles which should appear upon a shop drawing of a single bevel gear. The legend for a bevel gear should be similar to that shown in Fig. 18. The bevel gear shown in Fig. 24 has a plain web supporting the rim. If the gear is for heavy service, this web may be rein- forced by ribs from the rim to the backing. 24. Worm and Worm Wheel. — The combination shown in Fig. 25 known as the worm and worm wheel is used for connecting axes that are at right angles but which do not intersect. It is used for obtaining a large reduction in speed. Fig. 25. — Worm and worm wheel. Velocity Ratio of Worm Gears. — ^The velocity ratio does not depend upon the ratio of the pitch diameters, as in the case of gears connecting parallel or intersecting shafts, but rather upon the number of teeth in the wheel and upon whether the worm has a single or a multiple thread. The worm is the same as a screw thread and is shown in section in Fig. 26. If the worm wheel has 48 teeth, and the worm is single threaded, as in Fig. 27, it will take 48 revolutions of the worm to make one complete revolution of the wheel. If the worm is double threaded, as in Fig. 28, it will require 24 revolutions of the worm to turn the wheel once. Likewise, if the worm is triple threaded, 16 revolutions will be required for one turn of GEARING 37 SECTION ON LINE WORM AND WORM WHEEL. 28t bronze wheel. ^'■r,r.h. single thread steel worm '^"^% SECTION ON LINE A-B. Fig. 26. — Working drawing of worm and worm wheel. DEPTH OF THREAD ->|PITCHk- FiG. 27. — Single threaded screw. 38 ADVANCED SHOP DRAWING the wheel, and so on. From this it will be seen that the pitch diameter of the worm does not affect the velocity ratio. Pitch. — The circular pitch is always used in a worm and wheel combination, since the worms are cut in a lathe. Lathes are not equipped with the proper change gears for cutting diametral pitches. I«-LEAD FiG. 28. — Double threaded screw. 25. Shop Drawing of Worm and Worm Wheel. — As in the case of the bevel gears, it is not necessary to make a complete drawing showing the tooth outlines of the worm and wheel in order that they may be made in the shop. Figure 26 shows the necessary views and dimensions for a work- ing drawing. The left-hand view is a section through the axis of the worm wheel and an end view of the worm. The right-hand view is a section along the axis of the worm, although the wheel is shown in section only a't the rim. The sizes of the teeth are obtained from Table 2. The few teeth that are shown in the wheel may be drawn by the approximate method of Fig. 19. The angle Z, which the sides of the worm wheel make with each other, is usually made 60°, but it may be 90°. The 'Hhroat diameter" of the wheel is the same as the outside diameter of a spur gear of the same pitch and the same number of teeth. The face of the tooth is made concave to fit the worm. The teetxi on the wheel are cut by means of a ''hob." This is a cutter that looks a great deal like the worm except that its sides are fluted like a tap to form cutting edges. The diameter of the hob is greater than that of the worm by twice the clearance. It is necessary, of course, to use a different hob for every different diameter worm. If the drawing is made accurately, the outside diameter of the wheel can be scaled, and the dimension taken to the nearest hundredth of an inch: if greater accuracy is desired, it may be GEARING 39 calculated. This outside diameter is the diame.ter to which the blank, upon which the teeth are to be cut, must be turned. The thickness of the rim below the bottom of the teeth is made equal to one-half the circular pitch as in the case of spur and bevel gears. If the diameter of the wheel is not too great, it is made with a soHd web instead of spokes. This web is usually not over 3^^'' thick. 26. Special Gears. — Stepped Gears. — In order to obtain smoother contact than is possible with a single pair of spur gears, several spur gears may be placed side by side on the same shaft and each turned so that its teeth are slightly in advance of the Fig. 29. — Pair of twisted gears. one of the preceding gear. Such a gear is called a ''stepped gear." If there are two gears thus stepped on a shaft, the com- bination is known as a gear of two steps. The gears are usually placed so that the teeth of one come opposite the spaces of the other, or one is stepped one-half the circular pitch ahead of the other. There are twice as many teeth in contact at one time in these gears as there would be in a single pair of spur gears. Twisted Gears. — The number of steps on a stepped gear may be increased indefinitely. If this be done it may be imagined that the face of each step be decreased so that the resulting gear has the same width of face as a spur gear. As a further illus- 40 ADVANCED SHOP DRAWING tration, a gear may be considered as made of some plastic material such as rubber. If one end be fixed and the other twisted about its axis, and the teeth thus twisted be given a set form, the resulting gear will be what is known as a ^'twisted gear." Such a pair of gears is shown in mesh in Fig. 29. In a pair of twisted Fig. 30. — Train of twisted gears. gears, one of the gears always has a right-handed thread, and the other has a left-handed one. In the gear train shown in Fig. 30 the two gears B and C are twisted gears. Pitch for Twisted Gears. — There are three kinds of pitches used for twisted gears — normal, circular, and axial. Normal pitch is the shortest pitch distance between two consecutive teeth. It is Fig. 31. — Showing pitches for twisted gears. the distance ah, Fig. 31, and is measured on a line normal to the tooth outline. The normal pitch determines the cutter to be used. Circular pitch is the pitch distance between two teeth, measured in a plane vertical to the axis of the gear, as in the case of spur gears. It is the distance ac in Fig. 31. GEARING 41 Axial pitch is the pitch distance between two teeth, measured on a hne parallel to the axis of the gear. It is the distance ad in Fig. 31. Tooth Angle. — ^The tooth angle is the angle made by the tooth with the axis of the gear. It is the angle e in Fig. 31. This angle is sometimes called the '^spiral angle" or ''helical angle." Velocity Ratio of Twisted Gears. — The velocity ratio of twisted gears depends upon the number of teeth and the pitch diameters of the gears. The velocity ratio rules of spur gears are directly applicable to twisted gears; in fact, twisted gearing may be considered as a special case of spur gearing. In order for two twisted gears to mesh properly, they must have the same pitch and the same tooth angle. Fig. 32. — Herringbone gears. Herringbone Gears. — When two twisted gears are in mesh, they exert a thrust upon each other due to the curvature of the teeth, and thus tend to force each other in opposite directions along their respective shafts. This thrust may be taken up by thrust bearings or by placing together two twisted gears with equal but opposite tooth angles. Such gears, shown in Fig. 32, are known as ''herringbone gears." Spiral Gears. — Spiral or helical gearing is another name applied to twisted gearing. The term "twisted gears," however, always 42 ADVANCED SHOP DRAWING applies to twisted gears on parallel shafts. Both gears of the pair have opposite handed threads, or spirals. '' Spiral or helical gears" is a name applied more generally to twisted gears on shafts that are not parallel. In this case both gears of the pair always have the same handed thresLds or spiral, either right- or left-handed. The gears A and B, Fig. 30, form a pair of spiral gears. Worm gearing is the limiting case of spiral gearing; in fact, the transition of gears may be traced from the common spur gear to the twisted gear, to the spiral gear, and to the worm, successively. Pitches for Spiral Gears. — Spiral gears, like twisted gears, have the same three pitches — normal, circular, and axial. As for twisted gears, these pitches involve the tooth angle. The tooth angle in spiral gearing is highly important as it affects the velocity ratio. Velocity Ratio of Spiral Gears. — The velocity ratio of spiral gears does not depend upon the pitch diameters of the spirals. Instead, it depends upon the number of teeth, the revolutions being inversely proportional to the number of teeth as in the case of the worm and worm wheel. Since the number of teeth is depend- ent upon the tooth or helical angle, this angle becomes an im- portant factor in the determination of velocity ratios. On account of the curvature of the teeth of spiral gears, and the sliding motion with which they mesh, an end thrust is always produced on their shafts. When the gear shafts are at 90°, this end thrust is least. The efficiency of the gears is highest when the tooth angle of the gears is 45°. As in the case of twisted gears, the normal pitch determines the pitch or size of the cutter, either spur or special, that will be used in cutting the teeth. From this normal pitch and the tooth angle, the designer must compute the circular pitch, and finally the pitch diameter of the gear desired. The addendum is the same for spiral and spur gears. Consequently, if twice the adden- dum be added to the pitch diameter, the diameter of the blank from which the spiral is to be turned may be obtained. It may be assumed that Fig. 31 represents a blank for a spiral gear, and that the inclined lines represent the centers of gear teeth. Then the angle hac equals the tooth angle e, because their sides are perpendicular. Furthermore, ah ah ac = cos hac cos e GEARING 43 Hence, it may be stated as a general proposition for spiral gears that , ., , normal pitch circular pitch = — rr r cos tooth angle If the circular pitch and number of teeth are known, the pitch diameter can be found readily. Example. — Two spiral gears with a velocity ratio of 1 to 1, and with the shafts at 90° are to be cut with a B. & S. (Brown & Sharpe) 16 pitch cutter. Find the size of blanks required for 18 teeth. Since the shaft angle is 90°, the gears should have tooth angles of 45° for maximum efficiency. The teeth of the gears may be either both right-handed or both left-handed, depending upon the conditions of the problem. By reference to Table 1, it is found that for a 16 pitch cutter the normal circular pitch is 0.1963. Hence, ^. , ., , normal pitch Circular pitch = ^ — ~ r cos tooth angle Substituting Circular pitch = — — ~^ cos t:0 The pitch circumference = circular pitch X No. of teeth, or 0.277 X 18 = 4.986'' pitch circumference The pitch diameter = 4.986 = 1.587" P. D. 3.1416 The diameter of blank = pitch diameter + 2 X addendum. For 16 pitch, the addendum is 0.0625 (Table 1) Hence, 0. D. = P. D. + 2 X addendum or O. D. = 1.587 + (2 X 0.0625) = 1.587 + 0.125 = 1.712'' When the velocity ratio of two spirals is other than 1 to 1, it can not be determined from the pitch diameters as in spur gearing as before stated. Instead, it must be determined from the tooth or helical angle of each gear. If the tooth angles of both gears are the same, the velocity ratios will be inversely proportional 44 ADVANCED SHOP DRAWING to the pitch diameters. If the tooth angles are different, this rule will not apply since the axial pitch, and, therefore, the number of teeth, will vary. In the case of the single threaded worm, the velocity ratio of the worm to the worm wheel is simply as 1 to the number of teeth in the wheel. Increasing or decreasing the pitch diameter of the worm affects the tooth angle of both worm and worm wheel, but does not affect the velocity ratio, as long as the number of teeth in the wheel remains the same. The velocity ratio in all cases depends upon the number of teeth and the tooth angle. Hence, the velocity ratio of two gears is proportional to their pitch diameters only when their tooth angles are the same. The sum of the tooth angles must always be equal to the angle between their shafts; and, if the end thrusts of both are to be equal, their tooth angles must also be equal. When the tooth angle of one gear is greater than that of the other, the one with the greater tooth angle should be used as the driver. Example. — Two spiral gears with axes at 90° and a velocity ratio of 2 to 3, are to be cut with a 16 pitch cutter. The pitch diameter of the driving gear is IM", and its tooth angle 60°. Calculate the other dimensions of the gears. It was learned from Article 14 that the product of the diam- etral pitch and the circular pitch is a constant and equals t, or P' = — P The normal circular pitch of the driver is P' = ^^^ or 0.19635'' lb In the case just considered, the circular pitch is 0.19635 cos 60° = 0.3927 Number of teeth = ' or 12. Since the velocity ratio is 2 to 3, and the driver has 12 teeth, the number of teeth in the driven may be determined easily. If "x^' represents the number of teeth in the driven gear, then 2 :3 = 12 :x Therefore, x = — - — or 18 teeth GEARING 45 The angle between shafts is 90°. Since the tooth angle of the driver is 60°, the tooth angle of the driven must, therefore, be 90° - 60° = 30°. The normal circular pitch of the driven is P' = 0.19635 P = — — ^„o or 0.2267, the circular pitch of the driven cos 30 D = 0.2267 X 18 or 1.298, the pitch diameter of the driven The diameters of the required blanks upon which to cut the spirals 2 are obtained by adding p to the pitch diameter of each gear. For 16 pitch (P= 16) the addendum is 0.0625 or ^ = 0.125. The resulting blank or outside diameters are, therefore, 1.5'' + 0.125'' = 1.625" for driven and 1.298" + 0.125" = 1.423" for driver The number of the cutters to be used for cutting the teeth of the spiral gears is next determined. The tooth outline is con- sidered to be on a plane perpendicular to the helical outline of the teeth. Figure 33 shows a spiral gear of pitch diameter D, with Fig. 33. — Spiral gear blank. the inclined lines representing the center lines of the spiral teeth. If a plane AB be passed normal to the tooth outline, its true section may be projected, on lines normal to itself, as an ellipse C E F G. If the teeth were shown in outline on this ellipse, the teeth at G would show the true tooth outline produced by the cutter. This is the point of greatest curvature on the ellipse. The circle of equal curvature will be the ''equivalent spur gear'' 46 ADVANCED SHOP DRAWING having the proper number of teeth for which the cutter must be chosen. This circle, G H J K, is shown in outhne. It can be proved by involved mathematics that if N = No. of teeth in spiral gear A^' = No. of teeth in equivalent spur gear e = tooth angle then N N' = ^V (8) cos"^ e If this formula is applied to the problem under consideration, it will be found that 12 ^' = — TTTFTS 01* 96, tooth cuttcr for driver cos^ 60 and 18 ^' = TTTT^ or 28, tooth cutter for driven cos^ 30 These are the numbers of cutters to be used on the two spiral gears, respectively. Since the cosine of an angle is always less than unity, the cube of the cosine will be much less and, conse- quently, N' will always be greater than N. Problem 9 Make a full size drawing of a pair of bevel gears of 48 and 36 teeth; 8 pitch, shaft angle 90°; diameter of shafts iHe"') backing 1^" and IM" respectively, and width of face l^-^". Each gear is to have a single key way, the dimensions of which may be obtained from Table. 3. All necessary angles and dimensions are to be shown. Problem 10 Make a full size drawing of a single thread worm and worm wheel com- bination. Teeth in wheel 36"; pitch ^^"; distance between centers 4^^"; diameter of worm shaft iHeJ diameter of wheel shaft l^fe"; length of worm 3"; length of wheel hub 2}i". (Note: Use Table 2 for finding the size of teeth. Use a 12" X 18" sheet for the drawing.) Problem 11 Make a complete detail mechanical drawing of some gear of any type which may be readily accessible. Be sure that the drawing gives all the information necessary to make the gear. CHAPTER IV ISOMETRIC, CABINET, AND SHADED DRAWINGS 27. Isometric Drawing. — The work discussed thus far is known as mechanical drawing or orthographic projection. The different views of the object were projected upon planes parallel to the faces of the object. In making sketches or drawings it is often desirable to show the entire object in one view. Sometimes such a drawing can be readily made and be easily understood by one who does not under- stand ordinary mechanical drawing. In photography, the opera- tor generally takes a view of an object from one corner so as to give as complete an idea as possible, by showing the length, breadth, and depth of the object. So in pictorial representation, three faces of the object are usually shown in one view; in other words, the draftsman works from three axes, along which the various lines of the drawing are laid out. There are various methods of pictorial representation in use but the most important are isornetric and cabinet. In an isometric drawing the three axes make angles of 120° with each other. These are known as the isometric axes. One of the axes is usually vertical and the other two make angles of 30° with the horizontal. It is not necessary, however, that one of the axes should be vertical as long as the three axes make angles of 120° with each other. A mechanical drawing of a block 2J^" square and 4" long, drawn half size, is shown in Fig. 34. Figure 35 is an isometric drawing of this same block. An isometric drawing of this block standing on end would appear as in Fig. 36, the only difference being that edge ad is laid off on the vertical axis. The lines ah, ac, and ad make angles of 120° with each other. 47 b « r ■• ^ a d J * -2 " b a c 1 a c d Fig. 34. — Mechanical drawing of block. 48 ADVANCED SHOP DRAWING One of the isometric axes is spoken of as being vertical. As a matter of fact only its projection is vertical. In Fig. 36 the ob- ject is swung about the point a, or, the eye is above the surface abd and looking down on the block. Hence, none of the axes are seen in their true lengths, nor are the lines which are laid out along them. All dimensions appear shorter, or ''fore-shortened," and should, if the drawing were made correctly, be drawn to a smaller scale. This is ordinarily not done, as it complicates the drawing. It is unnecessary for the reason that the dimensions are fore-shortened in the same proportion along all the axes. The Fig. 35. — Isometric drawing of block shown in Fig. 34. Fig. 36. — Isometric drawing of block standing on end. full dimensions of an object are usually laid down. The error merely results in making the object look larger than it is, although the various parts are relatively proportioned. It is well known that in actual pictures, parallel lines appear to meet in the distance, like the rails of a railroad track. For the sake of; ^simplicity, parallel lines are drawn as parallel lines in isometric drawing as in the case of the square block just con- sidered. Broken lines are usually omitted from an isometric drawing unless necessary to give a full ^jud clear conception of the object. Lines not parallel to any of the isometric axes are known as non-isometric lines. It must be remembered that measurements can be laid down only on isometric lines; that is, on lines parallel to the isometric axes. To lay down such non-isometric lines, an isometric construction must first be built up from known iso- metric lines. If it is desired to make an isometric drawing of a segment of a hexagonal bar, one may proceed by the steps ISOMETRIC, CABINET, AND SHADED DRAWINGS 49 shown in Fig. 37, first making a mechanical drawing of two views, and then, by drawing a circumscribing rectangle about the hexagon of the upper plan locating the corners in isometric. Fig. 37. — Mechanical and isometric drawings of segment of hexagonal bar. A circle in any isometric plane always appears as an ellipse. It may be drawn either by coordinate projection, as in the case of the hexagon, or it may be drawn by the following approximate t^ ^ ca-^d J < t 1 ^ ^ ¥ sC< > ' f . 1 \ ^-^^" 'J^ '^ \ ^ Fig. 38. — Isometric drawing of segment of round bar. method. It may be assumed that it is desired to show a 4'' segment of a 2J^" round bar in isometric. First the circumscrib- ing 23-^'' square, Fig. 38, should be drawn. Since a circumscribing 4 50 ADVANCED SHOPJDRAWING square is tangent to its inscribed circle at the middle point of each side, it follows that the same holds true of its isometric projection; that is, the circle must be tangent to the square ahcd at the mid- points of its 4 sides, or at points, e, f, g, and h. Since the radius of a circle or arc is always perpendicular to the tangent at the point of tangency, lines perpendicular to the sides of the square at their mid-points should be drawn, these being the construction lines ga, ha, fc, and ec. Since the sides of the square make angles of 30° with the horizontal, these lines can be readily drawn per- pendicular to their respective sides by drawing them at angles of 60° with the horizontal. On account of the similarity and equality of the triangles thus constructed, it is found that the centers for the upper and lower arcs are in the upper and lower corners of the square. The centers for the two end arcs are at the points where ce and cf intersect on the line hd. With c as center a!nd/c as radius, arc/e should be drawn; with a as center and radius ga, arc gh should be drawn; with k as center and radius gk arc gf should be drawn; with m as center and radius Am arc he should be drawn. It will be noticed that fc = ga and gk = hm. A line ^" below hd and parallel to it will be the corresponding line upon which to construct the base of the cylinder. The elliptical form of the bottom will be exactly like the elliptical form of the top. It may be drawn by projecting the centers k and m along the lines ko and mr, and drawing the same corresponding arcs from the points o and r as centers, then connecting these with an arc of radius equal to cf. This drawing shows all the construc- tion lines that are necessary. These lines may be erased from the finished drawing. Figure 39 includes a mechanical drawing and an isometric drawing of a 4'' X 3'' X %" angle iron with rivet holes. This isometric drawing illustrates the principles of isometric represen- tation and serves to show the adaptability of this method- for simple cases. It should be noticed that all the lines of this sketch are either vertical or make angles of 30° with the hori- zontal. The rivet holes, being circular, are laid out by first drawing circumscribing squares whose sides make angles of 30° with the horizontal. The method of constructing these rivet holes and the %" fillet is shown in the enlarged views. It should be noticed that the holes appear different in the horizontal and vertical parts of the angle iron, although the construction is the same. If the accurate curvature of the ISOMETRIC, CABINET, AND SHADED DRAWINGS 51 %" fillet or any other such arc is desired, it may be deter- mined by the construction shown in the small sketch. The two isometric lines may be considered as parts of a square. The arc will be tangent to the two isometric lines, and the two points of tangency will be mid-points on a %" isometric square ff^^^^^^l , 3- 5'- -* 1 1""^ 8 <- u t — lOlQO 1 ' 1 1 1 ♦ -• 4"— ^ DETAIL OF CONSTRUCTION OP i" FILLET Detail of Construction of Hole in Horizontal Part. Detail of Construction or Hole in Vertical Part. Fig. 39. — Mechanical and isometric drawings of 4" X 3" X %" angle iron. constructed on these two iosmetric lines. Therefore, ab and ac, each equal to %", are laid off. At c and h, perpendiculars to the two lines respectively are erected. From their point of intersection d, as a center, an arc of radius db is struck. This arc is the required fillet. In Fig. 40 a mechanical drawing and an isometric drawing of 52 ADVANCED SHOP DRAWING Fig. 40. — Isometric and mechanical drawings of bearing block. Fig. 41. — Detail drawing of bearing block. ISOMETRIC, CABINET, AND SHADED DRAWINGS 53 the bearing block of Fig. 41 are shown. This figure shows all the necessary construction lines, but these should not appear on the finished drawing. The absence of broken lines should be noticed. A l}y^" square head nut blank with all construction lines is represented in Fig. 42 in both mechanical and isometric drawing. It should be noticed how the chamfer is provided for. Fig. 42. — Drawings of 1 34" square nut blank. 28. Cabinet Drawing. — Cabinet drawing is somewhat similar to isometric drawing but is simpler because of the fact that two of the axes are at right angles to each other. Upon these two axes all dimensions are laid out to full scale. The other axis may be at any angle whatever, the only difference in using the various angles being that the object will appear to be viewed from 54 ADVANCED SHOP DRAWING different angles. It is usual to draw the third axis on some common angle to the horizontal as 30°, 45°, or 60° as these angles can be laid down easily with the draftsman's triangles. In this book the oblique angle of 45° will be used. If dimensions are scaled full size on the oblique axis, the ob- ject appears to be distorted. A cabinet drawing of a cube is ZZT^ Fig. 43. — Incorrect method of cabinet drawing. Oblique dimen- sions full size. Fig. 44. — Correct method of cabinet drawing. Oblique dimen- sions half size. shown in Fig. 43 where the oblique dimensions are scaled full size. The great distortion should be noticed. To overcome this, dimensions on the oblique axis should be drawn half size. Figure 44 shows a drawing of the same cube with the oblique dimensions drawn to half size. The horizontal and vertical dimensions of these figures are full size as is the case in all cabinet drawings. Fig. 45.— Cabinet drawing of block. Fig. 46. — Cabinet drawing of round bar. A cabinet drawing of the square block which was shown in iso- metric in Fig. 35 is shown in Fig. 45. Figure 46 represents a cabinet drawing of the round bar which was shown in isometric in Fig. 38. It should be noticed that the end view of each is shown as a full end view regardless of the fact that the objects are viewed obhquely. The end view of Fig. 46 is a circle. ISOMETRIC, CABINET, AND SHADED DRAWINGS 55 An orthographic projection of the front of a tool chest is shown in Fig. 47, while a cabinet drawing of the same tool chest is shown in Fig. 48. The front of the chest in this figure is exactly the same as in Fig. 47. Figure 49 shows a cabinet drawing of the same chest with the drawers pulled part way out. ; o o 6 6 o o 6 II Fig. 47. — Front view of tool chest. ^ o II o Fig. 48. — Cabinet drawing of tool chest. Fig. 49. — Cabinet drawing of tool chest with drawers out. In Fig. 50 is shown the cube of Fig. 44 with circles inscribed on its faces, together with all the necessary construction lines. The front face is, of course, drawn full size, and the circle appears in full size inscribed in the square. This can be drawn most readily by drawing the two diagonals of the square and then, from their intersection as a center, striking a circle tangent 56 ADVANCED SHOP DRAWING to the sides of the square. The obhque hnes are drawn at an angle of 45°, and dimensions laid off to half scale along them. The projection of the upper surface hcde, being four-sided and having opposite sides parallel, is shown as a parallelogram. The projection of the circle will lie within this parallelogram and will be tangent to its four sides. It may be drawn as follows: The middle points of the four sides as /, g, h, and k are located. Then dh, gh, and fk are drawn. Next shis bisected at n and fm at 0. With radius nh and center n an arc is drawn tangent to line de. With radius bh and a center located by trial, another Fig. 50. — Cabinet drawing of cube with inscribed circles. arc is drawn that will connect the upper end of the arc just drawn and will be tangent to line cd. With the same radius hh another arc should be struck that will connect the lower end of this arc and will be tangent to the line be. The same procedure should be followed with o as a center and of as a radius and also with the arc tangent to be at k. The construction of the circle on the side face of the cube is similar. Any circle in cabinet projection can be thus readily drawn by first constructing the parallelogram which encloses it. Figure 51 shows a cabinet drawing of the bearing block which is shown by orthographic projection in Fig. 41 and by isometric drawing in Fig. 40. It should be noticed how the projection of the cylindrical part beyond both ends is provided for. The broken lines show how the contour of the ends would be shown if they did not project. Their centers would be at points a and c, respectively. Because of the projection of the ends, however, ISOMETRIC, CABINET, AND SHADED DRAWINGS 57 the centers of the ends must be offset by the distances ah and cd, respectively, equal to half of the projections at either distance. The bearing block, being irregular in outline on one face and of uniform outline throughout, is admirably adapted to cabinet drawing. In drawing such objects, the face with the irregular outline should always be placed in the plane of the paper; that is, the plane represented by the horizontal and vertical axes. Fig. 51. — Cabinet dra-wing of bearing block of Figs. 40 and 41. 29. Shading Drawings. — The shading of drawings is sometimes resorted to in order to make them appear more realistic. Shaded drawings are commonly used in engineering catalogs, display drawings, illustrations, patent office drawings, and the like. In fact, they are commonly used where they will be placed in the hands of people who might not understand an unshaded mechan- ical drawing. Patent drawings must be shaded in such a manner that they will be readily understood by attorneys and others concerned with the granting of patents, who may have no knowledge of mechanical drawing. In shading drawings, the draftsmen should always assume that the light ^strikes the object from over the left shoulder. There are two methods of shading drawings: (1) by shade lines; (2) by line shading. The first method is the simpler. 30. Shade Lines. — In all previous discussion, object lines were assumed to be made of- uniform weight. This is the general practice for all working drawings, and should be rigidly adhered to unless for some specific reason. 58 ADVANCED SHOP DRAWING In shading drawings, it is assumed that the light comes from over the left shoulder and strikes the object diagonally so that some of the surfaces are in the light while others lie in'the shadow. Edges of an object which lie between light and dark surfaces are often represented by lines two or three times as wide as the other lines as illustrated in Figs. 52 to 56. Such lines are called shade lines. Fig. 52. — Illustration of first rule of shade lines. In order to avoid the confusion that might arise as to just which lines should be shaded, the four following rules are ad- hered to in general practice and apply to the shading of all views of mechanical drawing. 1. Shade right-hand and lower edges in all views. 2. Shade left-hand and upper edges of all holes. Fig. 53. — Illustration of first and second rules of shade lines. 3. Do not shade the lines representing the junctions of visible surfaces having equal illuminations. 4. Shade the lower right-hand quadrants of outer circles and the upper left-hand quadrants of inner circles. The first rule is illustrated by Fig. 52 which is a shade line mechanical drawing of a cube, the front elevation and right side views being shown. The second rule is illustrated by Fig. 53 which shows a shade line drawing of a capping stone for a chimney. The lines to the ISOMETRIC, CABINET, AND SHADED DRAWINGS 59 right and bottom of the outhne are shaded according to the first rule, and the shading cf the two rectangular holes is in accordance with the second rule. The third rule must always be applied with a full consideration of the conditions involved. A mechanical drawing of a pyramid with the top cut off is illustrated in Fig. 54. The inclined lines in the left view are evidently governed by the third rule. A Fig. 54. — Illustration of third rule of shade lines. closer study will show that the inclined surfaces above and to the left are both illuminated and, therefore, the inclined line separating them is a light one. Since the inclined surfaces below and to the right are both shaded, a light inclined line will separate them. The other two inclined lines in this view separate illuminated and dark surfaces, and are, therefore, shaded. The lower inclined line in the right side view will be shaded if it makes an angle of 45° or less with the horizontal. Fig. 55. — Illustration of fourth rule of shade lines. The ring shown in Fig. 55 illustrates the popular method of shading inner and outer circles, according to the fourth rule. To shade a circle, it should first be drawn with a weight of line equal to the lightest part of the finished circle. The center of the circle should then be stepped upward to the left, on a line making 45° with the horizontal, a distance equal to the required width of the most heavily shaded part of the circle. With this new center and the same radius as before, a new semi-circular 60 ADVANCED SHOP DRAWING arc may be described tapering off gradually at its extremities into the circle originally drawn. Figure 56 is a shade line mechanical drawing of a slotted link and shows the application of the four essential rules of shade lines. When the above rules are applied to isometric drawing, Fig. 56. — Slotted link illustrating the four rules of shade lines. they are somewhat confusing. The popular practice among patent draftsmen and others using this method of illustration is to briilg out the nearest outside edges and the farthest inside edges with heavy lines as illustrated in the isometric drawing of the slotted bar, Fig. 57. In all work in shading drawings, the draftsman will find it necessary to use judgment and common sense. It should be Fig. 57. — Shade line isometric drawing of slotted bar. Fig. 58. — Line shading of pipe union. remembere/1 at all times that a shade line should lie between a light and a dark surface and that the light is coming from the upper left-hand corner of the paper. 31. Line Shading. — ^The ability to do good line shading is an unusual accomplishment among draftsmen because it is so ISOMETRIC, CABINET, AND SHADED DRAWINGS 61 rarely used. It requires a great deal of practice and artistic ability on the part of the draftsman to use it rapidly and effect- ively. Often, the artistic shading of one view will obviate the necessity for any more views. The line shading of a simple object is illustrated in the shaded drawing of the union, Fig. 58. This figure also illustrates the two essential rules of line shading. 1. A surface in the light grows darker as it recedes from the eye as shown by the shading on the left face of the hexagonal ring. 2. A surface in the shadow grows lighter as it recedes from the eye as shown by the shading on the right face of the hexagonal ring. By this method the light is assumed to come over the left shoulder of the draftsman, making angles of 45° with the paper as it is held vertically in front of him. The Cylinder. — The top and front views of a vertical cylinder are shown in Fig. 59. The top view is shown to determine the shading of the front view. The arrows show the projec- tions of the light rays striking the cylinder diagonally at an angle of 45° with the paper. The Brilliant Line. — The brilliant line is the line where the object ap- pears to be most highly illuminated. In the top view, Fig. 59, the point a receives the most direct and strongest light, since the light rays as shown by the arrow are vertical to the circle at that point. The point c, however, midway between a and h, reflects the strongest light to the eye as shown by the downward arrow at the point. The unshaded area in the front view beneath the vertical arrow at c is known as the brilliant line. The darkest shadow in the front view appears beneath the point d where the light ray in the top view is tangent to the circle. Fig. 59.- — Line shading of cylinder. 62 ADVANCED SHOP DRAWING Having thus located the lightest and darkest parts of the cylinder, the two rules for line shading should be applied. The shading should increase in depth as it recedes on each of the brilliant lines. To the right, the shading increases in depth up to the line of darkest shadow. Beyond this point, the cylinder lies wholly within the shadow and the shading must, therefore, become lighter toward the right as it recedes from the eye. Flat and Graded Tints. — ^There are two kinds of line shades; namely, flat and graded tints. The flat tint has lines of uniform weight and equally spaced throughout as shown in Fig. 60 at yl . It is used on fiat surfaces in the plane of the paper, but only when the drawing is to be heavily shaded. Patches of it are sometimes used on such surfaces to indicate '^high lights." Graded tints show shading of increasing depth either to the left or to the right as shown in Fig. 60 B and C. Graded B C Fig. 60. — Flat and graded tints of line shading. tints were employed in the shading of the union. Fig. 58 and in the cylinder, Fig. 59. In graded tints, the setting of the pen is not changed for every line, but several lines are drawn with one setting of the pen. The pen is then reset and another series drawn. For flat surfaces the spacing of the lines should be uniform, but for curved surfaces the spacing between the lines should be decreased gradually toward the darkest part. Figure 60 shows the uses of all these shadings in the bolt. It is usually necessary to practice freely before attempting to apply shading to a finished drawing. As a first aid, the spacing of the lines and also their widths should be checked off by short dashes. When the gradation of these appears satisfactory, the line shades, similarly graded, may be added. All spacing and widths of lines should be gaged by the eye. 32. Special Cases. — The Hollow Cylinder. — Figure 61 illustrates a section drawing of a hollow cylinder properly shaded in the front view by the aid of the auxiliary top view. The arrows indicate the projections of the light rays. A careful study of ISOMETRIC, CABINET, AND SHADED DRAWINGS 63 this figure will show that the gradation of shading is the reverse of that represented in Fig. 59 where the convex surface of the cylinder was exposed to view. Since the concave surface, Fig. 61, Hes almost wholly within the shadow, the line of greatest shadow will be where the arrow in the top view is tangent to the arc. The brilliant line is at c where the light would be reflected directly into the eye. The Cone. — A cone may be shaded by following the same rules of shading that apply to the cylinder, except that all the hne elements will converge toward the apex of the cone. The line shading of a cone is represented in Fig. 62. ^^ ^ V/ / Xy ^ 1/ / 1/ / WJ / \/ / Vy / 1 \/ < L- Vi Fig. 61. — Line shad- Fig. 62. — Line shad- ing of section of hollow ing of cone, cylinder. Fig. 63.— Method of determining the shad- ing of a sphere. The Sphere. — The determination of the shading of a sphere is represented in Fig. 63. The front and top views together with the projections of the conventional light rays are shown. If the two axes ef and gh in the front view are drawn at angles of 45°, it will be noticed that the half of the sphere above gh will be exposed to the light while the half of the sphere below it will lie in the shadow. The Brilliant Point. — ^In the case of the sphere, the lightest and the darkest parts will be points, rather than lines. Consequently, the hrilliant point on the illuminated half of the sphere, and the darkest point on the darkened half, will lie somewhere along 64 ADVANCED SHOP DRAWING the axis ef in the front view, since the light arrows at either end of this axis are normal to the circle at those points. In the top view^ it will be seen that the arrow at c locates the point in that view which reflects the greatest amount of light to the eye. Its projection on ef of the front view locates m as the brilliant point. In like manner d, determining the darkest point in the top view, projected upon ef, gives w as the darkest point in the front view. Above the axis gh, the shading will increase in depth on each side of the line ef. Below the same axis, the shading will decrease in depth on each side >of the line ef. y//////////y////77A CYLINDER SECTION OF CYLINDER SPHERE SECTION OF SPHERE RING HOOK Fig. 64. — Illustrations of line shading. The following simple method of shading a sphere, as illustrated in Fig. 64, is commonly used. After drawing the circumference, the brilliant point and the darkest point are located on the 45° axis. A small circle, enclosing the high light area, may then be lightly described about the brilliant point with the bow pencil. None of the shaded circles should be drawn within this area. This small circle should be erased from the finished drawing. The line shading is graded along the 45° axis as was done in the case of the cylinder. The line shading consists of a series of concentric shaded circles having the same common center as the center of the sphere. Figure 64 shows some good examples of line shading on simple objects. It will be noticed that the shade lines on these objects ISOMETRIC, CABINET, AND SHADED DRAWINGS 65 Fig. 65. — Illustrations of line shading on some simple shop objects. UNIVEIPSAL COUPLING f^OR I" SHAFT Fig. 66. — Universal coupling. 66 ADVANCED SHOP DRAWING are used sparingly. The draftsman should endeavor, as far as possible, to do line shading in a like manner. Some examples of line shading, as applied to simple shop objects, are shown in Fig. 65. Additional examples may be found in industrial magazines which contain many examples of this class of work. Problem 12 Make a complete isometric drawing of the universal coupling shown in assembly in the freehand sketch, Fig. 66. The isometric drawing should be full size, but no dimensions should be shown. The drawing paper should be placed on the board with its long dimension horizontal, and the coupling drawn with the axes of the shafts lying on the 30° isometric axis which extends upward toward the right. The ends of the shafts should be shown as broken off with uneven outlines. Problem 13 Make a cabinet drawing of some simple object of rectangular outline, such as a mission bookcase, chair, or table. No dimensions should be shown. Problem 14 Make a tracing of the isometric drawing of the universal coupling which constituted Problem 12. Practice shading this tracing in pencil with line shading. When it appears satisfactory, ink it in. The ends of the shafts should be shown broken off irregularly. CHAPTER V PATENT OFFICE DRAWINGS 33. Application. — ^The rules governing the application for, and issuance of, patents are very rigid. The Patent Office issues a pamphlet called the ^' Rules of Practice" which gives complete information covering these points. These rules are issued gratui- tously upon application to the Commissioner of Patents, Wash- ington, D. C. Although all matters governing the application should be left in the hands of a thoroughly competent patent attorney, they should be at least understood by the inventor. There are six parts to a complete application for a patent on an invention. These parts are: petition, power of attorney, specification, claims, oath, and drawings or models. The petition is merely a communication to the Commissioner of Patents, asking for a grant of a patent upon the invention. The petition contains information concerninn CQwi 0-Q^-&^-^^-^^-^^^^^ ^ Tzrnz. zti ^ J=, (^ r^r-. J-p Ar\ r\-\ r\-^ vi///////r^i;^^^/'^AyJ^^^^^^ Field R'ivets F'/ain i^Counter&unk &■ Countersunk A- Chipped S^ h^ ^^ ^ m k (O ^^ Chipped ■§ high F/attensd X high ^"5 ^^ ^^ ^(0 k • ^ — ^ THRO'CfMTEfJ Rivets ^' Open Holes J| r*ikt onc (.oat Red lead. Fig. 74. — Shop drawing of girder. give an even bearing for the bearing plate. The four black holes in the base plate are for the anchor bolts by means of which the column is secured to the foundation. The rivets of the base plate are countersunk on the lower surface so as to give a smooth surface. This face is shown by the conventional symbols. At the first floor level the floor beams in one direction consist of two 10''-25 lb. I-beams, while in a direction at right angles to this they consist of single 8''-18 lb. I-beams. These I-beams are fastened to the column by means of bolts. Notice should be taken how the ''out-standing" dimensions of the bolt holes for the 8" 6 82 ADVANCED SHOP DRAWING 6 STRUCTURAL DRAWING 83 I-beam supports are shown. The abbreviation ''o.s." means "out-standing." The '^gage" of an angle is the distance from the back of the angle to the line of rivets. By means of the view at the right it will be seen that the two "L's" 3>^'' X W2' X Ke'' are secured to the column by means of two "through bolts." The two "L's" 6" X 6'' X VW are bolted to the flanges of the two 10" channels. The number in parenthesis, following the size of a member, is the number of members of that exact type that is required for one complete column. Upon close examination it will be seen that that part of the drawing affected by the notation "42 spaces® 4" = 14' — 0"" is not drawn to scale because it is of uniform section throughout. Figure 74 shows a shop drawing of a girder. The girder is symmetrical about its center line so that it is necessary to show a drawing of only half of it. The detailed information as to the materials required is listed as a separate bill of material. This girder consists of a plate "v^ith pairs of flange angles at the top and bottom reinforced by web plates. Other plates called cover plates are shown outside of the web plates. The main plate of the girder is reinforced with angles called stiffeners. Fillers are used betw;,een the stiffeners and the plate so that it will not be necessary to crimp the stiffeners around the web angles. It will be noticed how the section through the center is shown. Instead of showing the bottom view, it is better practice to show a section taken through the girder looking down upon the lower flange angles. Figure 75 shows a working drawing of a roof truss. Because of its symmetry about the center line, only half of the truss is shown. A marking diagram is attached and the drawing is marked to conform to it. It should be noticed how the inclina- tion of the various members is noted by their tangents on a 12" base line. It is unnecessary to draw the 12" base line to scale. 40. Templet Shop. — ^After the shop drawings are made, checked, and approved, they are blue printed and sent into the templet shop. For small and general work each templet is made separately from the detailed shop drawings. A templet is either a board or framework of boards, the plane of one of its sides being an exact representation of the plane of one of the sides of the metal shape or piece which is to be made. Holes are bored in the wood at all points where rivets are to be driven. This templet is then 84 ADVANCED SHOP DRAWING clamped upon the piece, and the positions of the holes, bevels, and notches are marked upon the metal face. 41. Beam Shop. — The work on beams and channels is carried on in what is called a beam shop. In case the material has been shipped from the mill according to the mill bill made out in the drafting room, the beams are found in that portion of the stock yard reserved for the job in question. If the material is to be taken from stock, the proper lengths are cut from stock lengths with a cold saw* or beam shear, which is usually located in the stock yard. In the beam shop the templet is laid on the beam and the positions of the holes, bevels, and notches are marked upon the metal. The centers of the holes are marked with a center punch w.hich exactly fits the holes in the templet. The position of each hole is thus indicated by a small indentation in the metal. The bevel and notch lines are drawn on the metal by scratching or marking with chalk along the edges of the templet. The beam is then taken to the power punches where the holes are punched. If there is any special cutting or bending to be done, it is performed before the piece is taken to the riveting machine to have connections riveted on. The beam is then taken to the end of the shop nearest the yard and the parts not accessible after assembling are thoroughly painted. 42. Assembling Shop. — In this shop all the material is brought together, fitted, riveted, and made of exact dimensions; when the members leave this shop, they are ready to be prepared for ship- ment. Pneumatic portable riveters are used on the heavier pieces of work. For columns there is an additional operation of planing or milling the ends of the riveted sections before the caps or base plates are riveted on. 43. Yard. — After the material is finished in the shops, it is taken out into the yard and placed in that part of the yard assigned to the particular job number. It should be inspected carefully in order to see that it conforms in every way to the specifications and to the drawings. All work should be painted and have the approval of the company's inspector before being shipped. Problem 16 Make a working drawing of a column similar to Fig. 73 with the following exceptions: 1. Distance from back to back of the two 10"-20 lb. channels shall be 6K" instead of 6". STRUCTURAL DRAWING 85 2. Distance from milled base (or top of base plate) of column to top of first floor beams shall be 20' 0" instead of 18' 0". 3. Distance from top of first floor beams to upper milled end (or bottom of bearing plate) of column shall be 1' 4" instead of 1' 7". 4. The column to be for the corner of the building. This will require floor beams and their supports on only two sides of the column rather than on all four sides as shown in Fig. 73. The floor beams thus supported shall consist of one8"-181b. I-beam in one direction and two 10"-25 lb. I-beams in the other direction. This will cause changes in Fig. 73 as follows: 1. There will be a change in the width of the web plate. 2. There will be an increase in the number of rivets, spaced at 4", which fasten the web plates to the two 10"-20 lb. channels. 3. The distance between the lower end of the splice plate and the upper angle to which the two 10 "-25 lb. I-beams are bolted will be decreased by 3". 4. Angles for the support of the floor beams will be needed on only two sides of the column. Through bolts will still be needed for fastening the 33-^" X 33^" X Ke" *'L" to the column, because of the inaccessibility of the rear side of the web of 10" channel to which it is attached. CHAPTER VII ELECTRICAL DRAWING 44. Electrical Drawing. — Electrical drawing, like mechanical drawing, includes several specialized lines. Since the drafting of electrical machines, fixtures, and appliances is so much like mechanical drafting, this chapter will deal only with wiring dia- grams which illustrate electrical drawing in a specialized form. m Main or Feeder run Concealed under F loor • """" " " ' a\>o\ie - Branch Circuit run Concealed under Floor _ . • •. • MX obovc - • . n Expoeed rO- KXKKXXJtXi Lamp Circut ( Arc) — • •—Pole tine I Riser -4^ Crossing Wires (2i Joined Wires ©Ceiling Outlet .Electric only. Numeral in centfer indicotes number of Standard 16 CP Incandescent Lamf)s. r^ Drop Cord Outlet -(")- Chandelier Inc^jndcsccnt Lamps O 5P Switch Outlet S^ D.P. •• •• S 3- Way " Q Meter Outlet HBH Distribution Parxl Junction or Pull Box -o- -O -O- -O- -o- -o- Lamp Circuits (Incandescent) ( t j Galvanometer ~^WVWWW Resisfance rAj Ammeter — ^Wft^ ' — Variable Resistance — |«|ill|i|iH ®«««'-y Bell E-sJ — Buzxer III 1^ Condenser A.C Generator (Single Phase) 'T j^ D. C. Qencnatw Am meter Voltmeter Wot t meter Meter Transformer Rotary Trans|brmcr Motor Phcostat Knife Switch Fuse Lightning Arrester Ground Fig. 76. — Table of electrical symbols. 45. Symbols. — In electrical drawing, as in various other highly specialized branches, the draftsman has constant recourse to standard symbols by which the various appliances are desig- 86 ELECTRICAL DRAWING 87 nated. Figure 76 shows the most generally recognized symbols for the more common electrical devices. Many of these are taken from the Hst of standard wiring symbols adopted and copy- righted by the National Electrical Contractors' Association and the American Institute of Architects. Others are taken from the ^' Rules of Practice" of the United States Patent Office. These symbols are so generally used in practice that it is not necessary to show a table or ''key" of them on the drawings. 46. Wire Size. — Wire is usually sold by ''gage numbers," that is to say, manufacturers employ certain arbitrary numbers to indicate wires having various diame- ters. Figure 77 shows an American standard wire gage. Different slots on the gage should be tried on the wire until one is found which will just fit over the wire. The number of that slot is the gage number of the wire. The circular mil is another term em- ployed in dealing with wire sizes. The word mil means one-thousandths of ^ „^ , . , , , . . Fig. 77. — American standard an inch. A wire having a diameter of wire gage. .001 in. is said to have an area of one circular mil. The diameter of any wire expressed in mils is the diameter in one-thousandths of an inch with the decimal point removed. The area of any wire in circular mils is the square of the diameter in mils. This system of measurement is used mostly for wires of large diameter. After the size No. 0000 is reached, the area of the wire is usually expressed in circular mils as: 200,000, 300,000, etc. up to 2,000,000. 47. Bell Circuits. — Figure 78-A shows a simple bell circuit such as might serve for a doorbell. Power is supplied by a battery or dry cell. It should be noticed that one side of the battery is connected directly to one terminal of the bell. The other side of the battery is connected to the button, and then the button directly to the other terminal of the bell. Completing the circuit by a push on the button causes the bell to ring. In the symbol for a battery, each pair of lines represents a cell. Figure 78-5 shows a bell controlled by two push buttons. It should be understood that in order to ring a bell from either of two buttons, the circuit must be completed by pushing either button. This is done by connecting the two buttons in parallel, 88 ADVANCED SHOP DRAWING tons in parallel, or, in other words, an uninterrupted connection must be run from the battery to each button. The same must be true of the connections from the buttons to the bell. As before, one side of the battery is connected directly to the bell and the other side through both buttons to the bell. It can be seen from the figure that a complete circuit is established when either of the buttons is pushed. Figure 78-C shows an arrangement by which two bells may be rung simultaneously from a single push button. In this case it Fig. 78. — Simple bell circuits. should be noticed that the two bells are in parallel. One side of the battery is connected directly to each of the two bells. The other side of the battery goes to the button and there a direct connection is made to each of the bells. It may be seen that with this arrangement, when the button is pushed, the current has an uninterrupted connection to each bell and so causes them both to ring. Figure 79 shows connections for one bell and an indicator for several stations. Such an arrangement as this is widely used in hotel and elevator service. In a hotel the indicator would be located near the clerk's desk and the buttons in the various rooms. ELECTRICAL DRAWING 89 It should be noticed that as before the bell is connected directly to one side of the battery. The other side of the battery con- nects directly to each of the buttons. From the buttons the cur- d t I 66666 Fig. 79. — Bell and indicator circuit. rent flows through the indicator, to the other side of the bell. The indicator is merely a set of coils wound around small metal cores. When the current flows through the coil, it magnetizes the core. This magnetized core attracts the indicator needle. The core retains enough magnetism to hold the needle against it until freed by a slight jar. Figure 80 shows an apart- ment house arrangement whereby a call may be made from the front door; the door opened from the apartment; and a buzzer or bell rung from the apartment door. 48. Two-wire Circuits. — The simple two-wire system is a method of distribution very largely used, particularly in small isolated plants or jL/DOOR PEINER. where the power is not car- ItIt ried to great distances. The Fig. SO.-Bell system for apartment house. lamps are usually operated at 110 or 220 volts. Figure 81 shows such a system. The switches, fuses, and other accessories are omitted for the sake 90 ADVANCED SHOP DRAWING of simplicity. The sketch shows the two mains A-A running from the generator. Branch mains or laterals may be con- nected to the mains at any point. Where the mains are of any considerable length, they are usually designated as ^'feeders." In electrical drawing, when two wires cross, but do not inter- ■o o- -o o ^^^6^i> 7J o o o o <><><>(><;><> sect, one of the lines is crooked in the form of a semi-circle at the point of crossing. When two intersecting lines indicate wires that are connected at the point of crossing, that fact is denoted by a dot at the point of intersection. It should be noticed that all the lamps are put in in parallel and not in series. In other words, any one lamp may or may not o- o o- o o ^^^^ -0--0- -0--0 ■o-o JMM o-o o-o- -oo- oo oo -o -o- -o- -o- -o- -o- m Fig. 82. — Three-wire lighting circuit. burn, without interfering in the least with the operation of tne other lamps. In a series circuit, if one lamp goes out, the cir- cuit will be broken and all the lamps will go out. 49. Three -wire Circuits. — The three- wire system, as illustrated in Fig. 82, is used a great deal at the present time. In such ELECTRICAL DRAWING 91 a system two wires, A and B, supply the power. The return main for both of these wires is C. These circuits are used mainly in public buildings where some of the feeders must necessarily be long and where the load may Fig. 83. — Three-wire circuit with storage battery auxiliaries. be quite heavy. When wires are heavily loaded by attaching a great many lamps, the drop in voltage through the circuit may be so great as to cause the lamps to burn dim. This difficulty may ^ <^ 6 «-B<> Fig. 85. — Three-wire power and lighting circuit. is more heavily loaded than the other. These storage batteries placed in the line tend to balance the pull on the generator. Figure 84 shows a three-wire system with one main distribution center and three smaller panels. Sometimes the three service wires run only to the main distribution panel and the other feeders are run on two- wire circuits. Figure 85 shows another example of the same system where current is used for illuminating purposes and also for operating two motors. Two centers of distribution are shown here. It ELECTRICAL DRAWING 93 should be noticed that the motors are run from the two outside feeder wires. This means that they are 220- volt motors. 50. Wiring Diagrams. — Interior weiring diagrams are usually not necessary for electrical installations in residences and small factories. Verbal or written instructions are often sufficient. Usually the blue prints of the floor plans show the approximate location of lights and switches as well as the meter board and distribution panel. The location of the risers and feeders is left to the electrical contractor. Wiring diagrams are necessary, however, for elaborate systems such as are to be found in large office buildings or hotels. MAIN CUTOUT, METEF?, ETC. IN CORNIER OF BASEMEMT. CHAMBER 96* 10 O 5ECOND FLOOR PLAN. FIRST FLOOR PLAN. Fig. 86. — Wiring diagrams for cottage. Figure 86 shows typical wiring diagrams for the two floors of a cottage. The branches are usually strung under the floors and the risers concealed in the walls. Figure 87 and Fig. 88 show some typical wiring diagrams to- gether with a key of the symbols used, taken from catalogs of the General Electric Company. These diagrams give complete information to the electrician so that the system may be installed and wired without particular difficulty. Figure 89 shows a six-circuit panel with fuses such as is listed in the General Electric catalog. The first sketch shows the front of the panel giving the location of the switches and meters; the second sketch shows the wire sockets on the rear of the panel for the reception of the wires; the third sketch shows the wiring 94 ADVANCED SHOP DRAWING ,>-Ay\rsA/^^ (.-^vV^A^^ •*■ eus -P'oHj / CIRCUIT BREAKER AMMETER SHUNT |go} -Q X o— fooj f-A/VNAA^ OVERLOAD COIL ± BUS COMPENSATOR o— loot- = BUS X GENERATOR SERIES riELD eus- BUS- A.Mi= Ammeter. B.A.5.=Bell Alarm Switch. C. ^Compensator. C.B. =^CiRcuiT Breaker. C.C. =CoNSTANT Current Transformer. C.H. -Card Holder. C.T =CuRRENT Transformer D.R =DiscHAR6E Resistance. F. = Fuse. F. 5. = Field Switch G.L. =Ground Detector Lamp. LA. =Li-n-B-a&Ozl}fl s-asQ i&a Lte=aeCl=0^ s=asa=t)a =aecncia s=aeO=l}^ l)=g=a&Q=Da :D= :d: ELECTRICAL DRAWING 97 nection. The current flows from the Hne, through the choke coil and switch, out to the mill. The hghtning arrester consists of the choke coil and the series of gaps in the ground line. The choke coil has no appreciable effect on current of ordinary fre- quency and voltage, hence it offers no resistance to the power cur- rent. Lightning, however, is a current of extremely high fre- QROi/NO WIRE AT 'least no. 6 B4S WIRE SOLOCREO TO BRASS SCREWED TIGHTLY INTO CRUSHED COKE OB CHARCOAL.-- PEA Size . , ' ^ //^ //^ //Y //,%/ J^:.-..<,.'..V''ao V 7. ?Q(iOUND WIRE RIVETED IN A NUMBER OF PLACES TO :oL0 JCOPPER PLATE, AND t mwr/m SOLDERED roP. WHOLE ISTANCE ACROSS. NO. IS QAuaC COPPER PLATE ABOUT 3X6 FEET, AT LCVCL OF PCRMANEWTt.r DAMP EARTH. Fig. 90. — Lightning arrester house showing connections. quency and voltage. When it strikes the hne and attempts to flow through the choke coil, the coil builds up a counter voltage which checks the flow. On account of the high pressure the cur- rent jumps the gaps and is led off to the ground where it is dissipated. Problem 17 Figure 91, Fig. 92, and Fig. 93 are rough electrical sketches. Work these up into neat drawings and supply the missing symbols. 98 ADVANCED SHOP DRAWING If^ TJ^y.^ j(^ p:x.^ Fig. 91. — Bell wiring diagram for four-flat building. ^^}^»/iU44jL. ^ « litK uAA^ P^ Ayyi/tnitX^ Fig. 92. — Connections for measuring transformer losses during impedance test. ELECTRICAL DRAWING 99 n'^- Fig. 93.— Connection for electric lighting system with compound wound generator. CHAPTER VIII PLANS FOR PIPE SYSTEMS 51. Pipe. — There are several kinds of pipe commonly used in industry; as wrought iron, cast-iron, steel, lead, and brass pipe. Wrought iron pipe is the most commonly used. It is used for plumbing and heating purposes. Conduit for electric wiring purposes is the cheapest grade of wrought iron, lacquered both inside and outside to reduce the roughness. Cast-iron pipe is usually used in the larger sizes for water mains or underground systems. Boiler tubes are usually made of steel. A great deal depends on the quality of a boiler tube. There must be no weak places in it and it must be strong to withstand the pressures it is subjected to. Lead pipe is sometimes used for connecting plumb- ing fixtures to drains. In the smaller sizes it may be easily bent with the hands. This makes it easier to make a joint in difficult places. It is never used on supply water mains as it is liable to poison the water. Brass pipe is used in the smaller sizes; mainly as oil ducts on machinery. It is used also for hot water or pol- luted water since it does not corrode as iron pipe does. 52. Pipe Sizes. — Pipe is designated by the nominal inside diameter, which differs slightly from the actual inside diameter as will be seen in Table 4. OO Standard Extra Heavy Double Extra Heavy Fig. 94. — Thickness of pipe. Pipe is manufactured in three thicknesses or weights, known commercially as Standard, Extra Heavy, and Double Extra Heavy. Standard weight pipe is used on all hot water and steam heating work. The heavier weights of pipe are used in high pressure lines. Extra heavy and double extra heavy pipe have the same 100 PLANS FOR PIPE SYSTEMS 101 outside diameters as the standard weight pipe of the same nomi- nal size, the added thickness being on the side. An illustration of these is shown in Fig. 94. Table 4 — Dimensions of Standard Steel and Wrought Iron Pipe Nominal Actual outside diameter, inches Actual inside diameter, inches Internal area, square inches Threads per inch Distance pipe enters, inches Actual inside diameter inside diameter, inches Extra heavy, inches Double extra heavy, inches H 0.405 0.270 0.057 27 He 0.205 H 0.540 0.364 0.104 18 %2 0.294 H 0.675 0.494 0.191 18 ^%4. 0.421 >2 0.840 0.623 0.304 14 H 0.542 0.244 r4. 1.050 0.824 0.533 14 W32 0.736 0.422 1 1.315 1.048 0.861 IIH V2 0.951 0.587 iVi 1.660 1.380 1.380 UK ^H4. 1.272 0.885 IK 1.900 1.611 2.038 UK %6 1.494 1.088 2 2.375 2.067 3.356 UK »K4 1.933 1.491 2>^ 2.875 2.468 4.780 8 % 2.315 1.755 3 3.500 3.067 7.388 8 1^6 2.892 2.284 3K 4.000 3.548 9.887 8 1 3.358 2.716 4 4.500 4.026 12.730 8 iKe 3.818 3.136 4K 5.000 4.508 15.961 8 IK4 4.280 3.564 5 5.563 5.045 19.985 8 IH2 4.813 4.063 6 6.625 6.065 28.886 8 IK 5.751 4.875 7 7.625 7.023 38.743 8 IH 6.625 5.875 8 8.625 7.982 50.021 8 iKe 7.625 6.875 9 9.625 8.937 62 . 722 8 1%6 8.625 10 10.750 10.019 78 . 822 8 l^Ke 9.750 11 11.750 11.000 95.034 8 12^2 12 12.750 12.000 113.098 8 IK 11.750 53. Pipe Thread. — -All pipe is now threaded uniformly, the Briggs' standard of pipe thread sizes being used by all manufac- turers. The taper is an inclination of 1 in 32 to the axis, or %^" per foot. Figure 95 shows an enlarged view of a pipe thread with the relative sizes of the various parts noted. riat Tops Flat 3offoms -- 4- Threads —- Z Thds. riot Topi Round Bottoms Complete Ttireads Round Tops and Bottoms 60. f Tapar ^ t>er I" of Lengftti .8 outside diam. -h 4'.Q Number of Threads f^r f Fig. 95. — Section of Briggs' pipe thread. 102 ADVANCED SHOP DRAWING 54. Fittings. — The term fittings is applied to elbows, tees, crosses, unions, caps, plugs, etc. The dimensions of fittings vary somewhat with the different manufacturers. For this reason, if given at all, dimensions should be given from center to center of fittings. They are not usually given, however. The lengths of the various pipes and the arrangement of the coup- lings are generally left to the discretion of the pipe-fitter, though the drawings should always show the size of pipe. (Flange Croaa W^M i--v X — M=J 5izeof Pipe A B c E G H K L p s T V X 1 8 31 3Z 3 4- 5 /6 /J Hi Zl 3Z 1 4- 1 A 1 A- 'i 29 32 13 3Z /,-i zA 25 3Z 3 S 1 A- 3 a 'i 'k 1 Z //6 za 29 3Z 13 /€ 1 A- 3 S le 1 2 li li 9 16 ^3Z 3,-4 Ik /i 1 A- 3 6 s 16 3 4 1 '^ '7^ lA Zl 3Z 2^ ^3Z 3§i Ik Ik 1 7 76 3 e H /i 7 /« S a- 1 7^ iH 3 4- 2fl 4I li iM 3 e // 76 7 16 4- /« 7 /6 /I /6 li H 2 27 32 H 5A i'& 2 3 e 3 1 2 4-k z^ 1 2 3 A- fi H 24 29 3Z 3fi ■^3Z '16 2* 3 e /3 7S 1 2 3 2# 9 76 7 e z •3/6 2-S l£ 4* si z 2* 3 a //^ 9 /6 6 H £ a / 2-^ ^tI 2Si '32 li 5« 7/1 2i 3il 7 /e //4 8 7 3f II 16 Ik 3 5iz ^tk li ©32 ^7s ^& 4^2 1 z /i 3- e 7i 4^ 3 A l-k H 5¥. 3i li 7,-i lo-k Z^ s^ 1 z li 3 4- &i ^i /3 /« Ife 4 6i ^i li 8i life 3 -'32 1 z li 3 A 3 H IS IG li 4i 7k ^i lis '32 12^ 3i 631 9 76 2 13 ts ^i 3^e IS 16 iM 5 7i 4U '16 si i^i •^32 7,-i 9 /6 2^ 13 IG 10 e^ 15 16 lii 6 9 5'i 1 — '32 ii-k 15k 3- ■^32 ei 3 4- 2r 1 II 7^ / li Table 5. Table 5 shows some of the common cast-iron fittings and their corresponding dimensions for the various sizes of pipe with which they are used. Table 6 shows a similar table for malleable fittings. Malleable fittings are used almost universally for gas piping. They have a smooth exterior and are of uniform section through- PLANS FOR PIPE SYSTEMS 103 Check Va/ve /'^o^^fig °AVy^'on 9c'sn^ kJ ^'f^^^L^tlinj ^ t 4^ Size of Pipe A B C E G H J K L N P s T 1 6 £ 5 e 1 6 13 3Z 13 76 3 6 I& 3 6 li 1 4- s 3 A- 3 /G 3 irz 1 1 3- e I& 1 2 li 7 e 1 4- 3 8 ih 1 / Z9 3Z If. 1 Ik s e li / 2 li / f6 / Z li /^ 1 A '32 /A lA 1^ B 1^ / 2 li li 3 3 i li li 1 a: lik //4 /« li 7 e //f zA / 2. zi l-k 3 a 1 zh 1% If I'A /I z I7k li Zfz 9 /6 zi fi 7. /6 li z-k /* 3 e /|^ zm li z li 2* 3k 9 2f ^i / 2 li 2f 2 3 a 2i 2« z 2 1% 2# 3i f Zi Zi / 2 z H 2i 3 a z¥. 2* zi zh li Zi 4n a 3i 3 1 2 2i 4 2* /e 34 2:1 li- 2i ^n 3 ^i 4i S e 3 5 3 1 2 3ii 3h li 7 3 3i ^i 3 H H 3- S a 4ii 3rh z 6f •7 e 4i S 1 4 ei 4 s a 4% 3^ z 7& r e 4i 6i / 4i 6i ^i 1 ^3Z 3i Zir 7 / 5 li 5 e ei 4i zi 7i / 6 6i 6 s a 7£ 4i zi &i / Table 6. out. Cast-iron fittings are used in most other branches of work. The sketches accompanying Table 5 show cast-iron fittings with a flat bead, while the malleable fittings shown in Table 6 have a rounded bead. Unless otherwise ordered, all threads of fittings are right-handed. If a fitting has both right- and left-hand threads, its ex- terior is ribbed as shown in Fig. 96. 55. Piping Symbols. — Various attempts have been made to revolutionize piping ^i^- 96.— Right and left i . uxi-xix- PA- 1 malleable coupling. drawmg by the mtroduction of hne and symbol methods similar to the practice followed in electrical drawing. These methods have not met with universal favor, however, and no such set of symbols has ever been standardized. 104 ADVANCED SHOP DRAWING The universal and best practice today shows all piping, fittings, and apphances in their approximate outhnes. Whenever nec- essary, notes are attached to describe the fittings or apphances. 56. Piping Drawings.— Figure 97 shows a conventional drawing of a branch tee mitre coil. Such a drawing needs no explana- tory notes except to specify the size of pipe. Each piece is so represented that no one could mistake its identity. Sranch Tee - Mitre Coil Fig. 97. ConnQcHon to £.)^panxon Tank fWW^ Fig. 98. — Two-pipe system of hot water heating. Figure 98 shows a general elevation of a two-pipe system of hot- water heating. Figure 99 is a basement plan of the system shown in Fig. 98. A two-pipe system has both supply and return mains, thus insuring a positive circulation. In a one-pipe system only one pipe leaves the boiler. A tap is made from the upper side PLANS FOR PIPE SYSTEMS 105 of the pipe for the supply to the radiator and the return is tapped into the lower side of the pipe. The connections on the radiator are the same as in the two-pipe system. The only saving in the one-pipe system is that there is only one main in the basement. The hot supply water flows along the upper side of the pipe and the cold return water on the lower side. The one-pipe system gives very good satisfaction in small installations. Fig. 99. — Basement plan of piping — two-pipe system. Fig. 100. — Expansion tank connection with drip — overhead system. It will be noticed at the top of Fig. 98 that a note appears: ''Connection to Expansion Tank." The expansion tank is usually placed in the attic or above the highest radiator. Figure 100 shows a drawing of an expansion tank with its connections. Figure 101 shows a very good hne drawing of part of the steam heating plans for a building. The steam mains are represented 106 ADVANCED SHOP DRAWING by heavy lines, the risers by lighter Hnes. A prominent numeral appears alongside the main between each pair of risers to show the size of the steam main between those two points. Valves are shown by an ''X" placed in the Hne. Light lines are drawn 4-4-'''3 36° 2 56" I /i" fi' fi" 2" 2" QO"' 4 54-'' 3 60" 2 64-"' 1 4^"' a 34-'" 3 56' 60' 60' 60"' 4 iV /i' ir 2 - 64' 54' 3 56" 60" I 4A'' 3 7Z2ZZZZZZZZZZ3 Fig. 101. — Line drawing of steam heating plan. Fig. 102. — Corner pipe coil. at right angles to the risers to represent the various floors; upon each is shown the number of square feet of heating surface in the radiator for that particular floor, followed by the letter B to represent the basement, or the number of the floor, as the case PLANS FOR PIPE SYSTEMS 107 a=[F==^^===^ Dnm-c// «I3 "2=13 Fig. 103. — The circuit system of hot-water heating. Fig. 104. — Part of plan of drainage system in building. 108 ADVANCED SHOP DRAWING may be. The size of the riser is shown between the various floors, by heavier type. Piping plans are often shown as isometric drawings. Figure 102 shows an isometric drawing of a corner pipe coil. Such a I? 5 Q I W.P. / / / / \ / S,V/P. = sink Wa^ie Pipe PT. = Oiscont^ecfiMQ Trap s. ., / \ R.W.P. t in 30 fNDEX S.P.^ Soil Pipe W.P.= Waste Pipe Cl.T = alley Trap P.W.P. = Path Wafer Pipe V.R = Vehiilatmij Pipe 'V \zzz:^^ C if o f::::^ OX NOjZ. D.TNO.i. Fig. 105. — Drainage plan of a detached house. coil might be used as a radiator in a gymnasium or bathing pool where the good appearance of the radiator is not necessary. Fig- ure 103 is an isometric drawing of a hot-water heating system for the first floor of a building. This is a one-pipe system. PLANS FOR PIPE SYSTEMS 109 and V\e/^/7fs Fof Equal ix.inq Pipe ■ To Darnp iReguiaf ^Ma'in Return, \ [,[ Fig. 106. — Typical boiler connections. W///////////////.^ ^ Em. Si. for ^ Fig. 107. — Pipe plan for power house. no ADVANCED SHOP DRAWING A part of the plans of the drainage -system of a building is shown in Fig. 104. Cast-iron piping is commonly used in such systems. Underground pipe lines are usually line drawings, accompanied by a key. Figure 105 shows the plan for the drainage system of a detached house. The pipe sizes together with their gradients are shown. Pipe drawings for power plants are generally more complicated than those for dwellings, because of the greater number and £/ev<7^/or7. Fig. 108. — Plan for boiler feed piping. variety of fittings used. It is in this branch of drafting that one may expect the more common use of the diagrammatic drawings and line symbols. Figure 106 shows typical connections between two boilers. Figure 107 shows a plan and elevation drawing for the piping for a power house. The steam passes directly from the boilers to the steam drum or ''header" from which it passes to the various engine cylinders through individual pipes. Figure 108 is an example of feed piping and illustrates the use of crosses in the mains to designate the various pipe fittings. Appropriate notes are always placed at such points. PLANS FOR PIPE SYSTEMS 111 B Of/ens ^ ao QlQ f'eei/ kafer Main-^ Feed Water Httai^r i^Oil 3ef>anator ^Exhaust P,p>es Injector 4 V~\£ngine M I \ \Cyf1nder3 J FeedWdkr Supply -* — mfk Fig. 109. — Exhaust and feed piping for non-condensing plant. (A Q-Q •iG/ohe >taNe Gj3 /njecTor Main ^ Bo/'/ers All hiofi pressure drips, returns nea\ ^fnjector ^^ . By- Pass ■from heating system. e/K:., enter "^ opan heater ^-^^Open tfeater f<^ r .i.T — t — jF^ ffly Fig. 110. — Feed piping with open heater. 112 ADVANCED SHOP DRAWING Line diagrams are quite often used in laying out pipe systems for industrial plants. They are commonly used for making the prehminary sketches. Figure 109 and Fig. 110 are typical examples of diagrammatic pipe drawings though the sizes of the pipes are not shown. In both of these figures the boilers are Pipe Table of Pipe Symbol-S. o II Riser Union Elbow Tbe Cross ^S Elbow T Coc^ -5- Any TrnoF Yalve Globb Ya,lv£ -<>- Ch£ck Valve GAre Valvs Injector En(^ine Cylinder Pump Air Pump Receivbr £CCNCM/Z£R o 'METE.R o Hot Well. O H£ATE.R - COA/OMHSER Boiler Table 7. CUD Battery or Boil.ers. shown in elevation, while the rest of the drawings are plan views. Table 7 is a table of line symbols which are used by recognized authorities. These are recommended to the consideration of the reader. If a fitting is used, for which no symbol is shown in this PLANS FOR PIPE SYSTEMS 113 table, it may be represented in some such simple manner as will represent its outline, generally by means of a rectangle or circle with a name to indicate the fitting. 7 y Check li'a/fe Gtoie yafye /fijecfor ^'v. J^ tly-Paii ,G. V. 2/^i/)i.ili'ary \ Heafer 6y. Valves _<»-^ -^ ^ ^ d5.v. (3.V. Z ^ Val\re Y^ ^ot^e// '.->»J G.V. By Fa Si Hefizr Hfoter /Vote { Q.V~G/o6e Valve. CM- Check Va/vc O Surface Condenser \ \ Air Pt/mp C Surface Cont/pni G.V, Condenz^r ]{ Air fump r~) ■Svrfacv Condenser Fig. 111. — Feed piping for condensing plant. Problem 18 Figure 111 shows a pipe diagram of the feed piping for a condensing plant. The fittings are noted at their respective places but are not shown. The lines are to be laid out on a standard sheet of drawing paper. The drawing should be made as large as convenient, but the lines should be placed in somewhat the same relative position that they occupy in Fig. 111. The symbols for the fittings are to be added, and the drawing is to be finished after the method shown in Fig. 109 and Fig. 110. The symbols for the various fittings may be obtained from Table 7. CHAPTER IX SHEET-METAL WORK 57. Fundamental Principles. — Sheet-metal drafting deals pri- marily with the intersections and developments of surfaces. It is, therefore, necessary that the fundamental principles should be mastered in the abstract examples which follow. The appli- cations of these principles to practical problems are numerous, and a few of them will be mentioned. A few fundamental prin- ciples will first be explained without applying them to any particular problems. Fig. 112. — Development of cylinder intersected by plane. The case of a plane intersecting a cylinder, as in Fig. 112, will first be considered. This might be a case of a ventilator or a chimney passing through a sloping roof. The plan and elevation views are show^n to the left. The intersecting plane is perpen- dicular to the plane of the paper and is represented by the line AB. 114 SHEET-METAL WORK 115 If it is desired to see the intersection of the plane and cyhnder in true size, it must be viewed along a line perpendicular to AB. Therefore, its projection upward may be drawn on lines perpendicular to AB. Its long dimension Cs-is will evidently be the length 1-7, while its width /3-I3 will equal fi-l, of the upper plan view. To obtain the width of the true section at any other point as es-M^, projection lines parallel to/s-ls, as ms-S, to meet^B in 3 should be drawn; 3 should be projected to the upper plan thus obtaining width €i-nii equal to es-nis in the true section. Widths at any other points may be similarly found. It will be noticed that the true section formed by the intersection of a cylinder and a plane is an ellipse. If the case was that of a ventilator passing through a roof, the use of this intersection could be seen in laying out the hole to be cut in the roof. 58. Developments. — If it is desired to make this cylinder or one of the parts of it out of sheet metal, it will be necessary to lay it out or develop it on a flat surface. The procedure of development is as follows: The base line of the development should be projected over to the right from the elevation. The length of this base line, C2-C2, should be equal in length to the circumference of the cylinder, which equals 3.1416 times the diameter. The height of the develop- ment may be projected over from the elevation. The develop- ment of the complete cylinder is C2-P-0-C2. If it is desired to develop that part of the cylinder beneath the plane AB, the circle of the plan view should be divided into a number of equal parts. The base line, C2-C2, should be divided into the same number of equal parts and perpendiculars erected to it at each of the points of division. The points should be projected from the plan view upon the elevation. Such imagi- nary lines as appear on the surface of the elevation are known as ele- ments. They intersect the plane AB in points 1, 2, 3, etc. These points should be projected over to their positions on their respective elements in the development as shown. A smooth curve passed through these points will define the upper edge of the development. The development for that part of the cylinder below the plane AB is C2-l'-7'-l'-^2. 59. Curves and Circles. — ^For drawing curves such as l'-7'-l' in Fig. 112 the draftsman uses irregular curves. These are made of the same material as triangles but have edges of various irreg- ular outlines. The draftsman uses that part of the outline 116 ADVANCED SHOP DRAWING which approximates most closely the curve which he wishes to draw. For dividing circles into a number of equal parts, a protractor is often used. A protractor is usually made of amber or brass. It is semi-circular in form, and has its circular edge graduated in degrees. 60. Intersections. — Figure 113 shows the construction for a right cone intersected by a plane. Aright cone is one whose base Fig. 113. — Construction and development of right cone intersected by pi ane. is perpendicular to its axis. The apex of the cone is Wi; the base is ai-Qi. The intersecting plane lies at an angle with the horizon- tal, but in the elevation of the cone it is perpendicular to the plane of the paper. The^^Dlane, therefore, appears as a straight line l'-7' in the elevation. To find the intersection in the plan view the following procedure is suggested. SHEET-METAL WORK 117 In the plan view, the circular base a-g should be divided into a number of equal parts. From each of the points of division, lines should be drawn to the vertex m as shown. The points a, h, c, etc. should be projected down on the base hne a^-gi in the elevation. These points should be connected with the vertex mi. These lines in elevation will be the projections in the elevation of the corresponding lines just drawn in the upper plan. They represent elements on the surface of the cone. In eleva- tion, these elements intersect the cutting plane in the points V , 2' , 3', etc. These points should be projected up to their respec- tive elements in the upper plan as shown. A curve passed through the points thus determined outlines the intersection in the plan view. The section cut by the passage of this plane may be seen in the shaded view to the right. It is obtained in the same manner as was the true section in Fig. 112. The development of the cone is obtained by striking the sector of a circle mi-g^-g^ with a radius equal to nii-ai and with the computed circumference of the base pointed off as ^2-6^2- If this cone were cut by an inclined plane V-1' , the lower part of the cone, V-l'-gi-ai, would form what is known as the frustum of a cone. The development of this frustum is made as follows : The position of the various elements which have been deter- mined in the plan and elevation should be shown on the development. In the elevation, the elements rui-ai and mi-gi lying in the plane of the paper are the only elements which appear in true size. All the other elements do not appear in true size because they represent lines which are inclined to the surface of the paper. The several points in which these line elements intersect the cutting plane must, therefore, be projected over to the position of the line mi-ai by projection lines parallel to the base of the cone. From their projections on mi-ai and with m^ as center, the projections of V , 2', 3', etc. may be swung around on to their respective elements in the development as shown. A smooth curve 1"-l"-7'' passed through these points determines the line of intersection on the development. The development of the frustum of the cone is 1"-l"-l"-g2-g2. A piece of sheet metal cut out hke this development could be rolled up so as to form the frustum of the cone. It should be noticed in this devel- opment and future ones how the sheet-metal w^orker generally plots the developments so that the seam will come on the short edge. 118 ADVANCED SHOP DRAWING The aim should be to master all the elementary principles in- volved in these abstract problems. To follow the foregoing rules blindly will not aid in solving new problems as they arise. 61. Materials Used. — In applying these principles to actual problems in sheet-metal work, it would be well first to know something of the metals used, how they are sold, worked, etc. Sheet metals are made in various gages or thicknesses and may be designated by the gage numbers or by the actual thicknesses. There is a wide difference between the various gage systems now in use. For this reason it is always best to specify the thickness of the metal either in decimal or fractional parts of an inch. Table 8 shows the U. S. Standard Table for sheet and plate iron and steel adopted by Congress in 1893 for the sake of uni- formity, and is the table by which government duties and taxes are levied on these articles. For gages number 20 or thinner, it is assumed in the development of the pattern that one is dealing with no thickness, and no allowance is made for bending or rolling in the machine. But where the metal is of heavier gage than number 20, allowances must be made for the thickness of the metal. Table 8. — U. S. Standard Gage for Sheet and Plate Iron and Steel, 1893 Number of gage Approximate thick- ness in fractions of an inch Approximate thick- ness in decimal parts of an inch Weight per square foot in ounces Weight per square foot in pounds 0000000 1-2 0.5 320 20.0 000000 15-32 0.4688 300 18.75 00000 7-16 0.4375 280 17.50 0000 13-32 0.4063 260 16.25 000 3-8 0.375 240 15.0 00 11-32 0.3438 220 13.75 5-16 0.3125 200 12.50 1 9-32 0.2813 180 11.25 2 17-64 0.2656 170 10.625 3 1-4 0.25 160 10.0 4 15-64 0.2344 150 9.375 5 7-32 0.2188 140 8.75 6 13-64 0.2031 130 8.125 7 3-16 0.1875 120 7.5 8 11-64 0.1719 110 6.875 SHEET-METAL WORK 119 Table 8. — Continued. Number of gage Approximate thick- ness in fractions of an inch. Approximate thick- ness in decimal parts of an inch Weight per square foot in ounces Weight per square foot in pounds 9 5-32 0.1563 100 6.25 10 9-64 0.1406 90 5.625 11 1-8 0.125 80 5.0 12 7-64 0.1094 70 4.375 13 3-32 0.0938 60 3.75 14 5-64 0.0781 50 3.125 15 9-128 0.0703 45 2.813 16 1-16 0.0625 40 2.5 17 9-160 0.0563 36 2.25 18 1-20 0.05 32 2.0 • 19 7-160 0.0438 28 1.75 20 3-80 . 0375 24 1.50 21 11-320 0.0344 22 1.375 22 1-32 0.0313 20 .1.25 23 9-320 0.0281 18 1.125 24 1-40 0.025 16 1.0 25 7-320 0.0219 14 0.875 26 3-160 0.0188 12 0.75 .27 11-640 0.0172 11 0.688 28 1-64 0.0156 10 0.625 29 9-640 0.0141 9 0.563 30 1-80 0.0125 8 0.5 31 7-640 0.0109 7 0.438 32 13-1280 0.0102 6>^ 0.406 33 3-320 0.0094 6 0.375 34 11-1280 0.0086 5^^ 0.344 35 5-640 0.0078 5 0.313 36 9-1280 0.007 ^yi 0.281 37 17-2560 . 0066 m 0.266 38 1-160 0.0063 4 0.25 Table 9 is the table for sheet copper which was adopted as standard by the Association of Copper Manufacturers of the United States. For convenience, the nearest Stubbs' gage number is shown for the various thicknesses of copper but it is preferable to use the decimal thicknesses. The various com- mercial sizes of sheets and their weights are also shown. 120 ADVANCED SHOP DRAWING Tablf 9. — Adopted by the Association of Copper Mfrs. of the U. S. Stubbs' gage (nearest number) Thickness 1 in decimal parts of an inch Ounces per sq. ft. Sheets 14X48 in., weight in pounds Sheets 24X48 in., weight in pounds Sheets 30X60 in., weight in pounds Sheets 36X72 in., weight in pounds Sheets 48X72 in., weight in pounds 35 0.00537 4 1.16 2 3.12 4.50 6 33 0.00806 6 1.75 3 4.68 6.75 9 31 0.0107 8 2.33 4 6.25 9.00 12 29 0.0134 10 2.91 5 7.81 11.25 15 27 0.0161 12 3.50 6 9.37 13.50 18 26 0.0188 14 4.08 7 10.93 15.75 21 24 0.0215 16 4.66 8 12.50 18.00 24 23 . 0242 18 5.25 9 14.06 20.25 27 22 0.0269 20 5.83 10 15.62 22.50 30 21 0.0322 24 7.00 12 18.75 27.00 36 19 0.0430 32 9.33 16 25.00 36.00 48 • 18 0.0538 40 11.66 20 31.25 45.00 60 16 0.0645 48 14.00 24 37.50 54.00 72 15 0.0754 56 16.33 28 43.75 63.00 84 14 0.0860 64 18.66 32 50.00 72.00 96 13 0.095 70 35 55.00 79.00 105 12 0.109 81 40K 63.00 91.00 122 11 0.120 89 44K 70.00 100.00 134 10 0.134 100 50 78.00 112.00 150 9 0.148 110 55 86.00 124.00 165 8 0.165 123 61 96.00 138.00 184 7 0.180 134 67 105.00 151.00 201 6 0.203 151 753-^ 118.00 170.00 227 5 0.220 164 82 128.00 184.00 246 4 0.238 177 88K 138.00 199.00 266 3 0.259 193 96 151.00 217.00 289 2 0.284 211 105^^ 165.00 238.00 317 1 0.300 223 niy2 174.00 251.00 335 0.340 253 126M 198.00 285.00 380 Fig. 114.— Method of wiring edge. In dealing with tin plate, no considera- tion is given to thickness and, consequently, no allowance is made when rolling or bend- ing it in the machine. For wiring, that is, wrapping the metal around a wire along the edges for the sake of stiffness, an edge J^" wide is provided SHEET-METAL WORK 121 outside of the pattern. Figure 114 shows such an edge bent ready for wrapping at A, and wrapped at B. 62. Seams. — Figure 115 shows the lock seam such as is com- monly used for vertical seams. In this type of joint, allowance must be made for three times as much material as in the case of wiring, because the joint has three laps. Metal for one of the laps is provided on one edge of the pattern, while provision for the other two laps is made on the mating edge of the pattern. Figure 116 shows the two operations in making a joint that is used in fastening the bottom to the body of a vessel. The notching of patterns is an important detail. Notches are shown on those edges which are Fig. 116. — Lock seam for Fig. 115. — Lock seam for fastening the bottom to the vertical seams. body of a vessel. provided for seaming and wiring, and it is essential that they should be accurate so as to produce a finished job. When the patterns have been cut in paper, they are then placed on the sheet metal and a few weights laid on top of the paper to hold it down. Slight marks are then made through it with a sharp scratch awl or prick-punch, larger dots indicating a bend. The paper is then removed and lines scribed on the plate, using the scratch awl for making the straight lines and a lead pencil for making the curved lines. Laps are then added as required after which the shape is cut out of the metal. Figure 117 shows a typical sheet-metal design in which a half pattern has been developed for a bucket. Part patterns like this are often necessary, owing to the fact that sheet metal is sold in commercial sizes. The designer and workman should always aim to use material as economically as possible. It should be noted how provision has been made for wiring the upper edge; also how twice as much material has been provided on one edge as on the other on account of the lock seams. Figure 118 shows a ventilator with a hood and a deflector above and with a flare below. This is a problem in cone development entirely and is submitted as a sample problem for individual study. A detail of the joint between the hood and deflector will be 122 ADVANCED SHOP DRAWING Fig. 117. — Half pattern development of bucket. Fig. 118. — Ventilator with hood and deflector. SHEET-METAL WORK 123 found in the development of the hood. It will be noticed that provision has been made for a lock seam on the outer edge of the development of half of the pattern for the hood and the deflector. The outer diameters of the conical parts are usually made twice that of the pipe. The dimensions are omitted for the sake of clearness. Thus far only curved surfaces intersected by planes have been dealt with. The intersections and developments of bodies whose surfaces consist of many planes will now be considered. 63. Prism Intersection. — Figure 119 shows an octagonal prism intersected by a plane. This construction is a great deal like that for Fig. 112 except that it is not necessary to assume any f/O^ v^-k Fig. 119. — Octagonal prism intersected by plane. elements on the surface of the prism ; it is necessary to deal only with the corner elements a, b, c, etc. in the upper plan view. One of the fundamental principles of sheet-metal drafting is that two planes always intersect in a straight line. In this case, then, it is necessary merely to determine the intersection of the plane MN with the eight plane faces of the prism. The right side view of the prism might have been drawn by transferring the dimensions of width from the upper plan by means of the dividers. A simpler plan still, and one that is universally used in sheet-metal work, is to project the various dimensions of 124 ADVANCED SHOP DRAWING height in the upper plan over to a vertical line o-p, as shown in Fig. 119, then from some center on this line as r, revolve these several points of projection into the horizontal. This will determine the several points of projection on r-s as shown. By this means all dimensions of height in the upper plan may be readily revolved to determine the dimensions of width in the side view. It will be seen that p-h in the upper plan equals ai-bi in the right side view and that all other dimensions of height in the upper plan equal those of corresponding width in the right side view. The method by which the intersection is determined in the right side view should be given special attention. The true section appears to the left. In all of these cases it will be noticed that it is necessary only to determine the points in which the corner elements of the prism pierce the plane M-N and then to connect these consecutive points by a series of straight lines. 64. Prism Developments. — The development of the lower part of the prism of Fig. 119 is shown in Fig. 120. It will be > y^ ii N / 1 ■' 1 \ K, /^ 1 V T 1 -< k *] ^- ->-■« f- ->- k ■*{ k ^ ^- Fig. 120. — Development of lower part of prism of Fig. 119. noticed that the edge produced by the intersecting plane M-N is made up of straight lines. The system of dimensioning such developments is also indicated. The outside elements of pat- terns which close like this are always of equal height. It should be noticed again how developments are generally laid out so that the seam comes on the short edge. The intersections and developments of a pyramid follow the same general principles as are applied to a cone. Figure 121 shows the elevation and plan views of a square pyramid. The line mi-hi in the elevation represents the surface m-b-c in the plan view and is, therefore, not the true length of one of the corner elements, such as m-b, with which radius the development must SHEET-METAL WORK 125 be struck. The true length of the Hne 7n-x is represented by mi-bi, but the true length of m-h is desired. To obtain the true length of the corner element m-6 the following method may be used. The horizontal center line should be drawn in the plan view; also ai-bi should be extended in a horizontal direction toward the right. With m as a center and a radius m-b, an arc should be n. b, °Jt Fig. 121. — Development of square pyramid intersected by plane. described which will intersect the horizontal center line of the plan view in the point y. The point y should be projected upon the extension of ai-bi giving the point a2. Then mi-a2 will be the true length of the corner element m-b or any other corner element. With m as a center and mi-a2 as a radius the arc of the development a2-C2-«2 should be struck and the corner elements drawn. If the pyramid be intersected by a plane ei-/i, the various points where the plane intersects the corner edges in the eleva- 126 ADVANCED SHOP DRAWING tion must be projected over to mi-a2 by horizontal lines, thus locating the intersection on the true length of the corner elements. These points should then be projected upon their respective ele- ments in the development by means of arcs struck from rui as center. The intersection will then follow the lines e2-f2-g2-h2-e2 on the development, and will consist of a series of straight lines, because the plane ei-fi intersects the plane surfaces of the pyramid in straight lines. The true section appears to the left on projection lines per- pendicular to ei-fi. The problem shown in Fig. 121 involves principles which are commonly encountered in intersecting bodies which have plane surfaces. These problems are quite usual in ventilating and hot air heating systems. In Fig. 122 a square prism is shown standing on end, inter- sected on the right by a square prism, two of whose faces are hori- zontal. In determining the intersections of these two bodies one may proceed as follows: The upper plan and elevation views of the vertical prism should be drawn and then its right side view drawn by the method which was shown in Fig. 119. Next the end view of the horizontal prism should be drawn in the right side view as shown. The end views of figures should always be drawn first. Then the horizontal prism in the upper plan view should be drawn by the method of Fig. 119. From the points in which its corner ele- ments intersect the side faces of the vertical prism in the upper plan, vertical projection lines should be drawn downward to intersect horizontal projection lines drawn from the right end view. Connecting this series of intersecting points by a series of straight lines will determine the intersection in the elevation. The development for either prism may be readily plotted since all the elements of both prisms are parallel to the plane of the paper in the elevation. The left half of Fig. 122 represents the same vertical prism intersected on the left by a square prism, as before, with the exception__^that^in^this case two of its faces make angles of 30° with the horizontal. The drawing is fully marked so that the construction^may be readily followed. The intersection in the front elevation can be determined readily by projecting from the left and upper plan view, the various points being determined in the consecutive order in which they appear in the left end view SHEET-METAL WORK 127 along the lines i-j-k-l. Particular notice should be taken how the surfaces i-j and k-l each intersect the two faces a — h and a — d of the vertical prism, and how this affects the intersection in the front elevation. It will be noticed, as before, that the intersection consists of a series of straight lines, because it is determined by the intersections of a series of plane surfaces. It would be well to consider now the intersection and develop- ment of two bodies having curved surfaces; for instance, two cylinders. This problem is illustrated in a steam dome on a boiler, in tapping into pipe lines, in hot air heating pipes which are circular and intersect, and in numerous other cases. ni6Hr END VIEW ELEVATION Fig. 122. — Intersections of three square prisms. In determining the intersection of two cylinders, one may pro- ceed in the same order as in the previous examples, drawing the end views of each cylinder first as in Fig. 123. When the cyl- inders have been shown in the upper plan, front elevation, and right end views, it remains to determine their intersection in the front elevation. This may be done as follows: The circumference of the small cylinder in the upper plan view should be divided into a number of equal parts. These will determine the elements on its surface which are equally spaced, as 1, 2, 3, etc. They intersect corresponding horizontal ele- ments shown on the surface of the large cylinder in the same view. The positions of these several elements on the large cylinder may 128 ADVANCED SHOP DRAWING now be determined in the right end view by the method of pro- jection shown in the figm-e. By means of vertical projection Hnes drawn downward from the upper plan, and intersecting horizon- tal ones drawn from the right end view, a series of points which UPPER PLAN \ \ \\ \ .N\\\\V> Fig. 123. — Intersections of cylinders. ' r^ ■ • ■ ■— p-1 ■ ' r-n ■ ' , ' ' ■» ■* V 4.J I J > « • « * -• «■ ■» » » « • T 1 Fig. 124. — Development of small cylinder of Fig. 123. define the intersection in the elevation may be determined. Since both intersecting surfaces are curved, their intersection in the elevation will also be a curved line. A smooth curve should, therefore, be passed through the series of points just determined in the front elevation. SHEET-METAL WORK 129 The development for the small cylinder of Fig. 123 together with appropriate dimension lines is shown in Fig. 124. Problem 19 Develop patterns for the various parts of the hand scoop shown in Fig. 125. Also show a drawing of the scoop as shown in this figure. All these views should be arranged upon one sheet and should be drawn to appropriate Hand Scoop 3heef Copper -.0269''fhick Fig. 125. scales. Dimension all developments completely. In scaling the develop- ments to dimension them, be sure to use the same scale to which the devel- opments have been drawn so as to obtain the full size dimensions of the scoop. In the side view it will be seen that the center line of the handle is inclined 30° to the horizontal and that it meets the back of the scoop on the hori- FiG. 126. zontal center line of the body. A flaring boss serves to strengthen the handle where it meets the back. It will be noticed by the construction lines which have been supplied that this boss is a part of a right cone. The intersection of the boss and handle is at right angles to the center line of the handle. The body of the scoop should be developed first and provisions made for a lock seam on the upper surface. This can be developed according to the 9 130 ADVANCED SHOP DRAWING principles indicated in Fig. 112. First lay off a base line of appropriate length. Divide the left end view into a number of equal divisions. Project these over to the side view and thus determine the lengths of the several elements which should be erected on the base line. Pass a smooth curve through their ends. After the pattern has been thus determined, it may then be dimensioned at various points as shown in Fig. " 126. It is not necessary that the dimensions given should be those of the identical elements by which the outline of the pattern was obtained. When the circular pattern has been developed for the back, an edge must be provided outside of the pattern and properly notched, as shown in Fig. 127, so that it may be soldered onto the body. Fig. 127. The boss should have a lock seam along its top and a notched edge for soldering it to the back. The junction of the boss and handle is at right angles to the center line of the handle and may be considered as a plane intersecting a right cone on the left, and a plane intersecting a cylinder on the right. The cylindrical handle should have a lock seam along its length and have a notched edge for soldering into the boss. A circular piece properly notched is to be soldered into the outer end of the handle. Problem 20 Figure 128 shows a right pyramid with a base 3 ft. in. X 4 ft. in. and altitude 3 ft. in. intersected by a cylinder 2 ft. in., the center lines of both being coincident. Such an arrangement as this might serve for a smoke connection for a boiler; if inverted, it might serve as a hopper for a bin. Determine the intersections and developments of the two parts. In determining the development of the pyramid, it will be necessary to deter- SHEET-METAL WORK 131 mine the true length of each element as was explained in Fig. 121. Develop a full pattern for the cylindrical part and make provision for a lock seam. Show a half pattern for the pyramidal part with lock seams running up the center of the sides which are 3 ft. in. long. Also provide the pyramid with an edge for a seam where it connects to the cylindrical part. Fig. 128. CHAPTER X SHEET-METAL WORK (Continued) 65. Triangulation. — Thus far, only those surfaces have been con- sidered which have parallel-hne elements on their surfaces, as in the case of the cylinder and the prism, or radial-line elements, as in the case of the cone and the pyramid. Patterns are often re- quired which cannot be determined by either of these two meth- ods. Hence, in the development of any irregular article, it is necessary to measure up the surface part by part, and then add one to another until the entire surface is developed. This is known as development by triangulation, and depends for its results on two general principles : first, to find the true lengths of all lines, real or assumed, appearing on the surfaces of the solid; second, having determined the true lengths of such lines, to con- struct triangles similar in form and relation to those shown on the solid. 66. Development by Triangulation. — ^In the case of the pyra- mid, Fig. 121, it w^as necessary to determine the true length of one of the corner elements before the development could be drawn. A method for doing this was shown. It would be well to con- sider a few facts in connection with Fig. 121. The true length of a corner element was found to be m,ia2. This is the hypot- enuse of the right triangle, 7ninia2. It will be seen that nia2 = my = mh, which is the horizontal projection of this corner ele- ment in the upper plan. The vertical height of mi6i is mini, which is the projection of the corner element in the front eleva- tion. Hence, the general truth: The true length of a line is equal to the hypotenuse of a right triangle, one of whose legs is equal to the foreshortened line in the plan view, while the other leg is equal to the vertical height of the same line in the elevation. To illustrate the use of this principle, suppose it is desired to determine the true length of any other line in the frustum of this pyramid, as the line a-e, shown in the plan view. Let Fig. 129- A be a copy of the frustum of the pyramid shown in 132 SHEET-METAL WORK 133 Fig. 121. Then in Fig. 129-A to find the true length of the Hne a-e according to the rule just given, a vertical line should be j&rst passed through ei to meet the base in a point ii. The line ii-ei will then be the vertical height of the element ai-ei in the elevation. To the right in Fig. 129-B a right triangle a, L ^2 • '' (B) ' Fig. 129. — Development by triangulation. should be constructed in which one of the legs 12-62 equals ii-ei and the other leg 22-^2 equals ae in the upper plan. The hypotenuse of this triangle, 02-^2, is the true length of the corner element a-e. By the construction of similar right triangles, with the aid of construction lines to determine the 134 ADVANCED SHOP DRAWING vertical heights in the front elevation, the true lengths of the lines h-f and e-f as shown may be determined. The line d-h equals a-e; h-g equals e-f; and c-g equals h-f. The lines a-b, h-c, c-d, d-a, h-e, smdf-g are shown in true length in the plan view. To develop the side faces of this frustum by triangulation, it will be necessary first to divide the various surfaces up into triangular areas as shown by the broken lines in the upper plan. The true lengths of each of these lines is determined as in the previous cases. First a line should be drawn equal to the length of one edge, as as-es, Fig. 129-C, which is equal to 02-^2 as in Fig. 129-5. With radius 62-62 and ez as a center, an arc should be described. With radius a-h and a^ as a center, another arc should be de- scribed to intersect the first arc in point 63. Upon the line 63-63 the triangles 63-63-/3 may now be constructed in a similar manner, locating point /s with two intersecting arcs, one drawn with a radius 62-/2- This method may be continued to determine the entire development. This development by triangulation may be superimposed upon that obtained in Fig. 121 by the radial line method. The two will be found to coincide. This method of solving problems by triangulation is equally applicable to curved surfaces such as the flashing around chim- neys, gusset plates on locomotives, flaring ends of bathtubs, coalhods, foot-bath pans, etc. The case of the irregular solid shown in Fig. 130- A will now be considered. Its two bases are parallel. The upper base is circular, and the lower one is oval. In solving this problem by triangulation, the draftsman must first conceive that the upper and lower bases are joined by a series of triangular surfaces as suggested by the series of straight light lines connecting both bases. Seeing the construction and solu- tion of problems in the mind's eye like this is a valuable aid in the solution of sheet-metal problems. It will be seen that the object is symmetrical on both sides of the horizontal center line passing through the upper plan. If a development is made of the lower half of one figure, a duplication of it will give the com- plete development. In drawing the imaginary triangles, the outlines of both bases in the upper plan should be divided into the same number of equal parts, and the alternate points of division on each connected by a series of straight lines as shown. These points and their lines should then be projected down to the front elevation. It SHEET-METAL WORK 135 will be seen that the lines a-h and n-o appear in true length in the elevation. The true lengths of the other hnes must now be determined. This is best done by extending indefinitely toward the right the two lines which represent the bases in the elevation. Beginning at some point in this line as hi, hi-Ci should be pointed off equal to b-c in the upper plan, and Ci-di equal to c-d, etc. Since the vertical heights of all these lines in the elevation are equal, and are equal to the distance between the two parallel lines just extended to the right, perpendiculars may next be erected at each of the points just pointed off on the ex- tended base line. From the points where these perpendiculars Fig. 130. — Development of irregular solid by triangulation. intersect the upper base line extended, straight lines may be drawn to connect the alternate points on the lower base line ex- tended. These lines will represent the true lengths of the several lines forming the triangles. For instance, the diagonal line between bi-Ci equals the true length of h-c; the diagonal be- tween Ci-di equals the true length of c-d, etc. The true lengths of all the lines having now been determined, the development may be constructed. Fig. 130-C The line a2-b2 should be drawn equal in length to a-b in the front elevation. With ^2 as a center and a radius equal to a-c in the plan, an arc should be described. With 62 as a center and a radius equal to the diagonal between bi-Ci, an arc should be described to intersect the one just drawn in point C2. Similar constructions should be continued for the rest of the triangles. Smooth 136 ADVANCED SHOP DRAWING curves passed through the upper and lower rows of points thus determined will give a development of the half pattern desired. The principles shown in these few simple illustrations are applicable to the solution of any problem by triangulation. 67. Elbows. — No other article is so common to the sheet- metal worker's trade as the pipe elbow. The general method to be pursued when a development is required for a two-piece elbow forming an angle of 90° is the same as that for two inter- secting cylinders, or for a cylinder intersected by a plane at an angle of 45° to the axis. There is, however, a more simple method by means of which a pattern may be developed for an Fig. 131. — Pipe elbows. elbow of any number of pieces or for any given angle. The drafts- man should become familiar with this construction because it is very commonly used in the sheet-metal trade. Suppose it is desired to develop patterns for elbows of any number of pieces. The three elbows show in Fig. 131 are typical examples and will be referred to by way of illustration. The elbows shown at A and B in Fig. 131 are known as square elbows, because if lines be drawn perpendicular to the center lines of the two end sections they will intersect at an angle of 90°. The elbow shown at ^ is a four-piece elbow; the one shown at 5 is a six-piece elbow. At C is shown a 67J^° five-piece elbow. The two forms of elbows at A and B with the short throats are commonly used in stove-pipe work. The long throat used at C is more common in chutes, conveyor systems, etc., where the friction due to short bends is to be avoided. The middle sections of elbows are usually made equal to each other; the end sections are generally made half as long as the middle sections. The developments of the patterns for these three elbows are shown in Fig. 132. It will be sufficient to consider the construe- SHEET-METAL WORK 137 tion for the first elbow; the method is the same for the other two. The method shown here is in general use in the sheet-metal trade. a -^^ E (C) Fig. 132. — Developments of elbow sections. In developing the pattern for a section of the elbow shown in Fig. 131-A, a circle DEF should first be described to some definite 138 ADVANCED SHOP DRAWING scale to represent a plan view of one of the end sections as in Fig. 1S2-A. It will be noticed that in solving for the developments in the two examples, Fig. 132-5 and Fig. 132-C, only a half circle has been drawn. This is because the halves of the pattern are symmetrical, and, therefore, only a half pattern need be developed. Next, the circle DEF should be divided into a num- ber of equal parts. The right angle ahc should next be drawn above this circle to represent the 90° angle swept through by the elbow. With 6 as a center an arc adc should be described of any convenient radius ha; the angle ahc should be bisected by the line hd. The arc dc should be divided into a number of spaces one less than the number of sections in the elbow. For a four-pieced elbow this arc would be divided into three equal spaces; for a six-pieced elbow it would be divided into five equal spaces, etc. From the point of division nearest c a line should be drawn to the vertex h. This line represents the junction of the lower end section of the elbow with its mate, and the various points of division on the circle DEF should now be projected upon it. To the right, a base line MN should be laid out equal in length to the circumference of the pipe. It should be divided into a number of divisions equal to that into which the circle DEF was divided, and perpendiculars erected at the points of division. The various points in which the projectors of circle DEF intersect the line h-e may now be projected over to the corresponding base Hne elements in the development. A smooth curve passed through the series of points thus determined gives the developed outline of the intersection of two sections. This outline will be the same for any elbow of the same number of pieces, same diameter of pipe, and same angle swept through regardless of the throat radius of the elbow. Changing the throat radius will merely change the lengths of the line elements by equal amounts without in any manner affecting the development of the intersection. The length of the inside element, k-p, may now be pointed off with due allowance made for a joint with the straight pipe. It will be readily seen that the developed joutline for any middle section of pipe will be the same on both edges as the curve just determined. It will be evident from Fig. 132 that the pattern for an elbow may be developed without making a complete drawing of the elbow in front elevation. Figure 133 shows how sections of an elbow may be cut from sheet-metal without waste if the job is not a particular one. It SHEET-METAL WORK 139 will be evident, though, that when the patterns are cut this way, every alternate joint will be on the outside of the elbow and this will detract greatly from its appearance. 68. Allowance for Thickness of Metal. — As stated in Article 61 when metal of gage 20 or thinner is being used, no allowance need be made on the patterns for the thickness of metal. In the pre- vious discussion on sheet-metal work, no consideration was given to the thickness of metal. Before any pattern can be developed t Fig. 133. — Method of cutting patterns for elbows without waste of metal. by the draftsman, however, it is essential that he should have a knowledge of the properties of the material that he intends to use. The allowances for laps, lock seams, and wiring were referred to in Articles 61 and 62. One other important allow- ance must be made; namely, for bends in the material. For determining this allowance, the sheet-metal worker must rely partly on practical experience. A few general remarks will not be amiss, however. No allowance is made for bending, when working up sheet metal lighter than number 20 gage, unless extremely accurate work is desired, and this is rarely the case. When dealing with metal which is thicker than number 20 gage, and exact inside or outside dimensions are to be maintained, careful attention must be given to the thickness of the metal. In considering the cylinder shown in Fig. 134, which is made from metal of considerable thickness, it will be evident that the length of metal required to form this cylinder will be equal to the circumference of the center line circle, that is, equal to the length of the center line of the metal. The various parts may be designated as follows: D = the diameter of the center line Di = the inside diameter D2 = the outside diameter t = the thickness of metal 140 ADVANCED SHOP DRAWING By reference to Fig. 134, it will be seen that the following equa- tions may be written, D = Di + t D = D2- t The developed length of metal necessary, when an exact inside diameter is to be maintained, may be readily determined from the first equation. From the second equation, the length of metal necessary to preserve an exact outside diameter may be Fig. 134. — Sheet metal cylinder constructed of thick metal. computed. As a general rule, the first equation is the one more commonly used; that is, an exact inside diameter is to be main- tained. In such cases, shopmen compute the inside circumfer- ence and add an allowance for forming the curve. It will be seen that for a complete circle the length of the center line will be 3.1416 X D and that 3.1416 X D = 3.1416 X Di - 3.1416^ In making a simple bend, the metal will stretch on the outside and shorten on the inside of the curve, and the original length of the sheet will be at the center line of the metal or very close to it. Consequently, the pattern should follow the center line of the stock, and, if the dimensions of the inside of a curve are available, "3.1416 X the thickness" as an allowance for bending should be added. This is more often used as S^'jt, since 3J7 or 2% is near enough to 3.1416. SHEET-METAL WORK 141 The method of working the metal in making the bend may alter somewhat the necessary allowance. If the metal is hammered into shape, it will stretch and the allowance need not be so great. In some shops, an allowance anywhere from three to seven times the thickness of metal is made and the sm^plus metal removed after bending. It should be clearly understood that what has been said re- garding allowances in the preceding paragraph applies to com- plete cylinders. If the bent portion encloses only half of a cylinder, the allowance will be only half of that required for a complete cylinder, etc. For a quarter turn or 90° bend, the allowance should be one-fourth that for a complete cylinder. In the case of patterns of irregular outline, allowance must be made before the pattern is developed so that the metal may distribute itself evenly while being shaped. Square and angular bends are the kind most commonly encoun- tered by the shopman. When metal of any considerable thick- ness is used, its thickness may have an appreciable effect where accurate inside or outside dimensions are to be obtained. Where it is impossible to make sharp bends, either due to the thickness or the stiffness of the metal, the drawing must show" the corners rounded in the form which the metal will assume. The allow- ance to be made for such bends will be largely determined by the practical experience of the shopman. If the draftsman desires accuracy for such cases, he w^ill find it well to take a sheet of the specified metal and form it into the desired shape. In doing so he will know whether he has to obtain accuracy in the inside or outside measurement or on the center line. The length of the resulting center line of the section may then be readily deter- mined for plotting the development. A test like this is the only safe and definite method that can be recommended for all cases; the outline of the drawing should always follow the center line of the material. No definite rules can be given that will apply in all cases. Different flanging, bending, and forming machines take up differ- ent amounts of material. The experience of the workman must furnish the needed guidance. It has been evident in all allow- ances which have been made for seams in the previous problems in sheet-metal work, that the dirnensions for the seams were not noted. In working up heavier sheet metals, a great many of the details must be left to the shopman as these details are af- 142 ADVANCED SHOP DRAWING f ected considerably by the individual practice of the shopman and the machinery with which he has to work. However, allowances for sheet metals thicker than number 20 gage should be shown on the drawing. Problem 21 Make a development, by triangulation, of the transition piece shown in Fig. 135. Dimension the development completely so that the man in the Fig. 135. shop could make a pattern from it. Allow material on one edge for riveting. A transition piece is used to connect openings of different sizes as in pipe work. This one has one base 4 ft. in. square, and the other base is 2 ft. in. square. The two bases are spaced 3 ft. in. apart. Problem 22 Develop a half pattern for the gusset sheet A shown in Fig. 136. Longitudinal and cross-section views of this boiler are shown in Fig. 137. The part for which the pattern is to be developed is that which lies between the lines CD and ED in the cross-section view, Fig. 137. This boiler is made of sheet steel %" thick; 3-in. seams are provided for riveting. It should be noticed how the slope of the side seam B is de- termined by the horizontal center lines of the cylindrical parts. The bot- tom parts of the three sections of the boiler are horizontal. SHEET-METAL WORK 143 This problem is most readily solved by triangulation as was explained in Fig. 130. In this case, however, due to both bases being circular, it will simplify the work to divide both bases into the same number of equal parts. In dealing with metal of greater thickness than number 20 gage, it is always necessary to develop the pattern for the center line of the metal. Fig. 136. The circular bases of the center lines of this gusset sheet are 41% in. and 36^^ in. in diameter, respectively. The length of the quarter-circumfer- ence of each base should be computed, plotted as a straight line, and divided into the same number of parts as the corresponding section of the circular base The length of each part will then be the distance between the points MATeRlAL-SHEETSTEEL | THICK Fig. 137. of division on the circular base, and is the distance that is to be used as a radius in determining the development by triangulation. The true lengths of the lines drawn between the points of division on the two bases must next be determined. These constructions give all the data necessary for proceeding with the development of the half pattern. INDEX Acme threads, 4 Addendum circle, 19 bevel gear, 33 spur gear, 19 Annular gears, 25 Assembly drawings, 1 B Bevel gears, 31 Bevel gears, layout, 31 Bill of material, 4 Black prints, 13 Blue prints, 12 exposure, 12 machines, 12 mounting, 13 paper, 12 washing, 12 Cabinet drawings, 53 angles of axes, 54 circles, 56 Circles, addendum, 19 cabinet drawing, 56 clearance, spur gear, 21 dedendum, 21 isometric, 49 pitch, 15 root, 21 D Dedendum circle, 21 Detail drawings, 6 Details, 6 space given to, 8 Detail sheets, 2, 6 Development, by triangulation, 132 cones, 117 cylinders, 115 elbows, 136 prisms, 124 pyramids, 125 Diagram drawing, 1 E Electrical drawing, 86 bell circuits, 87 symbols, 86 three-wire circuits, 90, 93 two-wire circuits, 89 wire sizes, 87 wiring diagrams, 93 Erection drawings, 1 G Gear drawings, spur, 25 keys and keyways, 28 length of hub, 27 outside diameter, 26 pitch diameter, 26 root diameter, 26 thickness of arms, 27 thickness of rim, 27 tooth outlines, 28 width of arms, 27 width of face, 28 Gears, 15 annular, 25 bevel, 31 herringbone, 41 spiral, 41 spur, 15 stepped, 39 twisted, 39 Gears, bevel, 31 addendum, 33 145 146 INDEX Gears, bevel, backing, 33 cutting angles, 35 depth of teeth, 33 edge angles, 35 face angles, 34 outside diameter, 34 pitch angles, 34 thickness of rim, 33 Gears, spur, 15 addendum circle, 19 calculations, 17 clearance circle, 21 dedendum circle, 21 drawings, 25 velocity ratio, 23 Gear tables, 20, 22 General assembly drawings, 2 H Herringbone gears, 41 Intersections, 116 cone and plane, 116 plane and prism, 123 two cyUnders, 127 two prisms, 126 Isometric drawings, 47 arcs, 50 axes, 48 circles, 49 Part assembly drawing, 1 Patent office drawings, 67 application, 67 drawing, 68 examination, 68 Piping, 100 dimensions, table of, 101 drawings, 104 fittings, cast iron, 102 fittings, malleable, 103 isometric plans, 108 kinds of, 100 sizes, 100 symbols, 103 table symbols, 112 thread, 101 two-pipe system, 105 typical connections, 108 Pitch, 17 circles, 15 circular, 18 diameter, 17 diametral, 17 spiral gears, 42 twisted gears, 40 worm gears, 38 R Rack and pinion, 25 Root circles, 21 Legend, 8 Line shading, 60 brilliant line, 61 cone, 63 cylinder, 61 flat and graded tints, 62 hollow cylinder, 62 sphere, 63 O Outline assembly drawing, 1 S Scale, 8 Shaded drawings, 57 Shade lines, 57 rules of, 58 Sheet metal drafting, 114 allowance for thickness, 139 curves and circles, 115 development by triangulation, 132 elbows, 136 intersections, 116, 123 INDEX 147 Sheet metal drafting, materials, 118 principles, 114 seams, 120 table, copper, 120 table for iron and steel, 118 triangulation, 132 true length of line, 132 wiring edges, 120 Special gears, 25, 39 annular gears, 25 rack and pinion, 25 Spiral gears, 41 dimensions, 44 number of teeth of, 46 pitches for, 42 size of blanks for, 43 velocity ratio, 42 Spur gears, 15 Structural drawing, 75 assembly shop, 84 beam shop, 84 dimensions, 78 drafting department, 75 estimating department, 75 examples of, 79 lettering, 78 line conventions, 78 riveting conventions, 76 shop bills, 76 symbols, 77 templet shop, 83 yard, 84 Symbols, 77 electrical, 86 piping, 103 structural, 77 table of piping, 112 Tables, cast-iron fittings, 105 fitting symbols, 112 keys and keyways, 29 malleable iron fittings, 106 sheet copper, 120 sheet iron and steel, 118 standard steel and wrought iron pipe, 101 tooth gears, circular pitch, 22 tooth gears, diametral pitch, 20 Threads, Acme, 4 Titles, 9 Tracing, 11 inking in, 12 order of procedure of, 11 preparing cloth, 11 Triangulation, 132 True length of line, 132 Twisted gears, 39 tooth angle, 41 velocity ratio, 41 V Vandykes, 13 Velocity ratio, spiral gears, 42 spur gears, 23 twisted gears, 41 worm and worm wheel, 36 W Worm and worm wheel, 36 pitch, 38 shop drawing of, 38 velocity ratio, 36