ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN 25.85 Example: d ¼ 45 mm (1.8 in), kD ¼ 785 N/mm2 (80 kgf/mm2 or 114000 psi) q ¼ 0:2, forming height ¼ h ¼ 12:5mm: B ¼ 196 N/mm2 (20 kgf/mm2 or 28500 psi) Punch force ¼ PF ¼ 1225 kN (125 tf) [C0 -D0 -E ] (Fig 25-46) Blank area ¼ FB1 ¼ 1600 mm2 (2.46 in2 ) [A0 -B0 -C0 ] Body cross-section of product ¼ QF ¼ 400 mm2 (0.62 in2 ) [A0 -L0 -M -N ] The inside body height ¼ h1 ¼ 125 mm (5 in) Work done: AF ¼ 30896 m N (3150 mm tf or 22785 ft-lbf ) [E -H and G0 -H ] Press rating ¼ Psat ¼ 1960 kN (200 tf) [H -I -K ] 10 6.3 3.15 2.5 s die bo S Co I ho oli ldllo d a ex w nd tru bo de di d, es thi ck wa II lle St dh am oll ow p bo ing die s lid So Multiplication factor, π H,F,P 1.6 1.25 Degree of forming ∈, % 95 94 92 90 88 84 0.05 0.06 0.08 0.1 80 75 68 0.12 0.16 0.2 0.25 0.32 60 50 37 0.4 0.5 20 0.63 0.8 Cross-section ratio qH,F for extusion moulding and impact extrusion Height ratio S2 / S1 for stamping and cold working FIGURE 25-47 Determination of multiplication factor for impact extrusion and cold extrusion, and also for stamping and coining Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN II 10 12 60 00 50 31 X n sio es m2 pr m /m co , kg lflc K D ec ng Sp n d i lo B 50 8000 6300 5000 4000 3150 2500 2000 1600 1250 1000 800 A 630 A 500 400 315 250 200 160 125 100 C fo on r d ve ie rsi ar on ea c ur ve CHAPTER TWENTY-FIVE X 25.86 Fp I D FP PP hP Vstamp s1 s2 d E 20 25 31.5 40 50 63 Blank diemeter d mm E 80 100 F Y 3.1 2.5 1.2 C 80 12.5 20 31.5 50 80 125 200 315 500 10 12.5 16 6.3 10 16 25 40 63 100 160 250 400 5.3 0.63 20 C 0.8 25 Lim 10 it c 31 G H G urv 12.5 e 40 cap for 15 50 aci tion ty u al 20 63 tllls pres 25 atio sw 80 ork n 31.5 III ing 10 40 12 60 50 65 IV Stamping work Ap, m.kg or mm.tonnes 63 80 10 12 16 20 25 31 40 25 31 40 50 10 12 16 20 20 25 31 40 50 63 80 10 00 12 50 16 00 20 00 25 00 31 50 40 00 50 00 63 00 80 00 10 00 12 50 Y he c la Stamping volume Vstamp, cm3 X — Projected die area Fp, mm; Y — Stamping stroke hp, mm; Z — Stamping force FIGURE 25-48 Chart for calculating stamping and coining Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968) X- projected die area Fp , mm; Y- stamping stroke hp , mm; Z, stamping force Pp , tonnes Key to Fig 25-49 Equations and Examples: Forging temperature ¼ T ¼ 10008C Tensile strength of plain carbon steel ¼ B ¼ 588 N/mm2 (60 kgf/mm2 or 86000 lbf/in2 [point B ] (Fig 25-49) Static deformation resistance ¼ kFg ¼ 49 N/mm2 (5 kgf/mm2 or 7100 lbf/in2 ) [point C of curve] The deformation rate ¼ w ¼ "r=t(% sec) ¼ 500%/sec [point D ] The arithmetic proportions of upsetting ¼ "h ¼ 4h=ho ¼ ½1 À Fo =F1 100% The dynamic deformation resistance ¼ kFd ¼ 98 N/mm2 (10 kgf/mm2 or 14200 psi) [point E of the curve] (Fig 25-49) ¼ 2kFg where kFa ¼ static strength pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi The diameter of non-circular upset or forged component is calculated from d111 ẳ 4=ịF1 ẳ 1:13 F1 mm where F1 ¼ crosssection after forming (upsetting surface) The flash ratio ¼ b=s ¼ 4:8 (point F, scale 11) The deformation resistance ¼ kw ¼ 392 N/mm2 (40 kgf/mm2 or 57000 psi) [point G of the curve] The upsetting force ¼ Ps ¼ 24516 kN (2500 tf) [point I of the curve] A prescribed or theoretical upsetting or die diameter d1 [D ¼ 280 mm (11 in)] The corresponding upsetting or die area F1 ẵFtot ẳ 63000 mm2 (96 in2 ) [point H ] The maximum diameter D ẳ d1 ỵ 2b of forged component The crushed flash or the total cross-sectional area ẳ Ftot ẳ F1 ỵ Ub where U ¼ periphery of crushed area The mass ratio ¼ Ls =Bm ¼ 6:3 [point K ] The maximum upsetting force ¼ Pmax ¼ 30890 kN (3150 tf) [point L of the curve] The upset path ¼ h ¼ 16 mm (0.65 in) [point M ] The upsetting work ¼ As ¼ 348134 mm N (35500 mm tf or 256665 ft-lbf) [line N-O ] Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN I Free forging d /h 1m II Drop forging b/s III Form upsetting d /2h 1m Forging temperature T …C ia ls te st in g ac ne III rk N 40 M 16 6.3 2.5 Upsetting path h to BDC on upsetting mm 200 80 31.5 12.5 Upsetting path h to BDC on fininshed forging mm ter d1 or ttin D ga mm or nd Ft die ot mm are aF 250 me dia 25 G 50 100 160 12 100 80 63 3.15 800 20 0× 10 80 50 31 H 20 12 se 40 200 125 1250 Upsetting force P s tonnes 2000 I I 3150 5000 Ls 800 1250 e ur 2000 3150 5000 L t en m m /B s ea L s m io ie rat D V K 16 100 L Max upsetting work tonnes o gw kg Pres a t s w o r k in g % sp c e e d a p a c it y In c r e ase Pres swor at 15 k % s p in g c a p a eed d e c r c it y ease ps in ett 315 15 500 Bm 1.6 2.5 10 6.3 16 10 40 25 63 × 100 A m s 50 400 10 250 500 O VI 500 mm 6.3 150 U 250 G 10 Up 1.5 2.1 5.3 ig IV 0.8 0.6 0.5 0.4 0.31 0.2 0.2 F 0.1 0.12 0.1 H 2.5 n tio ma for cy De icien eff 1.6 2.4 3.4 4.8 6.3 8.5 11.2 14 h ~8 E C gt Dyn deformation strength kg/mm 6.3 2.5 2.5 σB H ig C h-p r- e N rc hs i st ent N pe ile ee ag i s rc ns ls e B te en Te C el ta (h s g st ig e ee h- C ls C pe st rs r e te cen els el ta s) g e n tre m ~5 6.3 10 hi /m 40 16 m 10 dd ie X E C 1400 g k ga n ~3 Z Y s er mm ) Ha m/s ff (ue s s e /s) os m p r 0.0 i c u l 0.02 r a f = y d (uef er 1250 I ttin H at 1150 A se 00 M Deformation resistance, kg/mm 50 te 1000 900 16 Up 50 160 500 600 000 25 2.5 8.5 12 16 Static deformation strength K Fs kg/mm 800 25 II n tio ec a m /s or % e f w, D D 25.87 X — Explosion deformatuon; Y — Highspeed presses (V eff ~ 0.53); Z — Longitudinal mechanical presses (V eff ~ 0) 125) FIGURE 25-49 Chart for calculating hot upsetting and drop forging Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.88 CHAPTER TWENTY-FIVE Particular Formula Refer to Table 25-64 for unit stiffness or specific stiffness E= The ratio of weights of two bars of same length whose weights are W1 ¼ A1 l and W2 ¼ A2 l W1 A1 l E2 E2 = 2 ¼ ¼ ¼ W2 A2 l E1 E1 = 1 ð25-169Þ where E= is the unit stiffness or specific stiffness Refer to Table 25-64, which gives E, and E= for some machine tool structural materials The ratio of weights of two bars of same length subjected to tensile load F W1 nPL 1 =ut1 ị ut2 = 2 ẳ ẳ W2 nPL 2 =ut2 Þ ut1 = 1 ð25-170Þ where ut = is unit strength under tension The ratio of weights of two bars of same length subjected to torque Mt 2=3 W1 ut = 2 ẳ 2=3 W2 ut = 1 25-171ị 2=3 where ut = is an index of the ability of a material to resist torsion and is known as unit strength under torsion The ratio of weights of two bars of same length subjected to bending Mb 2=3 W1 ð1=b1 Þ2=3 b2 = 2 ẳ ẳ W2 1=b2 ị2=3 2=3 = 1 b1 2=3 ð25-172Þ where b = is an index of the ability of a material to resist bending and is known as the unit strength under bending For specific stiffness (in tension) Refer to Table 25-64 For comparison of specific strength and stiffness/ rigidity of different section having equal cross sectional area Refer to Table 25-65 DESIGN OF FRAMES, BEDS, GUIDES AND COLUMNS: For machine frames Refer to Table 25-66 For stiffening effect of reinforcing ribs Refer to Fig 25-50 For characteristics of bending and torsional rigidities of models of various forms Refer to Table 25-67 For variations in relative bending and torsional rigidity for models of various forms Refer to Table 25-68 For effect of stiffener arrangement on torsional stiffness of open structure Refer to Table 25-69 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.89 Formula For effect of aperture and cover plate design in static and dynamic stiffness of box sections Refer to Table 25-70 For typical cross-sections of beds Refer to Fig 25-51A, B, C and D For classification and identification of machine tools Refer to Table 25-72 For machine tools sliding guides, ball and roller guides made of cast iron, steels and plastics Refer to Tables and Figures from 25-66 to 25-71 In addition to these, readers are advised to refer to books and handbooks on machine tools The design of machine tool slideways, guides, beds, frames and columns subjected to external forces are beyond the scope of this Handbook For design of spindle units in machine tools Refer to Chapter 14 on ‘‘Design of shafts’’ in this Handbook For design of power screws and lead screws of machine tools Refer to Chapter 18 on ‘‘Power screws and fasteners’’ in this handbook, and books on power screw design of machine tools For vibration and chattering in machine tools Refer to Chapter 22 on ‘‘Mechanical vibrations’’ in this Handbook For variable speed drives and power transmission Refer to Chapter 23 on ‘‘Gears’’ and Chapter 25 on ‘‘Miscellaneous machine elements’’ in this Handbook For lubrication of guides, spindles and other parts of machine tools Refer to Chapter 24 on ‘‘Design and bearings and Tribology’’ in this Handbook and other books on lubrication TOOLING ECONOMICS (Adopted from Tool Engineers Handbook) Symbols: a saving in labor cost per unit C first cost of fixture D annual allowance for depreciation, per cent H number of years required for amortization of investment out of earnings I annual allowance for interest on investment, per cent M N S t T V annual allowance for repairs, per cent number of pieces manufactured per year yearly cost of setup percentage of overhead applied on labour saved annual allowances for taxes, per cent yearly operating profit over fixed charges N¼ CI ỵ T ỵ D ỵ Mị ỵ S a1 ỵ tị 25-173ị Cẳ Na1 ỵ tị S I þT þDþM ð25-174Þ Number of years required for a fixture to pay for itself Hẳ C Na1 ỵ tị CI ỵ T ỵ Mị S 25-175ị Prot from improved xture designs V ẳ Na1 ỵ tị CI þ T þ D þ MÞ À S ð25-176Þ Number of pieces required to pay for fixture Economic investment in fixtures for given production Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.90 CHAPTER TWENTY-FIVE Particular Formula PROCESS—COST COMPARISONS: Symbols: c value of each piece, dollars Cx , Cy total unit cost for methods Y and Z respectively d hourly depreciation rate for the first machine (based on machine hours for the base years period) D hourly depreciation rate for the second machine (based on machine hours for the base years period) k annual carrying charge per dollar of inventory, dollar l labor rate for the first machine, dollar L lot size, pieces labor rate for the second machine, dollar m monthly consumption, pieces Nt total number of parts to be produced in a single run Number of parts for which the unit costs will be equal for each of two compared methods Y and Z (‘‘breakeven point’’) number of parts for which the unit costs will be equal for each of two compared methods Y and Z (break-even point) number of pieces produced per hour by the first machine number of pieces produced per hour by the second machine unit tool process cost for method Y unit tool process cost for method Z quantity of pieces at break-even point total tool cost for method Y total tool cost for method Z setup hours required on the first machine setup hours required on the second machine ratio of machining time piece Nb p P Py Pz Q Ty Tz s S V Nb ẳ Ty Tz Pz Py 25-177ị Cy ẳ Py Nt ỵ Ty Nt 25-178ị Total unit cost for method Z Cz ẳ Pz Nt ỵ Tz Nt 25-179ị Quantity of pieces at break-even point pPSL ỵ SD sl sdị Pl ỵ dị pL ỵ Dị s 24mS Lẳ kc1 ỵ mvị Total unit cost for methods Y Relatively simple formula for calculation of economic lot size, pieces Qẳ 25-180ị 25-181ị MACHINING COST: Machining time cost per work piece Non-productive time cost per work piece Tool change time cost per work piece Tool cost per work piece tm R 60 t R Cn ẳ tL ỵ s nb 60 Cm ẳ 25-182ị 25-183ị Cc ẳ tm tc R 60t1 25-184ị Ct ẳ Ct1 t t R ỵ sh m 60t1 ỵ ns ð25-185Þ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.91 Formula Total cost of machining Ctot ẳ Cm ỵ Cn ỵ Cc ỵ Ct 25-186ị Total tool cost per workpiece Cn ẳ Cc ỵ Ct 25-187ị where tm ẳ machining time per workpiece, tL ¼ loading and unloading time per workpiece, ts ¼ setting time per batch, tt ¼ tool life, tc ¼ tool charge time, tsh ¼ tool sharpening time, R ¼ cost rate per hour nb ¼ number of batch ns ¼ number of resharpening Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.92 CHAPTER TWENTY-FIVE TABLE 25–64 Unit stiffness/rigidity of some materials Modulus of elasticity, E Material GPa Aluminum Aluminum cast Aluminum (all alloys) Beryllium copper Carbon steel Cast iron, gray Malleable cast iron Inconel Magnesium alloy Molybdenum Monel metal Nickel-silver Nickel alloy Nickel steel Phosphor bronze Steel (18-8), stainless Titanium (pure) Titanium alloy Brass Bronze Bronze cast Copper Tungsten Douglas fir Glass Lead Concrete (compression) Wrought iron Zinc alloy Graphite HTS Graphite/5208 epoxy T50 Graphite 2011 Al Boron Boron carbide, BC Silicon carbide, SiC Boron/5505 epoxy Boron/6601 Al Kelvar 49 Kelvar 49/resin Silicon, Si Wood (along fiber) Nylon Paper E Glass/1002 epoxy 69 70 72 124 206 100 170 214 45 331 179 127 207 207 111 190 130 114 106 96 80 121 345 11 46 36 14–28 190 83 750 172 160 380 450 560 207 214 130 76 110 11–15.1 1–2 39 Mpsi 10.0 10.15 10.4 18.0 30.0 14.5 24.6 31.0 6.5 48.0 26.0 18.5 30.0 30.0 16.0 27.5 15.0 16.5 15.5 14.0 11.6 17.5 50.0 1.6 6.7 5.3 2.0–4.0 27.5 12 108.80 24.95 23.20 55.11 65.28 81.22 30.07 31.03 18.85 11.02 15.95 1.59–2.19 0.58 0.15–0.29 5.65 Modulus of rigidity, G Poisson’s ratio, GPa Mpsi 26 30 27 48 79 41 90 76 16 117 65 48 79 79 41 73 3.8 4.35 3.9 7.0 11.5 6.0 13.0 11.0 2.4 17.0 9.5 7.0 11.5 11.5 6.0 10.6 43 40 38 35 46 138 19 13 6.2 5.8 5.5 5.0 6.6 20.0 0.6 2.7 1.9 70 31 10.2 4.5 Density, a Unit weight, b Unit stiffness E= Mg/m3 kg/m3 kN/m3 lbf/in3 lbf/ft3 0.334 2.69 0.320 0.285 0.292 0.211 2.80 8.22 7.81 7.20 167 166 173 513 487 450 8.42 1.80 10.19 8.83 8.75 8.3 7.75 8.17 7.75 4.47 6.6 8.55 8.30 26.3 26.0 27.0 80.6 76.6 70.6 70.61 83.3 17.6 100.0 86.6 85.80 81.4 76.0 80.1 76.0 43.8 0.097 0.096 0.10 0.297 0.282 0.260 0.290 0.350 0.307 0.320 0.332 0.30 0.291 0.349 0.305 2,685 2,650 2,713 8,221 7,806 7,197 7,200 8,418 1,799 10,186 8,830 8,747 8,304 7,751 8,166 7,750 4,470 6,600 8,553 8,304 8,200 8,913 18,822 443 2,602 11,377 2,353 0.307 0.065 0.368 0.319 0.316 0.300 0.280 0.295 0.280 0.16 530 117 636 551 546 518 484 510 484 279 83.9 81.4 80.0 87.4 184.6 4.3 25.5 111.6 23.1 0.309 534 0.322 1.89 0.016 0.094 0.411 556 2:62  106 2:66  106 2:68  106 1:54  106 2:69  106 1:42  106 2:41  106 2:57  106 2:56  106 3:31  106 2:06  106 1:48  106 2:54  106 2:72  106 1:38  106 2:50  106 2:37  106 2:60  106 1:26  106 1:18  106 1:00  106 1:38  106 28 162 710 147 2:56  106 1:80  106 3:10  106 0:60  106 7,700 76.0 0.24 415 0.33 0.324 0.349 0.326 0.330 0.245 0.431 0.33 8.90 18.82 4.43 2.60 11.38 2.35 6.6 2.25 1.55 22.1 15.2 2.58 2.5 2.4 3.2 1.99 2.60 1.44 1.38 2.30 0.41–0.82 1.1 0.50 1.80 25.3 44.1 22.5 31.4 19.5 25.5 14.1 13.5 22.5 4.0–8.0 10.8 4.9 17.6 2:50  106 1:18  106 34:00  106 11:30  106 6:32  106 11:00  106 19:20  106 17:80  106 8:40  106 8:20  106 9:20  106 5:60  106 4:86  106 2.75–1:86  106 0:37  106 0.20–0:41  106 2:22  106 a , mass density , weight density; w is also the symbol used for unit weight of materials Source: K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook, Volume I (SI and Customary Metric Units), Suma Publishers, Bangalore, India and K Lingaiah, Machine Design Data Handbook, Volume II, (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986 b Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN 25.93 ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-65 Comparison of specific strength and Rigidity/Stiffness of different sections having equal cross sectional areas (in Flexure) Distance to farthest point, c Moment of inertia I Section modulus Z ¼ I=c i¼ Ià Ia Zà Za 0.14 1 0.083 0.166 1.06 1.16 B3r2/6 0.083r 0:166 1.9 1.6 0:05D4 ð1 À Þ 0:1D3 ð1 À ELEMENTS OF MACHINE TOOL DESIGN 25.102 CHAPTER TWENTY-FIVE TABLE 25-72 Classification and Identification code of Machine Tools – Kinematic Diagram (Cont.) Description Symbol Nut on power screw: Solid nuts Description Symbol Single-direction overrunning clutches Split nuts Two-direction overrunning clutches Clutches: Single-direction jaw clutches Brakes: Cone Spindle noses: Centre type Chuck type Shoe Bar type Band Drilling Boring spindles with faceplates Disk Milling Two-direction jaw clutches Grinding Cone clutches Electric motors: On feet Single disk clutches Twin disk clutches Flange-mounted Built-in Source: Courtesy: Acherkan, N., et1., ‘‘Machine Tool Design’’, Moscow, 1968 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN 25.103 REFERENCES 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994 Lingaiah, K., Machine Design Data Handbook, Vol I, Suma Publishers, Bangalore, India, 1986 Merchant, M E., Trans Am Soc Mech Engrs., 66, A-168, 1944 Ernst, H., and M E Merchant, Chip Formation, Friction and Finish, Cincinneti Milling, Machine Company, USA American Society of Tool and Manufacturing Engineers (ASTME), Tool Engineers Handbook, 2nd ed., F W Wilson, Editor, McGraw-Hill Book Publishing Company, New York, 1959 Cyril Donaldson, George H Lecain and V.C Goold, Tool Design, Tata-McGraw-Hill Publishing Company Ltd., New Delhi, India, 1976 Frank W Wilson, Editor-in-Chief, American Society of Tool and Manufacturing Engineers (ASTME), Fundamentals of Tool Design, Prentice Hall, New Delhi, India, 1969 Kuppuswamy, G., Center for Continuing Education, Department of Mechanical Engineering, Indian Institute of Technology, Madras, India, August 12, 1987 Sen, G C., and A B Bhattacharyya, Principles of Machine Tools, New Central Book Agency, (P) Ltd., Calcutta, India, 1995 Geoffrey Boothroyd, Fundamentals of Metal Machining and Machine Tools, McGraw-Hill Publishing Company, New York, 1975 Koenigsberger, F., Design Principles of Metal Cutting Machine Tools, the MacMillan Company, New York, 1964 Shaw, M C., and C J Oxford, Jr., (1) ‘‘On the Drilling Metals’’ (2) ‘‘The Torque and Thrust in Milling’’, Trans ASME., 97:1, January 1957 Hindustan Machine Tools, Bangalore, Production Technology, Tata-McGraw-Hill Publishing Company Ltd., New Delhi, India, 1980 Central Machine Tool Institute, Machine Tool Design Handbook, Bangalore, India, 1988 Acherkan, A., General Editor, V Push, N Ignatyev, A Kakoilo, V Khomyakov, Y U Mikheyev, N Lisitsyn, A Gavryushin, O Trifonov, A Kudryashov, A Fedotyonok, V Yermakov, V Kudinov, Machine Tool Design, Vol to 4, Mir Publishers, Moscow, 1968-69 Milton C Shaw, Metal Cutting Principles, Clarendon Press, Oxford, 1984 Martelloti, M E., Trans Am Soc Mech Engrs., 63, 677, 1941 Kovan, V M., Technology of Machine Building, Mashgiz, Moscow, 1959 Basu, S R., and D K Pal, Design of Machine Tools, 2nd ed., Oxford and IBH Publishing Company, New Delhi, 1983 Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag Muchen, 1961 (in German) Translated to English by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) Ltd., 1968 Dobrovolsky, K Zablonsky, S Mak, Radchik, L Erlikh, Machine Elements, Mir Publishers, Moscow, 1968 Rivin, E I., Stiffness and Damping in Mechanical Design, Marcel Dekker, Inc., New York, 1999 Machine Tool Design and Numerical Control Chernov, N., Machine Tools, Translated from Russian to English by Falix Palkin, Mir Publishers, Moscow, 1975 Greenwood, D C., Engineering Data for Product Design, McGraw-Hill Publishing Company, New York, 1961 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source: MACHINE DESIGN DATABOOK CHAPTER 26 RETAINING RINGS AND CIRCLIPS SYMBOLS a Ch Chmax CF d D f Ftg Fig Frt Fir F 0r F 00 r Ftrr Fsg Fsr l n nmax q r rmax t T w ðwaÞg ðwaÞr xo sy saw s acceleration of retained parts, m/s2 (ft/s2 or in/s2 ) actual chamfer, m (in) listed maximum allowable chamfer, m (in) conversion factor (refer to Table 26-1) depth of groove, m (in) shaft or housing diameter, m (in) frequency of vibration, cps allowable static thrust load on the groove wall, kN (lbf) allowable impact load on groove, kN (lbf) allowable static thrust load of the ring, kN (lbf) allowable impact load on a retaining ring, kN (lbf) listed allowable assembly load with maximum corner radius or chamfer, kN (lbf) allowable assembly load when cornor radius or chamfer is less than the listed, kN (lbf) allowable thrust load exerted by the adjacent part, kN (lbf) allowable sudden load an groove, kN (lbf) allowable sudden load on ring, kN (lbf) distance of the outer groove wall from the end of the shaft or bore as shown in Fig 26-2, m (in) factor of safety (about to may be assumed) maximum safe speed, rpm reduction factor from Fig 26-1 actual corner radius or chamfer, m (in) listed maximum allowable corner radius, m (in) ring thickness, m (in) largest section of the ring, m(in) weight of retained parts, kN (lbf) allowable vibratory loading on groove, kN (lbf) allowable vibratory loading on ring, kN (lbf) amplitude of vibration, m (in) tensile yield strength of groove material, Table 26-2, MPa (psi) maximum working stress of ring during expansion or contraction of ring, MPa (psi) shear strength of ring material, MPa (psi) (refer to Table 26-3) coefficient of friction between ring and retained parts whichever is the largest 26.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS 26.2 CHAPTER TWENTY-SIX Note: and with subscript s designates strength properties of material used in the design which will be used and observed throughout this Machine Design Data Handbook Other factors in performance or in special aspects are included from time to time in this chapter and, being applicable only in their immediate context are not given at this stage Particular Formula RETAINING RINGS AND CIRCLIPS: (Figs 26-1 to 26-28 and Tables 26-1 to 26-13) Load Capacities of Retaining Rings: Ftg ẳ CF Ddsy nq 26-1ị Fr ẳ CF Dt s n 26-2ị Ftrr saw tT 18D 26-3ị F 00 ẳ r Fr0 rmax r Fr00 ¼ Fr0 Chmax Ch Allowable sudden load on ring Fsr 0:5Fr ð26-6Þ Allowable sudden load on groove Fsg 0:5Ftg ð26-7Þ Allowable vibration loading on ring ðwaÞr 540Fr a ð26-8Þ Allowable vibration loading on groove ðwaÞg a ð26-9Þ Acceleration of retained parts for harmonic oscillation a % 40xo f ð26-10Þ Allowable impact loading on groove Fig ẳ Fr d=2 26-11ị Allowable static thrust load on the groove Allowable static thrust load on ring which is subject to shear The allowable thrust load exerted by adjacent part Allowable assembly load when the corner radius or chamfer is less than the listed (F 00 < F 0r ) r for radius for chamfer ð26-4Þ ð26-5Þ Dynamic Loading: Allowable impact loading on ring An empirical formula for maximum safe speed with standard types of rings 400Ftg Fir ¼ Fr t=2 nmax ¼ 5000000=D nmax ẳ 20000=D a 26-12ị where D in mm 26-13ị where D in inches ð26-14Þ Note: Actual tests should be conducted because of repeated or cyclic condition Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS RETAINING RINGS AND CIRCLIPS Particular 26.3 Formula For dimensions of external circlips—Type A—light series Refer to Table 26-5 and Fig 26-3 For dimensions of external circlips—Type A—heavy series Refer to Table 26-6 and Fig 26-4 Refer to Table 26-7 and Fig 26-5 For dimensions of internal circlips—Type B—light series Refer to Table 26-8 and Fig 26-6 For dimensions of internal circlips—Type B—Heavy series Refer to Table 26-9 and Fig 26-7 For dimensions of external circlip—Type C For dimensions, allowable static thrust load, allowable corner radii, chamfers, housing diameter and ring thickness of retaining rings—basic internal, bowed internal, beveled internal, inverted internal, double beveled internal, crescent-shaped, bowed Ering, reinforced, locking prong in grooved housing and on grooved shafts, self locking and triangular self locking ring etc Refer to Tables 26-10 to 26-13 and Figs from 26-1 to 26-28 Refer to Fig 26-1 For q reduction factor TABLE 26-1 Conversion or correction factor CF for calculating Fr and Ftg for use in Eqs (26-l) and (26-2) Conversion or correction factor CF Ring type Ring: Fr Basic, bowed internal Beveled internal Double-beveled internal Inverted internal, external Basic, bowed external Beveled external Groove: Ftg 1.2 1.2 1.2 1.2 Use d=2 instead of d 2/3 1/2 1 1 Use d=2 instead of d Crescent-shaped 1/2 1/2 Two-part interlocking 3/4 3/4 E-ring, bowed E-ring 1/3 1/3 Reinforced E-ring 1/4 1/4 Locking-prong ring See manufacturer’s 1.2 specifications Heavy-duty external 1.3 High-strength radial 1/2 1/2 Miniature high-strength See manufacturer’s specifications Thinner-gage high-strength 1/2 1/2 radial FIGURE 26-1 Reduction curve FIGURE 26-2 Edge margin Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-2 Tensile yield strength of groove material Tensile yield strength, sy Groove material MPa lbf/in2 Cold-rolled steel Hardened steel (Rockwell C40) Hardened steel (Rockwell C50) Aluminum (2024-T4) Brass (naval) 310 1034 1380 276 210 45,000 150,000 200,000 40,000 30,000 TABLE 26-3 Shear strength of ring material for use in Eq (26-2) Shear strength, s Ring material Carbon spring steel (SAE 1060– 1090) Ring type Ring thickness mm (in) MPa lbf/in2 Basic, bowed, beveled, inverted internal and external rings and crescent-shaped Up to and including 0.9 (0.035) 827 120,000 Double-beveled internal rings 1.07 (0.042) and over 1034 150,000 Heavy-duty external 0.90 (0.035) and over 1034 150,000 Miniature high-strength 0.510 (0.020) and 0.635 (0.025) 827 120,000 0.9 (0.035) and over 1034 150,000 Two-part interlocking, reinforced E-ring, high-strength radial All available 1034 150,000 Thinner high-strength radial All available 1034 150,000 E-ring, bowed E-ring 0.254 (0.010) and 0.380 (0.015) 690 100,000 0.635 (0.025) 827 120,000 1034 150,000 0.9 (0.035) and over Locking-prong 896 130,000 Basic external 0.254 (0.010) and 0.380 (0.015) sizes 12 through 23 758 110,000 Bowed external 0.380 (0.015) sizes 18 through 23 758 110,000 E-ring Beryllium copper (CDA 17200) All available 0.254 (0.010) (size  only) 662 95,000 26.4 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-4 Maximum working stress of ring during expansion or contraction Maximum allowable working stress, saw Ring material MPa lbf/in2 Carbon spring steel (SAE 1075) Stainless steel (PH 15-7 Mo) Beryllium copper (CDA 17200) Aluminum (Alclad 7075-T6) 1724 1724 1380 482 250,000 250,000 200,000 70,000 Courtesy: # 1964, 1965, 1973, 1981 Waldes Kohinoor, Inc., Long Island City, New York, 1985 Edward Killian, ‘‘Retaining Rings’’, Robert O Parmley, Editor-in-Chief ‘‘Mechanical Components Handbook’’, McGraw-Hill Publishing Company, New York, USA TABLE 26-5 Dimensions for external circlips—type A—light series FIGURE 26-3 All dimensions in millimeters Circlip Shaft Dia d1 Axial force s h11 a b Max Approx d3 Tol on d4 d5 d3 Expanded Min 0.8 3.2 ỵ0.09 0.18 ỵ0.15 1.5 1.7 10 7.4 8.4 9.3 1.8 3.4 15.2 16.4 10.2 11 11.9 1:2 d2 Tol on m1 d2 H13 7.6 8.6 0.9 m2 Min n Min 1.0 N lbf 1180 1360 265 305 1500 340 2060 2270 2940 460 510 660 0.6 17.6 À0.30 3.3 11 12 13 Shaft groove 9.6 1.5 18.6 19.6 20.8 10.5 11.5 12.4 h11 1:1 1:2 0.75 26.5 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS 26.6 CHAPTER TWENTY-SIX TABLE 26-5 Dimensions for external circlips—type A—light series (Contd.) All dimensions in millimeters Circlip Shaft Dia d1 14 15 16 17 18 19 20 21 22 24 25 26 28 29 30 32 34 35 36 38 40 42 45 48 50 52 55 56 58 60 62 63 65 68 70 72 75 78 80 82 85 88 90 Shaft groove Axial force s h11 a b Max Approx d3 Tol on d4 d5 d3 Expanded Min 3.5 3.6 3.7 3.8 3:9 þ0:18 À0.36 4.1 4.2 4.4 1.2 4.5 4.7 4.8 5.2 5.4 5.6 1.5 5.8 6.5 6.7 6.9 6.9 7.2 7.3 2.5 7.4 7.5 7.6 7.8 8.1 8.2 8.4 1.75 8.6 8.7 8.8 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.1 3.2 3.4 3.5 3.6 3.8 3.9 4.2 4.4 4.5 4.7 5.1 5.2 5.4 5.5 5.6 5.8 6.2 6.3 6.5 6.6 6.8 7.3 7.4 7.6 7.8 8.2 12.9 13.8 14.7 15.7 16.5 17.5 18.5 19.5 20.5 22.2 23.2 24.2 25.9 26.6 27.9 29.6 31.5 32.2 33.2 35.2 36.5 38.5 41.5 44.5 45.8 47.8 50.8 51.8 53.9 55.8 57.8 58.8 60.8 63.5 65.5 67.5 70.5 73.5 74.5 76.5 79.5 82.5 84.5 ỵ0.21 0.42 ỵ0.25 0.25 ỵ0.39 0.78 ỵ0.46 0.92 ỵ0.46 0.92 22 23.2 24.4 25.6 26.8 27.8 29 30.2 31.4 33.8 34.8 36 38.4 39.6 4.1 43.4 45.8 47.2 48.2 50.6 53 56 59.4 62.8 64.8 67 70.4 71.6 73.6 75.8 78 79.2 81.6 85 87.2 89.4 92.2 96.2 98.2 101 104 107 109 1:7 2.5 d2 Tol on m1 d2 H13 13.4 14.3 15.2 16.2 17 18 19 20 21 22.9 23.9 24.9 26.6 27.6 28.6 30.3 32.3 33 34 36 h12 37.5 39.5 42.5 45.5 47 49 52 53 55 57 59 60 62 65 67 69 72 75 76.5 h12 78.5 81.5 84.5 86.5 m2 Min n Min 0.9 1.1 1.2 1.5 1.3 1.4 1.7 2.1 1.6 1.7 2.6 1.85 2.15 3.8 2.3 4.5 4.5 2.65 2.8 3.15 3.3 5.3 N 3190 3920 4809 5100 6770 7110 7550 7900 8300 9900 10400 10790 14710 15300 15890 20590 21770 26180 27070 28540 37360 39230 42170 45110 55900 58350 61780 62760 65210 67665 69625 71100 73550 76880 78940 81395 84336 88260 104930 107870 111795 116700 118660 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website lbf 720 880 1080 1150 1520 1600 1700 1780 1860 2230 2335 2425 3310 3440 3570 4630 4890 5890 6085 6415 8400 8820 9480 10140 12565 13120 13890 14110 14660 15210 15650 15985 16535 17285 17748 18300 18960 19840 23590 24250 25130 26236 26675 RETAINING RINGS AND CIRCLIPS RETAINING RINGS AND CIRCLIPS 26.7 TABLE 26-5 Dimensions for external circlips—type A—light series (Contd.) All dimensions in millimeters Circlip Shaft Dia d1 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 210 220 230 240 250 260 270 280 290 300 Shaft groove Axial force s h11 a b Max Approx d3 9.4 9.6 9.9 10.1 10.6 11 11.4 11.6 11.8 12 12.2 13 13.3 13.5 8.6 9.3 9.6 9.8 10.2 10.4 10.7 11 11.2 11.5 11.8 12 12 12.5 12.9 Max 13.5 Max 14 Max 16 Max 89.5 94.5 98 103 108 113 118 123 128 133 138 142 146 151 155.5 160.5 165.5 170.5 175.5 180.5 185.5 190.5 198 208 218 228 238 245 255 265 275 285 d5 Tol on d4 d3 Expanded Min ỵ0.54 1.08 ỵ0.63 1.26 þ0.72 À1.44 þ0.81 À1.62 115 121 126 132 138 143 149 155 160 165 171 177 182 188 193 197 202 208 213 219 224 229 239 249 259 269 279 293 303 313 323 333 3.5 d2 Tol on m1 d2 H13 91.5 96.5 101 106 111 116 121 126 131 136 141 145 150 155 160 165 170 175 180 185 190 h13 195 204 214 224 234 244 252 262 272 282 292 m2 Min n Min 4.15 4.3 7.5 5.15 5.3 12 N lbf 125525 132390 158865 166712 174555 181422 189265 197110 204958 212800 220650 283410 294200 304000 313810 322640 331460 341270 331460 328520 320675 312830 478560 502095 524650 518770 493270 533480 514846 498175 491505 463850 28220 29764 35716 37490 39244 40785 42550 44315 46080 47840 49606 63716 66140 69346 70550 72535 74520 76724 74520 73858 72094 70330 107590 112880 117950 116630 110900 119936 115748 112000 108250 104280 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-6 Dimensions for external circlips—type A—heavy series FIGURE 26-4 All dimensions in millimeters Circlip Shaft Dia d1 15 16 17 18 20 22 24 25 28 30 32 34 35 38 40 42 45 48 50 52 55 58 60 65 70 75 80 85 90 100 Shaft groove Axial force s h11 a b Max Approx d3 4.8 1.5 1.75 5.1 5.5 6.3 6.4 6.5 2.5 6.6 6.7 6.8 7.2 7.5 7.8 8.2 8.5 8.8 9.3 9.5 9.7 9.8 10 10.2 10.5 2.4 2.5 2.6 2.7 3.1 3.2 3.4 3.5 4.1 4.2 4.3 4.4 4.5 4.7 5.1 5.2 5.4 5.6 5.8 6.3 6.6 7.4 7.8 8.2 13.8 14.7 15.7 16.5 18.5 20.5 22.2 23.2 25.9 27.9 29.6 31.5 32.2 35.2 36.5 38.5 41.5 44.5 45.8 47.8 50.8 53.8 55.8 60.8 65.5 70.5 74.5 79.5 84.5 94.5 Tol on d4 d5 d3 Expanded Min ỵ0.18 0.36 ỵ0.21 0.42 ỵ0.25 0.50 ỵ0.39 0.78 ỵ0.46 0.92 ỵ0.54 À1.08 25.5 27.5 28.5 29.5 32.5 35.5 38 39 42.5 44.5 46.5 49 50 53 55.5 58 61.5 65 68 70 73.5 77 79 85 90.5 96 101 106.5 112 124 2.5 3.5 d2 14.3 15.2 16.2 17 19 21 22.9 23.9 26.6 28.6 30.3 32.3 33 36 37.5 39.5 42.5 45.5 47 49 52 55 57 62 67 72 76.5 81.5 86.5 96.5 Tol on m1 d2 H13 m2 Min n Min 1.1 h11 1.6 1.7 1.85 1.2 1.5 1.7 2.15 2.3 2.1 2.6 2.65 2.8 3.8 h12 3.15 3.3 4.5 4.15 4.3 5.3 N 3922 4805 5100 6765 7550 8286 9905 10395 14710 15896 20594 21770 25890 28242 37658 39226 42168 45110 55898 58350 61780 65214 67665 70550 78942 84336 104930 111795 118660 132390 lbf 882 1080 1146 1520 1698 1862 2226 2336 3310 3570 4630 4895 5820 6350 9466 8820 9480 10140 12566 13118 13990 14660 15212 16535 17744 19956 23590 25134 26676 29764 Designation: A circlip of light series in type A for shaft diameter d1 equal to 50 mm shall be designated as: Circlip, Light A 50 IS: 3075, 1965 26.8 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-7 Dimensions for internal circlips—type B—light series FIGURE 26-5 All dimensions in millimeters Circlip Shaft Dia d1 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 28 30 32 34 35 36 37 38 40 42 Bore groove Axial force s a b h11 Max Approx d3 0.8 2.4 2.5 3.2 3.3 3.4 3.6 3.7 3.8 1.1 1.3 1.4 1.5 1.7 1.8 1.9 3.9 4.1 2.1 2.2 4.2 1.2 4.4 4.5 4.7 4.8 5.4 1.5 5.5 5.8 5.9 2.3 2.4 2.5 2.6 2.7 2.9 2.9 3.0 3.2 3.3 3.4 3.5 3.6 3.7 3.9 4.1 8.7 9.8 10.8 11.8 13.0 14.1 15.1 16.2 17.3 18.3 19.5 20.5 21.5 22.5 23.5 25.9 26.9 27.9 30.1 32.1 34.4 36.5 37.8 38.8 39.8 40.8 43.5 45.5 Tol on d4 d5 d3 Compressed Min ỵ0.36 0.18 ỵ0.42 0.21 ỵ0.50 0.25 ỵ0.78 0.39 2.8 3.5 3.1 3.9 4.7 5.3 7.7 8.4 8.9 9.8 10.6 11.6 12.6 14.2 15 15.6 17.4 19.4 20.2 22.2 23.2 24.2 25 26 27.4 29.2 1.2 1.5 1.7 d2 8.4 9.4 10.4 11.4 12.5 13.6 14.6 15.7 16.8 17.8 19 20 21 22 23 25.2 26.2 27.2 29.4 31.4 33.7 35.7 37 38 39 40 42.5 44.5 Tol on m1 d2 H13 m2 Min n Min 0.6 0.75 0.9 H11 1.1 1.2 1.1 1.2 1.5 1.8 1.3 1.4 2.1 2.6 1.6 1.7 N 1255 1412 1570 1725 2353 3080 3295 4138 5050 5364 7110 7492 7894 8286 8650 11375 11769 12258 15495 16572 21575 22750 27655 28440 29224 30106 39716 41678 lbf 282 318 352 389 530 692 740 930 1135 1205 1598 1684 1775 1862 1943 2558 2645 2756 3485 3726 4850 5115 6216 6394 6570 6768 8930 9370 26.9 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-7 Dimensions for internal circlips—type B—light series (Contd.) All dimensions in millimeters Circlip Shaft Dia d1 45 47 48 50 52 55 56 58 60 62 63 65 68 70 72 75 78 80 82 85 88 90 92 95 98 100 102 105 108 110 112 115 120 125 130 135 140 145 150 155 160 165 170 175 180 Bore groove Axial force s a b h11 Max Approx d3 1.75 6.2 6.4 6.5 6.7 6.8 6.9 7.3 7.6 7.8 2.5 4.3 4.4 4.5 4.6 4.7 5.0 5.1 5.2 5.4 5.5 5.6 5.8 6.1 6.2 6.4 6.6 6.8 8.5 8.6 8.7 8.8 9.2 9.5 10.4 10.5 11 11.2 11.4 12 13 7.0 7.2 7.4 7.6 7.8 8.1 8.3 8.4 8.5 8.7 9 9.1 9.3 9.7 10 10.2 10.5 10.7 10.9 11.2 11.4 11.6 11.8 12.2 Max 12.7 Max 13.2 48.5 50.5 51.5 54.2 56.2 59.2 60.2 62.2 64.2 66.2 67.2 69.2 72.5 74.5 76.5 79.5 82.5 85.5 87.5 90.5 93.5 95.5 97.5 100.5 103.5 105.5 108 112 115 117 119 122 127 132 137 142 147 152 158 164 169 174.5 179.5 d5 Tol on d4 d3 Compressed Min ỵ0.92 0.46 ỵ1.08 0.54 ỵ1.08 0.54 ỵ1.26 0.63 31.6 33.2 34.6 36 37.6 40.4 41.4 43.2 44.4 46.4 47.4 48.8 51.4 53.4 55.4 58.4 60 62 64 66.8 69.8 71.8 73.6 76.4 79 81 82.6 85.6 88 88.2 90 93 97 102 107 112 117 122 125 130 133 138 145 184.5 149 189.5 153 2.5 3.5 d2 Tol on m1 d2 H13 47.5 H12 49.5 50.5 53 55 58 59 61 63 65 66 68 71 73 75 78 81 83.5 85.5 88.5 91.5 93.5 95.5 H12 98.5 101.5 103.5 106 109 112 114 116 119 124 129 134 139 144 149 155 160 165 170 175 180 185 H13 m2 Min n Min 1.85 3.8 2.15 2.3 4.5 2.65 2.8 5.3 3.15 3.3 5.3 4.15 4.3 N lbf 44325 46286 47268 59526 61780 65214 66195 68646 71098 73354 74334 76688 80120 82572 84826 88260 91690 109834 112775 116699 120620 123562 126505 130428 134350 137292 159849 164750 169654 172596 175538 180440 188286 195150 202996 210940 219686 226532 226532 294198 312830 322936 332444 9965 10406 10626 13382 13766 14660 14882 15442 15984 16490 16712 17240 18012 18564 19070 19700 20614 24692 25354 26236 27118 27790 28440 29322 30205 30866 35936 37040 38142 38902 39465 40566 42330 43874 45238 47400 49165 50930 50930 66142 70330 72535 74740 341270 76724 338328 76062 26.10 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-7 Dimensions for internal circlips—type B—light series (Contd.) All dimensions in millimeters Circlip Shaft Dia d1 Axial force s a b h11 Max Approx d3 Max 13.7 Max 13.8 Max 185 190 195 200 210 220 230 240 250 260 270 280 290 300 Bore groove 14 Max 16 Max d5 Tol on d4 d3 Compressed Min d2 Tol on m1 d2 H13 m2 Min n Min N lbf 194.5 ỵ1.44 157 190 343230 77165 199.5 À0.72 204.5 209.5 222 232 242 252 262 275 ỵ1.62 285 0.81 295 305 315 162 167 171 181 191 201 211 221 227 237 247 257 267 195 200 205 216 226 236 246 256 268 278 288 298 308 333424 323618 318715 488368 511904 538392 514846 495232 529556 507980 490330 472678 456006 74960 72755 71652 109795 115096 121040 115748 111338 119055 114205 110236 106268 102520 5.15 5.3 12 26.11 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-8 Dimensions for internal circlips—type B—heavy series FIGURE 26-6 All dimensions in millimeters Circlip Shaft Dia d1 s h11 20 22 24 25 26 28 30 32 34 35 37 38 40 42 45 47 50 52 55 60 62 65 68 70 72 75 80 85 90 95 100 4.5 4.7 4.9 o 1.5 5.1 5.3 5.5 5.7 5.9 1.75 ) 6.2 6.3 6.5 6.7 7.2 7.5 2.5 7.7 8.5 8.6 8.7 8.8 9.2 9.3 9.5 9.7 10 10.3 10.5 Bore groove Axial force a Max b Approx d3 Tol on d3 2.4 2.8 ỵ0.42 0.21 3:1 3.2 3.3 3.4 3.7 3.8 3.9 4.1 4.3 4.4 4.6 4.7 5.4 5.5 5.8 6.1 6.2 6.4 6.6 7.2 7.6 8.1 8.4 21.5 23.5 25.9 26.9 27.9 30.1 32.1 34.4 36.5 37.8 39.8 40.8 43.5 45.5 48.5 50.5 54.2 56.2 59.2 64.2 66.2 69.2 72.5 74.5 76.5 79.5 85.5 90.5 95.5 100.5 105.5 ỵ0.50 0.25 ỵ0.78 0.39 þ0.92 À0.46 þ1.08 À0.54 d5 d4 Compressed Min d2 10 11.6 13.2 14 14.8 16.4 18 19.6 21.2 22 23.6 24.4 26 27.6 30 31.6 34 35.6 38 42 43.8 46.6 49.4 51 52.6 55.5 60 64.6 69 73.4 78 21 23 25.2 26.2 27.2 29.4 31.4 33.7 35.7 37 39 40 42.5 44.5 47.5 49.5 53 55 58 63 65 68 71 73 75 78 83.5 88.5 93.5 98.5 103.5 2.5 3.5 Tol on d2 m1 H13 m2 Min n Min 1.5 1.6 1.7 1.8 2.1 2.6 1.85 2.15 2.3 2.65 3.8 2.8 H12 4.5 3.15 3.3 4.15 4.3 5.3 N lbf 7895 8650 11375 11768 12259 15495 16572 21575 22750 27655 29224 30106 39716 41678 44325 46286 59526 61782 65214 71098 73354 76688 80120 82570 84926 89260 109834 116698 123564 130429 137292 1775 1945 2558 2646 2755 3484 3726 4950 5115 6218 6590 6768 8930 9370 9965 10406 13382 13890 14660 15984 16490 17240 18017 18564 19070 19942 24692 26236 27780 29322 30966 26.12 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website RETAINING RINGS AND CIRCLIPS TABLE 26-9 Dimensions for external circlips—type C FIGURE 26-7 All dimensions in millimeters Circlip Shaft Groove Nominal size d1 d4 Expanded a H10 s 0.8 1.2 1.5 1.9 2.3 3.2 10 12 15 19 24 4.5 11 12 14 16 18.5 20 23 29 37 44 0.58 1.01 1.28 1.61 1.94 2.70 3.34 4.11 5.26 5.84 6.52 7.63 8.32 10.45 12.61 15.92 21.88 0.2 0.3 0.4 0.5 0.6 0.6 0.7 0.7 0.7 0.9 1.0 1.1 1.2 1.3 1.5 1.75 2.0 Tol on s Ỉ0.02 Ỉ0.03 To d3 h11 m From d3 1.4 2.5 10 11 13 16 20 25 1.4 2.5 11 12 14 15 18 24 31 38 0.8 1.2 1.5 1.9 2.3 3.2 10 12 15 19 24 0.24 0.34 0.44 0.54 0.64 0.64 0.74 0.74 0.74 0.94 1.05 1.15 1.25 1.35 1.55 1.80 2.05 Tol on m Æ0:02 Æ0.03 Æ0.06 n Min 0.4 0.6 0.8 1 1.2 1.2 1.2 1.5 1.8 2 2.5 3.0 3.5 4.0 IS: 3075, 1965 REFERENCES Lingaiah K., Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994 Waldes Kohinoor, Inc., Long Island City, New York, U.S.A, 1985 Edward Killian, Retaining Rings, Waldes Kohinoor, Inc., Long Island City, New York, U.S.A, 1985 and Robert O Parmley, Editor-in-Chief, Mechanical Components Handbook, McGraw-Hill Publishing Company New York, 1985 IS: 3075, 1965, Circlips Industrial Fasteners Handbook, 2nd Edition, Trade and Technical Press Limited, Morden Surrey, England, 1980 ‘‘General Purpose Uniform Cross-section Spiral Retaining Rings’’, ANSI, B27.6, 1972 (R 1977) ‘‘General Purpose Tapered and Reduced Cross-section Retaining Rings (Metric)’’, ANSI B 27.7, 1977 ‘‘General Purpose Metric Tapered and Reduced Cross-section Retaining Rings’’ ANSI B27.8M, 1978 Joseph E Shigley, ‘‘Unthreaded Fasteners’’, and Shigley, J E., and Mischke, C R., Standard Handbook of Machine Design, McGraw-Hill Publishing Company, New York, 1996 26.13 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ... 24692 2 535 4 26 236 27118 27790 28440 2 932 2 30 205 30 866 35 936 37 040 38 142 38 902 39 465 40566 4 233 0 438 74 45 238 47400 49165 50 930 50 930 66142 7 033 0 72 535 74740 34 1270 76724 33 832 8 76062 26 .10 Downloaded...  106 3: 31  106 2:06  106 1:48  106 2:54  106 2:72  106 1 :38  106 2:50  106 2 :37  106 2:60  106 1:26  106 1:18  106 1:00  106 1 :38  106 28 162 710 147 2:56  106 1:80  106 3: 10. .. 5.9 2 .3 2.4 2.5 2.6 2.7 2.9 2.9 3. 0 3. 2 3. 3 3. 4 3. 5 3. 6 3. 7 3. 9 4.1 8.7 9.8 10. 8 11.8 13. 0 14.1 15.1 16.2 17 .3 18 .3 19.5 20.5 21.5 22.5 23. 5 25.9 26.9 27.9 30 .1 32 .1 34 .4 36 .5 37 .8 38 .8 39 .8 40.8