Machine Design Databook 2010 Part 9 doc

The general expression for size factor Wire diameter SELECTION OF MATERIALS AND STRESSES FOR SPRINGS For materials for springs 7 The torsional yield strength The maximum allowable torsional stress for static applications according to Joerres 8;9;11 The maximum allowable torsional stress according to Shigley and Mischke 9 The shear endurance limit according to Zimmerli 10 The torsional modulus of rupture e sz ¼ 0:86 þ 0:07 d USCS ð20-45cÞ for steel, where d in in e sz ¼ 0:986 þ 0:0043 d USCS ð20-45dÞ for monel metal, where d in in e sz ¼ 0:86 þ 1:8 d SI ð20-45eÞ for steel, where d in mm e sz ¼ 0:986 þ 0:1 d SI ð20-45fÞ for monel metal, where d in mm k sz ¼ 4:66h 0:35 where h in m SI ð20-46aÞ k sz ¼ 1:27h 0:35 where h in in USCS ð20-46bÞ k sz ¼ 0:415h 0:35 where h in mm SI ð20-46cÞ d ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffi 8kFD  d e sz s ð20-47Þ Refer to Tables 20-8 and 20-10 and Figs. 20-7b and 20-7c. 0:35 sut  sy 0:52 sut for steels ð20-47aÞ  sy ¼  a ¼ 0:45 sut cold-drawn carbon steel 0:50 sut hardened and tempered carbon and low-alloy steel 0:35 sut austenitic stainless steel and nonferrous alloys 8 > > > > > < > > > > > : ð20-47bÞ where  sy ¼ torsional yield strength, MPa (psi)  sy ¼  a ¼ 0:56 sut ð20-47cÞ  sf ¼ 310 MPa ð45 kpsiÞð20-47dÞ for unpeened springs  sf ¼ 465 MPa ð67:5 kpsiÞð20-47eÞ for peened springs  su ¼ 0:67 sut ð20-47f Þ Particular Formula 20.14 CHAPTER TWENTY Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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SPRINGS The weight of the active coil of a helical spring For free-length tolerances, coil diameter tolerances, and load tolerances of helical compression springs DESIGN OF HELICAL COMPRESSION SPRINGS Design stress The size factor The design stress W ¼  2 d 2 Di 4 ð20-47gÞ where  ¼ weight of coil of helical spring per unit volume Refer to Tables 20-11 to 20-13. k sz ¼ d 0:35 0:355 where d in m SI ð20-48aÞ k sz ¼ d 0:25 0:84 where d in in USCS ð20-48bÞ k sz ¼ d 0:25 1:89 where d in mm SI ð20-48cÞ  ds ¼  e n a k sz ¼ 0:335 e n a d 0:25 SI ð20-49aÞ where  e in MPa and d in m  ds ¼  e n a k sz ¼ 0:84 e n a d 0:25 USCS ð20-49bÞ where  e in psi and d in in TABLE 20-8 Spring design stress,  d , MPa (kpsi) Severe service Average service Light Wire diameter, mm MPa kpsi MPa kpsi MPa kpsi 2.15 413.8 60 517.3 75 641.4 93 2.15–4.70 379.0 55 476.6 69 585.4 85 4.70–8.10 331.0 48 413.8 60 510.0 74 8.10–13.45 289.3 42 358.4 52 448.2 65 13.45–24.65 248.1 36 310.4 45 385.9 56 24.65–38.10 220.6 32 275.6 40 344.7 50 TABLE 20-9 Factors for helical springs with wires of rectangular cross section Ratio b=h ¼ m 11.21.52.02.535101 Factor k 0.416 0.438 0.462 0.492 0.516 0.534 0.582 0.624 0.666 Factor k 2 0.180 0.212 0.250 0.292 0.317 0.335 0.371 0.398 0.424 Particular Formula SPRINGS 20.15 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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SPRINGS TABLE 20-10 Chemical composition and mechanical properties of spring materials Tensile properties Torsional properties of wire Analysis Ultimate strength Elastic limit Modulus of elasticity, E Ultimate strength Elastic limit Modulus in torsion, G Material Element % Mpa kpsi GPa kpsi GPa Mpsi Rockwell hardness MPa kpsi GPa kpsi GPa Mpsi Chief uses Flat Cold-rolled Spring Steel Watch spring steel C 1.10–1.19 2274–2412 330–350 2.14–2.28 310–330 220 32 C55–55 Not used Not used Not used Main springs for watches Mn 0.15–0.25 and similar uses Clock spring steel Clock and motor springs, AS 100 C 0.90–1.05 1240–2343 180–340 1.03–2.14 150–310 207 30 C40–52 Not used Not used Not used miscellaneous flat springs SAE 1095 Mn 0.20–0.50 for high stress Flat spring steel AS 101 C 0.65–0.80 1103–2206 160–320 0.86–1.93 125–280 207 30 Annealed, B70–85 Not used Not used Not used Miscellaneous flat springs SAE 1074 Mn 0.50–0.90 tempered C38–50 Carbon Steel Wires High–carbon wire C 0.85–0.95 1382–1725 200–250 1.10–1.45 160–210 207 30 C44–48 1103 160–200 0.76 110–150 79 11.5 High-grade helical springs AS 8 Mn 0.25–0.60 1377 1.03 or wire forms Oil-tempered wire (ASTM A229–41) C 0.60–0.70 1068–2059 155–300 0.83–1.73 120–250 794 115–200 0.55 80–130 General spring use AS10 Mn 0.60–0.90 200 29 C42–46 1377 0.90 79 11. 5 Music wire (ASTM A228–47) C 0.70–1.00 1725–3790 250–500 1.03–2.41 1 50–350 1034 150–300 0.62 90–180 79 11.5 Miscellaneous small AS 5 Mn 0.30–0.60 207 30 2069 1.24 82 12.0 springs of various types— depending high quality on size Hard-drawn spring wire (ASTM A227–47) C 0.60–0.70 1034–2068 150–300 0.69–1.38 100–200 828 120–220 0.51 75–130 Same uses as music wire AS 20 Mn 0.90–1.20 200 29 1515 0.90 79 11.5 but lower-quality wire Hot-rolled Special Steel Hot-rolled bars SAE 1095, C 0.90–1.05 1206–1377 175–200 0.73–0.97 105–140 760 110–140 0.51 75 Hot-rolled heavy coil or ASTM A14–42 Mn 0.25–0.50 196 28.5 C40–46 965 0.76 110 72 10.5 flat springs Alloy and Stainless Spring Materials Chrome-vanadium C 0.45–0.55 1377 200–250 1.24 180–230 965 0.69 100–130 alloy steel Mn 0.50–0.80 207 30 C42–48 140–175 79 11.5 Cold–rolled or drawn: (SAE 6150) Cr 0.80–1.10 1725 1.58 1206 0.90 special applications AS 32 V 0.15–0.18 Silico-manganese C 0.55–0.65 alloy steel Mn 0.60–0.90 Used as a lower–cost (SAE 9260) Si 1.80–2.20 About the same as chrome vanadium About the same as chrome vanadium material in place of Type 18–8 stainless C 17–20 1103 160–330 0.41 60–260 chrome vanadium (Type 302, Ni 7–10 193 28 C35–45 828 120–240 0.31 45–140 SAE 30915) C 0.08–0.15 2275 1.79 69 10 Best corrosion resistance, Mn 2 max 1653 0.97 fair temperature Si 0.30–0.75 resistance 20.16 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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SPRINGS Cutlery-type stainless Cr 12–14 1171 170–250 0.90 130–200 828 120–180 0.55 80–120 76 Resists corrosion when (Type 420) C 0.25–0.40 1725 1.38 193 28 C42–47 1240 0.83 11 polished; good temperature resistance Nonferrous Spring Materials Spring brass For electrical AS 55 Cu 64–74 691 100–130 0.27 308 45–90 0.21 30–60 conductivity at low AS 155 Zn balance 897 0.41 107 15 B90 622 0.41 38 5.5 stresses; for corrosion resistance Nickel silver Cu 56 897 130–150 0.55 80–110 588 85–100 0.41 60–70 Used for its color; Zn 25 1034 0.76 110 16 B95–100 691 0.48 38 5.5 corrosion resistance Ni 18 Phosphor bronze Cu 91–93 691 100–150 0.41 60–110 AS 60 Sn 7–9 554 0.35 Used for corrosion AS 160 or 103 15 B90–100 80–105 50–85 43 6.25 resistance and electrical Cu 94–96 102 0.76 725 0.59 conductivity Sn 4–6 Nonferrous Spring Materials Silicon bronze (made Si 2–3 under various trade Sn or Small Used as substitute for names) Mn amounts Properties similar to those of phosphor bronze Properties similar to those of phosphor bronze phosphor bronze AS 46 Cu balance AS 146 Monel Ni 64 691 100–140 0.55 80–120 519 75–110 0.31 45–70 Resists corrosion; AS 40 Cu 26 964 0.83 179 26 C23–28 760 0.48 65 9.5 moderate stresses to AS 140 Mn 2.5 204.58C Fe 2.25 Inconel Ni 80 965 140–175 0.76 110–135 651 95–120 0.38 55–80 Resists corrosion; high AS 40 Cr 14 1206 0.93 213 31 C30–40 828 0.55 76 11 stresses to 3438C AS140 Fe Balance K–Monel Ni 66 1103 160–180 0.79 115–145 725 105–125 0.45 65–85 Resists corrosion; high AS 40 Cr 29 1241 1.00 179 26 C33–40 862 0.58 65 9.5 stresses to 2328C AS 140 Al 2.75 Fe 0.90 Z–nickel Ni 98 1241 0.90 828 0.41 Cu 180–230 130–170 207 30 C36–46 120–150 60–90 76 11 Resists corrosion; high Mn Small 1583 1.17 1034 0.68 stresses to 2888C Fe amounts Si Beryllium-coppcr Cu 98 1103 160–200 0.69 100–150 110 16–18.5 691 100–130 0.45 65–95 41 6–7 Corrosion resistance like AS 45 Be 2 1377 1.03 127 Subject to C35–42 897 0.66 48 copper; high physical AS 145 heat Subject to properties for electrical treatment heat work; low hysteresis treatment Note: The property values given in this table do not specify the minimum properties. Source: Handbook of Mechanical Spring Design, courtesy Associated Spring, Barnes Group Inc., Bristol, Connecticut. 20.17 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. SPRINGS TABLE 20-11 Free-length tolerances of squared and ground helical compression springs a Tolerances: Æmm/mm (in/in) of free length Spring index (D=d) Number of active coilspermm(in)46810121416 0.02 (0.5) 0.010 0.011 0.012 0.013 0.015 0.016 0.016 0.04 (1) 0.011 0.013 0.015 0.016 0.017 0.018 0.019 0.08 (2) 0.013 0.015 0.017 0.019 0.020 0.022 0.023 0.2 (4) 0.016 0.018 0.021 0.023 0.024 0.026 0.027 0.3 (8) 0.019 0.022 0.024 0.026 0.028 0.030 0.032 0.5 (12) 0.021 0.024 0.027 0.030 0.032 0.034 0.036 0.6 (16) 0.022 0.026 0.029 0.032 0.034 0.036 0.038 0.8 (20) 0.023 0.027 0.031 0.034 0.036 0.038 0.040 a For springs less than 12.7 mm (0.500 in) long, use the tolera nces for 12.7 mm (0.500 in). For closed ends not ground, multiply above values by 1.7. Source: Associated Spring, Barnes Group Inc., Bristol, Connecticut. TABLE 20-12 Coil diameter tolerances of helical compression and extension springs Tolerances: Æmm (in) Spring index ðD=dÞ Wire diameter, mm (in) 4 6 8 10 12 14 16 0.38 0.05 0.05 0.08 0.10 0.13 0.15 0.18 (0.015) (0.002) (0.002) (0.003) (0.004) (0.005) (0.006) (0.007) 0.58 0.05 0.08 0.10 0.15 0.18 0.20 0.25 (0.023) (0.002) (0.003) (0.004) (0.006) (0.007) (0.008) (0.010) 0.89 0.05 0.10 0.15 0.18 0.23 0.28 0.33 (0.035) (0.002) (0.004) (0.006) (0.007) (0.009) (0.011) (0.013) 1.30 0.08 0.13 0.18 0.25 0.30 0.38 0.43 (0.051) (0.003) (0.005) (0.007) (0.010) (0.012) (0.015) (0.017) 1.93 0.10 0.18 0.25 0.33 0.41 0.48 0.53 (0.076) (0.004) (0.007) (0.010) (0.013) (0.016) (0.019) (0.021) 2.90 0.15 0.23 0.33 0.46 0.53 0.64 0.74 (0.114) (0.006) (0.009) (0.013) (0.018) (0.021) (0.025) (0.029) 4.34 0.20 0.30 0.43 0.58 0.71 0.84 0.97 (0.171) (0.008) (0.012) (0.017) (0.023) (0.028) (0.033) (0.038) 6.35 0.28 0.38 0.53 0.71 0.90 1.07 1.24 (0.250) (0.011) (0.015) (0.021) (0.028) (0.035) (0.042) (0.049) 9.53 0.41 0.51 0.66 0.94 1.17 1.37 1.63 (0.375) (0.016) (0.020) (0.026) (0.037) (0.046) (0.054) (0.064) 12.70 0.53 0.76 1.02 1.57 2.03 2.54 3.18 (0.500) (0.021) (0.030) (0.040) (0.062) (0.080) (0.100) (0.125) Source: Associated Spring, Barnes Group Inc., Bristol, Connecticut. 20.18 CHAPTER TWENTY Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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SPRINGS TABLE 20-13 Load tolerances of helical compression springs Tolerance: Æ% of load, start with tolerance from Table 20-11 multiplied by L F Deflection from free length to load, mm (in) Length tolerance Æ 1.27 2.54 3.81 5.08 6.35 7.62 10.2 12.7 19.1 25.4 38.1 50.8 76.2 102 152 mm (in) (0.050) (0.100) (0.150) (0.200) (0.250) (0.300) (0.400) (0.500) (0.750) (1.00) (1.50) (2.00) (3.00) (4.00) (6.00) 0.13 (0.005) 12 7 6 5 — — — — — — ————— 0.25 (0.010) — 12 8.5 7 6.5 5.5 5 — — — ————— 0.51 (0.020) — 22 15.5 12 10 8.5 7 6 5 — ————— 0.76 (0.030) — — 22 17 14 12 9.5 8 6 5 ————— 1.0 (0.040) — — — 22 18 15.5 12 10 7.5 6 5 ———— 1.3 (0.050) — — — — 22 19 14.5 12 9 7 5.5 ———— 1.5 (0.060) — — — — 25 22 17 14 10 8 6 5 — — — 1.8 (0.070) — — — — — 25 19.5 16 11 9 6.5 5.5 — — — 2.0 (0.080) — — — — — — 22 18 12.5 10 7.5 6 5 — — 2.3 (0.090) — — — — — — 25 20 14 11 8 6 5 — — 2.5 (0.100) — — — — — — — 22 15.5 12 8.5 7 5.5 — — 5.1 (0.200) — — — — — — — — — 22 15.5 12 8.5 7 5.5 7.6 (0.300) — — — — — — — — — — 22 17 12 9.5 7 10.2 (0.400) — — — — — — — — — — — 21 15 12 8.5 12.7 (0.500) — — — — — — — — — — — 25 18.5 14.5 10.5 First load test at not less than 15% of available deflection; final load test at not more than 85% of available deflection. Source: Associated Spring, Barnes Group Inc., Bristol, Connecticut. TABLE 20-14 Equations for springs with different types of ends 2,3 Particular Active coils, ii 0 i 0 À 1 2 i 0 À 2 i 0 À 2 Total coils, i 0 l o À d p l o p l o À 3d p l o À 2d p þ 2 Free length, l o or l f ip þ dip ipþ 3dipþ 2d Pitch, p l o À d i 0 l o i 0 l o À 3d i 0 l o À 2d i 0 Solid height, hdði 0 þ 1Þ dði 0 þ 1 2 Þ dði 0 þ 1Þ i 0 d Source: K. Lingaiah and B. R. Narayana Iyengar, Machine Design Data Handbook, Vol. I, Suma Publishers, Bangalore, India, 1986, and K. Lingaiah, Machine Design Data Handbook, Vol. 11, Suma Publishers, Bangalore, India, 1986. SPRINGS 20.19 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. SPRINGS The actual factor of safety or reliability factor The wire diameter for static loading The wire diameter where there is no space limitation ðD ¼ cdÞ  ds ¼  e n a k sz ¼ 1:89 e n a d 0:25 Metric ð20-49cÞ where  e in kgf/mm 2 and d in mm where n a ¼ actual factor of safety or reliability factor n a ¼ FðcompressedÞ FðworkingÞ ð20-50aÞ n a ¼ free length À fully compressed length free length À working length ¼ y þa y ð20-50bÞ where y is deflection under working load, m (mm), a is the clearance which is to be added when determining the free length of the spring and is made equal to 25% of the working deflection Generally n a is chosen at 1.25. d ¼ 1:445  6n a F  e  0:4 D 0:3 ¼ 2:945  n a F  e  0:4 D 0:3 SI ð20-51aÞ where F in N,  e in MPa, D in m, and d in m d ¼ 0:724  6n a F  e  0:4 D 0:3 ¼ 1:48  n a F  e  0:4 D 0:3 Metric ð20-51bÞ where F in kgf,  e in kgf/mm 2 , D in mm, and d in mm d ¼  6n a F  e  0:4 D 0:3 ¼ 2:05  n a F  e  0:4 D 0:3 USCS ð20-51cÞ where F in lbf,  e in psi, D in in, and d in in d ¼ 4:64  n a F  e  0:57 c 0:43 SI ð20-51dÞ where d in m, F in N,  e in Pa d ¼  6n a F  e  0:57 c 0:43 USCS ð20-51eÞ where d in in, F in lbf,  e in psi TABLE 20-15 Curvature factor k c c 34678910 k c 1.35 1.25 1.15 1.13 1.11 1.1 1.09 Particular Formula 20.20 CHAPTER TWENTY Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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SPRINGS Final dimensions (Fig. 20-7d) The number of active coils The minimum free length of the spring Outside diameter of cod of helical spring Solid length (or height) of helical spring Pitch of spring Free length of helical spring l f or l o Maximum working length of helical spring Minimum working length of helical spring Springs with different types of ends 1;2;3 STABILITY OF HELICAL SPRINGS The critical axial load that can cause buckling d ¼ 1:77  n a F  e  0:57 c 0:43 Metric ð20-51fÞ where d in mm, F in kgf,  e in kgf/mm 2 i ¼ yd 4 G 8FD 3 ¼ ydG 8Fc 3 ¼ kydG D 2 ð20-52Þ l f !ði þ nÞd þy þ a ð20-53Þ where a ¼ clearance, m (mm) n ¼ 2 if ends are bent before grinding ¼ 1 if ends are either ground or bent ¼ 0 if ends are neither ground nor bent D o ¼ D þ d ð20-53aÞ l s ¼ i t d ð20-53bÞ p ¼ y s i þ d ð20-53cÞ l f À l s þ y s ð20-53dÞ l max ¼ l f À y max ð20-53eÞ l min ¼ l f À y min ð20-53fÞ where i t ¼ total number of coild in the spring Refer to Table 20-14. F cr ¼ F o K l l f ð20-54Þ where K l is factor taken from Fig. 20-8 Particular Formula FIGURE 20-8 Buckling factor for helical compression springs. (V. L. Maleev and J. B. Hartman, Machine Design, International Textbook Company, Scranton, Pennsylvania, 1954.) SPRINGS 20.21 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. SPRINGS The equivalent stiffness of springs The critical load on the spring The critical deflection is explicitly given by REPEATED LOADING (Fig. 20-9) The variable shear stress amplitude The mean shear stress Design equations for repeated loadings 1;2;3 Method 1 The Gerber parabolic relation ðEIÞ spring ¼ Ed 4 l 32iDð2 þvÞ ð20-55Þ F cr ¼  2 Ed 4 32ð2 þvÞiDðl f À y cr Þ ð20-56Þ  y cr l f  2 À y cr l f þ  2 2 1 þv 2 þv  D l f  2 ¼ 0 ð20-57Þ where l ¼ðl f À y cr Þ  a ¼ k w 8D d 3 F max À F min 2 ð20-58Þ where k w ¼ k  k c Refer to Table 20-15 for k c .  m ¼ k  8D d 3 F max þ F min 2 ð20-59Þ where k  ¼ 1 þ 0:5=c  a  od þ   m  ud  2 ¼ 1 ð20-60Þ Particular Formula FIGURE 20-9 Cyclic stresses in spring. (K. Lingaiah and B. R. Narayana Iyengar, Machine Design Data Handbook, Engineering College Cooperative Society, Bangalore, India, 1962; K. Lingaiah and B. R. Narayana Iyengar, Machine Design Data Handbook, Vol. I, Suma Publishers, 1986; K. Lingaiah, Machine Design Data Handbook, Vol. II, Suma Publishers, Bangalore, India, 1986.) 20.22 CHAPTER TWENTY 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. SPRINGS The Goodman straight-line relation The Soderberg straight-line relation Method 2 The static equivalent of cyclic load F m Æ F a The relation between  e and  f for brittle material The static equivalent of cyclic load for brittle material The relation between F 0 m , F max and F min The diameter of wire for static equivalent load The wire diameter when there is no space limitation ðD ¼ cdÞ  a  od þ  m  ud ¼ 1 ð20-61Þ  a  od þ  m  yd ¼ 1 ð20-62Þ F 0 m ¼ F m þ  sd  o F a ð20-63aÞ or F 0 m ¼ F m þ  sd  fd F a ð20-63bÞ  e ¼ 2 f ð20-64Þ F 0 m ¼ F m þ 2F a ð20-65Þ F 0 m ¼ 1 2 ð3F max À F min Þð20-66Þ d ¼ 1:45  3n a ð3F max À F min Þ  e  0:4 D 0:3 SI ð20-67aÞ where F in N,  e in MPa, D in m, and d in m d ¼  3n a ð3F max À F min Þ  e  0:4 D 0:3 USCS ð20-67bÞ where F in lbf,  e in psi, D in in, and d in in d ¼ 0:724  3n a ð3F max À F min Þ  e  0:4 D 0:3 Metric ð20-67cÞ where F in kgf,  e in kgf/mm 2 , D in mm, and d in mm d ¼ 1:67  3n a ð3F max À F min Þ  e  0:57 c 0:43 SI ð20-68aÞ where F in N,  e in MPa, and d in m d ¼  3n a ð3F max À F min Þ  e  0:57 c 0:43 USCS ð20-68bÞ where F in lbf,  e in psi, and d in in d ¼ 0:64  3n a ð3F max À F min Þ  e  0:57 c 0:43 Metric ð20-68cÞ where F in kgf,  e in kgf/mm 2 , and d in mm Particular Formula SPRINGS 20.23 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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SPRINGS [...]... bar Rectangular bar a a a b=h k0 k01 k02 1.0 1.2 1.5 2.0 2.5 3.0 4.0 5.0 10.0 1 0.675 0.7 59 0.848 0 .93 0 0 .96 8 0 .98 5 0 .99 7 0 .99 9 1.000 1.000 0.140 0.166 0. 196 0.2 29 0.2 49 0.263 0.281 0. 291 0.312 0.333 0.208 0.2 19 0.231 0.246 0.258 0.267 0.282 0. 291 0.231 0.333 Values of k01 and k02 can be obtained from Table 20 -9 TABLE 20-18 Suggested allowable working stresses for rubber compression springs Limits of... 0.678 0.700 0. 496 0.520 0.554 0.575 0.605 0.624 0.650 0.667 0. 690 0.705 0.726 0.520 0.544 0.5 79 0.600 0.630 0.6 49 0.676 0. 692 0.715 0.730 0.750 0.542 0.567 0.602 0.624 0.654 0.673 0. 699 0.715 0.738 0.752 0.772 0.564 0. 590 0.624 0.646 0.676 0. 695 0.721 0.737 0.7 59 0.773 0. 793 0.585 0.610 0.645 0.667 0. 697 0.715 0.741 0.757 0.7 79 0. 792 0.811 0.502 0.553 0.684 0.705 0.735 0.753 0.777 0. 792 0.813 0.825... of  90 100 110 120 130 140 150 160 170 180 200 0.28 0.30 0.33 0.35 0.38 0.40 0.43 0.45 0.48 0.50 0.53 0.356 0.376 0.404 0.423 0.4 49 0.467 0. 491 0.507 0.5 29 0.544 0.565 0.387 0.408 0.438 0.457 0.485 0.502 0.528 0.544 0.567 0.582 0.603 0.416 0.438 0.4 69 0.4 89 0.518 0.536 0.562 0.5 79 0.602 0.617 0.638 0.444 0.467 0. 499 0.520 0.5 49 0.567 0. 593 0.610 0.634 0.6 49 0.670 0.470 0. 494 0.527 0.548 0.578 0. 597 ... 11.2 13.7 15 .9 — 1 09. 8 134.4 155 .9 — 20.4 27.2 34.0 — 200.1 266.7 333.4 15 8 — 23.0 28.0 32.7 — 225.6 274.0 320.7 Direction Belt designation B 6 .9 10.8 — — — 6 .9 kN/ m 0.7 1.1 — — — 0.7 kgf/ mm — 14.8 18.0 21.1 — 145.1 176.5 206 .9 — 29. 5 36.3 43.1 — 2 89. 3 356.0 422.7 15 8 — 32.1 39. 3 45.7 — 314.8 385.4 448.2 A 1B B 8.8 12.7 — — — 8.8 kN/ m B — 21.3 26.1 — — 2 09. 9 255.0 — — 90 .8 113.4 — — 890 .4 1112.1... Weight of fabric per square meter Warp Weft Type of fabric N/m2 kgf/m2 N/m kgf/mm N/m kgf/mm Soft Hard Soft Hard 8.0 8.8 9. 1 3.6 0.815 0 .90 0 0 .93 0 0 .97 5 61, 291 .3 61, 291 .3 69, 626 .9 73,5 49. 7 6.25 6.25 7.10 7.50 29, 4 19. 8 35,303.8 32,361.8 44,1 29. 7 3.00 3.60 3.30 4.50 Source: IS 1370, 196 5 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill... 378.5 461 .9 5 39. 4 A 1C TABLE 21-12 Properties of ply woven fire-resistant conveyor belting for use in coal mines B 1.4 2.3 — — — 1.2 kgf/ mm 25.5 25.5 — — — — kN/ m 21.4 27 .9 34.4 — 2 09. 9 273.6 333.4 — 90 .8 117 .9 1 49. 7 — 890 .4 1156.2 1468.0 — 17 18 39. 3 51.1 62.2 — 385.4 501.1 610.0 — A 2C 2.6 2.6 — — — — kgf/ mm — 57.2 87.7 — — 560 .9 860.0 — A 3A 28.4 28.4 — — — 13.7 kN/ m — 21.4 26.1 — — 2 09. 9 256.0... — — — — — — B 2 .9 2 .9 — — — 1.4 kgf/ mm 30.4 30.4 — — — — 3.1 3.1 — — — — B 33.3 33.3 — — — 15.7 kN/ m 3.4 3.4 — — — 1.6 kgf/ mm 89. 3 28.6 116.1 37.2 141.1 45.0 — — 875.7 280.5 1138.5 364.8 1383.7 441.3 — — — — — — — — — — — A 3C kgf/ mm 21.4 27 .9 34.0 — 2 09. 9 273.6 333.4 — — — — — — — — — — B kN/ m 62.5 81.3 99 .1 — 612 .9 797 .3 97 1.8 — A 3B FLEXIBLE MACHINE ELEMENTS 21.13 FLEXIBLE MACHINE ELEMENTS... Delhi, 197 5 13 Lingaiah, K., Machine Design Data Handbook of Machine Design, 2nd edition, McGraw-Hill Publishing Company, New York, 199 6) 14 Shigley, J E., and C R Mischke, Standard Handbook of Machine Design, 2nd edition, McGraw-Hill Publishing Company, New York, 199 6 BIBLIOGRAPHY Baumeister, T., ed., Marks’ Standard Handbook for Mechanical Engineers, McGraw-Hill Book Company, New York, 197 8 Black,... Black, P H., and O Eugene Adams, Jr., Machine Design, McGraw-Hill Book Company, New York, 196 8 Bureau of Indian Standards Chironis, N P., Spring Design and Application, McGraw-Hill Book Company, 196 1 Norman, C A., E S Ault, and I F Zarobsky, Fundamentals of Machine Design, The Macmillan Company, New York, 195 1 Shigley, J E., Machine Design, McGraw-Hill Book Company, 196 2 Downloaded from Digital Engineering... factor KP for flat beltsa Small-pulley diameter, in Material 1.6–4 4.5–8 9 12.5 14, 16 18–31.5 >31.5 Leather polyamide, F-0 F-1 F-2 A-2 A-3 A-4 A-5 0.5 0 .95 0.70 0.73 0.73 — 0.6 1.0 0 .92 0.86 0.86 0.70 — 0.7 1.0 0 .95 0 .96 0 .96 0.87 0.71 — 0.8 1.0 1.0 1.0 1.0 0 .94 0.80 0.72 0 .9 1.0 1.0 1.0 1.0 0 .96 0.85 0.77 1.0 1.0 1.0 1.0 1.0 1.0 0 .92 0 .91 a Average values of KP for the given ranges were approximated from . 20 -9. TABLE 20-17 Factors for computing rectangular bars in torsion b=hk 0 k 0 1 k 0 2 1.0 0.675 0.140 0.208 1.2 0.7 59 0.166 0.2 19 1.5 0.848 0. 196 0.231 2.0 0 .93 0 0.2 29 0.246 2.5 0 .96 8 0.2 49 0.258 3.0. 0.848 0. 196 0.231 2.0 0 .93 0 0.2 29 0.246 2.5 0 .96 8 0.2 49 0.258 3.0 0 .98 5 0.263 0.267 4.0 0 .99 7 0.281 0.282 5.0 0 .99 9 0. 291 0. 291 10.0 1.000 0.312 0.231 1 1.000 0.333 0.333 TABLE 20-18 Suggested. 1034 0.76 110 16 B95–100 691 0.48 38 5.5 corrosion resistance Ni 18 Phosphor bronze Cu 91 93 691 100–150 0.41 60–110 AS 60 Sn 7 9 554 0.35 Used for corrosion AS 160 or 103 15 B90–100 80–105 50–85