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CHAPTER 24 MISCELLANEOUS MACHINE ELEMENTS 2,3 24.1 CRANKSHAFTS 2,3 SYMBOLS A area of cross section, m 2 (in 2 ) b width of crank cheek, m (in) c distance from the neutral axis of section to outer fiber, m (in) d diameter (also suffixes), m (in) d e equivalent diameter, m (in) d o diameter of crankpin, m (in) d m diameter of main bearing, m (in) E modulus of elasticity, GPa (psi) F force acting on the piston due to steam or gas pressure corrected for inertia effects of the piston and other reciprocating parts, kN (lbf) F c the component of force F acting along the axis of connecting rod, kN (lbf) F comb combined force, kN (lbf) F ic magnitude of inertia force due to the weight of connecting rod itself, kN (lbf) F r total radial force acting on the crankpin, kN (lbf) F total tangential force acting on the crankpin, kN (lbf) G modulus of rigidity, GPa (psi) h thickness of cheek or web (also with suffixes), m (in) i 0 ¼ l o d o ratio of length to diameter of crank I moment of inertia, m 4 ,cm 4 (in 4 ) K ¼ D i D o ratio of inner to outer diameter of a hollow shaft K b numerical combined shock and fatigue factor to be applied to the computed bending moment K t numerical combined shock and fatigue factor to be applied to the computed twisting moment l length (also with suffixes), m (in) l e equivalent length, m (in) M b bending moment, N m (lbf in) 24.1 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. Source: MACHINE DESIGN DATABOOK M t twisting moment, N m (lbf in) p allowable pressure, MPa (psi) r radius, throw of crankshaft, m (in) Z section modulus, m 3 ,cm 3 (in 3 ) normal stress (also with suffixes), MPa (psi) shear stress, MPa (psi) SUFFIXES b bending c compressive comb combined e elastic m main max maximum r radial ra resultant in arm rh resultant in hub t torque s shaking tangential Other factors in performance or special aspects which are included from time to time in this chapter and are applicable only in their immediate context are not given at this stage. FORCE ANALYSIS (Fig. 24-1) The radial component of force F c acting along the axis of connecting rod (Fig. 24-1) The tangential component of force F c acting along the axis of connecting rod (Fig. 24-1) The radial component of force F ic (Fig. 24-1) The tangential component of force F ic (Fig. 24-1) The total radial force acting on the crank F c1 ¼ F c cosð þÞ¼ F ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 À sin n 0 2 s cosð þÞ ð24-1Þ F c2 ¼ F c sinð þÞ¼ F ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 À sin n 0 2 s sinð þÞ ð24-2Þ F ic1 ¼ 2 3 F ic cos ð24-3Þ where ¼ angle between the force F ic and the radial component of F ic F ic2 ¼ 2 3 F ic sin ð24-4Þ F r ¼ F ic1 Æ F c1 ð24-5Þ F r ¼ 2 3 F ic cos Æ F c cosð þÞð24-6Þ Particular Formula 24.2 CHAPTER TWENTY-FOUR 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. MISCELLANEOUS MACHINE ELEMENTS The total tangential force acting on the crank The resultant force on the crankpin SIDE CRANK Crankpin The maximum bending moment on the crankpin (Fig. 24-2) The crankpin diameter with respect to the bending moment The diameter of crankpin from the consideration of bearing pressure From Eqs. (24-10) and (24-11) neglecting t=2 and eliminating l o the equation for crankpin diameter Empirical relation to determine the length of crankpin F ¼ F ic2 Æ F c2 ¼ 2 3 F ic sin Æ F c sinð þÞð24-7Þ F comb ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 2 r þ F 2 q ð24-8Þ M bðmaxÞ ¼ F comb  l o 2 þ t 2 ð24-9Þ ¼ F comb  l where l ¼ l o 2 þ c 2 ¼ distance from centroidal axis to the application of load (Fig. 24-2), m (in) d o ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32lF comb b s ð24-10Þ where b ¼ allowable bending stress, MPa (psi) d o ¼ F comb l o p ð24-11Þ d o ¼ 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16F 2 comb p b s ð24-12Þ l o ¼ i 0 d o ð24-13Þ where i 0 ¼ l o d o ¼ 1:25 to 1.5 Particular Formula r F c 1 3 (θ + φ) θ α φ γ F c1 F i l F r = F ic1 – F c1 l F c2 F ic2 F ic1 F ic F c F s F (a) (b) Shaking force diagram F FIGURE 24-1 (a) Forces acting on crankshaft. (b) Vector sum of F and F r . c 2 Arm -x Neutral axis of arm h xxx l h 2 h 1 l m l 1 b 1 b 1 = 1.5 d 0 l 0 = 1.25 d 0 d 1 = 2 d 0 h 1 = 1.4 d 0 h 2 = 1.4 d d 2 = 1.75 d b 2 = 1.35 d d 1 d 2 d m b 2 r 1 l o d o r c 1 F comb FIGURE 24-2 Overhung built-up crank. MISCELLANEOUS MACHINE ELEMENTS 24.3 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. MISCELLANEOUS MACHINE ELEMENTS Another relation for the crankpin length/diameter ratio Another relation for the crankpin diameter HOLLOW CRANKPIN The crankpin length/diameter ratio The crankpin outside diameter Crank arm CRANK ON HEAD-END DEAD-CENTER POSITION When the crank is on the head-end dead-center posi- tion, the section XX (Fig. 24-2) of the arm is subjected to bending moment The direct compressive stress due to the load F comb (i.e., more specifically by its component F c ) The resultant stress in the crank arm at XX CRANK ON CRANK-END DEAD-CENTER POSITION The direct tensile stress in the plane of the hub of crankshaft section passing through the shaft center due to load F comb (Fig. 24-2) The bending stress in the section due to bending moment F comb  a i 0 ¼ l o d o ¼ ffiffiffiffiffiffiffiffiffiffiffi 0:2 b p s ð24-14Þ d o ¼ ffiffiffiffiffiffiffiffiffiffiffi F comb i 0 p s ð24-15Þ i 0 ¼ l o D o ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:2ð1 ÀK 4 Þ p s ð24-16Þ where K ¼ D i D o D o ¼ ffiffiffiffiffiffiffiffiffiffiffi F comb i 0 p s ð24-17Þ M b ¼ F comb  l ð24-18Þ c ¼ F comb A ð24-19Þ ra ¼ F comb A Æ M bC I ð24-20Þ where A ¼ area of cross section of the arm at XX,m 2 (in 2 ) c ¼ distance from the neutral axis of section to outer fiber of arm, m (in) I ¼ moment of inertia of the section, cm 4 (in 4 ) t ¼ F comb h 2 ðd 2 À dÞ ð24-21Þ b ¼ F comb  a Z ð24-22Þ where Z ¼ section modulus, cm 3 (in 3 ) Particular Formula 24.4 CHAPTER TWENTY-FOUR 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. MISCELLANEOUS MACHINE ELEMENTS The resultant stress in the plane of the hub of crank- shaft section passing through the shaft center CRANK PERPENDICULAR TO THE CONNECTING ROD The bending moment in the plane of rotation of the crank The bending stress The torsional moment The shear stress The maximum normal stress for crank made of cast iron The maximum shear stress for the crank made of steel DIMENSION OF CRANKSHAFT MAIN BEARING (Fig. 24-2b) The shaking force on the main bearing from F and F r (Fig. 24-1b) The diameter of main bearing taking into considera- tion the bearing pressure on the projected area of the crankshaft The bending movement on the crankshaft The torque on the crankshaft The diameter of crankshaft taking into consideration indirectly the fatigue and shock factors r ¼ t Æ b ð24-23Þ M b ¼ F comb  l ð24-24Þ b ¼ M b c 1 Z b ð24-25Þ M t ¼ F comb  r 1 ð24-26Þ ¼ M t c 1 Z t ð24-27Þ max ¼ 1 2 b þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 b þ 4 2 q hi ð24-28Þ max ¼ 1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 b þ 4 2 q ð24-29Þ F s ¼ vector sum of F and F r ð24-30Þ d m ¼ F s l m p ð24-31Þ where l m ¼ length of bearing, m (in) p ¼ allowable bearing pressure, MPa (psi) M b ¼ F comb  l 1 ð24-32Þ l 1 ¼ l o 2 þ h 2 þ l m 2 where h 2 ¼ hub length, m (in) l o ¼ length of crankpin, m (in) l m ¼ length of bearing on crankshaft, m (in) M t ¼ F comb  r ð24-33Þ where r ¼ throw of the crank, m (in) d m ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16 e K b M b þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðK b M b Þ 2 þðK t M t Þ 2 q s ð24-34Þ Particular Formula MISCELLANEOUS MACHINE ELEMENTS 24.5 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. MISCELLANEOUS MACHINE ELEMENTS The length of main bearing PROPORTIONS OF CRANKSHAFTS For proportions of crankshaft l m ¼ F s d m p ð24-35Þ Refer to Figs. 24-2 to 24-10. Particular Formula K 1.4d 0 1.1d 1 d 0 1.8d 1 d 1 FIGURE 24-3 Overhung built-up crank. d o d 3 h 1 h 2 h d o d 1 d 2 d L D t FIGURE 24-5 Disk crank. I I e FIGURE 24-7 Equivalent length of crankshaft. 0.8 to 1.1d o 0.5 to 0.9d o Throw 2 to 2.5d 1.1 to 1.2d d o d FIGURE 24-4 Overhung forged crank. Center of bearing r = Center of bearing b F comb 12mm L 2 12mm l o hh 22 d o c d m d m l m l m FIGURE 24-6 Center crank (American Bureau of Shipping method). d c d j ch e 2 h D c r D j d j b e 2 FIGURE 24-8 Center hollow crank. 24.6 CHAPTER TWENTY-FOUR 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. MISCELLANEOUS MACHINE ELEMENTS CENTER CRANK (Fig. 24-6) Crankpin The maximum bending moment treating the crankpin as a simple beam with concentrated load at the center M bc ¼ F comb ðl o þ h þ l m Þ 4 ð24-36Þ where l o ¼ length of crankpin, m (in) l m ¼ length of main bearing, m (in) h ¼ thickness of cheek, m (in) Particular Formula 0.825B + 9 0.58B 0.53 to 0.6B 31B + 9.5 All dimensions in mm 0.71 to 0.80B 0.5d 0.7B + 9.5 = d B = Cylinder bore R = 0.35B 0.06 to 0.12B FIGURE 24-9 Empirical proportion for center crank. 3.75d Throw 1.15d 0.580d d 1.5d1.5d 2.35d 3.25d0.58d 3.75d 2.1d 2.15d d d 2.25d MISCELLANEOUS MACHINE ELEMENTS 24.7 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. MISCELLANEOUS MACHINE ELEMENTS The diameter of the crankpin based on maximum bending moment M bc The diameter of crankpin based on bearing pressure between pin and the bearing Dimensions of main bearing The maximum bending moment treating the center crank as a simple beam with load concentrated at the center The twisting moment The diameter of crankshaft at main bearing taking into consideration the fatigue and shock factors The diameter of the crankshaft based on bearing pressure American Bureau of Shipping formulas for center crank The thickness h of the cheeks or webs (Fig. 24-6) The diameter of crankpins and journals (Fig. 24-6) The thickness h and the width b of crank cheeks must satisfy the conditions d o ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffi 32M bc b s ð24-37Þ where b ¼ design stress, MPa (psi) d o ¼ F comb l o p ð24-38Þ M bb ¼ F comb  l e 4 ð24-39Þ where l e ¼ equivalent length of crankshaft, m (in) M t ¼ F comb  r ð24-40Þ d m ¼ 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16 e K b M bb þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðK b M bb Þ 2 þðK t M t Þ 2 q s ð24-41Þ d m ¼ F s l m p ð24-42Þ h ¼ 0:4d to 0:6d ð24-43Þ d ¼ a 3 ffiffiffiffiffiffiffiffiffi Dpc b s ð24-44Þ where a ¼ coefficient from Table 24-1A D ¼ diameter of cylinder bore, m (in) p ¼ maximum gas pressure, MPa (psi) c ¼ distance over the crank web plus 25 mm (1.0 in) (Fig. 24-6) b ¼ allowable fiber stress, MPa (psi) bh 2 ! 0:4d 3 ð24-45aÞ b 2 h ! d 3 ð24-45bÞ Particular Formula 24.8 CHAPTER TWENTY-FOUR 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. MISCELLANEOUS MACHINE ELEMENTS EQUIVALENT SHAFTS A portion of a shaft length l and diameter d can be replaced by a portion of length l e and diameter d e The length h e equivalent to crank web The equivalent length crankshaft l e of Fig. 24-7 varies between The equivalent length of commercial crankshaft for solid journal and crankpin according to Carter (Fig. 24-8) The equivalent length of commercial crankshaft for hollow journal and crankpin according to Carter (Fig. 24-8) The equivalent length of crankshaft for solid journal and crankpin according to Wilson (Fig. 24-8) The equivalent length of crankshaft for hollow jour- nal and crankpin according to Wilson (Fig. 24-8) EMPIRICAL PROPORTIONS For empirical proportions of side crank, built-up crank, and hollow crankshafts The film thickness in bearing should not be less than the values given here for satisfactory operating condi- tion: Main bearings Big-end bearings The oil flow rate through conventional central circumferential grooved bearings l e ¼ l d e d 4 ð24-46Þ h e ¼ rC B ð24-47Þ where C ¼ 1 32 d 4 e G ¼ torsional rigidity of the crankpin B ¼ 1 12 hb 3 E ¼ flexural rigidity of the web 0:95l < l e < 1:10l ð24-48Þ L e ¼ d 4 e e þ0:8a D 4 J þ 0:75b D 4 c þ 1:5r ac 3 ð24-49Þ L e ¼ d 4 e e þ0:8a D 4 J À d 4 J þ 0:75b D 4 c À d 4 c þ 1:5r ac 3 ð24-50Þ L e ¼ d 4 e e þ0:4D J D 4 J þ b þ0:4D c D 4 c þ r À0:2ðD J þ D c Þ ac 3 ð24-51Þ L e ¼ d 4 e e þ0:4D J D 4 J À d 4 J þ b þ0:4D c D 4 c À d 4 c þ r À0:2ðD J þ D c Þ ac 3 ð24-52Þ Refer to Figs. 24-2 to 24-10. h ¼ 0:0025 mm (0.0001 in) to 0.0042 mm (0.0017 in) ð24-52aÞ h ¼ 0:002 mm (0.00008 in) to 0.004 mm (0.00015 in) ð24-52bÞ Q ¼ kpc 3 d L ð1 þ1:5" 2 Þð24-52cÞ Particular Formula MISCELLANEOUS MACHINE ELEMENTS 24.9 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. MISCELLANEOUS MACHINE ELEMENTS For oil flow rate in medium and large diesel engines at 0.35 MPa 0.5 psi The velocity of oil in ducts on the delivery side of the pump The velocity of oil in ducts on the suction side of the pump The delivery pressure in modern high-duty engines For housing tolerances where Q ¼ oil flow rate, m 3 /s (gal/min) k ¼ a constant ¼ 0:0327 SI units ¼ 4:86  10 4 US Customary System Units p ¼ oil feed pressure, Pa (psi) c ¼ D À d ¼ diametral clearance, m (in) ¼ absolute viscosity (dynamic viscosity), Pa s (cP) d ¼ bearing bore, m (in) L ¼ land width, m (in) " ¼ attitude or eccentricity ratio Refer to Table 24-1B. v ¼ 1:8 to 3.0 m/s (6 to 10 ft/s) ð24-52dÞ v ¼ 1:2m=sð4ft=sÞð24-52eÞ p ¼ 0:28 to 0.42 MPa (40 60 psi) ð24-52f Þ p max ¼ 0:56 MPa ð80 psiÞð24-52gÞ Refer to Table 24-1C. Particular Formula TABLE 24-1A Coefficient a in the American Bureau of Shipping formula [Eq. (24-44)] Number of cylinder Ratio of stroke to distance over crank webs ¼ l=c Type Four-stroke Two-stroke 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Explosion engines 1, 2, 4 1, 2 1.17 1.17 1.17 1.17 1.17 1.17 1.17 1.17 3, 5, 6 3 1.17 1.17 1.17 1.17 1.19 1.20 1.22 1.24 8 8 1.17 1.19 1.21 1.23 1.25 1.28 1.30 1.32 10, 11, 12 5, 6 1.18 1.20 1.23 1.25 1.28 1.31 1.33 1.35 Air-injection 1, 2, 4 1, 2 1.17 1.19 1.22 1.25 1.28 1.31 1.34 1.36 diesel engines 3, 5, 6 1.19 1.22 1.25 1.28 1.32 1.35 1.38 1.41 8 3 1.20 1.24 1.27 1.30 1.33 1.37 1.40 1.43 12 4 1.22 1.25 1.29 1.32 1.36 1.39 1.42 1.45 16 5, 6 1.25 1.29 1.33 1.36 1.40 1.44 1.47 1.50 8 24.10 CHAPTER TWENTY-FOUR 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. MISCELLANEOUS MACHINE ELEMENTS [...]... 20 18 26 22 32 29 36 31 40 35 45 39 51 44 57 49 62 52 67 58 74 64 3 3 5 4 6 6 8 7 10 9 13 11 14 12 16 14 18 16 20 18 23 20 25 21 27 23 30 26 15 12 20 20 30 25 35 35 45 40 55 50 60 56 70 60 80 70 85 80 100 85 110 100 120 110 130 120 11 11 11 11 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 28 26 35 35 52 47 68 60 85 78 105 95 110 105 125 110 140 125 150 140 190 150 210 190... 157 137 176 153 193 163 208 180 229 199 20 17 28 25 40 34 51 44 64 55 80 70 89 78 100 87 113 98 127 110 142 123 155 131 168 146 187 160 25 21 35 31 49 42 63 54 78 67 98 86 109 96 123 107 139 120 155 135 174 151 191 161 206 178 227 197 MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS MS HS 19 16 27 23 37 32 48 41 60 51 75 63 83 73 94 81 106 92 118 103 132 115 145 122 157 136 ... 588 35 38 50 43 69 60 89 71 111 96 140 122 156 136 176 152 198 171 221 193 248 215 271 229 293 254 324 280 27 23 38 33 53 46 68 59 85 73 107 93 119 104 134 116 151 131 169 147 189 164 207 175 224 194 247 214 39 33 55 48 76 66 98 85 122 105 154 134 171 150 193 167 217 189 243 211 272 236 298 252 323 279 356 308 34 29 48 41 66 58 85 74 106 91 134 116 149 130 168 145 189 164 211 184 236 205 259 219 280... structural efficiency; (c and d) alternate pin designs 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 MISCELLANEOUS MACHINE ELEMENTS 24.31 MISCELLANEOUS MACHINE ELEMENTS Particular Formula ð24 -130 Þ The thickness of wall under the ring... ð24 -132 aÞ SI ð24 -132 bÞ Dr ¼ D À ð2w þ 0:00D þ 0:06 inÞ at the oil grooves USCS where Dr and D in mm (in) Length L of piston L ¼ D to 1:5D For chemical composition and properties of aluminum alloy piston ð24 -133 Þ Refer to Table 24-10B Gudgeon pin The diameter of gudgeon pin sffiffiffiffiffi F dr ¼ i0 p ð24 -134 Þ where F ¼ maximum gas pressure corrected for inertia effect of the piston and other reciprocating parts,... Terms of Use as given at the website ð24 -136 aÞ ð24 -136 cÞ MISCELLANEOUS MACHINE ELEMENTS MISCELLANEOUS MACHINE ELEMENTS 24.35 Groove depth g, in 0.200 0.250 0.300 0.350 0.400 0.450 0.500 2400 2200 ALUMINIUM PISTON LAND WIDTH W TO DETERMINE LAND WIDTHS FOR PISTONS IN CAST IRON OR STEEL USE THE FOLLOWING CONSTANTS 16.0 15.0 0.600 1600 16 1400 0.550 1200 0.500 M 12 13 8 15 2 6 M N/ M m2 N/ 4 m2 11 M N/m... MISCELLANEOUS MACHINE ELEMENTS 24.16 CHAPTER TWENTY-FOUR Particular Formula F MA A F A A A B B r o r A D A B D θ B x r x (b) F 2 B MB B A F (a) FIGURE 24 -13 Bending moments in a ring The combined stress at any cross section MB B B MB MA A F FIGURE 24-14 Bending moments in a link r ¼ 1F M sin Æ b Ae 2A y rn þ y ð24-73Þ DEFLECTION The increase in the vertical diameter of the ring (Fig 24-13a) yv ¼... Use as given at the website 24.19 MISCELLANEOUS MACHINE ELEMENTS 24.20 CHAPTER TWENTY-FOUR Particular Formula The velocity 2rn 60 where r in m v¼ ð24-81Þ DESIGN OF CONNECTING ROD (Fig 24-17) Gas load Fg ¼ d2 p 4 f Fir ¼ Load due to gas or steam pressure on the piston Wv2 gr ð24-82Þ Inertia load due to reciprocating motion Inertia due to reciprocating parts and piston cos þ Fir ¼ 0:01095 Wrn2 g... ð24-94Þ MISCELLANEOUS MACHINE ELEMENTS 24.22 CHAPTER TWENTY-FOUR Particular Formula DESIGN OF SMALL AND BIG ENDS The diameter of crankpin at the big end dc ¼ F lc p ð24-95Þ where p ¼ allowable bearing pressure based on projected area, MPa (psi) ¼ 4.9 to 10.3 MPa (700 to 1500 psi), and lc ¼ 1:25 to 1:5 dc The diameter of the gudgeon pin at the small end dg ¼ F lg p ð24-96Þ where p ¼ 10.3 to 13. 73 MPa (1.2... 0.06 to 0.13B Rad 0.26 to 0.33B B = cylinder bore FIGURE 24-20 Two typical end designs for round and H-section connecting rods 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 MISCELLANEOUS MACHINE ELEMENTS F C MISCELLANEOUS MACHINE . 36 14 60 13 110 35 HS 286 136 104 150 130 104 55 M 52 97 78 96 HS 73 62 125 52 52 31 12 56 13 105 35 12.0 25 MS 369 176 134 193 168 134 70 M 68 125 100 123 MS 94 80 161 67 67 40 16 70 13 125 40 HS. 60 108 87 107 HS 81 70 139 58 58 35 14 60 13 110 35 16.0 32 MS 415 198 151 217 189 151 80 M 76 6 140 113 139 MS 106 91 181 76 76 45 18 80 13 140 44 HS 360 171 131 189 164 131 70 M 68 6 122 98 120. 36 22 9 40 13 78 26 8.0 16 MS 294 140 107 154 134 109 55 M 52 100 80 98 MS 75 64 128 54 54 32 13 55 13 105 35 HS 256 122 93 134 116 93 50 M 48 86 70 86 HS 63 56 112 46 46 29 11 50 13 95 31 10.0
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