Explanation Write the expression for diameter of pinion. d p = N p p (I) Here, the number of teeth on pinion is N P and the diametral pitch is p . Write the expression for diameter of the gear. d G = N G p (II) Here, the number of teeth on gear is N G and the diametral pitch is p . Write the expression for velocity of the pinion. V = π d p n p (III) Here, the number of rotation made by pinion is n p . Write the expression for constant of transmission accuracy level number. B = 0.25 ( 12 − Q v ) 2 3 . (IV) Here, the transmission accuracy level number is Q v . Write the expression for constant A . A = 50 + 56 ( 1 − B ) (V) Write the expression for dynamic factor. K v = ( A + V A ) B (VI) Write the expression for allowable bending stress number through hardened steels. S t = 77.3 H B + 12800 (VII) Here, the Brinel hardness number is H B . Write the expression for stress cycle factor for bending. Y N = 1.6831 ( N ) − 0.0323 (VIII) Here, the number of cycles is N . Write the expression for allowable stress. ( σ all ) = S t Y N S F K T K R (IX) Here, the reliability factor is K R , the temperature factor is is K T and the safety factor against failure is S F . Write the expression for load correction factor for uncrowned teeth. C m c = 1 . (X) Write the expression for pinion proportion factor. C p f = F 10 d − 0.0375 + 0.0125 F (XI) Here, the face width is F and the diameter is d . Write the expression for pinion proportion modifier for straddle mounted pinion. C p m = 1 (XII) Write the expression for mesh alignment factor. C m a = A + B F + C F 2 (XIII) Here, the empirical constant is A , B and C . Write the expression for mesh alignment correction factor. C e = 1 (XIV) Write the expression for load distribution factor K m . K m = 1 + C m c ( C p f C p m + C m a C e ) . (XV) Write the expression for overload factor for pinion. ( K o ) p = 1.192 ( F Y p p ) 0.0535 (XVI) Here, the Lewis form factor for pinion is Y P . Write the expression for overload factor for gear. ( K o ) G = 1.192 ( F Y G p ) 0.0535 (XVII) Here, the Lewis form factor for gear is Y G . Write the expression for transmitted load in pinion. W p t = F J p σ all ( K o ) p K v K s p K m K B (XIX) Here, the spur gear geometry factor for pinion is J P and the rim thickness factor is K B . Write the expression for power for pinion. H p = W p t V 33000 (XX) Write the expression for transmitted load for gear. W G t = F J G σ all ( K o ) G K v K s p K m K B (XXI) Here the spur gear geometry factor for gear is J G . Write the expression for power for gear. H G = W G t V 33000 (XXII) Write the expression for gear ratio. m G = N G N P (XXIII) Here, the number of teeth on gear is N G and the number of teeth on pinion is N P Write the expression for pitting resistance stress cycle factor for pinion. ( Z N ) p = 2.466 ( N ) − 0.056 (XXIV) Write the expression for pitting resistance stress cycle factor for gear. ( Z N ) G = 2.466 ( N m G ) − 0.056 (XXV) Write the expression for geometry factor. I = cos ϕ t sin ϕ t 2 m N ( m G m G + 1 ) . (XXVI) Here, the pressure angle is ϕ t . Write the expression for hardness ratio factor C H . C H = H B P H B G = 1 . (XXVII) Write the expression for contact fatigue strength for pinion. 0.99 ( S c P ) 10 7 = 322 ( H B ) + 29100 . (XXVIII) Write the expression for contact fatigue strength for gear. 0.99 ( S c G ) 10 7 = 322 ( H B ) + 29100 . (XXIX) Write the expression for pinion contact endurance strength. ( σ all ) P = 0.99 ( S c ) 10 7 ( Z N ) ( C H ) S H ( K T ) ( K R ) . (XXX) Write the expression for transmitted load. W 3 t = ( ( σ all ) p C P ) 2 F d p I K o K v ( K s ) p K m C f . (XXXI) Here, the elastic coefficient is C P . Write the expression for power of pinion. H 3 = W 3 t V 33000 (XXXII) Write the expression for gear contact strength. ( σ all ) G = S c ( Z N ) ( C H ) S H ( K T ) ( K R ) . (XXXIII) Write the expression for transmitted load. W 4 t = ( ( σ all ) G C P ) 2 F d p I K o K v ( K s ) G K m C f (XXXIV) Write the expression for power of gear. H 4 = W 4 t V 33000 (XXXV) Write the expression for rated power. H r a t e d = min ( H 1 , H 2 , H 3 , H 4 ) . (XXXVI) Conclusion: Substitute 22 teeth for N P and 4 teeth / in for p in Equation (I). d p = 22 teeth 4 teeth / in = 5.5 in Substitute 60 teeth for N P and 4 teeth / in for p in Equation (II) d G = 60 teeth 4 teeth / in = 15 in Substitute 5.5 in for d p and 1145 rpm / min for n p in Equation (III). V = π ( 5.5 in ) ( 1145 rev / min ) = π ( 5.5 in ) ( 1145 rev / min ) 12 in / ft = 19784.17 12 ft / min = 1648.68 ft / min Substitute 6 for Q v in Equation (IV). B = 0.25 ( 12 − 6 ) 2 3 = 0.25 ( 6 ) 2 3 = 0.25 × 3.3019 = 0.8255 Substitute 0.8255 for B in Equation (V). A = 50 + 56 ( 1 − 0.8255 ) = 50 + 56 ( 0.1745 ) = 50 + 9.772 = 59.772 Substitute 59.772 for A , 1648.68 ft / min for V and 0.8255 for B in Equation (VI). K v = ( 59.772 + 1648.68 59.772 ) 0.8255 = ( 59.772 + 40.603 59.772 ) 0.8255 = ( 100.375 59.772 ) 0.8255 = ( 1.679 ) 0.8255 K v = 1.53 Substitute 250 for H B in Equation (VII). S t = ( 77.3 ( 250 ) + 12800 ) psi = ( 19325 + 12800 ) psi = 32125 psi Substitute 3 ( 10 9 ) for N in Equation (VIII). Y N = 1.6831 ( 3 ( 10 9 ) ) − 0.0323 = 1.6831 ( 0.4941 ) = 0.8316 Substitute 32125 psi for S t , 0.8316 for Y N , 1 for K R , 1 for K T , 1 for S F in Equation (IX). ( σ a l l ) P = ( 32125 psi ) × 0.8316 1 × 1 × 1 = 26715.15 psi Substitute 3.25 in for F and 5.5 in for d in Equation (XI). C p f = 3.25 10 ( 5.5 ) − 0.0375 + 0.0125 ( 3.25 ) = 3.25 55 − 0.0375 + 0.04062 = 0 .059 − 0.0375 + 0.04062 = 0.06212 Refer to table 14-9, “Empirical constant A , B and C for Eq.(14-34),face width F in inches”, obtain the empirical constant A , B and C as 0.127 , 0.0158 and 0.930 × 10 − 4 . Substitute 0.127 for A , 0.0158 for B , 3.25 in for F and 0.930 × 10 − 4 for C in Equation (XIII). C m a = 0.127 + 0.0158 ( 3.25 ) − ( 0.930 × 10 − 4 ) ( 3.25 ) 2 = 0.127 + 0.05135 − ( 0

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

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ISBN: 9780077591670

Author: BUDYNAS

Publisher: MCG

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8.7 A pair of involute gears with 16° pressure angle and 6 mm module is in mesh. The number of teeth on pinion is 16 and its rotational speed is 240 r.p.m. When the gear ratio is just 1.75, find, in order that the interference is just avoided, (a) the addenda on pinion and gear wheel (b) the length of path of contact, and (d) the maximum velocity of sliding of teeth on either side of the pitch point. (DAV Indore, 1989) (Ans. a, 9.6 mm; a 4.2 mm; 35.41 mm; V = 95.58 cm/s) %3D

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Chapter 14 Solutions

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

Ch. 14 - A steel spur pinion has a pitch of 6 teeth/in, 22...Ch. 14 - A steel spur pinion has a diametral pitch of 10...Ch. 14 - Prob. 3P Ch. 14 - A steel spur pinion has 16 teeth cut on the 20...Ch. 14 - Prob. 5P Ch. 14 - A 20 full-depth steel spur pinion has 20 teeth and...Ch. 14 - A 20 full-depth steel spur pinion has a diametral...Ch. 14 - A steel spur pinion is to transmit 20 hp at a...Ch. 14 - A 20 full-depth steel spur pinion with 18 teeth is...Ch. 14 - Prob. 10P

Ch. 14 - A speed reducer has 20 full-depth teeth and...Ch. 14 - Prob. 12P Ch. 14 - Prob. 13P Ch. 14 - A 20 20-tooth cast-iron spur pinion having a...Ch. 14 - A steel spur pinion and gear have a diametral...Ch. 14 - A milled-teeth steel pinion and gear pair have Sut...Ch. 14 - A 20 full-depth steel spur pinion rotates at 1145...Ch. 14 - A steel spur pinion has a pitch of 6 teeth/in, 17...Ch. 14 - A commercial enclosed gear drive consists of a 20...Ch. 14 - A 20 spur pinion with 20 teeth and a module of 2.5...Ch. 14 - Repeat Prob. 14-19 using helical gears each with a...Ch. 14 - A spur gearset has 17 teeth on the pinion and 51...Ch. 14 - Prob. 23P Ch. 14 - Prob. 24P Ch. 14 - The speed reducer of Prob. 14-24 is to be used for...Ch. 14 - Prob. 26P Ch. 14 - Prob. 27P Ch. 14 - The gearset of Prob. 14-27 is going to be upgraded...Ch. 14 - Prob. 29P Ch. 14 - AGMA procedures with cast-iron gear pairs differ...Ch. 14 - Spur-gear teeth have rolling and slipping contact...Ch. 14 - In Ex. 14-5 use nitrided grade 1 steel (4140)...Ch. 14 - In Ex. 14-5 use carburized and case-hardened gears...Ch. 14 - Prob. 35P Ch. 14 - Prob. 36P Ch. 14 - The countershaft in Prob. 373, p. 152, is part of...Ch. 14 - Build on the results of Prob. 1340, p. 720, to...Ch. 14 - Build on the results of Prob. 1341, p. 721, to...

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Chapter 14 Solutions