Explanation Write the expression for tangential component of force for gear (A). F T A = F A cos 20 ° (I) Here, the force on the gear (A) is F A . Write the expression for torque acting on the shaft due to gear (A). T A = F T A × R A (II) Here, the radius of the gear (A) is R A . Write the expression for tangential component of force for gear (B). F T B = F B cos 20 ° (III) Here, the force on the gear (B) is F B . Write the expression for torque acting on the shaft due to gear (B). T B = F T B × R B (IV) Here, the radius of the gear (B) is R B . Write the expression for equilibrium condition for both the gear. T A = T B (V) Write the expression for speed after reduction. n = 240 0 rev / min 2 = 1200 rev / min Write the expression for velocity of the gear (B). V = π d B n B 12 (VI) Here, the diameter of the gear (B) is d b , the speed of the gear is n b . Write the expression for the face width. F = 4 ( π P ) (VII) Here, the diametrical pitch is P Write the expression for allowable bending stress. S t = 102 H B + 16400 psi (VIII) Here, Brinell hardness number is H B . Write the expression for allowable contact fatigue strength. S c = 349 H B + 34300 psi (IX) Write the expression for number of teeth in the gear (B). N = d P (X) Write the expression of geometry factor. J = 0.27 Write the expression for pitting geometry factor. I = cos ϕ t sin ϕ t 2 m N ( m G m G + 1 ) (XI) Here, the pressure angle is ϕ t , gear ratio is m g and load shearing ratio is m N . Write the expression for elastic coefficient of steel. C p = 2300 psi Write the expression for dynamic factor. K v = ( A + V A ) B (XII) Write the expression for constant of transmission accuracy level number. B = 0.25 ( 12 − Q v ) 2 3 (XIII) Here, the transmission accuracy level number is Q v . Write the expression for constant A . A = 50 + 56 ( 1 − B ) (XIV) Write the expression for overload factor for pinion. ( K o ) p = 1.192 ( F Y p p ) 0.0535 (XV) Here, the Lewis form factor for pinion is Y P . 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 ) (XVI) Here, lead correction factor is C m c , pinion proportion factor is C p f , pinion proportion modifier is C p m , mesh alignment factor is C m a and mesh alignment correction factor is C e . Write the expression for load correction factor for uncrowned teeth. C m c = 1 Write the expression for pinion proportion factor. C p f = F 10 d − 0.0375 + 0.0125 F (XVII) 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 Write the expression for mesh alignment factor. C m a = 0.23 Write the expression for mesh alignment correction factor. C e = 1 Write the expression for number of load cycles. N c y c l e s = 1500 h × n (XVIII) Write the expression for repeatedly applied bending strength stress cycle factor. Y N = 0.9 Write the expression for pitting stress cycle factor. Z N = 0.8 Write the expression for reliability factor. K R = 0.658 − 0.0759 ln ( 1 − R ) (XIX) Here, the reliability is R . Write the expression for applied stress in gear tooth bending. σ = W t K o K v K s ( P F ) ( K m K B J ) (XX) Here, tangential load is W t , overload factor is K o and rim thickness factor is K B . Write the expression for tangential transmitted load. W t = F B cos θ (XXI) Here, tangential load is W t , overload factor is K o and rim thickness factor is K B . Write the relation for factor of safety for tooth bending. S F = S t Y N K T K R σ (XXII) Write the expression for factor of safety for tooth wear. S H = S c Z N C H K T K R σ c (XXIII) Write the expression for contact stress in gear tooth wear. σ c = C p ( W t K o K v K s ( K m d p F ) C f I ) 1 2 (XXIV) Conclusion: Substitute 300 lbf for F A in Equation (I). F T A = 300 lbf cos 20 ° = 281.907 lbf Substitute 10 in for R A and 281

10th Edition

ISBN: 9781260243314

Author: BUDYNAS

Publisher: MCG CUSTOM

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Chapter 14, Problem 36P

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The factor of safety for bending.

The factor of safety for wear.

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Chapter 14, Problem 35P

Chapter 14, Problem 37P

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Shaft a in the figure has a power input of 75 kW at a speed of 1000 rev/min in the counterclockwise direction. The gears have a module of 5 mm and a 20° pressure angle. Gear 3 is an idler (b) Find the torque T4c that gear 4 exerts on shaft c.

A gear train is composed of four helical gears with the three shaft axes in a single plane, as shown in the figure. The gears have a normal pressure angle of 20 and a 30 helix angle. Gear is the driver, and is rotating counterclockwise as viewed from the top. Shaft b is an idler and the transmitted load from gear 2 to gear 3 is 500 Ibf. The gears on shaft b both have a normal diametral pitch of 7 teeth/in and have 54 and 14 teeth, respectively. Find the forces exerted by gears 3 and 4 on shaft b

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Chapter 14 Solutions

SHIGLEY'S MECHANICAL ENG.DESIGN W/CODE

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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The factor of safety for bending. The factor of safety for wear.

Solution Summary: The author analyzes the factors of safety for bending and wear, and writes the expression for torque acting on the shaft due to gear.