hwsol04

# hwsol04 - ME 358 Homework Solution 4 Problem 1 A...

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ME 358 Homework Solution 4 Problem 1 A 2.5-diametral pitch, 17-tooth pinion is to drive a 50-tooth gear. The spur gears are cut on the 20 o -full-depth-involute system. a) Calculate the following quantities: velocity ratio ω 2 / ω 3 , addendum a , dedendum b , clearance c , hole depth h t , working depth h k , pitch diameters d 2 and d 3 , center distance C , circular pitch p , arc tooth thickness at the pitch circle t p (assuming zero backlash), base circle radii r b2 and r b3 , base pitch p b , length of path of approach u a , length of path of recess u r , length of path of contact u , and contact ratio m c . b) Check for undercutting. c) Using MATLAB, calculate and plot the backlash that is introduced by increasing the center distance C by an amount C 05 . 0 C 0 Δ . Solution a) in 8 . 0 in 4 . 0 2 a 2 h in 9 . 0 in 5 . 0 in 4 . 0 b a h in 1 . 0 in 4 . 0 in 5 . 0 a b c in 5 . 0 in 1 5 . 2 250 . 1 P 250 . 1 b in 4 . 0 in 1 5 . 2 000 . 1 P 000 . 1 a 9412 . 2 17 50 N N k t 2 3 3 2 = = = = + = + = = = = = = = = = = = = = ω ω in 1809 . 1 20 cos in 2566 . 1 cos p p in 7939 . 18 20 cos in 20 cos d d in 3899 . 6 20 cos in 8 . 6 cos d d in 6283 . 0

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