Solve each problem below being sure to show all steps and state all assumptions

Question

Solve each problem below being sure to show all steps and state all assumptions made. Examine the gear-train. N_1 is the input and is rotating clockwise at 1650 rpm. The desired output is 50 rpm. The teeth value for N_1-N_7 are given in your handout. (last pays) What is the number of teeth for N_8 to provide an output as close to 50 rpm as possible? What is the actual rpm of the output gear N_8? What is the total train value of this gear system (to 3 decimal places)? Is the train value positive or negative? If P_d=5, and the total shaft lengths for the N_2-N_3, N_4-N_5 and N_6-N-7 shafts are 5 inches inside the gearbox, what are the dimensions of the gear box assuming 1/2^" of clearance on all sides? N_1=21 N_2=43 N_3=20 N_4=69 N_5=31 N_6=53 N_7=19 N_8=?

Explanation / Answer

>> As, V1 = Speed of Input = 1650 rpm clockwise = - 1650 rpm

>> V8 = Deisred Output = 50 rpm

>> Now, As, V1/V8 = [V1/V2]*[V2/V3]*[V3/V4]*[V4/V5]*[V5/V6]*[V6/V7]*[V7/V8]

As, V2 = V3, V4 = V5, V6 = V7

=> V1/V8 = [V1/V2]*[V3/V4]*[V5/V6]*[V7/V8]

and, as V1/V2 = T2/T1

=> V1/V8 = [T2/T1]*[T4/T3]*[T6/T5]*[T8/T7] = [43/21]*[69/20]*[53/31]*[N8/19]

=> 1650/50 =  [43/21]*[69/20]*[53/31]*[N8/19]

=> N8 = 21

Using N8 = 21,

1650/V8 = [T2/T1]*[T4/T3]*[T6/T5]*[T8/T7] = [43/21]*[69/20]*[53/31]*[21/19]

=> V8 = 87.92 rpm

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