Question

Given an external gear pair where N1=35N1 = 35N1=35, N2=55N2 = 55N2=55, and the circular pitch for the pinion is pc1=0.50pc1 = 0.50pc1=0.50 in, calculate the pitch diameters of both gears, the center distance, base pitch, and diametra.

Answer 1

To find the pitch diameters, center distance, base pitch, and diametral pitch of the external gear pair, use equations to calculate D1, D2, C, Pb, and Pd based on the given values of N1, N2, and pc1.

Step-by-step explanation:

To calculate the pitch diameters of the gears, we can use the formula:

D1 = N1 * pc1

D2 = N2 * pc2

Given that N1 = 35, N2 = 55, and pc1 = 0.50 in, we can calculate:

D1 = 35 * 0.50 = 17.5 in

D2 = 55 * pc2

Next, to find the center distance between the gears, we can use the formula:

C = (D1 + D2) / 2

Using the values we calculated, the center distance is:

C = (17.5 + D2) / 2

For the base pitch and diametral pitch, we can use the formulas:

Pb = 1 / dp

Pd = π / dp

Where dp is the diametral pitch. The diametral pitch can be calculated using the formula:

dp = N / D

Given that N = 35, and D = D1, we can calculate dp and then find the base pitch and diametral pitch:

dp = 35 / 17.5 = 2

Pb = 1 / dp = 1 / 2 = 0.5 in

Pd = π / dp = 3.14 / 2 = 1.57 in

So the pitch diameters are 17.5 in and D2, the center distance is (17.5 + D2) / 2, the base pitch is 0.5 in, and the diametral pitch is 2.