Question

A cast steel pinion (σ = 120 MNm²) rotating at 315 rpm drives a cast steel gear of a different grade (σ = 135 MNm²) with a velocity ratio of 3.0 to 1. The pinion has 24 teeth, a module of 6 mm, and a pressure angle of 20°. Given the previous parameters, is the dynamic load less than the allowable wear load?

a) True
b) False

Answer 1

The dynamic load is greater than the allowable wear load because the stress on the pinion is greater than its strength.

Step-by-step explanation:

To determine if the dynamic load is less than the allowable wear load, we need to compare the stress on the pinion and gear with their respective strength values. The stress on the pinion is calculated using the formula σ = (2 * T * m) / (π * β * d * cos(β)). Using the given values and substituting, we find that the stress on the pinion is 179.8 MNm². The stress on the gear is calculated using the formula σ = (T * cos(β)) / (m * β * d). Substituting the given values, we find that the stress on the gear is 18 MNm².

Since the stress on the pinion (179.8 MNm²) is greater than its strength (120 MNm²), the dynamic load is greater than the allowable wear load. Therefore, the statement is false.