Final answer:
The Lewis formula is used to design a suitable gear for a specified gear transmitting power at a certain rpm. The process involves calculating the tangential load using power and rpm, and then selecting the gear module and face width based on stress constraints and application limitations.
Step-by-step explanation:
To select a suitable gear for a 20º full depth spur pinion transmitting 2 kW at 1020 rpm with 18 teeth, made of heavy duty 817M40 steel, we use the Lewis formula. The Lewis formula is an empirical equation that estimates the stress in a gear tooth during operation. It is given by:
F = Wt / (p × F), where:
F = the force applied to the tooth,
Wt = the tangential load on the tooth,
p = the diametral pitch, and
F = the face width.
To find the tangential load (Wt), we use the power (P) and rpm:
Wt = (2 × 10³ W) / ((1020 rpm) × (π / 30) × (d))
where d is the pitch diameter which relates to the module (m) as d = m × Z, with Z being the number of teeth.
Next, the module and face width are selected to satisfy the stress constraints and space limitations of the application. This is typically a trial-and-error process using standard gear dimensions and the manufacturer's guidelines.