Question

While designing the gears, the Lewis equation is generally used for finding out the following stress?

• A. Shear stress
• B. Bending stress
• C. Axial stress
• D. Fatigue stress

Hint:

The Lewis equation is a cornerstone in gear design, specifically formulated to analyze the bending strength of gear teeth. It treats a gear tooth as a cantilever beam, with the critical bending stress occurring at the root of the tooth. Understanding this helps in preventing common gear tooth failures like bending fatigue.

Answer 1

The Correct Option is B

Step 1: Understand the purpose of the Lewis equation in gear design.
The Lewis equation (also known as the Lewis formula or Lewis bending equation) is a fundamental formula used in mechanical engineering, specifically in the design and analysis of spur gears. It was developed by Wilfred Lewis to determine the strength of gear teeth.
Step 2: Identify the type of stress calculated by the Lewis equation.
The Lewis equation considers the gear tooth as a cantilever beam, fixed at the root and loaded at the tip. When a force is applied to the gear tooth during meshing, it induces stresses within the tooth. The primary stress that the Lewis equation aims to calculate is the bending stress at the root of the gear tooth. This is because gear teeth are most likely to fail in bending fatigue at their root due to the stress concentration present there.
The Lewis equation takes into account factors such as the tangential load on the tooth, the face width, the circular pitch, and a form factor (Lewis form factor) that accounts for the tooth shape.
Step 3: Evaluate the given options based on the Lewis equation's application.
(1) Shear stress: While shear stresses are present in gear teeth, the Lewis equation primarily focuses on the bending stress, which is often the critical factor for tooth failure.
(2) Bending stress: This is the correct type of stress that the Lewis equation is specifically designed to calculate. The equation helps to ensure that the gear tooth has sufficient strength to resist bending failure.
(3) Axial stress: Axial stresses are generally negligible or not the primary concern for bending failure in spur gear teeth under normal operating conditions.
(4) Fatigue stress: Fatigue stress is a type of stress related to cyclic loading that leads to material failure over time. While the Lewis equation is used in the context of preventing fatigue failure by calculating bending stress, "bending stress" is the direct type of stress it calculates, not "fatigue stress" as a general category. The calculated bending stress is then compared against the material's endurance limit (which accounts for fatigue). Therefore, the Lewis equation is specifically used for finding out the bending stress in gear teeth. The final answer is \( \boxed{\text{Bending stress}} \).