Design of Arms of Spur Gears

Machine Design

Gear Drive

Introduction:

The cross-section of the arms is calculated by assuming them as a cantilever beam fixed at the hub and loaded at the pitch circle.

Design Procedure:

It is assumed that the load is equally distributed to all the arms.The arms are designed for the stalling load.The stalling load is a load that will develop the maximum stress in the arms and in the teeth.This happens at zero velocity, when the drive just starts operating.The stalling load may be taken as the design tangential load divided by the velocity factor.

                  

D_G = Pitch circle diameter of the gear,
n = Number of arms, and
σ_b = Allowable bending stress for the material of the arms.         

Now, maximum bending moment on each arm,

and the section modulus of arms for elliptical cross-section,

where a₁ = Major axis, and b₁ = Minor axis.

The major axis is usually taken as twice the minor axis. Now, using the relation, σ_b = M / Z, we can calculate the dimensions a1 and b1 for the gear arm at the hub end.

Note :

The arms are usually tapered towards the rim about 1/16 per unit length of the arm (or radius of the gear).
∴ Major axis of the section at the rim end