In the figure, the gear teeth are divided into several segments by the idea of integral, and the shadow part in the figure is the a segment. It is assumed that its thickness is Ta, its area is Aa, its section modulus is IA, the distance from segment a to the acting point of force along the transverse axis direction is lab, the tooth thickness of force acting point is 2yb, and the angle between force Fb and longitudinal axis is β.
The bending deformation and shear deformation of segment B under the action of force FB can be calculated, so that the deformation of action point B along the direction of force FB is expressed as follows:
Where ν is Poisson’s ratio of gear material and Ee is equivalent elastic modulus. EE is related to the ratio of gear tooth width B and pitch circle tooth thickness HP. When B / HP > 5, the equivalent elastic modulus can be expressed as follows:
When B / HP > 5, the equivalent elastic modulus Ee = E.
The whole gear is divided into a segment, and the bending deformation and shear deformation of each segment are calculated by the above method