Optimization model for static performance of involute spur gears

(1) Design variables

The design variables of static performance optimization model and dynamic performance optimization model are the same.

(2) Optimization objectives

In the previous optimization models based on static characteristics, the following four kinds of optimization objectives were used: the amplitude corresponding to the first order meshing frequency of static transmission error; the sum of the amplitude corresponding to the main meshing frequency of static transmission error; the weighted sum of the amplitude corresponding to the main meshing frequency of static transmission error; the sum of the square of the amplitude corresponding to the main meshing frequency of static transmission error. In this paper, the sum of the amplitudes corresponding to the first seven meshing frequencies of static transmission error under the action of average torque is taken as the objective of static performance optimization

Where, the amplitude corresponding to the i-th order engagement frequency of AI.

(3) Constraints

In the optimization model of tooth profile modification based on static characteristics, the influence of tooth profile modification on bearing capacity is generally not considered, and the constraints only include the boundary constraints of design variables

Since the influence of tooth profile modification on bearing capacity is not considered, the boundary conditions of tooth profile modification amount and modification length are wider than those of dynamic performance optimization model. The upper limit of optimal modification amount is 0.05mm, the upper limit of modification length is 10 mm, and the boundary conditions of modification correlation coefficient are 0 ≤ a ≤ 1.

Combined with design variables, constraints and objective functions, the mathematical model of static performance optimization can be obtained as follows:

Scroll to Top