MATHEMATICAL MODEL AND OPTIMIZATION ALGORITHM ACCORDING TO THE CRITERIA OF MINIMUM CONTACT STRESS FOR GEARS WITH CONVEX-CONCAVE CONTACT

Abstract

Reducing the mass and dimensions of gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with a convex-concave contact of the teeth. The study is devoted to the development of mathematical model and algorithm for the optimal design of cylindrical gears with convex-concave contact of the working surfaces. Optimality criteria: minimum contact stresses taking into account design, geometrical and technological constraints. An objective function is constructed for the case of minimizing contact stresses: contact stresses σH in the mesh must take the minimum possible value when all constraints are met. Variables planning are defined. These are pressure angle at the pole αС, the curvature radius at the upper part of contact path rkh, and the curvature radius at the lower part of contact path rkd. A method for solving the problem of optimal design is chosen – probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The algorithm for optimal design of gear has been developed. They take into account the constructive, technical and technological features. They also allow to reduce the error of the calculations due to the error-control of the calculations. The main stages of the algorithm are as follows: setting input data (numerical constraints on design variables, gear parameters and its load); generation of LPτ-sequence for variables planning with simultaneous consideration of their numerical constraints; checking of functional constraints; additional verification calculations (if necessary) of the gearing contact strength; formation of an array of possible solutions; searching of the best solution variant (the test point corresponding to the minimum value of the objective function) by sorting the array. Keywords: gear, convex-concave contact, optimization, objective function, variables planning, algorithm