OPTIMAL DESIGN OF CYLINDRICAL GEARS WITH CONVEX-CONCAVE CONTACT: OBJECTIVE FUNCTION AND VARIABLES PLANNING

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. Therefore, the study is devoted to the development of methods for the optimal design of cylindrical gears with convex-concave contact of the working surfaces. Optimality criteria: minimum contact stresses and (or) minimum relative sliding velocities, taking into account design, geometrical and technological constraints. C-C gearing was chosen as the object of research. It was proposed by the Slovak scientists M. Boshanski and M. Veresh. An objective function is constructed for the case of minimizing contact stresses. The optimality criterion is formulated as follows: contact stresses σH in the mesh must take the minimum possible value when all constraints are met. An objective function is also constructed for the case of minimizing the relative sliding velocities of profiles. The optimality criterion is formulated as follows: the relative sliding s velocities of profiles λ at the extreme points of mesh must take the minimum possible value when all the 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. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned to form a system of constraints on variables planning, to develop methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results. Keywords: gear, convex-concave contact, optimal design, objective function, variables planning