ПАРАМЕТРИЧЕСКАЯ ОПТИМИЗАЦИЯ ПО КРИТЕРИЮ ОБЪЕМА ДВУХСТУПЕНЧАТОГО ПЛАНЕТАРНОГО МЕХАНИЗМА ТИПА AI–II

Abstract

The task of parametric optimization on the criterion of total volume is considered for the two-stage planetary mechanism of type AI–II. The objective function of optimization is built as a sum of two dimensionless parametric functions of volume (analogs of volume) of the separate stages of planetary mechanism of type AI–II. Construction of analogs of volume of simple planetary mechanisms of type AI and II, corresponding the first and second to the stages of planetary mechanism of type AI–II, it is based on their presentation as conditional disks. Thus the volume of the conditional disk is equivalent to the volume of a simple planetary mechanism. The mathematical model of analogs of the volume is built taking into account the terms of the durability of the toothed hooking of the sun gear and planetary gears of simple planetary mechanism, and also taking into account an area possible his transmission relation. Considering terms of contact and bending durability of the toothed hooking, get the analogs of volume at a calculation on contact and bending to durability. Depending on the condition of durability (contact or bending) and type of simple planetary mechanism the analog of his volume appears as a parametric function of corresponding parameters of his kinematics diagram. As parameters transmission relation attitude of simple planetary mechanism, parameters of bringing a mechanism over, toward a conditional disk, and also the relation of reference diameters of planetary gears of the mechanism is chosen. An analysis over of influence of each is brought of parameters of the function of analog of volume on the pattern of behavior to it. On the basis of this analysis of function of analogs of volume of the stages of planetary mechanism of type AI–II appear as parametric functions of the guided parameters. For the simple planetary mechanism of type AI one guided parameter is chosen, namely transmission relation of mechanism. For the guided parameters of function of analog of volume for the simple planetary mechanism of type II a transmission relation and relation of reference diameters of planetary gears of mechanism are chosen, i.e. two guided parameters. Offered approach for the decision of optimization task, based on research of differential properties of objective functions of volume (analogs of volume) of the separate stages of planetary mechanism of type AI–II. It is given the example of the optimal designing of construction of minimum volume of planetary mechanism of type AI–II.