Cutter force and influence of elastic deformation of technological system of gear-hobbing machine on precision of radial-circumferential method of gear cutting

Abstract

The relevance of the problem which is solved in this article has been substantiated. In modern machines and equipment, rotary motions which cannot be implemented without gear wheels and gear trains are always present. Attainment of high performance of a machine – increase in loading with simultaneous increase in speed, increase in transmitted forces and moments, decrease in noise during operation, ensuring high indexes of failure-free performance and longevity of a machine – depends on precision in manufacturing the gear wheels and gear trains. These requirements to modern machines are put simultaneously with improvement of technology of their manufacturing and with creation of new effective methods of machine parts working. A new effective method of radial-circumferential (RC) gear cutting by disk-type cutting tool under the conditions of continuous generation (revolving) around is described; this way enables us to considerably reduce the expenditures for expensive and complicated cutting tools, to increase productivity of the process, and to increase precision of gear wheels. However, for application of this method in the course manufacturing, it is necessary to develop a technique of prediction of the precision of the gear cutting; such a technique being able to serve as a basis of substantiation of the choice of regimes of gear cutting. Principles of the mathematical model of cutting force of gear cutting, i.e. a model which is based on modelling of parameters of shearings made by a disk-type milling cutter, are presented in this article. This mathematical relation takes into account the intensity of deformation of the layer which is being removed and the strength of the material which is being machined; the model also enables us to determine the force on individual blades and its total value on all the active teeth in RC-method at any instant of time of milling as a function of the turn angle of the cutting tool. Analysis of cutting force has indicated that in one revolution of a milling cutter the cutting force varies according to aperiodic regularity, and its peak values are considerably less than the force of gear-tooth milling by a hobbing cutter under the same initial conditions. Since the disc-type gear milling cutter, as compared with the hobbing cutter, is considerably more sensitive to elastic deformations, the cutting force can essentially influence the error of gear cutting of ring gears. Proceedings from this, the influence of primary errors and that of elastic deformations which are caused by variable cutting force in the cycle of revolution of the milling cutter and formation of gears on the error of the working is investigated. Laws of the influence of radial, axial, and torque deformations of the elastic system of a machine on the deviations of parameters of the teeth from their rated ones and on the error of profiles in the process of gear milling according to radial-circumferential method are presented. The enhance of precision of tooth cutting and reduction of the total error becomes possible due to the choice of such regimes of cutting (first of all, axial feed) under which the necessary precision of the chosen parameter of precision, in particular, profile error, can be attained.