Model of parametric reliability of woodworking machine tools

Abstract

The aim of the article is to develop a model of the parametric reliability of woodworking machine tools based on the criterion of technological accuracy. A mathematical model of the operating time of a woodworking machine to parametric failure has been created using a scheme for changing the size of the workpiece. On the basis of the assumption of a linear relationship between the rate of wear of the machine tool components and the rate of change in its technological accuracy, a linear differential equation was obtained that characterizes the change in the dimensions of the machined workpiece. The differential equation is solved by the Bernoulli method, when the unknown value of the change in the dimensions of the workpiece is represented as a product of two functions. When solving the differential equation, the method of separation of variables and the method of integration by parts were used. An analytical dependence was obtained for changing the dimensions of the workpiece, which is a characteristic of the technological accuracy of the machine tool during the overhaul period. The operating time intervals for woodworking machines between parametric failures have been determined. Taking into account the alpha distribution of operating time intervals to failure of woodworking machine tools, the probabilities of failure-free operation were calculated. It is found that the values of probability of failure-free operation of machine tools significantly depends on the parameter of the operating time alpha distribution, which characterizes the relative durability of the machine tool.