Studying the dynamics of contact interactions during machining based on a system of nonlinear piecewise linear differential equations

Abstract

Abstract When manufacturing parts for thermal control systems for operation in especially difficult conditions of the North and in spacecraft, titanium and complex alloyed alloys are used. They are subject to increased quality requirements. They are achieved through simulation modeling. The solution is based on a dynamic model in which the contact interaction between the tool flank and the workpiece is differentiated. The process of contact interaction is considered as two-phase in the form of a sequence of states of adhesion and sliding. In the space of state variables, a system of nonlinear differential equations of piecewise linear type is constructed based on a set of rheological models. Based on this model, simulation modeling was carried out in the form of a computational experiment. A periodic solution is obtained which is formed as a result of switching the sliding and adhesion phases. In the graphs presented in the paper, the transition from the adhesion phase to the sliding phase is accompanied by a surge in displacement. In this case, in the phase portrait, the phase trajectory reaches the limit cycle with a limited amplitude. At the moment of transition from the adhesion phase to the sliding phase, a characteristic deviation of the phase trajectory from the limit cycle with an increased amplitude is observed, followed by a return to the limit cycle. With a wide variation in cutting speed, the conditions for technical stability are determined. During the simulation, a dynamic manifestation of the formation of chip elements was found, which did not have a serious impact on the nature of dynamic processes. The results obtained make it possible to study the dynamics of contact interactions during cutting in the framework of nonlinear dynamic models. This makes it possible to assess the level of vibration amplitudes and determine the regulated parameters of processing accuracy and surface roughness of manufactured products.