МОДЕЛЬ ТЕРТЯ ДЛЯ МОДЕЛЮВАННЯ РОБОЧОГО ПРОЦЕСУ СУХОГО ФРИКЦІЙНОГО ЗЧЕПЛЕННЯ

Abstract

Problem. Existing models used to reproduce the friction force during mathematical modeling are analyzed in the paper. The urgency of improving such models is shown. Typical problems of existing mathematical models are given. The analysis revealed that most of the models that combine the description of the mode of elastic deformations during the sticking of contact bodies together and the sliding mode with reproduction of the Stribeck effect and hysteresis have many state variables and a significant number of equations and conditions of application of variables. Goal. The goal is to improve complex modern models of friction in terms of reducing state variables and eliminating the drifting effect. Methodology. Methods of research and analysis of information, analytical methods of solving differential equations were used. During the formation of the equations of the mathematical model, the methods of divergence, transformation, convergence and harmonization were used. Results. The paper presents a mathematical model of friction and the logic of its construction. The results of the classic “drift” test for the known friction models and the one proposed for modeling the clutch and its control devices are given in the work. The block diagram of the friction model in Simulink and the simulation results in test modes are also presented to illustrate the reproduction of the model of the Stribek effect and hysteresis in the mode of elastic deformations without sliding of bodies and in the mode of sliding of counter bodies. The principle of combining two modes of modeling laid down in a mathematical model is graphically illustrated. Originality. The proposed system of equations has one state variable - the sliding speed. Additional parameters required to ensure the mode of elastic deformation are determined based on the sliding speed. Practical value. At the end of the work, a comparison of the simulation of the clutch operation using a simple model and an advanced one is given. Emphasis is placed on the possibility of using a single system of equations to simulate the operation of the clutch in the mode of slipping and moving the car and in the mode of further movement without slipping the clutch discs. The reason for stopping the calculation by the solver when using the model of friction with breakpoints is qualitatively shown. The conclusions made give a qualitative and quantitative estimation of the proposed mathematical model of friction and indicate the future steps of its improvement and use.Key words: mathematical model of friction, Stribeck effect, mathematical model of clutch, effect of slipping.