Аналіз нелінійної динаміки приводів гусеничних підйомно-транспортних машин з еластичністю, тертям і гістерезисом

The paper proposes a model of the dynamics of the above drives with nonlinear friction, elasticity, and hysteresis, combined with structural damping. Problem. An integral part of the development of mechatronic control systems for modern tracked lifting and transport machines and industrial robotics is the accurate modeling of the dynamic processes that occur in them. Among them, complex nonlinear effects that manifest themselves in drives with elastic elements and friction are of particular interest. Since similar nonlinear dynamics are observed in many physical systems, the current task is to study the corresponding nonlinear systems and their modeling. Many scientific works have been devoted to solving this problem. Goal. The aim of the work is to develop and substantiate a nonlinear friction model of reduced complexity, which allows us to describe the dynamics of the drive of tracked lifting and transporting machines/robots with mechanized control systems, in which, along with friction and elasticity, hysteresis is also present. Methodology. The work proposes a mathematical model that enables the description of the nonlinear dynamics of the drive of tracked lifting and transporting machines with elasticity and friction, which is controlled by a mechatronic (high-frequency) system. The model was obtained in the analysis of the dynamics of a second-order oscillator, in which the nonlinearities of friction and stiffness cause transient processes with memory. To describe the friction in the system, the well-known Lou Gre model was used. It was chosen, mainly, due to the small set of adjustable parameters in comparison with other models. The hysteresis feedback torque of a nonlinear spring with elastic-plastic properties was modeled using a nonlinear differential equation of state, similar to a simplified form of the classical Book-Ven hysteresis model. The applied weighting factors allow varying the proportion of elastic and plastic components in the total feedback torque. Practical value. The obtained drive model can be used to describe the dynamics of a precision rotary support device. To clarify and more adequately describe the characteristic stiffness curve, alternative friction models should be used that do not have the drift effect (which leads to errors in determining/predicting the phase trajectory of the system). Among modern friction models, a recently proposed model with elastic-plastic properties may be a possible candidate.