Abstract
The study examines the influence of clearances in mechanical transmissions on the positioning accuracy of the drive. The relevance of the study is due to the fact that the presence of backlash in gear, worm and screw drives is a structurally inevitable consequence of technological tolerances, assembly conditions and operational wear, and has a significant impact on the kinematic and dynamic characteristics of drive systems. A mathematical model of an electromechanical drive has been developed, taking into account a nonlinear kinematic element of the ‘backlash’ type. The model is implemented in MATLAB/Simulink and includes a proportional position controller, an inertial mechanical subsystem with damping, and a backlash simulation unit with a specified dead zone width. A numerical parametric study was conducted for different backlash values. During the simulation, transient characteristics, time dependencies of positioning errors, and hysteresis diagrams were obtained. It was found that an increase in the gap value leads to an increase in the maximum dynamic error of the drive, which is especially pronounced in reverse motion modes. It was shown that in the studied range, the dependence of the maximum error on the parameter ∆ is monotonic and close to linear. The constructed hysteresis characteristic confirms the nonlinear nature of the phenomenon under consideration and demonstrates the formation of an insensitivity zone with a width of 2∆. The scientific novelty of the work consists in the quantitative assessment of the dependence of the maximum dynamic positioning error on the gap value based on a unified nonlinear dynamic model of the drive, as well as in a comprehensive analysis of the influence of backlash using transient characteristics and hysteresis diagrams. The results obtained allow for a quantitative assessment of the permissible backlash value when designing drives for high-precision mechanisms and can serve as a basis for the development of algorithmic or design methods for backlash compensation.