Calculating the Frequency of Oscillation for Servo Axes Distressed by Clearance or Preloading

The main objective of this paper is to analyze the behavior of the servo systems, including the frequency of oscillations, in machine tools due to the nonlinear characteristics of the system. In order to demonstrate the dynamics of a rotary servo axis, two rotary mass loads with a nonlinear resonator are adopted. The feedback control system consisting of linear and nonlinear loops is then presented. To incorporate the describing function method, the multiloop nonlinear control system is reconfigured to a single-loop block diagram with separated linear and nonlinear terms. Analyzing the response of the system, two different self-oscillatory regimes, called resonance and impact, are predicted depending on the control parameters. The frequency of the resonance and impact regimes are also obtained using the describing function method and the impact equations, respectively. In addition, the stability of the limit cycle is investigated. In order to verify the simulation, a complete set of experimental data are collected using two industrial machine tools. It is shown that the deviation of the simulation and theoretical results with the experimental are quite small.