Analytical calculation of the CNC machines servo drives position loop gain

Purpose: One of the most important factors which influence on the dynamical behavior of the servo drives with rotary and linear motors for CNC machine tools is position loop gain or Kv factor. Design/methodology/approach: From the magnitude of the Kv-factor depends tracking or following error. In multi-axis contouring the following errors along the different axes may cause form deviations of the machined contours. Generally position loop gain Kv should be high for faster system response and higher accuracy, but the maximum gains allowable are limited due to undesirable oscillatory responses at high gains and low damping factor. Usually Kv factor is experimentally tuned on the already assembled machine tool. Findings: This paper presents a simple method for analytically calculation of the position loop gain Kv. A combined digital-analog models of the 6-th order (for rotary motors) and 4-th order (for linear motors) of the position loop are presented. In order to ease the calculation, the 6-th order system or 4-th order system is simplified with a second order model. With this approach it is very easy to calculate the Kv factor for necessary position loop damping. The difference of the replacement of the 6-th order system and 4-th order system with second order system is presented with the simulation program MATLAB. Analytically calculated Kv factor for the servo drives with rotary motors is function of the nominal angular frequency ů and damping D of the servo drive electrical parts (rotary motor and regulator), nominal angular frequency ům and damping Dm of the mechanical transmission elements, as well as sampling period T. Kv factor for the servo drives with linear motors is calculated as function of the nominal angular frequency ům and damping D of the linear motor servo drive electrical parts (motor and regulator) and sampling period T. Research limitations/implications: The influence of nonlinearities was taken with the correction factor Originality/value: Our investigations have proven that experimentally tuned Kv factor differs from analytically calculated Kv factor less than 10%, which is completely acceptable.