The machining of a cone frustum as specified in National Aerospace Standard NAS-979 is a widely accepted test to evaluate the performance of five-axis machining centers. By measuring the cross-sectional circularity or roundness of the cone, the contouring accuracy of five-axis computer numerical control (CNC) can be evaluated. Thus, reduction of circularity is directly related to improvement of the contouring accuracy in circular motions. Most CNC actuators are AC servo motors that are precisely controlled via two closed loops - one each for position and velocity. The circular contouring accuracy of a five-axis CNC can be improved by adjusting the loop gains and the time constant of velocity loop integration. Although higher gains enable the servomotors to reach the desired positions faster, the resulting contouring accuracy may not be satisfactory. Furthermore, excessively high gains may cause vibrations. This paper proposes a frequency domain approach for tuning the control parameters for each axis so that their frequency responses are very similar, thus reducing the circularity value of the cross sections of a manufactured cone frustum. The paper also describes a method to obtain the frequency response of each axis by using properly engineered input chirp sine signals. Simulated results showing the effect of tuning the control loop parameters based on the frequency response of each axis are presented. Moreover, a case study was conducted to show the variation in the circularity value when the control parameters of each axis were tuned to obtain similar frequency responses of the linear and rotary axes within a frequency range.
Hidalgo, D., Yeh, S. S., & Lee, J. I. (2017). A Frequency Domain Approach for Tuning Control Parameters of CNC Servomotors to Enhance its Circular Contouring Accuracy. In Procedia CIRP (Vol. 63, pp. 372–377). Elsevier B.V. https://doi.org/10.1016/j.procir.2017.03.084