Machining Process Power Monitoring: Bayesian Update of Machining Power Model

Abstract

Monitoring the CNC machine tool power provides valuable information that aids condition based maintenance, machine efficiency and machining process monitoring. Cutting force in machining process is an interesting variable to measure from monitoring and control point of view. Although the direct methods of measuring the cutting force exist, prohibitive costs do not allow deployment in industrial environment. In the indirect methods of measuring force, measuring the spindle motor current to estimate the cutting power and consequently the cutting force is popular. This work discusses the calibration of spindle current based torque sensor for the estimation of the cutting force in turning operation. The work undertakes handling uncertainty in measurement of the cutting torque measurement. Considering the steady state value, the cutting torque is represented as a polynomial function of the speed and measured power. Though the identification of the unknown coefficients can be done based on the offline tests, in current work, the Bayesian update of coefficients is proposed. This method allows online learning of these coefficients. The cutting torque value based on the model has some variability due to variation in the coefficients and unmodeled dynamics. The iterative learning happens in three stages, namely — Prior belief, likelihood function establishment and update in prior belief with observed data producing posterior belief. The establishment of the priors is done through some offline tests. The likelihood function accounts for noise in the measurement of torque. And finally, Markov Chain Monte Carlo (MCMC) simulations help sampling from unknown posterior distribution. This scheme has ability to sample from any distribution. A single update cycle shows high reduction in the variability of the torque. Experimental data is produced to verify the effectiveness of method; the Bayesian update scheme outperforms least-square polynomial fit method consistently for different cutting speeds and cutting load values.