Measurement of High-Frequency Milling Forces with Dynamic Compensation

Abstract

Piezoelectric dynamometers are widely used to measure cutting forces during milling operations for diagnostic, process monitoring, and research and development purposes. However, the bandwidth of tooth passing frequencies that can be measured has an upper limit due to the electromechanical dynamics of the measurement device. As a result, high-frequency forces cannot be accurately measured. Even if an effort is made to match the cutting conditions to the specifications of the dynamometer, the higher harmonics of the tooth-passing frequency are still affected so that the resulting measurements are distorted.

In this work, two new (for milling applications) methods are presented to reconstruct the machining forces from the distorted measurement signal and compared to an existing method, the Augmented Kalman Filter (AKF). The first method implements a Sliding Mode Observer (SMO) to estimate the machining forces at each time-step from the measured signal. The second method, referred to as Regularized Deconvolution (RD), considers the convolution sum of the input machining force and the impulse response of the system, and then reconstructs the machining force signal by regularizing a related inverse problem. All three methods are implemented in a simulation study that imitates the cutting conditions used in a latter experimental cutting test in which the above methods are again used to recover the true machining forces and their relative performance evaluated and compared. A transfer function model of the electomechanical dynamics of a Kistler dynamometer is identified and incorporated into the simulation study and the experiment.

The results of this work find that, while all three methods reconstruct the true machining forces reasonably well, SMO has clear advantages for processes carried out over time in which the system dynamics changes. AKF also performs better than RD, but is not robust against variations in system dynamics. Despite its drawbacks, RD does have the advantage of being the method that only requires one parameter to be tuned, whereas the other methods require the tuning of two or more parameters.