Sensor Comparison For Low-Cost Dynamic Force Measurement in Milling

Machine cutting forces are commonly measured using piezoelectric dynamometers. Such dynamometers can be prohibitively expensive and may still require extensive post processing. Previous work used a low-cost single degree of freedom constrained motion dynamometer (CMD) in conjunction with a knife edge sensor to determine the cutting forces through inverse force filtering. In that approach, the measured displacement of the CMD was transformed into the frequency domain by the fast Fourier transform (FFT) and convolved with the inverted receptance frequency response function (FRF) to yield force in the frequency domain. The force was then converted to the time domain using the inverse FFT. This research seeks to expand upon that inverse force filtering approach by measuring displacement, velocity, and acceleration and calculating force using the inverted FRF corresponding to each measurement type. Displacement was again measured by a knife edge sensor. The velocity was measured using a laser vibrometer, and the acceleration was measured using both a solid state accelerometer, and a piezoelectric accelerometer. The frequency domain velocity was convolved with the inverted mobility FRF to obtain the frequency domain force, and the acceleration signals were convolved with the inverted accelerance FRF. The forces determined from the velocity required a low-pass and high-pass filter to attenuate unwanted signal gain associated with the inverted mobility FRF. The acceleration signals required both a high-pass filter to attenuate the unwanted signal gain at low frequencies due to the inverted accelerance and a low-pass filter to attenuate affects due to high frequency noise associated with the accelerometers. The displacement-based forces showed good agreement with the forces determined by a time domain simulation and those measured by a commercially-available piezoelectric dynamometer. However, the forces determined from the velocity and acceleration signals suffered from loss of the average (or mean, or zero-frequency/DC) component of the signal, which meant that only the peak-to-valley force values could be compared to the other results.