Recovery of undersampled force measurement from high-speed milling process using approximate sparsity in frequency domain

During the monitoring of high-speed milling, the anti-aliasing filter is of great significance for the test signal to truly reflect the cutting state of the machine tool. The cutting force measurement of high-speed milling is similar to the sum of a series modulated sinusoidal waves (MSWs). In the frequency domain, the energy concentrated on several narrow bands, which show approximate sparsity. Aim to recover the information of the undersampled force measurement from the monitoring of aluminum alloy high-speed milling, this paper proposed a spectrum sensing algorithm based on this approximate sparsity. The principle of spectrum aliasing caused by undersampling was derived mathematically and the aliasing map was established. Based on the approximate sparsity of the force measurement, the proposed sensing algorithm divided the aliasing spectrum into several frequency subbands, and calculated the real frequency range of each subband according to the aliasing map. Bins of the spectrum were corrected to establish a new spectrum. The Inverse Fast Fourier Transform (IFFT) was used to reconstruct the actual signals. Numerical simulations and cutting experiments of aluminum alloys were conducted to verify the effectiveness of the proposed method. The maximum relative error of envelope is less than 4% in the engineering test signal application.Y