Prediction Model of Three-Dimensional Machined Potassium Dihydrogen Phosphate Surfaces Based on a Dynamic Response Machining System.

To comprehensively obtain the effect of the machining process on the three-dimensional surface topography of machined potassium dihydrogen phosphate crystals, a dynamic response model of a machining system was built to calculate the dynamic displacement variables in the different processing directions. This model includes almost all processing factors, such as cutting parameters, environment vibration, radial and axial runout of the spindle, cutting tool parameters, material parameters, guide way error, fast tool servo and lubrication condition errors, etc. Compared with the experimental results, the three-dimensional topographies and two-dimensional profiles of the simulation surfaces were nearly consistent with those of experimental machined surfaces. As the simulation shows, the cutting parameters, axial runout of the spindle, and the output noise of the fast tool servo can respectively impact the main, low, and high frequencies of the machined surface topography. The main frequency of all the simulated and experimental surfaces in this study was 0.0138 µm-1. The low and high frequencies of the simulation surfaces had slight differences, about 0.003 µm-1 from those of the experimental surfaces. The simulation model, based on dynamic response, can accurately predict the entire machining process and three-dimensional topographies of machined potassium dihydrogen phosphate surfaces.

Extraction and Reconstruction of Arbitrary 3D Frequency Features from the Potassium Dihydrogen Phosphate Surfaces Machined by Different Cutting Parameters.

To comprehensively analyze the effect of cutting parameters on the 3D surface topography of machined potassium dihydrogen phosphate crystals, 2D power spectrum density and continuous wavelet transform are used to extract and reconstruct the arbitrary actual 3D frequency features of machined potassium dihydrogen phosphate crystal surfaces. The 2D power spectrum density method is used to quantitatively describe the 3D surface topography of machined potassium dihydrogen phosphate crystals. The continuous wavelet transform method is applied to extract and reconstruct 3D topographies of arbitrary actual spatial frequency features in machined surfaces. The main spatial frequency features fx of the machined surfaces are 0.0056 µm-1, 0.0112 µm-1, and 0.0277 µm-1 with the cutting depth from 3 µm to 9 µm. With the feed rate changing from 8µm/r to 18 µm/r, the main spatial frequency features fx are 0.0056 µm-1-0.0277 µm-1. With the spindle speed from 1300 r/min to 1500 r/min, the main spatial frequency features fx are same as the main spatial frequency features of the cutting depths. The results indicate that the variation of cutting parameters affects the main spatial frequency features on the 3D surface topography. The amplitudes of the spatial middle-frequency features are increased with the increasing of cutting depth and spindle speed. The spatial low-frequency features are mainly affected via the feed rate. The spatial high-frequency features are related to the measurement noise and material properties of potassium dihydrogen phosphate. The distributional directions of the frequency features in the reconstructed 3D surface topography are consistent with the distribution directions of actual frequency features in the original surface topography. The reconstructed topographies of the spatial frequency features with maximum power spectrum density are the most similar to the original 3D surfaces. In this machining, the best 3D surface topography of the machined KDP crystals is obtained with a cutting depth ap = 3 µm, feed rate f = 8 µm/r and a spindle speed n = 1400 r/min.