On-site inspection with a laser displacement sensor installed on the spindle of a three-axis machine tool has found a wide range of applications in industrial processes. The calibration of the beam direction and the integration of the on-site scanned points are crucial for the measurement of free-form surfaces. This paper presents a method to calibrate the unit direction vector of the laser beam and integrate the on-site scanned points based on a standard ball. By scanning the fixed ball, a group of nonlinear equations is constructed. The nonlinear equations are solved by the Levenberg–Marquardt algorithm to get the unit direction vector of the laser beam and the center position of the standard ball. Then the coordinate transformation parameters between the world coordinate system and the sensor coordinate system are calculated. The scanned points from different coordinate systems are transformed into the world coordinate system by the coordinate transformation. The method simplifies the traditional calibration process and realizes the integration of the multi-angle scanned points on a three-axis machine tool. The feasibility and effectiveness of this method are verified through simulation and practical experiment. By comparing fitting value under different measuring conditions with the nominal, the measurement parameters including the incident angle and the scan depth are optimized. In the experiment, the measurement accuracy of this method reaches 0.02 mm.

When applying the non-parallel shear zone model to predict the cutting process parameters of carbon steel workpiece, it is found that there is a big error between the prediction results and the experimental values. And also, the former approach to obtain the relevant cutting parameters of the non-parallel shear zone model by applying coordinate transformation to the parallel shear zone model has a theoretical error – it erroneously regards the determinant (|J|) of the Jacobian matrix (J) in the coordinate transformation as a constant. The shape of the shear zone obtained when |J| is not constant is drew and it is found that the two boundaries of the shear zone are two slightly curved surfaces rather than two inclined planes. Also, the error between predicted values and experimental values of cutting force and cutting thrust is slightly smaller than that of constant |J|. A corrected model where |J| is a variable is proposed. Since the specific values of inclination of the shear zone (α, β), the thickness coefficient of the shear zone (as) and the constants related to the material (f0, p) are not given in the former work, a method to obtain the above-mentioned five constants by solving multivariable constrained optimization problem based on experimental data was also proposed; based on the obtained experimental data of AISI 1045 steel workpiece cutting force, cutting thrust, chip thickness, the results of five above-mentioned model constants are obtained. It is found that, compared with prediction from uncorrected model, the cutting force and cutting thrust of AISI 1045 steel predicted by the corrected model with the obtained constants has a better agreement with the experimental values obtained by Ivester.