Geometric parameter optimization in multi-axis machining

This paper presents a systematic method for the determination of optimal geometric machining parameters in multi-axis machining. Machining accuracy is considered to be determined by a set of geometric parameters: the design parameters of the cutter, the positioning of the cutter, the orientation of the cutter etc. First, we formulate the general nonlinear constrained optimization model of the machining process. The optimal machining result is expected to produce the least deviation between the designed surface and the actual surface. This objective is accomplished by minimizing the deviation between the designed surface and the actual surface during machining. The details of how to characterize and calculate the deviation is then discussed for both ruled surface milling and general free-form surface milling. The swept surface is developed based on robotic manipulation and is used to model the actual surface. A signed distance function is constructed to perform the comparison which returns the signed distance from each sampled point to the designed surface. The direct search algorithm (Nelder–Mead simplex algorithm and pattern search algorithm in this paper) is used to solve our optimization problems due to possible discontinuity of the objective function and large nonlinearity of the problem. Three numerical examples and necessary comparisons are given to demonstrate the effectiveness of our method. The first example shows the generation of the swept volume of a filled-end cutter. The second example employs the swept surface generation method to solve a parameter optimization problem. Sensitivity analysis is performed for the parameters critical to machining accuracy. The third example optimizes the cutter orientation relative to the part surface to minimize the kinematics error caused by kinematics transformation and interpolation of multi-axis machines.