A comprehensive adaptive approach to calculating the envelope surface of the digital models in CNC machining

Abstract

The digital models are the fundamental elements used in the virtual simulation of CNC machining for process planning, result prediction, analysis, etc. The essential work to build the digital models of machined parts is the calculation of the envelope surface generated by moving a cutter surface relative to workpieces. This calculation is usually complicated, and the requirements in different cases are also varied. Hence, it is very beneficial to develop an effective approach for different requirements. In this work, a comprehensive envelope approach is established, and it adaptively choose 1) the elimination parameter among two cutter surface parameters, 2) the representation form of envelope surface, and 3) the discretization way, so it is robust to satisfy different requirements. The elimination parameter and representation form are adaptively chosen to improve the calculation efficiency by obtaining the closed-form representation of the envelope surface prior to the implicit one. The discretization way is further adaptively chosen to obtain approximately even point distribution to the applications of 3D and FEA modeling. Finally, comprehensive algorithms are proposed to effectively implement this adaptive envelope approach for different applications. The examples are given to the manufacturing of spiral bevel gears and five-axis CNC milling.