An accurate and efficient approach to geometric modeling of undeformed chips in five-axis CNC milling

Abstract

Many important and complex parts, such as aero-engine compressors and automotive punch dies, are often machined in five-axis computer numerically controlled (CNC) milling. To machine the parts with accurate dimensions and shapes and low machining costs it is necessary to construct 3D models of the finished parts in the geometric simulation and in-process workpiece models of the parts in the physical simulation of their five-axis milling. A kernel technique of the geometric and the physical simulations is to accurately and efficiently model the geometry of the workpiece material removed at every moment of the machining, which is the instantaneous, undeformed chip geometry. Although in the past decades much research has been conducted on modeling cutter swept volumes in CNC milling to represent the finished part geometry in the geometric simulation, it is very time consuming to calculate the instantaneous, undeformed chip geometries using the cutter swept volumes. Besides, the existing method of modeling undeformed chip geometry in three-axis milling cannot be used for that in five-axis milling. To address this problem, our work proposes an accurate and efficient approach. In this article, a generic theory about the boundary of the area covered by the instantaneous cutting edges on a workpiece layer at any moment is established, which is called the boundary theory. A simple diagram of determining the boundary is invented, which is called boundary construction diagram. This approach lays a theoretical foundation for the geometric and the physical simulations of five-axis milling and will significantly promote them for high performance machining in industry.