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.

Introduction

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 material removed at every moment of the machining, which is the instantaneous, undeformed chip geometry.In the physical simulation, by using the instantaneous, undeformed chip geometries, in-process workpiece models of the parts being machined are built, and then the instantaneous cutting forces are predicted to optimize machining parameters. For the geometric simulation, the in-process workpiece model at the end is the model of the finished part and the parts’ geometric errors are calculated to verify the planned tool paths. Thus, it is vital to develop an accurate and efficient approach to geometric modeling of the instantaneous, undeformed chips in five-axis milling. Comparing the three-axis and the five-axis milling, the cutter is parallel at all locations in the three-axis milling while the cutter orientation is changed sometimes dramatically, in the five-axis milling (see Fig. 1). The instantaneous, undeformed chip geometries in the five-axis milling is much more complicated than those in the three-axis milling. For example, an instantaneous, undeformed chip geometry could be two discrete complex shapes in the five-axis milling. To better understand the existing techniques of the machining simulation, the literature is extensively reviewed in the following.