Time Domain Simulation of Surface Topography in Broaching Considering Tools with General Cutting Edge Geometries and Three DoF Parametric Dynamics

This study presents a time domain simulation and workpiece surface generation framework for broaching operations, carried out with broaching tools of arbitrary geometry by machine tools of general dynamics. First, a three degree of freedom simulation model is formulated by considering an adequately discretized infinitely rigid tool, and a broaching machine, which is compliant in all translational spatial directions. Taking contact loss events into account, this leads to system a piecewise-smooth delay differential equations with state dependent delays, due to the allowed deviations in the speed of cutting. Through numeric integration of these equations, the dynamic displacement and cutting edge engagement of the broaching tool are evaluated, which serve as inputs for the developed surface generation routines. Then, a discretized workpiece surface is generated by finding the last active cutting edge, and its corresponding displacement for each point, allowing the numeric investigation of surface roughness and integrity through standardized techniques. Finally, to demonstrate the capabilities of the proposed framework, force and displacement signals as well as the generated surface and its virtual quality assessment are presented for a typical broaching operation.