Modelling of end-milled floor surface topography considering system vibration and tool deflection

This paper presents a new model for predicting the 3D topography of end-milled floor surface, which comprehensively considers tool runout (radial and axial runout), tool setting error (radial offset and axial tilt), tool-workpiece vibration, tool deflection (deflection distance and deflection angle), front- and back-cutting motions, and toolpath overlap. This model consists of three fundamental sub-models: a geometric model of tool setting error and runout based on a series of homogeneous coordinates transformations, a milling time-domain simulation model which is based on regenerative effect and incorporates tool setting error and runout, and a finite element model of tool deflection which is embedded in the milling time-domain simulation model. This paper also presents a novel efficient algorithm for reconstructing the 3D topography from tool trajectories based on a coordinate transformation and 2D linear interpolation of tool trajectories over one rotation cycle. The measured 3D topography is in good agreement with the predicted one in terms of both texture pattern and surface height, proving that the proposed model is accurate. It is found that tool deflection angle determines the z-directional height of transition edges during front- and back-cutting motions, which therefore strongly influences the relative intensity of the right- and left-convex textures of end-milled surface. The proposed model and reconstruction algorithm are generic, i.e., they can be used not only to accurately predict the 3D topography of end-milled floor surface, but can also be extended to face mills with different geometries by simply updating the geometric equations of cutting edges.