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# Modelling and analysis of surface topography generated in face milling operations

Título de la revista: INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
ISSN: 0020-7403
Volumen: 163
Fecha de publicación: 2019
Resumen:
This paper presents a model for predicting the surface topography generated in face milling operations. In these operations, when the face mill inserts remove the workpiece material, they leave marks on the machined surfaces. The marks depend on the face mill geometry, the geometry and runout of the face mill inserts, and cutting conditions, e.g. feed and step over. In order to predict the surface topography, the geometry of the face mill cutting edges must first be modelled. The modelling of the cutting edge geometry is for round insert face mills and for square shoulder face mills. Due to the influence of insert runout on the final surface topography, axial and radial runouts of the face mill inserts are also taken into account in the modelling of the cutting edge geometry. Next, the equations expressing the trajectory of any cutting edge point are derived as a function of the feed value, the rotation angle of the face mill, its axial position, and its radial position with respect to the face mill axis. Finally, given the cutting edge geometry and the trajectory of cutting edge points, a methodology based on the discretization of the milled surface in a grid with a finite number of points is developed in this paper for the simulation of the surface topography. The methodology is based on the fact that at each grid point, the final height of the topography will be the height of the workpiece material remaining at this point after many face mill revolutions. For this reason, the procedure initially estimates the rotation angles of the face mill for which the face mill cutting edges in their front-cutting and back-cutting motion pass by the grid point being considered. In order to achieve this, a transcendental equation that is only dependent on the rotation angle is derived from the cutting edge trajectory equations. This equation is transformed into an equivalent polynomial equation by means of Chebyshev expansions. The transformed equation is solved for the rotation angle using a standard root finder that does not require a starting value. Then, by means of the estimated rotation angles and the cutting edge trajectory equations, the radial positions of the cutting edge points passing by the grid point are obtained. Finally, based on these radial positions and the cutting edge geometry, the heights of cutting edge points, which can generate the surface topography at this grid point, are estimated. The final height of the surface topography will correspond to the lowest value among the estimated height values. The methodology can be easily extended and applied to face mills with other insert geometries or to face mills with central and peripheral inserts. In addition, the simulation of the surface topography generated by lateral passes in face milling operations is simplified. The procedure allows the influence of the face mill geometry, the feed value and the step over between passes to be analysed and the roughness values to be predicted. In order to validate the model predictions, a series of face milling tests are carried out. Predicted surface topographies are compared with measured topographies and a good agreement between them is observed.