A new method for choosing between ball-end cutter and toroidal cutter when machining free-form surfaces
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ORIGINAL ARTICLE
A new method for choosing between ball-end cutter and toroidal cutter when machining free-form surfaces Mahfoud Herraz1 · Jean-Max Redonnet1 · Marcel Mongeau2 · Mohammed Sbihi2 Received: 21 June 2020 / Accepted: 14 September 2020 / Published online: 13 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract End-milling of free-form surfaces on multi-axis CNC machines are complex and expensive operations involved in the production of many high-value parts, molds and stamping dies. For such operations, the choice of the cutter type to use is very important given the considerable impact of this choice on the quality of the machined surface and the duration of the operation. In this paper, a new method for choosing between ball-end cutter and toroidal cutter is provided. This procedure gives a good hint on the best tool to employ with no need to carry out any machining simulation. Keywords End milling · Free-form surface · Ball-end cutter · Toroidal cutter · Principal components analysis
1 Introduction The quality constraint of the surface is commonly expressed in terms of maximum scallop height, denoted sh, which corresponds to the residual stock thickness left unmachined by the tool between two adjacent trajectories. This value imposes the step-over distance sod that can be used during the milling of the surface. Roughly speaking, the step-over distance is the distance between two adjacent trajectories. The relation between sh and sod is well known and fully developed in [1]. The step-over distance is a key parameter for end-milling of free-form surfaces because, for a given scallop height, a greater sod leads to fewer trajectories and thus a reduced machining time. Numerous authors have addressed these issues [2–6]. Most of them use the concepts of effective radius and sweep curve to do so. The sweep curve is the curve lying on the spinning cutter envelope surface that defines the final profile of the cutter passage [7, 8]. From a kinematics point of view, the sweep curve is given by n · F = 0, where F is the feed direction and n the normal vector that can be calculated at each point of the cutter surface of revolution. Jean-Max Redonnet
[email protected] 1
Universit´e Paul Sabatier and Institut Cl´ement Ader, Universit´e de Toulouse, Toulouse, France
2
ENAC, Universit´e de Toulouse, Toulouse, France
Then, for a given cutter, the effective radius (denoted Reff ) is defined as the radius of curvature at the cutter contact point of the projection, in a plane normal to the feed direction, of the sweep curve. The direct impact of the effective radius on machining time is thus well established [9]. However, effective radius calculation may indeed vary a lot depending on the cutter geometry in use. The remainder of this paper is organized as follows. Section 2 recalls Reff calculation methods, depending on the cutter shape. For each cutter type, kinematics considerations are also reminded in order to explain how machining time can be calculated. Section 3 is
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