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Prediction of tool deflection and tool path compensation in ball-end milling

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Abstract

This article presents a tool deflection calculation and compensation methodology based on a recent model developed for the prediction of cutting forces in free-form milling. From global and local geometry of the tool, initial surface and tool path, this approach allows predicting cutting forces and now surface form and roughness directly from CAM data. This model was developed and validated for a rigid case and some improvements are necessary in order to propose an efficient optimization tool for industrial and complex milling operations. In particular, the tool paths can be improved by targeting a reduction of cutting forces linked to cutting stability, tool’s life and part’s quality. In the same way, the tool deflection, predicted thanks to the cutting forces, can be limited and by the way the generated form defects. The cutting forces prediction can be performed analytically or numerically and the coupling with Computer Assisted Manufacturing data is necessary to optimize industrial milling operations but it is not sufficient to consider tool path and part quality. The idea is to make benefit from the fine geometrical description developed for tool-workpiece engagement calculation to deduce resultant cut surface, cutting forces and tool deflection directly from CAM data. For this reason, this work is based on the development of an analytical model and a comparison is made with a finite element model for the calculation of the tool deflection in 3 axes milling. The suggested model is confronted to another models already published in literature to show its specificity. This approach is enriched by a deflection compensation procedure efficient for sculptured surface milling and allowing limiting resultant errors on machined surfaces. Good results were observed, even for complex ball-end milling operations, and the combination of different calculation procedures opens the way to a more complete virtual milling approach.

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Abbreviations

(X,Y,Z):

Global reference system

CL :

Cutter location points considered along tool path

CC :

Cutter contact points considered along tool path

\(\theta \) :

Tool rotation angle

\(M(z) \) :

Bending moment

\(x(z)\) :

Tool deflection at altitude \(z\)

\(I_{Gy},I_{c},I_{s},I\) :

Moments of inertia

\(y\) :

Considered position along trajectory on Y axis

\(z\) :

Considered altitude along tool axis

\(E\) :

Young modulus

\(L_{f}\) :

Length of flute on tool

\(L\) :

Total length of tool

\(L_{c}\) :

Length of tool’s cylindrical part

Ls :

Length of tool’s spherical part

\(R\) :

Nominal radius of the cutter

\(F\) :

Resultant cutting force applied on the cutter

dx :

Tool deflection in the XY plane according to the X direction

dy :

Tool deflection in the XY plane according to the Y direction

\(\gamma _{0}\) :

Orthogonal rake angle

\(f\) :

Feed per rotation

\(f_{t}\) :

Feed per tooth

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Authors and Affiliations

  1. Laboratoire de Procédés de Fabrication/UERCFM/DRFPG, Ecole Militaire Polytechnique, EMP, Bordj El Bahri, BP 17, 16111, Alger, Algeria

    Nasreddine Zeroudi

  2. Department of Applied Mechanics, ENSMM, FEMTO-ST Institute, 24 rue de l’épitaphe, 25000, Besançon, France

    Michaël Fontaine

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  1. Nasreddine Zeroudi
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  2. Michaël Fontaine
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Correspondence to Nasreddine Zeroudi.

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Zeroudi, N., Fontaine, M. Prediction of tool deflection and tool path compensation in ball-end milling. J Intell Manuf 26, 425–445 (2015). https://doi.org/10.1007/s10845-013-0800-8

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