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New method to characterize a machining system: application in turning

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Abstract

Many studies simulates the machining process by using a single degree of freedom spring-mass system to model the tool stiffness, or the workpiece stiffness, or the unit tool-workpiece stiffness in modelings 2D. Others impose the tool action, or use more or less complex modelings of the efforts applied by the tool taking account the tool geometry. Thus, all these models remain two-dimensional or sometimes partially three-dimensional. This paper aims at developing an experimental method allowing to determine accurately the real three-dimensional behaviour of a machining system (machine tool, cutting tool, tool-holder and associated system of force metrology six-component dynamometer). In the work-space model of machining, a new experimental procedure is implemented to determine the machining system elastic behaviour. An experimental study of machining system is presented. We propose a machining system static characterization. A decomposition in two distinct blocks of the system “Workpiece-Tool-Machine” is realized. The block Tool and the block Workpiece are studied and characterized separately by matrix stiffness and displacement (three translations and three rotations). The Castigliano’s theory allows us to calculate the total stiffness matrix and the total displacement matrix. A stiffness center point and a plan of tool tip static displacement are presented in agreement with the turning machining dynamic model and especially during the self induced vibration. These results are necessary to have a good three-dimensional machining system dynamic characterization (presented in a next paper).

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Abbreviations

a:

Distance between displacement transducer

BT :

Block Tool

BW :

Block Workpiece

[C]:

Damping matrix

\({\left[C_{o}\right]}\) :

Compliance matrix

C i :

Displacement transducer (i = 1 to 6)

\(\textbf{CR}_{BT}\) :

Block Tool BT stiffness center

D 1 :

Holding fixture diameter (mm)

D 2 :

Workpiece diameter (mm)

\(\left\{D\right\}\) :

Small displacements torsor

D ij :

Straight line corresponding of the displacement direction of the point P i,j (i = x, y, z) and ( j=1, 2, 3)

d i,j :

Points displacements vectors P i,j (i = x, y, z) and ( j=1, 2, 3)

d x :

Distance between the line D ij

E :

Young modulus (N/mm2)

e x , f x :

Scale factors

F i :

Force vectors applied to obtain BT stiffness center (i = x, y, z)

I:

Inertial moment

\({\left[K\right]}\) :

Stiffness matrix (N/m)

\({\left[K_{C}\right]}\) :

Stiffness matrix of rotation (Nm/rad)

\({\left[K_{F}\right]}\) :

Stiffness matrix of displacement (N/m)

\({\left[K_{F,BT}\right]}\) :

Stiffness matrix of BT displacement (N/m)

\({\left[K_{F,BW}\right]}\) :

Stiffness matrix of BW displacement (N/m)

\({\left[K_{F,WAM}\right]}\) :

Stiffness matrix of machining system displacement (N/m)

\({\left[K_{errors}(\textrm{\%})\right]}\) :

Errors matrix for the matrix \(\left[K\right]\)

\({\left[K_{CF}\right]}\) :

Stiffness matrix of rotation / displacement (Nm/m)

\({\left[K_{FC}\right]}\) :

Stiffness matrix of displacement/rotation (N/rad)

L 1 :

Holding fixture length (mm)

L 2 :

Length workpiece (mm)

M i :

Point intersection between straight lines (Dij)(i = x, y, z) and ( j=1, 2, 3)

m :

Displacement measured at the charge point

\({\left[M\right]}\) :

Mass matrix

n i :

Plan normal P i

O :

Tool tip point

O c :

Cub center

P :

Force (N)

P i :

Plan including the point M i

\(\textbf{P}_{BT}\) :

Displacement plan considering tool point

P ij :

Charge points (i = x, y, z) and ( j=1, 2, 3)

\(\left\{T\right\}\) :

Mechanical actions torsor

\({\left[V\right]}\) :

Matrix eigenvector \(\left[K_{F,BT}\right]\)

v 1 :

Matrix eigenvalue \(\left[K_{F,BT}\right]\)

WTM :

Workpiece-Tool-Machine

x (z):

Cross (feed) direction

y:

Cutting axis

δ :

Displacement (mm)

ϵ i :

Displacement along i (i=1,2,3)

θ :

Measured angle at the force point

θ i :

Angular deviation of “Co-planarity” between lines Dij (i = x, y, z; and j = 1, 2, 3)

μ i :

Minimal distance between straight lines Dij (i = x, y, z; and j=1, 2, 3)

ρ i :

Rotation along i (i=x, y, z)

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Acknowledgements

The authors acknowledge Jean Pierre Larivière, Ingineer CNRS (Centre National de la Recherche Scintifique - France) for the numerical simulation with SAMCEF software and Professor Miron Zapciu for the helpful discussions on this subject.

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Authors and Affiliations

  1. University Politehnica from Bucharest, 313 Splaiul Independentei, 060042, Bucharest, Romania (UE)

    Claudiu F. Bisu

  2. Université de Bordeaux, 351 cours de la Libération, 33405, Talence-cedex, France (UE)

    Claudiu F. Bisu, Jean-Yves K’nevez, Raynald Laheurte & Alain Gérard

  3. Université de Bordeaux - IUT EA 496, 15 rue Naudet, 33175, Gradignan Cedex, France (UE)

    Philippe Darnis & Raynald Laheurte

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  1. Claudiu F. Bisu
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  2. Jean-Yves K’nevez
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  3. Philippe Darnis
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  4. Raynald Laheurte
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  5. Alain Gérard
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Correspondence to Alain Gérard.

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Bisu, C.F., K’nevez, JY., Darnis, P. et al. New method to characterize a machining system: application in turning. Int J Mater Form 2, 93–105 (2009). https://doi.org/10.1007/s12289-009-0395-y

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