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Prediction of cutting forces in 3-axes milling of sculptured surfaces directly from CAM tool path

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Abstract

In the present work a new approach for the modelling of milling is described. The cutting forces are calculated for milling operations directly from the tool path provided by a Computer Assisted Manufacturing program. The main idea consists in using tool position points coming from CAM data in order to calculate the local inclination angle of the generated surface and then the tool engagement in the machined material. A good approximation for global and local cutting forces can be obtained when an analytical model able to predict the cutting forces for 3-axes milling is used. Two approaches are proposed to calculate the local cutting forces to show the versatility of the method. The first method uses a thermomechanical approach using a Johnson & Cook constitutive law while the second is based on classical cutting coefficients. Some results are presented for wavelike form and free form machining tests and are compared with experimental data obtained in roughing and finishing of 42CrMo4 steel. Results are satisfactory and the capability of the method to predict the resultant surface roughness is shown.

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Abbreviations

(E,x,y,z) :

Tool reference system

(O,X,Y,Z) :

Global reference system

i :

Tool path index point (integer)

j :

Tooth index (integer)

k :

Tool path index (integer)

P :

Current point

(R(z), κ, ψ):

Spherical current point coordinates

ψ j :

Edge location angle

Δψ :

Shift angle

κ :

Inclination angle of vector e r

z :

Height along the rotation axis

R(z):

Local radius of tool envelope

R 0 :

Nominal radius of the cutter

θ :

Rotation angle

Ω:

Spindle frequency

i(z):

Local helix angle

(e r , e κ, e ψ ):

Local cutting edge base vectors

K r , K κ , K ψ :

Cutting force coefficients

λ S :

Local cutting edge inclination angle

γ 0 :

Orthogonal rake angle

γ n :

Normal rake angle

dw :

Local elementary cutting width

δ :

Local inclination angle along the surface

CL(i):

Cutter Location points considered along tool path

f :

Feed per rotation

f t :

Feed per tooth

\({\varphi_{x}, \varphi_{z}}\) :

Local feed angles

Δp :

Path interval

\({\varphi_{\Delta p}}\) :

Transverse inclination angle

z sp :

Height of the previous machined surface

C P , R P :

Parameters of tool envelope on the previous tool path

t 0 :

Undeformed chip thickness

e j :

Eccentricity vector for the considered tooth j

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Authors and Affiliations

  1. EMP, BP 17 Bordj El Bahri, 16111, Alger, Algeria

    N. Zeroudi & K. Necib

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

    M. Fontaine

Authors
  1. N. Zeroudi
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  2. M. Fontaine
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  3. K. Necib
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Correspondence to N. Zeroudi.

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Zeroudi, N., Fontaine, M. & Necib, K. Prediction of cutting forces in 3-axes milling of sculptured surfaces directly from CAM tool path. J Intell Manuf 23, 1573–1587 (2012). https://doi.org/10.1007/s10845-010-0460-x

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  • DOI: https://doi.org/10.1007/s10845-010-0460-x

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