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Application of mechanistic force models to features of arbitrary geometry at low material removal rate

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Abstract

This paper presents a workpiece discretization method to apply existing cutting force models to predict the forces generated during low material removal rate robotic machining operations of features with arbitrary geometry. Two machining operations along a straight edge which are modelled using this feature discretization method are shown, a chamfer pass on a sharp corner and the removal of a trapezoidal cross section. The workpiece features are measured using a high-resolution laser profile scanner to obtain the volume of the features to be removed. The identified features are discretized into rectangular sections such that the cutting force models can be applied to predict the cutting forces. A linear and an exponential mechanistic model which relate tool immersion and feed rate to the cutting force are applied to the scanned workpiece features. The linear and nonlinear models show good agreement with the measured data, with the exception that the linear model occasionally over predicts the forces depending on the radial depth of cut.

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Abbreviations

a :

Axial depth of cut

b :

Radial depth of cut

D :

Tool diameter

ē :

Mean error

F :

Force

f :

Feed per tooth

h :

Uncut chip thickness

J :

Number of segments in discretized cutter

dz :

Height of segments in discretized cutter

d Z :

Height of discretized feature elements

K tc, K te, K rc,:

Linear model empirical parameters

K re, K ac, K ae K t, K r, K a, β :

Exponential model empirical parameters

L s e g :

Length of discretized feature segment

m :

Generic axis

N :

Number of teeth on discretized cutter

r :

Tool radius

t, r, a :

Tangential, radial, and axial axes for orthogonal cutting element

V f e e d :

Linear feed velocity

x, y, z :

Cartesian coordinates or axes

δ :

Tool helix angle

ψ :

Angular offset of segments in discretized cutter

ϕ :

Angular position of cutting tool

ϕ st, ϕ ex :

Start and exit immersion angles

P i :

Single profile of point cloud aligned normal to toolpath

V i :

Set of vertices defining approximated chamfer area

v i, a, v i, b, v i, c :

Vertices of the approximated chamfer area

i :

Index

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Funding

This work received support from the Natural Sciences and Engineering Research Council of Canada (NSERC) grants RGPIN- 2017-06967, RGPIN-2015-04169, and CRDPJ 514258-17

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Authors and Affiliations

  1. Carleton University, Ottawa, Ontario, K1S 5B6, Canada

    Grael Miller, Rishad A. Irani & Mojtaba Ahmadi

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  1. Grael Miller
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  2. Rishad A. Irani
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  3. Mojtaba Ahmadi
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Corresponding author

Correspondence to Grael Miller.

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No ethical approval required for the experiments conducted, as no human or animal participants involved.

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The authors declare no competing interests.

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Author contribution

Grael Miller: conceptualization, methodology, validation, writing original draft, software. Rishad Irani: review, conceptualization, methodology, validation, writing—review and editing. Mojtaba Ahmadi: review, conceptualization, methodology, validation, writing—review and editing

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Raw data is protected under IP agreements associated with CRDPJ 514258-17.

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Miller, G., Irani, R.A. & Ahmadi, M. Application of mechanistic force models to features of arbitrary geometry at low material removal rate. Int J Adv Manuf Technol 117, 2741–2754 (2021). https://doi.org/10.1007/s00170-021-07830-9

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