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Surface morphology prediction model for milling operations

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Abstract

The capability of estimating the surface quality of workpieces in machining is still a challenging goal. The morphology of the processed surfaces does not only depend on nominal tool geometry and on machining parameters but it is also affected by several complex cutting phenomena and deviations from nominal conditions. In this paper, a framework model for estimating the surface texture in milling operations was developed. The model allows considering various tool geometries and the corresponding alignment/mounting errors. Since the back cutting phenomenon is adequately formalized, the model is particularly suitable for estimating the surface topography in face milling. Although the model does not consider the contribution due to the cutting forces, it is suitable for being fed by measured tool vibrations. The predicting capabilities of the conceived model were tested considering a high-feed milling operation that typically generates complex patterns on the processed surfaces. The model validation was carried out comparing the numerical and the real machined surface morphology. The analysis confirmed that the surface morphology can be predicted with negligible errors.

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Abbreviations

0 1 :

Reference system

\(\overline {\boldsymbol {0}}{_{\boldsymbol {2}}}\) :

Reference system associated to the tool center

x1, y1, z1 :

Coordinates of the reference system 01

p :

Vector describing the position of a generic point on the cutting edge with respect to reference system 01

Δp :

Vector describing the relative position of the reference \(\overline {\boldsymbol {0}}{_{\boldsymbol {2}}}\) with respect to framework 01

\(\overline {\boldsymbol {p}}\) :

Vector describing a generic position on the cutting edge with respect to reference \(\overline {\boldsymbol {0}}{_{\boldsymbol {2}}}\)

\(\overline {x}_{2}\), \(\overline {y}_{2}\), \(\overline {z}_{2}\) :

Coordinates of the reference system \(\overline {\boldsymbol {0}}{_{\boldsymbol {2}}}\)

ΔX, ΔY, ΔZ :

elements of the vector Δp

\(\hat {x}_{3}\), \(\hat {y}_{3}\), \(\hat {z}_{3}\) :

Coordinates of the reference system \(\boldsymbol {\hat {0}}{_{\boldsymbol {3}}}\)

R :

Rotation matrix

𝜃 :

Rotation angle

R :

Tool radius

I :

Identity matrix

\(\widetilde {\mathbf {v}}\) :

Cross-product matrix

v :

Unit vector linked to the tool rotation axis

v i b :

Tool vibration

ω :

Tool rotation velocity

t :

Time

f j :

Generic j th component of the axis feed velocity

Δt :

Time interval for the simulation

t i :

Generic discretized i th time instant

Δx1r :

Mesh size ratio along x1 direction

Δy1r :

Mesh size ratio along y1 direction

Δz1r :

Mesh size ratio along z1 direction

R a :

Surface roughness

f z :

Feed per tooth

𝜃 e :

Tool lead angle

R e :

Insert tip radius

s :

Curvilinear abscissa

Δs :

Discretization step of the curvilinear abscissa

a p :

Axial depth of cut

Z :

Number of teeth

D nom :

Nominal diameter of the tool

D int :

Internal diameter of the tool

a e :

Radial depth of cut

Δx1 :

Mesh size along x1 direction

Δy1 :

Mesh size along y1 direction

Δz1 :

Mesh size along z1 direction

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Funding

This work was supported by the regional project SENSE&MILL 803442 (POR-FESR 2014-2020, Regione Emilia Romagna) and the national project CLUSTER La fabbrica Intelligente High Performance Manufacturing (CTN0100163216758), founded by MIUR.

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Authors and Affiliations

  1. Consorzio MUSP, strada Torre della Razza, 29122, Piacenza, Italy

    Mattia Torta

  2. Mechanical Engineering Department, Politecnico di Milano, via La Masa 1, 20156, Milan, Italy

    Paolo Albertelli & Michele Monno

Authors
  1. Mattia Torta
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  2. Paolo Albertelli
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  3. Michele Monno
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Correspondence to Paolo Albertelli.

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Torta, M., Albertelli, P. & Monno, M. Surface morphology prediction model for milling operations. Int J Adv Manuf Technol 106, 3189–3201 (2020). https://doi.org/10.1007/s00170-019-04687-x

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