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An analytical model of the material removal rate between elastic and elastic-plastic deformation for a polishing process

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Abstract

This paper develops an analytical model for the material removal rate during specimen polishing. The model is based on the micro-contact elastic mechanics, micro-contact elastic-plastic mechanics and abrasive wear theory. The micro-contact elastic mechanics between the pad-specimen surfaces used the Greenwood and Williamson elastic model. The micro-contact elastic-plastic mechanics between specimen and particle, as well as the micro-contact elastic mechanics between particle and pad, are also analyzed. The cross-sectional area of the worn groove in the specimen is considered as trapezoidal area. A close-form solution of material removal rate from the specimen surface is the function of average diameter of slurry particles, pressure, the specimen/pad sliding velocity, Equivalent Young’s modulus, RMS roughness of the pad, and volume concentration of the slurry particle.

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Abbreviations

An :

Nominal contact area

At :

Total real contact area

C:

Removal rate constant

CP :

Preston coefficient

d:

Mean separation between pad and specimen based on asperity heights

D:

Average diameter of slurry particles

Epad :

Young’s modulus of pad

Epar :

Young’s modulus of slurry particles

Es :

Young’s modulus of specimen

Espad :

Equivalent Young’s modulus between the specimen and the pad

Espar :

Equivalent Young’s modulus between the specimen and the particle

Epp :

Equivalent Young’s modulus between the particle and the pad

H:

Hardness of softer material

h:

Separation based on surface heights

K:

Wear constant

l:

Line density of particles in polishing slurry

P:

Applied pressure (=Wt/An)

q:

Area density of particles in polishing slurry

R:

Asperity radius of curvature

rc :

Radius of the circular indentation area of a particle on specimen surface due to elastic deformation

rp :

Radius of the circular indentation area of a particle on specimen surface due to plastic deformation

s:

Sliding distance

t:

Polishing time

V:

Sliding velocity between pad and specimen

Wt :

Total contact load between pad and specimen

x:

Particle volume concentration in polishing slurry

ys :

Distance between the mean of asperity heights and that of surface heights

z:

Height of an asperity measured from the mean of asperity heights

ρ:

Material removal rate of specimen

σ:

RMS roughness of the pad

Φ:

Distribution function of asperity heights

ξ:

Volume of an individual slurry particle

δc :

Indentation depth of a particle in specimen due to elastic deformation

δe :

Indentation depth of a particle in polishing pad

δp :

Indentation depth of a particle in specimen due to plastic deformation

υpad :

Poisson’s ratio of the pad

υpar :

Poisson’s ratio of the slurry particles

υs :

Poisson’s ratio of the specimen

ω:

Local contact interference between pad and specimen

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Authors and Affiliations

  1. Department of Mechanical Manufacturing Engineering, National Formosa University, Hu-Wei, Taiwan, 632, Republic of China

    Tsann-Rong Lin

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  1. Tsann-Rong Lin
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Correspondence to Tsann-Rong Lin.

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Lin, TR. An analytical model of the material removal rate between elastic and elastic-plastic deformation for a polishing process. Int J Adv Manuf Technol 32, 675–681 (2007). https://doi.org/10.1007/s00170-005-0391-4

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  • DOI: https://doi.org/10.1007/s00170-005-0391-4

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