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Improving the accuracy of TIF in bonnet polishing based on Gaussian process regression

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Abstract

Based on the Gaussian process regression (GPR), this paper aims to provide a method to improve the accuracy of the classic tool influence function (TIF) model in bonnet polishing (BP). Firstly, we build the velocity and pressure distribution models in TIF according to kinematics relations and Hertz contact theory. And our investigating experiments about contacting forces indicate that the constant K in the Preston equation is actually not a constant and depends on the interfacial friction coefficient μ. According to the experimental results, several main processing parameters (i.e., rotation speed, polishing depth, inflated pressure) have dramatic effects on μ. Thus, the classic model of TIF based on Preston equation needs to be revised. Relevant experiments and researches are conducted to search a more accurate linkage between TIF model and the main processing parameters. By designing composite covariance kernel functions for μ, we apply GPR method in TIF model and promote the accuracy of TIF acquired in experiments. Two groups of experiments are conducted, and the prediction performance of the new modified TIF model in our researches is verified to surely improve the accuracy of TIF comparing with the classic model. Since few researches are focusing on this aspect, our work is to find out the relation between μ and processing parameters and provide a method of modelling μ to modify K.

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Abbreviations

GPR:

Gaussian process regression

TIF:

Tool influence function

BP:

Bonnet polishing

μ :

Interfacial friction coefficient

K :

Constant in Preston equation ∆Z = K · P(x, y) · V(x, y) · ∆t

CCBP:

Computer-controlled bonnet polishing

P :

Contacting pressure distribution on the contact area

V :

Relative velocity distribution on the contact area

∆Z :

Removed material amount

∆t :

Dwell time

R :

Radius of the bonnet

d :

Polishing depth

n :

Rotation speed

μ(n):

Function μ with variable n

μ(d):

Function μ with variable d

θ :

Precession angle

r c :

Radius of the contact area

\( {\upsigma}_{\mathrm{zz}}^{\mathrm{el}} \) :

Elastic part in the stress tensor

\( {\upsigma}_{\mathrm{zz}}^{\mathrm{dis}} \) :

Dissipative part in the stress tensor

Fx, Fy, Fz :

3-dimensional contacting polishing forces

SE:

Square exponential kernel function

PER:

Periodic kernel function

σ1, l1, σ2, l2T :

Hyperparameters

E :

Z divided by the width of TIF

ε :

z divided by the width of TIF

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Authors and Affiliations

  1. Institute of Robotics, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China

    Jingbo Feng, Yifan Zhang, Shuo Lin & Yuehong Yin

Authors
  1. Jingbo Feng
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  2. Yifan Zhang
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  3. Shuo Lin
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  4. Yuehong Yin
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Correspondence to Yuehong Yin.

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Assumptions

1. The contact area of bonnet and workpiece surface is a circle. The polishing spot is a circle in theory taking no account of bonnet vibration and deformation.

2. The bonnet and the target surface are assumed to be a viscous sphere and a rigid plane. Ignoring some secondary but complex factors to simplify the pressure model.

3. K is a not a constant. Experimental results show that it is a variable of several parameters.

4. The feeding speed is 0. There is no feeding speed when calculating a static TIF.

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Feng, J., Zhang, Y., Lin, S. et al. Improving the accuracy of TIF in bonnet polishing based on Gaussian process regression. Int J Adv Manuf Technol 110, 1941–1953 (2020). https://doi.org/10.1007/s00170-020-05917-3

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  • DOI: https://doi.org/10.1007/s00170-020-05917-3

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