Prediction research for surface topography of internal grinding based on mechanism and data model


Grinding surface topography is an important evaluation index of grinding surface integrity. In order to realize the prediction of the grinding surface topography, a three-dimensional theoretical model of the surface topography of internal grinding was established in terms of the mutual movement between the grinding wheel and the workpiece and a data model for the surface roughness of internal grinding was set up based on the grey wolf algorithm-support vector machine (GWO-SVM). Taking the inner ring of rolling bearing as an example, the grinding experiment was carried out to analyze the influence of technological parameters on the surface topography and surface roughness. Three traditional data models were compared with the GWO-SVM data model, the comparison results showed that the GWO-SVM data model had a small change in the relative error of the predicted value of the test sample, the maximum relative error was 5.42%, and the average relative error was 3.95%. Experimental results were compared with the results of theoretical model and data model, the results show that the error of both the theoretical model and the data model is within 10%. This work should be helpful in reflecting the formation mechanism of the surface topography of the internal grinding and provide theoretical and technical support for high-precision and high-efficiency manufacturing of high-end rolling bearing.

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Data availability

We confirm that data is open and transparent.


M :

A grinding wheel with particle size

d gmax :

The maximum grinding particle diameter (mm)

d gavg :

The average diameter of the abrasive particles (mm)

μ 0 :

The mean value of normal distribution

σ 0 :

The variance of normal distribution

h i :

Protruding height of abrasive particles (mm)


The average distance between adjacent grinding grains on the grinding wheel surface (mm)

S :

The structural parameter of the grinding wheel

V g :

The volume percentage of grinding grains of the grinding wheel (%)

N :

The number of grinding grains on a circle of the grinding wheel

r s :

The radius of the grinding wheel (mm)

k :

The percentage ratio of grinding grain to surface height of grinding wheel

H i :

The protruding height of the ith abrasive particle (mm)

r i :

The distance between the ith grinding grain and the center of the grinding wheel (mm)

r ω :

The radius of workpiece at the grinding point (mm)

t 0 :

The time of mutual movement(s)

θ S :

The rotation angle of a single abrasive particle of the grinding wheel (°)

θ ω :

The rotation angle of the workpiece (°)

ϕ ω :

The angular coordinates differ (°)

g mn :

Topological matrix of internal grinding surface

i :

The circumferential position of the grinding wheel

j :

The axial position of the grinding wheel


The height of the grinding grain at the circumferential and axial positions of the grinding wheel(mm)

N i :

The number of peaks and valleys

Y pi :

The peak height (mm)

Y vi :

The peak valley depth (mm)

ω T :

A vector

L(y i, y Ra):

The loss function

μ :

The penalty parameter of SVM

ε :

The insensitive loss factor of SVM

\( {\xi}_i,{\xi}_i^{\ast } \) :

The slack variable

λ, λ :

The Lagrangian multipliers

K(x i, x j):

The kernel function

σ :

The parameter of kernel function

t :

The number of iterations

X i :

The position of the grey wolf

d i :

The position between the grey wolf and prey

t max :

The maximum number of iterations

n w :

Workpiece speed (r/min)

v S :

Grinding wheel speed (m/s)

n r :

Feed speed mm/min)


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This work was supported by the National Natural Science Foundation of China (grant number U1809221), high-tech Industry of Science and Technology Innovation Leading Project of Hunan Province of China (grant number 2020GK003), and the Special project of National Independent Innovation Demonstration Zone of Changzhutan (grant number 2GK017XK2302).

Author information




Qianwei Gu: Investigation, data curation, writing of original draft, and editing.

Zhaohui Deng: Reviewing, editing, and funding acquisition.

Lishu Lv: Investigation, supervision, writing, reviewing, and editing.

Tao Liu: Supervision, writing, reviewing, and editing.

Hongzhao Teng: Reviewing, and editing.

Dongfeng Wang: Supervision, project administration.

Julong Yuan: Project administration, supervision, and reviewing.

Corresponding author

Correspondence to Zhaohui Deng.

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The authors declare that they have no conflict of interest.

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The codes generated during the current study are available from the corresponding author on reasonable request.

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Gu, Q., Deng, Z., Lv, L. et al. Prediction research for surface topography of internal grinding based on mechanism and data model. Int J Adv Manuf Technol (2021).

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  • Internal grinding
  • Theoretical model
  • Data model
  • Surface topography
  • Surface roughness