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Predictive modeling and experimental study of polishing force for ultrasonic vibration-assisted polishing of K9 optical glass

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Abstract

With the development of science and technology, many precision fields have higher requirements for the machining quality and precision of hard and brittle materials. Brittle materials such as glass and ceramics have fragile physical properties, resulting in poor stability during machining. Ultrasonic vibration-assisted polishing (UVAP) is suitable for machining various brittle materials and can well solve the machining problems caused by the characteristics of brittle materials. In order to ensure the machining quality, a polishing force model of K9 optical glass for different processing parameters is established in this paper. The new model mainly considers the following aspects: (1) Considering the randomness of shape, the truncated polyhedral model is used to model the abrasive particles. (2) Based on the fractal theory and mathematical statistics, a microscopic morphology model of the polishing tool is established. (3) Based on the N–S equation, a polishing force model considering the micro-contact states of the polishing tool, abrasive particles, and workpiece is established. By comparing with the experimental results, the new model has high accuracy in predicting the polishing force. The new model and results lay the foundation for the subsequent research of brittle materials.

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Data availability

The datasets supporting the conclusion of this article are included within the article.

Abbreviations

\(\text{a}_\text{t}\) :

Contact area between polishing tool and workpiece \((\text{mm}^2)\)

\(\text{d}_\text{e}\) :

Number of Euclidean spatial dimensions

\(\text{d}_\text{p}\) :

Diameter of abrasive particle (\(\mu \text{m}\))

\(\text{d}_\text{m}\) :

Diameter of asperity (\(\mu \text{m}\))

\(\text{D}_\text{f}\) :

Fractal dimension

\(\text{E}_\text{m}\) :

Elastic modulus of polishing tool (Gpa)

\(\text{E}_\text{mw}\) :

Equivalent elastic modulus of polishing tool and workpiece (Gpa)

\(\text{E}_\text{p}\) :

Elastic modulus of abrasive particle (Gpa)

\(\text{E}_\text{pw}\) :

Equivalent elastic modulus of abrasive particle and workpiece (Gpa)

\(\text{E}_\text{w}\) :

Elastic modulus of workpiece (Gpa)

\(\text{F}_{\text{a}-\text{l}}^{\text{t}-\text{i}}\) :

Maximum horizontal impact force (N)

\(\text{F}_{\text{a}-\text{z}}^{\text{t}-\text{i}}\) :

Maximum normal impact force (N)

\(\text{F}_\text{ep}\) :

Critical elastic-plastic contact force (N)

\(\text{F}_{\text{f}-\text{l}}^{\text{t}-\text{i}}\) :

Scratching force in horizontal direction (N)

\(\text{F}_{\text{f}-\text{z}}^{\text{t}-\text{i}}\) :

z-direction force generated by asperity (N)

\(\text{F}_{\text{X}-\text{t}}\) :

Polishing force in x-direction (N)

\(\text{F}_{\text{Y}-\text{t}}\) :

Polishing force in y-direction (N)

\(\text{F}_{\text{Z}-\text{t}}\) :

Polishing force in z-direction (N)

G:

Characteristic scale coefficient

\(\text{h}_{\text{s}}\) :

Thickness of slurry film (\(\mu \text{m}\))

\(\text{h}_{\text{t}}\) :

Distance between polishing tool and workpiece (\(\mu \text{m}\))

\(\text{k}_{\text{p}}\) :

Preston coefficient

\(\text{N}_{\text{a}}\) :

Total number of the free abrasive particles

\(\text{N}_{\text{m}}\) :

Total number of asperities subjected to extrusion

\(\text{P}_{\text{0}}\) :

Hydrostatic pressure of the slurry outside the bubble (pa)

\(\text{P}_{\text{b}}\) :

Pressure at the bubble collapse point (pa)

\(\text{P}_{\text{v}}\) :

Pressure inside the cavitation bubble (pa)

\(\text{r}_{\text{p}}\) :

Radius of abrasive particle (\(\mu \text{m}\))

\(\text{R}_{\text{q}}\) :

Radius of the cavitation bubble (\(\mu \text{m}\))

\(\text{u}_{\text{r}2-\text{t}}^{\text{i}}\) :

Radial velocity of polishing slurry (m/s)

\(\text{u}_{\theta 2-\text{t}}^{\text{i}}\) :

Circumferential velocity of polishing slurry (m/s)

\(\text{v}_{\text{0}}\) :

Initial velocity of abrasive particle (m/s)

\(\text{v}_{\text{t}}\) :

Feed rate of polishing tool (mm/s)

\(\text{z}_{\text{m}}\) :

Height of asperity (\(\mu \text{m}\))

\(\gamma_{\text{p}}\) :

Poisson’s ratio of abrasive particle

\(\gamma_{\text{s}}\) :

Specific heat capacity ratio

\(\gamma_{\text{w}}\) :

Poisson’s ratio of workpiece

\({\mu}_{\text{r}-\text{t}}^{\text{i}}\) :

Sliding friction coefficient

\({\rho}_{\text{f}}\) :

Density of polishing slurry (\(\text{g}/\text{cm}^3\))

\({\rho}_{\text{p}}\) :

Density of abrasive particle (\(\text{g}/\text{cm}^3\))

\(\sigma\) :

Surface tension coefficient of bubble 

\(\sigma_{\text{y}}\) :

Yield stress of the workpiece (Mpa)

\(\varphi\) :

Porosity of the polishing tool

\(\lambda_{\text{ep}}\) :

Critical elastic-plastic deformation depth (\(\mu \text{m}\))

\(\lambda_{\text{pb}}\) :

Critical brittle-plastic deformation depth (\(\mu \text{m}\))

\(\lambda_{\text{max}}^{\text{t}-\text{i}}\) :

Maximum deformation depth (\(\mu \text{m}\))

\(\lambda_{\text{max}-\text{al}}^{\text{t}-\text{i}}\) :

Maximum horizontal impact depth (\(\mu \text{m}\))

\(\lambda_{\text{max}-\text{az}}^{\text{t}-\text{i}}\) :

Maximum normal impact depth (\(\mu \text{m}\))

\(\chi_{\text{m}}\) :

Mass fraction of abrasive particles in polishing slurry

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Funding

This work was funded from Fundamental Research Funds for the Central Universities [Grant No.2103001]; the Major State Basic Research Development Program of China [Grant No. 2017YFA07].

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Chao Zhang, Sheng Qu, Yingdong Liang, Xin Chen, Ji Zhao & Tianbiao Yu

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  1. Chao Zhang
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  2. Sheng Qu
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  3. Yingdong Liang
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  4. Xin Chen
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  5. Ji Zhao
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  6. Tianbiao Yu
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Contributions

Chao Zhang performed conceptualization, methodology, software, validation, formal analysis, data curation, writing—original draft, and writing—review and editing. Sheng Qu and Xin Chen contributed to software and formal analysis. Yingdong Liang was involved in resources, supervision, and project administration. Ji Zhao done funding acquisition. Tianbiao Yu was involved in supervision.

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Correspondence to Tianbiao Yu.

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Zhang, C., Qu, S., Liang, Y. et al. Predictive modeling and experimental study of polishing force for ultrasonic vibration-assisted polishing of K9 optical glass. Int J Adv Manuf Technol 119, 3119–3139 (2022). https://doi.org/10.1007/s00170-021-08624-9

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