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Material removal rate prediction and surface quality study for ultrasonic vibration polishing of monocrystalline silicon

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Abstract

Ultrasonic vibration polishing (UVP) which integrates mechanical polishing and ultrasonic vibration technologies is applied to process monocrystalline silicon. The predictive model for material removal rate (MRR) is developed which includes the microscopic contact among the workpiece, abrasive grains, and polishing pad, the scratch effect of embedded abrasive grains, and the impact removal of free abrasive grain on the workpiece surface. This model unveils the reasons for the enhancement of MRR and the effect of different parameters on MRR during UVP. UVP experiments of monocrystalline silicon were carried out to validate this model. It is found that the MRR model is in excellent consistency with the measured MRR and the error rates could be controlled to less than 10%. The increase in spindle speed and ultrasonic amplitude increases the kinetic energy of the abrasive grains. The increase in abrasive grain size improves the contact area between the abrasive grains and the workpiece. Therefore, these contribute to the MRR of the UVP. In addition, different polishing parameters (spindle speed, ultrasonic amplitude, and abrasive grain size) were analyzed and compared on the surface roughness and microscopic local morphology. This work not only offers a novel method for predicting the machining efficiency of UVP but also provides an excellent reference for the evolution of ultrasonic vibration-assisted technologies.

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Data availability

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

Code availability

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Abbreviations

A :

Ultrasonic amplitude of electro-spindle system (μm)

a :

Distribution coefficient of the material removal profile (dimensionless)

E p :

Young’s modulus of the pad (MPa)

E w :

Young’s modulus of the workpiece (MPa)

E a :

Young’s modulus of the abrasive grain (MPa)

E pw * :

Relative Young’s modulus between the pad and the workpiece (MPa)

E aw * :

Relative Young’s modulus between the abrasive grain and the workpiece (MPa)

f :

Ultrasonic frequency of electro-spindle system (kHz)

f 1 :

Ultrasonic frequency of ultrasonic atomization system (kHz)

F 0 :

Pre-force (N)

F :

Contact force (N)

F t :

Impact force (N)

F max :

Maximum contact force (N)

F m :

Mean contact force (N)

h :

Projection height of the pad (mm)

h s :

Nominal separation between the pad and the workpiece (mm)

h e :

Critical nominal separation (mm)

h max :

Maximum height of projection (mm)

H p :

Pad hardness (GPa)

P m :

Mean pressure of the single projection (Pa)

H w :

Workpiece hardness (GPa)

n :

Speed of ultrasonic electro-spindle (rpm)

N :

Number of projections per unit area (mm−2)

N 1 :

Number of effective embedded abrasive grains

N 2 :

Number of free abrasive grains

R abr :

Abrasive grain size (μm)

R T :

End face radius of the pad (mm)

R p :

Average radius of the projection (mm)

S aw :

Contact area between a single projection and workpiece surface (mm2)

S 0 :

Nominal contact area (mm2)

S real :

Real contact area (mm2)

t :

Dwell time (s)

T :

Vibration cycle of electro-spindle system (min)

υ p :

Poisson’s ratio of the pad

υ w :

Poisson’s ratio of the workpiece

υ a :

Poisson’s ratio of the abrasive grain

V pw :

Removal amount of a single free abrasive grain impacting the workpiece (mm3)

v r :

Mean scratch linear speed (m/s)

Z t :

Movement distance of the pad (μm)

φ(h):

Probability distribution of microscopic projection height

ƞ :

Density of the single projection

σ :

Standard deviation of the projection height (mm)

θ :

Phase difference (rad)

λ e -p :

Critical depth of the embedded abrasive grain (μm)

ρ abr :

Abrasive grain density (g/cm3)

μ slu :

Bulk density of the polishing solvent

λ pw :

Interference depth between the single projection of the pad and the workpiece (mm)

λ w :

Indentation depth of the embedded abrasive grain (mm)

l :

Initial thickness of the pad (mm)

Ω:

Areal density (mm−2)

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Funding

The authors appreciate the Major State Basic Research Development Program of China (No. 2017YFA0701200), the 111 Project (No. B16009), the National Natural Science Foundation of China (No. 52005091), the Fundamental Research Funds for the Central Universities (No. N2203016), and China Postdoctoral Science Foundation (No. 2021M700717).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, People’s Republic of China

    Sheng Qu, Tao Yu, Fanwei Meng, Chao Zhang, Xuewei Zhang, Zhelun Ma, Zixuan Wang, Tianbiao Yu & Ji Zhao

  2. National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Shenyang, 110819, China

    Sheng Qu, Fanwei Meng, Chao Zhang, Xuewei Zhang, Zhelun Ma, Zixuan Wang, Tianbiao Yu & Ji Zhao

  3. Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University, Ministry of Education, Hebei, China

    Sheng Qu, Fanwei Meng, Chao Zhang, Xuewei Zhang, Zhelun Ma, Zixuan Wang, Tianbiao Yu & Ji Zhao

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  1. Sheng Qu
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  2. Tao Yu
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  3. Fanwei Meng
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  9. Ji Zhao
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Contributions

Sheng Qu: conceptualization, methodology, software, validation, formal analysis, writing-original draft, writing-review and editing. Tao Yu: software, formal analysis. Fanwei Meng: resources, project administration. Chao Zhang: software, formal analysis. Xuewei Zhang: funding acquisition. Zhelun Ma: data curation. Zixuan Wang: funding acquisition. Tianbiao Yu: supervision. Ji Zhao: funding acquisition.

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Correspondence to Tianbiao Yu or Ji Zhao.

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Qu, S., Yu, T., Meng, F. et al. Material removal rate prediction and surface quality study for ultrasonic vibration polishing of monocrystalline silicon. Int J Adv Manuf Technol 127, 4789–4802 (2023). https://doi.org/10.1007/s00170-023-11811-5

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