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Theoretical and experimental study of ceramic balls lapping with eccentric plates and eccentric V-groove

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Abstract

Ceramic balls are produced via powder metallurgy and compared to steel balls are preferred due to their special physical and mechanical properties. Ceramic balls can reach the desired surface finishing, sphericity, and diameter by finishing processes such as grinding, lapping, and polishing. By considering the length of time and high costs of the finishing process, creating an economic mechanism is of great importance in the use of ceramic balls. The present paper was conducted to investigate the eccentric lapping plates mechanism with eccentric V-grooves for ceramic balls lapping. This mechanism is proposed to increase the material removal rate (MRR) and to reduce the sphericity error of the ceramic balls. The effects of parameters including lower and upper lapping plate rotation speeds, the eccentricity of lapping plates, and lapping force were investigated on MRR, and the reduction of sphericity error. The kinematic analysis was performed to calculate the trajectory length and its distribution on the ball surface. Experimental tests were carried out to validate the kinematic analysis on the pre-sintered Al2O3 balls. The effects of the above-mentioned parameters on the lapping process were determined. The proposed mechanism provided an MRR of 0.766 mm/h; in this regard, sphericity error also reduced down 0.184 mm in 20 min.

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All data generated or analyzed during this study are included in this published article.

Abbreviations

A i :

Number of the points in area i

\( {\overline{A}}_i \) :

Average number of the points in all the areas of the ball surface

E:

Eccentricity of the groove from the axis of rotation of the lower lapping plate

e:

Distance between the axis of rotation of the upper and lower lapping plates

i:

The calculation step

L:

Trajectory length

N :

Number of areas of the ball surface

RA :

The distance between contact point A to the center of the V-groove

RB :

The distance between contact point B to the center of the V-groove

R g :

Radius of the V-groove

R b :

Radius of the ball

r A :

The distance from the center of the lower lapping plate to the contact point A of the ball

r B :

The distance from the center of the lower lapping plate to the contact point B of the ball

r u :

The distance from the center of the upper lapping plate to the center of the ball

r g :

The distance between the center of rotation of the lower lapping plate and the point of contact of the ball with the upper lapping plate

t :

Time

ω b :

Ball spin speed

ω c :

Ball circulation speed

β:

Spin angle

γ :

The angle between the linear velocity direction of the lower lapping plate and the direction of motion of the ball in the V-groove

∆θ:

The ball’s rotation increment in each calculation step

θ:

Half of the V-groove angle

τ:

Angle between the linear velocity vector of the upper lapping plate at the contact point of the ball with the direction of motion of the ball

∅:

The angle between the linear velocity direction of the lower lapping plate and the direction of motion of the ball in the V-groove

ΩL :

The lower lapping plate speed

Ωu :

The upper lapping plate speed

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Birjand, Birjand, Iran

    Mohammad Reza Darmiyani

  2. Department of Engineering, University of Neyshabur, P.O.B. 9319774400, Neyshabur, Iran

    Hossein Amirabadi

  3. Department of Mechanical Engineering, Birjand University of Technology, Birjand, Iran

    Mohammad Khosravi

Authors
  1. Mohammad Reza Darmiyani
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  2. Hossein Amirabadi
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  3. Mohammad Khosravi
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Contributions

Mohammad Reza Darmiyani: conceptualization, methodology, formal analysis, investigation, writing, original draft.

Hossein Amirabadi: conceptualization, methodology, supervision, writing, review, editing.

Mohammad Khosravi: supervision, writing, review, editing. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Hossein Amirabadi.

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We the authors, Mohammad Reza Darmiyani, Dr. Hossein Amirabadi and Dr. Mohammad Khosravi, consent and approve the publication of this article with identification number JAMT-D-21-00499.

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Darmiyani, M.R., Amirabadi, H. & Khosravi, M. Theoretical and experimental study of ceramic balls lapping with eccentric plates and eccentric V-groove. Int J Adv Manuf Technol 116, 3417–3430 (2021). https://doi.org/10.1007/s00170-021-07585-3

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  • DOI: https://doi.org/10.1007/s00170-021-07585-3

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