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Rounding mechanism of a novel double-disc arc-contact lapping for high-precision rollers

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Abstract

Centerless grinding is the main technology for mass processing of rotary parts, which can improve the roundness of rotary parts. With the demand for higher levels of roundness accuracy (within 0.3 μm), the development and operating costs of centerless grinding machines have increased dramatically. Taking cylindrical roller of bearing as research object, a new lapping process of double-disc arc-contact lapping (DDACL) is presented in this work. On the processing mechanism, it is expounded how DDACL overcomes the three fundamental technical difficulties of centerless grinding process in geometric lobing, workpiece instability and work-regenerative chatter vibration, and the unique rounding mechanism of DDACL process is established. At the same time, the machine has simple structure, low precision requirement, and low cost. After lapping with 45 steel groove on the developed test bench, the roundness accuracy of the cylindrical roller is effectively controlled within 0.2 μm, and the accuracy of some rollers can even reach 130 nm, which has significant precision advantages. According to the established DDACL rounding mechanism, the influence of 45 steel and PTFE groove material and electromagnetic driving force on the rounding speed of parts in the test is well explained. The process method proposed in this work paves the way for improving the roundness accuracy of other rotary parts, such as those seen in tapered roller and spherical roller.

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Data availability

The data presented and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\({A}_{i}\) :

Geometric rounding sensitivity coefficient of DDACL

\({A}_{j}\) :

Geometric rounding sensitivity coefficient of centerless grinding

\({B}_{i}\) :

Geometric rounding tangential coefficient of DDACL

\({B}_{j}\) :

Geometric rounding tangential coefficient of centerless grinding

\({C}_{i}\) :

Amplitude of the \(i\) th harmonic (mm)

\({E}_{i}\) :

Elastic modulus of the roller material

\({E}_{j}\) :

Elastic modulus of the linear groove material

\({E}_{*}\) :

Composite elastic modulus of the linear groove and the roller

\({E}_{45steel}^{*}\) :

Composite elastic modulus when the linear groove is made of 45 steel

\({E}_{PTEF}^{*}\) :

Composite elastic modulus when the linear groove is made of PTFE

\({f}_{1}\) :

Friction force of the upper disc on the roller (N)

\({f}_{2}\) :

Resultant tangential friction force of the linear groove on the roller (N)

\({F}_{1}\) :

Pressure of the upper disc on the roller (N)

\({F}_{2}\) :

Radial lapping force of the linear groove on the roller (N)

\({F}_{45steel}\) :

Radial lapping force on the roller when the linear groove is 45 steel (N)

\({F}_{PTEF}\) :

Radial lapping force on the roller when the linear groove is made of PTFE (N)

\({F}_{C}\) :

Electromagnetic force of the upper disc on the roller (N)

\({F}_{C}^{^{\prime}}\) :

The pressure of the upper disc on the roller caused by the electromagnetic force. \({F}_{C}={F}_{C}^{^{\prime}}\) (N)

\({F}_{N}\) :

Resultant force of the upper disc on the roller (N)

\({F}_{t}\) :

Total upper disc pressure (N)

\(i\) :

Number of wave crests on the roller surface; \(i\) is the \(i\) th harmonic

\(K\) :

Lapping residual coefficient

L :

Roller length (mm)

M :

The total frictional torque on the roller in the tangential direction

\({M}_{f}\) :

The frictional resistance torque (N/mm) on the roller in the tangential direction

\({M}_{d}\) :

The frictional driving torque (N/mm) on the roller in the tangential direction

\(\Delta n\) :

Roundness error of n-round lapping of the workpiece

\({N}_{1}\) :

The contact point on the original linear groove at angle \({\varphi }_{i}\)

\({N}_{2}\) :

The contact point of the roller surface at angle \({\varphi }_{i}\)

\({O}_{i}\) :

The center of the roller during lapping

\({O}_{j}\) :

Center of the arc of a linear groove

\({p}_{0}\) :

The contact pressure (N) on the roller surface at the maximum radial displacement

\({p}_{i}\) :

The radial pressure (N) on the contact point of the roller at roller surface distance \({\delta }_{0}\) and deflection angle \({\varphi }_{i}\)

\({P}_{1}\) :

The position of a point on the linear groove with no radial displacement

\({P}_{2}\) :

The position of a point on a linear groove with a radial displacement and the same angle as \({P}_{1}\)

\({r}_{W}(\theta )\) :

Roller surface radius variable (mm)

\({R}_{i}\) :

Roller radius (mm)

\({R}_{j}\) :

Radius of the arc surface of the linear groove (mm)

\({R}_{\theta }\) :

Surface error of the increment of the workpiece (mm)

\({R}_{W}\) :

Ideal radius of the workpiece (mm)

\(\Delta R\) :

Radius difference between the roller and the arc groove (mm)

\({\overline{R} }_{\Delta }\) :

Average change in radius for one rotation of the workpiece (mm)

\(\Delta S\) :

Composite error

\(\alpha\) :

Angular deflection (rad) of \({F}_{N}\) relative to \({F}_{1}\) generated due to \({f}_{1}\)

\(\beta\) :

Angular deflection (rad) of \({F}_{2}\) relative to \({F}_{N}\) generated due to \({f}_{2}\)

\(\gamma\) :

The central angle of the contact point between the roller and the linear groove (rad)

\({\delta }_{0}\) :

Maximum contact compression on roller surface (mm)

\({\delta }_{i}\) :

Contact compression at the deflection angle \({\varphi }_{i}\) of the roller surface relative to \({\delta }_{0}\) (mm)

\(\theta\) :

Roller central angle (rad)

\({\theta }_{i}\) :

Initial phase angle of the \(i\) th harmonic (rad)

\(\zeta\) :

Static rounding coefficient

\({\zeta }_{i}\) :

Static rounding coefficient of DDACL

\({\zeta }_{j}\) :

Static rounding coefficient of centerless grinding

\({\zeta }_{i\mathrm{max}}\) :

Maximum static rounding coefficient of DDACL

\({\nu }_{i}\) :

Poisson’s ratio of the roller material

\({\nu }_{j}\) :

Poisson’s ratio of the linear groove material

\({\nu }_{1}\) :

Positioning error coefficient of the guide wheel of the centerless grinding machine

\({\nu }_{2}\) :

Positioning error coefficient of the pallet of the centerless grinding machine

\(\lambda\) :

The amplitude of one peak on the workpiece surface (mm)

\(\eta\) :

Resistance torque coefficient

\(\varepsilon\) :

Positioning error at the central angle \(\gamma\) on the roller surface

\({\varphi }_{i}\) :

\(<{O}_{i}{O}_{j}{P}_{1}\) (Rad)

\({\varphi }_{j}\) :

\(<{O}_{i}{O}_{j}{N}_{1}\) (Rad)

\({\theta }_{j}\),\({\varphi }_{j}\) :

Angle parameters of centerless grinding

\({\mu }_{1}\) :

Coefficient of friction between the roller and the upper disc

\({\mu }_{2}\) :

Coefficient of friction between the roller and the linear groove

\({\Delta }_{Rw}\) :

Deviation from circular form (\(\mathrm{\mu m}\))

\({V}_{DwL}\) :

Variation in the roller gauge lot diameter (\(\mathrm{\mu m}\))

\(Ra\) :

Surface roughness of the roller outside diameter surface (\(\mathrm{\mu m}\))

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Funding

Funding was provided by National Natural Science Foundation of China (No. 51935008 and No. 52075381) and the Xinchang Research Institute of Zhejiang University of Technology (Grant number: 2021GKF-0316).

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Authors and Affiliations

  1. Key Laboratory of Equipment Design and Manufacturing Technology, Tianjin University, Tianjin, 300350, China

    Weifeng Liu, Chengzu Ren, Guang Chen, Jing Zhang, Yiwen Hao & Chunlei He

  2. International Institute for Innovative Design and Intelligent Manufacturing of Tianjin University in Zhejiang, Shaoxing, 312000, China

    Chengzu Ren

  3. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300354, China

    Guang Chen & Chunlei He

Authors
  1. Weifeng Liu
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  2. Chengzu Ren
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  3. Guang Chen
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  4. Jing Zhang
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Contributions

WeiFeng Liu performed the experiment and built model, Guang Chen contributed to the conception of the study, WeiFeng Liu and Jing Zhang contributed significantly to analysis and manuscript preparation, Yiwen Hao and Chunlei He performed the data analyses and wrote the manuscript, and Chengzu Ren helped perform the analysis with constructive discussions.

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Correspondence to Guang Chen.

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Liu, W., Ren, C., Chen, G. et al. Rounding mechanism of a novel double-disc arc-contact lapping for high-precision rollers. Int J Adv Manuf Technol 125, 5571–5589 (2023). https://doi.org/10.1007/s00170-023-11014-y

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