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An investigation into the impact of grinding residual stress on the meshing stress of spiral bevel gear

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Abstract

Grinding residual stress (GRS) has been understood to have a great impact on the strength of gear fatigue life. However, there are lack of detailed studies on the influences in terms of mechanism and magnitude. To fill this gap, this study proposed a new method based on finite element analysis (FEA) to calculate the overall meshing stress on a gear tooth surface by including both the GRS and elastohydrodynamic lubrication (EHL) film pressure. Applying this method to a spiral bevel gear has resulted in a number of interesting results that GRS produced to reveal its mechanism of action through a full meshing cycle. The acquired understanding would be useful for development of manufacturing processes.

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Abbreviations

\({\Sigma }_{\mathrm{gr}}\left\{{\mathrm{O}}_{\mathrm{gr}};\;{x}_{\mathrm{gr}},{y}_{\mathrm{gr}},{z}_{\mathrm{gr}}\right\}\) :

Cartesian coordinate system rigidly connected to the ground workpiece

\({v}_{\mathrm{gr}}\) :

Grinding velocity (m/s)

\(C\) :

Cutting depth (mm)

\({\Sigma }_{\mathrm{g}}\left\{{\mathrm{O}}_{\mathrm{g}};\;{x}_{\mathrm{g}},{y}_{\mathrm{g}},{z}_{\mathrm{g}}\right\}\) :

Cartesian coordinate system attached to the gear blank

\({\Phi }_{\mathrm{gr}}\) :

Grinding residual stress tensor expressed in \({\Sigma }_{\mathrm{gr}}\)

\({\Phi }_{\mathrm{g}}\) :

Grinding residual stress tensor expressed in \({\Sigma }_{\mathrm{g}}\)

\(\Sigma \left\{\mathrm{O}\;;x,y,z\right\}\) :

Fixed coordinate system rigidly connected to the machine centre

\({\Sigma }_{\mathrm{c}}\left\{{\mathrm{O}}_{\mathrm{c}};\;{x}_{\mathrm{c}},{y}_{\mathrm{c}},{z}_{\mathrm{c}}\right\}\) :

Cartesian coordinate system attached to the grinding wheel

\(\dot{{q}_{2}}\) :

Angular velocity of the revolution of grinding wheel (rad/min)

\({\omega }_{\mathrm{g}}\) :

Angular velocity of the gear blank (°)

\({M}_{\mathrm{c}}\) :

Arbitrary point on the grinding wheel cone

\(M\) :

The corresponding point in contact with \({M}_{\mathrm{c}}\) on gear

\({r}_{{\mathrm{OM}}_{\mathrm{c}}}\) :

Position vector of \({M}_{\mathrm{c}}\)

\({M}_{0\mathrm{c}}\) :

Tip apex

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

Length of \({{M}_{\mathrm{c}}M}_{0\mathrm{c}}\) (mm)

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

Unit normal on the grinding wheel cone at point \({M}_{\mathrm{c}}\)

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

Unit tangent on the grinding wheel cone at point \({M}_{\mathrm{c}}\)

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

Centre roll position (°)

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

Phase angle of both \({M}_{c}\) and \({M}_{0\mathrm{c}}\) (°)

\({v}_{{\mathrm{M}}_{\mathrm{c}}}\left(\Sigma \right)\) :

Velocity of point \({M}_{\mathrm{c}}\) in \(\Sigma\)

\({v}_{\mathrm{M}}(\Sigma )\) :

Velocity of point \(M\) in \(\Sigma\)

\({v}_{{\mathrm{M}}_{\mathrm{c}}\mathrm{M}}\) :

Relative velocity vector of point \({M}_{\mathrm{c}}\) and \(M\)

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

Radial distance (mm)

\({r}^{\mathrm{g}}\) and \({r}^{\mathrm{p}}\) :

The position vector of the meshing point on the gear and the pinion

\({v}^{\mathrm{g}}\) and \({v}^{\mathrm{p}}\) :

The velocity vector of the meshing point on the gear and the pinion

\({\omega }^{\mathrm{g}}\) and \({\omega }^{\mathrm{p}}\) :

The rotation speed vector of the gear and the pinion (r/min)

\({u}_{\mathrm{e}}\) :

The entrainment velocity vector

\({u}_{\mathrm{et}}\) :

The projection of \({u}_{\mathrm{e}}\) on the tangent plane (m/s)

\(b\) :

The short axis of contact ellipse

\(\theta\) :

The angle between \({u}_{\mathrm{et}}\) and \(b\) (rad)

\({\Sigma }_{\mathrm{L}}\left\{{O}_{\mathrm{L}};\;{x}_{\mathrm{L}},{y}_{\mathrm{L}}\right\}\) :

The 2D coordinate system established for EHL calculation area

\({\Sigma }_{\mathrm{g}2\mathrm{d}}\left\{{O}_{\mathrm{g}2\mathrm{d}};\;{x}_{\mathrm{g}2\mathrm{d}},{y}_{\mathrm{g}2\mathrm{d}}\right\}\) :

The 2D coordinate system in the gear shaft section \({x}_{\mathrm{g}}{\mathrm{O}}_{\mathrm{g}}{y}_{\mathrm{g}}\)

\({P}_{\mathrm{L}}\) :

An arbitrary point in EHL calculation area

\({\alpha }_{\mathrm{r}}\) :

Rotating angle (°)

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

Point contact force (N)

\({\mathrm{r}}_{\mathrm{min}}\) :

Minimum principal curvature radius (m)

\({r}_{\mathrm{max}}\) :

Maximum principal curvature radius (m)

\({P}_{\mathrm{max}}\) :

Maximum EHL film pressure (GPa)

\({H}_{\mathrm{min}}\) :

Minimum EHL film thickness (\(\mathrm{\mu m}\))

\({\sigma }_{\mathrm{gr}}\) :

Grinding residual stress (MPa)

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Funding

This research was supported by the National Science and Technology Support Program of China (grant number MKF20210012).

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Authors and Affiliations

  1. School of Mechanical Engineering & Automation, Beihang University, Beijing, 100191, China

    Yanzhong Wang, Wei Zhang, Bo Yu & Jihong Liu

  2. AVIC Beijing Changcheng Aeronautical Measurement and Control Technology Research Institute, Beijing, 101111, China

    Yanyan Chen

  3. Centre for Efficiency and Performance Engineering, University of Huddersfield, Huddersfield, HD1 3DH, UK

    Fengshou Gu

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  1. Yanzhong Wang
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Contributions

Yanzhong Wang: methodology, funding acquisition and supervision; Wei Zhang: investigation, method, simulation, data analysis and writing; Yanyan Chen: simulation; Bo Yu: data analysis; Fengshou Gu: review; Jihong Liu: picture making.

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Correspondence to Wei Zhang.

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Wang, Y., Zhang, W., Chen, Y. et al. An investigation into the impact of grinding residual stress on the meshing stress of spiral bevel gear. Int J Adv Manuf Technol 122, 3817–3835 (2022). https://doi.org/10.1007/s00170-022-10095-5

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