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Investigation of Contact Performance of Case-Hardened Gears Under Plasto-elastohydrodynamic Lubrication

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Abstract

Case-hardening is widely used to enhance gear loading capacity. Simulation of the material gradient properties and contact characteristics are the key issues in contact fatigue analysis of case-hardened gears. In this work, a plasto-elastohydrodynamic lubrication (PEHL) model incorporating the hardness gradient and surface roughness is developed to investigate the contact performance of case-hardened gears. The generalized Reynolds equation is solved to determine film thickness and contact pressure. The plastic deformation and residual stress are obtained via the half-space eigenstrain problem solving. The Dang Van multiaxial fatigue criterion and the Euler transformation are employed to evaluate the contact fatigue parameter based on the predetermined stress field. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for accelerating the computation. The influences of effective case depth, surface hardness and surface roughness on the contact performance are investigated. Numerical results indicate that as the surface hardness increases, the probability of fatigue crack nucleation decreases, and the depth of the crack initiation site increases. For a lower surface roughness case, the maximum von Mises stress and equivalent plastic strain appear at a deeper layer. As the surface roughness increases, the maximum values of pressure and stress increase sharply and move closer to the surface.

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Abbreviations

\(b\) :

Hertzian half contact width

\(C_{ij}^{n} ,C_{ij}^{t}\) :

Influence coefficients relating surface traction to stresses

\(D_{3kl}\) :

Influence coefficients relating plastic strain to plastic displacement

\(E_{0}\) :

Effective elastic modulus, \(E_{0} = 2/\left( {\left( {1 - v_{1}^{2} } \right)/E_{1} + \left( {1 - v_{2}^{2} } \right)/E_{2} } \right)\)

ECD :

Effective case depth

E T :

Tangent modulus in linear hardening law

\(\varvec{F}\) :

Galerkin vectors

\({\text{FP}}\) :

Fatigue parameter

\(h\) :

Film thickness

\(h_{0} ,h_{g}\) :

Initial and geometry gap between surfaces, respectively

\(H\) :

Material hardness

\(H_{\text{sur}} ,H_{\text{cor}}\) :

Gear surface and core hardness, respectively

\({\mathbf{M}}_{\text{u}}\) :

Euler transform matrix

\(m\) :

Meyer’s hardness coefficient

\(p\) :

Surface pressure

\(p_{H}\) :

Hertzian maximum pressure

\(q\) :

Fluid shear traction

\(Q_{y}\) :

Yield strength function

\(R\) :

Equivalent radius of curvature

\(\varvec{S}_{ij}\) :

The deviatoric stress tensor

S u :

Composite surface roughness

t :

Time

\(T_{ijkl}^{\left( 0 \right)}\) :

Influence coefficients relating plastic strain to residual stress

\(u_{i}^{r}\) :

Surface displacements

\(u_{r}\) :

Rolling velocity

V e :

Elastic deformation

V p :

Plastic deformation

\(W_{n}\) :

Applied normal load

\(x,y,z\) :

Coordinates (x is parallel to rolling direction)

\(z_{e}\) :

Pressure-viscosity constant

\(\mu ,\lambda\) :

Lamé constants

\(\nu\) :

Poisson’s ratio

\(\kappa\) :

Effective accumulative plastic strain

\(\eta ,\eta_{0}\) :

Viscosity and ambient viscosity of the lubricant, respectively

\(\eta^{*}\) :

Equivalent viscosity

\(\rho ,\rho_{0}\) :

Density and ambient density of the lubricant, respectively

\(\varepsilon_{ij}^{p}\) :

Plastic strain

\(\delta_{ij}\) :

Kronecker delta

\(\sigma_{y0}\) :

Initial yield stress

\({{\sigma }}_{ij}^{e}\) :

Elastic stresses

\(\sigma_{ij}^{r}\) :

Residual stresses

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

The ultimate strength of gear material

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

Von Mises equivalent stress

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

Hydrostatic stress

\(\sigma_{ - 1} , \tau_{ - 1}\) :

Fatigue limits under fully reversed bending and torsion

\(\tau_{ \hbox{max} }\) :

Maximum amplitude of shear stress

\({{\varOmega }}\) :

Plastic zone

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Acknowledgements

This work is supported by the National Key R&D Program of China (Grant No. 2018YFB2001300), the National Natural Science Foundation of China (Grant No. 51575061), and the Fundamental Research Funds for the Central Universities (Grant No. 2018CDXYJX0019). The authors are grateful to Dr. Nicholaos Demas for his help and discussions during the research.

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400030, China

    Ye Zhou, Caichao Zhu, Huaiju Liu & Hailan Song

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  1. Ye Zhou
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Zhou, Y., Zhu, C., Liu, H. et al. Investigation of Contact Performance of Case-Hardened Gears Under Plasto-elastohydrodynamic Lubrication. Tribol Lett 67, 92 (2019). https://doi.org/10.1007/s11249-019-1202-7

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