Analysis of Mixed Lubrication Characteristics of Cycloid Pin-Wheel Transmission


Cycloid pin-wheel transmission mechanism is the key transmission component of RV reducer. During the transmission, the entrainment speed along the tooth surface, the contact load and the radius of curvature always change sharply, which has a significant transient squeeze effect on the lubrication performance. The research on available elastohydrodynamic lubrication (EHL) and mixed EHL for cycloid pinwheel transmission is mainly conducted under the assumption of steady-state, and these transient effects are ignored. Therefore, a transient hybrid EHL model for cycloidal pinwheel transmission was presented, which takes into account key variable parameters along the meshing surface, including contact load, curvature contact radius, and entrainment speed. Besides, the lubrication characteristics of the meshing points with poor lubrication conditions at different entrainment speeds were also studied. The transient parameters of the cycloidal pin gear drive used in this paper are obtained through load tooth contact analysis. To improve the computational efficiency and convergence accuracy on relatively dense meshes, a progressive mesh densification method is applied. The comparison between the transient EHL and the corresponding steady-state EHL analysis results shows that the squeezing flow effect will affect the film thickness distribution of the contact area and the meshing trajectory line, and cause contact area increase. Operating speed is a key factor affecting the lubrication performance. The lower the speed, the worse the lubrication performance, and the higher the proportion of asperities contact in the mixed lubrication state.

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\(R_{p}\) :

The radius of center circle of pin-wheel

\(e\) :


\(\theta\) :

Swing angle to generate the cycloid profile

\(K_{1}\) :

Short amplitude factor

\(\Delta R_{p}\) :

Modification amount of radial-moving

\(\Delta R_{rp}\) :

Modification amount of equidistant

\(\Delta e\) :

Modification amount of tooth height

\(U_{1} ,U_{2}\) :

The velocity of cycloid gear and pin tooth, respectively

\(\omega_{p}\) :

Relative angular velocity when the cycloidal wheel is transformed from planetary motion to fixed-axis motion

\(\omega_{H}\) :

Angular velocity of the arm

\(T_{out}\) :

Output torque of RV reducer

\(B\) :

Width of cycloid gear

\(\rho\) :

Lubricant density

\(\eta\) :

Lubricant viscosity

\(\eta_{0}\) :

Lubricant viscosity at ambient pressure

\(p\) :

Lubricant film pressure

\(h\) :

Lubricant film thickness

\(R_{x} ,R_{y}\) :

Radii of curvature of original geometry in the x-axis and y-axis directions, respectively

\(\delta_{1} ,\delta_{2}\) :

Roughness amplitudes of contact surfaces

\(\nu\) :

Elastic deformation

\(E\) :

Equivalent elastic modulus

\(\alpha \prime\) :

Pressure-viscosity exponent

\(\rho_{0}\) :

Lubricant density at ambient pressure

\(R_{c}\) :

Radii of tooth end fillet

\(L_{c}\) :

Length of tooth end fillet

\(\lambda\) :

Film thickness ratio

\(h_{a}\) :

Average film thickness

\(\sigma\) :

Root mean square of contact surface roughness


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The present study was funded by the Natural Science Foundation of Hebei Province Project, China Nos. E2019209153.

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Correspondence to Ju Han.

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Han, J., Li, W. & Qiao, Z. Analysis of Mixed Lubrication Characteristics of Cycloid Pin-Wheel Transmission. Int. J. Precis. Eng. Manuf. 22, 453–472 (2021).

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  • Transient mixed EHL
  • Cycloid pin-wheel transmission
  • PMD method
  • Tooth modification