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Elastohydrodynamic lubrication characteristics of surface-textured slipper bearing in an axial piston pump

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Abstract

This paper aimed to reveal elastohydrodynamic lubrication characteristics for surface-textured slipper bearing of axial piston pump. The proposed model was established including slipper-tilting motion and surface deformation. Further, a numerical simulation was conducted under hydrodynamic and elastohydrodyamic lubrication conditions. Numerical solutions were obtained under this lubrication conditions in terms of the film pressure, film thicknesses, and bearing stiffness. The simulation results reveal that the film pressure in EHD solution increases slightly with the growth of the area density within the range of 10–30% and then tends to remain stable. When the area density of dimple is set to 38%, the dimensionless stiffness of oil film shows the highest value. If the dimple depth is set to 0.8 μm, there exists the maximum dimensionless stiffness of oil film in EHD solution when the optimum dimple depth-to-diameter ratio is set to 0.22.

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References

  1. Kazuyuki Y, Joichi S (2017) Performance of balancing wedge action in textured hydrodynamic pad bearings. J Tribol 139:011704-1–011704-8

    Google Scholar 

  2. Zhang Y (2012) Hydrodynamic lubrication in fully plastic asperity contacts. Theoret Comput Fluid Dyn 26(1–4):279–289

    Article  Google Scholar 

  3. Han J, Fang L, Sun JP, Ge SR (2010) Hydrodynamic lubrication of microdimple textured surface using three-dimensional CFD. Tribol Trans 53(6):860–870

    Article  Google Scholar 

  4. Shin JH, Kim KW (2014) Effect of surface non-flatness on the lubrication characteristics in the valve part of a swash-plate type axial piston pump. Meccanica 49:1275–1295

    Article  Google Scholar 

  5. Etsion I (2005) State of the art in laser surface texturing. J Tribol 127:248–253

    Article  Google Scholar 

  6. Papadopoulos CI, Efstathiou EE, Nikolakopoulos PG, Kaiktsis L (2011) Geometry optimization of textured three-dimensional micro- thrust bearings. J Tribol 133(4):041702-1–041702-14

    Article  Google Scholar 

  7. Papadopoulos CI, Kaiktsis L, Fillon M (2014) Computational fluid dynamics thermohydrodynamic analysis of three-dimensional sector-pad thrust bearings with rectangular dimples. J Tribol 136(1):249–256

    Article  Google Scholar 

  8. Papadopoulos CI, Nikolakopoulos PG, Kaiktsis L (2012) Characterization of stiffness and damping in textured sector pad micro thrust bearings using computational fluid dynamics. J Eng Gas Turbines Power 134(11):837–846

    Article  Google Scholar 

  9. Marian VG, Kilian M, Scholz W (2007) Theoretical and experimental analysis of a partially textured thrust bearing with square dimples. Proc IME J J Eng Tribol 221:771–778

    Article  Google Scholar 

  10. Fouflias DG, Charitopoulos AG, Papadopoulos CI, Kaiktsis L, Fillon M (2014) Performance comparison between textured, pocket, and tapered-land sector-pad thrust bearings using computational fluid dynamics thermohydrodynamic analysis. Proc IME J J Eng Tribol 229:376–397

    Article  Google Scholar 

  11. Yu H, Wang X, Zhou F (2010) Geometric shape effects of surface texture on the generation of hydrodynamic pressure between conformal contacting surfaces. Tribol Lett 37:123–130

    Article  Google Scholar 

  12. Siripuram RB, Stephens LS (2004) Effect of deterministic asperity geometry on hydrodynamic lubrication. J Tribol Trans ASME 126:527–534

    Article  Google Scholar 

  13. Han J, Fang L, Sun J, Wang Y, Ge S, Zhu H (2011) Hydrodynamic lubrication of surfaces with asymmetric microdimple. Tribol Trans 54(4):607–615

    Article  Google Scholar 

  14. Yagi K, Sato H, Sugimura J (2015) On the magnitude of load-carrying capacity of textured surfaces. Tribol Online 10(3):232–245

    Article  Google Scholar 

  15. Zouzoulas V, Papadopoulos CI (2017) 3-D thermohydrodynamic analysis of textured, grooved, pocketed and hydrophobic pivoted-pad thrust bearings. Tribol Int 110:426–440

    Article  Google Scholar 

  16. Nakano M, Korenaga A, Korenaga A, Miyake K, Murakami T, Ando Y, Usami H, Sasaki S (2007) Applying micro-texture to cast iron surfaces to reduce the friction coefficient under lubricated conditions. Tribol Lett 28(2):131–137

    Article  Google Scholar 

  17. Baker J, Ivantysynova M (2008) Investigation of power losses in the lubricating gap between cylinder block and valve plate of axial piston machines. In: Proceedings of the fluid power net international PHD symposium, Cracow, Poland, 1–5 July 2008

  18. Ivantysynova M, Baker J (2009) Power loss in the lubricating gap between cylinder block and valve plate of swash plate type axial piston machines. Int J Fluid Power 10(2):29–43

    Article  Google Scholar 

  19. Etsion I (2013) Modeling of surface texturing in hydrodynamic lubrication. Friction 1(3):195–209

    Article  Google Scholar 

  20. Zhao JX, Sadeghi F, Harvey MN (2000) A finite element analysis of surface pocket effects in hertzian line contact. J Tribol 122:47–54

    Article  Google Scholar 

  21. Kovalchenko A, Ajayi O, Erdemir A, Fenske G, Etsion I (2005) The effect of laser surface texturing on transitions in lubrication regimes during unidirectional sliding contact. Tribol Int 38(3):219–225

    Article  Google Scholar 

  22. Yilmaz E, Sinanoglu C, Topal ES (2014) Experimental analyses of the effects of slipper bearing geometry and working conditions on the system load-carrying capacity in axial piston pumps. J Balkan Tribol Assoc 20(2):247–258

    Google Scholar 

  23. Yu H, Deng H, Huang W et al (2011) The effect of dimple shapes on friction of parallel surfaces. Proc Inst Mech Eng J J Eng Tribol 225(8):693–703

    Article  Google Scholar 

  24. Qun Chao, Zhang Junhui Xu, Bing Wang Qiannan (2018) Discussion on the Reynolds equation for the slipper bearing modeling in axial piston pump. Tribol Inter 118:140–147

    Article  Google Scholar 

  25. Timoshenko S, Goodier Jn (1951) Theory of elasticity, 2nd edn. McGaw Hill, New York

    MATH  Google Scholar 

  26. Khonsari MM, Beaman JJ (1985) Thermohydrodynamic analysis of laminar incompressible journal bearings. ASLE Trans 29(2):141–150

    Article  Google Scholar 

  27. Su BB, Huang LR, Huang W, Wang XL (2017) The load-carrying capacity of textured sliding bearings with elastic deformation. Tribol Inter 109:86–96

    Article  Google Scholar 

  28. Li Lin GuLY, Luo GS (2015) Hydrostatic thrust bearing with central flow path based on circular flat slit fed restrictor. J Zhejiang Univ (Eng Sci) 49(2):282–286

    Google Scholar 

  29. Qiu M, Raeymaekers B (2015) The load-carrying capacity and friction coefficient of incompressible textured parallel slider bearings with surface roughness inside the texture features. ARCHIVE Proc Inst Mech Eng J J Eng Tribol 229(4):547–556

    Article  Google Scholar 

  30. Wang ZQ, Hu S, Zhang HY, Ji H, Yang J, Liang W (2018) Effect of surface texturing parameters on the lubrication characteristics of an axial piston pump valve plate. Lubricants 6(2):49–70

    Article  Google Scholar 

Download references

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Grant No. 51805376) and Zhejiang Provincial Natural Science Foundation of China (No. LQ17E050003) and Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (GZKF-201719) and Basic Scientific Research Projects Foundation of Wen Zhou (G20180019).

Author information

Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325035, China

    Chaoang Xiao & Hesheng Tang

  2. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Hesheng Tang

Authors
  1. Chaoang Xiao
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  2. Hesheng Tang
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Correspondence to Hesheng Tang.

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Technical Editor: Daniel Onofre de Almeida Cruz, D.Sc.

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Appendix: Discretization of Reynolds equation

Appendix: Discretization of Reynolds equation

The dimensionless Reynolds equation expressed in Eq. (2) was solved using the finite difference method. To improve the accuracy of calculation, the central nine-order discretization method is adopted in this study.

$$ \begin{aligned} & \left[ {\frac{\partial }{{\partial \bar{r}}}\left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)} \right]_{i,j} + \left[ {\frac{1}{{\bar{r}}}\frac{\partial }{{\partial \bar{\theta }}}\left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)} \right]_{i,j} \\ &\quad= \left[ {6\bar{v}_{Tr} \frac{{\partial \bar{h}}}{{\partial \bar{r}}} + 6\left( {\frac{{\bar{v}_{T\theta } }}{{\bar{r}}} + \bar{\omega }_{ss} } \right)\frac{{\partial \bar{h}}}{{\partial \bar{\theta }}} + 12\frac{{\partial \bar{h}}}{{\partial \bar{t}}}} \right]_{i,j} \end{aligned} $$
(36)

where

$$ \left[ {\frac{\partial }{{\partial \bar{r}}}\left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)} \right]_{i,j} = \frac{1}{{\Delta \bar{r}}}\left[ {\left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)_{i + 0.5,j} - \left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)_{i - 0.5,j} } \right] $$
(37)
$$ \left[ {\frac{1}{{\bar{r}}}\frac{\partial }{{\partial \bar{\theta }}}\left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)} \right]_{i,j} = \frac{1}{{\bar{r}_{i,j} }}\frac{1}{{\Delta \bar{\theta }}}\left[ {\left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{\theta }}}} \right)_{i,j + 0.5} - \left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{\theta }}}} \right)_{i,j - 0.5} } \right] $$
(38)
$$ \left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)_{i + 0.5,j} = \frac{{\bar{r}_{i + 0.5,j} \bar{h}^{3}_{i + 0.5,j} }}{{\bar{\mu }}}\frac{{\bar{p}_{i + 1,j} - \bar{p}_{i,j} }}{{\Delta \bar{r}}} $$
(39)
$$ \left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)_{i - 0.5,j} = \frac{{\bar{r}_{i - 0.5,j} \bar{h}^{3}_{i - 0.5,j} }}{{\bar{\mu }}}\frac{{\bar{p}_{i,j} - \bar{p}_{i - 1,j} }}{{\Delta \bar{r}}} $$
(40)
$$ \left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{\theta }}}} \right)_{i,j + 0.5} = \frac{{\bar{h}^{3}_{i,j + 0.5} }}{{\bar{\mu }}}\frac{{\bar{p}_{i,j + 1} - \bar{p}_{i,j} }}{{\Delta \bar{\theta }}} $$
(41)
$$ \left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{\theta }}}} \right)_{i,j - 0.5} = \frac{{\bar{h}^{3}_{i,j - 0.5} }}{{\bar{\mu }}}\frac{{\bar{p}_{i,j} - \bar{p}_{i,j - 1} }}{{\Delta \bar{\theta }}} $$
(42)

Submitting from Eqs. 37–42 into Eq. 36, and then arranging the dimensionless Reynolds equation as follows yield:

$$ \begin{aligned} \left[ {\frac{\partial }{{\partial \bar{r}}}\left( {\frac{{\bar{r}\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)} \right]_{i,j} &= \frac{1}{{\Delta \bar{r}}}\left[ {\frac{{\bar{r}_{i + 0.5,j} \bar{h}^{3}_{i + 0.5,j} }}{{\bar{\mu }}}\frac{{\bar{p}_{i + 1,j} - \bar{p}_{i,j} }}{{\Delta \bar{r}}} }\right.\\&\quad\left.{- \frac{{\bar{r}_{i - 0.5,j} \bar{h}^{3}_{i - 0.5,j} }}{{\bar{\mu }}}\frac{{\bar{p}_{i,j} - \bar{p}_{i - 1,j} }}{{\Delta \bar{r}}}} \right], \end{aligned} $$
(43)
$$ \begin{aligned} \left[ {\frac{1}{{\bar{r}}}\frac{\partial }{\partial \theta }\left( {\frac{{\bar{h}^{3} }}{{\bar{\mu }}}\frac{{\partial \bar{p}}}{{\partial \bar{r}}}} \right)} \right]_{i,j} &= \frac{1}{{\bar{r}_{i,j} }}\frac{1}{{\Delta \bar{\theta }}}\left[ {\frac{{\bar{h}^{3}_{i,j + 0.5} }}{{\bar{\mu }}}\frac{{\bar{p}_{i,j + 1} - \bar{p}_{i,j} }}{{\Delta \bar{\theta }}} }\right.\\&\quad\left.{- \frac{{\bar{h}^{3}_{i,j - 0.5} }}{{\bar{\mu }}}\frac{{\bar{p}_{i,j} - \bar{p}_{i,j - 1} }}{{\Delta \bar{\theta }}}} \right], \end{aligned} $$
(44)
$$ \begin{aligned} &\left[ {6\bar{v}_{Tr} \frac{{\partial \bar{h}}}{{\partial \bar{r}}} + 6\left( {\frac{{\bar{v}_{T\theta } }}{{\bar{r}}} + \bar{\omega }_{ss} } \right)\frac{{\partial \bar{h}}}{{\partial \bar{\theta }}} + 12\frac{{\partial \bar{h}}}{{\partial \bar{t}}}} \right]_{i,j} \\&\quad= 6\bar{v}_{Tr} \frac{{h_{i,j + 0.5} , - h_{i,j - 0.5} }}{{\Delta \bar{r}}} + 6\left( {\frac{{\bar{v}_{T\theta } }}{{\bar{r}}} + \bar{\omega }_{ss} } \right)\frac{{h_{i,j + 0.5} , - h_{i,j - 0.5} }}{{\Delta \bar{\theta }}} \\ & \quad\quad+ \,12\frac{{h_{i,j + 0.5} , - h_{i,j - 0.5} }}{{\Delta \bar{t}}}. \\ \end{aligned} $$
(45)

Then the solution for Eq. 36 is obtained as:

$$ \begin{aligned} &\frac{{\bar{r}_{i + 0.5,j} \bar{h}^{3}_{i + 0.5,j} }}{{\mu \Delta \bar{r}^{2} }}\bar{p}_{i + 1,j} + \frac{{\bar{r}_{i - 0.5,j} \bar{h}^{3}_{i - 0.5,j} }}{{\mu \Delta \bar{r}^{2} }}\bar{p}_{i - 1,j} \\ &\quad+ \frac{1}{{\bar{r}_{i,j} }}\frac{{\bar{h}^{3}_{i,j + 0.5} }}{{\bar{\mu }\Delta \bar{\theta }^{2} }}\bar{p}_{i,j + 1} + \frac{1}{{\bar{r}_{i,j} }}\frac{{\bar{h}^{3}_{i,j - 0.5} }}{{\bar{\mu }\Delta \bar{\theta }^{2} }}\bar{p}_{i,j - 1} \\ & \quad - \left( {\frac{{\bar{r}_{i + 0.5,j} \bar{h}^{3}_{i + 0.5,j} }}{{\bar{\mu }\Delta \bar{r}^{2} }} + \frac{{\bar{r}_{i - 0.5,j} \bar{h}^{3}_{i - 0.5,j} }}{{\bar{\mu }\Delta \bar{r}^{2} }} + \frac{1}{{\bar{r}_{i,j} }}\frac{{\bar{h}^{3}_{i,j + 0.5} }}{{\bar{\mu }\Delta \theta^{2} }} + \frac{1}{{\bar{r}_{i,j} }}\frac{{\bar{h}^{3}_{i,j - 0.5} }}{{\bar{\mu }\Delta \theta^{2} }}} \right)\bar{p}_{i,j} \\ &\quad= 6\bar{v}_{Tr} \frac{{h_{i,j + 0.5} , - h_{i,j - 0.5} }}{{\Delta \bar{r}}} \\ &\qquad + \,6\left( {\frac{{\bar{v}_{T\theta } }}{{\bar{r}}} + \bar{\omega }_{ss} } \right)\frac{{h_{i,j + 0.5} , - h_{i,j - 0.5} }}{{\Delta \bar{\theta }}} + 12\frac{{h_{i,j + 0.5} , - h_{i,j - 0.5} }}{{\Delta \bar{t}}}, \\ \end{aligned} $$
(46)

where

$$ A = \frac{{\bar{r}_{i + 0.5,j} \bar{h}^{3}_{i + 0.5,j} }}{{\bar{\mu }\Delta \bar{r}^{2} }} $$
(47)
$$ B = \frac{{\bar{r}_{i - 0.5,j} \bar{h}^{3}_{i - 0.5,j} }}{{\bar{\mu }\Delta \bar{r}^{2} }} $$
(48)
$$ C = \frac{1}{{\bar{r}_{i,j} }}\frac{{\bar{h}^{3}_{i,j + 0.5} }}{{\bar{\mu }\Delta \theta^{2} }} $$
(49)
$$ D = \frac{1}{{\bar{r}_{i,j} }}\frac{{\bar{h}^{3}_{i,j - 0.5} }}{{\bar{\mu }\Delta \theta^{2} }} $$
(50)
$$ E = A + B + C + D $$
(51)
$$ \begin{aligned} F &= 6\bar{v}_{Tr} \frac{{\bar{h}_{i,j + 0.5} , - \bar{h}_{i,j - 0.5} }}{{\Delta \bar{r}}} \\ &\quad+ 6\left( {\frac{{\bar{v}_{T\theta } }}{{\bar{r}}} + \bar{\omega }_{ss} } \right)\frac{{\bar{h}_{i,j + 0.5} , - \bar{h}_{i,j - 0.5} }}{{\Delta \bar{\theta }}} + 12\frac{{\bar{h}_{i,j + 0.5} , - \bar{h}_{i,j - 0.5} }}{{\Delta \bar{t}}} \end{aligned} $$
(52)

Submitting Eqs. 47–52 into Eq. 36 and then arranging the partial derivative equation of dimensionless Reynolds equation as follows yield

$$ A\bar{p}_{i + 1,j} + B\bar{p}_{i - 1,j} + C\bar{p}_{i,j + 1} + D\bar{p}_{i,j - 1} - \left( {A + B + C + D} \right)\bar{p}_{i,j} = F. $$
(53)

Thus, the relation of dimensionless pressure between the node and adjacent node in oil film pressure field is described by the equation as follows:

$$ \bar{p}_{i,j} = \frac{{A\bar{p}_{i + 1,j} + B\bar{p}_{i - 1,j} + C\bar{p}_{i,j + 1} + D\bar{p}_{i,j - 1} - F}}{E}. $$
(54)

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Xiao, C., Tang, H. Elastohydrodynamic lubrication characteristics of surface-textured slipper bearing in an axial piston pump. J Braz. Soc. Mech. Sci. Eng. 42, 199 (2020). https://doi.org/10.1007/s40430-020-02282-w

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