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Spiral angel is an important structure parameter of spiral oil wedge sleeve bearing, which produces greater impact on bearing performance. Based on JFO boundary condition, the generalized Reynolds equations considering four slip conditions are established. Using the concept of partial derivatives, stiffness and damping coefficients of sleeve bearing are calculated. The results show that carrying capacity and friction drag of oil film decrease, temperature rise decreases first and then increases, and end leakage rate, stiffness, and damping coefficients generally increase first and then decrease with the increase of spiral angle. The carrying capacity, friction drag, temperature rise, stiffness, and damping coefficients are smaller and the end leakage rate is higher considering wall slip and JFO condition compared with reckoning with no slip and Reynolds boundary condition.

Sleeve bearings are widely used in rotating machinery, and oil film force is an important factor that affects the stability of rotor system. At the current state of research on improving the stability performance of hydrodynamic bearings, there are several in-depth studies taking into account the journal misalignment, the bearing surface roughness, the cavitation phenomenon, and the impact of the texturing. And the effect of structural parameters on bearing stability can not be ignored, especially when the demand of precision and stability is more high with the development of high speed and precision rotating machinery. Ahmed et al. [

In recent years, many researchers studied the effect of structural parameters on the characteristics of different structural bearings. Ahmada et al. [

The structural diagram of spiral oil wedge sleeve bearing.

As shown in Figure

The oil film thickness of common surface can be expressed as

The oil film thickness of circular recess surface is as follows:

In the condition of high speed and super high speed, the shear stress of solid-liquid interface can exceed critical shear stress, and wall slip occurs. The traditional Reynolds boundary condition is fit for oil film rupture boundary but cannot explain the oil film reformation condition correctly; Jakobsson-Floberg-Olsson (JFO) boundary condition can ensure the mass conservation of oil film rupture location and reformation position. Therefore the generalize Reynolds equation considering wall slip is gained based on JFO boundary condition, which will be benefit for knowing lubrication characteristics of high speed journal bearing.

Critical shear stress model thinks that wall slip occurs when shear stress is larger than critical shear stress, then the value of shear stress is critical shear stress. The surface circle of spiral oil wedge sleeve bearing is not continuous, the working clearance of bearing is circumferential and axial function, so the circumferential and axial wall slip is considered when the numerical model is set; the models of four conditions are set separately. The four slip states are as follows: wall slip can not occur on the axial surface and sleeve surface, wall slip can only occur on the sleeve surface, wall slip can only occur on the axial surface, and wall slip can occur on the axial surface and sleeve surface [

When wall slip occurs on the axial surface and sleeve surface, the resultant shear stress is larger than critical shear stresses

where

Using boundary condition (

where

Similarly, the generalized Reynolds equations of remaining three slip states are obtained.

Based on JFO boundary condition, switch function modifies Reynolds equation which is similar with the application of Elrod method. Elrod method regards that the lubrication is compressible fluid, gets the relation of density and pressure, and controls that the full oil film region is 1 and cavitation region is 0 by switch function

where

Elrod used the change of density to reflect the continuous of oil film in cavitation region in the generalized Reynolds equation. Substituting

Similarly, the generalized Reynolds equations of remaining three conditions based on JFO boundary condition are obtained.

The generalized Reynolds equations of four slip conditions based on JFO boundary condition are solved using finite difference method. Perturbation pressure Reynolds equations are solved using the concept of partial derivatives and stiffness and damping coefficients of sleeve bearing are calculated [

Primary parameters of spiral oil wedge sleeve bearing.

parameter | symbol | unit | value |
---|---|---|---|

Bearing width | | mm | 110 |

Bearing radius | | mm | 50 |

Bearing radial clearance | | mm | 0.02 |

Depth of the arc groove | | mm | 0.12 |

Rotational speed | | r/min | 10000 |

Inlet oil pressure | | MPa | 0.3 |

Cavitation pressure | | MPa | −0.072 |

Oil viscosity | | Pa⋅s | 0.0018 |

Figures

Carrying capacity.

Friction drag.

Figures

End leakage rate.

Temperature rise.

The dynamic characteristics of bearing reflect the change of the oil film force when the journal deviates from the static equilibrium position and performs the displacement movement near this position, which has a greater impact on the performance of the entire bearing rotor system. Under the assumption of small amplitude, the instantaneous displacement and the instantaneous speed based on the journal center deviating from the static equilibrium position can be defined as the stiffness coefficients and the damping coefficients of bearing. Figure

Stiffness coefficients.

Figure

Damping coefficients.

The conclusions can be summarized as follows.

The authors declare that they have no conflicts of interest.

This work was supported by the grant from China Postdoctoral Science Foundation Funded Project (no. 2017M612304), Shandong Provincial Postdoctoral Innovation Foundation (no. 201701016), SDUST Research Fund (no. 2015JQJH104), and Qingdao Postdoctoral Research Funded Project and National Natural Science Foundation of China (no. 51305242).