Abnormal behavior of a hydrodynamic lubrication journal bearing caused by wall slip
Introduction
The classic Reynolds lubrication theory assumes that there is no slip between the solid surface and the lubricant, i.e. the lubricant speed at the solid surface equals the solid speed. Although the no-slip boundary condition has been used in many technical books and papers, the sudden occurrence of wall slip under certain conditions is a challenging problem in both fluid mechanics and lubrication mechanics. During recent years it has been found that wall slip often occurs not only in polymer flow [1], [2], but also in hydrodynamic [3], [4] and elasto-hydrodynamic lubrication [5]. Although many mechanisms for wall slip have been proposed, the experimental manifestation of wall slip is the existence of a critical or limiting wall-shear stress. In lubrication mechanics, if the lubricant has a limiting shear yield stress, for example a viscoplastic fluid [6], [7], grease [8] or lubricant at high pressure [9], [10], wall slip will occur at the wall/lubricant interfaces when wall shear stress is sufficiently high. Although there are reports of wall slip observations, no detailed theoretical studies has been reported for a journal bearing. Strozzi [11] gave a theoretical analysis for one wall slip situation using a complementarity method. Spikes [12] analyzed wall slip occurring at a slider bearing using a difference method.
In a journal bearing, it is known that if the journal and the bearing are made of the same material, the system will easily break down. Different materials of bearings have different limiting rotational speeds. Most explanations for this involve the heat induced by viscous flow or the strength of the bearing materials. This paper reports a new finding that wall slip in a journal bearing can give rise to many abnormal phenomena, including journal instability, vibration and even oil film collapse.
Section snippets
Control equations for wall slip
A parametric quadratic programming (PQP) method, which is described in detail in references [13], [14], is used to study the wall slip problems in the present paper The lubricant velocities at surfaces a and b, and , can be expressed by (see Fig. 1)where ua and ub denote the velocities of solid surfaces a and b, respectively, and and are the corresponding wall slip velocities. If (α=a, b) the wall slip goes in the positive x direction. Otherwise it goes in −x
Wall slip analysis of journal bearing
A journal bearing rotating with velocity ω is shown in Fig. 2, where θ=x/R, c=R0−Ri≪R0=R., ε=e/c. The unit length load support in the x and y directions are:
The total film load support is:and the load support angle is:
In the present paper, we use the dimensionless parameters: P=pc2/(ηωR2), H=h/c, T0α=τ0αc/(ηωR), TLα=τLαc/(ηωR), Tα=ταc/(ηωR), Uα=uα/U, Kα=kαR/c, , T=tU/R, Q=qs/(cU), where U=ua+ub. W=wc2/(ηωR3).
Discussions
The present paper describes a general method to analyze wall slip at lubricated surfaces. Numerical solutions show that if the two lubricated surfaces have the same limiting shear stress, wall slip may first occur at the outlet zone on the bearing surface. The dimensionless initial limiting shear stress at surface α is defined as T0α=τ0αc/(ηωR). Consequently a decrease in τ0α and an increase in ω will give rise to a small T0α. If the surface limiting shear strength is unchanged, increasing the
Conclusions
- (1)
If the two surfaces have exactly the same adhesion property with a lubricant, wall slip always makes the oil film load support capacity decrease. If there is wall slip in opposite directions over all of both lubricated surfaces, the hydrodynamic effect of the journal bearing vanishes and no load support exists.
- (2)
If the two lubricated surfaces have different adhesion properties, the wall slip effect is more complex. In order to avoid wall slip, the limiting shear stress at the bearing surface
Acknowledgements
This work was partly supported by NSFC (10272028) and by the Foundation of Doctor Discipline of Education Ministry.
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