Determination of the Load Capacity of a Finite Width Journal Bearing by a Finite-Element Method in the Case of a Non-Newtonian Lubricant

1984 ◽  
Vol 106 (2) ◽  
pp. 285-290 ◽  
Author(s):  
P. Bourgin ◽  
B. Gay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Journal Bearing ◽  
Load Capacity ◽  
Nonlinear Partial Differential Equation ◽  
Strain Tensor ◽  
Finite Width ◽  
Gradient Technique ◽  
Element Method

Additives are commonly used to improve the performance of lubricating oils. Correlatively, the lubricant viscosity depends on the rate of shear: the fluid becomes non-Newtonian. Assuming that the nonlinear relationship between the rate of strain tensor and the stress tensor is cubic, the film equations are derived within the approximations of lubrication theory. The governing equation, which generalizes the Reynolds’ equation, is a nonlinear partial differential equation, subject to two nonlinear constraints. The particular case of a finite width journal bearing is considered here; this problem is solved by the finite-element method, using a gradient technique. The numerical results are compared with established results for newtonian lubricants. The influence of the non-Newtonian parameter on the pressure field and on the bearing capacity is predicted.

An Extrapolation Method to Compute Far-Field Pressures From Near-Field Pressures Obtained by Finite Element Method

1995 ◽  
Author(s):  
Jamal Assaad ◽  
Christian Bruneel ◽  
Jean-Michel Rouvaen ◽  
Régis Bossut
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Near Field ◽  
Radiation Condition ◽  
Directivity Pattern ◽  
Extrapolation Method ◽  
External Boundary ◽  
Finite Width ◽  
Far Field ◽  
Element Method

Abstract The finite element method is widely used for the modeling of piezoelectric transducers. With respect to the radiation loading, the fluid is meshed and terminated by an external nonreflecting surface. This reflecting surface can be made up with dipolar damping elements that absorb approximately the outgoing acoustic wave. In fact, with dipolar dampers the fluid mesh can be quite limited. This method can provides a direct computation of the near-field pressure inside the selected external boundary. This paper describes an original extrapolation method to compute far-field pressures from near-field pressures in the two-dimensional (2-D) case. In fact, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition, the far-field directivity pattern can be expressed in terms of the near-field directivity pattern. These developments are valid for any radiation problem in 2D. One test example is described which consists of a finite width planar source mounted in a rigid or a soft baffle. Experimental results concerning the far-field directivity pattern of lithium niobate bars (Y-cut) are also presented.

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