An Evaluation of Eight-Node Quadrilateral Finite Elements for the Analysis of a Dynamically Loaded Hydrodynamic Journal Bearing

Abstract

A comparative study is presented for the finite element analysis of a dynamically loaded journal bearing showing the improvement in solution accuracy and decrease in computer time achieved when using eight-node quadilateral, rather than three-node triangular, elements. Results are presented for medium size diesel engine big end bearings using a wide variety of mesh gradings. NOTATIONThe application of the finite element method, as with many numerical analysis techniques, can require a considerable amount of computer time. The analysis of engine components, for example, can be very costly if the form of the dynamic analysis requires the discretization of time into small steps, hence requiring a large number of iterative steps to be carried out. This paper looks at the economy in time and the increase in solution accuracy possible by using quadratic, eightnode isoparametric elements as opposed to three-node c radial clearance (m) D bearing diameter (m) e eccentricity ratio h film thickness (m) L bearing length (m) M number of circumferential nodes N shape function P film pressure (N/mz) q volumetric flow (m3/s) R bearing radius (m) triangular elements. U journal surface velocity (m/s) W l o a d 0 p viscosity (N s/m) t, q local coordinates in the finite element method 1 INTRODUCITONIn recent Years the finite dement method has become well established as a convenient numerical solution technique for analYSing a wide variety OfhYdrodPeC lubrication problems, its main advantage being the relative ease with which complex geometries and boundary conditions can be handled. Reddi (1) and Booker and Huebner (2) were among the first to demonstrate the application of the finite element method to the lubrication problem and used three-node triangular elements three-, four-, five-and six-node elements to examine bearing performance, but only for a steadily loaded, plane, slider bearing with a movable free boundary.Although three-node triangular elements are easier to implement than higher-order elements they are not well suited to the resolution of the sharp pressure peaks that nient for modelling oil feed features. It is important to they occur at the most highly loaded phases of the engine cycle, which are usually the most crucial regions for accurate prediction of the bearing performance.Using triangular elements an accurate resolution can computationally expensive. The MsNowrnber 1987, 14/88 9 IMechE 1988 2 THE FINTlE ELEMENT METHOD The finite element method is to be used to analyse the behaviour of a fluid between two cylindrical surfaces, one inside the other, using the Navier-Stokes equations. The outer surface is fixed and the inner surface has variable angular and kentre velocities relative to the outer surface.Making the usual assumptions the Navier-Stokes equations reduce to the familiar twodimensional form of Reynolds equation (4, which may be written as to model the film in a finite bearing. Milne (3) used v h W P -6~ ( U -+ 2 -(1)Solving this equation is equivalent (2) to minimizing the discretized functional occur...

An analytical approach towards EHD analysis of connecting-rod bearing

“…Fantino et al [6] have shown that the elastic strain of the structures and the location at which the thickness is minimal are nearly independent of the viscosity of the lubricant and that the friction and the axial flow are more important in the elastic case than in the rigid case. To overcome numerical difficulties regarding finite element convergence, McIvor et al [7] advocate the necessity of using high order elements despite their important computational cost. The inertia influence of solids on the oil film thickness was evidenced by Aitken et al [8], and numerically confirmed in the work of Bonneau et al [9].…”