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ELASTOHYDRODYNAMIC CONTACT MODEL FOR CALCULATION OF AXIAL AND ANGULAR. . .457

according to the solution of stress-strain state of bearing components. The sliding surfaces displacements in the bearing, treated as absolutely rigid with

respect to each other, hgeom(r; '), are considered in calculation of h(r; ') in the following form:

hgeom(r ) hmin r" sin N ! R2 sin #

; = + 2 (n 1) hmax hmin + sin( ) tg( ) ;

(6) where n – lobe number, N – total number of lobes, hmin is a minimal gap value when the shaft axis is still.

Equation (4) is solved numerically with the usage of finite elements method and after the finite-element discretization procedure [7] being im-plemented it is reduced to the following system of nonlinear finite-element equations for pressure calculation:

h hK f hde fi fpg = nQf hde fo ; (7)

i

where K fhde f is the system matrix for pressure calculation, with the

coefficients depending on pressure distribution, valid for the case of the

bearing with compliant sliding surfaces; Qfhde f is the right side vector,

with the components also dependent on pressure distribution for the bearing

n o

with compliant sliding surfaces. Pressures on the contours of the calculation area are assumed to be equal to ambient pressure and stated as the boundary conditions.

3. Bearing fluid flow model verification

3.1. Comparison with the results obtained via STAR-CD software

Three-dimensional fluid film in the thrust bearing model was designed via STAR-CD software for verification of the model on the base of Reynolds equation. Calculations via STAR-CD were carried out on the basis of full Navier-Stokes equations. In the three-dimensional model, as well as in two-dimensional one, described above, a laminar incompressible fluid flow is assumed without slippage and with a constant temperature distribution over the calculation area. At the same time, in contrast to the model based on the Reynolds equation, the three-dimensional model takes into account the action of mass forces and also the influence of the fluid speeds along rotor revolution axis and fluid accelerations in the bearing plane. Finite volumes method was used in STAR-CD calculations. Calculation area for the fluid film was pided into approximately 2 million 8-node quadrilaterals. Meshing and

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458 MIKHAIL TEMIS, ALEXANDER LAZAREV

Fig. 2. Meshing: a – two-dimensional finite-element mesh of the lobe surface for Reynolds equation; b – three-dimensional meshing of the fluid film for STAR-CD

elements of the calculation area in STAR-CD and for Reynolds equation are shown in Fig. 2.

The comparison between the pressure distribution calculation results for two-dimensional Reynolds equation model and those obtained for the three-dimensional STAR-CD model is carried out for the 6-lobe bearing with the internal radius R1 = 50 mm, external radius R2 = 100 mm, lobe angle = 57.30 , water as a fluid and shaft rotating frequency of 2000 rpm.

The difference between maximal (hmax) and minimal (hmin) gap is assumed constant and equal to 80 m and the shaft axis is still ( = 0). The bearing

carrying force versus minimal gap hmin is determined as the result of the calculations.

Fig. 3. Comparison of thrust bearing carrying force for two models

As it can be seen from the graphs shown in Fig. 3, the calculation results obtained by means of the two-dimensional Reynolds equation model are quite similar to the results obtained with the use the three-dimensional STAR-CD model. Pressure distributions over the lobe surface for hmin = 50 m,

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ELASTOHYDRODYNAMIC CONTACT MODEL FOR CALCULATION OF AXIAL AND ANGULAR. . .459

presented in Fig. 4, also show high degree of coincidence between the results yielded by both models.