Fig. 4. Pressure over the lobe surface for hmin = 50 m: a – Reynolds model; b – STAR-CD model

3.2. Comparison with the Mote results

Fig. 5. Comparison of pressure at the lobe point with results from [1]

Theoretical and experimental results from [1] for the pressure in 6-lobe thrust bearing with the parameters mentioned above are used for verification of the developed model. The result of comparison at the point with polar coordinates r = 75 mm, ' = 43 shows a high degree of coincidence between the developed mathematical model and theoretical and experimental data from [1], which confirms the correctness of the developed model. Pressure at that point versus minimal gap is depicted in Fig. 5.

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460 MIKHAIL TEMIS, ALEXANDER LAZAREV

4. Sliding surfaces deformation calculation model

Determination of bearing sliding surfaces deformations under the action of fluid film pressure requires, in general case, finding the solution to the three-dimensional elasticity problem, which is done in the present paper with the help of the finite elements method. Three-dimensional 20-node solid finite elements are used for three-dimensional bearing model development [7]. Equations describing three-dimensional body deformations are reduced to the system of linear equations, as follows:

[Kd ] fUg = fQd g ; (8)

where [Kd ] and fQd g are the system matrix and right side vector of the system of finite-element equations. Typical finite-element mesh for the multilobe axial bearing is represented in Fig. 8. Solution to the problem is found in an iterative way. At the first step, the bearing is assumed rigid (hde f (r; ') = 0). In this case, pressure distribution in the fluid film is obtained from (7). Applying this pressure to the corresponding surfaces of the three-dimensional bearing model, we obtain the first deformation approximations and the first approximation for hde f (r; ') from (8). Correcting the fluid film thickness in (5) we get the new pressure distribution for the second step from (7) and then the second deformation approximations are obtained from (8) and so on. The iterative process is stopped when the changes in bearing carrying force and bearing elements deformations for two cumulative iterations are within the boundaries of the required tolerance.

5. Thrust bearing fluid flow and stiffness parameters calculation

5.1. Calculations for the case of runner angular displacements taken

into account

The calculations of bearing characteristics are carried out by using the verified thrust bearing model for the 6-lobe bearing with the parameters mentioned above for different runner rotations with the shaft axis and sliding surfaces closures. The dependence of total carrying force and the moment for all bearing lobes versus minimal gap are plotted in Fig. 6 with the assumption of equal to zero (see Fig. 1). The increase in bearing runner angular displacement causes that the same values of the carrying force are obtained

for a greater hmin value.

Three-dimensional graphs of bearing carrying force and moment versus shaft axis rotation angle and the location of the runner rotation plane, determined by , are shown in Fig. 7. The minimal initial gap is assumed 100 m in these calculations.

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ELASTOHYDRODYNAMIC CONTACT MODEL FOR CALCULATION OF AXIAL AND ANGULAR. . .461

Thrust bearing characteristics with axial displacements and runner ro-tations are determined by the obtained dependencies. The carrying force characterizes axial stiffness and moments – angular stiffness at the point of the runner fastening to the shaft. Angular stiffness of the bearing, similarly as the axial one, also has a characteristic nonlinear dependency, which may be the reason for its considerable contribution to rotor nonlinear bending vibrations.

It is necessary to mention that, when the bearing runner angular dis-placements are taken into account, it is hard to obtain the dependencies of carrying force and moment due to their dependency on minimal gap (hmin), runner angular displacement ( ) and the location of the runner rotation plane ( ). Therefore, for the finite element design of the thrust bearing support it is preferable to integrate the bearing’s mathematical model into the rotor dynamics calculation scheme for the purpose of direct calculation of bearing characteristics for each case of dynamic problem calculation.