Step Thrust Bearing

In this example the pressure distribution in a step thrust bearing is analyzed. A step thrust bearing consists of a stepped bearing surface on which the end of the shaft rotates. The entire assembly is submerged in a lubricant. A six step thrust bearing is considered in this example. The shaft collar is assumed to be spinning without any axial motion in the bearing. The simulation is performed using the Rotordynamics Module’s Hydrodynamic Bearing interface. This interface solves the Reynolds equation to compute the pressure developed in a thin fluid film.

Model Definition

A six pad step thrust bearing is considered. Pad inner and outer diameters are 0.1 m and 0.2 m, respectively. Groove angle between the pads is 15° and its depth is 0.0001 m relative to the pad surface. Clearance between the pad and the collar surface is 0.0001 m.

The shaft is spinning with an angular speed Ω (1000 rad/s). However, It is not moving in axial direction. So the film thickness does not change due to the shaft motion.

The bearing geometry is shown in Figure 1 below.

Figure 1: Step thrust bearing geometry.

Effect of the cavitation is also included to compute the pressure distribution in the fluid film. Following fluid properties are needed — the dynamic viscosity, the density at cavitation pressure, and the compressibility. The fluid parameters, whose values are summarized in Table 1, are close to those of lubricating oils used in real bearings.

Table 1: Fluid properties.
Property	value
Density ρ	866 kg/m3
Dynamic viscosityμ	0.072 Pa·s
Compressibility β	10-7 Pa-1

Results and Discussion

Figure 2 below shows the fluid pressure profile on the bearing.

Figure 2: Fluid film pressure profile.

For the above pressure distribution, the total vertical force on the collar is 15,488 N. This is the load carrying capacity of the bearing at the specified speed.

Mass fraction of the lubricant which is a measure of the cavitation is shown in Figure 3. From the figure it is clear that amount of cavitation is very small and is localized near the trailing edge of the pad.

Figure 3: Mass fraction.

The pressure distribution on the pad in radial and circumferential directions are shown in Figure 4 and Figure 5. Pressure at the inner and outer radius locations are zero with the distribution marginally biased toward the outer side. The velocity of the collar varies linearly from inner radius to outer radius. Since the pressure distribution is proportional to the shear velocity in the film, it should have increased linearly from inner point to the outer point. However, at the ends the film pressure is set to zero. Therefore, maximum pressure occurs toward the outer side from the mid position. In the circumferential direction the pressure suddenly rises at the step location (leading edge of the pad) and drops down slowly toward the trailing edge.

Figure 4: Pressure profile in radial direction.

Figure 5: Pressure profile in circumferential direction.

Figure 6 shows bearing profile computed using the film thickness.

Figure 6: Bearing profile.

Rotordynamics_Module/Tutorials/step_thrust_bearing

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
N	6	6	Number of pads
Ro	0.1[m]	0.1 m	Outer radius of pad
Ri	0.05[m]	0.05 m	Inner radius of pad
gAng	15	15	Groove angle (deg)
hg	2e-4[m]	2E-4 m	Groove depth

Geometry 1

Work Plane 1 (wp1)

In the toolbar, click

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type Ro.

In the text field, type gAng.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	Ro-Ri

Work Plane 1 (wp1)>Circle 2 (c2)

Right-click and choose .

In the window for , locate the section.

In the text field, type 360/N-gAng.

Locate the section. In the text field, type gAng.

Delete Entities 1 (del1)

In the window, right-click and choose .

On the object , select Boundaries 1 and 2 only.

Rotate 1 (rot1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type range(0,360/N,360-360/N).

Click

Click the

button in the toolbar.

In the step bearing, the film thickness varies in steps with one value in the groove and another on the pad. Define a film thickness variable hf in two separate Variable nodes with complementary selections to specify different values in different regions.

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
hf	hg	m

Locate the section. From the list, choose .

Select Boundaries 1, 4, 5, 8, 9, and 12 only.

It might be easier to select the correct boundaries by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)

Variables 2

Right-click and choose .

In the window for , locate the section.

In the table, enter the following settings: