Step Thrust Bearing

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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 0.05 m and 0.1 m, respectively. Groove angle between the pads is 15° and its depth is 0.0002 m relative to the pad surface. Clearance between the pad and the collar surface is 0.00036 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 7550.1 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 .

In the window, click

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1

In the window, click

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2

In the tree, select .

3

4

5

In the tree, select .

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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Browse to the model’s Application Libraries folder and double-click the file step_thrust_bearing.txt.

Work Plane 1 (wp1)

In the toolbar, click

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Work Plane 1 (wp1)>Plane Geometry

In the window, click .

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

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In the toolbar, click

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2

In the window for , locate the section.

3

In the text field, type Ro.

4

In the text field, type gAng.

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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)

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type padAng.

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

Work Plane 1 (wp1)>Delete Entities 1 (del1)

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In the window, right-click and choose .

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button in the toolbar.

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In the window for , locate the section.

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From the list, choose .

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On the object , select Domain 1 only.

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On the object , select Domain 1 only.

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Disk Selection: Leading Edge

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In the toolbar, click

and choose .

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In the window for , type Disk Selection: Leading Edge in the text field.

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Locate the section. From the list, choose .

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Locate the section. In the text field, type 1.01*Ro.

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In the text field, type 0.99*Ri.

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In the text field, type gAng-1.

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In the text field, type gAng+1.

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Locate the section. From the list, choose .

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Work Plane 1 (wp1)>Disk Selection: Leading Edge 1 (disksel2)

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type secAng-1.

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In the text field, type secAng+1.

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In the text field, type Disk Selection: Trailing Edge.

Disk Selection: Groove

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the text field, type 1.01*Ro.

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In the text field, type 0.99*Ri.

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In the text field, type gAng.

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Locate the section. From the list, choose .

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In the text field, type Disk Selection: Groove.

Work Plane 1 (wp1)>Disk Selection: Groove 1 (disksel4)

1

Right-click and choose .

2

In the window for , type Disk Selection: Pad in the text field.

3

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

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In the text field, type 360/N.

5

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Work Plane 1 (wp1)>Rotate 1 (rot1)

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In the toolbar, click

and choose .

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Click in the window and then press Ctrl+A to select both objects.

3

In the window for , locate the section.

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

5

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button in the toolbar.

Leading Edges of the Pads

1

In the window, right-click and choose .

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In the window for , type Leading Edges of the Pads in the text field.

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Locate the section. From the list, choose .

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Locate the section. Click

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In the dialog box, select in the list.

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Trailing Edges of the Pads

1

Right-click and choose .

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In the window for , type Trailing Edges of the Pads in the text field.

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Locate the section. Click .

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In the list, select .

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6

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In the dialog box, select in the list.

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In the window for , click

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. Click

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In the dialog box, select in the list.

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In the window for , type Grooves in the text field.

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Right-click and choose .

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In the window for , type Pads in the text field.

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Locate the section. Click .

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In the list, select .

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6

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In the dialog box, select in the list.

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In the window for , click

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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In the dialog box, select in the list.

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In the window for , locate the section.

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From the list, choose .

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In the text field, type Groove Edges.

Groove Inner Edges

1

In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

4

Locate the section. From the list, choose .

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6

In the dialog box, select in the list.

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8

In the window for , locate the section.

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In the text field, type 1.01*Ri.

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In the text field, type 0.99*Ri.

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Locate the section. From the list, choose .

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In the text field, type Groove Inner Edges.

Groove Edges (adjsel1), Groove Inner Edges (cylsel1)

1

In the window, under , Ctrl-click to select and .

2

Right-click and choose .

1

In the window for , type Pad Edges in the text field.

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Locate the section. Click .

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In the list, select .

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5

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In the dialog box, select in the list.

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8

In the window for , click

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Pad Inner Edges

1

In the window, under click .

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In the window for , type Pad Inner Edges in the text field.

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Locate the section. In the list, select .

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5

6

In the dialog box, select in the list.

7

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.

Variables: Grooves

1

In the window, expand the node.

2

Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
hf	hg+h_film	m

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In the text field, type Variables: Grooves.

Variables: Pads

1

Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
hf	h_film	m

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In the text field, type Variables: Pads.

Hydrodynamic Bearing (hdb)

1

button in the toolbar.

2

In the dialog box, in the tree, select the check box for the node .

3

Enable the formulation in the bearing.

4

In the window, under click .

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In the window for , locate the section.

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From the list, choose .

Reduce the for the sharper transition between the cavitated and non cavitated regions.

7

In the Δpsw text field, type 0.5[MPa].

Material 1 (mat1)

1

In the window, under right-click and choose .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Dynamic viscosity	mu	mu_f	Pa·s	Basic

Hydrodynamic Bearing (hdb)

Hydrodynamic Thrust Bearing 1

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

Because the reference surface is assumed to be located on the collar, change the to align it with the collar normal.

4

Locate the section. From the list, choose .

5

Locate the section. From the list, choose .

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In the hb1 text field, type hf.

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Locate the section. In the Ω text field, type angSpeed.

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Locate the section. In the ρc text field, type rho_c.

Bearing Orientation 1

1

In the window, click .

2

In the window for , locate the section.

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From the list, choose .

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Specify the vector as


1	x
0	y
0	z

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

From the list, choose .

Create one element per degree in the azimuthal direction to capture the pressure accurately.

1

Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

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

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In the window, right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

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

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Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section. In the text field, type 20.

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In the window, right-click and choose .

Step 1: Stationary

1

In the window, under click .

2

In the window for , click to expand the section.

3

Select the check box.

4

5

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
h_film (Film thickness)	range(6e-5,2e-5,16e-5)	m

6

7

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
angSpeed (Angular speed of shaft)	range(500,100,1000)	rad/s

8

From the list, choose .

9

In the toolbar, click

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Default plot shows the pressure distribution in the bearing. To generate the height plot for the pressure distribution shown in Figure 2 start by creating a .

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

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From the list, choose .

Pressure (Height)

1

In the toolbar, click

.

2

In the window for , type Pressure (Height) in the text field.

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Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type hdb.p.

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Locate the section. Click

.

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In the dialog box, select in the tree.

6

Height Expression 1

1

Right-click and choose .

2

In the window for , locate the section.

3

Select the check box. In the associated text field, type 2e-8.

4

button in the toolbar.

5

In the toolbar, click

.

The following instructions are to plot the mass fraction of the lubricant shown in Figure 3.

1

In the toolbar, click

and choose .

2

In the window for , type Mass Fraction in the text field.

1

Right-click and choose .

2

In the window for , click in the upper-right corner of the section. From the menu, choose .

3

Locate the section. From the list, choose .

4

Locate the section. In the text field, type 5.

5

Locate the section. Click

.

6

In the dialog box, select in the tree.

7

8

button in the toolbar.

9

In the toolbar, click

.

Figure 6 shows the bearing profile. Follow the instructions below to replicate it.

2D Plot Group 4

In the toolbar, click

and choose .

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type hg-hdb.h.

4

Locate the section. From the list, choose .

5

From the list, choose .

Height Expression 1

1

Right-click and choose .

2

In the window for , locate the section.

3

Select the check box. In the associated text field, type 100.

1

In the window, under click .

2

In the window for , type Pad Profile in the text field.

3

Locate the section. Clear the check box.

4

button in the toolbar.

5

In the toolbar, click

.

You can also analyze the pressure distributions along the radial and circumferential directions of the bearing shown in Figure 4 and Figure 5. Start by creating a along the radial line.

Cut Line 3D: Radial Line

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In row , set to 0.

4

In row , set to Ro.

5

6

In the text field, type Cut Line 3D: Radial Line.

Radial Distribution of Pressure (Film Thickness)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

From the list, choose .

4

From the list, choose .

5

In the text field, type Radial Distribution of Pressure (Film Thickness).

6

Click to expand the section. From the list, choose .

1

Right-click and choose .

2

In the window for , locate the section.

3

In the text field, type hdb.p.

4

Click to expand the section. Select the check box.

5

From the list, choose .

6

In the text field, type h = eval(h_film, um) \mu m.

7

In the toolbar, click

.

Radial Distribution of Pressure (Film Thickness)

1

In the window, click .

2

In the window for , locate the section.

3

From the list, choose .

Radial Distribution of Pressure (Angular Speed)

1

Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

From the list, choose .

5

In the text field, type Radial Distribution of Pressure (Angular Speed).

1

In the window, expand the node, then click .

2

In the window for , locate the section.

3

In the text field, type \Omega = eval(angSpeed) rad/s.

4

In the toolbar, click

.

Radial Distribution of Pressure (Film Thickness)

In the window, collapse the node.

Use the to create the circumferential sector line.

Parameterized Curve 3D: Circumferential Line

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

In the text field, type 2*pi/N.

4

Locate the section. In the text field, type 0.5*(Ro+Ri)*cos(s).

5

In the text field, type 0.5*(Ro+Ri)*sin(s).

6

In the text field, type Parameterized Curve 3D: Circumferential Line.

7

Radial Distribution of Pressure (Angular Speed), Radial Distribution of Pressure (Film Thickness)

1

In the window, under , Ctrl-click to select and .

2

Right-click and choose .

Circumferential Distribution of Pressure (Film Thickness)

1

In the window for , type Circumferential Distribution of Pressure (Film Thickness) in the text field.

2

Locate the section. From the list, choose .

3

In the toolbar, click

.

Circumferential Distribution of Pressure (Angular Speed)

1

In the window, under click .

2

In the window for , type Circumferential Distribution of Pressure (Angular Speed) in the text field.

3

Locate the section. From the list, choose .

4

In the toolbar, click

.

1

In the toolbar, click

and choose .

2

In the window for , type Lift Force in the text field.

3

Locate the section. From the list, choose .

1

Right-click and choose .

2

In the window for , click in the upper-right corner of the section. From the menu, choose .

3

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


Expression	Unit	Description
hdb.htb1.Fcz	kN	Fluid load on collar, z-component

4

Locate the section. From the list, choose .

5

In the text field, type h = eval(h_film, um) \mu m.

6

In the toolbar, click

.

1

In the window, click .

2

In the window for , locate the section.

3

From the list, choose .

4

Locate the section.

5

Select the check box. In the associated text field, type Angular speed of the shaft (rad/s).

6

In the toolbar, click

.