Effect of Bearing Misalignment on Rotor Vibration

In this example, a rotor shaft supported by two hydrodynamic bearings is analyzed. The gravity load acts on the rotor. An eccentric disk is also mounted on the rotor between the bearings. One of the bearings is misaligned with the axis of the rotor. The rotor whirls due to the mass imbalance.

The built-in multiphysics interface Beam Rotor with Hydrodynamic Bearing is used for the combined simulation of the rotor and bearings. A time dependent analysis is performed for two cases, first without misalignment and then including the misalignment. Results for both cases are compared to understand the effect of the misalignment.

The results include stress in the rotor, pressure distribution in the bearings, orbit of the rotor near the disk and the bearings.

Model Definition

The rotor is driven by a motor and is supported by two hydrodynamic bearings. The distance between the motor and the first bearing is a, and between the bearings is L. Thus, the rotor between the motor and first bearing is overhung with overhung length a. Diameter of the rotor is d. A disk is mounted on the rotor between the bearings, and it has certain amount of imbalance. The rotor rotates inside the bearings with an angular speed Ω . The bearing rotor assembly is shown in Figure 1 below.

Figure 1: Rotor configuration.

The material parameters of the rotor are listed in Table 1.

Table 1: Rotor Material Parameters.
Parameter	Value
Density	7780 kg/m3
Young’s modulus	2.00·1011 Pa
Poisson’s ratio	0.29

Geometric properties of the rotor are given in Table 2.

Table 2: ROTOR Geometric Parameters.
PARAMETER	VALUE
Shaft diameter, d	10 mm
Shaft length, L	100 mm
Shaft overhung length, a	20 mm
Angular speed of the shaft, Ω	210 rad/s
Disk distance from the left bearing	40 mm
Disk diameter, Dd	50 mm
Disk thickness, hd	10 mm
Disk unbalance magnitude	8e-9 kg-m

The parameters needed for the fluid-film simulation of the plain journal bearings are the dynamic viscosity, density at cavitation pressure, and compressibility. Values of the parameters are summarized in Table 3 below.

Table 3: Bearing Parameters.
PARAMETER	VALUE
Bearing length, Lb	5 mm
Bearing initial clearance, C	0.05 mm
Oil viscosity, μ	9.4 mPa-s
Density, ρ	866 kg/m3
Compressibility, β	10-7 Pa-1

Results and Discussion

Figure 2 shows the stress profile on the rotor for the misaligned rotor with the maximum bending stress in the middle part. The pressure distribution in the bearings is also shown.

Figure 2: Bearing pressure and rotor stress.

A comparison of the pressure in the first bearing for with and without misalignment is shown in Figure 3. In the case of misalignment, the pressure distribution in the bearing becomes skewed.

Figure 3: Comparison of bearing pressure with and without misalignment.

The orbit of the journal in the yz-plane in the first bearing is shown in Figure 4. The orbit consists of a transient response followed by steady state whirl. An equilibrium position in the orbit is decided by the gravity load, and the whirl around the equilibrium position is the response to the mass imbalance. The journal orbit in the left bearing is not significantly affected by the misalignment in the right bearing.

Figure 4: Journal orbit in left bearing.

An orbit of the journal in the second bearing is shown in Figure 5. The characteristics of the orbit in this bearing are similar to that in the left bearing. The only noticeable difference is that the equilibrium positions of the journal in this bearing depends on the misalignment. Note that the vertical component of the steady state equilibrium position with the misalignment is higher than the one without misalignment due to skewed pressure distribution.

Figure 5: Journal orbit in the right bearing.

A comparison of the velocity of the journal in the right bearing is shown in Figure 6. The oscillation in the velocity has a leading phase for the misaligned bearing as compared to the same for the normal bearing. Thus, the journal reaches the equilibrium position much quicker when the bearing is misaligned.

Figure 6: Horizontal velocity of the journal in the right bearing.

Figure 7 shows the orbit of the rotor at the disk. The equilibrium position of the orbit at this location is also affected by the misalignment in the right bearing. In steady state, the rotor is slightly inclined from its initial axis due to misalignment.

Figure 7: Rotor orbit at disk.

Rotordynamics_Module/Tutorials/misaligned_rotor

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

Start by defining the parameters of the rotor.

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
Ow	210[rad/s]	210 rad/s	Angular speed of shaft
d	10[mm]	0.01 m	Shaft diameter
L	100[mm]	0.1 m	Shaft length
a	20[mm]	0.02 m	Shaft overhung length
E_r	200[GPa]	2E11 Pa	Young's modulus
nu_r	0.29	0.29	Poisson's ratio
rho_r	7780[kg/m^3]	7780 kg/m³	Shaft and disk density
xd	40[mm]	0.04 m	Disk distance from left bearing
Dd	50[mm]	0.05 m	Disk diameter
hd	10[mm]	0.01 m	Disk thickness
me	8e-9[kg*m]	8E-9 kg·m	Disk unbalance magnitude
Lb	5[mm]	0.005 m	Bearing length
C	0.05[mm]	5E-5 m	Bearing initial clearance
mu0	9.4[mPa*s]	0.0094 Pa·s	Oil viscosity
para	0	0	Misalignment switch parameter

Geometry 1

Polygon 1 (pol1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type 0 a a+xd a+L.

In the text field, type 0.

Define the rotor selection for later use.

Locate the section. Find the subsection. Click .

In the dialog box, type Rotor in the text field.

Click .

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type d/2.

In the text field, type Lb.

Locate the section. In the text field, type a-Lb/2.

Locate the section. From the list, choose .

Define the bearing selection.

Locate the section. Find the subsection. Click .

In the dialog box, type Bearing 1 in the text field.

Click .

Cylinder 2 (cyl2)

Right-click and choose .

In the window for , locate the section.

In the text field, type a+L-Lb.

Define the selection for second bearing.

Locate the section. Find the subsection. Click .

In the dialog box, type Bearing 2 in the text field.

Click .

Define some more selections that will be useful in meshing.

Definitions

Bearings

In the toolbar, click

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

Locate the section. From the list, choose .

Locate the section. Under , click

In the dialog box, in the list, choose and .

Click .

Bearings Left Edges

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Edges 3 and 17 only.

Select the check box.

In the text field, type Bearings Left Edges.

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

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


Property	Variable	Value	Unit	Property group
Young’s modulus	E	E_r	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	nu_r	1	Young’s modulus and Poisson’s ratio
Density	rho	rho_r	kg/m³	Basic