Damping Coefficients of a Squeeze Film Damper

Squeeze film dampers are components that provide additional damping to rotating machines. To simplify the modeling of a rotor assembly, squeeze film dampers are often modeled in terms of their damping coefficients. This model computes damping coefficients for a short squeeze film damper and compares them to analytically computed values. The damping coefficients depend on the journal location in the damper.

Model Definition

The plain squeeze film damper has a radius of 0.1 m and length of 0.01 m. The journal undergoes a circular whirl at 100 rpm, and the clearance between the journal and the damper bushing is 0.001 m. The viscosity and density of the lubricant are taken as 0.02 Pa·s and 864 kg/m3, respectively. The relative eccentricity of the journal is varied from 0 to 0.95 in the steps of 0.05. The attitude angle is specified relative to the static load on the damper at

. The damping coefficients are computed for all eccentricity values by solving a perturbed form of Reynolds equation.

The local directions of the damper are aligned with the global y and z directions, with the negative z direction defining

. The attitude angle of the journal measured from the local y direction is therefore

.The coordinates of the journal location in the damper, in local directions, are given by

where C is the clearance and ε is the relative eccentricity of the journal. Analytical values for the radial and tangential dimensionless damping coefficients (Ref. 1) are given by:

A dimensional scaling factor for the damping coefficients is μR(L/C)3. The damping coefficients are transformed from global to local coordinates as:

Results and Discussion

Figure 1 shows the various components of the computed damping coefficients and compares them to their analytical counterparts. The computed values match the analytical values.

Figure 1: Damping coefficients.

Reference

1. W.J. Chen and E.J. Gunter, Introduction to the Dynamics of Rotor-Bearing Systems, sections 6.10 and 6.11, pp. 263–271, Trafford Publishing, 2007.

Rotordynamics_Module/Verification_Examples/squeeze_film_damper_damping_coefficients

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

Create the parameters for the damper and lubricants properties.

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
fr	100[rpm]	1.6667 1/s	Whirl speed
Rj	0.1[m]	0.1 m	Journal radius
H	0.01[m]	0.01 m	Journal length
C	1e-3[m]	0.001 m	Clearance
e	0	0	Eccentricity
phi	10[deg]	0.17453 rad	Attitude angle
mu0	0.02[Pa*s]	0.02 Pa·s	Oil viscosity
rho0	864[kg/m^3]	864 kg/m³	Oil density

Geometry 1

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type Rj.

In the text field, type H.

Locate the section. From the list, choose .

Click

Define the variables for the analytical damping coefficients in local y and z directions.

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
c0	mu0Rj(H/C)^3	kg/s	Damping scaling
c_rr	pi(1+2e^2)/(2*(1-e^2)^2.5)		Damping coefficient, rr component
c_rt	2*e/(1-e^2)^2		Damping coefficient, rt component
c_tr	c_rt		Damping coefficient, tr component
c_tt	pi/(2*(1-e^2)^1.5)		Damping coefficient, tt component
c_22	c_rr(sin(phi))^2+c_rtsin(2phi)+c_tt(cos(phi))^2		Damping coefficient, 22 component
c_23	(-c_rr+c_tt)sin(phi)cos(phi)-c_rtcos(2phi)		Damping coefficient, 23 component
c_32	c_23		Damping coefficient, 32 component
c_33	c_rr(cos(phi))^2-c_rtsin(2phi)+c_tt(sin(phi))^2		Damping coefficient, 33 component

Hydrodynamic Bearing (hdb)

In the window, under click .

In the window for , locate the section.

Select the check box.

Squeeze Film Damper 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

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

Locate the section. From the list, choose .

In the e text field, type C*e.

In the φy text field, type 270[deg]+phi.

In the ω text field, type 2*pi[rad]*fr.

Locate the section. From the list, choose .

Locate the section. From the μ list, choose . In the associated text field, type mu0.

From the ρ list, choose . In the associated text field, type rho0.

Use a mapped mesh to resolve the pressure.

Mesh 1

Mapped 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Distribution 1

Right-click and choose .

Select Edges 1, 2, 4, and 6 only.

In the window for , locate the section.

In the text field, type 50.

Distribution 2

In the window, right-click and choose .

Select Edge 3 only.

In the window for , click

Study 1

Step 1: Stationary

In the window, under click .

In the window for , click to expand the section.

Select the check box.

Click

In the table, click to select the cell at row number 1 and column number 3.

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
e (Eccentricity)	range(0,0.05,0.95)

In the toolbar, click

Results

Fluid Pressure (hdb)

In the toolbar, click

Pressure in the damper is the default plot. Follow the below instructions to compare the computed and the analytical values of the dimensionless damping for the damper as shown in Figure 1.

Damping coefficients (Dimensionless)

In the toolbar, click

and choose .

In the window for , type Damping coefficients (Dimensionless) in the text field.

Global 1

Right-click and choose .

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

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


Expression	Unit	Description
hdb.sfd1.c22/c0	1	c<sub>22</sub>, COMSOL
hdb.sfd1.c23/c0	1	c<sub>23</sub>, COMSOL
hdb.sfd1.c32/c0	1	c<sub>32</sub>, COMSOL
hdb.sfd1.c33/c0	1	c<sub>33</sub>, COMSOL