3.3. Modeling Bearings

To model bearings by inputting the stiffness and damping characteristics, select the most appropriate element type for your application from the following table.

Description Stiffness and Damping cross terms Nonlinear stiffness and damping characteristics Mass
COMBIN14 Spring-DamperNoneNoneNone
COMBI214 2D Spring-Damper BearingUnsymmetricFunction of the rotational velocityLumped
MATRIX27 Stiffness, Damping, or Mass MatrixUnsymmetricNoneMatrix
MPC184 Multipoint Constraint Element
Symmetric for linear characteristics
None for nonlinear characteristics
Function of the displacementNone

You can also model a plain cylindrical journal bearing or squeeze film damper with COMBI214 (KEYOPT(1) > 0) or FLUID218 (KEYOPT(1) = 1) which integrates the Reynolds equation for thin fluid film.

Both COMBI214 and FLUID218 elements can also be used in a nonlinear large deflection transient analysis where the fluid film pressure forces are calculated at each time step.

3.3.1. Using the COMBIN14 Element

The COMBIN14 element allows stiffness and/or damping characteristics in one direction. To define a bearing with characteristics KX and CX along X axis:

KX = 1.e+5         !Example stiffness value
CX = 100           !Example damping value

et,1,combin14
keyopt,1,2,1       ! X direction
r,1,KX,CX

KEYOPT(2) must be specified to define the active degree of freedom. This element operates in the nodal coordinate system.

3.3.2. Using the COMBI214 Element

The 2D element supports user-defined stiffness/damping characteristics (KEYOPT(1) = 0) or the calculation of the bearing characteristics (or the bearing forces) for a plain cylindrical journal bearing based on finite length assumption (KEYOPT(1) > 0).

3.3.2.1. User-Defined Stiffness and Damping Characteristics (KEYOPT(1) = 0)

The COMBI214 element allows stiffness and/or damping characteristics in 2 perpendicular directions as well as cross-terms. To define a bearing in the YZ plane:

et,1,combi214
keyopt,1,2,1		                        ! YZ plane
r,1,KYY,KZZ,KYZ,KZY,CYY,CZZ
rmore,CYZ,CZY

Note:  KEYOPT(2) must be specified to define active degrees of freedom. This element operates in the nodal coordinate system.


In the case of a hydrodynamic bearing for example, the characteristics may vary with the rotational velocity. In this case, you need to specify OMEGS as the table parameter primary variable (*DIM command). It is supported when activating the CORIOLIS command in a modal analysis (ANTYPE,MODAL), full harmonic analysis (ANTYPE,HARMIC), or full transient analysis (ANTYPE,TRANS).

An example of varying characteristics KYY and KZZ is given below:

et,1,combi214 
keyopt,1,2,1		                          ! YZ plane

! define table KYY
*DIM,KYY,table,3,1,1,omegs	              ! table of dimension 3 depending upon omegs 
KYY(1,0) = 0 , 1000 , 2000	              ! 3 rotational velocities (rd/s)
KYY(1,1) = 1.e+6 , 2.7e+6 , 3.2e+6       ! stiffness characteristic at each rotational velocity

! define table KZZ
*DIM,KZZ,table,3,1,1,omegs	              ! table of dimension 3 depending upon omegs
KZZ(1,0) = 0 , 1000 , 2000	              ! 3 rotational velocities (rd/s)
KZZ(1,1) = 1.4e+6 , 4.e+6 , 4.2e+6       ! stiffness characteristic at each rotational velocity

r,1,%KYY%,%KZZ%

Note:  If the characteristics of the COMBI214 element are varying with the rotational velocity and if the component rotational velocities are used (CMOMEGA), make sure the element is part of the appropriate rotating component.


In the case of a squeeze film damper, the characteristics may vary with the rotor eccentricity and/or the phase shift between the rotor displacements in the two nodal directions. In this case, you need to specify ECCENT and/or THETA as the table parameter primary variables (*DIM command). A basic example of varying characteristics KXX is given below:

*dim, KXX,table,2,2,, eccent, theta
KXX(1,0) = 0, 1.e-2		! 2 eccentricity values
KXX(0,1) = -180			! 2 theta values (in degree)
KXX(0,2) =  180
KXX(1,1) = 1.e+5, 1.e+4		! stiffness values for each
KXX(1,2) = 1.e+6, 1.e+5		!  value of eccentricity and theta (2x2)

The characteristics can be imported directly from an ASCII text file using the APDL macro importbearing1.mac. The format of this text file is described in Appendix A: Bearing Characteristics File Format. An example of the macro usage is shown below:

! Import the bearing characteristics read in file bearingAP.txt
!  and create the table parameters K11_3, K12_3...
importbearing1, ‘bearingAP’, 3
! Define the bearing element real constants
r,1, %K11_3%, %K22_3%,%K12_3%,%K21_3%,%C11_3%,%C22_3%,
rmore, %C12_3%, %C21_3%

3.3.2.2. Calculation of the Bearing Characteristics (KEYOPT(1) > 0)

In a static analysis, the stiffness and damping characteristics of a plain cylindrical journal bearing or squeeze film damper can be calculated using a small perturbation near a user-defined equilibrium position.

Example inputs are shown in Example: Calculation of a Plain Cylindrical Journal Bearing Characteristics and Example: Calculation of a Squeeze Film Damper Characteristics.

These characteristics can then be used as COMBI214 real constants (KEYOPT(1) = 0) in a subsequent modal or harmonic analysis.

3.3.2.3. Calculation of the Nonlinear Bearing Forces (KEYOPT(1) > 0)

In a nonlinear large-deflection transient analysis, the bearing forces are calculated based on the bearing definition (real constants and material viscosity) and the instantaneous displacements and velocities.

A simple example input is shown in Example: Transient Analysis of a Plain Cylindrical Journal Bearing.


Note:  A bearing element usually exhibits large stiffness values to be able to support the rotating structure. Also, the bearing clearance is very small and fluid film pressure is high, hence very small displacements induce a change in the bearing forces. When running such an analysis, make sure the time step is small enough to represent the nonlinearity of the bearing.


3.3.3. Using the FLUID218 Element

The FLUID218 element is based on the integration of the Reynolds equation for thin fluid film in a plain cylindrical journal bearing. Unlike COMBI214 and because it is a 3D element, any type of groove or supply hole can be modeled specifying pressure boundary conditions. It supports:

3.3.4. Using the MATRIX27 Element

The MATRIX27 element allows the definition of 12 x 12 stiffness and damping matrices. Those matrices can be symmetric or not.

Example of MATRIX27 use:

et,1,matrix27,,2,4,1                   ! unsymmetric [K] with printout
et,2,matrix27,,2,5,1                   ! unsymmetric [C] with printout

! define stiffness matrix   
KXX = 8.e+7		$ KXY = -1.e7          ! $ sign allows several commands on
KYX = -6.e+7		$ KYY = 1.e+8          ! the same line
	
r,1,  KXX,KXY               $ rmore,-KXX,-KXY
rmore,KYX,KYY               $ rmore,-KYX,-KYY
*do, ir, 1, 8
    rmore                              ! define zero values
*enddo
rmore,-KXX,-KXY             $ rmore,KXX,KXY
rmore,-KYX,-KYY             $ rmore,KYX,KYY

! define damping matrix
CXX = 8.e+3                 $ CXY = -3.e+3
CYX = -3.e+3                $ CYY = 1.2e+4

r,2,  CXX,CXY               $ rmore,-CXX,-CXY
rmore,CYX,CYY               $ rmore,-CYX,-CYY
*do, ir, 1, 8
    rmore                              ! define zero values
*enddo
rmore,-CXX,-CXY             $ rmore,CXX,CXY
rmore,-CYX,-CYY             $ rmore,CYX,CYY

3.3.5. Using the MPC184 General Joint Element

The MPC184 is a joint element with elastic stiffness and damping behavior. The characteristics are defined as 6 X 6 matrices using TB commands.

Example of MPC184 use:

keyopt,2,4,1             ! no rotations

sectype,2,joint,gene
local,11,0,4,0,0,0,0,0   ! coordinate system forming the joint element
secjoin,,11

KYY = 1.e+8
CYY = 1.e+6
KZZ = 1.e+10
CZZ = 1.e+2

tb,join,2,,,stiff
tbdata,7,KYY
tbdata,12,KZZ

tb,join,2,,,damp
tbdata,7,CYY
tbdata,12,CZZ