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-Damper | None | None | None | ||
COMBI214 | 2D Spring-Damper Bearing | Unsymmetric | Function of the rotational velocity | Lumped | ||
MATRIX27 | Stiffness, Damping, or Mass Matrix | Unsymmetric | None | Matrix | ||
MPC184 | Multipoint Constraint Element |
| Function of the displacement | None |
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.
The following topics provide more information about the element options listed in the table:
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).
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%
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.
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:
Pressure degree of freedom only (KEYOPT(1) = 0) to be used in a static analysis where the pressure distribution and pressure forces are determined. See Example: Calculation of the Pressure Profile of a Plain Cylindrical Journal Bearing with Supply Orifice.
Pressure and structural degrees of freedom (KEYOPT(1) = 1) to be used in a nonlinear large-deflection transient analysis where the time-dependent shaft position, pressure, and pressure forces are calculated. The note in Calculation of the Nonlinear Bearing Forces (KEYOPT(1) > 0) about the specificity of such a nonlinear analysis applies. See Example: Transient Analysis of a Plain Cylindrical Journal Bearing (3D Approach).
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