The TB,JOIN option enables you to impose linear and nonlinear elastic stiffness and damping behavior or Coulomb friction behavior on the available components of relative motion of an MPC184 joint element. Support for these behaviors varies among the different types of joints, as follows:
The TB command may be repeated with the same material ID number to specify both the stiffness and damping behavior.
The following joint material models are available:
Input the linear stiffness or damping behavior for the relevant components of relative motion of a joint element by specifying the terms as part of a 6 x 6 matrix with data-table commands as described below.
The 6 x 6 matrix for linear stiffness or damping behavior is:
Enter the stiffness or damping coefficient of the matrix in the data table with TB set of commands. Initialize the constant table with TB,JOIN,,,,STIF (for stiffness behavior) or TB,JOIN,,,,DAMP (for damping behavior). Define the temperature with TBTEMP, followed by the relevant constants input with TBDATA commands. Matrix terms are linearly interpolated between temperature points. Based on the joint type, the relevant constant specification is as follows:
| Joint Element | Constant | Meaning |
|---|---|---|
| x-axis Revolute joint | C16 | Term D44 |
| z-axis Revolute joint | C21 | Term D66 |
| Universal joint | C16, C18, C21 | Terms D44, D64, D66 |
| Slot joint | C1 | Term D11 |
| Point-in-plane joint | C7, C8, C12 | Terms D22, D32, D33 |
| Translational joint | C1 | Term D11 |
| x-axis Cylindrical joint | C1, C4, C16 | Terms D11, D41, D44 |
| z-axis Cylindrical joint | C12, C15, C21 | Terms D33, D63, D66 |
| x-axis Planar joint | C7, C8, C9, C12, C13, C16 | Terms D22, D32, D42, D33, D43, D44 |
| z-axis Planar joint | C1, C2, C6, C7, C11, C21 | Terms D11, D21, D61, D22, D62, D66 |
| Spherical joint | C16, C18, C21 | Terms D44, D55, D66 |
| General joint | Use appropriate entries based on unconstrained degrees of freedom. | --- |
| Screw joint | C12, C15, C21 | Terms D33, D63, D66 |
| Spotweld joint | C11 - C21 | Terms D11 - D66 |
| Genb joint | Use appropriate entries based on unconstrained degrees of freedom. | --- |
The following example define the uncoupled linear elastic stiffness behavior for a universal joint at the two available components of relative motion, with two temperature points:
TB,JOIN,1,2,,STIF ! Activate JOIN material model with linear elastic stiffness TBTEMP,100.0 ! Define first temperature TBDATA,16,D44 ! Define constant D44 in the local ROTX direction TBDATA,21,D66 ! Define constant D66 in the local ROTZ direction TBTEMP,200.0 ! Define second temperature TBDATA,16,D44 ! Define constant D44 in the local ROTX direction. TBDATA,21,D66 ! Define constant D66 in the local ROTZ direction.
You can specify nonlinear elastic stiffness as a displacement
(rotation) versus force (moment) curve using the TB,JOIN command with a suitable TBOPT setting.
Use the TBPT command to specify the data points or specify the name of a function that defines the curve on the TB command. (Use the Function Tool to generate the specified function.) The values may be temperature-dependent.
You can specify nonlinear damping behavior in a similar manner by supplying velocity versus damping force (or moment).
The appropriate TBOPT labels for
each joint element type are shown in the following tables. For a description
of each TBOPT label, see "JOIN -- Joint Element Specifications" in the TB command documentation.
| Nonlinear Stiffness Behavior | |
|---|---|
| Joint Element |
TBOPT on TB
command |
| x-axis Revolute joint | JNSA, JNS4 |
| z-axis Revolute joint | JNSA, JNS6 |
| Universal joint | JNSA, JNS4, and JNS6 |
| Slot joint | JNSA and JNS1 |
| Point-in-plane joint | JNSA, JNS2, and JNS3 |
| Translational joint | JNSA and JNS1 |
| x-axis Cylindrical joint | JNSA, JNS1, and JNS4 |
| z-axis Cylindrical joint | JNSA, JNS3, and JNS6 |
| x-axis Planar joint | JNSA, JNS2, JNS3, and JNS4 |
| z-axis Planar joint | JNSA, JNS1, JNS2, and JNS6 |
| Spherical joint | JNSA, JNS4, JNS5, JNS6 |
| General joint | Use appropriate entries based on unconstrained degrees of freedom |
| Screw joint | JNSA, JNS3, and JNS6 |
| Spotweld joint | JNSA, JNS1, JNS2, JNS3, JNS4, JNS5, JNS6 |
| Genb joint | Use appropriate entries based on unconstrained degrees of freedom |
| Nonlinear Damping Behavior | |
|---|---|
| Joint Element |
TBOPT on TB
command |
| x-axis Revolute joint | JNDA, JND4 |
| z-axis Revolute joint | JNDA, JND6 |
| Universal joint | JNDA, JND4, JND6 |
| Slot joint | JNDA, JND1 |
| Point-in-plane joint | JNDA, JND2, JND3 |
| Translational joint | JNDA, JND1 |
| x-axis Cylindrical joint | JNDA, JND1, JND4 |
| z-axis Cylindrical joint | JNDA, JND3, JND6 |
| x-axis Planar joint | JNDA, JND2, JND3, JND4 |
| z-axis Planar joint | JNDA, JND1, JND2, JND6 |
| General joint | Use appropriate entries based on unconstrained degrees of freedom |
| Screw joint | JNDA, JND3, JND6 |
| Spotweld joint | JNDA, JND1, JND2, JND3, JND4, JND5, JND6 |
| Genb joint | Use appropriate entries based on unconstrained degrees of freedom |
The following example specifies nonlinear stiffness behavior for a revolute joint having only one available component of relative motion (the rotation around the axis of revolution). Two temperature points are specified.
TB,JOIN,1,2,2,JNS4 TBTEMP,100. TBPT,,rotation_value_1,moment_value_1 TBPT,,rotation_value_2,moment_value_2 TBTEMP,200.0 TBPT,,rotation_value_1,moment_value_1 TBPT,,rotation_value_2,moment_value_2
When specifying a function that describes the nonlinear stiffness behavior, the Function Tool enables the force to be defined as a function of temperature and relative displacement; the two independent variables are named as TEMP and DJU. Similarly, when specifying a function that describes the nonlinear damping behavior, the Function Tool enables the damping force to be defined as a function of temperature and relative velocity; the two independent variables are identified as TEMP and DJV.
Example — Consider a function where the damping force varies with temperature and relative velocity:
F = (-0.005 * Temperature + 0.25) * Relative Velocity
Define the function using the Function Editor, then retrieve and load it using the Function Loader. (The editor and the loader are both components of the Function Tool.)
Assuming a function name of dampfunc, you
can then use the TB command to define the joint
material:
TB, JOIN, 1, , , JND4, , %dampfunc%
For more information about the Function Tool utility, see Using the Function Tool in the Basic Analysis Guide.
Frictional behavior along the unrestrained components of relative
motion influences the overall behavior of the Joints. You can model Coulomb friction for
joint elements via the TB,JOIN command with an appropriate
TBOPT label. The joint frictional behavior can be specified
only for the following joints: Revolute joint, Slot
joint, Translational
joint, Spherical joint.
The friction parameters are described below.
Coulomb Friction Coefficient Specification
There are three options for defining the Coulomb friction coefficient.
Define a single value of the Coulomb friction coefficient by specifying
TBOPT= MUSx, where the value ofxdepends on the joint under consideration. Use the TBDATA command to specify the value of the friction coefficient.Define the Coulomb friction coefficient as a function of the sliding velocity. Use
TBOPT= MUSx(as stated above) and use the TBPT command to specify the data values.Use the exponential law for friction behavior. Specify
TBOPT= EXPx, where the value ofxdepends on the joint under consideration, and use the TBDATA command to specify the values required for the exponential law. In this case, the TBDATA command format is:TBDATA, μs, μd, c
where μs is the coefficient of friction in the static regime, μd is the coefficient of friction in the dynamic regime, and c is the decay coefficient.
Maximum or Critical Force/Moment
The maximum allowable value of critical force/moment can be specified using
TBOPT= TMXx, wherexdepends on the joint under consideration.
Elastic Slip
The elastic slip can be specified by setting
TBOPT= SLx, wherexdepends on the joint under consideration.If the stick-stiffness value is not specified, then this value along with the critical force/moment is used to determine the stick-stiffness.
If the elastic slip is not specified, then a default value is computed for stick-stiffness calculations if necessary. The default value for the translational joint and the slot joint is set to 0.005*h, where h is a characteristic length value computed from overall dimensions of the model. The value of h defaults to 1.0 if a characteristic length cannot be computed properly. The default value for the revolute joint is set to 0.001 radians and 0.02 radians for spherical joint.
The frictional behavior is implemented using a penalty method. Thus, there will be relative elastic slip even when sticking conditions prevail. The amount of elastic slip depends on the value specified for elastic slip. In some cases, the default values may result in large elastic slip. Therefore, you should specify an amount of elastic slip that is appropriate for your model.
Stick-Stiffness
A stick-stiffness value can be specified for controlling the behavior in the stick regime when friction behavior is specified. Use
TBOPT= SKx, wherexdepends on the joint under consideration.If the stick-stiffness value is not specified, then the following procedure is adopted:
If both maximum force/moment and elastic slip are specified, then the stick-stiffness is calculated from these values.
If only maximum force/moment is specified, then a default elastic slip is computed and then the stick-stiffness is calculated.
If only the elastic slip is specified, then the stick-stiffness value is computed based on the current normal force/moment (Friction Coefficient * Normal Force or Moment/elastic-slip).
Interference Fit Force/Moment
If the forces that are generated during a joint assembly have to be modeled, the interference fit force/moment can be specified using
TBOPT= FIx, wherexdepends on the joint under consideration. This force/moment will contribute to the normal force/moment in friction calculations.
The appropriate TBOPT labels (TB command) for each joint element type are shown in the
table below:
TBOPT Labels for Elements Supporting Coulomb
Friction
| |||||
| Friction Parameter | x-axis Revolute Joint | z-axis Revolute Joint | Slot Joint | Translational Joint | Spherical Joint |
| Static Friction | MUS4 | MUS6 | MUS1 | MUS1 | MUS6 |
| Exponential Friction Law | EXP4 | EXP6 | EXP1 | EXP1 | -- |
| Max. Allowable Shear Force/Moment | TMX4 | TMX6 | TMX1 | TMX1 | -- |
| Elastic Slip | SL4 | SL6 | SL1 | SL1 | SL6 |
| Interference Fit Force/Moment | FI4 | FI6 | FI1 | FI1 | -- |
| Stick-Stiffness | SK4 | SK6 | SK1 | SK1 | SK6 |
The following examples illustrate how to specify Coulomb friction parameters for various scenarios.
Example 1 — Specifying a single value of coefficient of friction and other friction parameters for an x-axis revolute joint.
TB, JOIN, 1, , , MUS4 ! Label for friction coefficient TBDATA, 1, 0.1 ! Value of coefficient of friction TB, JOIN, 1, , , SK4 ! Label for stick-stiffness TBDATA, 1, 3.0E4 ! Value for stick-stiffness TB, JOIN, 1, , , FI4 ! Label for interference fit force TBDATA, 1, 10000.00 ! Value for interference fit force
Example 2 — Specifying temperature dependent friction coefficient and other friction parameters for a z-axis revolution joint.
TB, JOIN, 1,2 , 1, MUS6 ! 2 temp points, 2 data points and label for friction coefficient TBTEMP, 10 ! 1st temperature TBDATA, 1, 0.15 ! Value of coefficient of friction TBTEMP, 20 ! 2nd temperature TBDATA, 1, 0.1 ! Value of coefficient of friction ! TB, JOIN, 1, , , SK4 ! Label for stick-stiffness TBDATA, 1, 3.0E4 ! Value for stick-stiffness TB, JOIN, 1, , , FI4 ! Label for interference fit force TBDATA, 1, 10000.00 ! Value for interference fit force
Example 3 — Specifying the exponential law for friction and other friction parameters for a z-axis revolute joint.
TB, JOIN, 1, , , EXP6 ! Label for friction coefficient TBDATA, 1, 0.4, 0.2, 0.5 ! Static friction coeff, dynamic friction coeff, decay constant ! TB, JOIN, 1, , , SK6 ! Label for stick-stiffness TBDATA, 1, 3.0E4 ! Value for stick-stiffness
Example 4 — Specifying friction as a function of sliding velocity for a slot joint.
TB, JOIN, 1, , 3, MUS1 ! Label for friction coefficient TBPT, , 1.0, 0.15 ! Sliding velocity, coefficient of friction TBPT, , 5.0, 0.10 ! Sliding velocity, coefficient of friction TBPT, , 10.0, 0.09 ! Sliding velocity, coefficient of friction ! TB, JOIN, 1, , , TMX1 ! Label for max allowable frictional force TBDATA, 1, 3.0E4 ! Value for max allowable frictional force TB, JOIN, 1, , , SL1 ! Label for elastic slip TBDATA, 1, 0.04 ! Value of elastic slip