MPC184-Universal
Multipoint Constraint Element: Universal Joint
MPC184 Universal Joint Element Description
The MPC184 universal joint element is a two-node element that has two free relative rotational degrees of freedom. The two nodes forming the element must have identical spatial coordinates.
MPC184 Universal Joint Input Data
Set KEYOPT(1) = 7 to define a two-node universal joint element.
Figure 184univ.1: MPC184 Universal Joint Geometry shows the geometry and node locations for this element. Two nodes (I and J) define the element. The two nodes are expected to have identical spatial coordinates.
A local Cartesian coordinate system must be specified at the first node, I, of the element. The specification of the second local coordinate system at node J is optional. If the local coordinate system is not specified at node J, then the local coordinate system at node J is assumed to be the same as that at node I. The local 2 direction is usually aligned along the shaft axes of the universal joint. The orientation of local directions must follow the convention specified in Figure 184univ.1: MPC184 Universal Joint Geometry. These local coordinate systems evolve with the rotations at the respective nodes (if any). Use the SECJOINT command to specify the identifiers of the local coordinate systems.
The constraints imposed in a universal joint element are easily described by considering the two local coordinate systems (Cartesian) attached to node I and node J (Figure 184univ.1: MPC184 Universal Joint Geometry). At any given instant of time, the constraints imposed in a universal joint are as described below.
Displacement constraints:
uI = uJ
Where, uI is the displacement vector at node I, and uJ is the displacement vector at node J.
Rotation constraints:
If the axes
and
are not aligned at the start of the analysis,
then the angle between the two is held fixed at the initial value.
The relative position of the local coordinate system at node I with respect to node J is characterized by the first and the third Cardan (or Bryant) angles as:
The change in the relative angular position between the two local coordinate system is given by
ur4 = ϕ - ϕ0
ur6 = ψ - ψ0
Where, ϕ0 and ψ0 are the initial angular offsets between the two coordinate systems (that is, the first and third Cardan (or Bryant) angles measured in the reference configuration).
The constitutive calculations use the following definition of the joint rotation:
Where,
,
are the reference angles, angle1 and angle3,
specified on the SECDATA command. If these values
are not specified, then ϕ0 and ψ0 are used in place of
and
, respectively.
Other input data that are common to all joint elements (material behavior, stops and limits, locks, etc.) are described in "Joint Input Data" in the MPC184 element description.
MPC184 Universal Joint Input Summary
This input summary applies to the universal joint element option of MPC184: KEYOPT(1) = 7.
- Nodes
I, J
Note: For a grounded joint element, specify either node I or node J in the element definition and leave the other node (the grounded node) blank.
- Degrees of Freedom
UX, UY, UZ, ROTX, ROTY, ROTZ
- Real Constants
None
- Material Properties
Use the JOIN label on the TB command to define stiffness and damping behavior. (See MPC184 Joint in the Material Reference for detailed information on defining joint materials.)
- Surface Loads
None
- Body Loads
- Temperatures --
T(I), T(J)
- Element Loads
- Rotations --
ROTX, ROTZ
- Moments --
MX, MZ
- Special Features
- KEYOPT(1)
Element behavior:
- 7 --
Universal joint element
- KEYOPT(2)
Element constraint imposition method:
- 0 --
Lagrange multiplier method (default)
- 1 --
Penalty-based method
MPC184 Universal Joint Output Data
The solution output associated with the element is in two forms:
Nodal displacements included in the overall nodal solution
Additional element output as shown in Table 184univ.1: MPC184 Universal Joint Element Output Definitions and Table 184univ.2: MPC184 Universal Joint Element - NMISC Output.
These tables use the following notation:
A colon (:) in the Name column indicates the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.out. The R column indicates the availability of the items in the results file.
In either the O or R columns, Y indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and a - indicates that the item is not available.
Table 184univ.1: MPC184 Universal Joint Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element Number | - | Y |
| NODES | Element node numbers (I, J) | - | Y |
| FX | Constraint force in X direction | - | Y |
| FY | Constraint force in Y direction | - | Y |
| FZ | Constraint force in Z direction | - | Y |
| MY | Constraint moment in Y direction | - | Y |
| CSTOP4 | Constraint moment if stop is specified on DOF 4 | - | Y |
| CSTOP6 | Constraint moment if stop is specified on DOF 6 | - | Y |
| CLOCK4 | Constraint moment if lock is specified on DOF 4 | - | Y |
| CLOCK6 | Constraint moment if lock is specified on DOF 6 | - | Y |
| CSST4 | Constraint stop status on DOF 4[1] | - | Y |
| CLST4 | Constraint lock status on DOF 4[2] | - | Y |
| CSST6 | Constraint stop status on DOF 6[1] | - | Y |
| CLST6 | Constraint lock status on DOF 6[2] | - | Y |
| JRP4 | Joint relative position of DOF4 | - | Y |
| JRP6 | Joint relative position of DOF6 | - | Y |
| JCD4 | Joint constitutive rotation on DOF4 | - | Y |
| JCD6 | Joint constitutive rotation on DOF6 | - | Y |
| JEF4 | Joint elastic moment in direction -4 | - | Y |
| JEF6 | Joint elastic moment in direction -6 | - | Y |
| JDF4 | Joint damping moment in direction -4 | - | Y |
| JDF6 | Joint damping moment in direction -6 | - | Y |
| JRU4 | Joint relative rotation of DOF4 | - | Y |
| JRU6 | Joint relative rotation of DOF6 | - | Y |
| JRV4 | Joint relative rotational velocity of DOF4 | - | Y |
| JRV6 | Joint relative rotational velocity of DOF6 | - | Y |
| JRA4 | Joint relative rotational acceleration of DOF4 | - | Y |
| JRA6 | Joint relative rotational acceleration of DOF6 | - | Y |
| JTEMP | Average temperature in the element[3] | - | Y |
0 = stop not active, or deactivated 1 = stopped at minimum value 2 = stopped at maximum value 0 = lock not active 1 = locked at minimum value 2 = locked at maximum value Average temperature in the element when temperatures are applied on the nodes of the element using the BF command, or when temperature are applied on the element using the BFE command.
The following table shows additional non-summable miscellaneous (NMISC) output available for the universal joint element.
Note: This output is intended for use in the Ansys Workbench program to track the evolution of local coordinate systems specified at the nodes of joint elements.
Table 184univ.2: MPC184 Universal Joint Element - NMISC Output
| Name | Definition | O | R |
|---|---|---|---|
| E1X-I, E1Y-I, E1Z-I | X, Y, Z components of the evolved e1 axis at node I | - | Y |
| E2X-I, E2Y-I, E2Z-I | X, Y, Z components of the evolved e2 axis at node I | - | Y |
| E3X-I, E3Y-I, E3Z-I | X, Y, Z components of the evolved e3 axis at node I | - | Y |
| E1X-J, E1Y-J, E1Z-J | X, Y, Z components of the evolved e1 axis at node J | - | Y |
| E2X-J, E2Y-J, E2Z-J | X, Y, Z components of the evolved e2 axis at node J | - | Y |
| E3X-J, E3Y-J, E3Z-J | X, Y, Z components of the evolved e3 axis at node J | - | Y |
| JFX, JFY, JFZ | Constraint forces expressed in the evolved coordinate system specified at node I | - | Y |
| JMX, JMY, JMZ | Constraint moments expressed in the evolved coordinate system specified at node I | - | Y |
Table 184univ.3: MPC184 Universal Joint Item and Sequence Numbers - SMISC Items and Table 184univ.4: MPC184 Universal Joint Item and Sequence Numbers - NMISC Items list output available via the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table for further information. The table uses the following notation:
- Name
output quantity as defined in the Element Output Definitions table.
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
Table 184univ.3: MPC184 Universal Joint Item and Sequence Numbers - SMISC Items
| Output Quantity Name | ETABLE and ESOL Command Input | |
|---|---|---|
| Item | E | |
| FX | SMISC | 1 |
| FY | SMISC | 2 |
| FZ | SMISC | 3 |
| MY | SMISC | 5 |
| CSTOP4 | SMISC | 10 |
| CSTOP6 | SMISC | 12 |
| CLOCK4 | SMISC | 16 |
| CLOCK6 | SMISC | 18 |
| CSST4 | SMISC | 22 |
| CLST4 | SMISC | 28 |
| CSST6 | SMISC | 24 |
| CLST6 | SMISC | 30 |
| JRP4 | SMISC | 34 |
| JRP6 | SMISC | 36 |
| JCD4 | SMISC | 40 |
| JCD6 | SMISC | 42 |
| JEF4 | SMISC | 46 |
| JEF6 | SMISC | 48 |
| JDF4 | SMISC | 52 |
| JDF6 | SMISC | 54 |
| JRU4 | SMISC | 64 |
| JRU6 | SMISC | 66 |
| JRV4 | SMISC | 70 |
| JRV6 | SMISC | 72 |
| JRA4 | SMISC | 76 |
| JRA6 | SMISC | 78 |
| JTEMP | SMISC | 79 |
Table 184univ.4: MPC184 Universal Joint Item and Sequence Numbers - NMISC Items
| Output Quantity Name | ETABLE and ESOL Command Input | |
|---|---|---|
| Item | E | |
| E1X-I | NMISC | 1 |
| E1Y-I | NMISC | 2 |
| E1Z-I | NMISC | 3 |
| E2X-I | NMISC | 4 |
| E2Y-I | NMISC | 5 |
| E2Z-I | NMISC | 6 |
| E3X-I | NMISC | 7 |
| E3Y-I | NMISC | 8 |
| E3Z-I | NMISC | 9 |
| E1X-J | NMISC | 10 |
| E1Y-J | NMISC | 11 |
| E1Z-J | NMISC | 12 |
| E2X-J | NMISC | 13 |
| E2Y-J | NMISC | 14 |
| E2Z-J | NMISC | 15 |
| E3X-J | NMISC | 16 |
| E3Y-J | NMISC | 17 |
| E3Z-J | NMISC | 18 |
| JFX | NMISC | 19 |
| JFY | NMISC | 20 |
| JFZ | NMISC | 21 |
| JMX | NMISC | 22 |
| JMY | NMISC | 23 |
| JMZ | NMISC | 24 |
MPC184 Universal Joint Assumptions and Restrictions
The nodes I and J must be coincident.
The local coordinate systems at the nodes must be specified such that the axes of rotation are well defined. Otherwise, it is possible that the rotational motion might not be what is expected.
Boundary conditions cannot be applied on the nodes forming the universal joint.
Rotational degrees of freedom are activated at the nodes forming the element. When these elements are used in conjunction with solid elements, the rotational degrees of freedom must be suitably constrained. Since boundary conditions cannot be applied to the nodes of the universal joint, a beam or shell element with very weak stiffness may be used with the underlying solid elements at the nodes forming the joint element to avoid any rigid body modes.
If both stops and locks are specified, then lock specification takes precedence. That is, if the degree of freedom is locked at a given value, then it will remain locked for the rest of the analysis.
In a nonlinear analysis, the components of relative motion are accumulated over all the substeps. It is essential that the substep size be restricted such that these rotations in a given substep are less than π for the values to be accumulated correctly.
The element currently does not support birth or death options.
For the Lagrange multiplier element formulation (KEYOPT(2) = 0) and the penalty-based element formulation (KEYOPT(2) = 1), the equation solver (EQSLV) must be the sparse or the PCG solver.
Lagrange multiplier-based joint elements (KEYOPT(2) = 0) and penalty-based joint elements (KEYOPT(2) = 1) cannot be connected to each other.
The element coordinate system (/PSYMB,ESYS) is not relevant.