MPC184-Universal

Multipoint Constraint Element: Universal Joint

Compatible Products: – | Pro | Premium | Enterprise | Ent PP | Ent Solver | –

## 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.)

None

Temperatures --

T(I), T(J)

Rotations --

ROTX, ROTZ

Moments --

MX, MZ

Special Features
 Large deflection Linear perturbation
KEYOPT(1)

Element behavior:

7  --

Universal joint element

## MPC184 Universal Joint Output Data

The solution output associated with the element is in two forms:

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

NameDefinitionOR
ELElement Number-Y
NODESElement node numbers (I, J)-Y
FXConstraint force in X direction-Y
FYConstraint force in Y direction-Y
FZConstraint force in Z direction-Y
MYConstraint moment in Y direction-Y
CSTOP4Constraint moment if stop is specified on DOF 4-Y
CSTOP6Constraint moment if stop is specified on DOF 6-Y
CLOCK4Constraint moment if lock is specified on DOF 4-Y
CLOCK6Constraint moment if lock is specified on DOF 6-Y
CSST4Constraint stop status on DOF 4[1]-Y
CLST4Constraint lock status on DOF 4[2]-Y
CSST6Constraint stop status on DOF 6[1]-Y
CLST6Constraint lock status on DOF 6[2]-Y
JRP4Joint relative position of DOF4-Y
JRP6Joint relative position of DOF6-Y
JCD4Joint constitutive rotation on DOF4-Y
JCD6Joint constitutive rotation on DOF6-Y
JEF4Joint elastic moment in direction -4-Y
JEF6Joint elastic moment in direction -6-Y
JDF4Joint damping moment in direction -4-Y
JDF6Joint damping moment in direction -6-Y
JRU4Joint relative rotation of DOF4-Y
JRU6Joint relative rotation of DOF6-Y
JRV4Joint relative rotational velocity of DOF4-Y
JRV6Joint relative rotational velocity of DOF6-Y
JRA4Joint relative rotational acceleration of DOF4-Y
JRA6Joint relative rotational acceleration of DOF6-Y
JTEMPAverage temperature in the element[3]-Y

1. Constraint stop status:

 0 = stop not active, or deactivated 1 = stopped at minimum value 2 = stopped at maximum value
2. Constraint lock status:

 0 = lock not active 1 = locked at minimum value 2 = locked at maximum value
3. 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

NameDefinitionOR
E1X-I, E1Y-I, E1Z-IX, Y, Z components of the evolved e1 axis at node I-Y
E2X-I, E2Y-I, E2Z-IX, Y, Z components of the evolved e2 axis at node I-Y
E3X-I, E3Y-I, E3Z-IX, Y, Z components of the evolved e3 axis at node I-Y
E1X-J, E1Y-J, E1Z-JX, Y, Z components of the evolved e1 axis at node J-Y
E2X-J, E2Y-J, E2Z-JX, Y, Z components of the evolved e2 axis at node J-Y
E3X-J, E3Y-J, E3Z-JX, Y, Z components of the evolved e3 axis at node J-Y
JFX, JFY, JFZConstraint forces expressed in the evolved coordinate system specified at node I-Y
JMX, JMY, JMZConstraint 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
ItemE
FXSMISC1
FYSMISC2
FZSMISC3
MYSMISC5
MZSMISC6
CSTOP4SMISC10
CSTOP6SMISC12
CLOCK4SMISC16
CLOCK6SMISC18
CSST4SMISC22
CLST4SMISC28
CSST6SMISC24
CLST6SMISC30
JRP4SMISC34
JRP6SMISC36
JCD4SMISC40
JCD6SMISC42
JEF4SMISC46
JEF6SMISC48
JDF4SMISC52
JDF6SMISC54
JRU4SMISC64
JRU6SMISC66
JRV4SMISC70
JRV6SMISC72
JRA4SMISC76
JRA6SMISC78
JTEMPSMISC79

Table 184univ.4:  MPC184 Universal Joint Item and Sequence Numbers - NMISC Items

Output Quantity Name ETABLE and ESOL Command Input
ItemE
E1X-INMISC1
E1Y-INMISC2
E1Z-INMISC3
E2X-INMISC4
E2Y-INMISC5
E2Z-INMISC6
E3X-INMISC7
E3Y-INMISC8
E3Z-INMISC9
E1X-JNMISC10
E1Y-JNMISC11
E1Z-JNMISC12
E2X-JNMISC13
E2Y-JNMISC14
E2Z-JNMISC15
E3X-JNMISC16
E3Y-JNMISC17
E3Z-JNMISC18
JFXNMISC19
JFYNMISC20
JFZNMISC21
JMXNMISC22
JMYNMISC23
JMZNMISC24

## 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.

• The equation solver (EQSLV) must be the sparse solver or the PCG solver. The command PCGOPT,,,,,,,ON is also required in order to use the PCG solver.

• The element coordinate system (/PSYMB,ESYS) is not relevant.

## MPC184 Universal Joint Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.

ANSYS Mechanical Pro

• Linear perturbation is not available.