revolute 2

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6/22/2016 2.3. Connecting Multi body Components with Joint El ements

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2.3. Connecting Multibody Components with Joint Elements

The MPC184 family of elements serves to connect the flexible and/or rigid components toeach other in a multibody mechanism.

An MPC184 joint element is defined by two nodes with six degrees of freedom at each node(for a total of 12 DOFs). The relative motion between the two nodes is characterized by sixrelative degrees of freedom. Depending on the application, you can configure different kindsof joint elements by imposing appropriate kinematic constraints on any or some of these sixrelative degrees of freedom. For example, to simulate a revolute joint, the three relativedisplacement degrees of freedom and two relative rotational degrees of freedom areconstrained, leaving only one relative degree of freedom available (the rotation around therevolute axis). Similarly, constraining the three relative displacement degrees of freedomand one relative rotational degree of freedom can simulate a universal joint. Two rotational

degrees of freedom are unconstrained in this joint.

The kinematic constraints in the joint elements are imposed using the Lagrange multipliermethod. Because the Lagrange multiplier method is used to impose the constraints, theconstraint forces are available for output purposes.

The following topics about using joint elements in a multibody analysis are available:

Joint Element TypesMaterial Behavior of Joint Elements

Reference Lengths and Angles for Joint ElementsBoundary Conditions for Joint ElementsConnecting Bodies to Joints

2.3.1. Joint Element Types

All joint elements are classified as MPC184 elements. The various elements are available viathe MPC184 element's KEYOPT(1) setting and, in some cases, the KEYOPT(4) setting.

The following table lists the different types of joint elements and the required key optionsettings. The relevant element section in the Element Reference is also indicated.

Joint ElementType

KEYOPT(1) KEYOPT(4) MPC184 Element Constraints

Revolute 6 ---Revolute Joint 5

Z-axis revolute 6 1

Universal 7 --- Universal Joint 4

Slot 8 --- Slot Joint 2

Point-in-plane 9 --- Point-in-Plane Joint 1

Translational 10 --- Translational Joint 5
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Cylindrical 11 ---Cylindrical Joint 4

Z-axis cylindrical 11 1

Spherical 5 --- Spherical Joint 3

Planar 12 ---Planar Joint 3

Z-axis planar 12 1

Weld 13 --- Weld Joint 6

Orient 14 --- Orient Joint 3

General 16 --- General Joint

Depends onnumber offixed relativeDOFs

Minimumconstraints =0 (No DOF isfixed)

Maximumconstraints =6 (All DOFsare fixed)

Screw 17 --- Screw Joint

5

Relative axialmotion androtationalmotion arelinked via thepitch of thescrew

Following are some examples of joint element types:

Revolute Joint Constrained degrees of freedom: UX, UY, UZ, ROTX, ROTY
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Universal Joint Constrained degrees of freedom: UX, UY, UZ, ROTY

Slot Joint Constrained degrees of freedom: UY, UZ

Translational Joint Constrained degrees of freedom: UY, UZ, ROTX, ROTY, ROTZ

Cylindrical Joint Constrained degrees of freedom: UX, UY, ROTX, ROTY


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Spherical Joint Constrained degrees of freedom: UX, UY, UZ

Planar Joint Constrained degrees of freedom: UZ, ROTX, ROTY

2.3.1.1. Joint Element Connectivity Definition

A joint element is typically defined by specifying two nodes, I and J. These nodes may bearbitrarily located in space. There are instances, however, when one of the nodes needs to

be considered as a grounded node. In such cases, specify either node I or node Jappropriately. In cases when the node is grounded, the location of the grounded node istaken to be that of the other specified node.

Example


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If the first node of the joint element is a grounded node, then the element definition is: E,,Jor EN,ElementNumber,,J

Similarly, if the second node is the grounded node, then the element definition is: E,I, orEN,ElementNumber,I

2.3.1.2. Joint Element Section Definition

Each joint element must have an associated section definition. Use the SECTYPE commandto define the section type and subtype.

Example

The universal joint section definition is: SECTYPE,JOINT,UNIV,UNIV-01

2.3.1.3. Local Coordinate System Specification for Joint Elements

Local coordinate systems at the nodes are required to define the kinematic constraints of ajoint element. Use the SECJOINT command to do so.

The local coordinate systems and their required orientation vary from one joint element toanother. Input data requirements for each joint element differ. Typically, the localcoordinate system is always defined at the first node of a joint element.

The local coordinate system at the second node may be optional. If it is not specified, then

the local coordinate system at the first node is usually assumed.

The rotational components of the relative motion between the two nodes of the jointelements are quantified in terms of Bryant (or Cardan) angles that are evaluated based onthese coordinate systems.

Example

The following figure illustrates the specification of the local coordinate system for a universaljoint element:

Figure 2.8: MPC184 Universal Joint Geometry
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e I2

eJ3

e1I

e J2

e J2

eJ3

J

e J1

e1I

e I2

e I3I

I, J - Coincident nodes

J

e I2

e1I

I

eJ3

e J2

Z

X

Y

e I3

e J1

The local coordinate system specification is:

LOCAL,11,0

. . .

LOCAL,12,0

. . .

SECJOINT,LSYS,11,12

2.3.1.4. Stops or Limits with Joint Elements

Stops or limit constraints in joints are imposed on the available components of relativemotion between the two nodes of a joint element. The Lagrange multiplier method is usedto implement these constraints. For static analysis, the stop constraints are based on therelative displacements (or relative rotations) of the free degrees of freedom.

Caution: Use joint stops sparingly. The program treats a stop constraintinternally as a "must be imposed" or "hard" constraint, and no contact logicis used. As a result, during the given iteration of a substep, the stopconstraints activate immediately if the program detects a violation of a stoplimit.
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Depending upon the nature of the problem, the stop constraintimplementation may cause the solution to trend towards an equilibriatedstate that may not be readily apparent to you. In addition, do not use stopsto simulate zero-displacement boundary conditions. You should also avoidspecifying stops on multiple joints.Finally, do not use joint stops as a substitute for contact modeling. Wheneverpossible, use node-to-node or node-to-surface contact modeling to simulate

limit conditions.

Stops in Transient Dynamic Analysis

In a transient dynamic analysis, if relative displacement-based (or rotation-based) stopconstraints are used, then the relative velocities and relative accelerations becomeinconsistent (oscillatory velocity and/or accelerations are observed in many cases), implyingthat the energy and momentum due to the impact-like nature of the stops is not conserved.These inconsistencies are reasonably suppressed by imposing a numerical damping.However, numerical damping does not work appropriately in some cases. Thus, for the

transient dynamic case, an energy-momentum conservation scheme is adopted. By thismethod, the user specified relative DOF stop values are taken into account, and constraintsbased on the relative velocity are imposed in such a way that the overall energy andmomentum balance is achieved in a finite element sense.

Irrespective of the integration scheme specified for the transient dynamic analysis, theNewmark method is used for the joint element when stops are specified.

The energy-momentum conservation scheme for stops is implemented for all joints exceptthe screw joint. In the case of the screw joint, the stops are imposed based on the relative

displacements (or rotations).

Defining Stops for Joint Elements

You can impose stops or limits on the available components of relative motion between thetwo nodes of a joint element. The stops or limits essentially constrain the values of the freeDOFs within a certain range. To specify minimum and maximum values, issue the SECSTOPcommand.

The following figure shows how stops can be imposed on a revolute joint such that the

motion is constrained. The axis of the revolute is assumed to be perpendicular to the planeof paper and is along the e3 direction.

Figure 2.9: Stops Imposed on a Revolute Joint

The local coordinate system specified at node I is assumed to be fixed in its initial
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configuration. However, the local coordinate system specified at node J evolves with therotation of that node. The relative angle of rotation is given by:

Let the link with node J rotate with respect to the link with node I. This characteristic impliesthat the local coordinate system at node J rotates with respect to the local coordinatesystem at node I.

For the configuration shown, the initial relative angle of rotation is zero degrees. Acounterclockwise motion results in positive angles of rotation. Clockwise motion results innegative angles of rotation.

If stops limit the movement of the link with node J (as shown), the stop conditions arespecified as follows:

SECSTOP,6,PHImin ,PHImax

The next figure shows how stops can be imposed in a slot joint which involves

displacements in the local eI1 axis of node I. The relative distance between node J and node

I is given by:

where xI and xJ are the position vectors of nodes I and J. The initial distance between thenodes I and J is l0 and is a positive value.

Figure 2.10: Stops Imposed on a Slot Joint

The stops are defined as:

SECSTOP,1, min

, max

where

min and max are both positive.

The stops are defined as:

SECSTOP,1,- min , max

where
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min is negative and max is positive.

2.3.1.5. Joint Mechanism Locks

Locks or locking limits may also be imposed on the available components of relative motionbetween the two nodes of a joint element. Locks are basically used in joint mechanisms to

freeze the joint in a desired configuration during the course of deformation. When thelocks are activated on a particular component of relative motion, that component remainslocked for the rest of the analysis. Issue the SECLOCK command to define lock limits.

Referring to Figure 2.9: Stops Imposed on a Revolute Joint, the locks for a revolute joint arespecified as SECLOCK,6, Phi_Min,Phi_Max

Referring to Figure 2.10: Stops Imposed on a Slot Joint, the locks for the slot joint arespecified as SECLOCK,1,l_Min,l_Max

2.3.2. Material Behavior of Joint Elements

The following topics related to the material behavior of joint elements in a multibodyanalysis are available:

Stiffness and Damping Behavior of Joint ElementsFrictional Behavior

For more information, see MPC184 Joint in the Material Reference.

2.3.2.1. Stiffness and Damping Behavior of Joint Elements

Linear or nonlinear stiffness and damping behavior can be associated with the free orunrestrained components of relative motion of the joint elements. In the case of linearstiffness or linear damping, the values are specified as coefficients of a 6 x 6 elasticity matrixusing the TB,JOIN command with TBOPT = STIF or TBOPT = DAMP. The stiffness and

damping values can be temperature-dependent. Depending on the joint element in use, onlythe appropriate coefficients of the stiffness or damping matrix are used in the joint elementconstitutive calculations.

The nonlinear stiffness and damping behavior is specified using the TB,JOIN command withan appropriate TBOPT label. In the case of nonlinear stiffness, relative displacement

(rotation) versus force (moment) values are specified using the TBPT command. Fornonlinear damping behavior, velocity versus force behavior is specified using the TBPTcommand. (See Figure 2.11: Nonlinear Stiffness and Damping Behavior for Joints for arepresentation of the nonlinear stiffness or damping curve.) In either case, these values may

be temperature dependent use the TBTEMP command to define the temperature for thedata table.

Figure 2.11: Nonlinear Stiffness and Damping Behavior for Joints
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You can specify the linear or nonlinear stiffness or damping behavior independently for eachcomponent of relative motion. However, if you specify linear stiffness for an unrestrainedcomponent of relative motion, you cannot specify nonlinear stiffness behavior on the samecomponent of relative motion. The damping behavior is similarly restricted. If a jointelement has more than one free or unrestrained component of relative motion--for example,the universal joint has two free components of relative motion--then you can independentlyspecify the stiffness or damping behavior as linear or nonlinear for each of the unrestrictedcomponents of relative motion.

2.3.2.2. Frictional Behavior

Frictional behavior along the unrestrained components of relative motion influences theoverall behavior of the joints. You can model Coulomb friction for joint elements via theTB,JOIN command with an appropriate TBOPT label. Frictional behavior can be specified only

for the following joints:

Revolute Joint (x-axis and z-axis)

Slot Joint

Translational Joint

The laws governing the frictional behavior of the joint are described below.

Coulombs Law

The classical Coulomb friction model is implemented for joints using a penalty formulation.The Coulomb friction model for joints is defined as:
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Where, Fs is the equivalent tangential force (or moment), Fn is the normal force (or

moment) in the joint, and is the current value of the coefficient of friction. The calculationof the normal force depends on the joint under consideration.

If the equivalent tangential force Fs is less than Flim, the state is known as the sticking state.

If Fs exceeds Flim, sliding occurs and the state is known as the sliding state. The

sticking/sliding calculations determine when a point transitions from sticking to sliding or

vice versa.

Figure 2.12: Coulomb's Law

SlidingFlim

Fn

Fs

Exponential Friction Law

The exponential friction law is used to smooth the transition between the static coefficient offriction and the dynamic coefficient of friction according to the formula (Benson andHallquist):

where:

Vrel = the relative slip rate

s = the coefficient of friction in the static regime (stiction)

d = the coefficient of friction in the dynamic regime

c = decay coefficient

Figure 2.13: Exponential Friction Law
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2.3.2.2.1. Geometry specifications for Coulomb friction in Joints

The modeling of Coulomb friction in joints requires some geometry specifications, dependingon the type of joint under consideration. These quantities are used in the computation of thenormal force (or moment) for Coulomb friction calculations. The SECJOINT command isused to specify these quantities. The following table outlines the required geometricquantities:

Table 2.2: Required Geometric Quantities

Joint Type Geometric Quantities

Revolute Joint (x-axis and z-axis) Outer radius, Inner radius, Effective Length

Slot Joint None required

Translational Joint Effective Length, Effective Radius

If appropriate geometric quantities are not specified, then the corresponding normal forcecontributions will not be considered. The following section explains the normal forcecalculations and the geometric quantities required.

2.3.2.2.2. Calculation of Normal Forces for Coulomb Frictional Behavior

The normal force (or moment) that is used in the Coulomb frictional behavior is based onthe following forces that arise in a joint:

Lagrange Multiplier forces (or moments) due to the constraints

Interference fit forces (or moments)

Revolute Joint
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In order to compute the normal moment in a revolute joint, the revolute joint is visualized asa cylinder-pin assembly (for example, a door hinge consisting of a pin with a head insertedinto a cylinder).

The following geometric quantities are required in the calculations below. Note that thespecification of these quantities is optional. If some of these geometric quantities are notspecified, then the corresponding contribution to the normal moment calculations is ignored.

Router = Outer radius of the cylinder

Rinner = Inner radius of the cylinder or outside radius of pin

Leff = The effective length is the length over which the cylinder and pin are in

contact with each other

The contributions to the normal moment in an x-axis revolute joint are as follows:

An axial moment due to the axial component of the constraint Lagrange Multiplierforce (1 ).

This force acts in such a way as to push the cylinder against the pin head, therebycausing a frictional moment to develop.

where,

A tangential moment due to the constraint Lagrange Multiplier forces, 2 and 3:

A bending moment that is generated as a consequence of the constraint LagrangeMultiplier moments (5 and 6):

Leading to a bending moment:

Additionally, if interference fit moment (Minterference) is defined, the normal moment for

frictional calculations is given by:


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A similar calculation is carried out for the z-axis revolute joint by choosing the appropriateconstraint Lagrange multiplier forces in the above equations.

Slot Joint

The two displacement constraint Lagrange Multiplier forces (2 and 3) in the slot joint

contribute to a tangential force as follows:

Additionally, if interference fit force (Finterference) is defined, the normal force for frictional

calculations is given by:

Geometric quantities are not required for the slot joint.

Translational Joint

The geometric quantities required for the translation joint are:

Leff = Effective length. The effective length is the length over which the two parts

of the translation joint overlap. It is assumed that the change in this length issmall.

Reff = Effective radius. To simplify calculations, an effective radius is used in

torsional moment calculations, even though the cross section in a translationaljoint is rectangular. The effective radius is used in computing the force that arisesdue to the torsional moment.

The normal force used in frictional calculations is computed as follows:

An effective radial force due to the constraint forces (2

and 3

):

Bending force due to in-plane constraint moments (5 and 6):

Leading to a bending force


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Force due to the torsional constraint moment, 4:

Additionally, if interference fit force (Finterference) is defined, the normal force for frictional

calculations is given by:

2.3.3. Reference Lengths and Angles for Joint Elements

The initial configuration of the joint element may be such that nonzero forces or moments isnecessary. In such cases, you can define the constitutive behavior with respect to areference configuration such that these forces or moments are zero. To do so, define a

reference angle or a reference length (SECDATA).

If you do not define reference lengths and angles, Mechanical APDL calculates the valuesfrom the initial configuration of the joints. ANSYS uses the reference lengths and angles inthe stiffness and frictional behavior calculations.

2.3.4. Boundary Conditions for Joint Elements

Issue the DJ command to impose boundary conditions on the available components ofrelative motion of the joint element. You can list the imposed values via the DJLISTcommand. To delete the values, issue the DJDELE command.

To apply concentrated forces on the available components of relative motion of the jointelement, issue the FJ command. You can list the imposed values via the FJLIST command.To delete the values, issue the FJDELE command.

2.3.5. Connecting Bodies to Joints

Other than in idealized geometry (such as that shown in Figure 2.1: FE Slider-CrankMechanism ), an MPC184 joint element is defined by one or two nodes in space and requiresspecial modeling techniques to connect the joint to the body appropriately.

Figure 2.14: Pinned Joint Geometry shows a 3-D model of a pinned joint where thegeometry of the joint (the pin) is explicitly modeled. To perform a multibody analysis, thepin geometry is ignored and the behavior replaced by the appropriate MPC184joint element.

Figure 2.14: Pinned Joint Geometry
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Figure 2.15: Pinned Joint Mesh and Revolute Joint shows the meshed model including therevolute joint. To connect the bodies to the joint, you must use either elements (such asbeams) or constraint equations. The easiest way to do so is to use contact elements to

create surface-based constraints (multipoint constraints, or MPCs), as follows:

1. Define a pilot node at one end of the joint. The pilot node connects the joint to therest of the body.

2. Select the nodes on the surface of the body that you want to connect to this pilotnode.

3. Create contact surface elements on this surface. By sharing the same real constantnumber (REAL,N ), MPCs between the surface nodes and the pilot node are

generated during the solution.

Repeat the steps for eachbody-joint connection.

Figure 2.15: Pinned Joint Mesh and Revolute Joint
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Figure 2.16: Pinned Joint Contact Elements shows the contact elements and

Figure 2.17: Pinned Joint Constraint Equations shows the MPCs (constraint equations)created during the solution for the lower body.

Create the pilot node using the TARGE170 element--setting KEYOPT(2) = 1 so as not toallow the program to constrain any DOFs--and issuing the TSHAP,PILO command.

If you mesh the body with elements having no midside nodes (such as SOLID185), useCONTA173 as the element type for the surface mesh. For elements with midside nodes(such as SOLID186 or SOLID187), use CONTA174. Set the following element key options tocreate the necessary constraints:

KEYOPT(2) = 2 Constraint (MPC) option.

KEYOPT(4) = 2 Generate rigid MPC constraints.

KEYOPT(12) = 5 Bonded behavior between the pilot node and the contact

surface.

Figure 2.16: Pinned Joint Contact Elements
https://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_CONTA174.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_SOLID187.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_SOLID186.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_CONTA173.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_SOLID185.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_cmd/Hlp_C_TSHAP.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_elem/Hlp_E_TARGE170.htmlhttp://-/?-http://-/?-


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Figure 2.17: Pinned Joint Constraint Equations


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Instead of the rigid option, you can also choose a flexible (force-distributed or RBE3-type)

constraint option by setting KEYOPT(4) = 1. The following figures illustrate the difference inbehaviors:

Figure 2.18: Rigid Constraint (KEYOPT(4) = 2)

Imposed displacement at Pilot node

(UX, UY)Constraint surface

remains rigid

Contact elements

Figure 2.19: Flexible Constraint (KEYOPT(4) = 1)


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Imposed displacement at Pilot node

(UX, UY)

Deformed constraint surface

Contact elements

Typical Command Sequence

Following is a typical command sequence for connecting bodies to joints:

! Step 1: Define a pilot node at the joint nodeet,59,170 ! type ID=59 is an available IDkeyopt,59,2,1 ! do not allow program to constrain DOFsreal,59 ! real ID=59 is an available IDtshap,pilote,9536 ! 9536 is the joint node! Step 2: Select the nodes of the corresponding surfacecsys,15 ! CS at center of pinnsel,s,loc,x,15 ! nodes at r=15! Step 3: Create the contact elements on the surfaceet,60,173keyopt,60,2,2 ! constraint (MPC) optionkeyopt,60,4,2 ! rigid MPCkeyopt,60,12,5 ! bonded always contacttype,60real,59 ! same real ID: this connects the pilot ! to this surfaceesurf ! generate the contact elements on the surfacensel,all

Additional Information

For more information about using contact elements to generate constraints, see Surface-Based Constraints in the Contact Technology Guide.

Release 16.2 - SAS IP, Inc. All rights reserved.
https://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_ctec/ctectoc.htmlhttps://www.sharcnet.ca/Software/Ansys/16.2.3/en-us/help/ans_ctec/Hlp_ctec_surfcon.html

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