introduction to ansys rigid and flexible dynamic analysis

April 9, 2007© 2007 ANSYS, Inc. All rights reserved.

ANSYS, Inc. Proprietary Inventory #0024021-1

Introduction to ANSYS Rigid and Flexible Dynamic

Analysis

Chapter 1


Inventory #0024021-2

ANSYS, Inc. Proprietary

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A. Introduction

• What is Multi-body Analysis?

Parts are connected at Joints which allow some relative motion

Parts are modeled as rigid or flexible




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• What is multi-body analysis?– Typically the model will be connected in such a way that it forms a

mechanism that can be driven by a force or displacement. – The response will be based on the kinematics of the mechanism and in

the case of a force loading, the inertia of the parts.

• Product and Licensing Requirements:– A separate license is needed for the Rigid Dynamics module which is

used with the ANSYS Structural, Mechanical or Multiphysics licenses.– Flexible dynamic analyses require no special add on or licensing. Can

be performed using ANSYS Structural, Mechanical or Multiphysics products.

Introduction




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• Two Multi-body Dynamic Analysis types available in Simulation:– Rigid and Flexible.– These are described in detail in Modules 2 and 3.

• A Rigid analysis considers the large motion of the bodies in the model. The displacements and rotations are due only to the joints.

• A Flexible analysis may also have rigid bodies, but can also consider flexible bodies. The displacements and rotations are due to joints, but also flexible part deformation.

Introduction




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Introduction

• Advantages of Rigid Analysis:– Very fast. Rigid bodies are connected with joints resulting in a

minimum number of degrees of freedom.– Very robust, no convergence issues. Rigid bodies don’t generate high

frequency response.– Graphics provide complete visualization of the part motion.– Can be used interactively to test kinematics (configuration tool).– Powers the Connections Worksheet tab Joint Kinematics Evaluation.– Can include springs/dampers.




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Introduction

• Sample Rigid Analysis (animation):




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Introduction

• Advantages of Flexible Analysis:– Bodies can be flexible!– All nonlinearities supported.– All boundary conditions supported.– Surface to surface contact between bodies can be included.– Rigid or flexible can be used on a part by part base.




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Introduction

• Sample Flexible Analysis with a combination of three rigid and one flexible part.

Slot Joint Load drives the base of the plate up and down




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B. Rigid Solver

• Completely independent of ANSYS elements and solvers.• Uses an explicit solution (No stiffness matrix).• Solves for relative joint DOF velocities.• Can include spring/dampers.• Output file in Solution Information contains diagnostics.• Used by the configure tool to perform kinematic analysis.

Configure tool being used to check kinematics of mechanism




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Rigid Solver

• Explicit Time Integration efficient for rigid analyses:– Fourth order Runge Kutta is robust.– Energy-based automatic time stepping.

• Automatic time stepping is effective in preventing spurious high frequencies needlessly shortening the time step.

• Rigid Solver Relative DOF advantages:– A minimum number of DOF used, just two or three per joint.– Few constraint violations possible.– Clean numerical results, no spurious high frequency

response.




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C. Relative DOF – Minimum Number of DOF

1 relative dof / revolute joint

6 absolute dof / rigid body

5 constraint equations per revolute joint

Absolute: 12 dofs + 10 constraints (22 dofs including Lagrange Multiplier) Relative: 2 dofs

• Use of relative DOF velocity results in smaller model size




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Relative DOF – Few Constraint Violations Possible

1 relative dof / revolute joint

6 absolute dof / rigid body

5 constraint equations per revolute joint

Absolute: 12 dofs + 10 constraints (22 dofs including Lagrange Multiplier) Relative: 2 dofs

• Use of relative DOF velocity avoids the need for the constraint equations to enforce the joint kinematics with absolute DOF at left.




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• Shock and non-smooth loading in a flexible dynamics analysis excite all frequencies of the flexible bodies.

• Artificial high frequency response can slow down convergence, severely shorten the automatic time stepping and produce unrealistically high forces.

• Sources of shock loading are start-up and sudden contact.• The relative DOF are not a function of the stiffness of the rigid

parts, so no high frequency response is produced.

Relative DOF – Clean Numerical Results




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Relative DOF – Mass Matrix is Coupled

• Mass Matrix and Force vector are formed traversing the open loop model.

• Constraint Equations are added to close the loops.

• Constraint Redundancies handled at each time step.

Lagrange multiplier

y is Joint velocity

G

FyB

BM t

.

0




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Relative DOF – Boundary Conditions

• Imposition of an initial velocity of a body or model must be accomplished by a short time step.

• Loads are limited to Acceleration, Gravity and Joint Conditions.• A General joint between a body and ground with all dof free can be

used to specify initial conditions on a body as a joint condition of the General joint.




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D. Rigid Interface in Simulation

• User sees a 3d image of the rigid bodies and their original and displaced positions, not the abstraction.

Body Views used to help visualize parts when creating joints




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E. Flexible Solver

• The full transient ANSYS solver with HHT time integration

(HHT allows a large numerical damping without loss of accuracy).

• Implicit solution requires K, C and M reformulation each time step.– (Slow, but allows support for nonlinear contact, material and joint properties

in addition to flexible bodies)

• Uses displacement Degrees Of Freedom.

• Matrix form of Equation of Motion solved by Flexible Solver:

tFuKuCuM




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F. Body Representation

Bodies will be rigid in a Rigid analysis, rigid or flexible in a Flexible analysis




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G. Bodies in a Rigid Analysis

• Uses only rigid bodies and spring/dampers.• Bodies are implicitly rigid, but should be so specified.• Bodies only interact at joints, so their surface

interference is ignored.• At least one body must be connected to ground.– Configure tool will not be available until a body is connected to

ground.




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H. Bodies in a Flexible Analysis

• Use ANSYS elements.• Can be rigid or flexible.• Bodies are connected by joints but may also interact at their

surfaces.• Flexible bodies may contain material nonlinearities.




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Bodies in a Flexible Analysis

• A rigid body is modeled by a MASS21 element at the center of gravity. MPC based contact elements connect the MASS21 to pilot nodes at the joint locations.

Mass Element Pilot Node

Pilot nodes connect at revolute joint element (MPC184)

Pilot Node

MPC contact

Contact elements can be applied to the surface




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Bodies in a Flexible Analysis

• A flexible body is normally represented by the isoparametric 3D elements with which it is meshed.




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I. Joints - Definition

• A joint serves as a junction where bodies are joined together or to ground at a single point.

• Joint types are characterized by their rotational and translational degrees of freedom as being fixed or free.

• A joint consists of:– 2 nodes, or 1 node when connected to ground.– A reference and mobile coordinate system.– A restricted set of relative displacements.

• The kinematic constraints in the joint elements are imposed using the Lagrange multiplier method.

Universal Joint as depicted in the ANSYS Multibody Analysis Guide




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Joint Abstraction

• Joints are point to point connections between two bodies, however the user interface shows the actual geometry.

• Apparent geometry interference or overlap between parts may be seen during an animation.

These faces are used to define the joint coordinate systems, but they interact only at the node to node joint at their centers.




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Joints – Over-constraint

• An over-constrained model may solve successfully initially, then lock-up or not converge.

• A well-defined mechanism usually has one rigid body dof as below.

Revolute to Ground

Pendulum

Cylindrical

Revolute

Revolute to Ground

Revolute to Ground

3-Bar Mechanism

Rigid Body to Body

Slot to Ground

Slot to Ground

Double Slot




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• Is the planar mechanism below over-constrained?

ROTZ Revolute to Ground

ROTZ Revolute

UX Slot to Ground

Rigid LinkRigid Link X

Y

X

Y




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• Answer: Yes it is. The out of plane UZ dof is redundantly constrained. The body to body joint can be a cylindrical joint, which does not constrain relative UZ.

ROTZ Revolute to Ground

ROTZ Cylindrical

UX Slot to Ground

Rigid LinkRigid Link X

Y




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• User evaluation of complicated mechanisms is generally difficult or not possible.

• Use the Worksheet tab for Connections to get kinematic diagnostics.

This revolute joint removed

a dof




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• The Worksheet tab for Connections shows a summary of the joints and that the mechanism has 0 free dof (should have 1 free dof.)

Highlight Connections branch then pick the Worksheet tab




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Joints – Under-constraint

• A mechanism is under-constrained if it has an unintended rigid body degree of freedom. A modal analysis can show the source of the under-constraint in flexible bodies.

Cylindrical Joints are not preventing relative UZ motion of “Rod 1”




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J. Initial Conditions

• In a Rigid analysis, the initial relative velocity of the connected bodies is zero unless otherwise specified.

• A non-zero initial velocity is specified with a joint condition which can then be deactivated after a short time.

• In a Flexible analysis the initial velocity of the bodies is assumed to be zero, but a constant non-zero initial velocity can be specified.

• The initial velocity is uniform over the entire model or selected body(s).

Can apply to the whole model or a set of bodies




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• Example: Flexible analysis specification of a non-zero initial velocity applied to the lower body of a double pendulum.

Initial Conditions

Displacement after 0.25 sec.




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K. Joint Conditions

• Joint Conditions or loads are applied to the unconstrained relative DOF of the joint.

• For example, a revolute joint can be configured using relative rotation, rotational velocity, rotational acceleration or moment versus time (see below).




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L. Solution Results

• Typical Rigid analysis results: – Animation of model motion.– Max and min displacement, velocity and acceleration.– Force, moment, and relative motion at joints.




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• Typical Flexible Analysis– Animation of model motion.– Max and min displacement, velocity and acceleration.– Force, moment, and relative motion at joints.– Result contour displays on flexible bodies.

Solution Results




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M. Summary

• Use Rigid analysis for rapid kinematic evaluation of mechanisms.• Use Flexible analysis to include flexible bodies, contact between

surfaces, nonlinearities and more boundary conditions.• Use Simulation to automate all aspects of the analysis and provide

a 3D visualization of the model and motion.

introduction to ansys rigid and flexible dynamic analysis

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