# Multibody Dynamics Module

### Analyze Rigid- and Flexible-Body Assemblies with the Multibody Dynamics Module

Analysis of the swashplate mechanism to control orientation of helicopter rotor blades. Transient simulation with both rigid and flexible blade designs provides insight into useful performance metrics such as blade deformation and lift force.

#### Tools for Designing and Optimizing Multibody Systems

The Multibody Dynamics Module is an expansion of the Structural Mechanics Module that provides an advanced set of tools for designing and optimizing multibody structural mechanics systems using finite element analysis (FEA). The module enables you to simulate mixed systems of flexible and rigid bodies, where each body may be subjected to large rotational or translational displacements. Such analyses help identify critical points in your multibody systems, thus enabling you to perform more detailed component-level structural analyses. The Multibody Dynamics Module also gives you the freedom to analyze forces experienced by segments of the structure, and stresses generated in flexible components that may lead to failure due to large deformation or fatigue.

#### Utilize a Library of Joints

A library of predefined joints is included in the module so that you can easily and robustly specify the relationships between different components of a multibody system, where the components are interconnected such that only a certain type of motion is allowed between them. Joints connect two components through attachments, where one component moves independently in space while the other is constrained to follow a particular motion, depending on the joint type. The joint types in the Multibody Dynamics Module are generic to the extent that they can model any type of connection. Researchers and engineers can thereby design accurate multibody structural mechanics models, using the following joint types:

• Prismatic (3D, 2D)
• Hinge (3D, 2D)
• Cylindrical (3D)
• Screw (3D)
• Planar (3D)
• Ball (3D)
• Slot (3D)
• Reduced Slot (3D, 2D)
• Fixed Joint (2D,3D)
• Distance Joint (2D,3D)
• Universal Joint (3D)

Orientation of movement for the prismatic, hinge, cylindrical, and screw joints.
Orientation of movement for the planar, ball, slot, and reduced slot joints.
The stresses in the gearbox housing and the sound pressure level in the surrounding air (top and bottom-right) of a 5-speed synchromesh gearbox inside a manual transmission vehicle. The frequency spectrum of the normal acceleration at one of the points on the gearbox is also shown (bottom-left).
A swashplate mechanism is used to control the orientation of helicopter rotor blades. This example shows an application derived from the model where only the pitch of the blades can be changed, but where both transient and eigenfrequency analyses can be presented.
Model of a three-cylinder reciprocating engine, having both rigid and flexible parts, is used for maximizing the engine power and the design of structural components.
Plot of stresses in an induction motor's housing (top) and the magnetic flux density in the rotor (bottom-left). The rotor orbit at two bearing locations is also shown (bottom-right).

#### Complete Flexibility in Analyzing Multibodies

Components of a system that undergo deformations can be modeled as flexible, while other components, or even parts of these components, can be specified as rigid. You can also provide your multibody dynamics design and analyses with nonlinear material properties by combining models in the Multibody Dynamics Module with either the Nonlinear Structural Materials Module or the Geomechanics Module. At the same time, the rest of the physics that you can model with COMSOL Multiphysics and the suite of application-specific modules, can be coupled to the physics described by the Multibody Dynamics Module, such as the effects of heat transfer or electrical phenomena.

Transient, frequency-domain, eigenfrequency, and stationary multibody dynamics analyses can be performed. Joints can be assigned linear/torsional springs with damping properties, applied forces and moments, and prescribed motion as a function of time. Analysis and postprocessing capabilities include:

• Relative displacement/rotation between two components and their velocities
• Reaction forces and moments at a joint
• Local and global coordinate system frames of reference
• Stresses and deformations in flexible bodies
• Fatigue analysis of critical flexible bodies by combining with the Fatigue Module

Often, motion between two components is restricted due to the presence or functions of other physical objects. Limiting and conditionally locking the relative motion can be specified for the joints in order to fully define and model these complex systems. In robotics, for example, the relative motion between two arms can be defined as a pre-defined function of time. Joints can also be spring-loaded and appropriate damping factors can be included in the Multibody Dynamics Module.

# Multibody Dynamics Module

### Product Features

• Joints can be constrained to restrict the relative motion between the two connected components
• Joints can be locked to freeze the relative motion between the two connected components at the specified value
• Spring conditions can be applied on the relative motion at a joint, either at the equilibrium or with pre-deformation
• Lumped mechanical systems can be built, and can consist of masses, dampers, springs, and more
• Damping or dashpot conditions can be defined to specify losses on the relative motion at a joint
• Joints can be required to prescribe the relative motion between the connected components
• Frictional loss to a joint can be added for the joint types: Prismatic, Hinge, Cylindrical, Screw, Planar, and Ball.
• Cam-Follower condition
• Forces and moments can be applied to all types of joints at the attachments to the components
• Mechanisms can be initialized to translate and rotate rigidly with the given velocities about the specified center of rotation
• Part Library with parametric geometry parts for internal gears, external gears, and racks

### Application Areas

• Aerospace
• Automotive
• Engine dynamics
• Mechatronics
• Robotics
• Biomechanics
• Biomedical instruments
• Vehicle dynamics
• General dynamic simulations of mechanical assemblies

#### Vibrations in a Compound Gear Train

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