Required field
Required field
Required field
Required field

# Rotating Motion

The rotating motion boundary condition is used to define a rigid body rotation of the assigned entities. The user can define the rotation axis, the base point, and the rotation angle. Each component can be defined with a formula or table input.

This boundary condition is only available for static, dynamic, and thermomechanical analysis types. Find below its formulation and the required inputs.

If $$\mathbf{R}_{\theta}^{a}$$ denotes the rotation matrix of a general rotation about the axis $$a$$ with an angle of $$\theta$$, then the displacement $$\vec u$$ of a point $$\vec X$$ is calculated as:

$$\vec{u} = \mathbf{R}_{\theta}^{a} \cdot (\vec{X}- \vec{P}_0) + \vec{P} -\vec{X}$$

where $$\vec P$$  denotes the axis base point and $$\vec {P}_0$$ is the position at time $$t = 0$$.

## Base Point

This point is the base point for the rotation axis. A possible movement of the base point regarding the initial position at time $$t = 0$$ during the rotation process is taken into account.

## Rotation Axis

The rotation axis is defined by its three components in the global coordinate system. The right-hand rule applies, to determine the direction of the rotation.

Important

If a component of the rotation axis is input via formula or table, then the user has to make sure that the length of the axis vector is always positive.

## Rotation Angle

The rotation angle is defined in a mathematical positive sense around the rotation axis. The input can be in $$rad$$ or degrees.

Important

If a continuous, transient rotation is required, then the rotation angle has to be given either as a formula or table value.

## Example

In the example below, a unit cube is rotated around the z-axis. The base point is moving in positive z-direction at 1 $$m/s$$.

The bottom face was assigned and the corresponding settings were:

• Base Point: $$(0, 0, t)$$. This causes the cube to translate in the positive z-direction, at 1 $$m/s$$;
• Rotation axis: $$(0, 0, 1)$$;
• Rotation angle: $$2.\pi.t$$, representing a continuous rotating velocity of 60 rotations per minute around the z-axis.

The video below shows the result of a simulation with the described boundary condition:

Last updated: May 26th, 2021