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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 \(m/s\).

rotating motion boundary condition in simscale
Figure 1: Example of the set up of a rotating motion boundary condition.

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:

rotating and translation motion of a cube
Animation 1: Rotation of the unit cube around the z-axis with additional translation of the base point.

Last updated: June 17th, 2020

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