Reports for 6-DOF Bodies

Simcenter STAR-CCM+ provides specific reports for 6-DOF bodies. These reports allow you to visualize key quantities such as the acceleration and velocity of a body in a given direction, the length of spring and catenary couplings, and the orientation of a body.

Component of a Quantity along a Specified Direction

The following reports calculate the component of the respective quantity along a specified direction:

6-DOF Body Acceleration
6-DOF Body Angular Acceleration
6-DOF Body Angular Momentum
6-DOF Body Angular Velocity
6-DOF Body Translation
6-DOF Body Velocity
6-DOF Body Force
6-DOF Body Moment

In general, the component of a vector

q

along the direction defined by a unit vector

d

is given by:

Figure 1. EQUATION_DISPLAY

q_{d} = q \cdot d

(4966)

For example, the 6-DOF Body Velocity report calculates the component of velocity along the direction

d

as:

Figure 2. EQUATION_DISPLAY

v_{d} = v \cdot d

(4967)

where

v

is the total velocity of the body. Similarly, the 6-DOF Body Force report calculates the component of the resultant force along

d

as:

Figure 3. EQUATION_DISPLAY

f_{d} = f \cdot d

(4968)

where $f$ is the resultant force acting on the body (see Eqn. (4879)).

6-DOF Body Orientation

Calculates the rotation angle around a specified axis, with respect to the initial body orientation.

The body orientation follows the Euler angle convention, which is interpreted in the following manner. Consider Rotation X-Y-Z Axis as an example. For this convention, three rotations describe the orientation of the body. The first rotation is around the X axis of the laboratory coordinate system (giving the first Euler angle). The second rotation is around the Y axis of the laboratory system (giving the second Euler angle). The third is a rotation around the Z axis of the laboratory system (giving the third Euler angle). The Euler angles are given with respect to fixed rotation axes.

It is also possible to interpret the above Euler angles with respect to moving rotation axes that result from previous rotations. For this purpose, read the axes from back to front. For example, Rotation X-Y-Z Axis means that the first rotation is about the Z axis of the laboratory system. The second is around the Y axis of the new coordinate system created by rotating the laboratory system around the Z axis. The third rotation is about the X axis of another new coordinate system created by rotating the previous system around its Y axis.

When the second Euler angle reaches $\frac{π}{2}$ or $- \frac{π}{2}$ , a gimbal lock occurs. In a gimbal lock, only the sum of the first and the third Euler angles is determined. The reported Euler angles describe the orientation of the body correctly even in a gimbal lock. However, plots of Euler angles over time can show discontinuities. Therefore, try to avoid gimbal locks by choosing an Euler Angle Convention in which the Euler angle reaching a magnitude of $\frac{π}{2}$ is the first or the third angle.

6-DOF Body Rotational Energy

Calculates the rotational energy of a body as:

Figure 4. EQUATION_DISPLAY

K_{r o t} = \frac{1}{2} I ω \cdot ω

(4969)

where $I$ is the moment of inertia tensor of the body, and $ω$ is the angular velocity.

6-DOF Body Spring Elongation

Calculates the elongation of a linear spring that is held between a 6-DOF body and the environment, or between two 6-DOF bodies, as defined in a linear spring coupling (see Linear Spring Coupling). The total length is:

Figure 5. EQUATION_DISPLAY

r = | x_{2} - x_{1} |

(4970)

where $x_{1}$ and $x_{2}$ are the end points where the spring is attached. The elongation with respect to the relaxation length $l_{e q}$ is:

Figure 6. EQUATION_DISPLAY

r = | x_{2} - x_{1} | - l_{e q}

(4971)

6-DOF Body Total Distance

Calculates the total distance between two points as:

Figure 7. EQUATION_DISPLAY

r = | x_{2} - x_{1} |

(4972)

where $x_{1}$ and $x_{2}$ are the position vectors of the two points.

6-DOF Catenary Length

Calculates the length of a catenary that is held between a 6-DOF body and the environment, or between two 6-DOF bodies, as defined in a catenary coupling (see Catenary Coupling). The total length is:

Figure 8. EQUATION_DISPLAY

L = \int_{x_{1}}^{x_{2}} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x

(4973)

where $y$ is the catenary curve (see Eqn. (4952)) and $x_{1}$ and $x_{2}$ are the end points where the catenary is attached. The length of the catenary with respect to the relaxation length $l_{e q}$ is:

Figure 9. EQUATION_DISPLAY

r = L - l_{e q}

(4974)

6-DOF Component Distance

Calculates the distance between two points along a specified direction:

Figure 10. EQUATION_DISPLAY

r = (x_{2} - x_{1}) \cdot d

(4975)

where $x_{1}$ and $x_{2}$ are the position vectors of the two points and $d$ is the direction vector.