Kinematic Joint TYPE33 (/PROP/KJOINT)
Kinematic joints are declared by /PROP/KJOINT. Joints are defined by a spring and two local coordinate axes, which belong to connected bodies.
Assume that the connected bodies are rigid to ensure the orthogonality of their local axis. However, deformable bodies may also be connected with a joint. If the axis becomes non-orthogonal during deformation, the stability of the joint cannot be ensured.
There are several kinds of kinematic joints available in Radioss, which are listed in Kinematic Joint Types.
Kinematic Joint Types
Type No. | Joint Type | dx | dy | dz | $\theta $ x | $\theta $ y | $\theta $ z |
---|---|---|---|---|---|---|---|
1 | Spherical | √ | √ | √ | 0 | 0 | 0 |
2 | Revolute | √ | √ | √ | 0 | √ | √ |
3 | Cylindrical | 0 | √ | √ | 0 | √ | √ |
4 | Planar | √ | 0 | 0 | 0 | √ | √ |
5 | Universal | √ | √ | √ | √ | 0 | 0 |
6 | Translational | 0 | √ | √ | √ | √ | √ |
7 | Oldham | √ | 0 | 0 | √ | √ | √ |
8 | Rigid | √ | √ | √ | √ | √ | √ |
9 | Free | 0 | 0 | 0 | 0 | 0 | 0 |
√: denotes a blocked degree of freedom
0: denotes a free (user-defined) degrees of freedom
Joint properties are defined in a local frame computed with respect to two connected coordinate systems. They do not need to be initially coincident. If the initial position of the local coordinate axis coincides at any time, the joint local frames are defined at a mean position. Then the joint local frame will be computed with respect to these rotated axes.
In each type of joint you distinguish the blocked degrees of freedom and the free degrees of freedom. The blocked degrees of freedom are characterized by a constant stiffness. Selecting a high value with respect to the free degrees of freedom stiffness is recommended. The free degrees of freedom have user-defined characteristics, which can be linear or nonlinear elastic, combined with a sub-critical viscous damping.
The translational and rotational degrees of freedom are defined as:
Where, $d{x}_{1}$ and $d{x}_{2}$ are total displacement of two joint nodes in the local coordinate system.
Forces and Moments Calculation
- Linear spring: $F={K}_{t}\delta +{C}_{t}\dot{\delta}$
- ${K}_{t}$ : Translational stiffness (K_{tx}, K_{ty}, and K_{tz})
- ${C}_{t}$ : Translational viscosity (C_{tx}, C_{ty}, and C_{tz})
- Nonlinear spring: $F={K}_{t}\mathrm{f}\left(\delta \right)+{C}_{t}\mathrm{g}\left(\dot{\delta}\right)$
- Linear spring: $M={K}_{r}\theta +{C}_{r}\dot{\theta}$
- ${K}_{r}$ : Rotational stiffness (K_{rx}, K_{ry}, and K_{rz})
- ${C}_{r}$ : Rotational viscosity (C_{rx}, C_{ry}, and C_{rz})
- Nonlinear spring: $M={K}_{r}\mathrm{f}\left(\theta \right)+{C}_{r}\mathrm{g}\left(\dot{\theta}\right)$
The joint length may be equal to 0. It is recommended to use a zero length spring to define a spherical joint or a universal joint. To satisfy the global balance of moments in a general case, correction terms in the rotational degrees of freedom are calculated as:
Joints do not have user-defined mass or inertia, so the nodal time step is always used.