# Spring Joint TYPE45 (/PROP/KJOINT2)

In Radioss, property TYPE45 is the joint type spring.

## DOF of KJOINT2

The DOF (degrees of freedom) of KJOINT2 are defined with option “Type.” Different types of joint made by different DOF combinations. The following types are available in Radioss:

Table 1. DOF Only Free in Rotation
Type No. Joint Type dx dy dz $\theta$ x $\theta$ y $\theta$ z
1 Spherical 0 0 0
5 Universal (development source only) 0 0
2 Revolute 0

√: denotes a fixed degree of freedom

0: denotes a free (user-defined) degree of freedom

Table 2. DOF Only Free in Translation
Type No. Joint Type dx dy dz $\theta$ x $\theta$ y $\theta$ z
6 Translational 0
7 Oldham 0 0

√: denotes a fixed degree of freedom

0: denotes a free (user-defined) degree of freedom

Table 3. DOF Free in Translation and Rotation
Type No. Joint Type dx dy dz $\theta$ x $\theta$ y $\theta$ z
3 Cylindrical 0 0
4 Planar 0 0 0

√: denotes a fixed degree of freedom

0: denotes a free (user-defined) degree of freedom

Table 4. Specific DOF
Type No. Joint Type dx dy dz $\theta$ x $\theta$ y $\theta$ z
8 Rigid
9 Free 0 0 0 0 0 0

√: denotes a fixed degree of freedom

0: denotes a free (user-defined) degree of freedom
 Figure 1. Spherical Figure 2. Universal Figure 3. Revolute
 Figure 4. Translational Figure 5. Cylindrical Figure 6. Planar

The coordinate for DOF is the one used for spring force computation. It is not necessarily the spring local coordinate system. Depending on the different types of KJOINT2 and the definition of skew, different coordinate systems are used for spring force computations.

## Stiffness and Damping in KJOINT2

There are four types of stiffness used in the KJOINT2 property.
1. Blocked stiffness ${K}_{n}$ . For example, for blocked stiffness = Yes:
• If Type = 1 (Spherical), then ${K}_{n}$ are blocked stiffnesses in translational directions ${d}_{x},{d}_{y},{d}_{z}$ .
• If Type = 6 (Translational), then ${K}_{n}$ are blocked stiffnesses in translational directions ${d}_{y},{d}_{z}$ and in rotational directions ${\theta }_{X},{\theta }_{Y},{\theta }_{Z}$ .
Table 7.
Type No. Joint Type dx dy dz $\theta$ x $\theta$ y $\theta$ z
1 Spherical 0 0 0
6 Translational 0

If ${K}_{n}$ = 0 (default), Radioss computes blocked stiffness internally. If ${K}_{n}$ > 0, user-defined blocked stiffness is used.

2. Translational stiffness ${K}_{ti}$ and rotational stiffness ${K}_{ri}$ . These stiffnesses are used in free DOF direction and used for force and moment computation:
Table 8.
Linear Spring Nonlinear Spring
$F={K}_{ti}\delta$

$M={K}_{ri}\theta$

${K}_{ti}$ : translational stiffness $\left({K}_{tx},{K}_{ty},{K}_{tz}\right)$

${K}_{ri}$ : rotational stiffness $\left({K}_{rx},{K}_{ry},{K}_{rz}\right)$

$F={K}_{ti}\mathrm{f}\left(\delta \right)$

$M={K}_{ri}\mathrm{f}\left(\theta \right)$

${K}_{ti}$ : translational stiffness factor $\left({K}_{tx},{K}_{ty},{K}_{tz}\right)$

${K}_{ri}$ : rotational stiffness factor $\left({K}_{rx},{K}_{ry},{K}_{rz}\right)$

$\mathrm{f}\left(\delta \right)$ is translational stiffness function fct_ ${K}_{ti}$

$\mathrm{f}\left(\theta \right)$ is rotational stiffness function fct_ ${K}_{ti}$

3. Translational viscosity coefficient ${C}_{ti}$ and rotational viscosity coefficient ${C}_{ri}$ are for damping. These viscosity coefficients are used in free DOF direction and used for force and moment computation.
Table 9.
Linear Spring Nonlinear Spring
$F={C}_{ti}\stackrel{˙}{\delta }$

$M={C}_{ri}\stackrel{˙}{\theta }$

${C}_{ti}$ : translational stiffness $\left({C}_{tx},{C}_{ty},{C}_{tz}\right)$

${C}_{ri}$ : rotational stiffness $\left({C}_{rx},{C}_{ry},{C}_{rz}\right)$

$F={C}_{ti}\mathrm{g}\left(\stackrel{˙}{\delta }\right)$

$M={C}_{ri}\mathrm{g}\left(\stackrel{˙}{\theta }\right)$

${C}_{ti}$ : translational stiffness factor $\left({C}_{tx},{C}_{ty},{C}_{tz}\right)$

${C}_{ri}$ : rotational stiffness factor $\left({C}_{rx},{C}_{ry},{C}_{rz}\right)$

$\mathrm{g}\left(\stackrel{˙}{\delta }\right)$ is translational stiffness function fct_ ${C}_{ti}$

$\mathrm{g}\left(\stackrel{˙}{\theta }\right)$ is rotational stiffness function fct_ ${C}_{ri}$

For example, tensile spring (which used KJOINT2) with constant velocity = 1.33:
• If only translational stiffness is set to ${K}_{t}=100$ , then force (green curve in figure below) increases with ${K}_{t}$ .
• If only translational viscosity is set to ${C}_{t}=50$ , then force (orange curve in figure below) is constant since tensile velocity is constant. The force is $Force={C}_{t}\stackrel{˙}{\delta }=50×1.33=66.5$ .
• If both translational stiffness ${K}_{t}=100$ and translational viscosity ${C}_{t}=50$ are set, then force (blue curve in figure below) is the combination of the above two cases with $Force={K}_{t}\delta +{C}_{t}\stackrel{˙}{\delta }$ .
4. Frictional stiffness in translational direction ${K}_{fxi}$ and in rotational direction ${K}_{fri}$ . These are used to compute penalty force to prevent displacement exceeding the limit $S{D}_{i+},S{D}_{i-}$ or rotation exceeding the limit $S{A}_{i+},S{A}_{i-}$ .

If ${K}_{fxi},{K}_{fri}$ are not set, Radioss will compute it automatically with very high stiffness.

For example, in the following tensile test, setting $S{D}_{i+}=100$ , then:
• If ${K}_{fxi}$ are not set (figure below on the left), then very high stiffness is used after reaching limit $S{D}_{i+}=100$ .
• If ${K}_{fxi}=1000$ is set (figure below on the right), then ${K}_{fxi}=1000$ is used after reaching limit $S{D}_{i+}=100$ .
The above tests also show translational stiffness ${K}_{ti}$ . This only affects force before reaching the limit $S{D}_{i+}$ . The value of ${K}_{fxi}$ should not be set too small. This value is used to simulate blocking behavior after reaching the limit. Too small a value for ${K}_{fxi}$ leads to the following error message:
WARNING ID :          979
** WARNING IN FRICTION DEFINITION FOR KJOINT2
DESCRIPTION :
ELASTIC STIFFNESS 0.1000000000000 IS SMALLER THAN THE MAX DERIVATIVE 720.0000000000 OF THE
FRICTION FUNCTION 0

• If ${K}_{ti}$ is not set but ${K}_{fxi}=1000$ . The figure below on the left shows how constant friction force $F{F}_{i}=15000$ affects the spring force. With $F{F}_{i}=15000$ , force increases with ${K}_{fxi}$ to 15,000 and then remains constant until reaching the limit $S{D}_{i+}$ . After reaching $S{D}_{i+}$ , force increases with stiffness ${K}_{fxi}$ again.
• If, as in the previous case, an additionally set translation stiffness ${K}_{ti}=100$ (figure below on the right), then force increases with ${K}_{fxi}$ to $F{F}_{i}+{K}_{ti}{\delta }_{i}=15000+100×15=16500$ and then increases with translation stiffness ${K}_{ti}=100$ until reaching the limit $S{D}_{i+}$ . After reaching $S{D}_{i+}$ , force increases with stiffness ${K}_{fxi}$ again.

${K}_{fxi},{K}_{fri}$ must be defined if it is required to consider friction behavior after reaching the stop limit. Otherwise, even if friction (constant friction $F{F}_{i},F{M}_{i}$ or friction curve $fct_F{F}_{i},fct_F{M}_{i}$ ) has been defined, Radioss will still take the internally computed (very high) stiffness to treat the force (or moment) behavior after reaching the limit.