# Force: Bushing

Model ElementForce_Bushing defines a linear force and torque acting between
two Reference_Markers, `I` and
`J`.

## Format

```
<Force_Bushing
id = "integer"
[label = "string"]
i_marker_id = "integer"
j_marker_id = "integer"
kx = "real" ky = "real" kz = "real"
ktx = "real" kty = "real" ktz = "real"
cx = "real" cy = "real" cz = "real"
ctx = "real" cty = "real" ctz = "real"
preload_x = "real" preload_y = "real" preload_z = "real"
preload_tx = "real" preload_ty = "real" preload_tz = "real"
/>
```

## Attributes

`id`- Element identification number (integer>0). This number is unique among all Force_Bushing elements and uniquely identifies the element.
`label`- The name of the Force_Bushing element.
`i_marker_id`- Specifies the Reference_Marker at which the force is applied. This is designated as the point of application of the force.
`j_marker_id`- Specifies the Reference_Marker at which the reaction force and moment are applied. This is designated as the point of reaction of the force.
`kx``ky``kz``ktx``kty``ktz`- These define the diagonal entries for a 6x6 stiffness matrix that is used to calculate the spring force for Field_Bushing. All stiffness values must be non-negative.
`cx``cy``cz``ctx``cty``ctz`- These define the diagonal entries for a 6x6 damping matrix that is used to calculate the damping force for Field_Bushing. All damping values must be non-negative.
`preload_x``preload_y``preload_z``preload_tx``preload_ty``preload_tz`- These define the pre-loads in the Force_Bushing element. In other words, the forces at I when there is deformation. The force and torque components are measured in the J coordinate system. The data is optional. Their default values are 0.

## Example

The example demonstrates the definition of a bushing element commonly used in automotive suspensions such as bump stops for shocks and struts. The image below is an illustration of such a bushing.

The Force_Bushing definition for such a bushing could be:

```
<Force_Bushing
id = "26"
i_marker_id = "61"
j_marker_id = "71"
kx = "6000." ky = "6000." kz = "10000."
ktx = "1.0E5" kty = "1.0E5" ktz = "1.0 E5"
cx = "60." cy = "60." cz = "60."
ctx = "100" cty = "100" ctz = "100"
preload_x = "33" preload_y = "44" preload_z = "55"
preload_tx = "0." preload_ty = "0." preload_tz = "0."
/>
```

## Comments

- The force and torque consist of three major effects:
a spring force, a damping force, and a pre-load vector.
- The spring force is defined by the product of the stiffness matrix
and the relative displacement between the
`I`and`J`Reference_Markers. - The damping force is defined by the product of the damping matrix
and the relative velocity between the
`I`and`J`Reference_Markers. - A preload vector can also be added to the spring and damping
forces. The six components (three forces and three moments) are
defined in the coordinate system of the
`J`Reference_Marker.

- The spring force is defined by the product of the stiffness matrix
and the relative displacement between the
- Force_Bushing elements are used as compliant connectors in mechanical systems. They are typically used to reduce vibration and noise, absorb shock, and accommodate misalignments.
`kx`,`ky`and`kz`have units of force per unit length.`cx`,`cy`and`cz`have units of force per unit length per unit time.`ktx`,`kty`,`ktz`have units of torque units per radian.`ctx`,`cty`,`ctz`have units of torque units per radian per unit time. The actual units are governed by what are defined for the entire model.- Two of the three angular deflections, rotation about X, rotation about Y and rotation about Z, must remain small at all times. The rotation angles lose physical significance otherwise. Small means < 10 degrees.
`i_marker_id`is designated as the point of application of the Force_Field.`j_marker_id`is the point of reaction.- The forces acting at the
`I`and`J`markers are equal and opposite. Since there usually is a separation between`J`and`I`and the force does not act along the separation vector, the torque acting on the`I`marker is not the same as the torque acting on the`J`marker. This is shown in Figure 2 below. - The sign convention for the forces and torques is as
follows:
- A positive force tends to repel the
`I`and`J`Reference_Markers. A negative force tends to attract the`I`and`J`Reference_Markers. - A positive torque tends to rotate the
`I`Reference_Marker in a counterclockwise direction, relative to the`J`Reference_Marker. Thus, a positive value of TX tends to increase the value of included angle between the x-axes of Markers I and J.

- A positive force tends to repel the
- Force_Bushing is a linear element. If you wish to define a nonlinear force element, then use either the Force_Field or the Force_Vector_TwoBody modeling element.
- Force_Bushing does not model cross-coupling effects. Its stiffness and damping matrices are diagonal. If cross-coupling effects are important, use Force_Field or Force_Vector_TwoBody.
- Force_Bushing can act on all bodies: Body_Rigid, Body_Flexible, and Body_Point.
- The MotionSolve bushing implementation is slightly different from the one in Adams. In most cases, they yield the same results; however if the bushing undergoes 3-D deformation, the results can be somewhat different. Both products approximate large angles, but slight differently. Hence the results will be different.