# 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"
/>

## 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.
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"
/>

1. 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.
2. 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.
3. 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.
4. 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.
5. i_marker_id is designated as the point of application of the Force_Field. j_marker_id is the point of reaction.
6. 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.

7. 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.
8. 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.
9. 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.
10. Force_Bushing can act on all bodies: Body_Rigid, Body_Flexible, and Body_Point.
11. 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.