# Static Stiffness Models

## Constant Stiffness Model

The bushing stiffness properties are approximated by a single coefficient–the
stiffness at the operating point. The force generated by the bushing
is:

Where,

k is the stiffness.

x is the deflection.

## Cubic Stiffness Model

The bushing stiffness is approximated by two cubic polynomials that are derived from
the Static Force versus Deflection curve. Below, the measured static data is shown
as a blue curve:

The five points in the selected area of the plot above are:

Point | Description | Location on Plot |
---|---|---|

O | Operating point. | The force value, OF, and the slope of the static curve, OS, are selected. |

E_{p} |
End point for positive deformation. | This is usually the maximum positive deformation in the
static test. At E_{P}, the slope of the static curve,
E_{P}S, is selected. |

R_{p} |
Reference point for positive deformation. | As a default, R_{P} = (O + E_{P})/2. At
R_{P}, the force of the static curve,
R_{P}F, is selected. |

E_{N} |
End point for negative deformation. | This is usually the maximum negative deformation in the
static test. At E_{N}, the slope of the static curve,
E_{N}S, is selected. |

R_{N} |
Reference point for negative deformation. | As a default, R_{N} = (O + E_{N})/2. At
R_{N}, the force of the static curve,
R_{N}F, is selected. |

## Spline Stiffness Model

Spline data is derived by reducing the static data to a curve. A cubic spline is fitted through the measured static data. The spline is then used as the interpolating function for calculating the force at any deflection.