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:
Figure 1.
F=−k∗x

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:
Figure 2.


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.
Ep End point for positive deformation. This is usually the maximum positive deformation in the static test. At EP, the slope of the static curve, EPS, is selected.
Rp Reference point for positive deformation. As a default, RP = (O + EP)/2. At RP, the force of the static curve, RPF, is selected.
EN End point for negative deformation. This is usually the maximum negative deformation in the static test. At EN, the slope of the static curve, ENS, is selected.
RN Reference point for negative deformation. As a default, RN = (O + EN)/2. At RN, the force of the static curve, RNF, 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.