# Preload, Offset, and Scale

This section describes how preloads, offsets and scales enter into bushing force computations. You use Preloads, Offsets and Scales to alter the operating point of a bushing. You can offset the bushing displacement in any direction, and scale the input displacement and velocity. You can also offset the bushing force in any direction by adding a preload or scale-output force or moment in any direction.

## Displacement Offsets ans Scales

Displacement offsets change the origins of the force-deflection curves. Displacement scales expand or contract the force-deflection curves along the deflection axis.

Let:

- ${d}_{k}$
- be the displacement in the k
^{th}displacement direction (*x, y, z, ax, ay, az*) between the bushing I- and J-Markers reported in the coordinate system of the J marker. - ${H}_{k}$
- is the displacement (horizontal) scaling factor in the k
^{th}direction. - ${Q}_{k}$
- is the displacement offset in the k
^{th}direction.

Then the scaled and offset deflection, ${q}_{k}$ , is given by:

The velocity in the k^{th} direction, is given by:

## Preload and Force Scales

Preloads offset the forces or torques at zero displacement, while the force scale
applies an amplification factor to the force. If
${G}_{k}$
is the function computing the force in the
k^{th} direction, then the force in that direction is given as
follows:

Let:

- ${P}_{k}$
- is the preload in the k
^{th}direction. - ${V}_{k}$
- is the force (vertical) scaling in the k
^{th}direction. - ${G}_{k}$
- is the sum of all force methods in the k
^{th}direction. - ${F}_{k}$
- is the preload in the k
^{th}direction.

Then: