# 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 kth 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 kth direction.
${Q}_{k}$
is the displacement offset in the kth direction.

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

${q}_{k}={H}_{k}·{d}_{k}-{Q}_{k}$

The velocity in the kth direction, is given by:

${\stackrel{˙}{q}}_{k}={H}_{k}·{\stackrel{˙}{d}}_{k}$

## 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 kth direction, then the force in that direction is given as follows:

Let:

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

Then:

${F}_{k}={P}_{k}-{V}_{k}·{G}_{k}\left({q}_{k},{\stackrel{˙}{q}}_{k},{x}_{k},t\right)$