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:

$d_{k}$ $d_{k}$: 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.
$H_{k}$ $H_{k}$: is the displacement (horizontal) scaling factor in the k^th direction.
$Q_{k}$ $Q_{k}$: is the displacement offset in the k^th direction.

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

q_{k} = H_{k} \cdot d_{k} - Q_{k}

$q_{k} = H_{k} \cdot d_{k} - Q_{k}$

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

{˙ q}_{k} = H_{k} \cdot {˙ d}_{k}

${\dot{q}}_{k} = H_{k} \cdot {\dot{d}}_{k}$

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 $G_{k}$ $G_{k}$ is the function computing the force in the k^th direction, then the force in that direction is given as follows:

Let:

$P_{k}$ $P_{k}$: is the preload in the k^th direction.
$V_{k}$ $V_{k}$: is the force (vertical) scaling in the k^th direction.
$G_{k}$ $G_{k}$: is the sum of all force methods in the k^th direction.
$F_{k}$ $F_{k}$: is the preload in the k^th direction.

Then:

F_{k} = P_{k} - V_{k} \cdot G_{k} (q_{k}, {˙ q}_{k}, x_{k}, t)

$F_{k} = P_{k} - V_{k} \cdot G_{k} (q_{k}, {\dot{q}}_{k}, x_{k}, t)$