# Variable Translational Spring

Translational spring with variable spring stiffness

## Library

Couplings & Drives/Springs & Dampers

## Description

The block represents a translational spring with variable spring stiffness. A physical signal input port provides the variable spring stiffness. The magnitude of the spring force is equal to the product of the physical signal input and the relative linear displacement between the two translational conserving ports. A minimum spring rate prevents non-physical values.

The translational spring force satisfies the following expression:

`$F=\left\{\begin{array}{cc}K\cdot x,& K\ge {K}_{\mathrm{min}}\\ {K}_{\mathrm{min}}\cdot x& K<{K}_{\mathrm{min}}\end{array},$`

The parameters are:

• F — Force transmitted through the spring between the two translational conserving ports

• K — Spring rate (stiffness)

• Kmin — Minimum allowed spring rate (stiffness)

• x — Relative displacement between the two translational conserving ports according to $x={x}_{init}+{x}_{R}-{x}_{C}$

• xinit — initial spring deformation

• xR — Absolute displacement of translational conserving port R

• xC — Absolute displacement of translational conserving port C

The block applies equal and opposite spring forces on the two translational conserving ports. The sign of the spring force acting on port R is equal to the sign of the relative linear displacement between the two ports. A positive linear velocity corresponds to a positive spring force acting on port R, and a negative spring force of equal magnitude acting on port C.

## Assumptions and Limitations

• The value of the variable spring stiffness must be greater than zero.

## Parameters

Minimum spring rate

Minimum value allowed for the spring rate. The physical signal input saturates below the specified value. The parameter must be greater than zero. The default value is `1`. The default unit is `N/m`

Initial deformation

Initial displacement between the two translational conserving ports. The default value is `0`. The default unit is `m`.

## Ports

PortDescription
KPhysical signal input port representing the variable spring stiffness
CTranslational conserving port
RTranslational Conserving port