# 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.

### Variables

Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables (Simscape).

Unlike block parameters, variables do not have conditional visibility. The Variables tab lists all the existing block variables. If a variable is not used in the set of equations corresponding to the selected block configuration, the values specified for this variable are ignored.

### Assumptions and Limitations

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

## Ports

`K`

Physical signal input port representing the variable spring stiffness.

`C`

Translational conserving port.

`R`

Translational conserving port.

## 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` `N/m`.