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Translational spring with variable spring stiffness

**Library:**Simscape / Driveline / Couplings & Drives / Springs & Dampers

The Variable Translational Spring block represents a translational spring with variable 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 nonphysical values.

The translational spring force satisfies the following expression:

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

where:

*F*is the force transmitted through the spring between the two translational conserving ports.*K*is the spring rate coefficient.*K*is the minimum allowed spring rate._{min}*x*is the relative displacement between the two translational conserving ports according to $$x={x}_{init}+{x}_{R}-{x}_{C}$$.*x*is the initial spring deformation._{init}*x*is the absolute displacement of the translational conserving port_{R}**R**.*x*is the absolute displacement of the translational conserving port_{C}**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**.

The block limits the value of the variable spring stiffness to remain above zero.

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.