# Nonlinear Translational Damper

Nonlinear damper in a translational system

**Libraries:**

Simscape /
Driveline /
Couplings & Drives /
Springs & Dampers

## Description

The Nonlinear Translational Damper block represents a nonlinear translational damper. Polynomial and table lookup parameterizations define the nonlinear relationship between damping force and relative linear velocity. The damping force can be symmetric or asymmetric about the zero velocity point. The block applies equal and opposite damping forces on the two translational conserving ports.

The symmetric polynomial parameterization defines the damping force for both positive and negative relative velocities according to the expression:

$$F={b}_{1}v+sign(v)\cdot {b}_{2}{v}^{2}+{b}_{3}{v}^{3}+sign(v)\cdot {b}_{4}{v}^{4}+{b}_{5}{v}^{5},$$

where:

*F*— Damping force*b*,_{1}*b*,...,_{2}*b*— Damping coefficients_{5}*v*— Relative linear velocity between ports**R**and**C**, $$v={v}_{R}-{v}_{C}$$*v*— Absolute linear velocity associated with port_{R}**R***v*— Absolute linear velocity associated with port_{C}**C**

To avoid zero-crossings that slow simulation, eliminate the sign function from the
polynomial expression by specifying an odd polynomial (*b _{2}*,

*b*= 0).

_{4}The two-sided polynomial parameterization defines the damping force for both positive and negative relative velocities according to the expression:

$$F=\{\begin{array}{cc}{b}_{1e}v+{b}_{2e}{v}^{2}+{b}_{3e}{v}^{3}+{b}_{4e}{v}^{4}+{b}_{5e}{v}^{5},& v\ge 0\\ {b}_{1c}v-{b}_{2c}{v}^{2}+{b}_{3c}{v}^{3}-{b}_{4c}{v}^{4}+{b}_{5c}{v}^{5},& v<0\end{array},$$

where:

*b*,_{1e}*b*, ...,_{2e}*b*— Damping coefficients for positive relative velocities_{5e}*b*,_{1c}*b*, ...,_{2c}*b*— Damping coefficients for negative relative velocities_{5c}

Positive relative velocities correspond to damper extension when ports
**R** and **C** move apart. Negative relative
velocities correspond to damper contraction when ports **R** and
**C** move together.

Both polynomial parameterizations use a fifth-order polynomial expression. To use a lower-order polynomial, set the unneeded higher-order coefficients to zero. For polynomials of order greater than five, fit to a polynomial of order smaller than or equal to five, or use the table lookup parameterization.

The table lookup parameterization defines damping force based on a set of velocity and force vectors. If not included in the vectors, the block automatically adds a data point at the origin, that is, the intersection of zero velocity and zero force.

### Assumptions and Limitations

The block assumes viscous damping. The damping force depends only on velocity.

## Examples

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2013a**