# Nonlinear Translational Damper

Translational damper based on polynomial or table lookup parameterizations

## Library

Simscape / Driveline / Couplings & Drives / Springs & Dampers

## Description

The 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:

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

where:

• F — Damping force

• b1, b2, ..., b5 — Damping coefficients

• v — Relative linear velocity between ports R and C, $v={v}_{R}-{v}_{C}$

• vR — Absolute linear velocity associated with port R

• vC — Absolute linear velocity associated with port C

To avoid zero-crossings that slow simulation, eliminate the sign function from the polynomial expression by specifying an odd polynomial (b2,b4 = 0).

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

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

where:

• b1e, b2e, ..., b5e — Damping coefficients for positive relative velocities

• b1c, b2c, ..., b5c — Damping coefficients for negative relative velocities

Positive relative velocities correspond to damper extension (ports R and C moving away from each other). Negative relative velocities correspond to damper contraction (ports R and C moving towards each other).

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 (zero velocity and zero force).

### Assumptions and Limitations

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

## Ports

`C`

Rotational conserving port

`R`

Rotational conserving port

## Parameters

Parameterization

Select damping parameterization. Options are ```By polynomial``` and ```By table lookup```.