# Shock Absorber

Mechanism for damping translational vibrations

## Library

Couplings & Drives

## Description

The block represents a spring-damper system commonly used to dampen vibration in mechanical systems. An internal force acts between ports R and C. This force is the sum of spring stiffness, damping, Coulomb friction, and hard-stop contributions. All force contributions are optional.

The net internal force satisfies the expression

$F={F}_{spr}+{F}_{d}+{F}_{c}+{F}_{HS},$

where:

• F — Net internal force

• Fspr — Spring force, ${F}_{k}=-k\cdot x$

• Fd — Damping force, ${F}_{d}=-b\cdot v$

• Fc — Coulomb friction force,

${F}_{c}=\left\{\begin{array}{cc}-{F}_{k}\cdot \mathrm{sign}\left(v\right),& \text{when}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{unlocked}\\ -{F}_{s},& \text{when}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{locked}\end{array},$

• FHS — Hard stop force,

${F}_{HS}=\left\{\begin{array}{cc}-{k}_{HS}\cdot \left(x-UB\right)-{b}_{HS}\cdot v,& x\ge UB\\ 0& UB\ge x\ge LB\\ -{k}_{HS}\cdot \left(x-LB\right)+{b}_{HS}\cdot v,& LB>x\end{array},$

• k — Restoring spring stiffness

• b — Viscous damping coefficient

• x — Relative displacement between ports R and C

• v — Relative velocity between R and C

• Fk — Kinetic friction force

• Fs — Static friction force

• kHS — Hard stop contact stiffness coefficient

• kHS — Hard stop damping coefficient

• UB — Hard stop upper bound

• LB — Hard stop lower bound

The shock absorber block is based on the blocks listed in the table. For more information, see the corresponding block reference pages.

BlockLibrary
Loaded-Contact Translational FrictionSimDriveline Brakes & Detents/Translational
Translational SpringSimscape Foundation Library/Mechanical/Translational
Translational Damper
Translational Hard Stop

## Assumptions and Limitations

• The use of hard-stop and Coulomb friction enhances model fidelity, but reduces simulation speed. See Improve Performance in the product documentation.

## Dialog Box and Parameters

### Spring-Damper

Restoring spring stiffness

Enter the value of the viscous spring stiffness constant, k. The value must be greater than or equal to zero.

The default value is `1e+4`. the default unit is `N/m`.

Viscous friction coefficient

Enter the value of the viscous damping constant, b. The value must be greater than or equal to zero.

The default value is `100`. The default unit is `m/s`.

Coulomb friction force

Enter the value of the Coulomb friction force. The value must be greater than or equal to zero. Setting the value to `0` eliminates the Coulomb friction force contribution. This enhances simulation speed, making the model more suitable for HIL testing.

The default value is `0`. The default unit is `N`.

Ratio of static to kinetic friction

Enter the value of the static/kinetic friction ratio (Fs/Fk). The value must be greater than one.

The default value is `1.1`.

Velocity tolerance

Enter the value of the relative velocity below which ports R and C lock and translate together. The value must greater than zero.

The default value is `0.001`. The default unit is `m/s`.

### Hard Stops

Hard stop model

Select hard stop model. Selecting ```No hard-stops — Suitable for HIL simulation``` eliminates the hard stop force contribution. This enhances simulation speed.

The default setting is ```No hard stops — Suitable for HIL simulation```.

### Initial Conditions

Initial deformation

Enter the initial value of the spring deformation.

The default value is `0`. The default unit is `m`.

## Ports

PortDescription
CTranslational conserving port
RTranslational Conserving port