# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# Torsional Spring-Damper

Rotational spring and damper coupling, with Coulomb friction, locking, and hard stops

## Library

Couplings & Drives

## Description

The Torsional Spring-Damper block represents a dynamic element that imposes a combination of internally generated torques between the two connected driveshaft axes, the rod and the case. The complete torque includes these components:

• Linear damped spring

• Coulomb friction (including locking static friction)

• Hard stop compliance

The second and third components are optional. For model details, see Torsional Spring-Damper Model.

 Note:   Torsional Spring-Damper is based on the Loaded-Contact Rotational Friction block and the Simscape™ Rotational Spring, Rotational Damper, and Rotational Hard Stop blocks. (The first and fourth blocks are required for Coulomb friction and hard stops, respectively.) For more information, see these block reference pages.

### Ports

R and C are rotational conserving ports representing, respectively, the rod and case driveshafts. The relative motion is measured as the angular velocity of rod relative to case, that is

`$\omega ={\omega }_{R}-{\omega }_{C}$`

## Parameters

### Spring-Damper

Restoring spring stiffness

Torsional spring stiffness k acting between connected driveshafts. Must be greater than zero. The default is `1000`.

From the drop-down list, choose units. The default is newton-meters/radian (`N*m/rad`).

Viscous friction coefficient

Torsional damping μ acting between the connected driveshafts. Must be greater than or equal to zero. The default is `10`.

From the drop-down list, choose units. The default is Newton-meters/(radian/second) (`N*m/(rad/s)`).

Coulomb friction torque

Constant kinetic friction torque τK acting between connected driveshafts. Must be greater than or equal to zero. The default is `0`.

From the drop-down list, choose units. The default is newton-meters (`N*m`).

Ratio of static to kinetic friction

Constant ratio R of static Coulomb friction torque τS to kinetic Coulomb friction torque τK acting between connected driveshafts. Must be greater than one. The default is `1.1`.

Velocity tolerance

Minimum relative angular speed ωTol below which the two connected driveshafts can lock and rotate together. Must be greater than zero. The default is `0.001`.

From the drop-down list, choose units. The default is radians/second (`rad/s`).

### Hard Stops

Hard stop model

Select how to model the hard stops. The default is ```No hard stops — Suitable for HIL simulation```.

• `No hard stops` — Do not include hard stops in relative motion of connected driveshafts.

• `Compliant hard stops` — Model friction geometry in terms of annulus dimensions. If you select this option, the panel changes from its default.

### Initial Conditions

Initial deformation

Initial deformation of the torsional spring relative to the zero-torque reference angle ϕ = 0. The default is `0`.

From the drop-down list, choose units. The default is degrees (`deg`).

## Torsional Spring-Damper Model

The complete torque τ imposed by Torsional Spring-Damper between the connected driveshafts is the sum of three terms: stiff-damping, hard stop compliance, and Coulomb, that is

`$\tau ={\tau }_{SD}+{\tau }_{HS}+{\tau }_{C}$`

The table summarizes the torsional spring-damper variables.

Torsional Spring-Damper Variables

SymbolDefinitionSignificance
ϕRelative angle between ring and hubRelative angular position of ring and hub
ωRelative angular velocityω = ωRωC
kTorsional stiffnessSee the following model
μTorsional dampingSee the following model
δ+, δUpper and lower hard stop angular displacementsSee the following model
kHSContact stiffness applied in hard stop regionsSee the following model
μHSContact damping applied in hard stop regionsSee the following model
τKKinetic frictionConstant sliding Coulomb friction
τSStatic frictionConstant locking Coulomb friction
RτS/τKRatio of static to kinetic Coulomb friction
ωTolMaximum relative speed for clutch lockingSee the following model

### Stiffness and Damping

The stiff-damping torque is a simple linear spring-damping,

`${\tau }_{SD}=-k\varphi -\mu \omega$`

### Hard Stops

If ϕ moves outside the angular gap between the upper and lower hard stop bounds, the hard stop torque is applied.

τHSRange
`$-{k}_{HS}\left(\varphi -{\delta }_{+}\right)-{\mu }_{HS}\omega$`
`$\varphi >{\delta }_{+}$`
`$0$`
`${\delta }_{-}<\varphi <{\delta }_{+}$`
`$-{k}_{HS}\left(\varphi -{\delta }_{-}\right)-{\mu }_{HS}\omega$`
`$\varphi <{\delta }_{-}$`

### Coulomb Friction — Locking

If ω is nonzero (unlocked), the Coulomb friction torque is a constant τK. If ω is zero (locked), it is a constant τS.

`${\tau }_{S}=R{\tau }_{K}$`

#### Locking Conditions

The Torsional Spring-Damper locks the connected driveshafts together if the torque across the torsional spring-damper is less than τS and

`$|\omega |<{\omega }_{tol}$`

If the clutch locks, ω is reset to zero. If the torque across the torsional spring-damper exceeds τS, the driveshafts unlock from one another, and ω becomes nonzero.