Torsion Spring

Purpose

Ideal torsion spring

Library

Mechanical / Rotational / Components

Description

The Torsion Spring models an ideal linear spring in a rotational system described with the following equations:

\[\begin{split}\begin{aligned} \tau &{}= -c \cdot \Delta\phi \\ \Delta\theta &{}= \theta - \theta_0 \\ \frac{d}{dt}\theta &{}= \omega \end{aligned}\end{split}\]

where \(\tau\) is the torque flow from the unmarked towards the marked flange, \(\theta\) is the angle of the marked flange with respect to the unmarked one, and \(\theta_0\) is the equilibrium flange displacement.

Note

A torsion spring may not be connected in series with a torque source. Doing so would create a dependency between an input variable (the source torque) and a state variable (the spring torque) in the underlying state-space equations.

Parameters

Spring constant

The spring rate or stiffness \(c\), in \((\frac{\mathrm{Nm}}{\mathrm{rad}})\).

Equilibrium (unstretched) displacement

The displacement \(\theta_0\) between the two flanges of the unloaded spring, in radians.

Initial deformation

The initial deformation (torsion) \(\Delta\theta_0\) of the spring, in radians.

Probe Signals

Torque

The spring torque \(\tau\), in newton-meters \((\mathrm{Nm})\).

Deformation

The spring deformation \(\Delta\theta\), in radians.