# Variable Rotational Spring

Rotational spring with variable spring stiffness

## Library

Couplings & Drives/Springs & Dampers

## Description

The block represents a torsional spring with variable spring stiffness. A physical signal input port provides the value of the variable spring stiffness. The magnitude of the spring torque is equal to the product of the physical signal input and the relative angular displacement between the two rotational conserving ports. A minimum spring rate value prevents non-physical values.

The rotational spring torque satisfies the following expression:

`$T=\left\{\begin{array}{cc}K\cdot \theta & K\ge {K}_{\mathrm{min}}\\ {K}_{\mathrm{min}}\cdot \theta & K<{K}_{\mathrm{min}}\end{array},$`

The parameters are:

• T — Torque transmitted through the spring

• K — Spring rate (stiffness)

• Kmin — Minimum allowable spring rate (stiffness)

• θ — Relative angular displacement measured between the two rotational conserving ports according to $\theta ={\theta }_{init}+{\theta }_{R}-{\theta }_{C}$

• θinit — Initial angular deformation between the two rotational conserving ports

• θR — Absolute angular displacement of rotational conserving port R

• θC — Absolute angular displacement of rotational conserving port C

The block applies equal and opposite spring torques on the two rotational conserving ports. The sign of the spring torque acting on port R is equal to the sign of the relative angular velocity. A positive relative angular velocity corresponds to a positive damping torque acting on port R, and a negative damping torque of equal magnitude acting on port C.

## Assumptions and Limitations

• The value of the spring rate must be greater than zero.

## Parameters

Minimum spring rate

Minimum value allowed for the spring rate (stiffness). The physical signal input saturates below the specified value. The parameter must be greater than zero. The default value is `0.01`. The default unit is `(N*m/rad)`.

Initial Deformation

Initial angular displacement between rotational conserving ports R and C. The initial value is `0`. The initial unit is `rad`.

## Ports

PortDescription
KPhysical signal input port representing the variable spring stiffness
CRotational conserving port
RRotational conserving port