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# Nonlinear Rotational Spring

Torsional spring based on polynomial or lookup table parameterizations

## Library

Couplings & Drives/Springs & Dampers

## Description

The block represents a torsional spring with nonlinear torque-displacement curve. The spring torque magnitude is a general function of displacement. It need not satisfy Hooke's law. Polynomial and lookup-table parameterizations provide two ways to specify the torque-displacement relationship. The spring torque can be symmetric or asymmetric with respect to zero deformation.

The symmetric polynomial parameterization defines spring torque according to the expression:

where:

• T — Spring force

• k1, k2, ...,k5 — Spring coefficients

• θ — Relative displacement between ports R and C,

• θinit — Initial spring deformation

• θR — Absolute angular position of port R

• θC — Absolute angular position of port C

At simulation start (t=0), θR and θC are zero, making θ equal to θinit.

Specifying an odd polynomial (b2,b4 = 0) eliminates the sign function from the polynomial expression. This avoids zero-crossings that slow down simulation.

The two-sided polynomial parameterization defines spring torque according to the expression:

where:

• k1t, k2t, ..., k5t — Spring tension coefficients

• k1c, k2c, ..., k5c — Spring compression coefficients

Both polynomial parameterizations use a fifth-order polynomial expression. To use a lower-order polynomial, set the unneeded higher-order coefficients to zero. To use a higher-order polynomial, fit to a lower order polynomial or use the lookup table parameterization.

The lookup table parameterization defines spring torque based on a set of torque and angular velocity vectors. If not specified, the block automatically adds a data point at the origin (zero angular velocity and zero torque).

## Dialog Box and Parameters

The dialog box includes active area, Parameters.

Parameterization

Select spring parameterization. Options are By polynomial and By lookup table.

## Ports

PortDescription
CRotational conserving port
RRotational conserving port