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Torsional Spring-Damper

Represent damped torsional spring torque, with free play gap, acting between two rotating axes


Dynamic Elements


The Torsional Spring-Damper block models a damped torsional spring-like torque acting between two rotating axes, the base (B) and the follower (F). This torque is a function of the relative displacement angle θ = θF – θB and relative angular velocity ω = dθ/dt = ωF – ωB.

τ = –k( θ – θback) – bω , if θ > +θback

τ = –k( θ + θback) – bω , if θ < –θback

τ = 0 , if –θback < θ < +θback

You specify the restoring torque spring constant or spring rate k as the stiffness and the kinetic friction torque constant b as the damping. Both constants must be nonnegative.

Backlash and Initial Offset

The backlash interval is a free play gap of size 2θback across. If θ lies in this range, the spring and damping torques are not applied. Above and below the backlash range, both the spring and damping torques are applied.

You specify the initial relative displacement θ0 as the initial offset, relative to the midway point between the backlash interval endpoints.

Torsional Spring-Damper Torque Law (Spring Only)

Using Dynamic Element Blocks

Use the blocks of the Dynamic Elements library as a starting point for vehicle modeling. To see how a Dynamic Element block models a driveline component, look under the block mask. The blocks of this library serve as suggestions for developing variant or entirely new models to simulate the same components. Break the block's library link before modifying it and creating your own version.

Dialog Box and Parameters


The spring constant or spring rate k for the restoring torque imposed by the spring. Must be nonnegative. The units are newton-meters/radian (N·m/rad). The default is 1e3.


The damping constant b for the kinetic frictional torque imposed by the damper. Must be nonnegative. The units are newton-meters-seconds/radian (N·m·s/rad). The default is 0.1.

Initial Offset

The initial angular offset θ0 of the relative displacement θ, in radians (rad). The default is 0.


The angular free play θback allowed in the torsional spring. Must be nonnegative. The units are radians (rad). The default is 0.


The example model drive_spring illustrates a simple torsional spring-damper system.

See Also

Hard Stop

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