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

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 = θ_{F} – θ_{B} and
relative angular velocity ω = dθ/dt = ω_{F} –
ω_{B}.

τ = –*k*( θ –
θ_{back}) – *b*ω
, if θ > +θ_{back}

τ = –*k*( θ + θ_{back})
– *b*ω , if θ < –θ_{back}

τ = 0 , if –θ_{back} <
θ < +θ_{back}

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.

The backlash interval is a free play gap of size 2θ_{back} 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 θ_{0} as
the initial offset, relative to the midway point between the backlash
interval endpoints.

**Torsional Spring-Damper Torque Law (Spring Only)**

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.

**Stiffness**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`.**Damping**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 θ

_{0}of the relative displacement θ, in radians (rad). The default is`0`.**Backlash**The angular free play θ

_{back}allowed in the torsional spring. Must be nonnegative. The units are radians (rad). The default is`0`.

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

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