Documentation

Torsional Spring-Damper

Rotational spring and damper coupling, with Coulomb friction, locking, and hard stops

Library

Simscape / Driveline / Couplings & Drives

Description

The Torsional Spring-Damper block represents a dynamic element that imposes a combination of internally generated torques between the two connected driveshaft axes, the rod and the case. The complete torque includes these components:

  • Linear damped spring

  • Coulomb friction (including locking static friction)

  • Hard-stop compliance

The second and third components are optional.

The Torsional Spring-Damper block uses the models of these blocks:

BlockContributionLibrary
Loaded-Contact Rotational FrictionCoulomb frictionSimscape / Driveline / Brakes & Detents / Rotational
Rotational Damper, Rotational SpringDampingSimscape / Foundation Library / Mechanical / Rotational Elements
Rotational Spring Spring
Rotational Hard StopHard stop

Assumptions and Limitations

Ports

Conserving

C

Mechanical rotational port associated with the slider that travels between stops installed on the case.

R

Mechanical rotational port associated with the rod.

Parameters

Spring-Damper

Restoring spring stiffness

Torsional spring stiffness k acting between connected driveshafts. The default is 1000 N*m/rad. The value must be greater than zero.

Viscous friction coefficient

Torsional damping μ acting between the connected driveshafts. The default is 10 N*m/(rad/s). The value must be greater than or equal to zero.

Coulomb friction torque

Constant kinetic friction torque τK acting between connected driveshafts. The default is 0 N*m. The value must be greater than or equal to zero.

Ratio of static to kinetic friction

Constant ratio R of static Coulomb friction torque τS to kinetic Coulomb friction torque τK acting between connected driveshafts. The default is 1.1. The value must be greater than or equal to one.

Velocity tolerance

Minimum relative angular speed ωTol below which the two connected driveshafts can lock and rotate together. The default is 0.001 rad/s. The value must be greater than zero

Hard Stops

Hard stop

Include or exclude hard-stop torque by selecting one of these options:

  • No hard stops — Suitable for HIL simulation — To enhance simulation speed by excluding the hard-stop torque contribution, select this default option.

  • Compliant hard stops — To enhance model fidelity by including the hard-stop torque contribution, select this option. Selecting this option enables other parameters.

Upper bound

Upper hard-stop angular displacement δ+ from the zero-torque reference angle ϕ = 0. The default is 10 deg. The value must be greater than δ.

Selecting Compliant hard stops for the Hard stop parameter enables this parameter.

Lower bound

Lower hard-stop angular displacement δ from the zero spring force reference angle ϕ = 0. The default is -10 deg. The value must be less than δ+.

Selecting Compliant hard stops for the Hard stop parameter enables this parameter.

Contact stiffness

Hard-stop stiffness kHS applied if the relative angle ϕ moves into the hard-stop region. The default is 1e6. N*m/rad. The value must be greater than or equal to zero.

Selecting Compliant hard stops for the Hard stop parameter enables this parameter.

Contact damping

Hard-stop damping μHS applied if the relative angle ϕ moves into the hard-stop region.The default is 10 N*m/(rad/s). The value must be greater than zero.

Selecting Compliant hard stops for the Hard stop parameter enables this parameter.

Hard stop model

Select the hard-stop model:

  • Stiffness and damping applied smoothly through transition region, damped rebound — Specify a transition region, in which the torque is scaled from zero. At the end of the transition region, the full stiffness and damping are applied. This model has damping applied on the rebound, but it is limited to the value of the stiffness torque. In this sense, damping can reduce or eliminate the torque provided by the stiffness, but never exceed it. All equations are smooth and produce no zero crossings.

  • Full stiffness and damping applied at bounds, undamped rebound — This model has full stiffness and damping applied with impact at upper and lower bounds, with no damping on the rebound. Equations produce no zero crossings when velocity changes sign, but there is a position-based zero crossing at the bounds. Having no damping on rebound helps to push the slider past this position quickly. This model has nonlinear equations.

  • Full stiffness and damping applied at bounds, damped rebound — This model has full stiffness and damping applied with impact at upper and lower bounds, with damping applied on the rebound as well. Equations are switched linear, but produce position-based zero crossings. Use this hard stop model if simscape.findNonlinearBlocks indicates that this is the block that prevents the whole network from being switched linear.

Selecting Compliant hard stops for the Hard stop parameter enables this parameter.

Transition region

Region where the torque is ramped up from zero to the full value. At the end of the transition region, the full stiffness and damping are applied. The default value is 0.001 rad.

Selecting Stiffness and damping applied smoothly through transition region, damped rebound for the Hard stop model enables this parameter.

Initial Conditions

Initial deformation

Initial deformation of the torsional spring relative to the zero-torque reference angle ϕ = 0. The default is 0 deg.

Extended Capabilities

Real-Time and Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Hard Stops > Hard stop parameter default setting, No hard stops - Suitable for HIL simulation.

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