Rotational spring and damper coupling, with Coulomb friction, locking, and hard stops
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. For model details, see Torsional Spring-Damper Model.
Note: Torsional Spring-Damper is based on the Loaded-Contact Rotational Friction block and the Simscape™ Rotational Spring, Rotational Damper, and Rotational Hard Stop blocks. (The first and fourth blocks are required for Coulomb friction and hard stops, respectively.) For more information, see these block reference pages.
R and C are rotational conserving ports representing, respectively, the rod and case driveshafts. The relative motion is measured as ω = ωR– ωC, the angular velocity of rod relative to case.
The dialog box has one active area, Parameters, with three tabs.
Torsional spring stiffness k acting between connected driveshafts. Must be greater than zero. The default is 1000.
From the drop-down list, choose units. The default is newton-meters/radian (N*m/rad).
Torsional damping μ acting between the connected driveshafts. Must be greater than or equal to zero. The default is 10.
From the drop-down list, choose units. The default is newton-meters/(radian/second) (N*m/(rad/s)).
Constant kinetic friction torque τK acting between connected driveshafts. Must be greater than or equal to zero. The default is 0.
From the drop-down list, choose units. The default is newton-meters (N*m).
Constant ratio R of static Coulomb friction torque τS to kinetic Coulomb friction torque τK acting between connected driveshafts. Must be greater than one. The default is 1.1.
Minimum relative angular speed ωTol below which the two connected driveshafts can lock and rotate together. Must be greater than zero. The default is 0.001.
From the drop-down list, choose units. The default is radians/second (rad/s).
Select how to model the hard stops. The default is No hard stops — Suitable for HIL simulation.
The complete torque τ imposed by Torsional Spring-Damper between the connected driveshafts is the sum of three terms: stiff-damping, hard stop compliance, and Coulomb.
τ = τSD + τHS + τC .
The table summarizes the torsional spring-damper variables.
Torsional Spring-Damper Variables
|ϕ||Relative angle between ring and hub||Relative angular position of ring and hub|
|ω||Relative angular velocity||ω = ωR – ωC|
|k||Torsional stiffness||See the following model|
|μ||Torsional damping||See the following model|
|δ+, δ–||Upper and lower hard stop angular displacements||See the following model|
|kHS||Contact stiffness applied in hard stop regions||See the following model|
|μHS||Contact damping applied in hard stop regions||See the following model|
|τK||Kinetic friction||Constant sliding Coulomb friction|
|τS||Static friction||Constant locking Coulomb friction|
|R||τS/τK||Ratio of static to kinetic Coulomb friction|
|ωTol||Maximum relative speed for clutch locking||See the following model|
The stiff-damping torque is a simple linear spring-damping:
τSD = –kϕ – μω .
The hard stop torque is applied if ϕ moves outside the angular gap between the upper and lower hard stop bounds.
|–kHS(ϕ – δ+) – μHSω||ϕ > δ+|
|0||δ– < ϕ < δ+|
|–kHS(ϕ – δ–) – μHSω||ϕ < δ–|
The Coulomb friction torque is a constant τK if ω is nonzero (unlocked), and a constant τS if ω is zero (locked).
τS = RτK .
The Torsional Spring-Damper locks the connected driveshafts together if both:
|ω| < ωTol
The torque across the torsional spring-damper is less than τS.
If the clutch locks, ω is reset to zero. If the torque across the torsional spring-damper exceeds τS, the driveshafts unlock from one another, and ω becomes nonzero.
Hard stop and Coulomb friction simulation increases model fidelity but reduces simulation performance. See Adjust Model Fidelity.