Rotational spring and damper coupling, with Coulomb friction, locking, and hard stops
Couplings & Drives
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 the angular velocity of rod relative to case, that is
$$\omega ={\omega}_{R}-{\omega}_{C}$$
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 τ_{K} 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 τ_{S} to kinetic
Coulomb friction torque τ_{K} acting
between connected driveshafts. Must be greater than one. The default
is 1.1
.
Minimum relative angular speed ω_{Tol} 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
.
No hard stops
— Do not include
hard stops in relative motion of connected driveshafts.
Compliant hard stops
— Model
friction geometry in terms of annulus dimensions. If you select this
option, the panel changes from its default.
Initial deformation of the torsional spring relative to the
zero-torque reference angle ϕ =
0. The default is 0
.
From the drop-down list, choose units. The default is degrees
(deg
).
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, that is
$$\tau ={\tau}_{SD}+{\tau}_{HS}+{\tau}_{C}$$
The table summarizes the torsional spring-damper variables.
Torsional Spring-Damper Variables
Symbol | Definition | Significance |
---|---|---|
ϕ | Relative angle between ring and hub | Relative angular position of ring and hub |
ω | Relative angular velocity | ω = ω_{R} – ω_{C} |
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 |
k_{HS} | Contact stiffness applied in hard stop regions | See the following model |
μ_{HS} | Contact damping applied in hard stop regions | See the following model |
τ_{K} | Kinetic friction | Constant sliding Coulomb friction |
τ_{S} | Static friction | Constant locking Coulomb friction |
R | τ_{S}/τ_{K} | Ratio of static to kinetic Coulomb friction |
ω_{Tol} | Maximum relative speed for clutch locking | See the following model |
The stiff-damping torque is a simple linear spring-damping,
$${\tau}_{SD}=-k\varphi -\mu \omega $$
If ϕ moves outside the angular gap between the upper and lower hard stop bounds, the hard stop torque is applied.
τ_{HS} | Range |
---|---|
$$-{k}_{HS}\left(\varphi -{\delta}_{+}\right)-{\mu}_{HS}\omega $$ | $$\varphi >{\delta}_{+}$$ |
$$0$$ | $${\delta}_{-}<\varphi <{\delta}_{+}$$ |
$$-{k}_{HS}\left(\varphi -{\delta}_{-}\right)-{\mu}_{HS}\omega $$ | $$\varphi <{\delta}_{-}$$ |
If ω is nonzero (unlocked), the Coulomb friction torque is a constant τ_{K}. If ω is zero (locked), it is a constant τ_{S}.
$${\tau}_{S}=R{\tau}_{K}$$
The Torsional Spring-Damper locks the connected driveshafts together if the torque across the torsional spring-damper is less than τ_{S} and
$$\left|\omega \right|<{\omega}_{tol}$$
If the clutch locks, ω is reset to zero. If the torque across the torsional spring-damper exceeds τ_{S}, the driveshafts unlock from one another, and ω becomes nonzero.