Damper

Models a linear rotational mechanical damping element where torque is proportional to relative angular velocity.

This component describes a viscous damper for 1D rotational systems. It generates a torque that opposes the relative motion between its two mechanical rotational ports (flanges). The relationship between the torque $\tau$ and the relative angular velocity $w_{rel}$ across the damper is linear and governed by the damping constant d. The defining equation is:

$$\begin{gathered} \tau =d \\ cdot{w}_{rel} \end{gathered}$$

where d is the damping constant (parameter) and $w_{rel}$ is the relative angular velocity between the component's flanges.

This component extends from PartialCompliantWithRelativeStates

Usage

Damper(d)

Parameters:

Name	Description	Units	Default value
d	Damping coefficient, relating torque to relative angular velocity.	N.m.s/rad

Connectors

• spline_a - (Spline)

• spline_b - (Spline)

Variables

Name	Description	Units
phi_rel	Relative rotation angle between spline_b and spline_a	rad
tau	Torque transmitted between the splines	N.m
w_rel	Relative angular velocity between splines	rad/s
a_rel	Relative angular acceleration between splines	rad/s2

Behavior

$$\begin{array}{rl}\mathtt{phi}\mathtt{\_}\mathtt{rel}\left(t\right)& =\mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{phi}\left(t\right)-\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{phi}\left(t\right)\\ \mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{tau}\left(t\right)& =\mathtt{tau}\left(t\right)\\ \mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)& =-\mathtt{tau}\left(t\right)\\ \frac{\mathrm{d}\mathtt{phi}\mathtt{\_}\mathtt{rel}\left(t\right)}{\mathrm{d}t}& =\mathtt{w}\mathtt{\_}\mathtt{rel}\left(t\right)\\ \frac{\mathrm{d}\mathtt{w}\mathtt{\_}\mathtt{rel}\left(t\right)}{\mathrm{d}t}& =\mathtt{a}\mathtt{\_}\mathtt{rel}\left(t\right)\\ \mathtt{tau}\left(t\right)& =d\mathtt{w}\mathtt{\_}\mathtt{rel}\left(t\right)\end{array}$$

Source

# Models a linear rotational mechanical damping element where torque is proportional to relative angular velocity.
#
# This component describes a viscous damper for 1D rotational systems. It generates a torque that opposes
# the relative motion between its two mechanical rotational ports (flanges). The relationship between the
# torque \$\tau\$ and the relative angular velocity \$w_{rel}\$ across the damper is linear and
# governed by the damping constant `d`. The defining equation is:
# ```math
# \tau = d \\cdot w_{rel}
# ```
# where `d` is the damping constant (parameter) and \$w_{rel}\$ is the relative angular velocity
# between the component's flanges.
component Damper
  extends PartialCompliantWithRelativeStates
  # Damping coefficient, relating torque to relative angular velocity.
  parameter d::RotationalDampingConstant
relations
  tau = d*w_rel
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/Damper.svg"}}}
end

Flattened Source

# Models a linear rotational mechanical damping element where torque is proportional to relative angular velocity.
#
# This component describes a viscous damper for 1D rotational systems. It generates a torque that opposes
# the relative motion between its two mechanical rotational ports (flanges). The relationship between the
# torque \$\tau\$ and the relative angular velocity \$w_{rel}\$ across the damper is linear and
# governed by the damping constant `d`. The defining equation is:
# ```math
# \tau = d \\cdot w_{rel}
# ```
# where `d` is the damping constant (parameter) and \$w_{rel}\$ is the relative angular velocity
# between the component's flanges.
component Damper
  # First rotational spline interface
  spline_a = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Second rotational spline interface
  spline_b = Spline() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Relative rotation angle between spline_b and spline_a
  variable phi_rel::Angle
  # Torque transmitted between the splines
  variable tau::Torque
  # Relative angular velocity between splines
  variable w_rel::AngularVelocity
  # Relative angular acceleration between splines
  variable a_rel::AngularAcceleration
  # Damping coefficient, relating torque to relative angular velocity.
  parameter d::RotationalDampingConstant
relations
  phi_rel = spline_b.phi-spline_a.phi
  spline_b.tau = tau
  spline_a.tau = -tau
  der(phi_rel) = w_rel
  der(w_rel) = a_rel
  tau = d*w_rel
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/Damper.svg"}}}
end

Test Cases

This is setup code, that must be run before each test case.

using RotationalComponents
using ModelingToolkit, OrdinaryDiffEqDefault
using Plots
using CSV, DataFrames

snapshotsdir = joinpath(dirname(dirname(pathof(RotationalComponents))), "test", "snapshots")

"/home/actions-runner-10/.julia/packages/RotationalComponents/0VPxm/test/snapshots"

Related

• Examples

• Experiments

• Analyses

• Tests

  • TwoInertiasWithDrivingTorque