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

RotationalComponents.Damper(d)

Parameters:

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

Connectors

• spline_a - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

• spline_b - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (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_

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_

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

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • TwoInertiasWithDrivingTorque