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:

\[\tau = d \\cdot w_{rel}\]

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

PartialCompliantWithRelativeStates

Usage

Damper(d)

Parameters:

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

Behavior

\[ \begin{align} \mathtt{phi\_rel}\left( t \right) &= \mathtt{spline\_b.phi}\left( t \right) - \mathtt{spline\_a.phi}\left( t \right) \\ \mathtt{spline\_b.tau}\left( t \right) &= \mathtt{tau}\left( t \right) \\ \mathtt{spline\_a.tau}\left( t \right) &= - \mathtt{tau}\left( t \right) \\ \frac{\mathrm{d} \mathtt{phi\_rel}\left( t \right)}{\mathrm{d}t} &= \mathtt{w\_rel}\left( t \right) \\ \frac{\mathrm{d} \mathtt{w\_rel}\left( t \right)}{\mathrm{d}t} &= \mathtt{a\_rel}\left( t \right) \\ \mathtt{tau}\left( t \right) &= d \mathtt{w\_rel}\left( t \right) \end{align} \]

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

# 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

No test cases defined.

Related

• Examples
• Experiments
• Analyses
• Tests
  • TwoInertiasWithDrivingTorque