SpringDamper

Models a linear 1D rotational spring and damper acting in parallel.

This component represents a parallel combination of a linear rotational spring and a linear rotational damper. It calculates the total torque based on the relative angular displacement and velocity between its mechanical connection flanges. The spring torque ($\tau \ast c$) is proportional to the angular displacement from an unstretched reference angle ($\varphi \ast rel0$), defined by the spring constant ($c$). The damper torque ($\tau \ast d$) is proportional to the relative angular velocity ($w\ast rel$), defined by the damping constant ($d$). The governing equations are:

$$\begin{array}{rl}{\tau }_c& =c(\\ ph{i}_{rel}-\\ ph{i}_{rel0})\\ {\tau }_d& =d{w}_{rel}\\ \tau & ={\tau }_c+{\tau }_d\end{array}$$

PartialCompliantWithRelativeStates

Usage

SpringDamper(d, c, phi_rel0=0.0)

Parameters:

Name	Description	Units	Default value
d	Damping constant of the rotational damper	N.m.s/rad
c	Spring constant of the rotational spring	N.m/rad
phi_rel0	Unstretched (zero torque) relative angle of the spring	rad	0

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
tau_c	Spring torque contribution	N.m
tau_d	Damper torque contribution	N.m

Behavior

using RotationalComponents #hide
using ModelingToolkit #hide
@variables d #hide
@variables c #hide
@variables phi_rel0 #hide
@named sys = SpringDamper(d=d, c=c, phi_rel0=phi_rel0) #hide
full_equations(sys) #hide

<< @example-block not executed in draft mode >>

Source

# Models a linear 1D rotational spring and damper acting in parallel.
#
# This component represents a parallel combination of a linear rotational spring and a linear rotational damper. It calculates the total torque based on the relative angular displacement and velocity between its mechanical connection flanges.
# The spring torque (\$\tau_c\$) is proportional to the angular displacement from an unstretched reference angle (\$\\phi_{rel0}\$), defined by the spring constant (\$c\$).
# The damper torque (\$\tau_d\$) is proportional to the relative angular velocity (\$w_{rel}\$), defined by the damping constant (\$d\$).
# The governing equations are:
# ```math
# \begin{align*}
# \tau_c &= c (\\phi_{rel} - \\phi_{rel0}) \\
# \tau_d &= d w_{rel} \\
# \tau &= \tau_c + \tau_d
# \end{align*}
# ```
component SpringDamper
  extends PartialCompliantWithRelativeStates
  # Spring torque contribution
  variable tau_c::Torque
  # Damper torque contribution
  variable tau_d::Torque
  # Damping constant of the rotational damper
  parameter d::RotationalDampingConstant
  # Spring constant of the rotational spring
  parameter c::RotationalSpringConstant
  # Unstretched (zero torque) relative angle of the spring
  parameter phi_rel0::Angle = 0.0
relations
  tau_c = c*(phi_rel-phi_rel0)
  tau_d = d*w_rel
  tau = tau_c+tau_d
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/SpringDamper.svg"}}}
end

Flattened Source

# Models a linear 1D rotational spring and damper acting in parallel.
#
# This component represents a parallel combination of a linear rotational spring and a linear rotational damper. It calculates the total torque based on the relative angular displacement and velocity between its mechanical connection flanges.
# The spring torque (\$\tau_c\$) is proportional to the angular displacement from an unstretched reference angle (\$\\phi_{rel0}\$), defined by the spring constant (\$c\$).
# The damper torque (\$\tau_d\$) is proportional to the relative angular velocity (\$w_{rel}\$), defined by the damping constant (\$d\$).
# The governing equations are:
# ```math
# \begin{align*}
# \tau_c &= c (\\phi_{rel} - \\phi_{rel0}) \\
# \tau_d &= d w_{rel} \\
# \tau &= \tau_c + \tau_d
# \end{align*}
# ```
component SpringDamper
  # 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
  # Spring torque contribution
  variable tau_c::Torque
  # Damper torque contribution
  variable tau_d::Torque
  # Damping constant of the rotational damper
  parameter d::RotationalDampingConstant
  # Spring constant of the rotational spring
  parameter c::RotationalSpringConstant
  # Unstretched (zero torque) relative angle of the spring
  parameter phi_rel0::Angle = 0.0
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_c = c*(phi_rel-phi_rel0)
  tau_d = d*w_rel
  tau = tau_c+tau_d
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/SpringDamper.svg"}}}
end

Test Cases

No test cases defined.

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