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:

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

This component extends from PartialCompliantWithRelativeStates

Usage

RotationalComponents.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

$$\begin{array}{rl}\mathtt{phi}\mathtt{\_}\mathtt{rel}\left(t\right)& =\mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{phi}\left(t\right)-\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{phi}\left(t\right)\\ \mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{tau}\left(t\right)& =\mathtt{tau}\left(t\right)\\ \mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)& =-\mathtt{tau}\left(t\right)\\ \frac{\mathrm{d}\mathtt{phi}\mathtt{\_}\mathtt{rel}\left(t\right)}{\mathrm{d}t}& =\mathtt{w}\mathtt{\_}\mathtt{rel}\left(t\right)\\ \frac{\mathrm{d}\mathtt{w}\mathtt{\_}\mathtt{rel}\left(t\right)}{\mathrm{d}t}& =\mathtt{a}\mathtt{\_}\mathtt{rel}\left(t\right)\\ \mathtt{tau}\mathtt{\_}\mathtt{c}\left(t\right)& =c(-\mathtt{phi}\mathtt{\_}\mathtt{rel}\mathtt{0}+\mathtt{phi}\mathtt{\_}\mathtt{rel}\left(t\right))\\ \mathtt{tau}\mathtt{\_}\mathtt{d}\left(t\right)& =d\mathtt{w}\mathtt{\_}\mathtt{rel}\left(t\right)\\ \mathtt{tau}\left(t\right)& =\mathtt{tau}\mathtt{\_}\mathtt{d}\left(t\right)+\mathtt{tau}\mathtt{\_}\mathtt{c}\left(t\right)\end{array}$$

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}) MarkdownAST.LineBreak()

\tau_d &= d w_{rel} MarkdownAST.LineBreak()

\tau &= \tau_c + \tau_d \end

"""
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}) MarkdownAST.LineBreak()

\tau_d &= d w_{rel} MarkdownAST.LineBreak()

\tau &= \tau_c + \tau_d \end

"""
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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