SpringDamper Icon

`SpringDamper`

Linear 1D rotational spring and damper

This component extends from PartialCompliantWithRelativeStates

Parameters:

Name	Description	Units	Default value
`d`	Damping constant	N.m.s/rad
`c`	Spring constant	N.m/rad
`phi_rel0`	Unstretched spring angle	rad	0

Connectors

spline_a - (Spline)
spline_b - (Spline)

Variables

Name	Description	Units
`phi_rel`	Relative rotation angle between splines	rad
`tau`	Torque between 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	N.m
`tau_d`	Damper torque	N.m

\[ \begin{align} \mathtt{phi\_rel}\left( t \right) &= \mathtt{spline\_b.phi}\left( t \right) - \mathtt{spline\_a.phi}\left( t \right) \\ \mathtt{spline\_b.tau}\left( t \right) &= \mathtt{tau}\left( t \right) \\ \mathtt{spline\_a.tau}\left( t \right) &= - \mathtt{tau}\left( t \right) \\ \frac{\mathrm{d} \mathtt{phi\_rel}\left( t \right)}{\mathrm{d}t} &= \mathtt{w\_rel}\left( t \right) \\ \frac{\mathrm{d} \mathtt{w\_rel}\left( t \right)}{\mathrm{d}t} &= \mathtt{a\_rel}\left( t \right) \\ \mathtt{tau\_c}\left( t \right) &= c \left( - \mathtt{phi\_rel0} + \mathtt{phi\_rel}\left( t \right) \right) \\ \mathtt{tau\_d}\left( t \right) &= d \mathtt{w\_rel}\left( t \right) \\ \mathtt{tau}\left( t \right) &= \mathtt{tau\_d}\left( t \right) + \mathtt{tau\_c}\left( t \right) \end{align} \]

Source

# Linear 1D rotational spring and damper
component SpringDamper
  extends PartialCompliantWithRelativeStates
  # Spring torque
  variable tau_c::Torque
  # Damper torque
  variable tau_d::Torque
  # Damping constant
  parameter d::RotationalDampingConstant
  # Spring constant
  parameter c::RotationalSpringConstant
  # Unstretched spring angle
  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 {
  "JuliaSim": {"icons": {"default": "jsml://RotationalComponents/SpringDamper.svg"}}
}
end

Flattened Source

# Linear 1D rotational spring and damper
component SpringDamper
  spline_a = Spline() [{
    "JuliaSim": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}
  }]
  spline_b = Spline() [{
    "JuliaSim": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}
  }]
  # Relative rotation angle between splines
  variable phi_rel::Angle
  # Torque between splines
  variable tau::Torque
  # Relative angular velocity between splines
  variable w_rel::AngularVelocity
  # Relative angular acceleration between splines
  variable a_rel::AngularAcceleration
  # Spring torque
  variable tau_c::Torque
  # Damper torque
  variable tau_d::Torque
  # Damping constant
  parameter d::RotationalDampingConstant
  # Spring constant
  parameter c::RotationalSpringConstant
  # Unstretched spring angle
  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 {
  "JuliaSim": {"icons": {"default": "jsml://RotationalComponents/SpringDamper.svg"}}
}
end

Test Cases

Examples
Experiments
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