SpringDamper Icon

`SpringDamper`

Linear 1D translational spring and damper in parallel

This component extends from PartialCompliantWithRelativeStates

Parameters:

Name	Description	Units	Default value
`c`	Spring constant	N/m
`d`	Damping constant	N.s/m

Connectors

flange_a - (Flange)
flange_b - (Flange)

Variables

Name	Description	Units
`s_rel`	Relative distance between `flange_b` and `flange_a`	m
`v_rel`	Relative velocity between `flange_b` and `flange_a`	m/s
`f`	Forces between the flanges	N
`initial_stretch`	Unstretched spring length	m
`lossPower`		W
`f_c`		N
`f_d`		N

\[ \begin{align} \mathtt{s\_rel}\left( t \right) &= \mathtt{flange\_b.s}\left( t \right) - \mathtt{flange\_a.s}\left( t \right) \\ \mathtt{v\_rel}\left( t \right) &= \frac{\mathrm{d} \mathtt{s\_rel}\left( t \right)}{\mathrm{d}t} \\ \mathtt{flange\_b.f}\left( t \right) &= f\left( t \right) \\ \mathtt{flange\_a.f}\left( t \right) &= - f\left( t \right) \\ \mathtt{f\_c}\left( t \right) &= c \left( - \mathtt{initial\_stretch}\left( t \right) + \mathtt{s\_rel}\left( t \right) \right) \\ \frac{\mathrm{d} \mathtt{initial\_stretch}\left( t \right)}{\mathrm{d}t} &= 0 \\ \mathtt{f\_d}\left( t \right) &= d \mathtt{v\_rel}\left( t \right) \\ f\left( t \right) &= \mathtt{f\_c}\left( t \right) + \mathtt{f\_d}\left( t \right) \\ \mathtt{lossPower}\left( t \right) &= \mathtt{v\_rel}\left( t \right) \mathtt{f\_d}\left( t \right) \end{align} \]

Source

# Linear 1D translational spring and damper in parallel
component SpringDamper
  extends PartialCompliantWithRelativeStates
  # Spring constant
  parameter c::TranslationalSpringConstant
  # Damping constant
  parameter d::TranslationalDampingConstant
  # Unstretched spring length
  variable initial_stretch::Length(guess=0)
  variable lossPower::Power
  variable f_c::JSML.Force
  variable f_d::JSML.Force
relations
  f_c = c*(s_rel-initial_stretch)
  der(initial_stretch) = 0
  f_d = d*v_rel
  f = f_c+f_d
  lossPower = f_d*v_rel
metadata {
  "JuliaSim": {"icons": {"default": "jsml://TranslationalComponents/SpringDamper.svg"}}
}
end

Flattened Source

# Linear 1D translational spring and damper in parallel
component SpringDamper
  flange_a = Flange() [{
    "JuliaSim": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}
  }]
  flange_b = Flange() [{
    "JuliaSim": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}
  }]
  # Relative distance between `flange_b` and `flange_a`
  variable s_rel::Distance
  # Relative velocity between `flange_b` and `flange_a`
  variable v_rel::Velocity
  # Forces between the flanges
  variable f::JSML.Force
  # Spring constant
  parameter c::TranslationalSpringConstant
  # Damping constant
  parameter d::TranslationalDampingConstant
  # Unstretched spring length
  variable initial_stretch::Length(guess=0)
  variable lossPower::Power
  variable f_c::JSML.Force
  variable f_d::JSML.Force
relations
  s_rel = flange_b.s-flange_a.s
  v_rel = der(s_rel)
  flange_b.f = f
  flange_a.f = -f
  f_c = c*(s_rel-initial_stretch)
  der(initial_stretch) = 0
  f_d = d*v_rel
  f = f_c+f_d
  lossPower = f_d*v_rel
metadata {
  "JuliaSim": {"icons": {"default": "jsml://TranslationalComponents/SpringDamper.svg"}}
}
end

Test Cases

Examples
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