SpringDamper

Models a linear translational spring and a linear translational damper connected in parallel.

This component describes the behavior of an ideal translational spring and an ideal translational viscous damper that are arranged in parallel. The total force f generated by the component is the sum of the force from the spring f_c and the force from the damper f_d. The relative displacement across the component is s_rel and the relative velocity is v_rel. The spring force is determined by Hooke's Law:

$$f_c=c\cdot (s_{rel}-initial\mathrm{\_}stretch)$$

where c is the spring constant and initial_stretch is the value of s_rel at which the spring is relaxed (exerts no force). The initial_stretch remains constant during the simulation. The damper force is proportional to the relative velocity:

$$f_d=d\cdot v_{rel}$$

where d is the damping constant. The total force exerted by the component is:

$$f=f_c+f_d$$

Power dissipated by the damper is calculated as:

$$lossPower=f_d\cdot v_{rel}$$

The component typically inherits s_rel, v_rel, and f from a base class like PartialCompliantWithRelativeStates.

This component extends from PartialCompliantWithRelativeStates

Usage

SpringDamper(c, d)

Parameters:

Name	Description	Units	Default value
c	Spring constant defining the stiffness of the spring element	N/m
d	Damping constant defining the viscous friction of the damper element	N.s/m

Connectors

• flange_a - (Flange)

• flange_b - (Flange)

Variables

Name	Description	Units
s_rel	Relative displacement between flange_b and flange_a (flange_b.s - flange_a.s).	m
v_rel	Relative velocity between flange_b and flange_a, defined as der(s_rel).	m/s
f	Internal force exerted by the compliant element between the flanges.	N
initial_stretch	Relative displacement at which the spring is in its relaxed (zero force) state; remains constant after initialization	m
lossPower	Power dissipated by the damper element due to viscous friction	W
f_c	Force exerted by the spring element	N
f_d	Force exerted by the damper element	N

Behavior

$$\begin{array}{rl}\mathtt{s}\mathtt{\_}\mathtt{rel}\left(t\right)& =\mathtt{flange}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{s}\left(t\right)-\mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{s}\left(t\right)\\ \mathtt{v}\mathtt{\_}\mathtt{rel}\left(t\right)& =\frac{\mathrm{d}\mathtt{s}\mathtt{\_}\mathtt{rel}\left(t\right)}{\mathrm{d}t}\\ \mathtt{flange}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{f}\left(t\right)& =f\left(t\right)\\ \mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{f}\left(t\right)& =-f\left(t\right)\\ \mathtt{f}\mathtt{\_}\mathtt{c}\left(t\right)& =c(-\mathtt{initial}\mathtt{\_}\mathtt{stretch}\left(t\right)+\mathtt{s}\mathtt{\_}\mathtt{rel}\left(t\right))\\ \frac{\mathrm{d}\mathtt{initial}\mathtt{\_}\mathtt{stretch}\left(t\right)}{\mathrm{d}t}& =0\\ \mathtt{f}\mathtt{\_}\mathtt{d}\left(t\right)& =d\mathtt{v}\mathtt{\_}\mathtt{rel}\left(t\right)\\ f\left(t\right)& =\mathtt{f}\mathtt{\_}\mathtt{c}\left(t\right)+\mathtt{f}\mathtt{\_}\mathtt{d}\left(t\right)\\ \mathtt{lossPower}\left(t\right)& =\mathtt{v}\mathtt{\_}\mathtt{rel}\left(t\right)\mathtt{f}\mathtt{\_}\mathtt{d}\left(t\right)\end{array}$$

Source

# Models a linear translational spring and a linear translational damper connected in parallel.
#
# This component describes the behavior of an ideal translational spring and an ideal translational viscous damper
# that are arranged in parallel. The total force `f` generated by the component is the sum of the force from the
# spring `f_c` and the force from the damper `f_d`. The relative displacement across the component is `s_rel`
# and the relative velocity is `v_rel`.
# The spring force is determined by Hooke's Law:
# ```math
# f_c = c \cdot (s_{rel} - initial\_stretch)
#
# ```
# where `c` is the spring constant and `initial_stretch` is the value of `s_rel` at which the spring is relaxed (exerts no force).
# The `initial_stretch` remains constant during the simulation.
# The damper force is proportional to the relative velocity:
# ```math
# f_d = d \cdot v_{rel}
# ```
# where `d` is the damping constant.
# The total force exerted by the component is:
# ```math
# f = f_c + f_d
# ```
# Power dissipated by the damper is calculated as:
# ```math
# lossPower = f_d \cdot v_{rel}
# ```
# The component typically inherits `s_rel`, `v_rel`, and `f` from a base class like `PartialCompliantWithRelativeStates`.
component SpringDamper
  extends PartialCompliantWithRelativeStates
  # Spring constant defining the stiffness of the spring element
  parameter c::TranslationalSpringConstant
  # Damping constant defining the viscous friction of the damper element
  parameter d::TranslationalDampingConstant
  # Relative displacement at which the spring is in its relaxed (zero force) state; remains constant after initialization
  variable initial_stretch::Length(guess=0)
  # Power dissipated by the damper element due to viscous friction
  variable lossPower::Power
  # Force exerted by the spring element
  variable f_c::Dyad.Force
  # Force exerted by the damper element
  variable f_d::Dyad.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 {
  "Dyad": {"icons": {"default": "dyad://TranslationalComponents/SpringDamper.svg"}}
}
end

Flattened Source

# Models a linear translational spring and a linear translational damper connected in parallel.
#
# This component describes the behavior of an ideal translational spring and an ideal translational viscous damper
# that are arranged in parallel. The total force `f` generated by the component is the sum of the force from the
# spring `f_c` and the force from the damper `f_d`. The relative displacement across the component is `s_rel`
# and the relative velocity is `v_rel`.
# The spring force is determined by Hooke's Law:
# ```math
# f_c = c \cdot (s_{rel} - initial\_stretch)
#
# ```
# where `c` is the spring constant and `initial_stretch` is the value of `s_rel` at which the spring is relaxed (exerts no force).
# The `initial_stretch` remains constant during the simulation.
# The damper force is proportional to the relative velocity:
# ```math
# f_d = d \cdot v_{rel}
# ```
# where `d` is the damping constant.
# The total force exerted by the component is:
# ```math
# f = f_c + f_d
# ```
# Power dissipated by the damper is calculated as:
# ```math
# lossPower = f_d \cdot v_{rel}
# ```
# The component typically inherits `s_rel`, `v_rel`, and `f` from a base class like `PartialCompliantWithRelativeStates`.
component SpringDamper
  # Port for the first mechanical translational flange.
  flange_a = Flange() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Port for the second mechanical translational flange.
  flange_b = Flange() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Relative displacement between flange_b and flange_a (flange_b.s - flange_a.s).
  variable s_rel::Distance
  # Relative velocity between flange_b and flange_a, defined as der(s_rel).
  variable v_rel::Velocity
  # Internal force exerted by the compliant element between the flanges.
  variable f::Dyad.Force
  # Spring constant defining the stiffness of the spring element
  parameter c::TranslationalSpringConstant
  # Damping constant defining the viscous friction of the damper element
  parameter d::TranslationalDampingConstant
  # Relative displacement at which the spring is in its relaxed (zero force) state; remains constant after initialization
  variable initial_stretch::Length(guess=0)
  # Power dissipated by the damper element due to viscous friction
  variable lossPower::Power
  # Force exerted by the spring element
  variable f_c::Dyad.Force
  # Force exerted by the damper element
  variable f_d::Dyad.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 {
  "Dyad": {"icons": {"default": "dyad://TranslationalComponents/SpringDamper.svg"}}
}
end

Test Cases

This is setup code, that must be run before each test case.

using TranslationalComponents
using ModelingToolkit, OrdinaryDiffEqDefault
using Plots
using CSV, DataFrames

snapshotsdir = joinpath(dirname(dirname(pathof(TranslationalComponents))), "test", "snapshots")

"/home/actions-runner-10/.julia/packages/TranslationalComponents/khJb7/test/snapshots"

Related

• Examples

• Experiments

• Analyses