Spring

Linear 1D translational spring relating force to displacement via Hooke's Law.

This component represents a one-dimensional translational mechanical spring. It models the linear relationship between the force ($f$) exerted by the spring and its deformation ($s_{rel}$) relative to an unstretched length ($s_{rel0}$). The governing equation is Hooke's Law:

$$f=c\cdot (s_{rel}-s_{rel0})$$

Here, c is the spring constant (stiffness), $s_{rel}$ is the current relative displacement between the spring's two connection flanges (typically inherited from PartialCompliant), and $s_{rel0}$ is the relative displacement at which the spring exerts no force.

This component extends from PartialCompliant

Usage

Spring(c, s_rel0=0)

Parameters:

Name	Description	Units	Default value
c	Spring constant, representing the stiffness of the spring.	N/m
s_rel0	Unstretched relative displacement of the spring, where the spring force is zero.	m	0

Connectors

• flange_a - (Flange)

• flange_b - (Flange)

Variables

Name	Description	Units
s_rel	Relative distance between flange_b and flange_a	m
f	Internal force exerted by the compliant connection on flange_b (and -f on flange_a).	N

Behavior

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

Source

# Linear 1D translational spring relating force to displacement via Hooke's Law.
#
# This component represents a one-dimensional translational mechanical spring.
# It models the linear relationship between the force ($f$) exerted by the
# spring and its deformation ($s_{rel}$) relative to an unstretched length ($s_{rel0}$).
# The governing equation is Hooke's Law:
# ```math
# f = c \cdot (s_{rel} - s_{rel0})
# ```
# Here, `c` is the spring constant (stiffness), $s_{rel}$ is the current
# relative displacement between the spring's two connection flanges (typically
# inherited from `PartialCompliant`), and $s_{rel0}$ is the relative displacement
# at which the spring exerts no force.
component Spring
  extends PartialCompliant
  # Spring constant, representing the stiffness of the spring.
  parameter c::TranslationalSpringConstant
  # Unstretched relative displacement of the spring, where the spring force is zero.
  parameter s_rel0::Distance = 0
relations
  f = c*(s_rel-s_rel0)
metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Spring.svg"}}}
end

Flattened Source

# Linear 1D translational spring relating force to displacement via Hooke's Law.
#
# This component represents a one-dimensional translational mechanical spring.
# It models the linear relationship between the force ($f$) exerted by the
# spring and its deformation ($s_{rel}$) relative to an unstretched length ($s_{rel0}$).
# The governing equation is Hooke's Law:
# ```math
# f = c \cdot (s_{rel} - s_{rel0})
# ```
# Here, `c` is the spring constant (stiffness), $s_{rel}$ is the current
# relative displacement between the spring's two connection flanges (typically
# inherited from `PartialCompliant`), and $s_{rel0}$ is the relative displacement
# at which the spring exerts no force.
component Spring
  # Port representing the first translational 1D shaft flange.
  flange_a = Flange() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Port representing the second translational 1D shaft flange.
  flange_b = Flange() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Relative distance between `flange_b` and `flange_a`
  variable s_rel::Distance
  # Internal force exerted by the compliant connection on flange_b (and -f on flange_a).
  variable f::Dyad.Force
  # Spring constant, representing the stiffness of the spring.
  parameter c::TranslationalSpringConstant
  # Unstretched relative displacement of the spring, where the spring force is zero.
  parameter s_rel0::Distance = 0
relations
  s_rel = flange_b.s-flange_a.s
  flange_b.f = f
  flange_a.f = -f
  f = c*(s_rel-s_rel0)
metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Spring.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

• Tests

  • MassDamperSpringFixedTest