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TwoInertiasWithDrivingTorque.md

TwoInertiasWithDrivingTorque ​

A mechanical system of two rotational inertias coupled by a spring and damper, driven by a sinusoidal torque.

This model represents a dynamic system where a primary rotational inertia (inertia1) is subjected to an external torque generated by a sinusoidal source. This first inertia is mechanically coupled to a second rotational inertia (inertia2) through a torsional spring and a torsional damper, which are arranged in parallel. The torque source is referenced to a fixed ground. Initial conditions for angular positions, and implicitly angular velocities through the initial acceleration constraint, define the starting state of the system.

Usage ​

TwoInertiasWithDrivingTorque()

Behavior ​

[sine.y(t)=torque.tau(t)connect(torque+support,fixed+spline)connect(torque+spline,inertia1+splinea)connect(inertia1+splineb,spring+splinea,damper+splinea)connect(spring+splineb,damper+splineb,inertia2+splinea)fixed.spline.phi(t)=fixed.phi0torque.support.phi(t)=torque.phi_support(t)torque.support.tau(t)=−torque.spline.tau(t)torque.phi(t)=torque.spline.phi(t)−torque.phi_support(t)torque.spline.tau(t)=−torque.tau(t)inertia1.phi(t)=inertia1.spline_a.phi(t)inertia1.phi(t)=inertia1.spline_b.phi(t)dinertia1.phi(t)dt=inertia1.w(t)dinertia1.w(t)dt=inertia1.a(t)inertia1.Jinertia1.a(t)=inertia1.spline_b.tau(t)+inertia1.spline_a.tau(t)inertia2.phi(t)=inertia2.spline_a.phi(t)inertia2.phi(t)=inertia2.spline_b.phi(t)dinertia2.phi(t)dt=inertia2.w(t)dinertia2.w(t)dt=inertia2.a(t)inertia2.Jinertia2.a(t)=inertia2.spline_b.tau(t)+inertia2.spline_a.tau(t)spring.phi_rel(t)=spring.spline_b.phi(t)−spring.spline_a.phi(t)spring.spline_b.tau(t)=spring.tau(t)spring.spline_a.tau(t)=−spring.tau(t)spring.tau(t)=spring.c(−spring.phi_rel0+spring.phi_rel(t))damper.phi_rel(t)=−damper.spline_a.phi(t)+damper.spline_b.phi(t)damper.spline_b.tau(t)=damper.tau(t)damper.spline_a.tau(t)=−damper.tau(t)ddamper.phi_rel(t)dt=damper.w_rel(t)ddamper.w_rel(t)dt=damper.a_rel(t)damper.tau(t)=damper.ddamper.w_rel(t)sine.y(t)=ifelse(sine.start_time<t,sine.offset+sine.amplitudesin⁡(sine.phase+6.2832sine.frequency(−sine.start_time+t)),sine.offset)]

Source ​

dyad
# A mechanical system of two rotational inertias coupled by a spring and damper, driven by a sinusoidal torque.
#
# This model represents a dynamic system where a primary rotational inertia
# (inertia1) is subjected to an external torque generated by a sinusoidal source.
# This first inertia is mechanically coupled to a second rotational inertia
# (inertia2) through a torsional spring and a torsional damper, which are arranged
# in parallel. The torque source is referenced to a fixed ground.
# Initial conditions for angular positions, and implicitly angular velocities
# through the initial acceleration constraint, define the starting state of the system.
test component TwoInertiasWithDrivingTorque
  # Represents a fixed mechanical ground or reference frame.
  fixed = Fixed()
  # Source that applies a torque to the system, driven by an external signal.
  torque = TorqueSource()
  # First rotational inertia with moment of inertia J=2 kg.m^2.
  inertia1 = Inertia(J=2)
  # Second rotational inertia with moment of inertia J=4 kg.m^2.
  inertia2 = Inertia(J=4)
  # Torsional spring connecting the two inertias, with spring constant c=1e4 N.m/rad.
  spring = Spring(c=1e4)
  # Torsional damper in parallel with the spring, with damping coefficient d=10 N.m.s/rad.
  damper = Damper(d=10)
  # Generates a sinusoidal signal for the driving torque, with amplitude=10 and frequency=5 Hz.
  sine = BlockComponents.Sine(amplitude=10, frequency=5)
relations
  initial inertia1.phi = 1
  initial inertia2.phi = 0.5
  initial inertia2.a = 0
  connect(sine.y, torque.tau)
  connect(torque.support, fixed.spline)
  connect(torque.spline, inertia1.spline_a)
  connect(inertia1.spline_b, spring.spline_a, damper.spline_a)
  connect(spring.spline_b, damper.spline_b, inertia2.spline_a)
metadata {
  "Dyad": {
    "tests": {
      "case1": {
        "stop": 1,
        "expect": {
          "initial": {"inertia1.phi": 1, "inertia2.phi": 0.5, "inertia1.w": -500, "inertia2.w ": 0}
        }
      }
    }
  }
}
end
Flattened Source
dyad
# A mechanical system of two rotational inertias coupled by a spring and damper, driven by a sinusoidal torque.
#
# This model represents a dynamic system where a primary rotational inertia
# (inertia1) is subjected to an external torque generated by a sinusoidal source.
# This first inertia is mechanically coupled to a second rotational inertia
# (inertia2) through a torsional spring and a torsional damper, which are arranged
# in parallel. The torque source is referenced to a fixed ground.
# Initial conditions for angular positions, and implicitly angular velocities
# through the initial acceleration constraint, define the starting state of the system.
test component TwoInertiasWithDrivingTorque
  # Represents a fixed mechanical ground or reference frame.
  fixed = Fixed()
  # Source that applies a torque to the system, driven by an external signal.
  torque = TorqueSource()
  # First rotational inertia with moment of inertia J=2 kg.m^2.
  inertia1 = Inertia(J=2)
  # Second rotational inertia with moment of inertia J=4 kg.m^2.
  inertia2 = Inertia(J=4)
  # Torsional spring connecting the two inertias, with spring constant c=1e4 N.m/rad.
  spring = Spring(c=1e4)
  # Torsional damper in parallel with the spring, with damping coefficient d=10 N.m.s/rad.
  damper = Damper(d=10)
  # Generates a sinusoidal signal for the driving torque, with amplitude=10 and frequency=5 Hz.
  sine = BlockComponents.Sine(amplitude=10, frequency=5)
relations
  initial inertia1.phi = 1
  initial inertia2.phi = 0.5
  initial inertia2.a = 0
  connect(sine.y, torque.tau)
  connect(torque.support, fixed.spline)
  connect(torque.spline, inertia1.spline_a)
  connect(inertia1.spline_b, spring.spline_a, damper.spline_a)
  connect(spring.spline_b, damper.spline_b, inertia2.spline_a)
metadata {
  "Dyad": {
    "tests": {
      "case1": {
        "stop": 1,
        "expect": {
          "initial": {"inertia1.phi": 1, "inertia2.phi": 0.5, "inertia1.w": -500, "inertia2.w ": 0}
        }
      }
    }
  }
}
end


Test Cases ​

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

julia
using RotationalComponents
using ModelingToolkit, OrdinaryDiffEqDefault
using Plots
using CSV, DataFrames

snapshotsdir = joinpath(dirname(dirname(pathof(RotationalComponents))), "test", "snapshots")
"/home/actions-runner-10/.julia/packages/RotationalComponents/0VPxm/test/snapshots"

Test Case case1 ​

julia
@mtkbuild model_case1 = TwoInertiasWithDrivingTorque()
u0_case1 = []
prob_case1 = ODEProblem(model_case1, u0_case1, (0, 1))
sol_case1 = solve(prob_case1)
retcode: Success
Interpolation: 3rd order Hermite
t: 85-element Vector{Float64}:
 0.0
 0.001741101126589462
 0.004219151423183404
 0.007390864690109434
 0.011322960645592586
 0.015896047994834458
 0.020955577415067525
 0.02747487111254223
 0.033626680113946
 0.04109101569458323
 ⋮
 0.9304547216375303
 0.9396185689845381
 0.9496806215701978
 0.9595166735894302
 0.9671742935600001
 0.9762955183064588
 0.9861108909071538
 0.9962774736550695
 1.0
u: 85-element Vector{Vector{Float64}}:
 [0.5, 1.0, -0.0, -500.0]
 [0.4989052349941844, 0.1316391048747763, -1.8828569522820653, -496.2340480665899]
 [0.4845789392409978, -1.0787316255265904, -10.887648273020629, -478.2233073936973]
 [0.4187186117814805, -2.5328590275740974, -32.39365247078328, -435.2084240704959]
 [0.2176930137676368, -4.096828584375997, -71.89733672908721, -356.1953627306581]
 [-0.23955971781536456, -5.46880070877337, -129.49468675523957, -240.99118973836]
 [-1.0667244288415147, -6.344104100049989, -197.14929701800887, -105.66814410899657]
 [-2.6057053121857585, -6.52550183337916, -270.66772021991585, 41.39113700716393]
 [-4.405446612131925, -6.001505473451473, -308.16480553726495, 116.41046213612312]
 [-6.711992508605791, -5.11985191790964, -299.9408977757787, 99.99698487088443]
 ⋮
 [-154.42544770878945, -154.2242290591094, -165.1518846818742, -169.44496370176682]
 [-155.92212534071598, -155.81067983722372, -161.70706560013207, -176.3754510247057]
 [-157.54545452781116, -157.59317912706567, -161.30098852090114, -177.23720639613833]
 [-159.14569489408223, -159.30938308379544, -164.28919189745494, -171.30946755480207]
 [-160.41670649649814, -160.59544627877116, -167.6680191357831, -164.58678505084706]
 [-161.96114351739865, -162.06664538585008, -170.8046956163836, -158.34881309421922]
 [-163.64202034800542, -163.61230733249562, -171.40596090840387, -157.1736081145332]
 [-165.37291602040156, -165.23373775280427, -168.89554858495282, -162.20831664129014]
 [-165.99900204853537, -165.8428290590023, -167.472359729937, -165.0557820733616]