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

RotationalComponents.TwoInertiasWithDrivingTorque()

Behavior

using RotationalComponents #hide
using ModelingToolkit #hide
@named sys = RotationalComponents.TwoInertiasWithDrivingTorque() #hide
full_equations(sys) #hide

<< @example-block not executed in draft mode >>

Source

"""
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() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 190, "y1": 650, "x2": 290, "y2": 750, "rot": 0}
      },
      "tags": []
    }
  }
  "Source that applies a torque to the system, driven by an external signal."
  torque = TorqueSource() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 190, "y1": 450, "x2": 290, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "First rotational inertia with moment of inertia J=2 kg.m^2."
  inertia1 = Inertia(J = 2) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 340, "y1": 450, "x2": 440, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Second rotational inertia with moment of inertia J=4 kg.m^2."
  inertia2 = Inertia(J = 4) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 680, "y1": 450, "x2": 780, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Torsional spring connecting the two inertias, with spring constant c=1e4 N.m/rad."
  spring = Spring(c = 1e4) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 500, "y1": 450, "x2": 600, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Torsional damper in parallel with the spring, with damping coefficient d=10 N.m.s/rad."
  damper = Damper(d = 10) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 500, "y1": 300, "x2": 600, "y2": 400, "rot": 0}
      },
      "tags": []
    }
  }
  "Generates a sinusoidal signal for the driving torque, with amplitude=10 and frequency=5 Hz."
  sine = BlockComponents.Sine(amplitude = 10, frequency = 5) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 450, "x2": 100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial inertia1.phi = 1
  initial inertia2.phi = 0.5
  initial inertia2.a = 0
  initial inertia2.w = 0
  connect(sine.y, torque.tau) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(torque.support, fixed.spline) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(torque.spline, inertia1.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(inertia1.spline_b, spring.spline_a, damper.spline_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [], "E": 2},
        {"S": -1, "M": [{"x": 470, "y": 350}], "E": 3}
      ],
      "junctions": [{"x": 470, "y": 500}],
      "renderStyle": "standard"
    }
  }
  connect(spring.spline_b, damper.spline_b, inertia2.spline_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [{"x": 630, "y": 350}], "E": 2},
        {"S": -1, "M": [], "E": 3}
      ],
      "junctions": [{"x": 630, "y": 500}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 1,
        "expect": {
          "initial": {"inertia1.phi": 1, "inertia2.phi": 0.5, "inertia1.w": -500, "inertia2.w ": 0}
        }
      }
    }
  }
}
end

Flattened Source

"""
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() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 190, "y1": 650, "x2": 290, "y2": 750, "rot": 0}
      },
      "tags": []
    }
  }
  "Source that applies a torque to the system, driven by an external signal."
  torque = TorqueSource() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 190, "y1": 450, "x2": 290, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "First rotational inertia with moment of inertia J=2 kg.m^2."
  inertia1 = Inertia(J = 2) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 340, "y1": 450, "x2": 440, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Second rotational inertia with moment of inertia J=4 kg.m^2."
  inertia2 = Inertia(J = 4) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 680, "y1": 450, "x2": 780, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Torsional spring connecting the two inertias, with spring constant c=1e4 N.m/rad."
  spring = Spring(c = 1e4) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 500, "y1": 450, "x2": 600, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Torsional damper in parallel with the spring, with damping coefficient d=10 N.m.s/rad."
  damper = Damper(d = 10) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 500, "y1": 300, "x2": 600, "y2": 400, "rot": 0}
      },
      "tags": []
    }
  }
  "Generates a sinusoidal signal for the driving torque, with amplitude=10 and frequency=5 Hz."
  sine = BlockComponents.Sine(amplitude = 10, frequency = 5) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 0, "y1": 450, "x2": 100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial inertia1.phi = 1
  initial inertia2.phi = 0.5
  initial inertia2.a = 0
  initial inertia2.w = 0
  connect(sine.y, torque.tau) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(torque.support, fixed.spline) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(torque.spline, inertia1.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(inertia1.spline_b, spring.spline_a, damper.spline_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [], "E": 2},
        {"S": -1, "M": [{"x": 470, "y": 350}], "E": 3}
      ],
      "junctions": [{"x": 470, "y": 500}],
      "renderStyle": "standard"
    }
  }
  connect(spring.spline_b, damper.spline_b, inertia2.spline_a) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [], "E": -1},
        {"S": -1, "M": [{"x": 630, "y": 350}], "E": 2},
        {"S": -1, "M": [], "E": 3}
      ],
      "junctions": [{"x": 630, "y": 500}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 1,
        "expect": {
          "initial": {"inertia1.phi": 1, "inertia2.phi": 0.5, "inertia1.w": -500, "inertia2.w ": 0}
        }
      }
    }
  }
}
end

Test Cases

using RotationalComponents
using DyadInterface: TransientAnalysis, rebuild_sol
using ModelingToolkit: toggle_namespacing, get_defaults, @named
using CSV, DataFrames, Plots

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

<< @setup-block not executed in draft mode >>

Test Case case1

@named model_case1 = TwoInertiasWithDrivingTorque()
model_case1 = toggle_namespacing(model_case1, false)

model_case1 = toggle_namespacing(model_case1, true)
result_case1 = TransientAnalysis(; model = model_case1, alg = "auto", start = 0e+0, stop = 1e+0, abstol=1e-6, reltol=1e-6)
sol_case1 = rebuild_sol(result_case1)

<< @setup-block not executed in draft mode >>

Related

• Examples

• Experiments

• Analyses

• Tests

  • Damper

  • Fixed

  • Inertia

  • Sine

  • Spring

  • TorqueSource