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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 ​

Test Case case1 ​