LIBRARY

Sources.SignTorque

Constant torque changing sign with speed.

Model of constant torque which changes sign with direction of rotation. Positive torque accelerates in both directions of rotation. Negative torque brakes in both directions of rotation. Around zero speed regularization avoids numerical problems.

This component extends from RotationalComponents.Interfaces.PartialTorque

Usage

RotationalComponents.Sources.SignTorque(tau_nominal, w0=0.1)

Parameters:

Name	Description	Units	Default value
reg	Type of regularization	–	RotationalC...ation.Exp()
tau_nominal	Nominal torque (if negative, torque is acting as load)	N.m
w0	Regularization below w0	rad/s	0.1

Connectors

• spline - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

• support - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

Variables

Name	Description	Units
phi_support	Absolute angle of the support spline	rad
phi	Angle of spline with respect to support	–
w	Angular velocity of spline with respect to support (= der(phi))	rad/s
tau	Accelerating torque acting at spline (= -spline.tau)	N.m

Behavior

using RotationalComponents #hide
using ModelingToolkit #hide
@variables tau_nominal #hide
@variables w0 #hide
@named sys = RotationalComponents.Sources.SignTorque(tau_nominal=tau_nominal, w0=w0) #hide
full_equations(sys) #hide

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

Source

"""
Constant torque changing sign with speed.

Model of constant torque which changes sign with direction of rotation.
Positive torque accelerates in both directions of rotation.
Negative torque brakes in both directions of rotation.
Around zero speed regularization avoids numerical problems.
"""
component SignTorque
  extends RotationalComponents.Interfaces.PartialTorque
  "Nominal torque (if negative, torque is acting as load)"
  parameter tau_nominal::Torque
  "Type of regularization"
  structural parameter reg::RotationalComponents.Sources.Regularization = RotationalComponents.Sources.Regularization.Exp()
  "Regularization below w0"
  parameter w0::AngularVelocity(min = eps(Float64)) = 0.1
  "Angular velocity of spline with respect to support (= der(phi))"
  variable w::AngularVelocity
  "Accelerating torque acting at spline (= -spline.tau)"
  variable tau::Torque
relations
  w = der(phi)
  tau = -spline.tau
  switch reg
    case Exp
      tau = tau_nominal * (2.0 / (1.0 + exp(-w / (0.01 * w0))) - 1.0)
    case Sine
      tau = tau_nominal * ifelse(abs(w) >= w0, sign(w), sin(π / 2 * w / w0))
    case Linear
      tau = tau_nominal * ifelse(abs(w) >= w0, sign(w), w / w0)
    case Cosine
      tau = tau_nominal * ifelse(abs(w) >= w0, sign(w), sign(w) * (1.0 - cos(π / 2 * w / w0)))
  end
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/SignTorque.svg"}}}
end

Flattened Source

"""
Constant torque changing sign with speed.

Model of constant torque which changes sign with direction of rotation.
Positive torque accelerates in both directions of rotation.
Negative torque brakes in both directions of rotation.
Around zero speed regularization avoids numerical problems.
"""
component SignTorque
  "Primary rotational shaft spline connector"
  spline = Spline() {"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}
  "Support spline connector"
  support = Spline() {
    "Dyad": {
      "placement": {"icon": {"iconName": "support", "x1": 450, "y1": 950, "x2": 550, "y2": 1050}}
    }
  }
  "Absolute angle of the support spline"
  variable phi_support::Angle
  "Angle of spline with respect to support"
  variable phi::Real
  "Nominal torque (if negative, torque is acting as load)"
  parameter tau_nominal::Torque
  "Type of regularization"
  structural parameter reg::RotationalComponents.Sources.Regularization = RotationalComponents.Sources.Regularization.Exp()
  "Regularization below w0"
  parameter w0::AngularVelocity(min = eps(Float64)) = 0.1
  "Angular velocity of spline with respect to support (= der(phi))"
  variable w::AngularVelocity
  "Accelerating torque acting at spline (= -spline.tau)"
  variable tau::Torque
relations
  support.phi = phi_support
  support.tau = -spline.tau
  phi = spline.phi - phi_support
  w = der(phi)
  tau = -spline.tau
  switch reg
    case Exp
      tau = tau_nominal * (2.0 / (1.0 + exp(-w / (0.01 * w0))) - 1.0)
    case Sine
      tau = tau_nominal * ifelse(abs(w) >= w0, sign(w), sin(π / 2 * w / w0))
    case Linear
      tau = tau_nominal * ifelse(abs(w) >= w0, sign(w), w / w0)
    case Cosine
      tau = tau_nominal * ifelse(abs(w) >= w0, sign(w), sign(w) * (1.0 - cos(π / 2 * w / w0)))
  end
metadata {"Dyad": {"icons": {"default": "dyad://RotationalComponents/SignTorque.svg"}}}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • TestBraking