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`PowerSensor`

Measures the instantaneous rotational power transmitted between two mechanical rotational splines.

This component acts as an ideal sensor to determine the power flowing through a rotational mechanical connection. Relative angular displacement between its two connectors is zero.

\[\\phi_a = \\phi_b\]

The output signal, power, represents the instantaneous power. It is calculated as the product of the torque at spline_a and the angular velocity of spline_a. The angular velocity is the time derivative of the angle of spline_a ($\dot{\phi}a$) which corresponds to `der(splinea.phi)` in the model's equations. The power is thus defined by the equation:

\[P = \\tau_a \\cdot \\dot{\\phi_a}\]

where P is the output power, $\taua$ is the torque at `splinea, and \$\\dot{\\phi}_a\$ is the angular velocity ofspline_a`.

PartialRelativeSensor

Usage

PowerSensor()

Connectors

spline_a - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
spline_b - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
power - This connector represents a real signal as an output from a component (RealOutput)

Behavior

\[ \begin{align} 0 &= \mathtt{spline\_b.tau}\left( t \right) + \mathtt{spline\_a.tau}\left( t \right) \\ \mathtt{spline\_a.phi}\left( t \right) &= \mathtt{spline\_b.phi}\left( t \right) \\ \mathtt{power}\left( t \right) &= \mathtt{spline\_a.tau}\left( t \right) \frac{\mathrm{d} \mathtt{spline\_a.phi}\left( t \right)}{\mathrm{d}t} \end{align} \]

Source

# Measures the instantaneous rotational power transmitted between two mechanical rotational splines.
#
# This component acts as an ideal sensor to determine the power flowing through a
# rotational mechanical connection. Relative angular displacement between its two
# connectors is zero.
# ```math
# \\phi_a = \\phi_b
# ```
# The output signal, `power`, represents the instantaneous power. It is calculated
# as the product of the torque at `spline_a` and the angular velocity of `spline_a`.
# The angular velocity is the time derivative of the angle of `spline_a`
# (\$\\dot{\\phi}_a\$) which corresponds to `der(spline_a.phi)` in the
# model's equations. The power is thus defined by the equation:
# ```math
# P = \\tau_a \\cdot \\dot{\\phi_a}
# ```
# where `P` is the output power, \$\tau_a\$ is the torque at `spline_a`, and \$\\dot{\\phi}_a\$ is the angular velocity of `spline_a`.
component PowerSensor
  extends PartialRelativeSensor
  # Power in spline `spline_a` as output signal
  power = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 100, "y1": 950, "x2": 200, "y2": 1050, "rot": 90}}
    }
  }]
relations
  spline_a.phi = spline_b.phi
  power = spline_a.tau*der(spline_a.phi)
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/Sensor-Power-Torque.svg"}}
}
end

Flattened Source

# Measures the instantaneous rotational power transmitted between two mechanical rotational splines.
#
# This component acts as an ideal sensor to determine the power flowing through a
# rotational mechanical connection. Relative angular displacement between its two
# connectors is zero.
# ```math
# \\phi_a = \\phi_b
# ```
# The output signal, `power`, represents the instantaneous power. It is calculated
# as the product of the torque at `spline_a` and the angular velocity of `spline_a`.
# The angular velocity is the time derivative of the angle of `spline_a`
# (\$\\dot{\\phi}_a\$) which corresponds to `der(spline_a.phi)` in the
# model's equations. The power is thus defined by the equation:
# ```math
# P = \\tau_a \\cdot \\dot{\\phi_a}
# ```
# where `P` is the output power, \$\tau_a\$ is the torque at `spline_a`, and \$\\dot{\\phi}_a\$ is the angular velocity of `spline_a`.
component PowerSensor
  # Left spline connector for the sensor.
  spline_a = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Right spline connector for the sensor.
  spline_b = Spline() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Power in spline `spline_a` as output signal
  power = RealOutput() [{
    "Dyad": {
      "placement": {"icon": {"x1": 100, "y1": 950, "x2": 200, "y2": 1050, "rot": 90}}
    }
  }]
relations
  0 = spline_a.tau+spline_b.tau
  spline_a.phi = spline_b.phi
  power = spline_a.tau*der(spline_a.phi)
metadata {
  "Dyad": {"icons": {"default": "dyad://RotationalComponents/Sensor-Power-Torque.svg"}}
}
end

Test Cases

No test cases defined.

Examples
Experiments
Analyses

PowerSensor