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.

$$\begin{gathered} ph{i}_a= \\ ph{i}_b \end{gathered}$$

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 ($\dot{\varphi }\ast a$) which corresponds to der(spline*a.phi) in the model's equations. The power is thus defined by the equation:

$$\begin{gathered} P= \\ ta{u}_a \\ cdot \\ dot \\ ph{i}_a \end{gathered}$$

where P is the output power, $\tau \ast a$ is the torque at spline*a, and ${\dot{\varphi }}_a$ is the angular velocity ofspline_a.

This component extends from 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

$$\begin{array}{rl}0& =\mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{tau}\left(t\right)+\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)\\ \mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{phi}\left(t\right)& =\mathtt{spline}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{phi}\left(t\right)\\ \mathtt{power}\left(t\right)& =\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{tau}\left(t\right)\frac{\mathrm{d}\mathtt{spline}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{phi}\left(t\right)}{\mathrm{d}t}\end{array}$$

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.

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