PartialCompliantWithRelativeStates

Defines relative angular states for compliant rotational connections.

This partial component extends a base compliant model by explicitly defining the relative angular velocity ($w_{rel}$) and relative angular acceleration ($a_{rel}$) between two connected rotational elements. These variables are intended to be used as preferred state variables. The core dynamics are described by the differential equations:

$$\begin{array}{r}\frac{d{\varphi }_{rel}}{dt}=w_{rel}\\ \frac{d{w}_{rel}}{dt}=a_{rel}\end{array}$$

where ${\varphi }_{rel}$ (relative angle) is assumed to be defined in the extended or extending components. This formulation is common in mechanical systems where relative motion is of primary interest.

PartialCompliant

Usage

PartialCompliantWithRelativeStates()

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)

Variables

Name	Description	Units
phi_rel	Relative rotation angle between spline_b and spline_a	rad
tau	Torque transmitted between the splines	N.m
w_rel	Relative angular velocity between splines	rad/s
a_rel	Relative angular acceleration between splines	rad/s2

Source

# Defines relative angular states for compliant rotational connections.
#
# This partial component extends a base compliant model by explicitly defining the relative angular velocity ($w_{rel}$) and relative angular acceleration ($a_{rel}$) between two connected rotational elements. These variables are intended to be used as preferred state variables. The core dynamics are described by the differential equations:
# ```math
# \begin{align*}
# \frac{d\phi_{rel}}{dt} = w_{rel}\\
# \frac{dw_{rel}}{dt} = a_{rel}
# \end{align*}
# ```
# where $\phi_{rel}$ (relative angle) is assumed to be defined in the extended or extending components. This formulation is common in mechanical systems where relative motion is of primary interest.
partial component PartialCompliantWithRelativeStates
  extends PartialCompliant
  # Relative angular velocity between splines
  variable w_rel::AngularVelocity
  # Relative angular acceleration between splines
  variable a_rel::AngularAcceleration
relations
  der(phi_rel) = w_rel
  der(w_rel) = a_rel
end

Flattened Source

# Defines relative angular states for compliant rotational connections.
#
# This partial component extends a base compliant model by explicitly defining the relative angular velocity ($w_{rel}$) and relative angular acceleration ($a_{rel}$) between two connected rotational elements. These variables are intended to be used as preferred state variables. The core dynamics are described by the differential equations:
# ```math
# \begin{align*}
# \frac{d\phi_{rel}}{dt} = w_{rel}\\
# \frac{dw_{rel}}{dt} = a_{rel}
# \end{align*}
# ```
# where $\phi_{rel}$ (relative angle) is assumed to be defined in the extended or extending components. This formulation is common in mechanical systems where relative motion is of primary interest.
partial component PartialCompliantWithRelativeStates
  # First rotational spline interface
  spline_a = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Second rotational spline interface
  spline_b = Spline() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Relative rotation angle between spline_b and spline_a
  variable phi_rel::Angle
  # Torque transmitted between the splines
  variable tau::Torque
  # Relative angular velocity between splines
  variable w_rel::AngularVelocity
  # Relative angular acceleration between splines
  variable a_rel::AngularAcceleration
relations
  phi_rel = spline_b.phi-spline_a.phi
  spline_b.tau = tau
  spline_a.tau = -tau
  der(phi_rel) = w_rel
  der(w_rel) = a_rel
metadata {}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses