Interface between hydraulic and mechanical rotational domains

Hydraulic Elements

The Rotational Hydro-Mechanical Converter block models an ideal transducer that converts hydraulic energy into mechanical energy, in the form of rotational motion of the converter shaft, and vice versa. Physically, the converter represents the main component of a single-acting rotary vane actuator. The compressibility option makes the converter account for dynamic variations of the fluid density.

Using this block as a basic element, you can build a large variety of rotary actuators by adding application-specific effects, such as leakage, friction, hard stops, and so on.

The converter is simulated according to the following equations:

$$q=\frac{d\left(\frac{\rho}{{\rho}_{l}^{0}}V\right)}{dt}=\frac{d\left(\frac{\rho}{{\rho}_{l}^{0}}\right)}{dt}V+\frac{\rho}{{\rho}_{l}^{0}}\cdot \epsilon \cdot ({\omega}_{S}-{\omega}_{C})\cdot D$$

$$T=\epsilon \cdot p\cdot D$$

$$\rho =\{\begin{array}{ll}\frac{\left(\frac{\alpha}{1-\alpha}\right){\rho}_{g}^{0}+{\rho}_{l}^{0}}{\left(\frac{\alpha}{1-\alpha}\right){\left(\frac{{p}_{0}}{p}\right)}^{\frac{1}{\gamma}}+{e}^{-\frac{p-{p}_{0}}{{\beta}_{l}}}}\hfill & \text{ifcompressibilityison}\hfill \\ {\rho}_{l}^{0}\hfill & \text{ifcompressibilityisoff}\hfill \end{array}$$

where

q | Flow rate to the converter chamber |

D | Converter displacement, or fluid volume needed to rotate the shaft per angle unit |

ω_{S} | Converter shaft angular velocity |

ω_{C} | Converter case angular velocity |

T | Torque on the shaft |

p | Gauge pressure of fluid in the converter chamber |

V | Piston volume |

α | Relative amount of trapped air |

ρ_{l}^{0} | Fluid density at atmospheric conditions |

ρ_{g}^{0} | Gas density at atmospheric conditions |

p_{0} | Atmospheric pressure |

γ | Specific heat ratio |

β_{l} | Bulk modulus at atmospheric conditions and no gas |

ε | Converter orientation with respect to the globally assigned
positive direction. If pressure applied at port A generates torque
in positive direction, ε equals 1. If pressure
applied at port A generates torque in negative direction, ε equals
–1. |

The piston volume is computed according to

$$\begin{array}{l}V={V}_{dead}+D\cdot \left({\theta}_{0}+\theta \right)\\ \frac{d\theta}{dt}=\epsilon \cdot \left({\omega}_{S}-{\omega}_{C}\right)\end{array}$$

where

V_{dead} | Chamber dead volume |

θ_{0} | Shaft initial angle |

θ | Shaft rotation from initial position |

Port A is a hydraulic conserving port associated with the converter
inlet. Ports S and C are mechanical rotational conserving ports associated
with the shaft and the case of the converter, respectively. Pressure
at port A generates torque in the direction specified by the **Converter
orientation** parameter.

The block dialog box does not have a **Source code** link.
To view the underlying component source, open the following files
in the MATLAB^{®} editor:

For incompressible converter implementation —

\toolbox\physmod\simscape\library\m\+foundation\+hydraulic\+elements\rotational_converter_incompressible.ssc`matlabroot`

For compressible converter implementation —

\toolbox\physmod\simscape\library\m\+foundation\+hydraulic\+elements\rotational_converter_compressible.ssc`matlabroot`

where * matlabroot* is your root folder.

The block simulates an ideal converter, with an option to account for fluid compressibility. Other effects, such as hard stops, inertia, or leakage, are modeled outside of the converter.

**Displacement**Effective converter displacement. The default value is

`1.2e-4`

m^3/rad.**Converter orientation**Specifies converter orientation with respect to the globally assigned positive direction. The converter can be installed in two different ways, depending upon whether it generates torque in the positive or in the negative direction when pressure is applied at its inlet. If pressure applied at port A generates torque in negative direction, set the parameter to

`Acts in negative direction`

. The default value is`Acts in positive direction`

.**Compressibility**Specifies whether fluid density is taken as constant or varying with pressure. The default value is

`Off`

, in which case the block models an ideal transducer. If you select`On`

, the block dialog box displays additional parameters that let you model dynamic variations of the fluid density without adding any extra blocks.**Shaft initial angle**Initial offset of the piston from the cylinder cap. The default value is

`0`

.**Chamber dead volume**Volume of fluid in the chamber at zero piston position. The default value is

`1e-4`

m^3.**Specific heat ratio**Gas-specific heat ratio. The default value is

`1.4`

.**Initial pressure**Initial pressure in the chamber. This parameter specifies the initial condition for use in computing the block's initial state at the beginning of a simulation run. The default value is

`0`

.

The block has the following ports:

`A`

Hydraulic conserving port associated with the converter inlet.

`S`

Mechanical rotational conserving port associated with the shaft of the converter.

`C`

Mechanical rotational conserving port associated with the case of the converter.

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