Interface between pneumatic and mechanical rotational domains

Pneumatic Elements

The Rotational Pneumatic-Mechanical Converter block provides an interface between the pneumatic and the mechanical rotational domains. Use it as a building block for modeling pneumatic pumps and motors.

The pneumatic flow rate and mechanical rotation are related by the following equations:

$$Q=D\xb7\omega $$

$$T=\{\begin{array}{ll}D\xb7\left({p}_{A}-{p}_{B}\right)\xb7\eta \hfill & \text{for}\left({p}_{A}-{p}_{B}\right)\xb7\omega \text{=}0\hfill \\ D\xb7\left({p}_{A}-{p}_{B}\right)/\eta \hfill & \text{for}\left({p}_{A}-{p}_{B}\right)\xb7\omega \text{}0\text{}\hfill \end{array}$$

where

Q | Volumetric flow rate flowing from port A to port B |

p_{A} | Pressure at port A |

p_{B} | Pressure at port B |

ω | Shaft angular rotational speed |

T | Mechanical torque |

D | Volumetric displacement per unit rotation |

η | Converter efficiency |

The torque equation depends on the direction of power flow, and is always such that the conversion results in some thermal losses.

From considering energy flow, the heat flow out (*q _{o}*)
of the converter must equate to the heat flow in (

$${q}_{i}=\left|G\right|\xb7{c}_{p}\xb7{T}_{i}$$

$${q}_{o}=\{\begin{array}{ll}{q}_{i}-D\xb7\left({p}_{A}-{p}_{B}\right)\xb7\omega \xb7\eta \hfill & \text{for}\left({p}_{A}-{p}_{B}\right)\xb7\omega \text{=}0\hfill \\ {q}_{i}-D\xb7\left({p}_{A}-{p}_{B}\right)\xb7\omega /\eta \hfill & \text{for}\left({p}_{A}-{p}_{B}\right)\xb7\omega \text{}0\text{}\hfill \end{array}$$

where *G* is the mass flow rate.

If the pneumatic pressure drops from port A to port B, then the resulting torque is positive acting from the mechanical port C to port R.

Conversion efficiency is constant, that is, it does not depend on torque or speed.

Gas flow rate is linearly dependent of pump speed.

The process is adiabatic, that is, there is no heat transfer with the environment.

Gravitational effects can be neglected.

**Displacement**Specify the effective piston displacement, as volume per unit angle. The default value is

`.001`

m^3/rad.**Efficiency**Specify the converter efficiency. The default value is

`0.2`

.

Use the **Variables** tab in the block dialog
box (or the **Variables** section in the block Property
Inspector) to set the priority and initial target values for the block
variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

The block has the following ports:

`A`

Pneumatic conserving port associated with the converter inlet.

`B`

Pneumatic conserving port associated with the converter outlet.

`R`

Mechanical rotational conserving port associated with the piston (rod).

`C`

Mechanical rotational conserving port associated with the reference (case).

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