# Rotational Pneumatic-Mechanical Converter

Interface between pneumatic and mechanical rotational domains

## Library

Pneumatic Elements

## Description

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:

`$Q=D·\omega$`

where

 Q Volumetric flow rate flowing from port A to port B pA Pressure at port A pB 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 (qo) of the converter must equate to the heat flow in (qi) minus mechanical work done. Therefore, the heat equations are:

`${q}_{i}=|G|·{c}_{p}·{T}_{i}$`

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.

## Basic Assumptions and Limitations

• 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.

## Dialog Box and Parameters

### Parameters Tab

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`.

### Variables Tab

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.

## Ports

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).