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RESEARCH PAPERS

# Profiling Rotors for Limaçon-to-Limaçon Compression-Expansion Machines

[+] Author and Article Information
Ibrahim A. Sultan

School of Science and Engineering, The University of Ballarat, P.O. Box 663, Ballarat 3353 Victoria, Australiai.sultan@ballarat.edu.au

J. Mech. Des 128(4), 787-793 (Aug 13, 2005) (7 pages) doi:10.1115/1.2202877 History: Received April 07, 2005; Revised August 13, 2005

## Abstract

Limaçon-to-limaçon compression-expansion machines have housings and rotors whose profiles are manufactured of limaçon curves. For these machines to perform satisfactorily, extreme care should be given to the geometric particulars of their rotor profile. The main characteristics that govern the quality of the rotor profile are the volumetric efficiency and the prevention of interference. In this work, the interference problem is handled from two different mathematical standpoints: the slope of tangents to both the rotor and housing curves at the apices; and the value of the minimum radial clearance that separates the two limaçon curves. In the first case, mathematical expressions, relating the radii of the limaçon base circles is presented to ensure that interference would not take place during normal operations of the limaçon-to-limaçon machine. The second mode of analysis produces a set of nonlinear equations that can be solved to obtain a value of the radial clearance. This value has to be machined off the rotor profile to prevent interference. A numerical example is given at the end of the paper to prove the validity of the models proposed and graphs are produced to support the claims presented.

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## Figures

Figure 3

The limaçon rotor at its horizontal position

Figure 4

Volume calculations

Figure 5

Interference based on apex tangents

Figure 6

Developing the interference equations

Figure 1

A limaçon mechanism

Figure 2

A limaçon compression-expansion machine

Figure 7

Δ, as calculated at α=20°, b=0.18, and C=0mm

Figure 8

Δ3∕2π∕L against the aspect ratio and the a value

Figure 9

Rvol against the aspect ratio and the a value

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