positive displacement machines

Technical paper by John E. Beard of the Michigan Technological University + G.R. Pennock of the Purdue University

2000, 11 pages

> Content
  » Abstract  2
  » Nomenclature  2
  » 1. Introduction  3
  » 2. Kinematics of the seal motion  3
  » 3. Results + conclusions  6
  » References  7
  » Figures 1-6 » 8

german keywords: Wankelmotor / Kreiskolbenmotor
English Keywords: Wankel Engine / Wankel Rotary Engine / Rotary Piston Engine / Rotary Combustion Engine

PurposeThis paper aims to replace the complicated iterative procedure used to prevent interference in limaçon‐to‐limaçon machines by a simplified mathematical equation which can be solved by a straightforward substitution of the required clearance value.Design/methodology/approachThe input data to the iterative procedure and the obtained results have been employed in regression models to construct the sought after equation. Searching for a proper form of this equation involved numerical experiments to study the effects of the various model parameters on the system response.FindingsThe numerical experiments conducted proved to be an effective model construction technique, and the regression model proposed has been found extremely accurate in the specified parameter space.Research limitations/implicationsThe proposed equation is applicable within the parameter range chosen for the study. This range is the one often used for industrial applications. Should the parameters selected for a...

Rotary machines, and limaçon machines in particular, offer a better power to weight ratio compared to reciprocating machines; however, leakage due to improper apex and side sealing have prevented rotary machines from thriving. In this paper, a modelling approach is presented to analyse the vibration of apex seal during the machine operation and the power loss caused by the seal friction. The seal and spring are modelled as a spring-mass system in which the seal deformation is negligible. The seal-groove relative positions have then been categorised into nine different possible cases based on the number of contact points between the seal and the seal groove. A case study has been presented to demonstrate the reliability of the model.

Rotary machines, and limaçon machines in particular, offer a better power to weight ratio compared to reciprocating machines; however, leakage due to improper apex and side sealing have prevented rotary machines from thriving. In this paper, a modelling approach is presented to analyse the vibration of apex seal during the machine operation and the power loss caused by the seal friction. The seal and spring are modelled as a spring-mass system in which the seal deformation is negligible. The seal-groove relative positions have then been categorised into nine different possible cases based on the number of contact points between the seal and the seal groove. A case study has been presented to demonstrate the reliability of the model.

Inverse design techniques in the area of fluid mechanics are normally conducted for continuous flow turbomachines rather than positive displacement devices. However, the work in this paper is concerned with a class of rotary positive displacement device referred to as the limaçon-to-limaçon machine. The rotors and housings of these machines are manufactured of limaçon profiles, and are likely to suffer from interference if the rotors are not carefully profiled. Published literature indicates that solutions proposed to tackle the interference problem in these machines will adversely affect their efficiency figures. This notion motivated the work presented in this paper, which first introduces the relevant mathematical models of the limaçon-to-limaçon machine and then uses these models to construct an inverse geometric design problem formulation. The proposed model has been coded in a computer program that utilises a Marquardt-Levenberg technique to converge to the required geometric parameters. Case studies are presented at the end of the paper to verify the validity of the proposed inverse design model.

A circolimaçon positive displacement machine is driven by a limaçon mechanism, but the profiles of its rotor and housing are circular arcs. As such its design models are different from those of the limaçon-to-limaçon machines, whose profiles are cut to the limaçon equations. For the benefit of the reader, the paper starts with a brief background on the general geometric aspects of the limaçon fluid processing technology. However the focus is then turned to the circolimaçon machine, where its design parameters are introduced and geometric models are proposed to assist with the design process. Also, a computational inverse design model has been employed to work out a set of congruent geometric parameters to meet certain design requirements. Case studies are presented at the end of the paper to give the reader a numerical perspective on the design process of this class of positive displacement machines.

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 which 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 stand points: 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 non-linear 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.

The limaçon of Pascal is a plane curve that possesses some characteristics which qualify it for fluid processing applications. However, the curve has not yet attracted enough attention, neither from industry nor from the mechanical engineering research community, despite the few attempts that have been conducted over the past century.

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 which 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 stand points: 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 non-linear 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.

Inverse design techniques in the area of fluid mechanics are normally conducted for continuous flow turbomachines rather than positive displacement devices. However, the work in this paper is concerned with a class of rotary positive displacement device referred to as the limaçon-to-limaçon machine. The rotors and housings of these machines are manufactured of limaçon profiles, and are likely to suffer from interference if the rotors are not carefully profiled. Published literature indicates that solutions proposed to tackle the interference problem in these machines will adversely affect their efficiency figures. This notion motivated the work presented in this paper, which first introduces the relevant mathematical models of the limaçon-to-limaçon machine and then uses these models to construct an inverse geometric design problem formulation. The proposed model has been coded in a computer program that utilises a Marquardt-Levenberg technique to converge to the required geometric parameters.

A circolimaçon positive displacement machine is driven by a limaçon mechanism, but the profiles of its rotor and housing are circular arcs. As such its design models are different from those of the limaçon-to-limaçon machines, whose profiles are cut to the limaçon equations. For the benefit of the reader, the paper starts with a brief background on the general geometric aspects of the limaçon fluid processing technology. However the focus is then turned to the circolimaçon machine, where its design parameters are introduced and geometric models are proposed to assist with the design process. Also, a computational inverse design model has been employed to work out a set of congruent geometric parameters to meet certain design requirements. Case studies are presented at the end of the paper to give the reader a numerical perspective on the design process of this class of positive displacement machines.