Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.

Thesis (PhD)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: Control of beta-type free-piston Stirling engines has been the topic of research and development for many years. In this dissertation, an alternative approach to free-piston Stirling engine control, namely direct piston displacement control, is proposed. Direct piston displacement control entails the instantaneous and direct control of the piston displacement to control the engine according to preferred criteria, e.g. maximum power conversion or efficiency. To control free-piston engines in this manner, it is necessary to independently control both the displacement of the displacer and the power piston in real time. The primary arrangement by which to achieve this is through external control of the instantaneous forces exerted by the linear electrical machines fixed to the pistons. The challenge of displacement control is whether suitable linear machine technology exists or whether technology could be established that would adhere to the requirements of real time direct control. To answer the question whether direct piston displacement control is at all possible, a process was followed to set specifications that linear machines should adhere to and to set design guidelines for linear machines and free-piston Stirling engines. The first step was to establish the ability to simulate free-piston Stirling engine dynamics accurately. This was done by adapting a second order formulation and to verify and improve the accuracy thereof by comparing simulated results with experimental results of one of the best documented Stirling engines, namely the GPU-3 engine. It was found that this second order formulation could simulate the GPU-3 engine to a fair degree of accuracy. Key indicators were defined and later refined with the view of setting specifications. A case study of the influence of a range of variations, including operational, dimensional and other variations, on the dynamics of the GPU-3 was then undertaken. From the findings of this case study, specifications of the key indicators and design guidelines were established. A design optimisation approach was proposed to evaluate linear machine topologies. This approach makes specific provision for the specifications that linear machines need to adhere to, as well as for representative dynamic responses of the forces exerted on the linear machine by the displacer or the power piston. These representative responses and the associated piston displacement were determined for the displacer, the power piston and the combination of the two from the study conducted to set specifications. An air-core, longitudinal flux linear machine with surface mounted permanent magnets (LFPM) was then evaluated to determine its suitability for direct piston displacement control. This linear machine topology was optimised for the traditional approach to establish a benchmark with which to compare subsequent optimisations. The LFPM linear machine not only compared well with other topologies for the traditional application in resonant free-piston Stirling engines, but it was found also to be able to perform displacement control for both the displacer and the power piston. For both pistons, displacement should however be limited to sinusoidal displacement, and in the case of the displacer, an important qualification is that the linear machine should be assisted by spring forces to reach practical design optimisations. Direct piston displacement control is shown to be possible. Future work should concentrate on the practical implementation thereof in free-piston Stirling engines. / AFRIKAANSE OPSOMMING: Die beheer van beta-tipe vrysuier Stirling enjins is al vir baie jare die onderwerp van navorsing en ontwikkeling. In hierdie proefskrif word ’n alternatiewe benadering tot vrysuier Stirlingenjins voorgestel, naamlik direkte suierverplasingsbeheer. Direkte suierverplasingsbeheer behels die oombliklike en direkte beheer van die suierverplasing om die enjin volgens voorkeur kriteria, soos maksimum drywingsomsetting of benuttingsgraad, te beheer. Om vrysuier enjins op hierdie wyse te beheer, is dit noodsaaklik om intyds die verplasing van beide die verplaser en die werksuier onafhanklik te beheer. Die primêre wyse om dit te bereik is deur eksterne beheer van die oomblikskragte wat uitgevoer word deur die lineêre masjiene wat vas is aan die suiers. Die uitdaging van verplasingsbeheer is of toepaslike lineêre masjien tegnologie bestaan en of tegnologie gevestig kan word wat sal voldoen aan die vereistes van intydse direkte beheer. Om die vraag te beantwoord of direkte suierverplasingsbeheer hoegenaamd moontlik is, is ’n proses gevolg om spesifikasies daar te stel waaraan lineêre masjiene moet voldoen en om ontwerpsriglyne vir lineêre masjiene en vrysuier Stirling enjins te stel. Die eerste stap was om die vermoë daar te stel om vrysuier Stirling enjin dinamika akkuraat te simuleer. Dit is gedoen deur ’n tweede orde formulering aan te pas en om die akkuraatheid daarvan te kontroleer en te verbeter deur gesimuleerde resultate met eksperimentele resultate van een van die bes gedokumenteerde Stirling enjins, naamlik die GPU-3 enjin, te vergelyk. Daar is bevind dat die tweede orde formulering die GPU-3 tot ’n redelike mate akkuraat kon simuleer. Sleutel aanwysers is gedefinieer en later verfyn met die oog op die daarstelling van spesifikasies. ’n Gevallestudie van die invloed van ’n reeks variasies, insluitende operasionele, dimensionele en ander variasies, op die dinamika van die GPU-3 is onderneem. Gegrond op die bevindinge van hierdie gevallestudie kon spesifikasies en ontwerpsriglyne vasgestel word. ’n Ontwerpsoptimeringsbenadering is voorgestel om lineêre masjiene te evalueer. Hierdie benadering maak spesifiek voorsiening vir die spesifikasies waaraan lineêre masjiene moet voldoen, sowel as verteenwoordigende dinamiese response van die kragte wat op die lineêre masjien van die verplaser en die werksuier uitgeoefen word. Vanaf die bevindinge van die studie wat uitgevoer is om spesifikasies daar te stel, is verteenwoordigende response en gepaardgaande suierverplasing bepaal vir die verplaser, die werksuier en die kombinasie van die twee. ’n Lugkern, longitudinale vloed lineêre masjien met oppervlak-gemonteerde permanente magnete (LVPM) is toe geëvalueer om die geskiktheid daarvan te bepaal vir direkte suierverplasingsbeheer. Hierdie lineêre masjien topologie is geoptimeer vir die tradisionele benadering om ’n maatstaf te vestig waarteen daaropvolgende optimerings vergelyk kan word. Die LVPM lineêre masjien vergelyk nie net goed met ander topologieë vir die tradisionele toepassing in resonante vrysuier Stirling enjins nie, maar daar is ook bevind dat dit in staat is om verplasingsbeheer te doen vir beide die verplaser en die werksuier. Vir beide suiers moet die verplasing egter tot sinusvormige verplasing beperk word en in die geval van die verplaser, is ’n belangrike kwalifikasie dat die lineêre masjien ondersteun moet word deur veerkragte om praktiese ontwerpsoptimerings te bereik. Daar is aangetoon dat direkte suierverplasingsbeheer moontlik is. Toekomstige werk moet konsentreer op die praktiese implementering daarvan in vrysuier Stirling enjins.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 198-201). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 198-201). Also available on the Internet.