An Analytical model of a radially magnetised longitudinal-flux permanent magnet air-cored linear oscillatory machine

Chembe, Dickson Kanungwe (2019-12)

Thesis (PhD)--Stellenbosch University, 2019.


ENGLISH ABSTRACT: The research presented in this dissertation is focused on the pre-optimisation-design stages of the design optimisation of air-cored radially magnetised longitudinal flux permanent magnet (LFPM) linear oscillatory machines. Electrical linear machine design optimisation involves the determination of the magnetic field, the output force and the inductance as the pre-optimisation parameters. Once the pre-optimisation parameters are solved, the design moves into the optimisation design stage and finally the experimental testing stage. The pre-optimisation stage can be achieved by employing either the finite element method (FEM) or the analytical model method. The pre-optimisation stage is as critical as the optimisation design stage for the final design of the machine to be accurate. While FEM is accurate, the determination of the pre-optimisation design parameters is time consuming and in addition, the commercial packages are expensive. This dissertation therefore focuses on the development of an analytical model to accurately simulate the pre-optimisation design parameters of an air-cored radially magnetised longitudinal flux permanent magnet linear oscillatory machine. The developed analytical model takes into consideration the finite permeability and finite thickness of the yoke materials. This has not been not been done for this kind of machine according to literature. This allows for the capability to monitor the flux concentration in the yokes to determine the saturation levels. The development of the analytical model is approached by firstly developing a model that assumes the machine to be infinitely long, while taking the machine yokes to have a finite permeability and thickness. The model is then extended to model the actual finite length of the machine and its end effects. Again the yokes are considered to have the finite permeability and thickness. The analytical model has the advantage of being much faster than FEM and can be adopted as a cheaper option for the pre-optimisation design stage. The topology of the linear oscillatory machine for which the analytical model has been developed has an air-cored tubular structure machine with surface mounted radially magnetised permanent magnets and with longitudinal flux pattern. The machine is singlephase and is intended to operate at resonant frequency (with free-piston Stirling engines as the prime mover). The analytical model for the presumably infinitely long machine as well as the analytical model for the finite (actual) length of the machine have been validated by the commercial finite element method package MagNet by infolytica inc.. The results for the analytical models correlate well with the results obtained from the FEM package. This indicates that the analytical model can be adopted in the pre-optimisation design stage as a design tool.

AFRIKAANSE OPSOMMING: Die navorsing wat in hierdie proefskrif aangebied word fokus op die vooroptimeringstadiums van die ontwerpsoptimering van lugkern radiaalgemagnetiseerde longitudinale vloed permanente magneet (LVPM) lineêre ossillerende masjiene. Lineêre elektriese masjien ontwerpsoptimering behels die bepaling van die magnetiese veld, die uittreekrag en die induktansie as die vooroptimeringsparameters. As die vooroptimeringsparameters bepaal eers is, beweeg die ontwerp aan na die optimeringsontwerpstadium en uiteindelik na die eksperimentele toetsstadium. Die vooroptimeringstadium kan bereik word deur die aanwending van of die eindige element metode (EEM) of die analitiese model metode. Die vooroptimeringstadium is net so krities as die optimeringstadium vir die finale ontwerp van die masjien om akkuraat te wees. Terwyl EEM akkuraat is, is die bepaling van die vooroptimeringsontwerpsparameters tydrowend en daarmee saam is kommersiële pakkette duur. In hierdie proefskrif word daarom gefokus op die ontwikkeling van π analitiese model om die vooroptimeringsontwerpsparameters van π lugkern radiaalgemagnetiseerde longitudinale vloed permanente magneet lineêre ossillerende masjien topologie. Die ontwikkelde analitiese model neem die eindige permeabiliteit en eindige dikte van die jukmateriaal in ag. Volgens die literatuur vir hierdie tipe masjien is dit nie voorheen gedoen nie. Dit maak die vermoë moontlik om die vloedkonsentrasie in die jukke te moniteer om die versadigingsvlakke te bepaal. Die ontwikkeling van die analitiese model is benader deur eers π model te ontwikkel wat die masjien benader as oneindig lank, terwyl die jukke geneem word met eindige permeabiliteit en dikte. Die model is dan uitgebrei om die werklike eindige lengte van die masjien en die eindeffekte te modelleer. Die jukke is weereens geneem met eindige permeabiliteit en dikte. Die analitiese model het die voordeel om baie vinniger te wees as EEM en kan aangepas word as π goedkoper opsie vir die vooroptimeringsontwerpstadium. Die topologie van die lineëre ossillerende masjien waarvoor die analitiese model ontwikkel is, het π lugkern tubulêre struktuur met oppervlakgemonteerde radiaalgemagnetiseerde permanente magnete en π longitudinale vloedpatroon. Die masjien is enkelfase en werk teen π resonante frekwensie (met vrysuier Stirling enjins as aanlegger). Die akkuraatheid van die analitiese model vir die veronderstelde oneindige lengte masjien sowel as die eindige (werklike) lengte masjien is bevestig deur die kommersiële eindige element metode pakket Magnet deur Infolytica Inc.. Die resultate van die analitiese model korreleer goed met die resultate wat van die EEM pakket verkry is. Dit dui daarop dat die analitiese model gebruik kan word in die vooroptimeringsontwerpstadium as π ontwerpsinstrument.

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