Mathematical models and solutions for the embedded design of ...

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MOTOR DESIGN MATHEMATICAL MODELS EMEBEDDED DESIGN

NATURAL AND ARTIFICIAL RESOURCES RATIONAL USE

Mathematical models and solutions for the embedded design of motors with a view to a rational use of natural and artificial resources NICOLAE VASILE, MIHAELA CHEFNEUX, LEONARD MELCESCU, MIRCEA RĂDULESCU, ALECSANDRU SIMION, ION VONCILĂ∗

Modele matematice şi soluţii pentru proiectarea integrată a motoarelor în vederea asigurării unei utilizări raţionale a resurselor naturale şi artificiale The project objective aims at the sustainable management of resources, carrying out mathematical models for a new approach to the electric machines design, finding the optimum solutions from the environmental point of view. The purpose is to elaborate an algorithm for the optimum design and a design guide and to identify solutions for selecting minimum criteria from both technical and environmental point of view.

1. Introduction Electrical machines are nowadays among the most used products and are mostly used to transform electrical energy into mechanical energy, priority should be given to the reuse of the waste electrical equipment according to the European directives. Producers should be encouraged to integrate recycled material in the new equipment. In order to give maximum effect to the concept of producer responsibility, each producer should be responsible for financing the management of the waste from his own products. Would be necessary that any electrical machine producer, when placing a product on the market, provide a financial guarantee to prevent costs of the management of the waste electrical machine. The European Parliament, in its Resolution of 14 November 1996 asked the European Commission to present proposals for directives on a number of priority waste streams, including electrical and electronic waste and to base such proposals on the principle of the producer responsibility. These directives, among which we have to mention especially the Directive 2002/96/EC of The European Parliament and of The Council of 27 January 2003 on the waste electrical and electronic equipment, insist on the fact that the management of the particular categories of waste cannot be achieved effectively by the Member States acting individually; different national applications of the producer responsibility principle may lad to substantial disparities in the financial burden on economic operators. Having different national policies on the ∗

Prof.dr.ing. Vasile Nicolae, ing. Chefneux Mihaela - ICPE-SA Institutul de Cercetări Electrotehnice; drd.ing. Melcescu Leonard Universitatea POLITEHNICA Bucureşti, Centrul de Cercetare Ştiinţifică Echipamente de conversie electromecanică a energiei; prof.dr.ing. Rădulescu Mircea - Universitatea Tehnică din ClujNapoca, UTCN, prof.dr.ing. Simion Alecsandru - Universitatea Tehnică „Gh. Asachi” – UTI (Iaşi), conf.dr.ing. Voncilă Ion Universitatea „Dunărea de Jos” UDJ, Galaţi.

management of the waste electrical and electronic equipment hampers the effectiveness of the recycling policies. That is why the essential criteria should be laid down at the Community level. The establishment, by these Directives, of the producer responsibilities is one of the means of encouraging the design and production of electrical equipment which takes into full account and facilitates their repair, the possible upgrading, reuse, disassembly and recycling. The amount of the waste generated by the electrical equipment is growing rapidly, the content of hazardous components is a major concern during the waste management. The purpose of the Directives is the prevention of waste electrical and electronic equipment and the reuse, recycling and other forms of recovery of such wastes so as to reduce the disposal of waste. It also seeks to improve the environmental performance of all operators involved in the life cycle of products (producers, distributors and consumers). 2. New approach to electric machines design The development approach to the electrical machines was always done for improving their technical characteristics. The reducing of electrical machine gauge was done taking into consideration, as main machine characteristics, the values of power/mass and torque/mass parameters, especially for servomotors. Servomotors will be studied in this project and all the results will be applied to the other electrical machines such as: generators, speed transducers, position transducers, a.s.o. The researches in the field of the materials used for electrical machines’ construction were made in order to look for those material types which could assure maximum technical characteristic values for minimum gauge value of the electric machine. For example, laminations having specific iron losses as low as possible (there are used laminations with values < 0.9W/kg) were developed for making the magnetic

50 ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 3 - 4 yoke or, regarding insulating materials, nowadays with very good and competitive technical there are used in electrical machine construction performances. The specialists, members of this consortium are materials for H class insulation degree (180 °C) instead of the traditional ones for F class insulation known abroad for their work. They succeeded in designing and implementing in production electrical degree (155 °C). machines with original constructive configurations, In the main, a rotating electric machine is made of: • stator- has magnetic yoke made of laminations patented ones, and they took into consideration the with slots in which there is the copper winding, project theme (regarding electrical equipment waste) the insulation layer being put between the without having it in mind as main goal. The consortium includes by the following laminations and the wires; after the winding has been made the stator is impregnated in order to universities and research institutes: • ICPE- Research Institute for Electrical stuff the construction; this magnetic circuit Engineering. could be induction type for motors or inducted • “Politehnica” University from Bucharest. type for generators; on the stator for different • UTCN (Cluj-Napoca University). machine constructions there could be placed • UTI (Gh. Asachi Iaşi University). permanent magnets (d.c. electric machine); • UDJ Galaţi. • rotor- can be made of laminations or of iron in The existence of an implementation plan for various constructions :squirrel cage rotor, with windings, with permanent magnets, with 2002/96/EC Directive with responsibilities for the Ministry of Environment and Water Management, commutator (for d.c. electric machines) • other components: shields, housing, shaft, Ministry of Economy and Trade proves the desirability of the proposed theme, which offers the theoretic connectors. Obviously, we cannot synthesize all kinds of instrument for waste electrical machine management rotating electric machines this project works with, nor since their research and design phase. Project objective: Mathematical models and the various construction solutions. All these will be analysed in this project in order to get a solutions for the design of motors with a view to a systematization of all the rotating electric machine rational use of natural and artificial RESOURCES, will constructions and new solutions will be proposed, so be carried out by getting over the 6 stages included in all the elements which have a negative impact on the the project execution plan:
study concerning the project execution; environment will be discovered.
mathematical modelling of the variants of The disassembling of a rotating electric machine in electrical machines; its components (main components: laminations,
analysis and evaluation systems for d.c. copper, aluminium, etc.) is very difficult because, in motors; the design process, this aspect was not taken into
analysis and evaluation systems for a.c. consideration. The impregnation process used to stuff motors; the construction causes all the problems of
transfer of results and implementation in the disassembling. In order to recover copper from the partners’ organising structures; winding we have to burn the insulating materials, so
large – scale dissemination of the project the noxious gas appears with negative impact on the results. environment; also, the energy used for burning is The project objective aims at the sustainable important as value. For the induction motors with squirrel cage rotors in order to recover the aluminium it management of resources by introducing some terms is necessary to melt the rotor and a lot of energy is since the design stage of rotating electrical machine used for this process. That is why usually, we don’t construction which will foresee that at the production recover aluminium from the induction machine rotors waste, the dismantling and recovery of the used materials will be made (iron, copper, aluminium, etc.); only for big or very big size machines. We can say that, nowadays, regarding the waste so, there will result design methods in accordance with management for the rotating electric machines it is the European directives in environmental field. In order to execute the project objective, there were very difficult to observe the stipulations of the European Community. It is obviously necessary to stipulated measurable specific objectives within each have a new design concept for the new rotating stage:
establishing the direction for reaching the level electric machines introduced in production in order to of compatibility with the European research recover a major part of the component materials when area in the field of sustainable management of they will be wasted (now, we can recover maximum natural and artificial resources for electrical 5% of materials for the existing products). machines (for all life cycle);
elaborating the mathematical models for 3. Main objectives of the projects electrical machine design; The consortium that is carrying out the present
elaborating the mathematical models and project has special achievements in the field of criteria for an electrical machine design theme research, design and production of electrical machines taking into consideration not only its technical

51 as it is a far-reaching project for the research activity development, aiming at:
developing the fundamental research for the acquisition of advanced knowledge in the field of optimal electrical machine design from the environmental point of view;
increasing the scientific value and visibility at the international level large scale dissemination of project results;
integrating in the technological platform PT4 (Advanced engineering materials and technologies);
developing research activities and infrastructures at the regional level with a social and economic impact;
joining the priorities and objectives specific to the European research area.

ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 55 (2007), Nr. 3 - 4

characteristics but also the construction elements for a sustainable waste management;
estimation of environment impact on the chosen solutions;
developing the design algorithms of electrical machines from the environmental point of view;
evaluation of the solution efficiency from the technical and environmental point of view;
implementation of the results at the partners’ place;
establishing the directions from the research activity of the participating units, as well as the optimal way of the research capitalization with a view to developing some sustainable management systems of resources by optimizing electrical machine design;
large- scale dissemination of information by organizing some scientific events (workshops) for project results’ presentation;
elaboration of a design guide which will be used in universities and research institutes in order to ensure the efficient design of the electrical machine prototypes;
elaboration of scientific papers with a view to increasing the visibility at the international level;
developing a Web site. Proposed theme: Mathematical models and solutions for the design of motors with a view to a rational use of natural and artificial resources belongs to the general and specific objectives of the programme “Excellence research”, pursuing:
increase of the R-D-I system capacity from Romania to store knowledge, results and first rate experience in the scientific and technological field by offering a new electrical machine design concept, taking into consideration the environment management respectively not only the technical characteristics but also the sustainable management of natural and artificial resources;
concentration and optimal capitalization of the scientific and technological potential from Romania in the field of electrical machine;
setting up, development, integration and consolidation in the field of electrical machine whose activity should reach the excellence level;
expediting the process of technological integration and compliance with the EU requirements and regulations in the field of electrical machine production which will take into consideration the rational use of natural and artificial resources;
increasing Romania’s capacity of ensuring highly efficient partners for the international scientific co-operation programmes (especially PC7) in the thematic field: Environment; Sustainable management of resources. The project is proposed within Module 1: “The module of complex research-development projects”,

4. State of the art and results obtained until now The project started with the study concerning the project execution for establishing the direction for reaching the level of compatibility with the European research area in the field of sustainable management of natural and artificial resources for electrical machines (for all life cycle). The second stage of the project consisted in the mathematical modelling of the variants of electrical machines, that was performed by elaborating the mathematical models and criteria for an electrical machine design theme taking into consideration not only its technical characteristics but also the construction elements for a sustainable waste management. Elaborating the mathematical models for electrical machine design and estimation of environment impact of the chosen solutions. The consortium set up for the project execution has had in view, in the last few years, the punctual approach to some issues specific to the rotating electric machine design. ICPE, the project coordinator, especially the research team that will work for this project, has remarkable performances regarding electric machine research and design, especially brushless servomotors which are manufactured with competitive performances and are sold abroad: in Germany, USA, Israel, etc. Until now there was not approached the optimised design of rotating electric machines regarding the environment that is why it is absolutely necessary to proceed soon in this direction. The directions that have been taken into consideration to achieve the project objective are:
finding the polluting elements among the rotating electric machine components, from the construction process, running period and waste;
identifying the percentage of recovering the materials from rotating electric machine component according to the European directives;

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finding out the directions of changes in the rotating electric machines’ technological process as: • design and execution of windings outside the magnetic circuit; • magnetic circuit design without slots- if it is possible; • assemble components to be used in making the windings; • squirrel cage aluminium to be made outside the magnetic yoke. analyzing different components’ materials and choosing some that could be disassembled in an easier way; analyzing the influence of the optimum solutions found from the environmental point of view on the main technical characteristics of the machines; selection of minimum criteria from the technical performance point of view; studies over d.c. motors with commutator and a.c. motors; mathematical modelling of design method for both studies; solution generalization for rotating electric machine (including its modelling); elaboration of an algorithm for optimum design and of a design guide;




identifying some solutions to promote the rotating electric machine design regarding the environment.

4.1. Mathematical model of the ideal electric machine For the ideal electric machine, we start from the following conditions: • the magnetic energy is stored only in the gap; • the magnetic fields have spatial and time sinusoidal variations; • the magnetic field has a plan symmetry; • we may use the superposition of effects for magnetic fields produced by several windings; • there are no losses. Because there are no losses and the machine functions in thermal stabilized regime, the equivalent converter communicates with the outer space only by two types of circuits: • electric circuits • mechanic circuits In Fig. 1.a, there is presented the energetic model of an equivalent converter, functioning as a generator, where, for simplifying, there are represented only two electric circuits, one generator and the other receiver, and the mechanical circuit.

Fig. 1. Energetic model of an equivalent convertor, functioning as a generator.

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For this structure the mathematical model is made up of the circuit voltage equation system, the magnetic flux equation system, the conversion equation corresponding to the electromagnetic torque and the speed

• •

mem •

[Φ] = [L pm ] [i ]

m em

Ω=

dt 1 d = [i ]T [Φ ] 2 dθ

• •

dθ( t ) dt

•

[ueu ] is the column matrix of output voltages,

•

[i ], [i ]

4.2. Mathematical model of the real electric machine The mathematical model of the real machine is obtained by completing the mathematical model of the ideal machine, with the elements needed for the energy. For obtaining the mathematical model of the real converter, we need to complete the equivalent converter model, so to consider: • energy corresponding to Joule losses; • magnetic energy (inductance losses); • magnetic energy – mutual inductance; • correction regarding saturation effects; • mechanical losses; • external torque. The mathematical model of the real converter is:

[u b ] = [Re ] [i ] + d [Φ] dt [L] = [Lσ ] + [Lu ] [Φ ] = [ L ] [i ], 1 T d [i ] [Φ ] 2 dθ d 2θ dθ J + ka + k e θ = m mec + m em 2 dt dt dθ (t ) Ω= dt m em =

[ ]

matrix,

[Lu ]

[Lσ ]

is the

is the proper

• •

mem is the electromagnetic torque; mmec is the mechanical torque

of

the

converter; Ω is the speed; J is the inertia;

ka ke

is the mechanical damping constant; is the constant corresponding to the elastic

torque. The next steps that will be done shall be to carry out the modelling for: • d.c. motors • a.c. motors The modelling will be carried out for specific cases, targeting the physical model and the experimental validation of the results. 5. Conclusions Nowadays, there are no unitary solutions for the embedded rotating electrical machine design in which to be included since the research stage of the execution the strategy of waste management. Some chapters regarding the impact on the environment were included in the electrical machine technical specifications in the last few years mostly for their work period but there were not taken into consideration all aspects about the entire life cycle. Such an approach to the electrical machine in which the natural and artificial resource management should be considered is not a specific one in Romania. Regarding the European Community, though research began in this field, the problems weren’t solved, they are discussed and tried to be solved punctually. In this way, reaching the project object becomes a European value added to the field of scientific knowledge, according to the objects regarding the essential role of scientific research and technological development in order to increase the economic European competition, as was stated by Lisbon strategy, 2000. The project presents a high complexity degree, through its themes, which implies the co-operation among the specialists from various scientific fields. Bibliography

where: •

•

[L pm ] is the inductance matrix, proper and

are the column matrix of current, respective the transposed current matrix; • θ (t) is the rotor position coordinate, function of time; For the equivalent converter, the inductance matrix, proper and mutual, has all the elements constant. •

•

[Φ ] is the flux matrix for each circuit; mutual; T

[Φ ] is the flux matrix, L is the inductance matrix;

•

equal to the e.m.f., considerate of opposite sign; •

[Re ] is the equivalent resistance matrix dispersion matrix and

where: •

matrix of

current;

Ω:

[u eu ] = d [Φ ]

[i ] is the column matrix of current; [i ]T is the column transposed

[ub ] is the column matrix of output voltages;

[1]

Bulearcă, M.: Acte normative referitoare la mediu, Ed. Universitatea Bucureşti, 2004.

54 [2]

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Avram, N., ş.a.: Management de mediu in industria materialelor metalice, Ed. Fair. Partners. 2002. [3] Ministerul Apelor şi Protecţiei Mediului, Institutul Naţional de Cercetare şi Dezvoltare de Ingineria Mediului. Strategia naţională de gestiune a deşeurilor, Bucureşti, 2002. [4] Vasile, N., ş.a.: Maşini electrice. Construcţie. Tehnologie. Aplicaţii speciale, Ed. ICPE, 2000. [5] Măgureanu, R., Vasile, N., Motoare sincrone cu magneţi permanenţi cu reluctanţă variabilă, Ed. Tehnică, Bucureşti, 1983. [6] Măgureanu, R., Vasile, N., Motoare sincrone fără perii, Ed. Tehnică, Bucureşti, 1990. [7] Bâlă, C.: Maşini electrice, Ed. Tehnică, Bucureşti, 1979. [8] Bâlă, C.: Proiectarea maşinilor electrice, Ed. Pedagogică, Bucureşti, 1967. [9] Gheorgihiu, I. S., Fransua , Al.: Tratat de maşini electrice, vol 4, Ed. Academiei, 1968. [10] Fransua, Al. ş. a.: Introducere în teoria convertoarelor electromecanice, Ed. Printech, Bucureşti, 1999. [11] Măgureanu, R.: Maşini electrice speciale pentru sisteme automate, Ed. Tehnică, Bucureşti, 1980. [12] Cioc, I., Nica, C.: Proiectarea Maşinilor electrice, Ed. Didactică şi pedagogică, Bucureşti, 1994.

[13] Covrig, M.: Maşini electrice – probleme specifice, vol. I, Ed. ICPE, Bucureşti, 1996, 140 pag., ISBN 973-97863- M 0-8. [14] Fransua, Al, Covrig, M., Morega, N. Vasile: Convertoare electromecanice, Ed. Tehnică, 1999, 200 pag., ISBN 973-31-1373-5. [15] Pârlog-Cristian, R., Covrig, M. Năvrăpescu, V., David, F.: Maşini electrice – probleme specifice, vol. II, Maşina asincronă, Ed.ICPE, Bucureşti, 2001, 220 pag., ISBN 973-8067-30-8. [16] Covrig,.M., Cepişcă, C., Pârlog-Cristian, R., Melcescu, L.: Convertoare electrice, Ed. Printech, 2002, 204 pag., ISBN 973-652-660-7. [17] Covrig, M., Melcescu, L., Vasile, N., Pârlog-Cristian, R.: Maşini electrice – probleme specifice, vol. III, Ed. Printech, Bucureşti, 2002, ISBN 973-652-562-7. [18] Cepişcă,C., Covrig,M., ş.a.: Mecatronica – convertoare electromecanice, Ed. Râmnicu-Vâlcea, 2002, ISBN 973-8488-08-7, 198 pag. [19] Covrig, M., Melcescu, L., Vasile, N., Maşini electrice – Probleme specifice, vol. IV, Maşini de tip sincron, Editura Printech, 2004, ISBN 973-718-264-2, 210 pag. [20] Simion Al.: Maşini electrice, vol I, Transformatoare electrice, Ed. “Gh. Asachi”, Iaşi, 2000.