Universal motor efficiency improvement using

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 3, JUNE 2003

Universal Motor Efficiency Improvement Using Evolutionary Optimization Gregor Papa, Barbara Korouˇsic´-Seljak, Boris Benediˇciˇc, and Tomaˇz Kmecl

Abstract—We present a new design procedure that improves the efficiency of a universal motor, the type of motor that is typically used in home appliances and power tools. The goal of our optimization was to find the independent geometrical parameters of the rotor and the stator with the aim of reducing the motor’s power losses, which occur in the iron and the copper. Our procedure is based on a genetic algorithm (GA) and by using this procedure we were able to significantly improve the motor’s efficiency—the ratio of the motor’s output power to its input power. The GA proved to be a simple and efficient search-and-optimization method for solving this day-to-day design problem in industry. It significantly outperformed a conventional “direct” design procedure that we had used previously. Index Terms—Design automation, genetic algorithms (GAs), losses, manufacturing automation software, optimization methods, universal motors (UMs).

I. INTRODUCTION

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OME appliances, such as vacuum cleaners and mixers, as well as power tools, such as drills and saws, are generally powered by a universal motor (UM) [10]. This particular type of motor has many advantages and disadvantages. A brief look at the advantages shows why the UM is such a popular choice for home appliances and power tools. • It is a very powerful motor in relation to its small size. • It has high starting and running torque. • It has variable speed that can be regulated in a simple way. • It is inexpensive to manufacture. Disadvantages of the UM are as follows. • It has a shorter life than other types of motors. • Its commutator and brushes tend to be high-maintenance items. • It generates a lot of radio interference due to the current switching in the commutator. In home appliances and power tools it is very important that the energy consumption of the motor, i.e., its input power, is as low as possible, while still satisfying the needs of the user by providing sufficient output power. The ratio of the output power to the input power defines the efficiency of the motor, which can be improved by reducing some of the main power losses in the motor, i.e., those that originate in the iron and the copper. Manuscript received November 26, 2001; revised September 20, 2002. Abstract published on the Internet March 4, 2003. G. Papa and B. Korouˇsic´-Seljak are with the Computer Systems Department, “Joˇzef Stefan” Institute, SI-1000 Ljubljana, Slovenia (e-mail: [email protected]; [email protected]). B. Benediˇciˇc and T. Kmecl are with the R&D Department, Domel ˇ d.d., SI-4228 Zelezniki, Slovenia (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TIE.2003.812455

In this paper we propose a method for reducing these power losses by optimizing the geometry of both the rotor and the stator. Because of the high magnetic saturation of the iron in a UM the problem is a highly nonlinear one. For this reason we adopted an artificial approach using a genetic algorithm (GA) [2], [5]. This algorithm has already proved to be very efficient in a wide range of different optimization procedures where the exact equations are not available or some nonlinearities are present [4]. In addition, due to its simplicity, the initial investment in such a method is low. The rest of the paper is organized as follows. In Section II, we provide a definition of the UM, describe the geometry of its rotor and stator and show how the efficiency of a UM is calculated. In Section III, we describe the GA and its operators. In Section IV, we present our new algorithm-based design approach. In Section V, we evaluate the new algorithm, and in Section VI, we list our conclusions and suggest possible future work. II. UM Universal motors [see Fig. 1(a)] are built to operate with either a dc or an ac power supply. A UM uses a commutator and its basic construction resembles the design of a dc series motor. A UM performs like a series motor—the same current, regardless of the power supply, passes through both the armature (rotor) windings and the field-excitation (stator) windings via the brushes in one continuous path. When operating with ac the magnetic field of the armature and the field coils reverse with the frequency of the current. Fig. 1(b) shows the rotor and the stator parts of a UM. A. Geometry of the Rotor and the Stator The rotor-and-stator unit of a UM is constructed by stacking the rotor/stator iron laminations (see Fig. 2). The shape and the profile of the rotor/stator lamination are described by several two-dimensional (2D) geometrical parameters. There are two types of parameter: the invariable and the variable. Invariable parameters are fixed; they cannot be altered, either for technical reasons or because of the physical constraints of the motor. Following is a list of some of the more important invariable parameters of a UM: • air gap; • external radius of the stator; • radius of the rotor’s shaft; • radius on the stator’s side hole; • radius on the stator’s rivet; • width of the rotor’s jag, etc.

0278-0046/03$17.00 © 2003 IEEE

PAPA et al.: UM EFFICIENCY IMPROVEMENT USING EVOLUTIONARY OPTIMIZATION

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(a)

(a)

(b) Fig. 1. (a) UM used in a vacuum cleaner. (b) Rotor and stator parts of a UM used in a vacuum cleaner.

Variable parameters are those that do not have predefined optimum values. Some of these variable parameters are mutually independent and without any constraints, they include the following: • • • • • • • • • • • •

thickness of the horizontal of the stator’s yoke; thickness of the vertical of the stator’s yoke; width of the stator; height of the stator; radius of the stator’s internal edge; thickness of the stator’s yoke at the hole; length between bisector and slot edge; radius of the stator’s teeth; external radius of the rotor; width of the rotor’s pole; thickness of the rotor’s yoke; height of the rotor’s teeth.

Other variable parameters are dependent, either on some invariable parameters or on mutually independent ones. Some of these parameters (with their dependencies in the brackets) are as follows:

(b) Fig. 2.

Geometrical parameters of a UM. (a) Stator. (b) Rotor.

• internal radius of the stator (the external radius of the rotor, the air gap); • radius of the rotor’s slot end (the radius of the rotor’s shaft, the thickness of the rotor’s yoke); • internal height of the stator (the height of the stator, the thickness of the stator’s yoke); • internal width of the stator (the width of the stator, the thickness of the vertical of the stator’s yoke).

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When optimizing the 12 mutually independent parameters important constraints have to be taken into account. • The parameters should be changed simultaneously (both independent and dependent parameters) to achieve proper electromagnetic conditions in the material. • Each parameter dimension should only be varied within a predefined limit. • Parameter transformations and their evaluation should be done as quickly as possible. B. Efficiency of the Motor The efficiency of a UM is defined as the ratio of the output power to the input power and it depends on various power losses. These losses include the following: • copper losses: the joule losses in the windings of the stator and the rotor; • iron losses: including the hysteresis losses and the eddycurrent losses, which are primarily in the armature core and in the saturated parts of the stator core; • other losses: like brush losses, friction losses, and ventilation losses. The equations that are used to calculate the overall efficiency of a UM are presented in the following sections. 1) Copper Losses: Copper losses per slot (in the stator and the rotor) are calculated using

the square of the frequency and the hysteresis losses increase linearly with the frequency, the main iron losses in the rotor are the eddy-current losses. On the other hand, these losses also depend on the square of the flux density. If the hysteresis losses in the rotor are neglected, the rotor’s iron losses can be calculated using (5). In practice, the major problem is finding a proper value for . It can be estimated from an analytical was obtained using magnetic calculation, but in our case, of the rotor the finite-element method (FEM). The overall values of all the rotor was calculated as an average of the nodes. When calculating the stator losses, the hysteresis losses and the eddy-current losses must be added together. Furthermore, the factor must be roughly estimated, but since the overall stator losses are approximately five times smaller than the rotor losses, even a nonexact estimation of the factor does not have a significant influence on the overall iron-losses calculation for the motor. Consequently, a motor’s iron losses can be expressed by the following equation:

(6) Finally, the sum of the iron and the copper losses is defined as (7)

(1) (2) where is the current density, is the current, is the number of turns, is the slot area, is the copper’s specific resistance is the length of the winding turn. and The overall copper losses are as follows: (3) where stands for each slot. 2) Iron Losses: Because of the nonlinear magnetic characteristic, the calculation of the iron losses is less exact. The iron losses are separated into two components: the hysteresis losses and the eddy-current losses. An empirical formula [10] for the hysteresis losses is defined as follows: (4) is a hysteresis material constant of 50 Hz, is the where is the maximum magnetic flux density, is the frequency, mass, and is a material-dependent exponent between 1.6 and 2.0. The eddy-current losses are defined as follows: (5) where is an eddy-current material constant of 50 Hz. The frequency of the magnetic field density in the stator is 50 Hz—the same as the frequency of the power supply—while in the rotor the frequency is much higher and depends on the motor’s speed. Since the eddy-current losses depend on

3) Other Losses: Besides the iron and the copper losses, three additional types of losses also occur in a UM, i.e., brush ), ventilation losses ( ), and friction losses losses ( ). All three types of losses mainly depend on the speed ( of the motor. When optimizing the geometry of the rotor and the stator we can fix the motor’s speed so that the brush, ventilation, and friction losses have no impact on the efficiency of the motor. In other words, these parameters are not significantly affected by the geometry of the rotor and the stator. 4) Impact of the Losses on the Motor’s Efficiency: We can also calculate the electromagnetic torque on selected rotor regions. Torque is a vector product of the distance from origin and the electromagnetic force (8). The force is calculated via a circular path integral of the Maxwell stress tensor (9). (8) (9) is entirely in the air and encloses the The circular path part—in our case the rotor—on which the force or the torque is exerted. The vector denotes the magnetic flux-density vector and is a unit vector normal to the path. of the motor is a product of the electroThe output power magnetic torque and the angular velocity (10), where is set by the motor’s speed. Since we are dealing with a 2D anal, so the ysis, the vector only has a component scalar represents, at the same time, an absolute value of the vector and its component (10)


By considering all the above-mentioned losses and the output power, the overall efficiency of a UM can be defined as follows: find parameters (mutually independent) which maximize

subject to (1)-(10)

(11)

Our goal was to find the maximal efficiency. III. GA FOR THE MOTOR GEOMETRY OPTIMIZATION The two problems we face when trying to reduce the main power losses in a UM by optimizing the geometry of the rotor/stator lamination are: 1) a complex search space and 2) nonlinear behavior. Because traditional search-and-optimization methods have proved to be inefficient at finding the solution under such conditions, we decided to apply a genetic algorithm. This is a heuristic method, which requires only a little information to provide a robust, yet flexible, search in a wide and complex search space. A. Basic Mechanism of the GA The GA codes parameters of the problem’s search space as finite-length strings over some finite alphabet. It works with a coding of the parameter set, not the parameters themselves. The algorithm employs an initial population of strings, which evolve into the next generation under the control of probabilistic transition rules—known as randomized genetic operators—such as selection, crossover, and mutation. The objective function evaluates the quality (or fitness) of solutions coded as strings. This information is then used to perform an effective search for better solutions. There is no need of other auxiliary knowledge. The GA tends to take advantage of the fittest solutions by giving them greater weight and concentrating the search in the regions of the search space that show likely improvement. The GA is different from traditional techniques because of its intrinsic parallelism (in evaluation function, selections) that allows working from a broad database of solutions in the search space simultaneously, climbing many peaks in parallel. Thus, the risk of converging on a local optimum is low. The random decisions made in the GA can be modeled using Markov chain analysis to show that each finite GA will always converge to its global optimum region [6]. In spite of its simplicity, the GA has proved to be an efficient method for solving various optimization and classification problems, in areas ranging from economics and game theory to control-system design [7], [9].

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In our case, the mutually independent variable geometrical parameters of the rotor/stator lamination (listed in Section II-A) were coded as strings over the alphabet of real values. Using a symbolic presentation of a string with 12 parameters gives

There is no need to normalize the physical parameters. They do differ in ranges but the crossover operation switches the values of the same parameter, no matter where the crossover point is, since each parameter is always encoded at the same place in the chromosome. The initial population of strings was gener) times. The starting ated by reproducing a starting string ( string was formed by coding the parameters of an initial UM. A was added to each parandom value distributed linearly on rameter value of the starting string to define a reproduced string. The selected encoding type was chosen because of its convenience. When strings had to be further transformed, checked and analyzed, there was no need for any additional conversion of their values. C. Genetic Operators To evolve the best solution candidate, the GA employs the genetic operators of selection, crossover and mutation for manipulating the strings in a population. The GA uses these operators to combine the strings of the population in different arrangements, seeking a string that optimizes the objective function. This combination of strings results in a new population. The first selection operator is used for creating a new generation. To create two offspring two strings have to be selected from the current population as parents. In our implementation of the GA, most fit strings were selected for reproduction. We applied the elitism strategy, where a number of least-fit members of the current population were interchanged with an equal number of the best-ranked strings. This approach ensured better starting positions for the best-ranked solutions, as all solutions had equal chances for reproduction. Generally, the elitism is applied via the roulette-wheel approach, but when there is one solution that is much better than the others in the population, the problem of getting stuck in a locally optimal solution could happen. In other words, this better solution would become the only one to be multiplied within a population. To avoid this problem, we realized the elitism through the interchange ratio of least-fit to best-ranked solutions. For example, considering the population of ten strings and was an order of strings that were ranked according to their fitness. Here, represents the th best solution ranked by its fitness. Applying the selection approach by using the least-fit per best-ranked solutions ratio of 30% we got a new selected population ordered as in

B. Encoding One of the most important parts of the GA is the encoding. By encoding the proper parameters and using the proper encoding type we can significantly influence the efficiency of the algorithm. Roughly speaking, the strings of the “artificial genetic system” are analogous to the chromosomes in biological systems. The entire set of strings upon which the GA operates is called a population.

The second crossover operator is used for exchanging information between the selected strings. In our case it proceeded in two steps. First, the strings were mated randomly to pair off the couples. Second, the mated string couples crossed over, using a given probability , to select the one-point crossing sites.

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An integer position was randomly selected between 1 and the . Swapping all the characteristic string length less one and inclusively, created two values between the positions new strings. For example, consider strings and , where and represent the th parameter of the solution

Suppose that by choosing a random number between 1 and 11 . The resulting crossover would yield two we obtained and new strings

D. Fitness Evaluation Following the genetic operators the new population had to be evaluated. Here, each string (solution candidate) of the population was decoded into a set of the rotor and stator (mutually independent variable) parameters. Its fitness was estimated by performing an FEM numerical simulation to calculate the iron and the copper power losses (using (6) and (3), respectively). Their sum [see (7)] corresponded to the solution’s fitness. An important criteria for the solution’s evaluation was the price of the material needed to make a motor. This was considered by means of additional boundaries for the stator’s external dimensions, which led to solutions with the same external dimensions and which used the same amount of iron. E. Termination Criteria

Moreover, we might use a constant probability to select a case in which the values of the swapped characteristics were calculated as a mean value of the parent characteristic values

where (12) While the first crossover approach ensured that the offspring solutions preserved the “genetic material” from both parents, the second approach helped to seek for other solutions near to the solutions that appeared to be good. Mutation is a process by which strings resulting from selection and crossover are perturbed. The process serves to create random diversity in the population. We used a mutation approach where each string was subjected to the mutation operator. Mutation was performed on a characteristic-by-characteristic basis, each . Assuming that characteristic mutating with a probability was a constant of 0.001, we expected 0.1% of parameters to undergo a mutation during a given population (13) is a mutation noise size that is normally up to 10% where of the parameter value. However, since a high mutation rate rehad sulted in a random walk through the GA search space, to have a relatively low value. We also applied the possibility of was the variable mutation annealing the mutation rate, where probability that decreased linearly with each new population. In other words, we assumed that each new population was generally fitter than the previous one. Such an approach was used to overcome a possible disruptive effect of mutation and to speed up the convergence of the GA to the optimum solution. In our implementation, after crossover and mutation were performed, each transformed solution was checked to see whether its parameters were still within the predefined dimension limits. If not, those that exceeded the limits were set to fit the limits.

The GA operates repetitively, with the idea that, on average, the solutions of the population defining the current generation have to be as good (or better) at maximizing the fitness function as those of the previous generation. When a certain number of populations are generated and evaluated, the system is assumed to be in a nonconverging state. This criterion is a “time-out” approach. The fittest member of the current generation at the time the GA terminates can be taken as the solution of the design problem. Besides this termination criterion, we also applied a wanted-solution approach, where the optimization stopped as soon as a solution with a predefined value of the fitness function was found. IV. DESIGN PROCEDURES FOR THE ROTOR AND THE STATOR The idea of using the genetic algorithm for the optimization of the geometry of the rotor and the stator with the aim of increasing the motor’s efficiency can be made part of the design procedure for a UM. First, the current traditional practice of designing the motor is presented and second, the “evolutionary” design approach is described. A. Conventional Design Procedure In a conventional (or direct) design procedure for a motor, the following occurs. 1) The initial estimation for the geometry of the rotor and the stator is made based on experience. 2) The appropriateness of this geometry is then usually analyzed by means of a numerical simulation of the electromagnetic field. In our case, the analysis is performed with commercial ANSYS software [1], which applies a FEM with an automatic finite-element-mesh generation. This software then performs several computational iterations to find a numerical solution that is convergent. The result is a magnetic vector potential on every node of the finite-element mesh. From these potentials, the values of the flux density, the field strength and the magnetic energy are calculated. Before running the software, a well-defined geometry of the analyzed lamination, material properties (such as the iron’s B–H hysteresis loop, the copper’s specific resistance) as well as the density of the electric current in the conductor area are to be defined.


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The drawbacks of this approach are that: a) the improper use of genetic operators, or b) an initial solution that is too loosely set, can lead to a longer convergence time. The GA has proved to be an efficient method in various areas of design as well as in industry. There are many applications in mechanical and industrial engineering that have made use of GAs [3].

V. EVALUATION OF THE EVOLUTIONARY DESIGN APPROACH

Fig. 3.

Design approach.

3) If the results of the numerical simulation show an inconvenient electromagnetic field structure, the direct design procedure is repeated until the motor geometry is optimized. The advantage of this approach is that engineers can significantly influence the progress of the design process by using their experience and they can react intelligently to any noticeable electromagnetic response with proper geometry redesign. The drawback of this approach is that an experienced engineer and a large amount of time—that is mostly spent on computations—are needed. B. Evolutionary Design Procedure The conventional motor design can be upgraded with the genetic algorithm (see Fig. 3) into a new direct system. This is based on a stochastic process that can find an optimum global solution in a short computation time. The concept of the applied design system can be roughly explained as follows. 1) The GA provides a set of problem solutions (i.e., different configurations of the mutually independent geometrical parameters of the rotor and the stator). It works from the initial set of solutions that are defined according to an initial UM. 2) In order to evaluate the fitness, each geometrical configuration is analyzed using the ANSYS FEM program. This step requires a prior decoding of the strings into a set of geometrical parameters for the rotor and the stator. 3) After the calculation of the fitness, the reproduction of the individuals and the application of the genetic operators to a new population are made. The GA repeats this procedure until a predefined number of iterations have been accomplished. The advantages of this approach are the following. • There is no need for an experienced engineer to be present during the whole process, only at the beginning to decide on the initial design. • There is no need to know the mechanical and physical details of the problem. The problem can be solved irrespective of any knowledge about the problem.

According to the proposed evolutionary design approach described above we developed software, that links together: 1) the GA that optimizes the geometry of the rotor and the stator of a UM and 2) the FEM program needed to evaluate the optimized geometry. The program was developed using the Microsoft Visual C++ programming tool and runs under the Microsoft Windows operating systems on a Pentium PC. A. Parameters Setup In order to evaluate the proposed evolutionary design approach, we optimized an initial UM using our DoptiMeL [8] software. First, we defined a few details about the geometrical parameters that were to be optimized, as well as certain statements about the GA parameter settings. Later, we evaluated the results, which showed an improved efficiency of the motor. 1) Geometrical Parameters: As stated in Section II-A, there are 12 mutually independent geometrical parameters that need to be optimized. These parameters can only be varied within their predefined dimension limits to find an optimum configuration that will increase the motor’s efficiency. Solutions in which the parameters exceed the limits are rejected as being inoperable. There are some invariable parameters that have a strong influence when defining the outline of the lamination: a) External radius of the stator: This roughly defines the amount of iron and copper and, consequently, the price of the motor (which is related to the product of the stator’s width and length). This was held constant during the optimization to ensure cost-comparable solutions. b) Radius of the rotor’s shaft: We fixed this at 5.5 mm. From our experience we know that when the rotor-shaft radius is less than 5.5 mm the rotor’s natural frequency can fall below the maximum frequency of the motor (defined under the normal working conditions) and the resulting resonance would cause the rotor’s vibrations to exceed allowable limits. c) Radius of the stator’s side-hole: This would be 0 mm in the ideal case, and it was set to a small positive (constant) value (defined by the mechanical requirements) because holes for the rivets were required in order to bind the stator. d) Air gap: The angles of the symmetrical and tangential parts of the air gap were set to fixed values because the commutation, which is conditioned by the air gap, was not taken into account during the optimization. 2) GA Parameters: Finding good settings for the parameters of the GA that work for the problem was not a trivial task. Robust parameter settings had to be found for population size,

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number of generations, selection criteria, and genetic operator probabilities. • If the population was too small, the GA converged too quickly to a local optimum solution and might not find the best solution. On the other hand, large populations required a long time to converge to a region of the search space with significant improvement. The best results were obtained when the population size was between 30–50. • By applying the elitism strategy, fitter solutions had a greater chance of reproducing. But when the ratio of least-fit solutions to be exchanged with best-fit ones (the selection criteria) was too high, the GA was trapped too quickly into a local optimum solution. However, this number was subject to the population size and appeared to be acceptable within 20%–30% of population size. • As a crossover probability that was too low preserved solutions from being interchanged and a longer time was required for them to converge, the probability was set to at least 60% so that the algorithm could act satisfactorily, i.e., almost all mated solutions could be crossed over. • A mutation rate that was too high introduced too much diversity and took a longer time to reach an optimum solution. A mutation rate that was too low tended to miss some near-optimum solutions. Using the annealing strategy—a linearly decreasing mutation probability rate with each new generation—the effects of a too high or too low mutation rate could be overcome. There was enough influence from this operator even if the value of the probability was 0.1%, while in the annealing strategy it started with 1% and ended at 0.1%. B. Evaluation Results We evaluated the proposed evolutionary design approach by estimating the actual improvement in the efficiency of an initial UM that was designed using the conventional direct design approach. The comparison of UM designs was made at the same output power. Since efficiency differs from one design to another, input power (and current) varies as well. FEM analysis follows the procedure: current is input variable and torque is output variable. Output power is product of torque and shaft speed. To make comparison at the same output power, two FEM field calculations at different currents had to be made and from these two calculations the right current for required torque (output power) was interpolated. 1) With the ANSYS software we calculated the efficiency of an initial UM. An outline of the rotor/stator lamination of this motor is shown in Fig. 4. The power losses of this motor were calculated to be 313 W and the output power was calculated to be 731 W (Table I). In the outline, the levels of magnetic flux density through the rotor/stator lamination are shown, expressed as T. The darkest gray color indicates areas with the highest level of magnetic flux density, which results in high iron losses. The copper losses are not shown in this area. 2) After several runs of the DOptiMeL software, a set of promising solution candidates was collected. We applied the following settings for the GA parameters: population


Fig. 4. Initial stator/rotor lamination.

size 30, number of generations 100, selection ratio 30%, crossover probability 70%, and mutation rate 0.1%. For each candidate we made a FEM numerical simulation followed by the calculation of the objective function value (fitness). Because each design was verified with FEM numerical calculations, the optimization was a lengthy process. It took around 3000 runs for the optimization to converge and since one FEM analysis took about 7 min, the whole optimization lasted for two weeks. Most of the solutions that were given by the DOptiMeL program show a significant reduction of the iron and the copper losses in comparison with the losses in the initial motor. The best solution results in a power-loss reduction of 24% and gives us a motor with iron and copper losses of 239 W (see Fig. 5). The main differences between the initial design (Fig. 4) and the optimized design (Fig. 5) are: 1) the height of the rotor-andstator laminations is increased by 13%; 2) the rotor radius is increased by 5%; 3) the slot (copper) areas in the stator and the rotor are larger; and 4) the iron area in the rotor is larger. A comparison of the magnetic flux densities in the initial and the optimized motor shows a clear reduction of the areas with the highest levels of magnetic flux density in the optimized motor. 1) Iron and Copper Losses: The iron and the copper losses in the initial and the optimized lamination designs are shown in Table II and Fig. 6. In the optimized lamination the copper losses in the rotor and the stator are significantly lower than in the initial lamination. The reason for this effect is that the slot area of the optimized stator lamination is larger. The number of ampere-turns in the optimized lamination that are necessary for obtaining the required torque are lower in comparison with the initial lamination due to the optimized lamination design. If in (2) is substituted with (1), the equation is as follows:

(14) From the equation above we can see that the copper losses increase with the square of the number of ampere turns and they are inversely proportional to the slot area. In the rotor, the slot , area is increased and combined with the effect of reducing this results in a reduction of 52% for the copper losses in the


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TABLE I EVALUATION RESULTS

Fig. 5. Optimized stator/rotor lamination.

rotor. For the same reason, the stator’s copper losses are 52% lower as well. In contrast, the iron losses are higher than in the initial lamination. The iron losses are increased in both the rotor and the stator, mainly because of the slightly larger iron area in the optimized design. The magnetic flux density in the stator remains in the same range as in the initial design. In the rotor, the magnetic flux density is decreased, but the iron area of the rotor is larger. Overall, the optimized design has a much better torque capability and this results in a total loss reduction of 24%. After considering these results we might be tempted to think that the next step after a reduction of the copper losses would be a reduction of the iron losses. However, if we designed a motor that had lower iron losses, the copper losses would automatically increase—and at an even higher rate. It should be remembered that a lamination is optimized when the sum of the copper and the iron losses is a minimum. 2) Material Costs: The results presented above consider an optimized UM. During the optimization procedure the material costs of the motor were not taken into account, i.e., the external radius of the stator was not considered to be a variable parameter. The solution resulted in a much larger stator dimensions than in the initial lamination. As the amount of iron used for manufacturing the motor depends only on the width and the height of the stator, the 13% increase in the stator’s height (as in our optimized solution) would cause the same increase in the amount and consequently the cost, of the iron required. The amount of copper that is used in the motor depends on the size of the slot areas; assuming the copper-fill factor is constant during the optimization. In the optimized solution, the slot area

was 18% larger than in the initial one. As a consequence, the copper costs increased by the same percentage. The figures for the estimated costs suggest that the optimized design would be much more expensive than the initial design. Therefore, we repeated the optimization procedure, this time by considering the material price criterion. We extended the definition of the technical quality of the UM to be a function of both power losses and materials costs. The new criterion was based on product of efficiency and estimation of material costs (material costs factor). A unity factor was set to the material costs of initial design; increase in material costs decreased the material costs factor linearly and vice versa. The goal of the optimization was to maximize this new criterion. The outline of the new costs-optimized rotor/stator lamination is shown in Fig. 7. This lamination has a different profile than the first optimized design. The stator covers the same area as the initial design, so the amount of iron would not increase. The slot areas are slightly larger than in the initial design, so 6.5% more copper would be needed. This would mean a more expensive motor, but the increases in cost would be negligible in comparison with the much better performance. Such a motor would have a power loss of 251 W, which is 20% better than the initial design. Comparing the optimized design that does not consider the material costs criterion with this new costs-optimized design, the first one is better: its power loss was estimated to be 12 W lower. By fixing the stator outer radius, we mostly lose the gain of the first design in the decrease of the stator’s copper losses. 3) Prototyping: We made prototypes of both the optimized and the costs-optimized motors and measured the real power losses and the efficiencies of the motors. These values are shown in Table I. The results are only slightly different from those calculated with the ANSYS FEM program. The main reason for this difference can be explained by the nonexact calculation of the iron losses, due to a variation in the material’s properties.

VI. CONCLUSION In this paper, we have presented an evolutionary optimization technique, with constraints on the geometry of the rotor/stator lamination, for designing an efficient UM for home appliances and power tools. Our approach uses the GA at a very early stage of the motor’s design, when an optimum configuration of the geometrical parameters has to be found. The GA generates sets of solution candidates that are evaluated using the FEM. We demonstrated that by repeating the process by which the GA

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TABLE II POWER LOSSES OF INITIAL AND OPTIMIZED MOTORS

Fig. 6. Power losses for the exisiting and the optimized motors.

By using the GA we were able to reduce the iron and the copper losses of an initial UM by at least 20% and increasing the GA running time or setting its parameters more appropriately could improve on this result. Our future work will involve investigating the effects of the motor’s other components on the efficiency. In addition, we will develop a better algorithm for calculating the iron losses, with emphasis on the rotor, since the present calculation does not take into account the problem of the weakening magnetic field due to the eddy currents and the high rotor-field frequency. REFERENCES [1]

Fig. 7. Costly unvaried optimized stator/rotor lamination.

generates these sets of solutions an optimum configuration with reduced power losses can be found in a very short time.

ANSYS User’s Manual, Version 5.6, ANSYS Inc., Canonsburg, PA, 2000. [2] T. Bäck, Evolutionary Algorithms in Theory and Practice. New York: Oxford Univ. Press, 1996. [3] D. Dasgupta and Z. Michalewicz, Evolutionary Algorithms in Engineering Applications. Berlin, Germany: Springer-Verlag, 1997.


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Barbara Korouˇsic´-Seljak received the M.Sc. and Ph.D. degrees in computer science and informatics from the University of Ljubljana, Ljubljana, Slovenia, in 1992 and 1997, respectively. She is currently a Research Assistant in the Computer Systems Department, “Joˇzef Stefan” Institute, Ljubljana, Slovenia. Her research interests include embedded systems, combinatorial optimization, and applications of new techniques to industrial problems.

Gregor Papa received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Ljubljana, Ljubljana, Slovenia, in 2000 and 2002, respectively. He is a Research Assistant in the Computer Systems Department, “Joˇzef Stefan” Institute, Ljubljana, Slovenia. His research interests include optimization techniques, high-level synthesis of integrated circuits, and parallel computing.

Tomaˇz Kmecl received the Ph.D. degree in mechanical engineering from the University of Ljubljana, Ljubljana, Slovenia, in 1998. He is Manager of the R&D Department, Domel ˇ d.d., Zelezniki, Slovenia, the second biggest supplier of vacuum cleaner motors worldwide.

Boris Benediˇciˇc received the M.Sc. degree in electrical engineering from the University of Ljubljana, Ljubljana, Slovenia, in 1999. ˇ He is a Researcher with Domel d.d., Zelezniki, Slovenia. His research interests include motor design, magnetic field analysis, and optimization techniques.