Recent Developments of Electrical Drives - Part 43 potx

422 Pereirinha and Antunes It was also numerically verified that, as expected, the thermal equivalent conductivity k e for each mesh is independent of the thermal source densities and boundary temperature. Indeed the problem was solved for two other different values of current densities (two and four times more) and two different values of boundary temperatures, which lead to the same results as those obtained by the original bar with the same conditions. Conclusions The presented method seems to be able to calculate very accurately the global equiva- lent thermal conductivity of any bar with several thin insulation materials and not trivial geometries with only conduction heat transfer. It has been shown that the equivalent thermal conductivity depends on the mesh used. The method performs a very good fitting of the hot spot temperature in the considered multilayer insulated bar in electrical machine slot with much less computational costs than modeling all the insulation materials. The numerical thermal solution was checked by verifying that the total heat flux through the bar boundary was equal to the thermal sources applied. References [1] E. Matagne, “Macroscopic Thermal Conductivity of a Bundle of Conductors”, Conference on Modelling and Simulation of Electrical Machine and Static Converters (IMACS TC1’90), Nancy, France, September 1990, pp. 189–193. [2] E. Chauveau, E. Zaim, D. Trichet, J. Fouladgar, A statistical approach of temperature calculation in electrical machines, IEEE Trans. Magn., Vol. 36, pp. 1826–1829, 2000. [3] M. Dodd, “The Application of FEM to the Analysis of Loudspeaker Motor Thermal Behavior”, 112th Audio Engineering Society Convention (AES 112th Convention), M¨unchen, Germany, May 2002. [4] J. Holman, Heat Transfer, 6th edition, New York: McGraw-Hill Book Company, 1986. [5] J.C. Coulomb, J.C. Sabonnadiere, CAO en ´ Electrotechnique, Paris, France: Hermes Publishing, 1985, pp. 41–43. [6] J. Pinto, C.L. Antunes, A.P. Coimbra, “Influence of the Thermal Dependency of the Windings Resistivity in the Solution of Heat Transfer Problem Using the Finite Element Approach”, Proc. of the International Conference on Electrical Machines (ICEM94), Paris, France, September 1994, pp. 448–451. III-3.2. LOSS CALCULATIONS FOR SOFT MAGNETIC COMPOSITES G¨oran Nord 1 , Lars-Olov Pennander 1 and Alan Jack 2 1 H¨ogan¨as AB, SE-263 83 H¨ogan¨as, Sweden, Goran.Nord@hoganas.com, Lars-olov.pennander@hoganas.com 2 University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU England, alan.jack@ncl.ac.uk Abstract. This paper focuses on iron loss measurements and simulations in perspective to evaluate a loss model that can be used for SMC materials in FEA. Introduction Soft Magnetic Composites (SMCs) are today a viable alternative to steel laminations in a range of electromagnetic applications, such as machines, sensors, and fast switching solenoids. SMC componentsare efficiently manufactured using thewell established powder compaction process. The isotropic nature of the SMCs combined with the unique shaping possibilities opens up for new 3D-design solutions. If carefully implemented advantages such as better performance, reduced size, and weight, less number of parts at low cost can be obtained. In Fig. 1 an example of an SMC component is displayed and in Fig. 2 the stator assembly is displayed with one SMC part missing. This paper focuses on simulation models of losses in SMC components. A method for the simulation of iron losses in SMC components is presented. The approach is different from what is described in [1]. Iron losses During the design process for a machine it is essential to predict the iron losses. This also applies when using SMC in the soft magnetic parts. The total iron losses are basi- cally divided into hysteresis, eddy current, and anomalous losses according to the general equation: P t = P h + P e + P a (1) Simulation tools such as FEA software have built-in models for the simulation of iron losses. These models are developed and adapted mainly for lamination steel materials and are normally not directly applicable on SMCs without modifications. S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 423–433. C  2006 Springer. 424 Nord et al. Figure 1. SMC stator component. Design Alan Jack, Newcastle University. When using laminations the size factor is the lamination thickness that is equal through the whole motor. In a motor using SMC material the size factor is different depending on the components geometry and has to be calculated for each design. The components cross-section geometry will influence the value of the eddy current losses, the question is how much and in what way. Materiallossdatainthecaseoflaminationsemanatesfromthe Epstein testthatmainlyre- flects the resultsin the plane ofa single sheet.Therefore the simulated resultsare usually ad- justed based on experience using established design factors. TheSMCmaterialmustbe con- sidered from a different perspective due to its homogeneous isotropic magnetic properties. Simulation of losses using FEA for laminations are often done for a single sheet in 2D and then are the results multiplied by the total number of sheets of the actual core. The geometrical distribution of losses is made by the calculated B-field. SMC components can theoretically be seen as single lamina structures with variable cross-sections/thickness and thereby cannot be treated as a modular system like the laminated structure. For SMCs it is though possible to separately calculate the eddy current losses by FEA for a homogeneous isotropic core with known electrical conductivity. A limited Steinmetz model can be used covering the basic hysteresis loss. Figure 2. SMC stator. One SMC tooth missing. Design Alan Jack, Newcastle University. III-3.2. Loss Calculations for Soft Magnetic Composites 425 Figure 3. Ring test samples. Experimental measurements Twelve slugs of different heights were compacted from a SMC powder material. The slugs were heat-treated using a non-optimized procedure with an estimated time and temperature resulting in slightly reduced material performance compared to parts in production. The electrical conductivities and BH-curves were therefore fluctuating somewhat between the rings. From the slugs 12 ring samples of different diameters and heights were manufactured by wire erosion, Fig. 3. The choice of ring dimensions were determined with a view to maintain the recommended ratio of inner to outer diameter of not less than 0.82 according to standard IEC60404-6 in order to limit non-uniform flux distribution. To more easily be able to recognize the connection between eddy current losses and component size, the rings were made in three different logical series according to Fig. 4 using ring size 1 as the basic size. There were two rings of size 1A and B. Two separate windings were put on each of the rings. Inner winding was used as a sense winding and outer winding to apply the AC field, Fig. 5. The number of coil turns Figure 4. Ring test samples A, B, and C series. Series A: decreasing rectangular cross-section; Series B: decreasing square cross-section, and Series C: increasing rectangular cross-section—constant cross-section area. 426 Nord et al. Figure 5. Wounded test ring. Table 1. Ring sample data Density Conductivity Ring no. ID (Mm) OD (mm) Th (mm) Weight (g) (kg/m 3 ) (S/m) 1A 94.08 115.24 10.62 269.92 7,301.8 14,451 1B 94.06 115.20 10.57 268.15 7,298.7 18,373 2 80.43 98.37 9.00 166.05 7,320.2 19,697 3 68.72 84.11 7.72 104.42 7,319.9 22,693 4 58.79 71.91 6.62 65.44 7,340.6 27,370 5 50.22 61.45 5.73 41.34 7,325.8 24,970 6 80.41 98.40 12.34 227.83 7,307.5 23,794 7 68.77 84.10 14.41 194.61 7,338.9 24,840 8 58.76 71.89 16.80 166.07 7,333.8 26,049 9 50.26 61.45 19.76 142.67 7,356.4 25,872 10 94.05 115.19 7.94 201.19 7,300.2 19,109 11 93.98 115.16 5.38 136.04 7,266.8 17,201 was optimized for each ring in order to run the hysteresisgraph within its measurement range. The hysteresis and eddy current losses were measured by using a Brockhaus MPG- 100D hysteresisgraph. The applied cur rent was automatically adapted to ensure a pure single frequency sinusoidal B-field. The electrical conductivity of the rings was mea- sured by a four-point method on the ring surface. Measured ring data is summarized in Table 1. FEA loss simulations Commercial FEAsoftware JMAG-Studio [2] was used to run models of all the ring samples according to Table 1, with applied AC currents, measured electrical conductivities, and measured BH-curves. The FEA model was made very close to the measurement conditions. Model size was reduced by symmetries. In Fig. 6 the FEA model for ring sample number III-3.2. Loss Calculations for Soft Magnetic Composites 427 Ring 7 1972 Elements Air SMC Ring Coil Figure 6. FEA model ring sample no. 7. 7 can be seen. Only a sector of one degree and the upper half of the ring were modeled. The boundary conditions were applied on the symmetry planes and on the outside of the air region. The current was set to give a flux density of1Tinthecross-section. It can be seen in Fig. 7 that the flux density is almost uniform over the cross-section. In Fig. 8 simulated eddy currents together with the flux density are shown in a ring cross-section. Figure 7. Simulation of B-field distribution in the ring cross-section. Part of ring (11 ◦ ) and coil (1 ◦ ). 428 Nord et al. Figure 8. Simulation of B-field distribution and eddy currents in the ring cross-section. Results The separation of hysteresis and eddy current losses from the measured total loss is demon- strated mainly on ring sample 1A. The hysteresis loss was assumed to be of first order in frequency and eddy current losses of second order in frequency. In Table 2, with the frequency in the first column, measured flux density, the total measured losses, and the ratio total loss/frequency are shown. The ratios are plotted in Fig. 9 and it can be seen that the ratio is a straight line. The value where the line is cutting the y-axle is the hysteresis loss at 0 Hz and for ring 1A this value is 0.1194 J/kg. By subtracting the measured total loss by this hysteresis loss value a separationcanbemade betweenhysteresislossesandeddy currentlossesforeachfrequency, Table 2. In Table 3 measured and calculated AC-slopes with the measured conductivity (1.0 × conductivity) are shown. The mean value of the ratio measured slope/simulated AC-slope wascalculated to 1.2. The measured conductivitiesaremultipliedwith 1.2 to create modified measured conductivities (1.2 × conductivity), Table 3. Definition: AC-slope = dP e /df The AC-slopes for ring 1A are calculated in Table 4 and plotted in Fig. 10. Table 2. Ring 1A total loss measurements, ratio total loss/frequency, and extracted eddy current losses Frequency F Flux density Total loss P t Ratio P t /f Eddy current loss (Hz) B (T) (W/kg) (J/kg) P e = P t – 0.1194 (W/kg) 99.99 1.0 13.1910 0.1319 0.0125 249.97 1.0 38.3170 0.1533 0.0339 500.00 1.0 93.8360 0.1877 0.0683 750.00 1.0 165.7000 0.2209 0.1015 III-3.2. Loss Calculations for Soft Magnetic Composites 429 Ratio (Total Losses / Frequency) vs Frequency - Ring 1A y = 0,0001x + 0,1194 R 2 = 0,9997 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0 200 400 600 800 1000 Frequency (Hz) Loss (J/kg) Figure 9. Ring 1A—measured ratio (total loss/frequency) vs. frequency—AC-slope and hysteresis value at 0 Hz. Table 3. Measured and simulated AC-slopes for rings 1–11 Measured slope FEA slope Ratio FEA slope Ring no. 1.0 ×conductivity 1.0 × conductivity M/FEA Difference % 1.2 ×conductivity 1A 1.345E–04 1.19E–04 1.131 11.6 1.384E–04 1B 1.725E–04 1.45E–04 1.188 15.8 1.707E–04 2 1.424E–04 1.14E–04 1.245 19.6 1.328E–04 3 1.287E–04 9.85E–05 1.306 23.4 1.150E–04 4 1.088E–04 8.71E–05 1.249 19.9 1.021E–04 5 8.920E–05 6.06E–05 1.471 32.0 7.171E–05 6 1.945E–04 1.67E–04 1.163 14.0 1.893E–04 7 1.715E–04 1.56E–04 1.102 9.2 1.776E–04 8 1.562E–04 1.40E–04 1.119 10.6 1.615E–04 9 1.338E–04 1.14E–04 1.169 14.5 1.338E–04 10 1.298E–04 1.14E–04 1.136 11.9 1.329E–04 11 9.095E–05 6.41E–05 1.419 29.5 7.585E–05 Mean value 1.2 17.7 Standard deviation 0.120 Standard deviation 9.8% Table 4. Ring 1A—measured and calculated AC-slopes Frequency (Hz) JMAG 14,451 S/m Measured 14,451 S/m JMAG 17,341.2 S/m 100 0.013 0.013 0.016 1,000 0.120 0.134 0.140 AC-slope 0.0001188 0.0001345 0.0001384 430 Nord et al. AC-slopes - Ring 1A 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0 200 400 600 800 1000 Frequency (Hz) Loss (J/kg) JMAG 14451S/m Measured 14451S/m JMAG 17341.2 S/m Figure 10. Ring 1A—AC-slopes. It can be seen that the AC-slope calculated from FEA simulations using the modified conductivity is very close to the AC-slope calculated from measurements. In Fig. 11 themeasured and simulatedAC-slopes are shown for ring samples 1A, 1B, and 2–5. It can be seen that the simulated results witha modified measuredconductivity are quite close to the measured ones. For ring samples 3 and 5, though the correspondence is lower especially for the smallest one, ring 5. Tests with different numbers of finite elements came out to have very little impact on the results and could not explain why the FEA simulation of eddy current losses seemed to be more difficult with smaller ring samples. 0,0E+00 2,0E-05 4,0E-05 6,0E-05 8,0E-05 1,0E-04 1,2E-04 1,4E-04 1,6E-04 1,8E-04 2,0E-04 1A 1B 2 3 4 5 AC-loss slope Meas slope 1.0*Cond FEM slope 1.0*Cond FEM slope 1.2*Cond Figure 11. AC-slopes—ring samples 1A, 1B, and 2–5. III-3.2. Loss Calculations for Soft Magnetic Composites 431 Table 5. Hysteresis losses—mean values measured for all ring samples with standard deviation and calculated losses using the calibrated formula B (T) Mean measurement (J/kg) Standard deviation P h /f =K h × B a J/kg 0 0.0000 0.0000 0.0000 0.50 0.0354 0.0003 0.0361 1.00 0.1193 0.0018 0.1190 1.50 0.2390 0.0013 0.2390 An important conclusion from Fig. 11 is that the component size has big influence on the AC losses. This fact has to be considered when a new component is designed for an application. K h and α factors The mean values of measured hysteresis losses for the 12 ring samples at three differ- ent flux densities are summarized in Table 5. The standard deviation between the differ- ent ring samples and the corresponding calculated hysteresis loss can also bee seen in Table 5. The hysteresis loss calculations were using formula (2) with K h = 0.119, αg 1.72, and B = magnetic flux density (T). P h /f(J/kg) = K h · B α . (2) K h and α were created by curve fitting. How well the values are corresponding to mea- surements is shown in Fig. 12. The formula is a part of the built-in iron loss calculation model that can be found in most FEA packages. How the K h factor is modified depends on the FEA software in use, due to different implementations. When using JMAG-Studio [2] the K h has to be multiplied with the mass density for each ring sample. Ph/f 0,00 0,05 0,10 0,15 0,20 0,25 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 B(T) Ph/f (J/kg) Mean meas. Ph / f = Kh * Ba Figure 12. Measured and calculated curve for P h /f. The curves are almost completely overlapping. . samples. 0,0E+00 2,0E-05 4,0E-05 6,0E-05 8,0E-05 1,0E-04 1,2E-04 1,4E-04 1,6E-04 1,8E-04 2,0E-04 1A 1B 2 3 4 5 AC-loss slope Meas slope 1.0*Cond FEM slope 1.0*Cond FEM slope 1.2*Cond Figure 11. AC-slopes—ring. cross-section. In Fig. 8 simulated eddy currents together with the flux density are shown in a ring cross-section. Figure 7. Simulation of B-field distribution in the ring cross-section. Part of. applicable on SMCs without modifications. S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 423 433 . C  2006 Springer. 424 Nord et al. Figure 1. SMC stator component. Design