Recent Developments of Electrical Drives - Part 31 ppt

298 Choi et al. Figure 3. Dynamic constraints between dynamic capability and required motional profiles. Design strategy using dynamic constraints In principle, dynamic capability shown in (1) should be at least larger than Force-Speed relation of required trajectory shown in (2). This relation is showninFig. 3, where static and dynamic capability and the required motional trajectory are compared. Particularly between two forces from maximum voltage and current respectively, the smaller one could be the final dynamic capability, which is based on (1). Therefore, heavy-line in Fig. 3 indicates the final capability of PMLSM, which should be larger than motional profile, and this conclusion gives effective design criteria referred as dynamic constraints. Therefore, it is reasonable that only dynamic capability at the velocity of v 1 ,v 2 ,v max should be larger than the required one, which is summarized as follows. < Constraint 1;v = v 1 , J = J max , a = a max > 3 2 K e C 1 + √ C 2 −C 3 R 2 s + (π/τ) 2 L 2 s v 2 >> ma max + Bv 1 + F l (3) < Constraint 2;v = v 2 , J = 0, a = a max > 3 2 K e min  C 1 + √ C 2 −C 3 R 2 s + (π/τ) 2 L 2 s v 2 , I max  >> ma max + Bv 2 + F l (4) < Constraint 3;v = v max , J =−J max , a = 0 > 3 2 K e C 1 + √ C 2 −C 3 R 2 s + (π/τ) 2 L 2 s v 2 >> 0 (5) In (3), the dynamic constraints only from voltage limitation are considered, because the other constraints from maximum input current can be neglected due to the same kind of constraints in (4). In practical application, it is not fixed which one between dynamic capability and the force from maximum input current has larger value. Thereby, at velocity of v 2 in (4), both of them must be satisfied at the same time, where dynamic capability (J = 0, a = a max ) and static capability (J = 0, a = 0) show little difference which can be verified through (1). In constraints 3, it is sufficient to judge whether motor has an III-1.1. Design and Manufacturing of Steel-Cored PMLSM 299 ability to produce the force or not. However, constraints 3 can be replaced by other different constraint like ∂ F e,max /∂v >> ∂ F e (v)/∂v (at v = v 2 ) which means that, if the slope of dynamic capability is larger than that of required motional profile at v = v 2 (slope < 0), constraint 3 at v = v max is satisfied by itself. However, this constraint is so strict that a lot of combination of design variables could fail to be selected even though they could survive through constraint 3. Therefore, it is reasonable to apply constraint 3 at design procedure, and then check the force margin in the interval of v 2 <v<v max after work. In addition to three basic constraints, such a relations as v max = V max /K e and another constraint, C 2 >> C 3 , should be obeyed also in all of dynamic constraints. Meanwhile,majordifferencebetweenconstraints from conventional staticcapabilityand proposed dynamic capability would be noticed at v = v 1 and v = v 2 . Although the properly designed machinecan satisfy constraintsgiven bystatic capability, requiredmotional profile cannot be realized due to the dynamic constraints, especially at v = v 1 (at v = v 2 , there is little difference due to the zero jerk). Since discontinuous force change at v = v 1 and v = v 2 results purely from jerk and acceleration, high accelerating PMLSM used in short traveling displacements should be designed along the dynamic constraints. Defined design parameters in (1) will be τ, K e , R s , L s which are strongly regulated by dynamic constraints, and used as decision criteria to the combination of the design variables judging that the dynamic constraints are fully satisfied, i.e. designed machine can be driven successfully satisfying the required motional profile. Actually, sensitivity to the design parameter variance is most serious to τ and K e relatively than R s , L s which are occasionally neglected in simplified design flow. Accordingly, in addition to the dynamic constraints, more generalized design consideration at the primary stage should be done focusing on the influence of τ and K e , which makes entire design process performing more effectively. Generalized design consideration and determination of design variables In Fig. 4, the point where the maximum output power could be generated will be near v = V max /K e /2 (half to the no-load velocity). Likewise, the maximum required mechanical power exists at v = v 2 , therefore a design basis should be oriented as v 2 ≈ V max /K e /2(K e2 Figure 4. Generalized design schematic diagram (K e1 > K e2 > K e3 ). 300 Choi et al. 45 40 35 30 25 20 15 10 45 40 35 30 25 20 15 10 5 45 40 35 30 25 20 15 10 5 45 40 35 30 25 20 15 10 5 0.10 0.15 0.20 0.25 0.30 0 K e = 10 R s L s L s L s L 5 R s R s R s (5956) K e = 30 (11461) K e = 20 K e = 39 (13769) (1070) tt t t 0.0 0.0 0.5 1.0 1.5 2.0 0 2 4 6 8 10 0.2 0.4 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 0 2 4 6 8 10 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 0.6 Figure 5. Admissible design combination vs. K e (where V max = 160 V, I max = 150 A, m = 37 kg, B = 100 N/(m/s), F l = 50 N, a max = 20 m/s 2 , V max = 4 m/s, J max = 3,000 m/s 3 ). model in Fig. 4). However, if required input current (I s = F e,max /(1.5K e )) is considered, K e1 model needs smaller current (I s1 ) than K e2 model (I s2 ), which could be also interpreted as better efficiency. In conclusion, EMF coefficient, K e [V/(m/s)], should be designed at least in the interval as follows. V max /v max ≤ K e ≤ V max /(2v max ) (6) Another sensitive design parameter, pole pitch (τ ), should be defined from the magnetic combination (four poles and three coils) and the manufacturing feasibility. One module length τ m corresponding to 4τ and 3τ c (where, τ c is coil pitch) should be multiplied with 12, which has validated itself compared with the other combinations. Hence, its mini- mum andmaximum sizeare stronglyrestrictedbythe manufacturingfeasibilityand thecost. Acceptable τ m range for relatively larger power in continuous operation is approximately from 36 mm (τ = 9 mm) to 180 mm (τ = 45 mm). In Fig. 5, distribution of design combination vs. K e is shown, and if it is applied to Fig. 4, K e = 20 corresponds to K e2 model manifesting the best design point from a viewpoint of size-effectiveness and usefulness in application. As K e increases, better efficiency (lower input current) can be realized, and near the no-load speed (K e = 39), dynamic constraints strongly restrict the design combinations in the speed range of v 2 ≤ v ≤ v max . Particularly, the number of admissible design combination is maximum at the K e = 20, which means the possibility to implement the machine successfully is highest at the best design point. Design parameters (τ, K e , R s , L s ) are electrically and magnetically composed of the designvariablesexpressingthe machinedimension,hence thedesignprocess willbedone by changing the design variables and checking the validity of sets of the design variables under III-1.1. Design and Manufacturing of Steel-Cored PMLSM 301 Figure 6. Optimal design flowchart. the criteria proposed by dynamic constraints. Particularly, pole pitch (τ ) will be sufficient to represent the moving-directional (longitudinal) design aspects, because coil pitch and one module-length are also determined accordingly. Then, the other variables including pole pitch can be summarized as air-gap length (g 0 ), height of magnet (h m ), height of slots (S h ) (or number of turns in slots), which are flexible to the normal direction. With the proposed design variables, the optimization method can be applied to the design process under the constraints such as dynamic constraints, the maximum mover length, and the maximum machine height, which are shown in Fig. 6 as a flowchart. Detent force reduction Theoretically, the detent force is the resultant one of two different reaction forces, i.e. the core detent force and the teeth detent force. The core detent force is the existing force between the permanent magnets and the primary core, which has a large period equal to the pole pitch. Whereas, the teeth detent force between the permanent magnets and the primary teeth has a relatively small period, the greatest-common-divider (GCD) of the pole pitch and the tooth pitch (τ c , same with coil pitch) Reduction of core detent force Reduction of the core detent force can be done by giving the core a suitable length in order to cancel the core detent force at both end cores each other by adjusting the phase difference between the two core detent forces, and by reforming the edge of the core to minimize the reluctance variation. To begin with, making the geometric length such that the two forces at both end cores cancel each other can be effective, which could be realized by adjusting the electrical phase difference as follows [5]. θ = (2k −1)π, (7) where k is integer. 302 Choi et al. The other candidate is reforming the edge of core, which is induced from avoiding a rapid reluctance change when the mover approaches or leaves the magnets. Reduction of teeth detent force The teeth detent force, the main component to be reduced, not only occupies the total detent force up to 80%, but also is frequently produced along the motion track. Feasible ways to minimize the teeth detent force based on the practical utilization are chamfering the teeth edges and skewing the magnet. Firstly, chamfering the teeth edge, which is a similar idea to core chamfering, intends to make abrupt the reluctance changes minimal due to the sharp tooth edge. The other one, skewing the permanent magnet which is similar in principle to rotary machines, can remove theteethdetent force outstandingly. Theoptimized skew-angle should be determined through the following relation. Skew-angle = GCD(τ,τ c ) 2 1 τ 180 [Electrical degree] (8) Equation (7)manifests the electrical30 ◦ in fourpoles and threecoils combination. However, this is so small one in a mechanical length. In case of τ = 45 mm, mechanical skew-length correspondent to skew-angle (electrical 30 ◦ ) is 7.5 mm. Investigation on reduction result Fig. 7 shows the reduction of the detent force. The peak detent force of conventional model is about 300 N. But the peak value is reduced to 150 N after applying the chamfering and the skew, about 5% of the continuous thrust force. The detent force pattern has many harmonics because the width of magnet is very large and many teeth affect same magnet. In this case the effect of the skew is not so notable. Figure 7. Detent force reduction by proposed methods. III-1.1. Design and Manufacturing of Steel-Cored PMLSM 303 Figure 8. Manufactured PMLSM. Design, manufacturing, and testing The designed steel-cored PMLSM is manufactured and tested. The picture of the manufac- tured PMLSM is presented in Fig. 8 and specifications of the designed machine are listed in Table 1. The magnetic flux distribution and air-gap flux density are shown in Figs. 9 and 10. In this model, very large input current is needed to get large thrust force, so that sufficient amount of iron core should be secured to avoid magnetic saturation. The stroke of the linear motor is 1,000 mm and the maximum force/continuous force is 15,000 N/3,000 N. This motor can run up to 4 m/s under the input voltage of 220 V and the maximum current of 300 A. Table 1. Design specification of sample steel-cored PMLSM Specification Dimension General (with water cooling) Voltage/current 220 V/41 A Stack length 200 mm Magnet height 9 mm Magnet width 41 mm Stator (NdFeB, 45 H) Pole pitch 45 mm Slot width 22 mm Tooth height 30 mm Tooth width 38 mm Mover (coil size = 1.2 Ø) No of turns 90 per coil Coil connection 3 parallel Chamfering 10 × 6mm 304 Choi et al. Figure 9. Magnetic flux density distribution. The dynamic capability of the designed PMLSM is shown in Fig. 11 and the capability curve has force margin about 500 N. By using the load cell, the thrust force is measured and the input current is measured with the current probe and the oscilloscope. Fig.12showsthemeasured current-thrust force curve. Thegraph showsvery good linear relation of the input current to the thrust force. The continuous thrust force is generated with the input current of 58 A and the maximum thrust force with the input current of 305 A is 15,890 N, which satisfies the objective output. Over 300 A region, the linearity of the curve is broken, because it is the highest available measuring value of the current probe. The thrust force constant resulting from the measured curve is 54.81 [N/A] and EMF constant is 36.54 V/(m/s). The measured results have a good agreement with calculated thrust force constant 51.53 [N/A] and EMF constant is 34.35 V/(m/s). The measured input current is shown in Fig. 13 when the motor is operated with the maximum speed. The pole pitch of the machine is 90 mm and the pitch of the measured Length mm Bn. Tesla 0 −2 −1 0 1 2 50 100 150 200 250 300 Figure 10. Air-gap flux density distribution. III-1.1. Design and Manufacturing of Steel-Cored PMLSM 305 Figure 11. Running characteristics of designed motor. Figure 12. Current-thrust force curve. Figure 13. Measured input current. 306 Choi et al. current wave form is 22.6 ms. Therefore the moving speed can be calculated and the result is 3.98 m/s. Because the stroke is short, very large acceleration is needed to achieve the speed of 4 m/s. In addition, the power capability of the testing building is not sufficient, so that the resultant speed is not over 4 m/s. If long stroke or better power source is available, the machine can achieve the speed of 4 m/s. Conclusion In this paper, steel-cored permanent magnet linear synchronous motor for large thrust force and high speed operation is designed, manufactured, and tested. The machine is analyzed by finite element method considering dynamic and static constraints. The designed model is optimized to reduce force ripples and to avoid magnetic saturation. Test machine is manufactured and the measured result of EMF constant shows good agreement with designed one. Thrust force characteristic shows good linearity and the measured maximum thrust force is over 15,000 N, the objective value. The measured max- imum velocity is 3.98 m/s. The performances of the designed motor can guarantee the objective large thrust force and high speed. References [1] T. Sebastian, V. Gangla, Analysis of induced EMF waveforms and torque ripple in a brushless permanent magnet machine, IEEE Trans. Ind. Appl., Vol. 32, No. 1, pp. 195–200, 1996. [2] T. Yoshimura, H.J. Kim, M. Watada, S. Torii, D. Ebihara, Analysis of the reduction of detent force in a permanent magnet linear synchronous motor, IEEE Trans. Magn., Vol. 31, No. 6, pp. 3728–3730, 1995. [3] D.L.Trumpher, W J. Kim,M.E. Williams,Design andanalysis frameworkfor linearpermanent- magnet machines, IEEE Trans. Ind. Appl., Vol. 32, No. 2, pp. 371–379, 1996. [4] S Y. Jung, H K. Jung, J S. Chun, Performance evaluation of slotless permanent magnet linear synchronous motor energized by partially excited primary current, IEEE Trans. Magn., Vol. 28, No. 2, pp. 3757–3761, 2001. [5] N. Bianchi, S. Bolognani, F. Tonel, “Design Criteria of a Tubular Linear IPM Motor”, Proc. of IEMDC’03, 2001, pp. 1–7. [6] S Y. Jung, S Y. Kwak, S K. Hong, C G. Lee, H K. Jung, “Design Consideration of Steel- Cored PMLSM for Short Reciprocating Travel Displacements”, Proc. of IEMDC’03, Vol. 2, June 1–4, 2003, pp. 1061–1067. [7] S Y. Jung, J K. Kim, H K. Jung, C G. Lee, S K. Hong, Size optimization of steel-cored PMLSM aimed for rapid and smooth driving on short reciprocating trajectory using auto-tuning niching genetic algorithm, IEEE Trans. Magn., Vol. 40, No. 2, pp. 750–753, 2004. III-1.2. HIGH POLE NUMBER, PM SYNCHRONOUS MOTOR WITH CONCENTRATED COIL ARMATURE WINDINGS Antonino Di Gerlando, Roberto Perini and Mario Ubaldini Dipartimento di Elettrotecnica—Politecnico di Milano Piazza Leonardo da Vinci, 32-20133 Milano, Italy antonino.digerlando@polimi.it, roberto.perini@polimi.it, mario.ubaldini@polimi.it Abstract. A high pole number, PM synchronous motor is presented, employing novel two-layer, special armature windings consisting of concentrated coils wound around the stator teeth. This kind of machine is characterized by excellent e.m.f. and torque waveform quality: it is well suited not only as an inverter driven motor, but also for mains feeding, self-starting, applications. In the paper, the main features of the machine are shown, together with some design, FEM, and test results. General features of the windings In recent times, a large attention has grown toward the electrical machines equipped with concentrated coils, thanks to their great constructional and functional advantages [1–12]; nevertheless, a general approach to the concentrated winding theory seems not fully de- veloped yet. In the proposed paper, a PM machine is considered, with two-layer, armature concentrated windings [13]. The features of this kind of machines are (see Figs. 1 and 2): r uniformly distributed and equally shaped magnetic saliencies of the structures (stator teeth and rotor PMs); r practical equality among tooth pitch τ t and PM pitch τ m (it can be τ m < τ t or τ m > τ t ,but τ m = τ t ); r series inverted connection of coils belonging to adjacent teeth of the same phase (contro- verse coils). By adopting the representation of Fig. 1 (right) to specify the winding sense of each coil around its tooth, a typical three-phase, two-layer, winding appears as shown in Fig. 2. Referring to Fig. 2, the following quantities and properties should be defined and con- sidered: r cycle: space period (periphery portion at which bounds the faced structures show the same mutual disposition); S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 307–320. C  2006 Springer. . validity of sets of the design variables under III-1.1. Design and Manufacturing of Steel-Cored PMLSM 301 Figure 6. Optimal design flowchart. the criteria proposed by dynamic constraints. Particularly,. relatively small period, the greatest-common-divider (GCD) of the pole pitch and the tooth pitch (τ c , same with coil pitch) Reduction of core detent force Reduction of the core detent force can be. mechanical length. In case of τ = 45 mm, mechanical skew-length correspondent to skew-angle (electrical 30 ◦ ) is 7.5 mm. Investigation on reduction result Fig. 7 shows the reduction of the detent force. The