International Journal of Applied Electromagnetics and Mechanics 45 (214) 581 588 581 DOI 1.3233/JAE-14188 IOS Press Comparative investigation of permanent magnet linear oscillatory actuators used in orbital friction vibration machine Fei Xu, Jianhui Hu, Jibin Zou, Yong Li, Yongxiang Xu and Hua Fan Department of Electrical Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China Abstract. The paper describes the alternative designs and performances of a single-phase moving-magnet linear oscillating actuator (LOA) which has been developed for orbital friction welding. The influences of the pole ratio on the performance of the LOAs are investigated and the optimal parameters have been identified with reference to the thrust force characteristics. It can be illustrated that a quasi-halbach magnetized LOA, in which the magnets are assembled on a nonmagnetic mover yoke, represents the best electromagnetic performances. Finally, the predicted thrust force-current characteristic of quasi-halbach magnetized LOA is validated by measurements on a prototype actuator. Keywords: Orbital friction vibration welding, linear oscillatory actuator, thrust force, optimal design 1. Introduction Orbital Friction Vibration Actuator (OFVA) is a core component of Orbital Friction Welding Machine (OFWM), which is a novel apertureless welding driving device. It can produce a force upon the still mover which then vibrates according to the predetermined orbital [1 4]. This paper proposes a highthrust force permanent magnet (PM) machine used to weld metals which employs rare earth magnet to generate magnetic field. It has some advantages, such as great transferring energy, high efficiency and high thrust force density. The displacements are decoupled with air gap as it moves in the xy plane. The reluctance cogging force is small and it shows a slight inverted pendulum effect. As can be seen in Fig. 1, PM OFVA is composed of four identical linear PM actuators and spring. There are two distributed in x and y directions which can control the motion in x and y directions respectively. Due to the decoupled relationship between the amplitudes in x and y directions, only one linear oscillating actuator (LOAs) in one direction should be analyzed. PM LOAs have aroused extensive study interests recently, due to their high efficiency and high power density, and have fell into a wide range of industries, such as artificial heart, compressors, pumps, vibrators, robots etc. [5 8]. [5,7] has reported on tubular moving-magnet topologies with C-cored stator back iron. [9] has studied comparative design of C-cored and E-cored single-phase tubular moving-magnet LOAs and has summed up that the feasible combinations of stator tooth number N t and the mover pole Corresponding author: Jianhui Hu, Department of Electrical Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China. Tel.: +86 451 8641 3613; E-mail: hujianhui@hit.edu.cn. 1383-5416/14/$27.5 c 214 IOS Press and the authors. All rights reserved
582 F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators (a) (b) C2 (c) C3 (d) (e) Fig. 1. Schematic of PM orbital friction welding actuator. Fig. 2. Schematics of unit C-cored PM LOAs. number N p were ruled by N t N p =1. A 2-pole, E-core tubular LOA equipped with quasi-halbach surface-mounted permanent magnets (HSPM) was investigated and some important performances had been predicted and validated by measurements. A linear single phase permanent magnet oscillating motor used in domestic refrigerator had been designed and tested and mainly investigated optimizing cost and efficiency [1]. By considering the references above and according the feature of short stroke which friction welding requires, the paper proposes a type of single-phase permanent magnetic linear LOA. Alternative design concepts for single-phase PM linear LOAs are reviewed. The performances of LOA equipped with radially, tangentially and quasi-halbach magnetized movers, and C-cored stator, are then predicted by finite element analysis. The predicted thrust force-current characteristic of the quasi-halbach magnetized LOA is validated by measurements. 2. Magnetized topologies and analysis of unit C-cored LOAs Figure 2 shows the schematics and the on-load flux distributions of five linear PM LOAs equipped with C-cored stator cores. The movers differ from each other in terms of pole number and magnetization. As is shown in Fig. 2(a), which has one radially magnetized magnet sandwiched between two axially magnetized magnets is simple to manufacture. The mover in Fig. 2(b) has three radially magnetized magnets of alternate polarity which can yield a three-pole magnet field. An actuator has one radially magnetized magnet which is sandwiched between two iron blocks and its mover employs a nonmagnetic yoke, as shown in Fig. 2(c), and also a three-pole magnetic field can be yielded., as shown in Fig. 2(d), is originally proposed in [5]. This topology is easier to manufacture, because it has two tangentially magnetized magnets sandwiched between three iron blocks. The mover yoke is made of nonmagnetic material. Considering the magnetizing technique and cost, a quasi-halbach magnetized mover can be obtained commonly by employing assembling method. A quasi-halbach array commonly consists of 3 to 5 magnets which have different magnetized directions. A good sinusoidal property can be acquired by increasing the number of each magnetic pole. However, the magnetizing technique will be complicated. The mover in Fig. 2(e) employs three magnets which contain one radially magnetized and two axially magnetized magnets to comprise a quasi-halbach array. The flux which passes through the mover yoke of is much, however, the flux which remains in the mover of yoke is so little. Therefore, can employ
F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators 583 Table 1 Design Parameters Items Symbol Units Value Stroke range x mm ± 1 Air-gap length g mm 2 Magnet length in the magnetized direction h m mm 1 Remanence of magnets (N38SH) B r T 1.23 Length of stator core L ef mm 5 Winding turns N 1 Current density J A/mm 2 3 12 8 6 4 2 C2 C3-2 -4-6 -8 Fig. 3. Variations of thrust force produced by, C2 and C3 with α p (I = 2.8 A). 12 8 6 4 2 2 4 6 8 1 12 14 16 18 2 22 24 26 28 3 τp3 =.9 =.13 =.16 =.19 =.22 Fig. 4. Variations of thrust force with τ p3 under different α p (I = 2.8 A). a nonmagnetic mover yoke. The topology can enhance the air-gap flux density and provide the main flux return path, and also has a good thrust force capability. These models are unit actuators, because they are set to be periodical in FE predictons, and therefore, it is unnecessary to consider air-gap fringe effect. 3. Optimization of unit C-cored LOAs The preliminary design principles are to maximize thrust force per unit area of the proposed unit actuator, i.e., small volume of the actuator should be kept to maximize the thrust force per unit area under the premise of satisfying the prescribed thrust force. The pole ratio α p = τ p1 /τ p (Fig. 2) has a great impact on the thrust force-displacement characteristic. Therefore, α p will be optimized to maximize thrust force per unit area. Various moving-magnet LOAs with C-cored stator are investigated and the design parameters are listed in Table 1. 3.1. Radial magnetized topology Figure 3 shows the variations of the thrust forces produced by, C2 and C3 with α p. As will be seen, the optimal α p of and C2 are identical, 1 and at this time, the thrust force is maximal. As α p is smaller than 1, the thrust force produced by is larger than that of C2 because C2 suffers from significant leakage flux between magnets; As α p exceeds.47, the thrust force will not increase noticeably, since the magnets consume most of their permanent magnetic motive force on the internal magnetic resistance; As α p decreases below.16, the reverse effect of the magnet field is
584 F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators 175 15 125 75 5 25 nonmagnetic ferromagnetic Fig. 5. Variations of thrust force with α p when mover employs ferromagnetic and nonmagnetic mover yoke (I = 2.8 A). 12 nonmagnetic ferromagnetic 8 Fig. 6. Variations of thrust force with α p when mover employs ferromagnetic and nonmagnetic mover yokes (I = 2.8 A). enhanced and therefore a negative thrust force is produced. C3 fails to take full advantage of the space and suffers from large flux leakage which makes it difficult to enhance its thrust force. Thrust forces produced by the three topologies with ferromagnetic mover yoke are larger than those with nonmagnetic mover yoke. Therefore, there is no need to discuss the topologies with nonmagnetic mover yoke. 3.2. Tangential magnetized topology τ p3 (τ p3 =2τ p2 )andα p are optimized simultaneously and Fig. 4 shows the variations of thrust force with τ p3.asτ p3 is 27 mm and α p is.16, the actuator with a nonmagnetic mover yoke can generate the maximal thrust force, 189 N. The optimal axially magnetized configuration is one iron block sandwiched between two axially magnetized magnets without iron block on the either side of the model. The variations of thrust force with τ p3 as it employs a ferromagnetic and nonmagnetic mover yoke, Fig. 5. The thrust force produced by the LOA which employs a nonmagnetic mover yoke is noticeably greater than that employs a nonmagnetic mover yoke. However, the saturation level in the middle iron block is relatively high, and therefore the air-gap flux density cannot be further improved and then the thrust force will be limited, and more eddy current loss will be generated. 3.3. Quasi-Halbach magnetized topology Figure 6 shows the variations of thrust force produced by with α p when it employs a ferromagnetic and nonmagnetic mover yoke. As will be seen, the maximal thrust force (182 N) will occur when α p is.19 for possessing a nonmagnetic mover yoke. Therefore, a nonmagnetic mover yoke can be selected for reducing the mover weight and enhancing the dynamic response of the system. 4. Comparison of characteristics of unit C-cored LOA 4.1. Comparison of the thrust force, excitation force and cogging force Figure 7 shows the variations of thrust forces with α p of,,. As can be seen, α p corresponding to the maximal thrust force of the three magnetized configuration are various. can obtain the largest
F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators 585 12 8 6 4 2 Fig. 7. Variations of thrust force of three magnetized topologies with α p (I = 2.8 A). Thrust force (N) -1 -.8 -.6 -.4 -.2 Position (mm) Fig. 8. Variations of thrust force with position (I = 2.8 A). Excitation force (N) 19 17 15 13-1 -.8 -.6 -.4 -.2 Position (mm) Fig. 9. Variations of excitation force with position (I = 2.8 A). Cogging force (N) 25 2 15 1 5-5 -1-15 -2-25 -1 -.8 -.6 -.4 -.2 Position (mm) Fig. 1. Variations of cogging force with position. thrust force and the maximal thrust force produced by is 3.7% lower than that produce by. The excitation force, produced by the interaction of PMs and current and the only force component contributing to the power output, is obtained by minus the cogging and reluctance forces from the thrust force. Figures 8 1 show the variations of thrust, excitation and cogging force with position. As will be seen in Figs 8 and 9, the thrust force and excitation force produced by are larger than the other topologies. The variations of thrust force produced by and are 5.9% and 5.3% respectively and those of excitation force are 3.5% and 2.3% over the stroke range. Obviously, although can produce larger thrust force and excitation force, it presents larger thrust force fluctuation correspondingly over the stroke range. The curve of excitation force of has a better flatness than the other ones. As can be seen in Fig. 1, the cogging force produced by is larger than the others over the stroke range and the cogging force of is the smallest. 4.2. Comparison of nonlinearity of thrust force-current characteristic Figure 11 shows the characteristics of thrust force-current which, and possess. As can be seen, the thrust force-current characteristic curves appear various tendencies as the ampereturns of the coils exceed 25 A. Among them, the linearity of the thrust force-current characteristic of
586 F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators Table 2 Average flux densities along A, B and C lines Stator position A line 1.449 T 1.458 T 1.41 T B line 1.415 T 1.428 T 1.344 T C line 1.385 T 1.232 T 1.29 T Thrust force (N) 175 15 125 75 5 25 5 15 25 3 Ampere-turn (A) Fig. 11. Characteristics of thrust force-current. is superior to the other topologies, which illustrates that the quasi-halbach magnetized topology has a better overload performance. 4.3. Comparison of stator iron loss The influence of stator iron loss on the operational efficiency shouldn t be neglected and the distribution states of flux density in the stator tooth can reflect indirectly the state of the stator iron loss, therefore, the variations of the average flux densities along A, B, and C lines in the stator teeth of, and with α p are investigated, as evident in Fig. 12. As can be seen, α p has little impact on the average flux densities along A and B lines and the stator core around the both lines are not saturated. The average flux densities along A and B lines of decrease slightly with increasing α p andtendtobeno saturated, and that along C line increases gradually with increasing α p. The average tooth flux densities along the three lines of decrease gradually with increasing α p and those are obviously larger than the two other topologies when α p is small, and also the saturation level of the stator region which B line locates is the most severe. The average tooth flux densities along the A and B lines of both appear first dropping and then ascending slowly, and that along C line first increases and then decreases with increasing α p. The average flux densities along C lines of all the topologies are far from saturation. The average flux densities along A, B and C lines as the three topologies obtain their respective maximal thrust force are shown in Table 2. As will be seen, the average flux densities of are smaller than the others along the three lines. Overall, can not only produce a great thrust force, but possesses very small flux densities in the stator teeth. Therefore, the stator iron loss generated by is also smaller and its efficiency will be higher than the other topologies. 5. Thrust force per unit area Thrust force per unit area, F σ, is one of the most significant criteria to evaluate the performance of LOA. Great thrust force per unit area indicates smaller volume of LOA can produce a larger thrust force and a higher utilization of permanent magnets. The formula of thrust force per unit area is defined by Eq. (1). F σ = F avg τ p L ef (1)
F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators 587 A Line (T) B Line (T) C Line (T) 1.7 1.6 1.5 1.4 1.3 1.9 1.7 1.5 1.3 1.5 1.4 1.3 1.2 1.1 1 A B C Thrust Force Per Unit Area (N/mm 2 ) 1.18 x 15 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.1 28 3 32 34 36 τp (mm) Fig. 12. Comparison of variations of average tooth flux densities with α p along stator tooth lines. Fig. 13. Variations of thrust force per unit area with τ p (I = 2.8 A). Spring Stator top cap Stator Winding Thrust force (N) 175 15 125 75 5 FE Measured Magnet Mover yoke 25 5 15 25 3 Ampere-turn (A) Fig. 14. Prototype LOA. Fig. 15. Thrust force-current characteristics. Where F avg is the average thrust force over the stroke range, L ef is the stator core length. Figure 13 shows the variations of thrust force per unit area produced by and whose stator core lengths L ef are identical, 5 mm with τ p.asτ p of is 1, the maximal thrust force density of can reach 1127 N/mm 2 and can obtains its maximal thrust force density, 116776 N/mm 2.Aswillbe seen, the discrepancy between them is not considerable. 6. Prototyping and experiment A prototype of has been manufactured so as to experimentally validate the foregoing analyses (Fig. 14). However, for the consideration of practical application, the prototype employed four topologies combined together to yield a larger thrust force. Some of flux leakage will be brought about on either side of the actuator. Therefore, the practical thrust force will correspondingly be less than four
588 F. Xu et al. / Comparative investigation of permanent magnet linear oscillatory actuators times as much as the maximal thrust force of. The predicted thrust force-current is compared with measurement (Fig. 15), and a good agreement is achieved. 7. Conclusions This paper aims at introducing a new design method to maximize the thrust force per unit area and decrease the thrust force fluctuation of single-phase PM LOA. The radial, tangential and quasi-halbach magnetized topologies and performances are analyzed. The influences of the pole ratio α p on the performance of the LOAs are investigated and the optimal parameters have been identified to maximize the thrust force per unit area. It can be concluded that a quasi-halbach magnetized LOA with a nonmagnetic mover yoke, represents a large thrust force, a good linearity of thrust force-current characteristic and low stator iron loss. Finally, the predicted thrust force-current characteristic of quasi-halbach magnetized LOA is validated by measurements on a prototype actuator and a good agreement between them has been achieved. Acknowledgment This work was supported by the National Key Basic Research Program of China (973 Program) under Grant 213CB3565. References [1] M.J. Troughton, Handbook of plastic joining: A practical guide 2nd edition, William Andrew Inc, Georgia, 8, pp. 37 47. [2] F. Xu, J. Hu, Y. Li, J. Zou, Y. Xu and J. Shang, System modeling and operational characteristic analysis for an orbital friction vibration actuator used in orbital vibration welding, AECE 13(2) (213), 11 16. [3] D.A. Grewell and A. Benatar, Comparsion of orbital and linear vibration welding of thermoplastics, Polymer Engineering and Science 49(7) (9), 141 142. [5] Dicnamesta 44(3), 222 263. [4] Y. Li, Z. Nie, Y. Lu and Z. Guo, Structure and working principle of orbital electromagnetic vibrating head, Small and Special Electrical Machines 35(11) (7), 8 1. [5] M. Watada et al., Improvement on characteristics of linear oscillatory actuator for artificial hearts, IEEE Trans Magn 29(6) (1993), 3361 3363. [6] I. Boldea and S.A. Nasar, Linear electric actuators and generators, IEEE Trans on Energy Conversion 14(3) (Sep 1999), 712 717. [7] K.B. Park, E.P. Hong and H.K. Lee, Development of a linear motor for compressors of household refrigerators, Proc of 3rd Int, USA, (1995). [8] T. Mizuno, Y. Bu, M. Ohkubo, F. Tsuchiya and H. Yamada, Static thrust analysis of a moving magnet linear oscillatory actuator for vibration cancel system, Proc of 5th Int LDIA, Japan (5), 282 285. [9] Z.Q. Zhu, X. Chen, D. Howe and S. Iwasaki, Electromag-netic modeling of a novel linear oscillating actuator, Proc of the 8 IEEE Int Magnetics Conf, Paper ID. CQ-1, Spain, 8. [1] Z.S. Al-Otaibi, Utilising SMC in single phase permanent magnet linear motors for compressor applications, 8.