advertisement

A Novel Brushless Synchro: Operation Principle and Experimental Results Davood Pazouki*, Mahdi Ghafarzadeh**, Rezvan Abedini***, Aliakbar Damaki Aliabad****, Ali Kamali E.***** *Iran University of Science and Technology, Tehran, Iran, [email protected] **Sharif University of Technology, Tehran, Iran, [email protected] ***Amirkabir University of Technology, Tehran, Iran, [email protected] ****Yazd University, Yazd, Iran, [email protected] *****Amirkabir University of Technology, Tehran, Iran, [email protected] Abstract- In synchroes and resolvers, brushes and slip-rings produce a lot of noise in the output signal. Compared to encoders, the application of such position sensors in precision control systems are restricted because of their lower accuracy. In this research, a novel scheme of a brushless synchro is introduced. In this scheme, the secondary windings are mounted on the stator and the stator magnetic flux passes a certain path in the rotor and induces voltage in the secondary windings. The operation principle is clearly described in the paper and by using 2D finite element method the novel synchro is initially designed and analyzed. The stator winding’s turns is calculated by a method based on desired harmonic elimination to have a sinusoidal magneto motive force. A prototype has been fabricated and tested. The experimental results are in good agreement with simulations and verify the theoretical concepts. Keywords— Three-phase brushless synchro, E-shaped stator, harmonic elimination 1. Introduction Among the various absolute position sensors, resolvers/synchroes and encoders are often utilized in many industrial applications for precision control purposes [1]-[4]. Compared to the resolvers/synchroes, the absolute encoders are much more complicated, of larger size, and expensive [5]. Conventional resolvers/synchroes are constructed with a wound rotor that is excited with an ac voltage through slip rings and brushes [6]-[7]. Slip rings and brushes produce noise and reduce the accuracy of the sensor [8]. Using rotary transformer, the brushes and slip rings can be eliminated [9]. However, compared to the brushed types, the resolvers/synchroes with rotary transformers have higher power consumption, lower impedance angle, higher phase shift, and lower unit torque gradient [10], [11]. In this research, a novel brushless synchro is introduced. Unlike the other counterparts, in this scheme both the primary and secondary windings are mounted on the stator. The magnetic flux is conducted in a certain path within the rotor and induces voltage in the secondary windings. Compared to the synchroes with rotary transformer, the induced voltage directly appears in the output winding and therefore, the loading effects are suppressed. Moreover, this scheme has a simple structure with lower cost of fabrication as it consists of one stator and one non-wound rotor, without any additional devices like brushes and slip-rings existing in the traditional brushed structures, or the coupling transformer in brushless ones. In this paper first we describe the operation principle of the scheme. Then, the initial (non-optimal) design procedure of the synchro together with 2D finite element results is presented. Finally, in order to verify the theoretical concepts the experimental results of the fabricated synchro are exhibited. 2. Principle of the Scheme Figure 1 represents the principle of the proposed scheme. As shown in the figure, the three-phase voltage applied to the primary windings generates a magnetic flux in E-shaped cores of the stator. The produced flux passes the air gap, enters to the rotor, and then returns to the stator from up or down side of the rotor cores. In this way, if the secondary windings are mounted on the stator (according to Fig. 1) the magnetic flux crosses it and without using brush and slip-ring the voltage is induced in the secondary winding. To this end, the rotor should be composed of two magnetic parts isolated by a non-magnetic medium. The non-magnetic part can be made of aluminum and the magnetic parts should be made of perpendicular laminated cores. In addition, the stator should be fabricated as E-shaped cores so that the flux passes through the two upper/lower stator teeth. On the other hand, one of the magnetic cores of the rotor should be placed in front of two upper teeth of the stator cores, and the other one in front of two lower teeth. Otherwise, no voltage is induced in the secondary windings. Furthermore, the polarity of the induced voltage of the upper and lower portions of secondary windings should be considered when they are connected to each other. The three-phase primary windings, mounted between stator slots, are wound the same as those of the common synchroes. Fig. 2. Assembling process of E-cores on the body of the stator. Fig. 1. Schematic view of proposed brushless synchro. 3. Design Considerations 3.1. Stator The stator is composed of several sets of E-shaped, laminated magnetic core. As described in the next section, the more the number of slots, the more winding space harmonics could be eliminated. However, considering mechanical and fabrication restrictions 18 core sets have been selected for the stator. As shown in Fig. 2, teeth of E-shaped cores are mounted on the perimeter of a polyamide cylinder in equal distances. While the longitudinal positions of E-cores are adjusted by the polyamide cylinder, two rings from up and down fix the angular position of E-cores on a unique circle. Note that the primary and the secondary windings will be wound before placing the stator’s cores. Coil-winding in this way is very easier than the coil-winding method implemented for the traditional synchroes. Fig. 3. Stator winding connections diagram for three phases, a, b, c 3.2. Windings In order to have a sinusoidal magneto motive force (MMF) with minimum harmonics, the primary windings have been distributed sinusoidally and the coils are connected to each other in a spiral form as illustrated in Fig. 3. The number of turns of the primary windings is calculated by a method founded on desired harmonic elimination. In this method, the coefficients of Fourier expansion of the generated MMF are equated to zero in order to obtain the each winding turns. Thus, one can write the Fourier expansion of the generated MMF in the following form f (t ) = ∞ ∑ S n sin(nωt ) (1) n=0 in which Sn = 2 T T ∫ f (t ) sin(nωt ) dt (2) 0 Note that in three-phase winding the harmonics of 3, 9, 15, … as well as even harmonics are identically zero; therefore, the other harmonics such as 5, 7, 11, 13, … can be arbitrarily eliminated. In a 18-slot concentrated winding, there are three unknowns, as N1 = a3a3′ = a4 a4′ , N 2 = a2 a2′ = a5 a5′ , and, N 3 = a1a1′ = a6 a6′ for phase (a) and so on for other phases. Since the total number of windings is achieved from FEM analysis, only two harmonics can be eliminated. Here, one may vanish 5th and 7th harmonics which are the most powerful terms, as follows: ⎛ 3π 18 ⎜ ⎜ N1 sin(5ωt ) dωt ⎜ ⎜ π 18 ⎜ 5π ⎜ 18 8i S5 = ⎜ + ( N1 + N 2 ) sin(5ωt ) dωt T⎜ ⎜ 3π 18 ⎜ ⎜ π2 ⎜ ( N1 + N 2 + N 3 ) sin(5ωt ) dωt ⎜+ ⎜ 5π 18 ⎝ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟= 0 ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎛ 3π 18 ⎜ ⎜ N1 sin(7ωt ) dωt ⎜π ⎜ 18 ⎜ 5π ⎜ 18 8i S 7 = ⎜ + ( N1 + N 2 ) sin(7ωt ) dωt T⎜ ⎜ 3π 18 ⎜ ⎜ π2 ⎜ ( N1 + N 2 + N 3 ) sin(7ωt ) dωt ⎜+ ⎜ 5π 18 ⎝ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟= 0 ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ∫ ∫ ∫ ∫ ∫ ∫ (3) figure confirms the calculations of winding turns and shows that the low-order harmonics have been eliminated. As shown in the figure, only the slot harmonics (17th and 19th) have little values. Using FEM analysis, the number of secondary windings is determined equal to 400 turns to generate an output voltage with peak amplitude of about 6 volts. 3.3. Rotor The laminated rotor cores are placed aligned with the flux path. The angle of rotor sector should be a multiple of stator pitch angle, 20 degrees, to have a uniform reluctance from rotor point of view. Here, we select 80 degrees for rotor sector considering mechanical aspects. To eliminate the slot harmonics, the rotor should be skewed 20 degree, which is equal to one stator pitch. It should be noted because the stator E-shaped cores are separated from each other; the magnetic flux of each core should be closed by itself. For this purpose, the rotor’s cores should be skewed in a reverse form at the middle height such as Fig. (6). (4) Fig. 4. The MMF waveform based on the calculated primary windings Carrying out the preceding integrations results in 0.6428N1 − 0.866 N 2 − 0.342 N3 = 0 0.342 N1 − 0.866 N 2 + 0.9848 N3 = 0 (5) In addition, as discussed later in the paper, FEM yields the total number of windings of each phase as 2 × ( N1 + N 2 + N3 ) = 480 (6) Hence, solving the above equations, N1 , N 2 , and N 3 are obtained (7) N1 = 128, N 2 = 83, N3 = 29 Using the above number of turns for primary windings and considering the rotor skew, the MMF waveform is calculated as Fig. 4. The Fourier series analysis depicted in Fig. 5 shows that the resulted MMF is very close to a sinosuidal wave and has a Total Harmonic Distortion (THD) of about 0.46%. This Fig. 5. Fourier analysis of the MMF produced by primary windings Table I: Designed data of the synchro Fig. 6. Schematic view of the fabricated rotor and stator. 4. Simulation Finite element software is used for modeling of the designed synchro. To simplify the calculations we have used an equivalent two-dimensional model shown in Fig. (7). The magnetic paths in this model is the same as the designed synchro (in both of them the magnetic flux crosses two airgaps and then returns to stator cores) and therefore, it can be a good approximation. Although in this model the rotor skew has not been considered, it is precise for calculation of the synchro parameters such as winding turns, input current, and the induced output voltage. By this method, the designed data of the synchro are summarized in Table I. The output voltage of the synchro in this condition is about 6V (peak) that is shown in Fig. 8 and the magnetic flux distribution is shown in Fig. 9. The calculated input current of the synchro, depicted in Fig. 10, shows that in this condition the amplitude of the input current is about 0.1 A (rms) and the current density of wires is about 3.4 A/mm2. Parameter Value Unit Input voltage (peak) 12 V Frequency 50 Hz Output voltage (peak) 6 V Total turns of primary windings in each phase 480 - Secondary winding’s turns 400 - Stator and rotor wire thickness 0.2 mm Stator outer diameter 40 mm Rotor outer diameter 30 mm Stator length 87 mm Number of Stator E-cores 18 - Stator E-core thickness 3.8 mm Fig. 8. Simulated output voltage signal. Figure 9. The distribution of magnetic flux density. Fig. 7. Schematic view of the equivalent 2D synchro. Figure 10. Simulated input current of the synchro. 5. Fig. 11(b). Input line to line voltage and output signal at 90 degree difference with respect to zero reference angle. Experimental Results Fig. 6 represents the fabricated synchro. The synchro has been tested under two conditions: single and double (transmitter- receiver) arrangements. In the single arrangement the three phase input voltage is applied to primary windings and the output voltage induced in the secondary winding is as relation (8) [11]. The following relation shows that in this arrangement the amplitude of output signal is constant and its phase is proportional to the rotor angle with respect to the reference angle. Vˆ = k V Sin (ω t + θ − θ ) (8) out s in r ref In this relation Vˆout , k s , Vin , ω , θ r , and θ ref are respectively the output instant voltage, transformer ratio of synchro, the amplitude of the input voltage, the frequency of input voltage in radian per second, the rotor angle, and the reference angle. To implement first test, we have used a three-phase 9V (rms), 50Hz voltage signal. Fig. 11(a) shows the measured input (line to line) and output voltages at zero reference angle. Figs. 11(b) and 11(c) illustrate results of the test corresponding to the rotor angle of 90 and 180 degrees with respect to the reference angle. It can be seen that the phase of output voltage is proportional to the rotor angle and confirms the operation principle of the proposed synchro. Fig. 11(a). Input line to line voltage and output signal at zero reference angle. Fig. 11(c). Input line to line voltage and output signal at 180 degree difference with respect to zero reference angle. In the second test, two synchroes are connected to each other by their three-phase terminals in a star arrangement, as shown in Fig. 12. In this condition, the voltage induced in the secondary winding of the receiver synchro follows the relation (9) [11]. As deduced from this relation, the phase of the output voltage is constant and its amplitude is cosine function of the angle difference between the rotors of two synchroes. Vˆ = k V Cos (θ − θ ) Sin (ω t + ϕ ) (9) out d in rr rt In this relation k d , θ rr , θ rt , and ϕ are respectively the transformer ratio of this arrangement, the transmitter rotor angle, the receiver rotor angle, and the phase difference caused by the inductances of synchroes. For this test, A single-phase 9V (rms), 50Hz voltage is applied to the secondary winding of transmitter synchro. The results for various difference angles are presented in Figs. 13 (a) to (c). As seen from these figures, the maximum amplitude of the output voltage is occurred if the difference angle is 0 degree. In addition, in case of 60 and 90 difference angles the amplitude of output voltage become half and zero, respectively. These results meet the desired conditions and verify the theoretical concept of the presented scheme. 6. Fig. 4. Synchroes connection for transformer/ receiver arrangement Fig. 5(a). Transformer and receiver voltage in case of aligned synchroes. Fig. 13(b). Transformer and receiver voltage in case of 45 degree angular difference between synchroes. Fig. 13(c)6. Transformer and receiver voltage in case of 90 degree angular difference between synchroes. Conclusion In this research, a new brushless scheme for three-phase synchroes is proposed. This scheme opens a new way to eliminate the brush and slip rings’ noises and enhance the accuracy of the synchroes and resolvers. The concept of the scheme was described clearly in the paper. Then, using 2D finite element method the synchro was designed and analyzed. In order to validate the theoretical concepts, two prototypes were fabricated based on the designed parameters. The test was performed in two ways; single and double arrangement. The results confirmed the employed concept and also were in good agreement with simulations. The research is going on and the authors are now dealing with the optimal design of the synchro as well as making a digital convertor to compare the accuracy of present scheme with conventional synchroes. These researches will be present at the next occasion. References [1] R. Setbacken, ‘‘System performance and Application Tradeoffs Determine the Choice Between Encoders and Resolvers in Brushless Servos,’’ Power Convers. Intell. Motion, vol. 22, no. 5, pp. 69---76, 1996. [2] L. Harnefors, H.-P. Nee, ‘‘A General Algorithm for Speed and Position Estimation of AC Motors’’, IEEE Trans. On Industrial Electronics, Vol. 47, No. 1, Page(s): 77 --- 83, February 2000 [3] Yokozuka, Tsutomu, ‘‘Velocity Errors of the Resolver Phase Shifter ’’, IEEE Trans. On Industrial Electronics, Vol. IE-30, No.4, Page(s): 386 --- 389, Nov. 1983 [4] R. Hoseinnezhad, A. Bab-Hadiashar, P. Harding, ‘‘Calibration of Resolver Sensors in Electromechanical Braking Systems: A Modified Recursive Weighted Least-Squares Approach ‘‘’’, IEEE Trans. On Industrial Electronics, Vol. 54, No. 2, Page(s): 1052 --- 1060, April 2007. [5] L. Sun, ‘‘Analysis and Improvement on the Structure of Variable Reluctance Resolvers’’, IEEE Trans. Magn., Vol. 44, No. 8, Aug. 2008 [6] V. Del Toro, ‘‘Electric Machines and Power Systems’’, Englewd Cliffs, NJ: Prentice-Hall, 1985. [7] D.C. Hanselman, ‘‘Techniques for improving resolver-to-digital conversion accuracy’’, IEEE Trans. On Industrial Electronics, Vol. 38, No. 6, Page(s): 501 --- 504, December 1991 [8] D.C. Hanselman, ‘‘Resolver Signal Requirements for High Accuracy Resolver-to-Digital Conversion’’, IEEE Trans. On Industrial Electronics, Vol. 37, No. 6, Page(s): 556 --- 561, December 1990. [9] H. Martinez, ‘‘Measuring the Position of Mechanical Shafts,’’ Power Conv. Znt., vol. 9, no. 9, pp. 39-42, Oct. 1983. [10] J. Wan, X. Li, and G. Hong, ‘‘The analysis and design of high-speed brushless resolver plus R/D converter shaft-angle measurement system,’’ in Electr. Mach. Syst., ICEMS, 2001, pp. 289---292. [11] Moog component group, ‘‘Synchro and Resolver Engineering Handbook’’, available on www.moog.com, downloaded at June 1, 2011.