Magnetic Resistance Analysis and Minimization of Permanent Magnet Linear Synchronous Motor

NdFeB) with high thrust, low loss, small electrical time constant, fast response speed, etc., in lifting systems (elevators, mine hoisting systems), electronic manufacturing equipment (such as MEMS micro-manufacturing and micro-assembly systems, high-speed SMT Machines, micro-encapsulation platforms, high-speed and high-precision numerical control systems (such as high-speed machining centers, precision grinding machines) and other occasions have a wide range of application prospects and have been widely studied and developed by scholars from South Korea, Japan, Germany, and China.

Fund Project: Zhejiang Provincial Science and Technology Plan Key Scientific Research Project (No.011103979).

The equivalent circuit and its operating characteristics of the permanent magnet linear synchronous motor are analyzed and studied. However, the thrust fluctuation is one of the main defects in its application. Because the fluctuation of the thrust is the cause of motor vibration and noise generation, especially at low speeds, it may also cause resonance, which deteriorates its servo operation characteristics (such as positioning accuracy). Therefore, the thrust ripple analysis of permanent magnet linear synchronous motor is one of the main contents of the analysis and research of its operating characteristics. One of the main sources of thrust ripple of permanent magnet linear synchronous motor is the generation of magnetic resistance DF. DF is similar to the magneto-resistive (or positioning) torque of permanent magnet synchronous rotating motor (Cogging Torque), so some permanent magnet linear synchronous motors DetentForce is called CoggingForce. But the difference is that DetentForce not only originates from the same cogging as the reluctance torque, but also comes from the limited primary length-induced edge effect, as shown by the DF generation principle. As there is no corresponding Chinese term for DetentForce, but from the point of view of the production mechanism, it is related to the change of magnetic resistance caused by cogging and edge. Therefore, it is temporarily called magnetic resistance. This article is abbreviated as DF.Fsbt and the pitch is close. The correlation is the periodic function of the pitch. Fd is closely related to the pole length and the primary length. It is a periodic function of the pole pitch and its amplitude mainly depends on the ratio of the pole pitch to the effective air gap.

Primary core secondary note: Fs! Ot is the DF caused by the cogging effect; Fend is the schematic diagram of the principle of DF DF caused by the edge effect. At present, the analysis and minimization of DF are mainly based on Korean and Japanese scholars. In terms of DF analysis due to edge effects, a basic analysis model was established, but unfortunately DF was assumed to be symmetrical about the peak at the time of specific optimization, and thus optimization was not made from a strict basic model.

Using the above basic model, but directly removing the Fourier cosine term of the DF (see equations (1), (2)), the error is large, and then using the phase difference method to optimize the primary length has greater limitations, such as the calculation model for this article You can't get real optimizations. Domestic Tsinghua University conducted a preliminary analysis of the DF produced by the edge effect when analyzing thrust fluctuations. Based on the basic model, this paper uses finite element numerical analysis combined with Fourier series nonlinear regression analysis to optimize the primary length to reduce the DF. The optimized S value caused by the edge effect but in general, it is impossible to completely eliminate DF, DF Analytical Model for Elimination of DF PMLSMs DF Analytical Physical Model For the purpose of this paper only analyzing the DF resulting from edge-effects due to limited primary length, the physical model is equivalent to a slotless PMLSM, as shown. DF is the thrust of the primary iron core when it opens the magnetic field. As mentioned above, this is due to the limited primary length causing the two segments of the iron core to break and causing side edge effects. This is a phenomenon unique to linear motors.

Physical model of DF analysis of PMLSM Generally, the primary length is 23 poles or more, and there is basically no mutual influence between the two ends. Therefore, it can be seen as the result of the composite force of two half-infinite primary core single-end forces, such as As shown. The thrust of the primary core is not the same in different positions, but because the secondary permanent magnets are arranged in a polar interval, the corresponding thrust is a periodic function of the secondary pole pitch. For the two semi-infinite single-end core structures, the stress properties, conditions, and amplitudes are exactly the same, but in the opposite direction, that is, the right end is always positive, while the left end is always negative, and there is a phase difference between the two, and the phase difference depends on the primary length. Single-end forces are shown in (a), (b). It was previously analyzed that if the phase difference between the two ends of the force is (2k-1)n, they can cancel each other after synthesis. However, the geometric phase difference does not coincide with the DF phase difference. Therefore, this method cannot be directly used to optimize the primary length reduction DF. DF analysis mathematical model = kT-Ls; Ls is the primary length; k is an integer; T is the polar distance.

From equations (1) and (2), therefore, for a primary core of any finite length Ls = kT-S, the Fdf for DF minimization analysis can be derived from the above analysis. The resultant DF amplitude is closely related to the primary length. Related. Therefore, we can choose an appropriate length to reduce the amplitude of DF, even if the absolute value of Fn in formula (5) is the smallest, that is, the optimal length of the fundamental wave is DF engineering calculation and regression analysis of PMLSM. First, the entire length is selected as the initial calculation. Values, using finite element for single-ended DF modeling and analysis of PMLSM. The basic parameters of the DF analysis model are shown in Table 1. The distribution of magnetic lines of force at the right end of the primary core at 178 mm is shown, showing the distribution of magnetic flux density in the direction r of the air gap at the center of the primary core at 176 mm. After solving the electromagnetic field, the DF is obtained using the principle of virtual work. Table 1 DF analysis Basic model specifications Primary core Air gap height Secondary pole permanent magnet Length Width Height mmmmmm Type Width High remanence mm mm Density/T polar distance Using finite element numerical analysis When the right and left ends of the primary core are found to move within a polar distance range (since DF is a periodic function with respect to the pole pitch, only one pole pitch range can be analyzed), the DF received is as shown, using the fourth-order Fourier series. (Because the difference between the fourth-order and fifth-order Fourier series is very small, it means that the fourth-order Fourier series regression analysis is enough.) The non-linear regression analysis can be seen from the figure, the fourth-order Fourier series and single-ended calculations There is a fairly high degree of consistency between the various data points. Therefore, the Fdf of the model primary core as a whole is verified in order to verify the validity of the single-ended analysis and then the synthesis of DF analysis. The results of the DF obtained by the synthesis of the single-ended analysis and the results of the overall analysis of the DF (represented by *) are compared and analyzed. It can be seen that there is good consistency, indicating that analysis using single-ended analysis and then synthesis of DF is correct and effective.

PMLSM's DF Minimization Technique In order to achieve a DF minimization, the pre-analysis can select the appropriate primary length. From Equation (8), the optimal length 4pt for eliminating the DF fundamental component is as described above. The fourth-order Fourier analysis is sufficient because the above optimization value pt = 6.925 when using the five-order Fourier series nonlinear regression analysis. It is very close to the optimal value obtained by the fourth-order Fourier analysis. Therefore, the optimized primary core length Lsopt is Lsopt = kt = 361 (13) In this optimized primary core length, the right end F + = F + holds not the above optimization analysis and finite element verification As shown, after optimizing the primary core length Fdf It is greatly reduced. Compared with the initial value, the peak value from the original 35N will be close to 10N. It can be seen from the figure that the fundamental wave of the synthetic FdF has been eliminated, and the rest is the high harmonic with period 2r and above. In order to verify the validity of the analysis method, the optimization results were compared with the overall analysis after optimization of the core length. It can be seen from the figure that the results are in good agreement with the finite element analysis results, indicating that the primary core is analyzed by single-end analysis. Length optimization to reduce FdF is feasible.

5 Conclusion Permanent-magnet linear synchronous motor with its unique advantages constitutes the preferred motor type of linear motor direct drive servo system. However, thrust fluctuation is one of the main defects in its application, and DetentForce is one of the key sources of thrust fluctuations. Firstly, this paper establishes the analysis model of DetentForce caused by the finite edge length and produces the DetentForce. The characteristics of semi-infinite single-ended structure are used to analyze the characteristics of DF and its reduction principle. The finite element numerical analysis and the higher order Fourier series nonlinear regression analysis are used. Combine, DetentForce analysis of the basic model, and optimize the primary length reduction DF based on the previous model, and through the overall analysis of the basic model and the optimization model were compared and verified, indicating that the use of single-ended semi-infinite structural analysis and then synthesized DetentForce is correct Using the above-mentioned single-ended semi-infinite analysis model for primary length optimization to reduce DetentForce is feasible.

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