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The research on the design of the air-gap magnetic field of the polar machine based on the magnetic network model Zhang Weixiong, Zhang Jinghua, Zheng Yijun (Hefei University of Technology, Hefei 230009, Anhui, China) Iteratively established a more accurate equivalent magnetic network model of the polar motor. The method of solving the three-dimensional field magnetic network model is based on the equivalent magnetic network method. The distribution of the air gap magnetic field of the pole motor is analyzed and used in the electromagnetic calculation of the pole generator. The experimental results show that the motor with special structure is superior to other methods by using magnetic network model, which improves the calculation speed and high precision, and is suitable for engineering applications.
1 Introduction Polar motors are widely used in the automotive industry, wind power generation and small hydropower generation. Due to the complexity of the polar structure, the magnetic path length, the multi-leakage magnetic path, the air gap magnetic field and the leakage magnetic field are all three-dimensional, which brings difficulties for analyzing and designing the pole motor. The traditional magnetic circuit calculation accuracy can not meet the requirements, while the numerical calculation accuracy of the extreme three-dimensional electromagnetic field is high, but the modeling is complicated, and the operation is time-consuming, which is not conducive to motor optimization. The equivalent magnetic network (E) is based on the principle of the equivalent flux tube. The part of the motor with a relatively uniform magnetic flux distribution and a more regular geometrical shape is used as a unit to calculate the equivalent permeance, and the nodes pass through the nodes. Connection, using the similarity between the magnetic network and the electrical network, the magnetic position of each node or the magnetic flux of the unit is obtained to obtain relevant parameters. Vlado. Ostovi proposed the equivalent magnetic network method and applied it to the dynamic analysis of some electrical equipment, and the effect was good.
The establishment of the 2 pole motor magnetic network model 2. The establishment of the pole magnetic network model The stator part of the pole motor is exactly the same as the general AC motor, but its rotor magnetic circuit is special, the pole shape is more complicated, and the magnetic flux leakage path is more. And the magnetic flux in the pole is a three-dimensional field, both radial flux and axial flux. As shown in Figure 1, the equivalent magnetic network of the body is a three-dimensional network structure. In order to facilitate the analysis, the body and the stator core are equally divided into segments in the axial direction. In each segment, the stator magnetic circuits are assumed to be independent of each other, and each segment is connected by a nonlinear magnetic permeability, and each segment is circumferentially in the range of the opposite pole. Divided into j equal parts, as shown in Figure 2. Thus for each segment, we can get the two-dimensional equivalent magnetic network of the upper part of the segment, such as the equivalent of = 1 , 2,..., n), the body is connected by nonlinear magnetic permeability, so A three-dimensional equivalent magnetic network of the pole motor can be formed, as shown in FIG.
2. The specific calculation method of permeance-related permeance in the equivalent network refers to the literature [1]. Here, only a few different permeances in the lower-pole magnetic network are briefly introduced.
(1) Each section flows through the equivalent permeability G di of the radial flux H, and the axial flux H flows between each section (2) Considering the direction of each section of the body in the circumferential direction of the motor load armature reaction The permeance G = 1 , 2,..., j) between the unit bodies, the depth of influence of the armature reaction on the body is assumed to be the tip thickness.
(3) The leakage flux G between the different poles of each segment includes the side leakage flux and the bottom leakage flux.
3 pole motor air gap magnetic field analysis 3.1 Network equation establishment and solution In order to analyze the distribution of the pole air gap magnetic field, in Figure 1, we choose to assume a magnetic potential drop F between the AB and D planes, taking the node h as For the reference point, the nodal method is used to establish the node magnetic equation system of Fig. 4: where: [G] - permeance matrix h - magnetic matrix - magnetic flux source matrix.
Since the equivalent nonlinear permeance G in the permeance matrix [G] is itself a nonlinear network, the magnitude of its value is determined by the magnetic difference between the two ends of the permeance. The solution of equation (1) is as follows: (1) Under a magnetic potential F, assuming that the initial value of the magnetic position of each node is a certain value h, the magnetic potential drop at the opposite end of G can be obtained as ΔF as the equivalent magnetic potential source, and the magnetic network equations corresponding to G are obtained. Through the total flux H i of G, then (2) solve the node magnetic equation system (1) by Newton's Lawson method, and obtain k (k 1 ) times from the following linear equations after k iterations are obtained. Iterative solution h where: [J] - Jacobian matrix.
After a number of iterations, the right-hand vector of equation (3) approaches zero and tends to converge. When satisfied, the solution has reached the accuracy requirement and X is a sufficiently small positive amount.
3. 2 analysis of no-load characteristics (1) The dynamic potential of the armature tooth at no load is F = 0. Under a certain excitation current, the magnetomotive force F f between AB and D is solved to solve the node magnetic equation system ( 1), the magnetic potential drop across the nonlinear magnetic conductance G can be obtained as ΔF i , and the node magnetic position in the circumferential direction of each corresponding body surface and the top magnetic position of the armature ( 2) along the armature can be obtained. The axial s segment passes through the air gap flux of the first unit body to obtain a magnetic flux value of the corresponding segment, so that a three-dimensional air gap magnetic flux (magnetic density) distribution map can be drawn, as shown in FIG. (3) The total air gap flux in the axial direction through the (1) unit body is the magnetic field model based on the magnetic network model. (4) The radial component of the air gap magnetic density is: t is the width of the unit magnet, and l is the effective length of the core. Thus, the magnetic density values ​​corresponding to the unit magnets are obtained, so that the air gap magnetic density distribution curve for the range of the pole pitch can be obtained, as shown in FIG.
(5) The magnetic density of the i-th segment along the axial direction is: where: S is the area of ​​the body along the ith segment of the axial direction.
In this way, the magnetic density distribution curve in the body can be obtained, and FIG. 7 is a graph showing the axial magnetic flux distribution in the body when the thickness of the root is constant.
(6) The air gap magnetic-tight radial component curve, through harmonic analysis, obtains the amplitude of the radial air-gap magnetic-dense fundamental component: f-pole distance.
The no-load potential is: where: f - frequency - the number of turns in each phase of the armature - the fundamental winding coefficient.
3. 3 load characteristic analysis Synchronous generator phasor diagram shown in Figure 8, set the electric excitation pole generator, rated power P, rated voltage U, and rated power factor are known values, so the rated current I can be calculated, rated The excitation current is determined as follows: the angle between the axis of the A-phase winding is λ, and the instantaneous value of the three-phase current of the armature is: Solving the node magnetic potential equation in this case.
(2) According to the same method of calculating the no-load potential, the air-gap magnetic-density distribution can be obtained as shown in the figure. The harmonic fundamental analysis and the angle between the q-axis and the q-axis are obtained by harmonic analysis: Coefficient.
(3) Calculate the armature terminal voltage type: X - armature leakage reactance and armature resistance.
From the calculated terminal voltage U, when not satisfied, the λ angle is adjusted according to the following formula, and steps (1) to (3) are repeated until the formula (19) is satisfied.
(4) Calculate the power factor angle and power factor. If the calculated osh does not satisfy the following formula, adjust the excitation current I and repeat the calculation of steps (1) to (4) until the equation (23) is satisfied. The current is the rated excitation current I fN , and the air gap magnetic field distribution diagram is shown in Figure 9 and 10 : 4 Test results In order to verify the accuracy of the magnetic network method to calculate the motor through the electromagnetic field, we calculate and test the 1200W automobile generator. The test results and calculation results are within the allowable range, and the performance indicators meet the technical requirements of the automotive industry standard Q / T29094 92. The test requirements are as follows: the motor is energized (with voltage regulator) to adjust the load current at different speeds, so that the output voltage is 27V ±0. 5V, and the excitation current meter reads a constant value.
(1) Excitation current I = 1A, the actual measured value at the voltage of 26. 8V (2) Excitation current I measured value 5 Result analysis Through the air gap magnetic field distribution diagram of the pole motor, it can be found that the air gap magnetic tight edge The axial root gap has the lowest magnetic density, and the tip air gap magnetic density is the highest. The average air gap magnetic density along the circumferential direction is related to the shape of the pole. As can be seen from Fig. 6, the average air gap magnetic density waveform of the pole is approximately polar shape. The well-designed pole shape can minimize the maximum harmonic component of the fundamental component of the air gap magnetic density in the body. When the tip thickness is timed, in order to achieve the equal magnetic density design, the root thickness has the best value, as shown in Fig. 7. Show. Therefore, in the pole motor, the rational design of the pole shape and the use of the equal magnetic density design play an important role in improving the magnetic field waveform of the pole motor, reducing the magnetic flux leakage and improving the efficiency of the motor. Through the calculation of the equivalent three-dimensional magnetic network and the air gap magnetic density distribution, we can improve the design of the optimized pole shape to achieve the change of the magnetic flux distribution and realize the magnetic density design of the body, which is superior to other methods.
The equivalent magnetic network method is also a kind of finite element method, which has two important characteristics. First of all, the number of elements of the equivalent magnetic network is much less than that of the finite element. The nodes are mainly concentrated in the air gap, the precision is high, and the calculation time is greatly reduced. Second, each unit can only have two directions of flux. The equivalent magnetic network is between the equivalent magnetic circuit method and the finite element method, which is more accurate than the equivalent magnetic circuit method and less computation time than the finite element method. The accuracy of both the field analysis and the simplicity of the road calculation. The equivalent magnetic network method can be used to analyze the steady-state characteristics of the motor and also to analyze the dynamic characteristics of the motor. It has many advantages in practical applications. It can exhaustive simulation of the motor, including the discrete distribution of the windings, the form of the stator and rotor slots, and the saturation of the core, etc., due to the study of the amplitude of the air gap magnetic field based on the magnetic network model pole motor. Turn off the stator vibration, increase the amplitude of the bias vibration by W and decrease W, and the corresponding image is I. The amplitude is: thus the amplitude and phase of the stator surface of the ultrasonic motor are measured simultaneously, that is, the vibration of the stator is measured. Modal.
4 Measurement results When actually measuring the stator vibration of the micro ultrasonic motor, the stator is clamped with a small clip and placed on the optical vibration isolation platform to change the vibration frequency of the stator by changing the frequency of the signal source. Figure 3 shows the measurement results of the stator at 41k Hz: (a) is the amplitude measurement shown in grayscale (b) is the vibration phase displayed in grayscale (white is π/2, black is π/2) The amplitude value (d) of each point at the position indicated by the white line in Fig. 3a is the phase value of each point at the position indicated by the white line in Fig. 3b.
The vibrational shape of the stator can be easily seen from Fig. 3. Fig. 3 shows that the maximum amplitude of the stator midline is 21n, and there is a pitch line at the left end of 1.8. The gray level of Fig. 3a is examined, indicating that the resolution of the system can reach 0.4 n. If the position of the white line in Fig. 3a, b is changed, the amplitudes of other points on the surface of the stator can be clearly seen from Fig. 3 and d. And phase values. The above measurement results show that the system can easily analyze the vibration mode of the stator of the micro-ultrasonic motor, thus providing a basis for the research and development of the micro-ultrasonic motor.
5 Conclusions The micro-ultrasonic motor stator mode DSPI measurement system established in this paper can easily, accurately and quickly measure the vibration mode of the micro-ultrasonic motor stator, thus providing a powerful tool for the research and development of micro-ultrasonic motors. It will promote the development of the theory and practice of micro-ultrasonic motors.
(a) amplitude expressed in gray scale (b) phase distribution expressed in gray scale () amplitude curve shown in white line in graph a (d) phase distribution at white line in graph b Brief introduction: Jia Shuhai (1969), male, doctoral student, mainly engaged in research on photoelectric detection technology.
Prime. Its other advantage is that it can transform a complex magnetic circuit into a simple electrical impedance network, expressing the common nature of the motor, and the model difference between different motors is small. Especially in the complex structure of the motor, the magnetic network method can show its unique advantages.
Zhang Weixiong. Research on air gap magnetic field of square wave permanent magnet motor based on magnetic network model [J].
The first author: Zhang Weixiong (1974 ~), male, master, research direction for the motor and its control.