Calculation of Permanent Magnet motor electromagnetic torque 1 Introduction In recent years, due to the excellent performance of the permanent magnet brushless DC motor and the continuous increase in market demand, more and more attention has been paid to the research of the permanent magnet brushless DC motor. The design of the permanent magnet brushless DC motor is a comprehensive design of the motor body and control system. It not only involves the basic theory of motor design, but also includes the control theory, materials science and power electronics technology disciplines. It is a very complex jobs. From the standpoint of the design of the permanent magnet brushless DC motor, the existing design theory and design procedures are not yet mature and perfect, and most of them are based on manual calculations, which is difficult to meet the needs of the actual situation. This article starts with the motor body design, applies the motor basic theory to discuss the calculation of inductance, average current and electromagnetic torque of the main parameters that affect the motor performance, and puts forward some simple and practical new methods.
2 The calculated inductance of the inductor is a parameter that has a significant influence on the performance of the motor. However, in the previous design procedure of the permanent magnet brushless DC motor, a direct current model was often used, and thus the influence of the inductance was neglected, which would inevitably lead to a calculated value of performance. Large deviations between actual values. This article discusses the calculation of the inductance from the basic principle of the motor.
Permanent magnet brushless DC motor circuit is generally asymmetric. Taking a three-phase six-state as an example, in each energized state, only two phase windings are energized at the same time, and the circuit structure is asymmetrical. Therefore, its calculation is more complicated.
Although the inductance calculation of the permanent magnet brushless DC motor is different from that of the general motor, its physical nature is not different. Therefore, it can be calculated similarly to the induction motor inductance calculation method. The specific derivation is as follows: 2.1. Fundamental magnetic potential of each pole Armature The magnetic flux amplitude per phase F is a design of a permanent magnet brushless DC motor when considering the influence of inductance. I - Fundamental current RMS W - Each phase Number of winding turns - winding coefficient P - number of pairs of poles Let H be the spatial position angle of the winding, take the axis of the A-phase winding as the origin, then the two-phase magnetic potential expression of the energization is two-phase composite magnetic potential is 2 . 2 Air Gap Radial Magnetostrictive Amplitude Modulus k - Air Gap Coefficient - First Air Gap Length 2.3 Per Fundamental Fundamental Magnetic Flux A - Calculation of Pole Arc - Stator Core Effective The length 2.4 magnetic flux generated by the fundamental magnetic field 2.5 per phase inductance in the L → ∞ condition, the flux and the current is proportional to the change, the inductance can be calculated as follows 3 The calculation of the average current and the electromagnetic torque 3. 1 not When considering the inductance, the average current and the electromagnetic torque are usually calculated as the square wave of the permanent voltage brushless DC motor terminal voltage waveform, because the air gap magnetic field (or the fundamental magnetic field) is sinusoidal distribution, so in the permanent magnet brushless DC motor There is a waveform matching problem between the terminal voltage and the back-EMF waveform. In general, the components in the control circuit need to be forward voltage drop in order to turn on, and in the permanent magnet brushless DC motor, because the terminal voltage waveform is usually a square wave, the back-EMF fundamental waveform is a sine wave, the size of the two The relationship changes over time, so when the speed increases to a certain degree, the instantaneous value of the back-EMF may exceed the terminal voltage, making the control element unable to conduct and the winding temporarily powered off. The relationship between the terminal voltage and the resultant back-EMF is shown in Fig. 1, where the slashed portion indicates the conduction interval. At this time, the conduction angle and the state angle in each energization state are different and the higher the rotation speed, the smaller the conduction angle. This will cause the average value of the stator current and the electromagnetic torque to not be linear with the rotational speed after the rotational speed exceeds a certain value, and the mechanical characteristics of the electrical machine are nonlinear.
Taking into account the above phenomenon, in the calculation of the average current, you can not simply calculate the average value of the entire power-on condition but should first calculate the critical speed of the above phenomenon, calculate the turn-on and turn-off in the range of speeds where the above phenomenon occurs. The critical angle is then integrated over the conduction interval and the average value is calculated over the entire power-on state. Detailed steps are as follows: 3.1.1 1 per phase winding back EMF E type - motor speed 5 - per pole magnetic flux - air gap magnetic field coefficient 3. 1. 2 critical speed N so-called critical speed is Refers to the ability to make the magnitude of the two-phase synthetic back EMF equal to the rotational speed of the two phase winding terminal voltages. When the motor speed exceeds N, the conduction angle will be smaller than the state angle and change with the change of the rotation speed. When the motor rotation speed is less than N, the conduction angle is always equal to the state angle.
According to the definition can be obtained in the following equation where U - motor terminal voltage - the pressure drop of the control element can be resolved from the critical speed N expression 3. 1 3. The average current I according to the conduction state of the armature winding different points Two cases are calculated.
When the rotational speed is less than the critical rotational speed, the design speed of the permanent magnet brushless DC motor when considering the influence of the inductance is greater than the critical rotational speed. In the formula, A is the critical angle, that is, the back electromotive force is generated when the combined back electromotive force amplitude of the energized two-phase winding is greater than the terminal voltage. The instantaneous value is equal to the angle of the terminal voltage.
When the phase angle of the back EMF is greater than A and less than PA, the control element is turned off, and the current in the winding is zero, and the winding is normally supplied. 3.1.4 When the average electromagnetic rotation M speed is less than the critical rotation speed, the rotation speed is greater than the critical rotation speed, The equations of average current and electromagnetic torque derived after considering the waveform matching problem are applicable not only in the vicinity of the operating point of the motor, but also in the entire operating range from zero to ideal no-load speed.
3.2 Considering the inductance, the calculation of the average current and the electromagnetic torque counts into the influence of the inductance. For example, if an AC motor model is used, the effect of the inductance is included in the form of a parameter. This article mainly introduces a simple approximation method.
In a permanent magnet brushless DC motor, the armature current is generated by the combined effect of the winding-end voltage and the mean value of the back-EMF of the winding. Therefore, the armature current can be regarded as the step response of the combined voltage of the two. If you do not consider the influence of inductance, then this step response current is also a square wave but the influence of the inductance cannot be ignored. According to the circuit theory, for the circuit composed of inductance and resistance, the current response under step voltage is exponential. Rising waveform. For the three-phase six-state operation mode, two windings are turned on at the same time at any time, so the expression of the instantaneous value of the armature current can be written as U in the formula—the step voltage acting on the armature circuit—the two-phase winding back EMF The composite value of S—the time constant of the armature loop inductance and resistance—integrates equation (18) in each conduction state to obtain the average current of each phase winding. It can be seen from FIG. 2 that the areas of the 2nd region and the 3rd region are equal in the illustration, so that the integral in one state can be calculated from the 1 and 2 regions. Therefore, in the formula, the T-commutation period is known from the above formula. The armature current after the influence of the inductance is different from the armature current without inductance by a factor of k i. Therefore, when calculating the average current of the permanent magnet brushless DC motor, , you can first calculate the average current without considering the inductance, and then introduce the current correction factor to account for the influence of the inductance. The average electromagnetic torque is proportional to the average current, so this correction factor also applies to the calculation of the average electromagnetic torque. Using this correction method based on the DC model greatly simplifies the calculation and improves the accuracy.
4 Calculation results Experimental verification of a permanent magnet brushless DC motor with external rotor for motorcycles is as follows: rated power 500W, rated voltage 36V, rated permanent magnet brushless DC motor design considering the influence of inductance Shanghai Shanghai Small and Medium Motor Industry Technology Innovation The first meeting of the Board of Directors and the Technical Committee of the Center held the first meeting of the Board of Directors and Technical Committee of the Technical Innovation Center of the Shanghai Small and Medium Motor Industry in Shanghai on April 17-18, 2001 in Shanghai. Attending the meeting were members of the Shanghai Municipal Commission of Economics, the China Electrical Equipment Industry Association Small and Medium Motors Branch and the Psychological Department of Technological Innovation, and members of the Technical Committee, and specially invited Lanzhou Electric Co., Ltd., Hebei Electric Machinery Co., Ltd., and Shandong Huali Electric Group. Co., Ltd. and Shunde Desheng Motor Co., Ltd. attended the meeting.
The conference heard, reviewed and passed the "Shanghai Science and Technology Innovation Center of the Center for Short-term Technology Development and 2001 Work Plan", "Shanghai Middle and Small Motor Industry Technology Innovation Center Management Organization and Institutional Functions," and "2001 Annual Financial Budget Plan." The conference believed that the recent technological development plan and the 2001 work plan of the Technology Innovation Center are timely and feasible. The time to develop China's high-efficiency motors has matured, and the task is to urgently develop intelligent motors to increase the technological content of motor products and improve small and medium-sized motors. The effective way of enterprise economic benefit. The representative also put forward many positive suggestions on the principles and research directions of the science and technology development plan of the technology innovation center.
The meeting accepted Lanzhou Electric Co., Ltd., Hebei Electric Co., Ltd., Shandong Huali Electric Group Co., Ltd., and Shunde Desheng Electric Co., Ltd. as members of the Technology Innovation Center.
Rotation speed 400r / min, pole pair 9, phase number 3, number of teeth 27, stator inner diameter 6cm, stator outer diameter 15cm, rotor outer diameter 17. 4cm, rotor inner diameter 16cm, rotor magnet is tile-shaped, its thickness 0. 4cm With a central angle of 15°, concentrated windings are used.
Calculate according to the test given voltage, and use the calculation results and test results to draw the characteristic curve, as shown in Figure 3.
From this figure can be more intuitive to see: the entire characteristic curve, especially near the rated point of the calculated results and experimental results are in good agreement.
Take the rated point for analysis, can obtain the rated torque at the same rated power, rated speed relative to the error of their respective test values ​​are 0. 333, 0335. Visible, using this method to calculate the error is small, fully meet the project The need for calculations.
(1) The inductance has a great influence on the performance of the permanent magnet brushless DC motor, so the influence of the inductance can not be ignored in the design. In this paper, the calculation formula of the inductance of each phase is deduced when the two phases of windings are energized at the same time.
(2) There is a waveform matching problem between the terminal voltage of the permanent magnet brushless DC motor and the back EMF, which will affect the calculation of the average current and the electromagnetic torque.
(3) Although the influence of the inductance cannot be ignored, the average current and the electromagnetic torque can be obtained without considering the inductance, and then a coefficient determined by the rotation speed and the inductance can be used to correct it, and the inductance can be obtained more. For precise results. This method is more suitable for computer-aided design, but also can meet the needs of engineering calculations.
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