CN103986397B - Brshless DC motor permanent magnet fault detection method - Google Patents

Abstract

The invention discloses a method for detecting a permanent magnet fault of a brushless direct current motor, which comprises the following steps: fixing the rotor, and performing a locked-rotor experiment on the motor to obtain the following relational formula: e=-K _s Isin(γ')=-K _s i _β ; the coefficient K _s of the corresponding stator current I and coil flux linkage can be obtained from this relation; during the operation of the motor, the counter electromotive force e on the motor coil is detected, and the electrical angle of the permanent magnet in space is calculated according to the counter electromotive force e is the spatial magnetic field density amplitude B _f sin (γ) generated at γ‑90 place; comparing the obtained permanent magnet spatial magnetic field density amplitude B _f sin (γ) with the preset reference amplitude, it can be determined whether Demagnetization or loss of magnetization occurs. The method for detecting the fault of the permanent magnet of the brushless direct current motor of the present invention has the advantages of knowing the fault status of the permanent magnet without disassembling the permanent magnet, fast and effective detection, and the like.

Description

Fault Detection Method of Permanent Magnet of Brushless DC Motor

technical field

The invention relates to a fault detection method for a permanent magnet of a brushless DC motor.

Background technique

The brushless DC motor consists of a motor body and a driver, and is a typical mechatronic product. A brushless motor refers to a motor without a brush and a commutator (or slip ring), also known as a commutator-less motor. Magnetized permanent magnets are attached to the rotor of the motor. In order to detect the polarity of the motor rotor, a position sensor is installed in the motor.

Permanent magnet fault location is often a difficult point in brushless DC motor applications. Due to the influence of the winding method of the stator coil, the failure of the permanent magnet of the motor can be detected through a specific algorithm, but it cannot be accurately positioned, which causes great difficulties in the maintenance of the motor, because the removal of the permanent magnet , installation, and detection are more troublesome.

Contents of the invention

The purpose of the present invention is to avoid the deficiencies in the above-mentioned prior art, and provide a method for detecting the fault of the permanent magnet of the brushless DC motor, so as to quickly and effectively detect the fault condition of the permanent magnet.

The present invention adopts the following technical solutions to solve the technical problems.

A brushless DC motor permanent magnet fault detection method is characterized in that it includes the following steps:

Step 1: Fix the rotor, and conduct a locked-rotor experiment on the motor, and the following relationship can be obtained:

e=-K _s Isin(γ′)=-K _s i _β (1);

In formula (1), e: counter electromotive force; I: stator current; K _s : coefficient of coil flux linkage, γ′ is the electrical angle of stator current in the stationary αβ coordinate system.

Step 2: From the relational expression (1) in step 1, the coefficient K _s of the corresponding stator current I and the coil flux linkage can be obtained;

Step 3: During the operation of the motor, detect the counter electromotive force e on the motor coil, and calculate the spatial magnetic field density amplitude B _f sin(γ) of the permanent magnet at the space electrical angle of γ-90 according to the counter electromotive force e;

Step 4: Comparing the spatial magnetic field density amplitude B _f sin(γ) of the permanent magnet obtained in Step 3 with the preset reference amplitude, it can be determined whether there is demagnetization or demagnetization. First, when the permanent magnet does not lose its magnetism, the value of K _f BB _f sin(γ) is obtained through no-load experiment measurement, and BB _f sin(γ) can be calculated from K _f =K _s and saved as a reference value; then The B _f sin(γ) during operation will be detected. If the detected value is less than the reference value saved in the original measurement, it means that the permanent magnet has demagnetized or lost magnetism.

In said step 3, the calculation process of the spatial magnetic field density amplitude B _f sin (γ) is:

When the motor is running, the detection coil is disconnected. At this time, there is no current flowing in the detection coil, which has no effect on the motor space magnetic field. The detected coil terminal voltage is equal to its counter electromotive force:

$\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; d\&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d\&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

At this time, the above formula (2) can be changed into:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

According to the above formula (3), the spatial magnetic field density amplitude B _f sin (γ) can be calculated.

Compared with the prior art, the beneficial effects of the present invention are reflected in:

The brushless DC motor permanent magnet fault detection method of the present invention can obtain the spatial magnetic field density amplitude B _f sin (γ) of the permanent magnet through calculation, and the spatial magnetic field density amplitude B _f sin (γ) of the permanent magnet is compared with the previous By comparing the set reference amplitudes, it can be determined whether there is demagnetization or loss of magnetism, and the fault status of the permanent magnet can be known without disassembling the permanent magnet, and the detection is fast and effective.

The method for detecting the fault of the permanent magnet of the brushless direct current motor of the present invention has the advantages of knowing the fault status of the permanent magnet without disassembling the permanent magnet, fast and effective detection, and the like.

The present invention will be further described below through specific embodiments.

detailed description

The brushless DC motor permanent magnet fault detection method of the present invention comprises the following steps:

Step 1: Fix the rotor and conduct a stall experiment on the motor, the following relationship can be obtained:

e=-K _s Isin(γ′)=-K _s i _β (1);

In formula (1), e: counter electromotive force; I: stator current; K _s : coefficient of coil flux linkage, γ′ is the electrical angle of stator current in the stationary αβ coordinate system.

Step 2: From the relational expression (1) in step 1, the coefficient K _s of the corresponding stator current I and the coil flux linkage can be obtained;

Step 3: During the operation of the motor, detect the counter electromotive force e on the motor coil, and calculate the spatial magnetic field density amplitude B _f sin(γ) of the permanent magnet at the space electrical angle of γ-90 according to the counter electromotive force e;

Step 4: Comparing the spatial magnetic field density amplitude B _f sin(γ) of the permanent magnet obtained in Step 3 with the preset reference amplitude, it can be determined whether there is demagnetization or demagnetization. (First, when the permanent magnet does not lose its magnetism, the value of K _f BB _f sin ( _γ ) is obtained by measuring the no-load experiment, and BB _f sin (γ) can be calculated from K _f =K _s and saved as a reference value; Then the B _f sin(γ) during the operation will be detected, if the detected value is less than the reference value saved in the original measurement, it means that the permanent magnet has demagnetized or lost magnetism.)

In said step 3, the calculation process of the spatial magnetic field density amplitude B _f sin (γ) is:

When the motor is running, the detection coil is disconnected. At this time, there is no current flowing in the detection coil, which has no effect on the motor space magnetic field. The detected coil terminal voltage is equal to its counter electromotive force:

$\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; d\&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d\&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

At this time, the above formula (2) can be changed into:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

According to the above formula (3), the spatial magnetic field density amplitude B _f sin (γ) can be calculated.

At this time, the fault diagnosis of the permanent magnet can be carried out by the waveform of the back electromotive force and the β component of the stator current, where B _f sin(γ) is the magnetic field density of the permanent magnet at the space electric angle of γ-90, by detecting the corresponding magnetic field density The change of the amplitude can determine whether the permanent magnet has demagnetized.

The invention proposes to detect the motor by adding an auxiliary induction coil, which can avoid the influence brought by the connection of the stator coil, effectively detect the fault condition of the permanent magnet, and make the coil axis consistent with the A-phase axis, and the coil is The whole pole distance is long, and its detection principle is as follows:

1. The magnetomotive force of the space air gap is generated by the linear superposition of the stator current and the permanent magnet;

The maximum amplitude of the fundamental magnetomotive force generated by the single-phase concentrated full-pitch winding on the air gap is:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; \&phi;</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; QUR</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; QUR</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.9</span>}\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

When the motor is a three-phase symmetrical winding, take the axis + A of the A-phase winding as the origin, then when any current flows, the spatial distribution of the synthetic magnetomotive force in the αβ coordinate system is:

In the above formulas (4) and (5), N ₁ : the number of series turns per phase; q: the number of full-pitch coils for each pair of poles; a: the number of parallel branches; I: phase current; I _k : coil current;

At this time, the air gap synthetic magnetomotive force is

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; ji</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j\&gamma;</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j\&theta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

In the above formula (6), γ: the space electric angle angle between the permanent magnet axis and the A-phase axis; θ: the space electric angle with the A-axis axis as the origin.

2. The synthetic air gap magnetic field is generated by the linear superposition of stator current and permanent magnet;

When the motor is running in the linear region but not in the saturation region, the magnetic field intensity is linearly related to the magnetic field density, and its synthesized magnetic field satisfies the principle of linear superposition, and its magnetic field density is the linear superposition of the magnetic field density generated by the permanent magnet and the magnetic field density generated by the stator current:

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

In the above formula (7), μ: air gap magnetic permeability; l _air : air gap length.

3. Magnetic linkage in the coil;

The flux linkage generated by the stator current in the coil is:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&theta;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; lR\&mu;</span>}}{{\mathrm{<span\; class="notranslate">\; pl</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&theta;</span>}\\ <span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; lR\&mu;</span>}}{{\mathrm{<span\; class="notranslate">\; pl</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}}\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

In the above formula (8), γ′: the angle between the magnetomotive force of the stator and the A-axis axis.

The flux linkage generated by the permanent magnet in the coil is:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&theta;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&theta;</span>}\\ <span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

The synthetic flux linkage in the coil is linearly superimposed by the respective flux linkages generated by the permanent magnet and the stator coil as follows:

$\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}\mathrm{<span\; class="notranslate">\; d\&theta;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; lR\&mu;</span>}}{{\mathrm{<span\; class="notranslate">\; pl</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; air</span>}}\mathrm{<span\; class="notranslate">\; d\&theta;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

4. Back electromotive force detection permanent magnet method

When the motor is running, the detection coil is disconnected. At this time, there is no current flowing in the detection coil, which has no effect on the motor space magnetic field. The detected coil terminal voltage is equal to its counter electromotive force:

$\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; d\&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d\&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

At this time, the above formula (2) can be changed into:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

At this time, the fault diagnosis of the permanent magnet can be carried out by the waveform of the back electromotive force and the β component of the stator current, where B _f sin (γ) is the magnetic field density of the permanent magnet at the space electric angle of γ-90, by detecting the corresponding magnetic field density The change of the amplitude can determine whether the permanent magnet has demagnetized.

The brushless DC motor permanent magnet fault detection method of the present invention can obtain the spatial magnetic field density amplitude B _f sin (γ) of the permanent magnet through calculation, and the spatial magnetic field density amplitude B _f sin (γ) of the permanent magnet is compared with the previous By comparing the set reference amplitudes, it can be determined whether there is demagnetization or loss of magnetism, and the fault status of the permanent magnet can be known without disassembling the permanent magnet, and the detection is fast and effective.

In the above formula (1), e: counter electromotive force; I: stator current; K _s : coefficient of coil flux linkage.

In the above formula (2), e is the back electromotive force, ψs is the flux linkage generated by the stator current, ψ _f is the flux linkage generated by the permanent magnet, γ is the angle between the permanent magnet and the A-axis axis, and γ′ is the magnetomotive force of the stator The included angle with the axis of A-axis, K _s is the flux linkage coefficient of the stator coil, K _f is the flux linkage coefficient of the permanent magnet, and ω is the electrical angular velocity.

In the above formula (3), e is the back electromotive force, γ is the angle between the permanent magnet and the A-axis axis, γ′ is the angle between the stator magnetomotive force and the A-axis axis, K _s is the coefficient of the flux linkage of the stator coil, K _f is the flux linkage coefficient of the permanent magnet, and ω is the electrical angular velocity.

In the above formulas (4) and (5), N ₁ : the number of series turns per phase; q: the number of full pitch coils per pair of poles; a: the number of parallel branches; I: phase current; I _k : coil current; p is the number of pole pairs, k is the winding coefficient of the space magnetomotive force generated by the input current, and N _k is the number of series coils per turn. I _A1 refers to the magnitude of the input current of phase A, I _B1 refers to the magnitude of the input current of phase B, and I _C1 refers to the magnitude of the input current of phase C. Specify the fundamental magnetomotive force vector generated by sub-phase A current in space, Specify the fundamental magnetomotive force vector generated by sub-phase B current in space, Specify the fundamental magnetomotive force vector generated by sub-phase C current in space, Specify the magnetomotive force vector generated by the sub-current in space, i _α and i _β specify the components of the sub-current in the αβ coordinate system, and θ is the space electrical angle with the A-axis axis as the origin.

In the above formula (6), γ: the space electric angle angle between the permanent magnet axis and the A-phase axis; θ: the space electric angle with the A-axis axis as the origin. F _f refers to the magnitude of the magnetomotive force generated by the permanent magnet in the space air gap.

In the above formula (7), μ: air gap magnetic permeability; l _air : air gap length; is the synthesized magnetic field density vector in the space air gap; is the magnetic field density vector generated by the permanent magnet in the space air gap; is the magnetic field density vector generated by the stator current in the space air gap.

In the above formulas (8) and (9), γ′: the angle between the magnetomotive force of the stator and the axis of the A axis, I is the amplitude of the stator current, K _s is the coefficient of the flux linkage of the stator coil, p is the number of pole pairs, N ₂ is the number of turns in series of detection coils, R is the radius of the inner circle of the stator, l is the length of the axis of the inner circle of the stator, BB _I is the magnitude of the fundamental magnetic flux density generated by the stator current in space; BB _f is the fundamental wave generated by the permanent magnet in space The magnitude of magnetic density; θ is the spatial electrical angle expanded by the central axis of the detection coil as the origin. K _s : coefficient of stator current coil flux linkage, K _f : coefficient of permanent magnet flux linkage.

In the above formula (10), ψ is the flux linkage generated by the stator current and the permanent magnet in the detection coil, ψ _s is the flux linkage generated by the stator current in the detection coil, and ψ _f is the flux generated by the permanent magnet in the detection coil The magnetic chain.

Claims (1)

1. brshless DC motor permanent magnet fault detection method, is characterized in that, comprises the steps:

Step 1: fixed rotor, carries out stall experiment to motor, can obtain following relational expression:

E=-K_sIsin (γ ')=-K_si_β(1)；

In formula (1), e: counter electromotive force；I: stator current；K_s: the coefficient of coil flux linkage；γ ' is stator magnet kinetic potential and A The angle of axle axis；

Step 2: the COEFFICIENT K of corresponding stator current I and coil flux linkage can be obtained by the relational expression (1) in step 1_s；

Step 3: in motor operation course, the counter electromotive force e on detection motor coil, and calculate permanent magnet according to counter electromotive force e It is space magnetic field density amplitude B that γ-90 place produces in space electrical angle_fsin(γ)；

Step 4: space magnetic field density amplitude B of permanent magnet that will obtain in step 3_fSin (γ) and reference amplitude set in advance Contrast, it may be determined that whether have demagnetization or loss of excitation to occur；

In described step 3, space magnetic field density amplitude B_fThe calculating process of sin (γ) is:

Motor makes detection coil open circuit when running, now in detection coil, no current flows through, and it does not produce shadow to motor space magnetic field Ringing, the coil-end voltage of detection is equal to its counter electromotive force:

$e=-\frac{{\mathrm{d\&psi;}}_s+{\mathrm{d\&psi;}}_f}{dt}=-K_{s}I\frac{d\cos \left({\mathrm{\&gamma;}}^{\&prime;}\right)}{dt}-K_f{B}_f\frac{d\cos \left(\mathrm{\&gamma;}\right)}{dt}=-{\mathrm{\&omega;K}}_{s}I\sin \left({\mathrm{\&gamma;}}^{\&prime;}\right)-{\mathrm{\&omega;K}}_f{B}_f\sin \left(\mathrm{\&gamma;}\right)---\left(2\right);$

In above formula (2), e is back-emf, and ψ s is the magnetic linkage that stator current produces, ψ_fThe magnetic linkage produced for permanent magnet, γ is forever Magnet and the angle of A axle axis, γ ' is the angle of stator magnet kinetic potential Yu A axle axis, K_sFor the coefficient of stator coil magnetic linkage, K_fFor permanent magnet flux linkage coefficient, ω is angular rate；

Now above formula (2) can be become:

$K_f{B}_{f}sin\left(\mathrm{\&gamma;}\right)=-\frac{e+{\mathrm{\&omega;K}}_{s}Isin\left({\mathrm{\&gamma;}}^{\&prime;}\right)}{\mathrm{\&omega;}}=-\frac{e+{\mathrm{\&omega;K}}_s{i}_{\mathrm{\&beta;}}}{\mathrm{\&omega;}}---\left(3\right);$

Acquisition space magnetic field density amplitude B can be calculated according to above formula (3)_fsin(γ)；

In above formula (3), e is back-emf, and γ is the angle of permanent magnet and A axle axis, and γ ' is stator magnet kinetic potential and A axle axis Angle, K_sFor the coefficient of stator coil magnetic linkage, K_fFor permanent magnet flux linkage coefficient, ω is angular rate；

i_αAnd i_βSpecify electron current component in α β coordinate system.