CN110378027B - Motor no-load loss and electromagnetic torque calculation method considering magnetic flux density axial distribution - Google Patents

Abstract

The invention discloses a method for calculating no-load loss and electromagnetic torque of a motor considering the axial distribution of magnetic density. For a hybrid stator iron-core motor, the magnetic density amplitude in the classical loss calculation is replaced by a constant value that varies along the axial direction. The distribution function of the magnetic density amplitude value, taking the measurement points at four typical positions of the stator for simulation analysis, to obtain the magnetic density amplitude value of the measurement point at each axial position point, and use it with the magnetic density amplitude value in the corresponding single-material stator. The difference between the magnetic density amplitudes is obtained and the least squares method is used to fit them to obtain the magnetic density amplitude distribution function. Then, multiply the loss density function of each measuring point by the area of the corresponding measuring point, and integrate it in the axial direction to obtain the motor. No-load stator loss; and on the basis of the original electromagnetic torque calculation, a number of axial position points are taken at equal intervals in the motor air gap, the corresponding magnetic density amplitude is obtained through simulation, and the electromagnetic torque is obtained through axial integration; Accurately calculate no-load losses and electromagnetic torque for hybrid stator core motors.

Description

Calculation method of motor no-load loss and electromagnetic torque considering axial distribution of magnetic density

technical field

The invention relates to a method for calculating no-load loss and electromagnetic torque of a motor, in particular to a method for calculating no-load loss and electromagnetic torque of a hybrid stator iron core permanent magnet synchronous motor considering the axial distribution of magnetic density.

Background technique

The scrapping of motors produces a large amount of waste silicon steel cores. The loss of traditional silicon steel core motors is about 1.14W/kg, while the loss of iron-based amorphous alloy iron core motors is only 0.25W/kg, which is about 22% of silicon steel materials. In order to improve the energy efficiency and resource reuse of the motor, in the patent publication number CN105119396A, a "power motor remanufacturing method using a hybrid laminated stator core" is proposed, so that the silicon steel sheet of the scrapped motor can be obtained in the motor remanufacturing process. Reuse to avoid environmental pollution and make full use of resources; the hybrid laminated stator core is made of disassembled waste motor silicon steel laminated core and iron-based amorphous alloy core in the axial direction. In this structure, the internal magnetic density of the motor will be uneven in the axial direction due to the change of the stator material, so that the magnetic density of the motor is no longer a fixed constant in the axial direction, which will affect the relationship with the magnetic field. The calculation accuracy of the motor performance parameters related to the density value, especially the calculation of the motor stator loss and electromagnetic torque performance.

In the prior art, the basic iron loss P of the motor is:

Ph and P _e are the hysteresis loss and eddy current loss of the motor, respectively; K _h and _Ke are the hysteresis loss coefficient and eddy current loss coefficient _, respectively; f is the frequency of the alternating current; B _m is the magnetic density amplitude; α is the constant coefficient;

The tangential electromagnetic force density f _t acting on the stator or rotor of the motor in the two-dimensional electromagnetic field is:

Among them: μ ₀ is the air permeability; B _n is the radial air-gap magnetic density; B _t is the tangential air-gap magnetic density;

The electromagnetic torque T _em of the motor is generated by the tangential force:

Among them: L _Fe is the length of the motor iron core; r is any circle radius in the air gap; B _r and B _θ are the radial and tangential components of the air gap magnetic density at the air gap radius r, respectively; θ is the mechanical radian;

However, the calculation method for the no-load loss and electromagnetic torque of the motor in the above-mentioned prior art is to calculate the magnetic density as a uniformly distributed constant along the axial direction, which is only suitable for the case where the stator and rotor of the motor are made of a single material. In the hybrid stator iron core motor, the axial distribution of the magnetic density corresponding to the iron core segments of different materials is not uniform, especially at the interface between the two materials. Therefore, the existing calculation methods for the no-load loss and electromagnetic torque of the motor cannot be used. Fully considering the influence of the difference in the axial distribution of the magnetic density, the calculation error is large, and it cannot be applied to the power motor of the hybrid laminated stator core.

SUMMARY OF THE INVENTION

In order to avoid the above-mentioned deficiencies in the prior art, the present invention provides a method for calculating the no-load loss and electromagnetic torque of a motor considering the axial distribution of the magnetic density, so as to more accurately calculate the motor no-load loss considering the axial distribution of the magnetic density. load loss and electromagnetic torque.

To achieve the above object, the present invention adopts the following technical solutions:

The invention considers the no-load loss and electromagnetic torque calculation method of the motor with the axial distribution of the magnetic density, and is aimed at a motor with a mixed stator iron core. It is formed by stacking at intervals, and the two different materials are recorded as material S and material A, respectively, and the one-to-one corresponding core segments are respectively recorded as core segment S and core segment A, and the core made of a single material S is recorded as is the iron core S, and the iron core made of a single material A is recorded as the iron core A; it is characterized in that, for the motor with the mixed stator iron core, the no-load loss of the motor stator is calculated and obtained according to the following steps:

Step 1: The basic iron loss P of the motor is represented by equation (1):

in:

Ph and P _e are the hysteresis loss and eddy current loss of the motor, respectively; K _h and _Ke are the hysteresis loss coefficient and eddy current loss coefficient _, respectively; f is the frequency of the alternating current; B _m is the magnetic density amplitude; α is the constant coefficient;

Step 2: For the simultaneous existence of alternating and rotating magnetization in the motor, the basic iron loss P is expressed as formula (2):

Among them: B _xm is the radial magnetic density amplitude; _Bym is the tangential magnetic density amplitude;

Step 3: For a motor with a hybrid stator core, correct the basic iron loss P represented by equation (2) according to the axial position l, and obtain the loss density function of each measuring point of the stator represented by equation (3):

P _i (l)=K _h f(B _xmi (l) ^α +B _ymi (l) ^α )+K _e f ² (B _xmi (l) ² +B _ymi (l) ² ) (3)

in:

P _i (l) is the loss density function along the axial direction at the position of measuring point i;

B _xmi (l) is the radial magnetic density amplitude distribution function along the axial direction at the position of measuring point i;

_Bymi (l) is the tangential magnetic density amplitude distribution function along the axial direction at the position of measuring point i;

The measuring point is represented by i, i=a, b, c, d, which means that the measuring point i is the measuring point a at the tip of the stator, the measuring point b in the tooth, the measuring point c at the root of the tooth, and the measuring point on the yoke. d a total of four measuring points;

Step 4: Express B _xmi (l) as formula (4):

in:

B _A0xi refers to the radial magnetic density amplitude of iron core A at the position of measuring point i;

B _S0xi refers to the radial magnetic density amplitude of the iron core S at the measuring point i;

F _Bxi (l) is the radial magnetic density amplitude difference function between the mixed stator iron core and the corresponding iron core A or iron core S at the position of measuring point i;

Obtain B _xmi (l), B _A0xi and B _S0xi through simulation, and use formula (4) to obtain the radial magnetic density amplitude difference function F _Bxi (l);

Obtain the tangential magnetic density amplitude difference function F _Byi (l) in the same way;

Step 5: Calculate and obtain the magnetic density loss density function P _i (l) of each measuring point of the stator according to formula (3) and formula (4); finally calculate and obtain the no-load loss P ₀ of the hybrid motor stator by formula (5):

S _j is the area of different measurement areas of the stator; the measurement area is represented by j, j=Ra, Rb, Rc, Rd, which means that the measurement area j is the measurement area Ra centered on the tooth tip measurement point a, and the tooth There are four measurement areas in total: the measurement area Rb centered on the middle measurement point b, the measurement area Rc centered on the tooth root measurement point c, and the measurement area Rd centered on the yoke measurement point d;

For the motor with the hybrid stator core, the electromagnetic torque of the motor is obtained by calculating the following steps:

Step a: The tangential electromagnetic force density f _t of the motor is represented by equation (6):

Among them: μ ₀ is the air permeability; B _n is the radial air-gap magnetic density; B _t is the tangential air-gap magnetic density;

Step b: The electromagnetic torque T _em of the motor is generated by the tangential force, which is represented by equation (7):

Among them: L _Fe is the length of the motor iron core; r is any circle radius in the air gap; B _r and B _θ are the radial and tangential components of the air gap magnetic density at the air gap radius r, respectively; θ is the mechanical radian;

Then, for a motor with a mixed stator core, the electromagnetic torque T _mix of the motor can be obtained by formula (8):

Where: B _rk and B _θk are the radial and tangential components of the air-gap magnetic density when the k-th axial position point is taken in the axial direction l, respectively.

The invention considers the no-load loss and electromagnetic torque calculation method of the motor with the axial distribution of the magnetic density, and is also characterized in that: the radial magnetic density amplitude difference function F _Bxi (l) and the tangential magnetic density amplitude difference The function F _Byi (l) is obtained as follows:

Setting: The core segments of the hybrid stator core from one end to the other end are S1, A1, S2, A2 and S3 in sequence, with a total of five segments. Based on the symmetry of the motor’s axial structure, the axial direction of the core segment S2 The axial position l of each measuring point on the intermediate section is taken as 0, and at each measuring point position of the tooth top measuring point a, the tooth middle measuring point b, the tooth root measuring point c and the tooth yoke measuring point d, since l=0 Starting from the position of , and toward one end of the hybrid stator core along the axial direction, take each axial position point _{l 1} , l ₂ ... The magnetic density amplitude of core A and core S at each measuring point is obtained by dimensional simulation, and the core segment A in the mixed stator core at the measuring point i is calculated at each axial position point l ₁ , l ₂ . . . l The magnitude difference of the magnetic density between _N and the iron core A, and the magnetic flux between the iron core segment S in the mixed stator iron core at each axial position point l ₁ , l ₂ ... l _N and the iron core S at the measuring point i If the density amplitude difference is calculated, the radial magnetic density amplitude difference function F _Bxi (l) and the tangential magnetic density amplitude difference function F _Byi (l) are represented by equations (9) and (10), respectively:

in:

_pxi11 , _pxi21 , _pxi31 , _pxi41 , _qxi11 , _qxi21 , _pxi12 , _pxi22 , _pxi32 , _pxi42 , _qxi12 , _qxi22 , _pyi11 , _pyi21 , _pyi31 , _pyi41 , _qyi11 , q _yi21 , p _yi12 , p _yi22 , p _yi32 , p _yi42 , q _yi12 and q _yi22 are all coefficients, and each coefficient is changed according to the absolute value of the stator radial magnetic density amplitude difference in the corresponding axial interval The curve, and the absolute value change curve according to the difference of the stator tangential magnetic density amplitude, are obtained by the least squares method;

The present invention considers the motor no-load loss and electromagnetic torque calculation method considering the axial distribution of magnetic density is also characterized in that:

In order to improve the convergence speed and ensure the fitting accuracy, the values of each axial position point l ₁ , l ₂ ... l _N are standardized according to formula (11):

Where: l′ _n is the value of the normalized axial position point, where n=1,2...,N; μ ₁ and σ ₁ are the axial direction between [0,0.5(LS + _{L A )} ] respectively The mean and standard deviation of the values of the position points; μ ₂ and σ ₂ are the mean and standard deviation of the values of the axial position points between [0.5(L _S +L _A ), 1.5L _S +L _A ], respectively.

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

1. For the hybrid stator iron core motor, the present invention can obtain the distribution law of its magnetic density amplitude along the axial direction. Compared with the original no-load loss and electromagnetic torque calculation method for a single-material stator motor, the calculation accuracy is improved. , more accurately calculate the no-load loss and electromagnetic torque of the motor;

2. In the present invention, a number of axial position points are taken at equal intervals at four typical measuring points of the tooth top, middle tooth, tooth root and tooth yoke of the motor stator, and the magnetic density amplitude of each point is obtained by simulation. Amplitude difference and fitting to obtain the distribution function of the magnetic density amplitude along the axial direction. On the basis of the original relevant theory, the motor loss and electromagnetic torque considering the axial distribution of the magnetic density are more accurately calculated, reducing the The error caused by the original calculation method for traditional motors;

3. The method for calculating the no-load loss and electromagnetic torque of the motor in the present invention is not only applicable to remanufactured motors, but also applicable to new motors with stators of any two materials mixed in any proportion.

Description of drawings

Fig. 1 is the three-dimensional schematic diagram of the hybrid stator core aimed at by the present invention;

Fig. 2 is the position of the measuring point taken in the stator magnetic density analysis method;

Figure 3 shows the magnetic density difference of the hybrid stator iron core motor at each axial position;

Figure 4 shows the unit electromagnetic torque of the motor at each axial position point under two working conditions;

Reference numerals in the figure: 11 first silicon steel core segment, 12 second silicon steel core segment, 13 third silicon steel core segment, 21 first amorphous alloy core segment, 22 second amorphous alloy core segment.

Detailed ways

In this embodiment, the no-load loss and electromagnetic torque calculation method of the motor considering the axial distribution of the magnetic density is for a motor with a mixed stator iron core. The mixed stator iron core is composed of two different iron core segments in the axial direction Laminated, the two different materials are recorded as material S and material A, the one-to-one corresponding iron core segments are recorded as iron core segment S and iron core segment A, respectively, and the iron core made of a single material S is recorded as Iron core S, the iron core made of a single material A is recorded as iron core A;

For a motor with a hybrid stator core, calculate the no-load loss of the motor stator as follows:

Step 1: The basic iron loss P of the motor is represented by equation (1):

in:

Ph and P _e are the hysteresis loss and eddy current loss of the motor, respectively; K _h and _Ke are the hysteresis loss coefficient and eddy current loss coefficient _, respectively; f is the frequency of the alternating current; B _m is the magnetic density amplitude; α is the constant coefficient;

Step 2: For the simultaneous existence of alternating and rotating magnetization in the motor, the basic iron loss P is expressed as formula (2):

Among them: B _xm is the radial magnetic density amplitude; _Bym is the tangential magnetic density amplitude;

Step 3: For a motor with a hybrid stator core, correct the basic iron loss P represented by equation (2) according to the axial position l, and obtain the loss density function of each measuring point of the stator represented by equation (3):

P _i (l)=K _h f(B _xmi (l) ^α + ^B _ymi (l) ^α )+K _e f ² (B _xmi (l) ² +B _ymi (l) ² ) (3)

in:

P _i (l) is the loss density function along the axial direction at the position of measuring point i;

B _xmi (l) is the radial magnetic density amplitude distribution function along the axial direction at the position of measuring point i;

_Bymi (l) is the tangential magnetic density amplitude distribution function along the axial direction at the position of measuring point i;

The measuring point is represented by i, i=a, b, c, d, which means that the measuring point i is the measuring point a at the tip of the stator, the measuring point b in the tooth, the measuring point c at the root of the tooth, and the measuring point on the yoke. d A total of four measuring points;

Step 4: Express B _xmi (l) as formula (4):

in:

B _A0xi refers to the radial magnetic density amplitude of iron core A at the position of measuring point i;

B _S0xi refers to the radial magnetic density amplitude of the iron core S at the measuring point i;

F _Bxi (l) is the radial magnetic density amplitude difference function between the mixed stator iron core and the corresponding iron core A or iron core S at the position of measuring point i;

Obtain B _xmi (l), B _A0xi and B _S0xi through simulation, and use formula (4) to obtain the radial magnetic density amplitude difference function F _Bxi (l);

Obtain the tangential magnetic density amplitude difference function F _Byi (l) in the same way;

Step 5: Calculate and obtain the magnetic density loss density function P _i (l) of each measuring point of the stator according to formula (3) and formula (4); finally calculate and obtain the no-load loss P ₀ of the hybrid motor stator by formula (5):

S _j is the area of different measurement areas of the stator; the measurement area is represented by j, j=Ra, Rb, Rc, Rd, which means that the measurement area j is the measurement area Ra centered on the tooth tip measurement point a, and the tooth There are four measurement areas in total: the measurement area Rb centered on the middle measurement point b, the measurement area Rc centered on the tooth root measurement point c, and the measurement area Rd centered on the yoke measurement point d;

For a motor with a hybrid stator core, calculate the electromagnetic torque of the motor as follows:

Step a: The tangential electromagnetic force density f _t of the motor is represented by equation (6):

Among them: μ ₀ is the air permeability; B _n is the radial air-gap magnetic density; B _t is the tangential air-gap magnetic density;

Step b: The electromagnetic torque T _em of the motor is generated by the tangential force, which is represented by equation (7):

Among them: L _Fe is the length of the motor iron core; r is any circle radius in the air gap; B _r and B _θ are the radial and tangential components of the air gap magnetic density at the air gap radius r, respectively; θ is the mechanical radian;

Then, for a motor with a mixed stator core, the electromagnetic torque T _mix of the motor can be obtained by formula (8):

Where: B _rk and B _θk are the radial and tangential components of the air-gap magnetic density when the k-th axial position point is taken in the axial direction l, respectively.

In this embodiment, the radial magnetic density amplitude difference function F _Bxi (l) and the tangential magnetic density amplitude difference function F _Byi (l) are obtained as follows:

Setting: The core segments of the hybrid stator core from one end to the other end are S1, A1, S2, A2 and S3 in sequence, with a total of five segments. Based on the symmetry of the motor’s axial structure, the axial direction of the core segment S2 The axial position l of each measuring point on the mid-section is taken as 0, and at the four measuring point positions of tooth tip measuring point a, tooth middle measuring point b, tooth root measuring point c and tooth yoke measuring point d, since l=0 Starting from the position of , and toward one end of the hybrid stator core along the axial direction, take each axial position point _{l 1} , l ₂ ... The magnetic density amplitude of core A and core S at each measuring point is obtained by dimensional simulation, and the core segment A in the mixed stator core at the measuring point i is calculated at each axial position point l ₁ , l ₂ . . . l The magnitude difference of the magnetic density between _N and the iron core A, and the magnetic flux between the iron core segment S in the mixed stator iron core at each axial position point l ₁ , l ₂ ... l _N and the iron core S at the measuring point i If the density amplitude difference is calculated, the radial magnetic density amplitude difference function F _Bxi (l) and the tangential magnetic density amplitude difference function F _Byi (l) are represented by equations (9) and (10), respectively:

in:

_pxi11 , _pxi21 , _pxi31 , _pxi41 , _qxi11 , _qxi21 , _pxi12 , _pxi22 , _pxi32 , _pxi42 , _qxi12 , _qxi22 , _pyi11 , _pyi21 , _pyi31 , _pyi41 , _qyi11 , q _yi21 , p _yi12 , p _yi22 , p _yi32 , p _yi42 , q _yi12 and q _yi22 are all coefficients, and each coefficient is changed according to the absolute value of the stator radial magnetic density amplitude difference in the corresponding axial interval The curve, and the absolute value change curve according to the difference of the stator tangential magnetic density amplitude, are obtained by the least squares method;

In the specific implementation, in order to improve the convergence speed and ensure the fitting accuracy, the values of the selected axial position points l ₁ , l ₂ ... l _N are subjected to standard deviation standardization processing according to formula (11):

Where: l′ _n is the value of the normalized axial position point, where n=1,2...,N; μ ₁ and σ ₁ are the axial direction between [0,0.5(LS + _{L A )} ] respectively The mean and standard deviation of the values of the position points; μ ₂ and σ ₂ are the mean and standard deviation of the values of the axial position points between [0.5(L _S +L _A ), 1.5L _S +L _A ], respectively.

Take a hybrid stator core remanufactured motor as an example. The hybrid stator core is made of silicon steel stator stack segments and amorphous alloy stator stack segments. These two materials are mixed and superimposed in a ratio of 1:1, and the silicon steel material is recorded as Material S, the amorphous alloy material is denoted as A. As shown in FIG. 1, the core segment S1 is the first silicon steel core segment 11, the core segment A1 is the first amorphous alloy core segment 21, and the core segment S2 is The second silicon steel core segment 12 , the iron core segment A2 is the second amorphous alloy iron core segment 22 , and the iron core segment S3 is the third silicon steel core segment 13 .

As shown in Figure 2, the measuring points are selected at four typical positions of the motor stator tooth tip, tooth middle, tooth root and tooth yoke, which are the tooth tip measurement point a, the tooth middle measurement point b, the tooth root measurement point c, and the tooth root measurement point c. The yoke measurement point d; the one-to-one corresponding measurement area is the measurement area Ra, the measurement area Rb, the measurement area Rc and the measurement area Rd;

Take each axial position point l ₁ , l ₂ ... l _N at equal intervals along the axial direction, obtain the magnetic density amplitude of each axial position point through three-dimensional simulation, and obtain the core A and iron core S in each position through two-dimensional simulation. The magnetic density amplitude value of the measuring point position, the difference between the magnetic density amplitude value of the core segment A in the mixed stator core at each axial position point l ₁ , l ₂ ... l _N and the iron core A is calculated at the position of the measuring point i value, and the magnetic density amplitude difference between the iron core segment _S in the mixed stator iron core at each axial position point l ₁ , l ₂ . The difference function of the axial magnetic density amplitude, and finally calculate the iron loss of the entire stator when the motor is no-load through the axial integral.

For silicon steel, the fitted loss coefficients K _h and Ke are respectively: K _h = _177.802w /m ³ , Ke = _0.448701w /m ³ ;

For amorphous: the loss coefficients K _h and Ke obtained by fitting are respectively: K _h = _12.7799w /m ³ , Ke =0w/m ³ _;

According to the size of the magnetic density inside the stator, the constant coefficient α is taken as 2;

Obtain B _xmi (l) through Maxwell three-dimensional simulation, obtain B _A0xi and B _S0xi through two-dimensional simulation, and obtain radial magnetic density amplitude difference function F _Bxi (l) by using formula (4); The magnetic density amplitude difference function F _Byi (l), as shown in Figure 3, the curve a1 in Figure 3 is the tangential magnetic density difference curve of the yoke measuring point d, and the curve a2 is the diameter of the tooth root measuring point c To the magnetic density difference curve, the curve a3 is the radial magnetic density difference curve of the measuring point b in the tooth, the curve a4 is the tangential magnetic density difference curve of the tooth root measuring point c, and the curve a5 is the tooth yoke measuring point d. The radial magnetic density difference curve, L1 is the interface between the core segment S2 and the core segment A2; L2 is the interface between the core segment A2 and the core segment S3.

Set the axial length of the motor core to 105mm, the lengths of the core segments S1, S2 and S3 are equal, denoted as L _S , L _S =17.5mm; the lengths of the core segments A1 and A2 are equal, denoted as L _A , L _A = 26.25mm; take the middle axial position of the core segment S2 as the reference plane M, that is, on the reference plane M, l = 0; on the stator tooth tip measurement point a, tooth middle measurement point b, tooth root measurement point At the four measuring point positions of c and yoke measuring point d, the points are taken at equal intervals of 2.5mm along the axial direction, and a total of 21 axial position points are 1.25mm, 3.75mm...51.25mm, and each axis is obtained through 3D simulation. The magnetic density amplitude at the position point is obtained, and the magnetic density amplitude at each measuring point is obtained when the motor only uses iron core A and only iron core S through two-dimensional simulation. The magnetic density amplitude difference between the core segment A in the core and the core A at each axial position point l ₁ , l ₂ ... l ₂₁ , and the core segment S in the mixed stator core at each measuring point i Axial position points l ₁ , l ₂ ... l ₂₁ and the magnetic density amplitude difference of the iron core S; in order to improve the convergence speed and ensure the fitting accuracy, the axial position points l ₁ , l ₂ ... l ₂₁ The value of the standard deviation is standardized according to the formula (11):

Among them, n=1, 2..., 21; μ ₁ and σ ₁ are the mean and standard deviation of the values of the axial position points between [0, 21.875], respectively, and it is calculated that μ ₁ =11.25, σ ₁ =6.847; μ ₂ and σ ₂ are the mean and standard deviation of the values of the axial position points between [21.875, 52.5], respectively, and it is calculated that μ ₂ =37.5, σ ₂ =9.014.

After the standard deviation of the axial position points is normalized, the obtained mapping is l' ₁ , l' ₂ ... l' ₂₁ . The average difference value is used at the measuring point a due to the complex magnetic density, and the tangential magnetic density value at the measuring point b is relatively high. is small and therefore ignored, then:

Formula (9) is expressed as:

Formula (10) is expressed as:

The coefficients p _xi11 , p _xi21 , p _xi31 , p _xi41 , q _xi11 and q _xi21 are in the axial interval [0, 21.875], according to the absolute value change curve of the stator radial magnetic density amplitude difference through least squares fitting get;

The coefficients p _xi12 , p _xi22 , p _xi32 , p _xi42 , q _xi12 and q _xi22 are in the axial interval [21.875, 52.5], according to the change curve of the absolute value of the stator radial magnetic density amplitude difference through least squares fitting get;

The coefficients p _yi11 , p _yi21 , p _yi31 , p _yi41 , q _yi11 and q _yi21 are in the axial interval [0, 21.875], according to the change curve of the absolute value of the stator tangential magnetic density amplitude difference through least squares fitting get;

The coefficients p _yi12 , p _yi22 , p _yi32 , p _yi42 and q _yi12 and q _yi22 are in the axial interval [21.875, 52.5], according to the change curve of the absolute value of the stator tangential magnetic density amplitude difference through least squares fitting. get;

The values of the coefficients obtained by the least squares fitting are shown in Table 1:

Table 1 Various coefficients of the magnetic density amplitude difference function

The calculation results of the final loss are shown in Table 2:

Table 2 Loss calculation results

The losses of the rotor, permanent magnets and other parts are ignored in the calculation, and the total no-load loss of the motor obtained by simulation is 86.18W minus the basic iron loss of the hybrid motor calculated without correction of 59.63W, and the hybrid stator is obtained except for the basic iron loss. The sum of other losses of the motor is about 26.55W, which is used as the calculation result of other losses. The no-load loss of the motor is the sum of the stator iron loss and other losses.

The stress generated in the actual machining process of the motor has a certain influence on the loss characteristics of the material. At the same time, the stray loss and the uneven distribution of the magnetic density in different parts are not considered in the loss calculation. Therefore, the calculation results are usually too small. Use the empirical coefficient K for correction. According to the design experience, the loss correction coefficient of silicon steel material takes K _S = 1.27, and the loss correction coefficient of amorphous alloy material is K _A = 5.42. The corrected results are shown in Table 3:

Table 3: Corrected calculation results

Silicon steel Amorphous Stator as a whole Hybrid stator calculation loss/W 73.12 10.40 83.52 Single material stator calculation loss/W 67.86 11.46 79.32

The no-load loss of the motor measured by the experiment is 123.27W, the no-load loss of the motor obtained by the traditional calculation method is 105.87W, and the no-load loss of the motor calculated by the method of the present invention is 110.07W, and the calculation accuracy is improved by 3.4%.

Calculation of Motor Electromagnetic Torque for Motors with Hybrid Stator Core:

Through Maxwell three-dimensional simulation, B _rk and B _θk in formula (8) are obtained;

The stator core is made of a mixture of two materials, which causes the magnetic field formed by the permanent magnet to be biased, the internal magnetic density of the stator is unevenly distributed along the axial direction, and the tangential force density of the motor fluctuates along the axial direction. Under the condition of the unit tangential electromagnetic force density at each axial position, and integral along the curve circumference, the unit electromagnetic torque of the motor at each axial position point is obtained, as shown in Figure 4, the curve b1 in Figure 4 is under the rated working condition The unit electromagnetic torque of the motor at each axial position point, curve b2 is the unit electromagnetic torque of the motor at each axial position point under the peak working condition; under the rated working condition, the average unit electromagnetic torque of the silicon steel core section is 0.42N m/mm, the average unit electromagnetic torque of the amorphous alloy iron core segment is 0.37N m/mm; the peak working condition curve trend is similar to the rated working condition, the electromagnetic torque of the silicon steel stator is 0.82N m/mm, the non- The crystal stator is only 0.74N·m/mm, which shows that there is a big difference in the electromagnetic torque of the motor in the axial direction. In order to simplify the analysis, only part of the position of the motor is taken for calculation, and the unit electromagnetic torque of the entire axial position of the motor is obtained by symmetry, and then the electromagnetic torque of the hybrid stator motor is obtained by integrating along the axial direction.

The method of the invention fully considers the influence of the material difference in the axial direction of the hybrid stator iron core motor, and improves the accuracy of the performance calculation of this type of motor; by constructing the magnetic density amplitude difference function, the motor magnetic density amplitude along the axial direction is obtained. Then, on the theoretical basis of the existing motor loss and electromagnetic torque calculation methods, the magnetic density amplitude is replaced by a constant value of the magnetic density amplitude distribution function that changes along the axial position, and a new method for the hybrid stator is determined. The calculation method of no-load loss and electromagnetic torque of iron-core motor makes up for the deficiency of the original loss and electromagnetic torque calculation method, can improve the accuracy of calculation of motor-related performance parameters, and lay a foundation for the wide application of hybrid stator iron-core motors .

Claims (3)

1. A method for calculating the no-load loss and the electromagnetic torque of a motor considering the axial distribution of magnetic densities is provided, and the method is directed at a motor with a mixed stator core, wherein the mixed stator core is formed by laminating two different material core sections at intervals in the axial direction, the two different materials are respectively marked as a material S and a material A, the one-to-one corresponding core sections are respectively marked as a core section S and a core section A, an iron core made of a single material S is marked as an iron core S, and an iron core made of a single material A is marked as an iron core A; the method is characterized in that aiming at the motor with the mixed stator core, the motor stator no-load loss is obtained by the following steps:

step 1: the basic iron loss P of the motor is characterized by the formula (1):

wherein:

P _h and P _e Hysteresis loss and eddy current loss of the motor respectively; k _h And K _e Hysteresis loss coefficient and eddy current loss coefficient; f is the alternating current frequency; b is _m The magnetic density amplitude value; alpha is a constant coefficient;

step 2: for the simultaneous presence of alternating and rotating magnetization in the machine, the basic iron loss P is expressed as formula (2):

wherein: b is _xm Is the radial magnetic flux density amplitude; b is _ym Is a tangential flux density amplitude;

and step 3: for a motor with a mixed stator core, correcting the basic iron loss P represented by the formula (2) according to the axial position l to obtain a loss density function of each measuring point of the stator represented by the formula (3):

P _i (l)＝K _h f(B _xmi (l) ^α +B _ymi (l) ^α )+K _e f ² (B _xmi (l) ² +B _ymi (l) ² ) (3)

wherein:

P _i (l) The loss density function along the axial direction at the position of a measuring point i is obtained;

B _xmi (l) The radial flux density amplitude distribution function along the axial direction at the position of a measuring point i is obtained;

B _ymi (l) A tangential flux density amplitude distribution function along the axial direction at the position of a measuring point i is obtained;

representing the measuring points by i, wherein i is a, b, c and d, and means that the measuring points i are four measuring points in total, namely a tooth top measuring point a, a tooth middle measuring point b, a tooth root measuring point c and a tooth yoke measuring point d in the stator respectively;

and 4, step 4: b is to be _xmi (l) Expressed as formula (4):

wherein:

B _A0xi the radial magnetic flux density amplitude of the iron core A at the position of a measuring point i is represented;

B _S0xi the radial flux density amplitude of the iron core S at the position of the measuring point i is represented;

F _Bxi (l) The radial flux density amplitude difference function between the hybrid stator core and the corresponding core A or core S at the position of the measuring point i is obtained;

obtaining B by simulation _xmi (l)，B _A0xi And B _S0xi Obtaining a radial magnetic density amplitude difference function F by using the formula (4) _Bxi (l)；

Obtaining a tangential flux density amplitude difference function F in the same way _Byi (l)；

And 5: calculating and obtaining a flux density loss density function P of each measuring point of the stator according to the formula (3) and the formula (4) _i (l) (ii) a Finally, the no-load loss P of the stator of the hybrid motor is obtained by calculating the formula (5) ₀ ：

S _j Areas of different measurement areas of the stator; the measurement region is represented by j, wherein j is Ra, Rb, Rc and Rd, and means that the measurement region j comprises four measurement regions including a measurement region Ra taking a tooth crest measuring point a as a center, a measurement region Rb taking a tooth middle measuring point b as a center, a measurement region Rc taking a tooth root measuring point c as a center and a measurement region Rd taking a tooth yoke measuring point d as a center;

aiming at the motor with the mixed stator core, the electromagnetic torque of the motor is obtained by calculation according to the following steps:

step a: tangential electromagnetic force density f of an electric machine _t Characterized by formula (6):

wherein: mu.s ₀ Air permeability; b is _n Radial air gap flux density; b is _t Tangential air gap flux density;

step b: electromagnetic torque T of an electric machine _em Is generated by a tangential force, characterized by equation (7):

wherein: l is _Fe Is the motor core length; r is any circumferential radius in the air gap; b is _r And B _θ The radial component and the tangential component of the air gap flux density at the air gap radius r are respectively; theta is the mechanical radian of the solution area;

then, for the motor having the hybrid stator core, the electromagnetic torque T of the motor is obtained by the calculation of equation (8) _mix ：

Wherein: b is _rk And B _θk Respectively, radial sum of air gap magnetic density when taking k axial position point in axial direction lA tangential component.

2. The method for calculating the no-load loss and the electromagnetic torque of the motor considering the magnetic flux density axial distribution as claimed in claim 1, wherein the method comprises the following steps: the radial magnetic density amplitude difference function F _Bxi (l) And tangential magnetic flux density amplitude difference function F _Byi (l) Is obtained as follows:

setting: the mixed stator core comprises five core segments from one end to the other end, namely S1, A1, S2, A2 and S3 in sequence, based on the symmetry of the axial structure of the motor, the axial position l of each measuring point on the axial middle section of the core segment S2 is taken as 0, and axial position points l are taken at equal intervals from the position where l is 0 to the position where l is towards one end of the mixed stator core along the axial direction from the position where l is 0 at each measuring point of a tooth crest measuring point a, a tooth middle measuring point b, a tooth root measuring point c and a tooth yoke measuring point d ₁ 、l ₂ …l _N Obtaining the magnetic density amplitude of each axial position point through three-dimensional simulation, obtaining the magnetic density amplitude of the iron core A and the iron core S at each measuring point position through two-dimensional simulation, and calculating to obtain the point l of the iron core section A in each axial position of the mixed stator iron core at the position of the measuring point i ₁ 、l ₂ …l _N The difference value of the magnetic density of the stator core A and the magnetic density of the iron core A, and the axial position points l of the iron core section S in the mixed stator core at the position of a measuring point i ₁ 、l ₂ …l _N The difference of magnetic density amplitude of the magnetic core S and the radial magnetic density amplitude difference function F _Bxi (l) And tangential magnetic flux density amplitude difference function F _Byi (l) Characterized by the formulae (9) and (10), respectively:

wherein:

p _xi11 、p _xi21 、p _xi31 、p _xi41 、q _xi11 、q _xi21 、p _xi12 、p _xi22 、p _xi32 、p _xi42 、q _xi12 、q _xi22 、p _yi11 、p _yi21 、p _yi31 、p _yi41 、q _yi11 、q _yi21 、p _yi12 、p _yi22 、p _yi32 、p _yi42 、q _yi12 and q is _yi22 And all the coefficients are obtained by least square fitting in the corresponding axial interval according to an absolute value change curve of the stator radial flux density amplitude difference and according to an absolute value change curve of the stator tangential flux density amplitude difference.

3. The method for calculating the no-load loss and the electromagnetic torque of the motor considering the flux density axial distribution as claimed in claim 2, wherein the method comprises the following steps:

in order to improve the convergence speed and ensure the fitting precision, each axial position point l is taken ₁ 、l ₂ …l _N The standard deviation normalization processing is performed according to equation (11):

wherein: l' _n The axial position point value after normalization processing is shown, wherein N is 1,2 …, N; mu.s ₁ And σ ₁ Are respectively [0,0.5 (L) _S +L _A )]Mean and standard deviation of the values of the axial position points in between; mu.s ₂ And σ ₂ Are respectively [0.5 (L) _S +L _A ),1.5L _S +L _A ]The mean and standard deviation of the values of the axial position points in between.

Images