CN110378027B - Motor no-load loss and electromagnetic torque calculation method considering magnetic flux density axial distribution - Google Patents
Motor no-load loss and electromagnetic torque calculation method considering magnetic flux density axial distribution Download PDFInfo
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Abstract
The invention discloses a method for calculating the no-load loss and electromagnetic torque of a motor considering the axial distribution of magnetic density, which aims at a mixed stator core motor, replaces the magnetic density amplitude in the classical loss calculation from a constant to a magnetic density amplitude distribution function changing along the axial direction, takes test points at four typical positions of a stator for simulation analysis to obtain the magnetic density amplitude of the test points at each axial position point, makes a difference with the magnetic density amplitude in the stator corresponding to a single material to obtain a magnetic density amplitude difference value, fits by a least square method to obtain a magnetic density amplitude distribution function, multiplies the loss density function of each test point by the area of the corresponding test point, and integrates in the axial direction to obtain the no-load stator loss of the motor; on the basis of original electromagnetic torque calculation, a plurality of axial position points are taken at equal intervals in an air gap of the motor, corresponding magnetic flux density amplitude values are obtained through simulation, and electromagnetic torque is obtained through axial integration; the method can accurately calculate the no-load loss and the electromagnetic torque of the hybrid stator core motor.
Description
Technical Field
The invention relates to a method for calculating the no-load loss and the electromagnetic torque of a motor, in particular to a method for calculating the no-load loss and the electromagnetic torque of a hybrid stator core permanent magnet synchronous motor considering the axial distribution of magnetic flux density.
Background
The motor is scrapped to generate a large amount of waste silicon steel cores, the loss of the traditional silicon steel core motor is about 1.14W/kg, and the loss of the iron-based amorphous alloy core motor is only 0.25W/kg, which is about 22% of the silicon steel material. In order to improve the energy efficiency and resource recycling of the motor, in a patent with the publication number of CN105119396A, a method for remanufacturing a power motor by adopting a hybrid laminated stator core is provided, so that silicon steel sheets of a scrapped motor are recycled in the remanufacturing of the motor, the environmental pollution is avoided, and meanwhile, the resource is fully utilized; the mixed laminated stator core is formed by laminating the disassembled silicon steel laminated iron core of the waste motor and the iron-based amorphous alloy iron core at intervals in the axial direction, and in the structural form, the magnetic density in the motor is uneven along the axial direction due to the change of stator materials, so that the magnetic density of the motor is no longer a fixed constant in the axial direction, and the calculation precision of motor performance parameters related to the magnetic density value is further influenced, particularly the calculation of the loss of a motor stator and the performance of electromagnetic torque.
In the prior art, the basic iron loss P of the motor is:
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;
tangential electromagnetic force density f acting on motor stator or rotor in two-dimensional electromagnetic field t Comprises the following steps:
wherein: mu.s 0 Air permeability; b is n Radial air gap flux density; b t Tangential air gap flux density;
electromagnetic torque T of an electric machine em Is generated by tangential forces:
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;
however, the method for calculating the motor no-load loss and the electromagnetic torque in the prior art calculates the magnetic densities as constants uniformly distributed along the axial direction, and is only suitable for the case that the stator and the rotor of the motor are made of a single material, while for the hybrid stator core motor, the magnetic densities corresponding to the core segments made of different materials are not uniformly distributed in the axial direction, especially at the interface between the two materials, so that the existing method for calculating the motor no-load loss and the electromagnetic torque cannot fully consider the influence caused by the difference in the axial distribution of the magnetic densities, has a large calculation error, and cannot be applied to the power motor of the hybrid stator core.
Disclosure of Invention
In order to avoid the defects in the prior art, the invention provides the method for calculating the no-load loss and the electromagnetic torque of the motor considering the magnetic flux density axial distribution, so that the no-load loss and the electromagnetic torque of the motor considering the magnetic flux density axial distribution can be calculated more accurately.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a method for calculating the no-load loss and the electromagnetic torque of a motor considering magnetic density axial distribution, which aims at the motor with a mixed stator iron core, wherein the mixed stator iron core is formed by laminating two iron core sections made of different materials at intervals in the axial direction, the two different materials are respectively marked as a material S and a material A, the iron core sections in one-to-one correspondence are respectively marked as an iron core section S and an iron core section A, the iron core made of a single material S is marked as an iron core S, and the 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 m The magnetic density amplitude value; alpha is a constant coefficient;
and 2, step: 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 3, 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) The distribution function of the tangential flux density amplitude at the position of a measuring point i along the axial direction is obtained;
representing measuring points by i, wherein the i is a, b, c and d, and means that the measuring points i are four measuring points, namely 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 in the stator respectively;
and 4, step 4: b is to be xmi (l) Expressed as formula (4):
wherein:
B A0xi the radial flux density amplitude of the iron core A at the position of the measuring point i is represented;
B S0xi the radial magnetic flux density amplitude of the iron core S at the position of a measuring point i is defined;
F Bxi (l) For mixing stator cores at the position of a measuring point iThe radial magnetic density amplitude difference function between the magnetic flux density function and the corresponding iron core A or iron core S;
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 according to the formula (3) and the formula (4) to obtain a magnetic density loss density function P of each measuring point of the stator 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; j represents a measurement region, wherein j is Ra, Rb, Rc and Rd, and refers to four measurement regions of the measurement region j, namely a measurement region Ra taking a tooth top 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 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 The radial and tangential components of the air gap flux density at the point of the k-th axial position taken in the axial direction l, respectively.
The invention relates to a method for calculating the no-load loss and the electromagnetic torque of a motor considering the axial distribution of magnetic densities, which is characterized in that: the radial magnetic flux 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 the mixed stator iron core at each axial position 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 All the coefficients are obtained by least square fitting in a 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;
the method for calculating the no-load loss and the electromagnetic torque of the motor considering the axial distribution of the magnetic flux density is also characterized in that:
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 ]Mean and standard deviation of the values of the axial position points in between.
Compared with the prior art, the invention has the beneficial effects that:
1. the method can obtain the distribution rule of the magnetic density amplitude values along the axial direction aiming at the mixed stator core motor, and compared with the original method for calculating the no-load loss and the electromagnetic torque of the stator motor made of a single material, the method has the advantages that the calculation precision is improved, and the no-load loss and the electromagnetic torque of the motor are calculated more accurately;
2. according to the invention, a plurality of axial position points are taken at four typical measurement points of the motor stator tooth top, the tooth middle, the tooth root and the tooth yoke at equal intervals, the magnetic density amplitude of each point is obtained through simulation, the distribution function of the magnetic density amplitude along the axial direction is obtained through constructing and fitting the magnetic density amplitude difference, on the basis of the original correlation theory, the motor loss and the electromagnetic torque considering the magnetic density axial distribution are more accurately calculated, and the error caused by the original calculation mode aiming at the traditional motor is reduced;
3. the method for calculating the no-load loss and the electromagnetic torque of the motor is not only suitable for remanufacturing the motor, but also suitable for a new motor with stators made of any two materials mixed according to any proportion.
Drawings
Fig. 1 is a perspective view of a hybrid stator core to which the present invention is directed;
FIG. 2 shows the positions of the measuring points taken in the stator flux density analysis method;
FIG. 3 is a magnetic density difference at each axial position point of the hybrid stator core motor;
FIG. 4 shows the unit electromagnetic torque of the motor at each axial position point under two operating conditions;
reference numbers in the figures: 11 a first silicon steel iron core section, 12 a second silicon steel iron core section, 13 a third silicon steel iron core section, 21 a first amorphous alloy iron core section, 22 a second amorphous alloy iron core section.
Detailed Description
In the embodiment, a method for calculating the motor no-load loss and the electromagnetic torque considering the magnetic density axial distribution is directed at a motor with a mixed stator core, wherein the mixed stator core is formed by laminating two different core sections made of different materials at intervals in the axial direction, the two different materials are respectively marked as a material S and a material A, the core sections corresponding to each other one by one 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;
aiming at a motor with a 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 equation (1):
wherein:
P h and P e Hysteresis loss and eddy current loss of the motor respectively; k is h And K e Hysteresis loss coefficient and eddy current loss coefficient; f is the alternating current frequency; b m Is the magnetic flux density amplitude; alpha is a constant coefficient;
and 2, step: 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) For the loss density along the axial direction at the position of a measuring point iA degree function;
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) The distribution function of the tangential flux density amplitude at the position of a measuring point i along the axial direction is obtained;
representing measuring points by i, wherein the i is a, b, c and d, and means that the measuring points i are four measuring points, namely 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 in the stator respectively;
and 4, step 4: b is to be xmi (l) Expressed as formula (4):
wherein:
B A0xi the radial flux density amplitude of the iron core A at the position of the measuring point i is represented;
B S0xi the radial magnetic flux density amplitude of the iron core S at the position of a measuring point i is defined;
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, and j is Ra, Rb, Rc, and Rd, and represents the measurement region Ra, Rb, and Rc, and Rd centered on the addendum measurement point a, respectively,A measurement region Rb centered on the tooth middle point b, a measurement region Rc centered on the tooth root point c, and a measurement region Rd centered on the tooth yoke point d are four measurement regions in total;
for a motor with a 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 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 The radial and tangential components of the air gap flux density at the point of the k-th axial position taken in the axial direction l, respectively.
The embodiment obtains the radial magnetic density amplitude difference function F as follows Bxi (l) And tangential magnetic flux density amplitude difference function F Byi (l)：
Setting: hybrid stator core from one end to the otherBased 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 iron core section S2 is taken as 0, and axial position points l are taken at equal intervals from the position of 0 at four measuring point positions 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 toward one end of the hybrid stator core along the axial direction from the position of l equal to 0 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 the mixed stator iron core at each axial position at the position of the measuring point i 1 、l 2 …l N The difference value of the magnetic density amplitude of the mixed stator core and the magnetic density amplitude 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 All coefficients are coefficients, and each coefficient is in a corresponding axial interval according to an absolute value change curve of the stator radial magnetic flux density amplitude difference value and according toObtaining an absolute value change curve of the stator tangential flux density amplitude difference value through least square method fitting;
in specific implementation, in order to improve convergence speed and ensure fitting accuracy, 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 ]Mean and standard deviation of the values of the axial position points in between.
Taking a remanufactured motor with a mixed stator iron core as an example, the mixed stator iron core is formed by mixing and superposing a silicon steel stator laminated section and an amorphous alloy stator laminated section according to a ratio of 1:1, the silicon steel stator laminated section is marked as a material S, the amorphous alloy stator laminated section is marked as an material A, as shown in fig. 1, an iron core section S1 is a first silicon steel iron core section 11, an iron core section A1 is a first amorphous alloy iron core section 21, an iron core section S2 is a second silicon steel iron core section 12, an iron core section A2 is a second amorphous alloy iron core section 22, and an iron core section S3 is a third silicon steel iron core section 13.
As shown in fig. 2, measuring points are selected at four typical positions of the tooth top, the tooth middle, the tooth bottom and the tooth yoke of the motor stator, namely a tooth top measuring point a, a tooth middle measuring point b, a tooth bottom measuring point c and a tooth yoke measuring point d; the measurement areas corresponding to each other are a measurement area Ra, a measurement area Rb, a measurement area Rc and a measurement area Rd;
taking axial position points l at equal intervals along the axial direction 1 、l 2 …l N Obtaining the flux density amplitude of each axial position point through three-dimensional simulation, obtaining the flux 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 mixture at the position of the measuring point iThe axial position points l of the iron core section A in the stator iron core 1 、l 2 …l N The difference value of the magnetic density amplitude of the mixed stator core and the magnetic density amplitude 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 And fitting a difference function of the magnetic density amplitude along the axial direction with the magnetic density amplitude difference of the iron core S, and finally calculating the iron loss of the whole stator when the motor is in no-load through axial integration.
For silicon steel, the loss coefficient K obtained by fitting h And K e Respectively as follows: k is h ＝177.802w/m 3 ，K e ＝0.448701w/m 3 ；
For amorphous: loss coefficient K obtained by fitting h And K e Respectively as follows: k h ＝12.7799w/m 3 ，K e ＝0w/m 3 ；
According to the magnitude of the magnetic flux density in the stator, the constant coefficient alpha is taken as 2;
obtaining B through Maxwell three-dimensional simulation xmi (l) Obtaining B by two-dimensional simulation A0xi And B S0xi And obtaining a radial magnetic density amplitude difference function F by using the formula (4) Bxi (l) (ii) a Obtaining a tangential flux density amplitude difference function F in the same way Byi (l) As shown in fig. 3, a curve a1 in fig. 3 is a tangential flux density difference curve of a tooth yoke measuring point d, a curve a2 is a radial flux density difference curve of a tooth root measuring point c, a curve A3 is a radial flux density difference curve of a tooth middle measuring point b, a curve a4 is a tangential flux density difference curve of a tooth root measuring point c, a curve a5 is a radial flux density difference curve of a tooth yoke measuring point d, and L1 is an interface between a core segment S2 and a core segment a 2; l2 is the interface of core segment a2 and core segment S3.
The axial length of the motor iron core is set to be 105mm, and the lengths of the iron core sections S1, S2 and S3 are equal and are marked as L S ,L S 17.5 mm; the core segments A1 and A2 are of equal length and are designated L A ,L A 26.25 mm; taking the middle axial position of the iron core segment S2 as a reference plane M, i.e., on the reference plane M, l is 0; at four measuring point positions of 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 on the stator, points are taken at equal intervals of 2.5mm along the axial direction, and the total number is 21The axial position points are 1.25mm and 3.75mm … 51.25.25 mm in sequence, the flux density amplitude of each axial position point is obtained through three-dimensional simulation, the flux density amplitude of the motor at each measuring point position when only an iron core A and only an iron core S are adopted is obtained through two-dimensional simulation, and the flux density amplitude of the iron core section A in the mixed stator iron core at each axial position point l at the position of the measuring point i is calculated 1 、l 2 …l 21 The difference value of the magnetic density amplitude of the mixed stator core and the magnetic density amplitude 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 21 The difference value of the magnetic density amplitude of the magnetic core S and the magnetic density amplitude of the iron core S; in order to improve the convergence speed and ensure the fitting precision, each axial position point l is taken 1 、l 2 …l 21 The standard deviation normalization processing is performed according to equation (11):
wherein n is 1,2 …, 21; mu.s 1 And σ 1 Are respectively [0,21.875]The mean and standard deviation of the values between the axial position points are calculated to obtain mu 1 ＝11.25，σ 1 ＝6.847；μ 2 And σ 2 Are respectively [21.875,52.5 ]]Calculating the mean and standard deviation of the values between the axial position points to obtain mu 2 ＝37.5，σ 2 ＝9.014。
The axial position point is normalized by the standard deviation to obtain a mapping of l' 1 、l′ 2 …l′ 21 If the tangential magnetic density value at the measuring point b is small and is ignored, then:
formula (9) is expressed as:
formula (10) is expressed as:
coefficient p xi11 、p xi21 、p xi31 、p xi41 、q xi11 And q is xi21 Is in the axial interval [0,21.875 ]]Inner, according to the diameter of the statorObtaining an absolute value change curve of the flux density amplitude difference value through least square fitting;
coefficient p xi12 、p xi22 、p xi32 、p xi42 、q xi12 And q is xi22 Is in the axial interval [21.875,52.5 ]]Obtaining an absolute value variation curve of the stator radial flux density amplitude difference value through least square fitting;
coefficient p yi11 、p yi21 、p yi31 、p yi41 、q yi11 And q is yi21 Is in the axial interval [0,21.875 ]]Obtaining an absolute value variation curve of the stator tangential flux density amplitude difference through least square fitting;
coefficient p yi12 、p yi22 、p yi32 、p yi42 And q is yi12 And q is yi22 Is in the axial interval [21.875,52.5 ]]Obtaining an absolute value variation curve of the stator tangential flux density amplitude difference through least square fitting;
the values of the coefficients obtained by the least squares fit are shown in table 1:
TABLE 1 coefficients of the magnetic density amplitude difference function
The final loss calculation is shown in table 2:
TABLE 2 loss calculation results
The loss of the rotor, the permanent magnet and the like is ignored in the calculation, the basic iron loss 59.63W of the hybrid motor obtained by calculation without correction is subtracted from the total no-load loss 86.18W of the motor obtained by simulation, the sum of other losses of the hybrid stator motor except the basic iron loss is about 26.55W, and the motor no-load loss is the sum of the stator iron loss and the other losses.
Electric machineStress generated in the actual machining process has certain influence on the loss characteristic of the material, and stray loss, nonuniformity of magnetic density distribution at different positions and the like are not considered in loss calculation, so the calculation result is usually small and needs to be corrected by using an empirical coefficient K. According to design experience, taking K as loss correction coefficient of silicon steel material S 1.27, loss correction factor K of amorphous alloy material A The results after correction are shown in table 3, when 5.42:
table 3: corrected calculation result
| Silicon steel | Amorphous form | Stator assembly | |
| Hybrid stator calculated loss/W | 73.12 | 10.40 | 83.52 |
| Single material stator calculated loss/W | 67.86 | 11.46 | 79.32 |
The motor no-load loss measured by the experiment is 123.27W, the motor no-load loss obtained by the traditional calculation method is 105.87W, the motor no-load loss obtained by the calculation method is 110.07W, and the calculation precision is improved by 3.4%.
Calculation of motor electromagnetic torque for a motor with hybrid stator core:
b in the formula (8) is obtained through Maxwell three-dimensional simulation rk And B θk ；
The stator core is made of two mixed materials, so that a magnetic field formed by the permanent magnet is deflected, the magnetic density in the stator is unevenly distributed along the axial direction, the tangential force density of the motor fluctuates along the axial direction, unit tangential electromagnetic force densities of axial positions under a rated working condition and a peak working condition are respectively calculated, and integration is carried out along the circumference of a curve to obtain unit electromagnetic torque of the motor at each axial position point, as shown in fig. 4, a curve b1 in fig. 4 is the unit electromagnetic torque of the motor at each axial position point under the rated working condition, and a curve b2 is the unit electromagnetic torque of the motor at each axial position point under the peak working condition; under a rated working condition, the mean value of the unit electromagnetic torque of the silicon steel iron core section is 0.42 N.m/mm, and the mean value of the unit electromagnetic torque of the amorphous alloy iron core section is 0.37 N.m/mm; the trend of the peak working condition curve is similar to that of a rated working condition, the electromagnetic torque of the silicon steel stator is 0.82 N.m/mm, and the electromagnetic torque of the amorphous stator is only 0.74 N.m/mm, so that the electromagnetic torque of the motor has larger difference in the axial direction. In order to simplify analysis, only the position of the motor part is calculated, the unit electromagnetic torque of the whole axial position of the motor is calculated by utilizing symmetry, and then the electromagnetic torque of the hybrid stator motor is obtained by axial integration.
The method fully considers the influence of the axial material difference of the mixed stator core motor, and improves the performance calculation accuracy of the motor; the method is characterized in that a change rule of the motor flux density amplitude along the axial direction is obtained by constructing a flux density amplitude difference function, and then the flux density amplitude is replaced by a flux density amplitude distribution function changing along the axial position from a constant on the basis of the theory of the existing motor loss and electromagnetic torque calculation method, so that a no-load loss and electromagnetic torque calculation method for the mixed stator core motor is determined, the defects of the original loss and electromagnetic torque calculation method are overcome, the calculation accuracy of relevant performance parameters of the motor can be improved, and a foundation is laid for the wide application of the mixed stator core motor.
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.
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