CN114154372A - Rapid finite element calculation method for electromagnetic performance of speed regulating motor considering chute effect - Google Patents
Rapid finite element calculation method for electromagnetic performance of speed regulating motor considering chute effect Download PDFInfo
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Abstract
The invention discloses a method for quickly calculating the electromagnetic property of a speed regulating motor by considering the skewed slot effect, which comprises the steps of constructing a two-dimensional electromagnetic field analysis finite element model of the speed regulating motor, and solving and obtaining the main electromagnetic property under different current amplitudes and current lead angles; based on the chute multi-section segmentation principle, coordinate transformation and two-dimensional interpolation calculation are carried out on the main electromagnetic performance to obtain the corresponding electromagnetic performance of the main electromagnetic performance on other sections, finally the overall electromagnetic performance considering the chute effect is obtained, and the electromagnetic performance is expanded to other rotating speeds; the invention can effectively reduce the calculation dimension, reduce the calculation time and save the calculation resources.
Description
Technical Field
The invention relates to a two-dimensional finite element analysis method, which is a rapid calculation method for electromagnetic performance of a speed regulating motor under multiple working conditions by adopting a multi-section segmentation principle and carrying out coordinate transformation and interpolation calculation on the obtained electromagnetic performance of the motor.
Background
The chute related in the field of motors is generally a structure that a motor rotor slot inclines at a certain angle along the axial direction, and is widely applied to the processing and manufacturing of small and medium-sized motors. According to the production process and the type of the motor, the chute can be generally divided into a stator chute, a rotor chute, a permanent magnet oblique pole and the like, and the chute mainly has the advantages of weakening a harmonic magnetic field in an air gap, inhibiting torque pulsation, reducing synchronous and asynchronous additional torque, reducing vibration noise and the like.
The finite element analysis method is a numerical calculation method commonly used in the field of motor electromagnetic field analysis modeling, and after a motor adopts a chute process, the structural dimension of the motor can change along the axial direction of the motor, so that the motor can be accurately modeled by adopting a three-dimensional finite element method. However, the analytical modeling of the motor using the three-dimensional finite element method consumes much computer resources and requires a long simulation time. To solve this problem, the industry usually adopts a multi-section method based on two-dimensional finite element analysis to consider the chute effect of the motor. The method equally divides the motor adopting the chute structure into a plurality of sections along the axial direction, each section adopts a two-dimensional finite element analysis method for modeling, and the position and excitation of the stator and the rotor of each section are correspondingly adjusted, so that the chute effect of the motor can be accurately and effectively calculated. Compared with the traditional three-dimensional finite element modeling method, the multi-section method based on the two-dimensional finite element analysis method can remarkably reduce the subdivision units of the finite element model, save computer resources and shorten the simulation calculation time.
However, for the speed regulating motor, in the design and analysis stage of the speed regulating motor, electromagnetic characteristics of the speed regulating motor under multiple working conditions are generally required to be examined, so that multiple finite element analysis calculations are required, and the calculation time is obviously prolonged. If the chute effect of the motor needs to be further considered, even if a multi-section method based on a two-dimensional finite element analysis method is adopted to analyze and model the motor, the required computer resources and the calculation time length are further increased. Therefore, it is necessary to explore a rapid finite element analysis modeling method capable of ensuring the calculation accuracy and reducing the calculation resources for the problem that the finite element simulation calculation of the speed regulating motor takes too long time when considering the chute effect.
Disclosure of Invention
The invention provides a novel motor electromagnetic field finite element analysis modeling method improved by a multi-section method based on a two-dimensional finite element analysis method, aiming at the problem that finite element analysis modeling calculation time is too long when a skewed slot effect is considered for a speed regulating motor, so as to guarantee calculation precision, reduce calculation resources and shorten calculation time.
The invention realizes the purpose through the following technical scheme, which comprises the following steps: :
a rapid finite element calculation method for electromagnetic performance of a speed regulating motor considering a chute effect comprises the following steps:
(1) establishing a two-dimensional finite element analysis model of the speed regulating motor without considering the chute effect, and performing primary simulation calculation on the electromagnetic performance to obtain the basic electromagnetic performance of the motor;
(2) by a scanning voltage u1、u2…unOr current excitation i1、i2…inObtaining the electromagnetic performance y of the speed regulating motor under different working conditions without considering the chute effect, and obtaining each electromagnetic performance and the dq axis current (i)d,iq) The mathematical mapping relation between the two is that y is f (i)d,iq)；
(3) In order to consider the chute effect of the speed-regulating motor, the motor is axially divided into N sections along the rotating shaft, each section is a two-dimensional straight-slot model, and the total skew angle of each motor chute is thetaskThe initial position of the stator or rotor between each section is staggered by an angle thetask/N；
(4) In the step (3), the initial position of the stator or the rotor in different cross sections is changed, so that the dq axis of the stator or the rotor is changed, a coordinate system after the change is represented by d 'q', and the dq axis current (i) in the step (2) is represented byd,iq) Transforming to d 'q' coordinate system of other cross sections, transformed current (i)d',iq') is expressed as:
in the formula: gamma is a current lead angle under the original dq coordinate system; p is the number of pole pairs of the motor; n is the number of the sequence of the cross section;
(5) comparing the electromagnetic performance in step (2) with the dq-axis current (i)d,iq) The mathematical mapping relationship between y and f (i)d,iq) To carry outTwo-dimensional interpolation is carried out to obtain the electromagnetic performance and the d 'q' axis current (i) on other sectionsd',iq') the mathematical mapping relationship y' ═ f (i)d',iq')；
(6) According to the characteristic of electromagnetic performance to be inspected, carrying out superposition summation or averaging after summation on each section obtained in the step (5), and obtaining the overall electromagnetic performance of the speed regulating motor after the chute effect is considered;
(7) and (4) according to the characteristic of electromagnetic performance required to be inspected and the characteristic of conversion along with the rotating speed, expanding the specific electromagnetic performance of the speed regulating motor considering the chute effect in the step (6) to other rotating speeds, and obtaining the electromagnetic performance of the speed regulating motor considering the chute effect at other rotating speeds.
As a further optimized scheme of the invention, basic electromagnetic properties of the motor in the step (1) comprise motor voltage, current, torque and iron loss.
As a further optimized scheme of the invention, in the step (2), the voltage u is scanned1、u2…unOr current excitation i1、i2…inAnd selecting according to the actual requirements of the specific engineering.
As a further optimized scheme of the present invention, in the step (3), the skew angle of the motor is θskThe range is 0.9 to 1.2 stator pitches.
As a further optimized scheme of the present invention, in the step (3), the chute motor is segmented along the axial direction according to a two-dimensional finite element multi-section segmentation principle to form a plurality of two-dimensional sections.
As a further preferable scheme of the present invention, in the step (3), the number N of the cross sections axially divided into the chute motor is a positive integer greater than 2.
As a further optimized scheme of the present invention, in the step (5), the two-dimensional interpolation adopts bilinear interpolation or cubic spline interpolation.
As a further optimized scheme of the invention, in the step (7), the specific electromagnetic performance at other rotating speeds mainly comprises stator voltage and iron loss, and the stator voltage is converted according to the proportional relation of the rotating speeds; the iron loss mainly comprises hysteresis loss and eddy current loss, the hysteresis loss is converted according to the proportional relation of the rotating speed, and the eddy current loss is converted according to the square relation of the rotating speed.
Compared with the prior art, the invention has the beneficial effects that:
the method not only ensures the calculation precision of the chute effect of the speed regulating motor, but also reduces the calculation resources and shortens the finite element simulation calculation time, and the conception mechanism is as follows: for the speed regulating motor, in the design and analysis stage, the electromagnetic characteristics of the speed regulating motor under a plurality of working conditions are generally required to be inspected, so that finite element analysis and calculation are required for a plurality of times, and the calculation time is obviously prolonged; if the chute effect of the motor needs to be further considered, even if a multi-section method based on a two-dimensional finite element analysis method is adopted to analyze and model the motor, the required computer resources and the calculation time length can be further increased; in order to reduce the simulation calculation amount, voltage or current can be scanned firstly, and the electromagnetic performance of the motor without considering the chute effect is obtained; segmenting the chute motor along the axial direction according to a two-dimensional finite element multi-section segmentation principle, and carrying out coordinate transformation and interpolation on the obtained motor electromagnetic performance without considering the chute effect to obtain the motor electromagnetic performance with the chute effect considered; the invention can obviously reduce the computing resources and shorten the finite element simulation time.
Drawings
FIG. 1 is a schematic flow chart of a rapid finite element calculation method for electromagnetic performance of a speed regulating motor based on a two-dimensional finite element multi-section method, which takes the chute effect into consideration;
FIG. 2 is a schematic diagram of modeling a motor chute structure by a two-dimensional finite element multi-section method according to the present invention;
FIG. 3 is a diagram of the operating phasors of the motor at each section when the chute structure of the motor is modeled according to the present invention;
FIG. 4 is a comparison graph of the simulated calculated electromagnetic torque and the measured electromagnetic torque of the present invention;
FIG. 5 is a comparison graph of the stator voltage of the present invention calculated by simulation and the actually measured stator voltage;
FIG. 6 is a diagram of the variation of iron loss with rotation speed and torque of a motor according to the present invention.
Reference numbers in the figures: 1 is the q' axis of the section of the n-th layer, and 2 is the section of the 1 st layerQ-axis current i of surfaceqAnd 3 is the stator current i of the 1 st layer cross sectionsAnd 4 is a q-axis current i of the cross section of the 1 st layerdAnd 5 is d' axis current i of the section of the nth layerd', 6 is the electrical angle pn theta of the difference between the d ' q ' axis coordinate system of the section of the n-th layer and the dq axis coordinate system of the section of the first layerskPermanent magnet flux linkage psi of layer 1 cross section/N, 7PM8 is d-axis of the 1 st layer cross section, and 9 is stator flux linkage psi of the 1 st layer cross sectionsAnd 10 is the q-axis armature reaction flux linkage psi of the 1 st layer cross sectionaqAnd 11 is the d-axis armature reaction flux linkage psi of the 1 st layer cross section ad12 is d 'axis of section of n-th layer, 13 is q' axis armature reaction magnetic linkage psi of section of n-th layeraq', 14 is the stator flux linkage psi of the section of the n-th layers'15 th layer section d' axis armature reaction flux linkage psiad', 16 is the permanent magnet magnetic chain psi of the section of the n-th layerPM', 17 is the stator current lead angle γ of the 1 st layer cross section, 18 is the q ' axis of the n layer cross section, and 19 is the q ' axis current i of the n layer cross sectionq'。
Detailed Description
For the purpose of clearly illustrating the objects, technical solutions and advantages of the embodiments of the present invention, the present invention will be fully and clearly described below with reference to the accompanying drawings in the embodiments of the present invention. However, the embodiments described in the present invention are a part of the embodiments of the present invention, not all of the embodiments, and the description of the embodiments is only for assisting understanding of the core idea of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any inventive step, are intended to be included within the scope of the invention as claimed.
As shown in fig. 1, the invention discloses an embodiment of a fast finite element calculation method considering a skewed slot effect based on a permanent magnet-assisted synchronous reluctance motor, which comprises the following steps:
(1) a two-dimensional electromagnetic field finite element model of a 380V, 3.5kW, 36-slot and 4-pole permanent magnet auxiliary type synchronous reluctance motor without considering a skewed slot effect is established, preliminary simulation calculation of electromagnetic performance is carried out, and motor voltage, torque and iron loss are obtained.
(2) Excitation of i by sweeping stator currentsThe step length of the epsilon (10A, 400A) is 10A, 40 steps are counted, the step length of the stator current advance angle gamma epsilon (90 degrees and 180 degrees) is 5 degrees, 19 steps are counted, 760 working points are counted, each working point adopts a two-dimensional finite element transient field to carry out simulation calculation on 1 electric cycle containing 40 time steps, all the working points are 30400 time steps, and the electromagnetic torque T without considering the chute effect of the motor under different working conditions is obtainedemAnd stator voltage UsAnd obtaining its current (i) with the dq axisd,iq) The mathematical mapping relation between the two is Tem＝f(id,iq) And Us＝f(id,iq)。
(3) As shown in fig. 2, in order to consider the skewed slot effect of the permanent magnet-assisted synchronous reluctance motor, the motor rotor is divided into 5 sections along the axial direction of the rotating shaft, each section is a two-dimensional straight slot model, and the total skew angle θ of the motor skewed slot issk10 degrees, i.e. one stator pitch, the initial position of the rotor is staggered by an angle theta between sectionssk/N＝2°。
(4) As shown in FIG. 3, the critical parameters 1 are q' axis of the n-th layer cross section, and 2 is q-axis current i of the 1 st layer cross sectionqAnd 3 is the stator current i of the 1 st layer cross sectionsAnd 4 is a q-axis current i of the cross section of the 1 st layerdAnd 5 is d' axis current i of the section of the nth layerd', 6 is the electrical angle pn theta of the difference between the d ' q ' axis coordinate system of the section of the n-th layer and the dq axis coordinate system of the section of the first layerskPermanent magnet flux linkage psi of layer 1 cross section/N, 7PM8 is d-axis of the 1 st layer cross section, and 9 is stator flux linkage psi of the 1 st layer cross sectionsAnd 10 is the q-axis armature reaction flux linkage psi of the 1 st layer cross sectionaqAnd 11 is the d-axis armature reaction flux linkage psi of the 1 st layer cross section ad12 is d 'axis of section of n-th layer, 13 is q' axis armature reaction magnetic linkage psi of section of n-th layeraq', 14 is the stator flux linkage psi of the section of the n-th layers'15 th layer section d' axis armature reaction flux linkage psiad', 16 is the permanent magnet magnetic chain psi of the section of the n-th layerPM', 17 is the stator current lead angle γ of the 1 st layer cross section, 18 is the q ' axis of the n layer cross section, and 19 is the q ' axis current i of the n layer cross sectionq'; since the initial position of the stator or rotor in different sections is found to be changed in step (3), the method has the advantages of being simple and convenient to operate and being capable of reducing the cost of the stator or rotorThe dq axis is also changed, the coordinate system after the change is represented by d 'q', and the current (i) of the dq axis in step (2) is represented byd,iq) Transforming to d 'q' coordinate system of other cross sections, transformed current (i)d',iq') can be expressed as:
in the formula: gamma is a current lead angle under the original dq coordinate system; p is the number of pole pairs of the motor; n is the number of the sequence of the cross section.
(5) Electromagnetic torque T in single-phase step (2)em＝f(id,iq) And stator voltage Us＝f(id,iq) Two-dimensional interpolation is carried out by adopting a bilinear interpolation method to obtain the electromagnetic performance and the d 'q' axis current (i) on other sectionsd',iq') mathematical mapping relation T betweenem'＝f(id',iq') and Us'＝f(id',iq')。
(6) And (5) superposing the electromagnetic torque and the stator voltage of each section obtained in the step (5) to obtain the overall electromagnetic performance of the permanent magnet auxiliary type synchronous reluctance motor after considering the chute effect.
(7) Expanding the stator voltage and iron loss after considering the skewed slot effect in the step (6) to other rotating speeds according to the characteristic of the electromagnetic performance required to be considered and the characteristic of the electromagnetic performance changing along with the rotating speed, and obtaining the electromagnetic performance of the permanent magnet auxiliary type synchronous reluctance motor considering the skewed slot effect at other rotating speeds; FIG. 4 is a comparison graph of the electromagnetic torque of the present invention, wherein the maximum error is 15.00% and the average absolute error is 0.70%; FIG. 5 is a comparison graph of the stator voltage of the present invention, wherein the maximum error is-14.00% and the average absolute error is 2.20%; FIG. 6 is a diagram of the variation of iron loss with rotation speed and torque of a motor according to the present invention.
Wherein, in the step (2), the stator current excites isCan be selected according to the actual requirements of specific projects. Example sweeping stator Current excitation isE (10A, 400A) stepThe length of the stator current lead angle gamma belongs to (90 degrees and 180 degrees) and the step length is 5 degrees, the total number of the steps is 19, 760 working points are total, each working point adopts a two-dimensional finite element transient field to carry out simulation calculation on 1 electric cycle containing 40 time steps, and the total number of all the working points is 30400 time steps; if the chute effect is not considered by using the method of the invention, and the motor is divided into 5 sections by using the traditional two-dimensional multi-section method, then the total of all the working points to be calculated is 5 × 30400-152000 time steps.
Wherein, in the step (3), the skew angle of the motor is thetaskThe value range is 0.9 to 1.2 stator tooth pitches, and the motor skew angle is theta in the embodimentskI.e. 10 deg. i.e. one stator pitch.
And (3) segmenting the chute motor along the axial direction according to a two-dimensional finite element multi-section segmentation principle to form a plurality of two-dimensional sections.
In the step (3), the number N of the sections axially divided into the chute motor is a positive integer greater than 2, and the number of the selected sections in the embodiment is 5.
In the step (5), the two-dimensional interpolation may be performed by using bilinear interpolation or cubic spline interpolation, and the bilinear interpolation is used in the embodiment.
In the step (7), the specific electromagnetic performance at other rotating speeds mainly comprises stator voltage and iron loss, and in the embodiment, the stator voltage is converted according to the proportional relation of the rotating speeds; the iron loss mainly comprises hysteresis loss and eddy current loss, the hysteresis loss is converted according to the proportional relation of the rotating speed, and the eddy current loss is converted according to the square relation of the rotating speed.
Claims (8)
1. A rapid finite element calculation method for electromagnetic performance of a speed regulating motor considering a chute effect is characterized by comprising the following steps:
(1) establishing a two-dimensional finite element analysis model of the speed regulating motor without considering the chute effect, and performing primary simulation calculation on the electromagnetic performance to obtain the electromagnetic basic performance of the motor;
(2) by a scanning voltage u1、u2…unOr current excitation i1、i2…inTo obtain a speed-regulating motorUnder the same working condition, the electromagnetic performance y of the chute effect is not considered, and the electromagnetic performance and the dq axis current (i) are obtainedd,iq) The mathematical mapping relation between the two is that y is f (i)d,iq)；
(3) In order to consider the chute effect of the speed-regulating motor, the motor is axially divided into N sections along the rotating shaft, each section is a two-dimensional straight-slot model, and the total skew angle of each motor chute is thetaskThe initial position of the stator or rotor between each section is staggered by an angle thetaskN is a positive integer;
(4) in the step (3), the initial position of the stator or the rotor in different cross sections is changed, so the dq axis is also changed, the changed coordinate system is represented by d 'q', and the dq axis current (i) in the step (2) is represented byd,iq) Transforming to d 'q' coordinate system of other cross sections, transformed current (i)d',iq') is expressed as:
in the formula: gamma is a current lead angle under the original dq coordinate system; p is the number of pole pairs of the motor; n is the number of the sequence of the cross section;
(5) comparing the electromagnetic performance in step (2) with the dq-axis current (i)d,iq) The mathematical mapping relationship between y and f (i)d,iq) Two-dimensional interpolation is carried out to obtain the electromagnetic performance and the d 'q' axis current (i) on other sectionsd',iq') the mathematical mapping relationship y' ═ f (i)d',iq')；
(6) According to the characteristic of electromagnetic performance to be inspected, carrying out superposition summation or averaging after summation on each section obtained in the step (5), and obtaining the overall electromagnetic performance of the speed regulating motor after the chute effect is considered;
(7) and (4) according to the characteristic of electromagnetic performance required to be inspected and the characteristic of conversion along with the rotating speed, expanding the specific electromagnetic performance of the speed regulating motor considering the chute effect in the step (6) to other rotating speeds, and obtaining the electromagnetic performance of the speed regulating motor considering the chute effect at other rotating speeds.
2. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: the basic electromagnetic properties of the motor in the step (1) comprise motor voltage, current, torque and iron loss.
3. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: in the step (2), the voltage u is scanned1、u2…unOr current excitation i1、i2…inAnd selecting according to the actual requirements of the specific engineering.
4. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: in the step (3), the skew angle of the motor is thetaskThe range is 0.9 to 1.2 stator pitches.
5. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: and (3) segmenting the chute motor along the axial direction according to a two-dimensional finite element multi-section segmentation principle to form a plurality of two-dimensional sections.
6. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: in the step (3), the number N of the sections axially divided into the chute motor is a positive integer greater than 2.
7. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: in the step (5), the two-dimensional interpolation adopts bilinear interpolation or cubic spline interpolation.
8. The method for rapidly calculating the finite element of the electromagnetic performance of the speed regulating motor considering the chute effect as claimed in claim 1, wherein the finite element is as follows: in the step (7), the specific electromagnetic performance at other rotating speeds comprises stator voltage and iron loss, and the stator voltage is converted according to a rotating speed proportional relation; the iron loss comprises hysteresis loss and eddy current loss, the hysteresis loss is converted according to the proportional relation of the rotating speed, and the eddy current loss is converted according to the square relation of the rotating speed.
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