CN111241735B - Method for calculating load electromagnetic excitation force wave of built-in permanent magnet synchronous motor - Google Patents
Method for calculating load electromagnetic excitation force wave of built-in permanent magnet synchronous motor Download PDFInfo
- Publication number
- CN111241735B CN111241735B CN202010042551.XA CN202010042551A CN111241735B CN 111241735 B CN111241735 B CN 111241735B CN 202010042551 A CN202010042551 A CN 202010042551A CN 111241735 B CN111241735 B CN 111241735B
- Authority
- CN
- China
- Prior art keywords
- air gap
- load
- force
- magnetic
- permanent magnet
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
- H02K21/02—Details
- H02K21/021—Means for mechanical adjustment of the excitation flux
- H02K21/022—Means for mechanical adjustment of the excitation flux by modifying the relative position between field and armature, e.g. between rotor and stator
- H02K21/025—Means for mechanical adjustment of the excitation flux by modifying the relative position between field and armature, e.g. between rotor and stator by varying the thickness of the air gap between field and armature
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
- H02K21/12—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets
- H02K21/14—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating within the armatures
Landscapes
- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Permanent Field Magnets Of Synchronous Machinery (AREA)
- Iron Core Of Rotating Electric Machines (AREA)
- Control Of Electric Motors In General (AREA)
- Permanent Magnet Type Synchronous Machine (AREA)
Abstract
The invention provides a method for calculating a load electromagnetic excitation force wave of a built-in permanent magnet synchronous motor, which is characterized in that a finite element is used for calculating the air gap flux density under the condition of no load to obtain the relation between magnetomotive force and flux conductance under the condition of no load; a d-axis magnetic conductance model of an armature magnetic field is obtained through simulation by using a frozen magnetic conductance method, and the magnetomotive force and magnetic conductance relation generated by the independent action of the winding under the load condition is accurately calculated according to the model, so that the air gap flux density generated by the winding is obtained; superposing the air gap flux densities generated by the permanent magnet and the armature winding by utilizing a superposition principle to obtain a built-in load air gap flux density expression; according to the Maxwell tensor method, the results of all components of the magnetomotive force and the air gap magnetic conductance are substituted into an electromagnetic force density expression, and the amplitude of each force wave under different frequencies and different orders is accurately obtained.
Description
Technical Field
The disclosure belongs to the technical field of permanent magnet synchronous motors, and particularly relates to a method for calculating a load electromagnetic excitation force wave of a built-in permanent magnet synchronous motor.
Background
The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
Noise pollution is combined with air pollution, water pollution and solid waste pollution and is known as four major pollutants in the world today. Noise pollution is one kind of environmental pollution, and is now a great harm to human beings, and a series of physiological and pathological changes of the nervous system, the cardiovascular system, the endocrine system and the digestive system of a human body can be caused by working in a noise environment for a long time. In recent years, the permanent magnet synchronous motor has a wide application prospect in various fields due to the advantages of simple structure, high efficiency, high power density and the like. With the advance and development of the permanent magnet synchronous motor technology, various indexes such as the performance, the precision and the like of the motor become the aspects of attention and research of numerous scholars. Under the condition of the same other performances, the vibration noise index directly reflects the quality of a permanent magnet motor, and the low-vibration noise motor can not only improve the running precision of the motor, but also reduce the stimulation to the sense of human body. As a main source of motor vibration and noise, the electromagnetic vibration of the motor is excited by an electromagnetic excitation force wave which is generated by a motor air gap magnetic field acting on a motor stator core and changes along with time and space, so that the accurate analysis and calculation of the electromagnetic excitation force wave become the key of the motor electromagnetic vibration analysis.
The key of solving the electromagnetic excitation force wave is the solution of the air gap magnetic field of the motor, and at present, three methods are mainly adopted for the calculation and analysis of the air gap magnetic field and the excitation force wave: analytic method, magnetomotive force-magnetic conductance method, finite element method. The magnetomotive force-magnetic conductance method can give the frequency, order and phase of electromagnetic excitation force wave according to the principle that the air gap flux density is equal to the magnetomotive force multiplied by the magnetic conductance, and can deduce the generation item of the corresponding order electromagnetic force wave, so that the method has limitations, cannot obtain the accurate value of the electromagnetic force wave, can only carry out fixed analysis and cannot carry out quantitative analysis, and the application range is limited; although the magnetic field analysis method can conveniently calculate the air gap magnetic field and the vibration force wave, when the saturation of the iron core and the complex shape of the tooth socket are considered, the calculation period is prolonged, the calculation precision is reduced, and the method has certain difficulty and is not easy to calculate quickly and accurately; the finite element method can consider the influence of various factors such as saturation and the like, can accurately calculate the air gap magnetic field and the electromagnetic force density, but cannot effectively analyze the source of the excitation force wave and deduce the source item of the specific excitation force wave, and can only carry out quantitative analysis and not carry out qualitative analysis.
The three methods for calculating the electromagnetic force have advantages and disadvantages, can not accurately determine a complete expression of each electromagnetic force wave including amplitude, rotating speed, frequency and phase, can not accurately evaluate the influence of a single electromagnetic force wave on vibration, can not accurately evaluate the overall effect of each electromagnetic force wave on vibration, and is not beneficial to analysis and attenuation of electromagnetic vibration.
For the built-in permanent magnet motor, because saturation and air gaps exist in the rotor, the internal structure of the rotor can affect an electromagnetic field, and the influence is different under different current amplitudes and different power angles, so that certain difficulty is brought to derivation of the load magnetic field of the built-in permanent magnet motor.
Disclosure of Invention
The method comprises the steps of calculating an armature magnetic field by taking the load diversity of the internal structure of the rotor into consideration and combining an equivalent d-axis reluctance model. The method can accurately determine the radial electromagnetic waves of each order including the amplitude, the rotating speed, the frequency and the phase by considering the influence of the complex structure of the motor and the iron core saturation.
According to some embodiments, the following technical scheme is adopted in the disclosure:
a method for calculating a load electromagnetic excitation force wave of a built-in permanent magnet synchronous motor comprises the following steps:
calculating the air gap flux density under the no-load condition by using a finite element to obtain the relation between the magnetomotive force and the flux guide under the no-load condition;
a d-axis magnetic conductance model of an armature magnetic field is obtained through simulation by using a frozen magnetic conductance method, and the magnetomotive force and magnetic conductance relation generated by the independent action of the winding under the load condition is accurately calculated according to the model, so that the air gap flux density generated by the winding is obtained;
superposing the air gap flux densities generated by the permanent magnet and the armature winding by utilizing a superposition principle to obtain a built-in load air gap flux density expression;
according to the Maxwell tensor method, the results of all components of the magnetomotive force and the air gap magnetic conductance are substituted into an electromagnetic force density expression, and the amplitude of each force wave under different frequencies and different orders is accurately obtained.
As an alternative implementation mode, the finite elements are used for calculating the air gap flux densities of stator slotting and non-slotting under the no-load condition, the influence of stator slotting is converted into the change of the effective length of the air gap by using the finite elements twice, and the relation between the magnetomotive force and the magnetic conductance under the no-load condition is obtained.
As an alternative embodiment, during no load, the air gap permeance expression is obtained by considering the influence of core saturation and the complicated shape of the tooth slot.
In an alternative embodiment, the space-time relation of radial electromagnetic force waves acting on the surface of the motor stator is calculated by using Maxwell tensor, and the source of each order force wave is calculated by using the mutual influence relation of magnetic density harmonics of each air gap.
As an alternative embodiment, according to the electromagnetic wave as a quadratic function in time and space, two-dimensional space fourier decomposition is performed on the calculation result of the electromagnetic wave and the finite element result, so as to obtain specific amplitudes of the electromagnetic wave of each order and frequency in two cases.
The method is suitable for any built-in permanent magnet synchronous motor and is not limited by factors such as rotor shape, materials, permanent magnet placement mode and rotor saturation degree.
A computing system for a built-in permanent magnet synchronous motor loaded electromagnetic excitation force wave comprises:
the no-load calculation module is configured to calculate the air gap flux density under the no-load condition by using a finite element to obtain the relation between the magnetomotive force and the magnetic conductance under the no-load condition;
the load calculation module is configured to obtain a d-axis magnetic conductance model of an armature magnetic field in a simulation mode by using a frozen magnetic conductance method, accurately calculate the magnetomotive force and magnetic conductance relation generated by the independent action of the winding under the load condition according to the model, and obtain the air gap flux density generated by the winding;
the superposition module is configured to superpose the air gap flux densities generated by the permanent magnet and the armature winding by utilizing a superposition principle to obtain a built-in load air gap flux density expression;
and the derivation calculation module is configured to substitute the magnetomotive force and the air gap magnetic conductance component results into an electromagnetic force density expression according to a Maxwell tensor method, and accurately obtain the force wave amplitude values under different frequencies and different orders.
A computer readable storage medium stores a plurality of instructions, and the instructions are suitable for being loaded by a processor of a terminal device and executing the method for calculating the electromagnetic excitation force wave of the built-in permanent magnet synchronous motor load.
A terminal device comprising a processor and a computer readable storage medium, the processor being configured to implement instructions; the computer readable storage medium is used for storing a plurality of instructions, and the instructions are suitable for being loaded by a processor and executing the calculation method of the built-in permanent magnet synchronous motor load electromagnetic excitation force wave.
Compared with the prior art, the beneficial effect of this disclosure is:
starting from the root source of electromagnetic vibration and noise, namely the radial excitation force wave, the amplitude of each order of radial excitation force wave of the built-in permanent magnet synchronous motor under the conditions of no load and load is accurately calculated by a method of combining a magnetomotive force-magnetic conduction method and a finite element, and the specific source of each order of excitation force wave is determined, so that a good foundation is laid for the analysis and design of the low-noise permanent magnet motor.
The method combines the magnetomotive force-magnetic conductance method and the finite element method, and the solution of the magnetomotive force of the permanent magnet and the magnetic conductance of the air gap only needs to use two times of finite element simulation, so that the calculation time is greatly shortened; meanwhile, the influence of rotor saturation on an armature magnetic field under the load condition can be considered, a uniform air gap flux density expression is obtained, the amplitude, the order frequency and the phase of each force wave under the load condition can be accurately obtained, and the source of each order electromagnetic force wave is researched through the interaction of air gap flux density harmonic waves.
The method provides convenience for quick and accurate calculation of each order of electromagnetic excitation force wave and weakening of subsequent specific order of electromagnetic excitation force wave, and lays a foundation for weakening the electromagnetic vibration of the permanent magnet synchronous motor.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.
FIGS. 1(a) - (b) are two-dimensional Fourier exploded views of unloaded and loaded electromagnetic waves;
FIG. 2 is a relative position of the permanent magnets and stator of the present disclosure;
FIGS. 3(a) - (b) are schematic diagrams of the open air gap flux density waveform and its Fourier decomposition results;
FIGS. 4(a) - (b) are graphs illustrating the notching coefficient waveform of the present disclosure and its Fourier decomposition results;
5(a) - (b) calculating a comparison graph of a no-load air gap flux density result and a simulation result and a Fourier decomposition result;
FIGS. 6(a) - (b) are schematic diagrams of air gap flux density waveforms for frozen permeability;
FIG. 7 is a d-axis flux guide model;
FIG. 8 is a comparison graph of the air gap flux density generated by the q-axis magnetomotive force;
FIG. 9 is a comparison graph of air gap flux density generated by a 5 th harmonic magnetomotive force;
FIGS. 10(a) - (b) are graphs comparing the simulation results and calculation results of air gap flux density finite elements and Fourier decomposition results.
The specific implementation mode is as follows:
the present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
In order to solve the problems in the background art, the invention discloses a method for quickly and accurately calculating the no-load electromagnetic excitation force wave of a built-in permanent magnet synchronous motor. And then obtaining a no-load air gap flux density time-space expression. And then according to the characteristics (different d-axis and q-axis magnetic resistances) of the built-in permanent magnet motor, a d-axis magnetic conductance model of an armature magnetic field is obtained through simulation by using a frozen magnetic conductance method, the magnetomotive force and the magnetic conductance expression generated by the independent action of the winding under the load condition are accurately calculated according to the model, and then the air gap flux density generated by the winding can be obtained. And the air gap flux density time-space complete expression can be obtained by superposing the two. According to the complete expression of the air gap flux density, a space-time expression of radial electromagnetic force waves acting on the surface of the motor stator is obtained by using a Maxwell tensor method, and the specific source of each order of force waves can be obtained by using the mutual influence relation of each air gap flux density harmonic wave, so that a theoretical basis is provided for weakening the electromagnetic force waves. Meanwhile, according to the fact that the electromagnetic wave is a quadratic function in time and space, two-dimensional space Fourier decomposition is conducted on the calculation result of the electromagnetic wave and the finite element result, specific amplitude values of the electromagnetic wave of each order and frequency under two conditions can be obtained, and accuracy of theoretical calculation can be verified conveniently.
Specifically, as a main source of motor vibration and noise, electromagnetic vibration of the motor is generated by radial electromagnetic excitation force waves acting on the surface of a stator armature, so that accurate calculation of the electromagnetic excitation force waves becomes a key of electromagnetic vibration analysis of the motor, and the key of accurate calculation of the electromagnetic excitation force waves is solving of an air gap magnetic field of the motor. Aiming at the defects of a finite element method and a magnetomotive force-magnetic conductance method in electromagnetic excitation force wave calculation and considering the influence of a rotor structure, the invention provides a rapid and accurate calculation method of a built-in permanent magnet synchronous motor load electromagnetic excitation force wave, which comprises the following steps:
(1) simulating a structural model with or without tooth grooves of the motor based on a two-dimensional static field to obtain permanent magnet magnetomotive force distribution and air gap magnetic conductance distribution;
(2) carrying out Fourier decomposition on the magnetomotive force of the permanent magnet and the magnetic conductance of the air gap, obtaining an air gap flux density expression in a multiplication mode, and then obtaining an unloaded electromagnetic force wave by utilizing a Maxwell tensor method;
(3) and (3) solving the magnetomotive force generated by the armature magnetic field according to the arrangement of the windings, and dividing the armature magnetomotive force into d-axis magnetomotive force, q-axis magnetomotive force and harmonic magnetomotive force according to the power angle characteristic.
(4) By utilizing the freezing magnetic conductivity principle, the air gap flux density generated by d-axis magnetomotive force, q-axis magnetomotive force and harmonic magnetomotive force is respectively researched, a new d-axis reluctance model is given, and a load air gap flux density expression is deduced.
(5) And deducing an electromagnetic excitation force wave including amplitude and frequency phase according to a load air gap flux density expression by using a Maxwell tensor method.
(6) The accuracy of the rapid and accurate calculation method is verified by a finite element method.
For the calculation of the air gap flux density under the no-load condition of the motor, for convenience of analysis, a relative position angle α between a permanent magnet and an armature in the motor is defined as an included angle between a phase center line of a current a and a center line of a permanent magnet pole, and a position θ is set to be 0 ° on the center line of the pole, as shown in fig. 2. Assuming that the relative magnetic permeability of the stator core is infinite, and the magnetic voltage drop of the magnetomotive force generated by the permanent magnet on the stator core can be ignored, the no-load air gap flux density can be expressed as:
in the formula, mu 0 For air permeability, delta (theta, alpha) is the distribution of equivalent air gap length along the motor motion direction along with the relative position change of a stator, and is related to the stator tooth slot distribution and the structural parameters thereof, and F (theta) is air gap equivalent magnetomotive force.
When the stator has no tooth space, the air gap is uniform, and delta is a constant, and the air gap magnetic voltage drop can be calculated by the following formula:
therefore, the air gap flux density B in the motor model with the tooth-slot-free structure can be obtained through finite element simulation 0 (theta) distribution in the circumferential direction is shown in FIG. 3(a), and the permanent magnet magnetomotive force F can be obtained by substituting formula (2) 1 (theta). Meanwhile, the permanent magnet magnetomotive force can be expressed as:
when the stator is slotted, the air gap magnetic voltage drop corresponding to the motor tooth part at this time can be expressed as:
under the condition of slotting or not slotting the motor, the magnetomotive force produced by the permanent magnet is basically unchanged, so that the air gap permeance can be obtained as
The stator slotting effect is equivalent to the effective length variation of the air gap, so that the stator slotting factor can be obtained by derivation as shown in fig. 4 (a).
The stator slotting effect result can be expressed as:
by utilizing a method combining magnetomotive force-magnetic conduction method and finite element method, the magnetomotive force generated by the deduced permanent magnet is multiplied by the equivalent slotting influence to obtain a no-load air gap flux density expression:
the result of the no-load air gap flux density calculated by the new method and the air gap flux density obtained by simulation is shown in fig. 5(a), the graphs are basically the same, and the accuracy of the result can be verified.
When the armature magnetic field is calculated, due to the fact that the rotor magnetic circuits are asymmetric, the magnetomotive force generated by the armature magnetic field is divided into d-axis magnetomotive force and q-axis magnetomotive force to be studied respectively.
Because the rotor is internally provided with the slot, the d-axis magnetic field is replanned, and the magnetic resistance of the magnetic line of force passing through different areas is different, so that the magnetic pressure divided in the rotor is different, and the air gap flux density amplitude is further influenced. The air gap radial flux density waveform is shown in fig. 6(a), wherein B (i) represents the air gap flux density in the case that permanent magnet slotting is not present in the rotor, and B (FP, i) represents the air gap flux density generated by d-axis fundamental current in the case of frozen permeability.
The path change of the magnetic line and the line magnetic resistance are equivalent to the air gap flux guide, namely the magnetomotive force is calculated to generate sinusoidal magnetomotive force under the condition that the rotor is not grooved, and the magnetic flux generated by the armature magnetic field can be expressed as follows:
in the formula, F new Magnetomotive force, R, produced by armature magnetic field g Expressed as air gap reluctance, R 1-n Internal reluctance of rotor, J d Representing the surface current generated by the d-axis magnetomotive force.
The rotor internal reluctance can be expressed as:
R＝l/μ 0 μ r A (9)
wherein l represents the length of the magnetic path, μ 0 Represents the relative permeability, mu r The magnetic steel has relative air permeability, and A is the magnetic circuit area.
The air gap flux density can be expressed as:
substituting the formulas (9) and (10) into the formula
The variation caused by rotor slotting is equivalent to a new air gap magnetic conductance model, and meanwhile, the change of the rotor position and the magnetomotive force along with time and the change of the space position are considered, and the expression is as follows:
in the formula F g And (theta, t) represents sinusoidal magnetomotive force generated in an air gap by sinusoidal surface current under the condition that the rotor is not grooved, and the variation is equivalent to a magnetic conductance model.
When t is 0
Based on the above analysis, the air gap flux density generated by the d-axis magnetomotive force can be expressed as
The derived d-axis magnetoresistance model is shown in FIG. 7.
Also by utilizing the frozen permeability method, the air gap flux densities generated by the q-axis magnetomotive force and the harmonic magnetomotive force are respectively researched as shown in fig. 8 and fig. 9, and the result shows that the generated air gap flux densities are basically not influenced by the rotor and can be ignored.
In conclusion, an air gap flux density expression under the condition of the load of the built-in permanent magnet motor can be deduced:
in the formula, θ represents a mechanical angle, p represents a pole pair number, and ω represents an electrical angular velocity.
The air gap flux density generated under the motor load condition is the superposition of the air gap flux density generated by the permanent magnet magnetomotive force and the air gap flux density generated by the armature magnetic field influenced by the rotor structure, and the air gap flux density under the load is shown in fig. 10 (a).
According to maxwell's tensor, the radial electromagnetic force density acting on the inner surface of the stator core of the motor can be expressed as:
in the formula, B n (θ, α) is the radial component of the air gap flux density.
The generation mechanisms of the force waves of all orders are arranged, so that main unloaded electromagnetic force wave sources are obtained and are shown in table 1 (data in the table are in an a/b form, wherein a represents the force wave order, and b represents the multiple of the force wave frequency relative to the fundamental frequency), and the electromagnetic force waves under the load condition are shown in table 2.
TABLE 1 order and frequency of force wave generated by air gap flux density interaction generated by permanent magnet at no-load
TABLE 2 order and frequency of force wave generated by air gap flux density interaction between permanent magnet and armature under load
It can be seen that the electromagnetic excitation force wave in the motor is generated by the interaction of air gap flux density harmonics, and the electromagnetic excitation force wave generated between the no-load magnetic field and the load magnetic field, that is, the electromagnetic force density amplitudes of different order frequencies of the motor under the no-load and load conditions can be obtained by substituting the obtained magnetomotive force, armature magnetomotive force, d-axis reluctance model and slotting influence equivalent magnetic conductance function related to the permanent magnet into the relationship of the harmonic interaction, so that the accurate amplitudes of the electromagnetic excitation force wave of each order and frequency in the motor can be accurately known, and the electromagnetic force densities under the no-load and load conditions are shown in fig. 1(a) and fig. 1 (b).
The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.
Claims (8)
1. A method for calculating a load electromagnetic excitation force wave of a built-in permanent magnet synchronous motor is characterized by comprising the following steps: the method comprises the following steps:
calculating the air gap flux density under the no-load condition by using a finite element to obtain the relation between the magnetomotive force and the flux guide under the no-load condition;
the variation caused by rotor slotting is equivalent to a new air gap magnetic conductance model, and the variation of the rotor position and the magnetomotive force along with time and the variation of the space position are considered; according to the difference of d-axis and q-axis magnetic resistance of the built-in permanent magnet motor, a d-axis magnetic conductance model of an armature magnetic field is obtained through simulation by using a frozen magnetic conductance method, and the magnetomotive force and magnetic conductance relation generated by the independent action of the winding under the load condition is accurately calculated according to the model to obtain the air gap flux density generated by the winding;
the built-in permanent magnet motor rotor is internally grooved, a d-axis magnetic field is re-planned, and the magnetic resistance of magnetic lines of force passing through different areas is different, so that the magnetic pressure obtained in the rotor is different, and the air gap flux density amplitude is further influenced;
the path change of the magnetic line and the line magnetic resistance are equivalent to the air gap flux guide, namely the magnetomotive force is calculated to generate sinusoidal magnetomotive force under the condition that the rotor is not grooved, and the magnetic flux generated by the armature magnetic field can be expressed as follows:
in the formula, F new Magnetomotive force, R, produced by armature magnetic field g Expressed as air gap reluctance, R 1-n Rotor internal reluctance, J d Representing the surface current generated by the d-axis magnetomotive force;
the rotor internal reluctance can be expressed as:
R＝l/μ 0 μ r A
wherein l represents the length of the magnetic path, μ 0 Represents the relative permeability, mu r The magnetic steel has relative air permeability, and A is the area of a magnetic circuit;
the air gap flux density can be expressed as:
finishing to obtain:
the variation caused by rotor slotting is equivalent to a new air gap magnetic conductance model, and meanwhile, the change of the rotor position and the magnetomotive force along with time and the change of the space position are considered, and the expression is as follows:
in the formula F g (theta, t) represents sinusoidal magnetomotive force generated by sinusoidal surface current in an air gap under the condition that the rotor is not grooved, and the variation is equivalent to a magnetic conductance model;
when t is equal to 0, the first step is,
B g (θ)＝B(FP，i)
considering magnetomotive force rotation, rotor rotation, and spatial position, the air gap flux density produced by d-axis magnetomotive force can be expressed as:
superposing the air gap flux densities generated by the permanent magnet and the armature winding by utilizing a superposition principle to obtain a built-in load air gap flux density expression;
according to the Maxwell tensor method, the results of all components of the magnetomotive force and the air gap magnetic conductance are substituted into an electromagnetic force density expression, and the amplitude of each force wave under different frequencies and different orders is accurately obtained.
2. The method for calculating the load electromagnetic excitation force wave of the interior permanent magnet synchronous motor according to claim 1, which is characterized in that: and calculating the air gap flux density of stator slotting and non-slotting in the no-load condition by using the finite elements, converting the stator slotting influence into the change of the effective length of the air gap by using the finite elements twice, and obtaining the relationship between the magnetomotive force and the magnetic conductance in the no-load condition.
3. The method for calculating the load electromagnetic excitation force wave of the interior permanent magnet synchronous motor according to claim 1, which is characterized in that: and during no load, considering the influence of iron core saturation and the complicated shape of the tooth socket to obtain an air gap magnetic conductance expression.
4. The method for calculating the load electromagnetic excitation force wave of the interior permanent magnet synchronous motor according to claim 1, which is characterized in that: the method comprises the steps of calculating the space-time relation of radial electromagnetic force waves acting on the surface of a motor stator by using a Maxwell tensor method, and calculating the source of each order of force waves by using the mutual influence relation of air gap flux density harmonics.
5. The method for calculating the load electromagnetic excitation force wave of the interior permanent magnet synchronous motor according to claim 1, which is characterized in that: and performing two-dimensional space Fourier decomposition on the calculation result of the electromagnetic wave and the finite element result according to the electromagnetic wave as a quadratic function in time and space to obtain the specific amplitude of the electromagnetic wave of each order and frequency under two conditions.
6. A computing system for a built-in permanent magnet synchronous motor loaded electromagnetic excitation force wave is characterized in that: the method for calculating the electromagnetic excitation force wave of the built-in permanent magnet synchronous motor load according to any one of claims 1 to 5 is adopted, and comprises the following steps:
the no-load calculation module is configured to calculate the air gap flux density under the no-load condition by using a finite element to obtain the relationship between the magnetomotive force and the flux guide under the no-load condition;
the load calculation module is configured to enable the variation caused by rotor slotting to be equivalent to a new air gap magnetic conductance model, and meanwhile, the time variation and the space variation of the rotor position and the magnetomotive force are considered; according to the difference of d-axis and q-axis magnetic resistance of the built-in permanent magnet motor, a d-axis magnetic conductance model of an armature magnetic field is obtained through simulation by using a frozen magnetic conductance method, and the magnetomotive force and magnetic conductance relation generated by the independent action of the winding under the load condition is accurately calculated according to the model to obtain the air gap flux density generated by the winding; the superposition module is configured to be a slot in the rotor of the built-in permanent magnet motor, the d-axis magnetic field is re-planned, and the magnetic resistance of the magnetic lines of force passing through different areas is different, so that the magnetic pressure obtained in the rotor is different, and the air gap flux density amplitude is further influenced; superposing the air gap flux densities generated by the permanent magnet and the armature winding by utilizing a superposition principle to obtain a built-in load air gap flux density expression;
and the derivation calculation module is configured to substitute the magnetomotive force and the air gap magnetic conductance component results into an electromagnetic force density expression according to a Maxwell tensor method, and accurately obtain the force wave amplitude values under different frequencies and different orders.
7. A computer-readable storage medium characterized by: the method comprises the steps of storing a plurality of instructions, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the method for calculating the electromagnetic excitation force wave of the built-in permanent magnet synchronous motor load according to any one of claims 1-5.
8. A terminal device is characterized in that: the system comprises a processor and a computer readable storage medium, wherein the processor is used for realizing instructions; the computer readable storage medium is used for storing a plurality of instructions, and the instructions are suitable for being loaded by a processor and executing the method for calculating the electromagnetic excitation force wave of the load of the interior permanent magnet synchronous motor according to any one of claims 1-5.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010042551.XA CN111241735B (en) | 2020-01-15 | 2020-01-15 | Method for calculating load electromagnetic excitation force wave of built-in permanent magnet synchronous motor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010042551.XA CN111241735B (en) | 2020-01-15 | 2020-01-15 | Method for calculating load electromagnetic excitation force wave of built-in permanent magnet synchronous motor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111241735A CN111241735A (en) | 2020-06-05 |
| CN111241735B true CN111241735B (en) | 2022-09-09 |
Family
ID=70871095
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010042551.XA Active CN111241735B (en) | 2020-01-15 | 2020-01-15 | Method for calculating load electromagnetic excitation force wave of built-in permanent magnet synchronous motor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111241735B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112069709B (en) * | 2020-09-04 | 2022-05-17 | 天津大学 | Motor electromagnetic vibration rapid calculation method considering stator tooth modulation effect |
| CN112468051B (en) * | 2020-11-13 | 2022-06-03 | 中国人民解放军海军工程大学 | Multiphase permanent magnet motor high-frequency vibration rapid analysis method and suppression strategy thereof |
| CN113507189B (en) * | 2021-07-01 | 2022-07-26 | 山东大学 | Design parameter optimization method for built-in permanent magnet synchronous motor |
| CN114157198B (en) * | 2021-11-02 | 2023-09-22 | 河海大学 | Method for calculating electromagnetic exciting force of permanent magnet synchronous motor stator under power supply of PWM inverter |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108539935B (en) * | 2018-05-14 | 2020-01-21 | 上海电力学院 | Wide-range speed-regulating vibration noise source analysis method for permanent magnet synchronous motor of electric automobile |
| CN109039215B (en) * | 2018-09-05 | 2021-09-07 | 上海电力学院 | Method for analyzing influence of inverter harmonic waves on vibration noise of permanent magnet synchronous motor for vehicle |
-
2020
- 2020-01-15 CN CN202010042551.XA patent/CN111241735B/en active Active
Non-Patent Citations (2)
| Title |
|---|
| The Analysis and Calculation of Load Radial;Xin Zhang等;《2019 22nd International Conference on Electrical Machines and Systems (ICEMS)》;20191205;第1-5页 * |
| 表贴式永磁同步电机电磁激振力波的快速准确计算与分析;刑泽智;《中国优秀硕士学位论文全文数据库》;20190915;第2、3章 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111241735A (en) | 2020-06-05 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111241735B (en) | Method for calculating load electromagnetic excitation force wave of built-in permanent magnet synchronous motor | |
| Lin et al. | Modeling and analysis of electromagnetic force, vibration, and noise in permanent-magnet synchronous motor considering current harmonics | |
| Deng et al. | Analytical modeling of the electromagnetic vibration and noise for an external-rotor axial-flux in-wheel motor | |
| CN113258696B (en) | Method for reducing electromagnetic vibration of fractional-slot concentrated winding permanent magnet motor | |
| He et al. | Two-dimensional field analysis on electromagnetic vibration-and-noise sources in permanent-magnet direct current commutator motors | |
| Knight et al. | Use of a permeance model to predict force harmonic components and damper winding effects in salient-pole synchronous machines | |
| Zhang et al. | Analytical prediction of Halbach array permanent magnet machines considering finite tooth permeability | |
| Hong et al. | Piecewise stagger poles with continuous skew edge for vibration reduction in surface-mounted PM synchronous machines | |
| CN111199124A (en) | Method for calculating no-load electromagnetic excitation force wave of surface-mounted permanent magnet synchronous motor | |
| Wang et al. | Mechanical and magnetic pivot roles of tooth in vibration of electrical machines | |
| CN113765251B (en) | Method for determining rotor segmentation mode for weakening vibration of integer slot permanent magnet motor | |
| Mao et al. | Vibration investigation of spoke-type PM machine with asymmetric rotor considering modulation effect of stator teeth | |
| CN108319768B (en) | Permanent magnet motor armature reaction magnetic field prediction method based on computer | |
| Zhao et al. | A novel quasi-3D analytical model for axial flux motors considering magnetic saturation | |
| Guo et al. | Analysis of a tubular linear permanent magnet oscillator with auxiliary teeth configuration for energy conversion system | |
| Xu et al. | Fast evaluation of high frequency electromagnetic force and vibration for PMSMS based on field reconstruction technique | |
| Faiz et al. | Analytical calculation of magnetic field in surface-mounted permanent-magnet machines with air-gap eccentricity | |
| Dai et al. | A hybrid calculation method of radial electromagnetic force based on finite element method and analytic method in a permanent magnet synchronous machine | |
| Deken et al. | Enhanced field reconstruction method for the efficient analysis of permanent magnet synchronous machines | |
| Lubin et al. | Improved analytical model for surface-mounted PM motors considering slotting effects and armature reaction | |
| Du et al. | Characterization of radial electromagnetic force and vibration response in squirrel-cage induction motor under PWM supply | |
| Du et al. | Research on the influence of vibration response of permanent magnet motor under harmonic current | |
| Zhang et al. | Analysis of electromagnetic force waves of solid cylindrical permanent magnet synchronous motors | |
| Chen et al. | Vibration and noise of high speed amorphous alloy permanent magnet synchronous motor with different slot width | |
| Du et al. | Research on electromagnetic vibration response of squirrel-cage induction motor based on multi-section method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |