A method for modeling torque ripple of surface-mounted permanent magnet synchronous motor

Abstract

The present invention relates to a method for modeling torque pulsation of a surface-mounted permanent magnet synchronous motor, and belongs to the technical field of motor design and analysis. The method is characterized in that: a method for modeling torque pulsation of a surface-mounted permanent magnet synchronous motor based on magnetic field modulation theory is proposed. The method can not only analyze the no-load torque pulsation (i.e., cogging torque) of the surface-mounted permanent magnet synchronous motor, but also analyze the total torque pulsation of the motor under load. On the basis of the method, a torque pulsation model of the surface-mounted permanent magnet synchronous motor is established. The torque pulsation modeling method can accurately describe the torque pulsation of the surface-mounted permanent magnet synchronous motor under different loads. Compared with finite element simulation, the method can improve the analysis efficiency. The torque pulsation model established according to the method has the characteristics of simple structure, clear meaning, and accurate numerical value, and can provide guidance for the precision servo control of the surface-mounted permanent magnet synchronous motor.

Description

Technical Field

[0001] The present invention relates to the technical field of motor design and analysis, and in particular to a method for modeling torque pulsation of a surface-mounted permanent magnet synchronous motor. Background Art

[0002] Surface-mounted permanent magnet synchronous motor is a typical topological structure among permanent magnet synchronous motors. It has been widely used in industrial production due to its high power density, small size, good electromagnetic performance and other characteristics. With the continuous development of industrial technology, the requirements for motor operation accuracy are getting higher and higher. The existence of torque pulsation will reduce the dynamic performance of the motor, especially under low speed or heavy load conditions. Therefore, it is necessary to analyze the source of torque pulsation of surface-mounted permanent magnet synchronous motor and establish a more accurate model to optimize the torque pulsation of the motor.

[0003] There are two traditional methods for modeling motor torque pulsation. One is to use finite element software for simulation, select several armature current values, study the motor torque pulsation under the working condition, and fit according to a series of data. This method can establish the torque pulsation model of the motor more accurately, but in order to obtain a more accurate model, it is necessary to increase the number of sampling points, which brings a large amount of calculation. In addition, this method directly uses finite element software for calculation, which is difficult to reflect the mathematical relationship between the motor magnetic field and torque pulsation when the motor working condition changes. The second is to establish an analytical model of motor torque pulsation. This method can reduce the amount of calculation and can deeply explain the relationship between the motor air gap magnetic field and torque pulsation. However, this method is currently mainly used to model the cogging torque, and is rarely used to analyze the torque pulsation of the motor when it is running under load. The motor generally runs under load. Therefore, studying the changes in the total torque pulsation of the motor when it is loaded is of great significance to further reduce the total torque pulsation of the motor when it is running, improve the performance of the servo system based on the surface-mounted permanent magnet synchronous motor, and improve the system quality. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention proposes a method for modeling torque ripple of a surface-mounted permanent magnet synchronous motor.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A method for modeling torque ripple of a surface-mounted permanent magnet synchronous motor comprises the following steps:

[0007] The source excitation magnetic field generated by the surface-mounted permanent magnet is asynchronously modulated by the stator salient pole reluctance modulator, and the source armature magnetic field generated by the energized armature winding is synchronously modulated to obtain a synthetic magnetic field; the total torque pulsation is further calculated.

[0008] Optionally, the torque pulsation includes: torque pulsation generated by the excitation magnetic field alone, and torque pulsation generated by the interaction between the armature magnetic field and the excitation magnetic field.

[0009] Optionally, the motor only contains a cogging torque component when running at no-load, and contains a cogging torque component and a modulation torque pulsation component when running with load.

[0010] Alternatively, the expression for the total torque ripple is:

[0011]

[0012] Where R s , R r are the stator inner diameter and rotor outer diameter of the motor, respectively, l stk is the effective axial length of the motor, μ 0 is the vacuum permeability, ο is a positive integer, is the amplitude of the armature field harmonics of the ο-pole pair, are the fundamental amplitude and nth harmonic amplitude of o-pole excitation field harmonics, δ and ξ are the spatial rotation speed coefficients of o-pole armature field harmonics and excitation field harmonics, Γ is the least common multiple of the number of stator and rotor poles, p is the number of stator pole pairs, ω is the speed of the motor, and t is time.

[0013] A computer-readable storage medium stores instructions, which, when executed, can implement the above-mentioned surface-mounted permanent magnet synchronous motor torque pulsation modeling method.

[0014] Beneficial effects:

[0015] Compared with the traditional surface-mounted permanent magnet synchronous motor torque ripple modeling method, the technical solution provided by the present invention has the following beneficial effects:

[0016] (1) The surface-mounted permanent magnet synchronous motor torque pulsation modeling method described in the present invention can model the total torque pulsation during the operation of the surface-mounted permanent magnet synchronous motor, thereby improving the accuracy of the torque pulsation model.

[0017] (2) The torque pulsation modeling method of the surface-mounted permanent magnet synchronous motor described in the present invention can analyze the influence of single-order magnetic field harmonics on torque pulsation and provide guidance for motor optimization design.

[0018] (3) The method for modeling the torque pulsation of a surface-mounted permanent magnet synchronous motor described in the present invention has a simple process and clear meaning, which is helpful for relevant personnel to learn and apply.

[0019] (4) The surface-mounted permanent magnet synchronous motor torque pulsation modeling method described in the present invention can be extended to surface-mounted permanent magnet synchronous motors of any structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below in conjunction with the accompanying drawings.

[0021] Figure 1 This is a flow chart for analyzing the torque pulsation modeling method described in the present invention.

[0022] Figure 2 It is the cogging torque generated by each harmonic of the exciting magnetic field obtained based on the torque modeling method described in the present invention.

[0023] Figure 3 This is a comparison chart between the cogging torque result obtained by the method of the present invention and the finite element simulation result.

[0024] Figure 4 This is a comparison chart between the total torque pulsation result obtained by the method described in the present invention and the finite element simulation result. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] In some examples of the present invention, a method for modeling torque ripple of a surface-mounted permanent magnet synchronous motor is disclosed, which may specifically include the following steps:

[0027] A. Calculation of excitation magnetic field expression:

[0028] For a surface-mounted permanent magnet synchronous motor, the magnetomotive force generated by its source excitation magnetic field can be approximately regarded as a square wave, and its Fourier expansion form is as follows:

[0029]

[0030] Among them, N rt is the number of rotor poles, φ is the angle along the air gap circumference (rad), ω is the mechanical speed of the motor (rad / s), ν is the harmonic order, and k is a positive integer.

[0031] The modulation function of the stator salient pole reluctance modulator can be expressed as

[0032]

[0033] Among them, N st is the number of stator poles, ε st is the stator pole arc coefficient, and / is the harmonic order of the salient pole reluctance modulation function.

[0034] We can further obtain the expression of modulated excitation magnetomotive force:

[0035]

[0036] Where p is the number of rotor pole pairs, C p , C sum , C dif They are the modulation coefficients of original modulation, sum modulation, and difference modulation, respectively. The specific expressions are as follows:

[0037]

[0038] B. Calculation of armature magnetic field expression:

[0039] The armature winding of the surface-mounted permanent magnet synchronous motor is generally wound on the stator teeth and is subjected to the synchronous modulation of the stator salient pole reluctance modulator. According to the connection mode and distribution of the winding, the winding function expression can be determined as follows:

[0040]

[0041] Where κ is the harmonic order of the winding function, σ is a positive integer, and C w is the winding function coefficient, and its specific expression is as follows:

[0042]

[0043] The armature current expression is established as follows

[0044]

[0045] Where δ is the armature current harmonic order.

[0046] Furthermore, the expression of the armature magnetomotive force after being modulated by the stator salient pole reluctance modulator can be expressed as

[0047]

[0048] C. Calculation of synthetic magnetic field expression:

[0049] Furthermore, the synthetic magnetic field expression can be calculated. For ease of understanding, the excitation magnetic field expression and the armature magnetic field expression are simplified in form. The synthetic magnetic field expression can be expressed as:

[0050]

[0051] in, is the phase of the resultant magnetomotive force, are the amplitudes of the υth harmonic of the field magnetomotive force and the armature magnetomotive force, respectively. is the amplitude of the υth harmonic of the synthetic magnetomotive force, and its specific expression is as follows:

[0052]

[0053] Due to the asynchronous modulation of the stator salient pole reluctance modulator on the excitation magnetomotive force, the amplitude of the excitation magnetomotive force has periodic oscillations, which can be expressed as follows:

[0054]

[0055] in, are the DC component and AC component of the magnetomotive force amplitude respectively, and Γ is the least common multiple of the number of stator and rotor poles.

[0056] D. Total torque ripple calculation:

[0057] Furthermore, by substituting the synthetic magnetomotive force into the torque ripple calculation expression, the expression of the total torque ripple can be obtained:

[0058]

[0059] Where R s , R r are the stator inner diameter and rotor outer diameter of the motor (mm), l stk is the effective axial length of the motor (mm), μ 0 is the vacuum permeability, ο is a positive integer, is the amplitude of the armature field harmonics of the ο-pole pair, are the fundamental amplitude and nth harmonic amplitude of o-pole excitation field harmonics, δ and ξ are the spatial rotation speed coefficients of o-pole armature field harmonics and excitation field harmonics, Γ is the least common multiple of the number of stator and rotor poles, p is the number of stator pole pairs, ω is the motor speed (rad / s), and t is time (s).

[0060] Through the above modeling method, not only the cogging torque under no-load condition can be obtained, but also the total torque pulsation under load condition can be obtained. Furthermore, the contribution of each magnetic field harmonic to the torque pulsation can be obtained.

[0061] In other embodiments of the present invention, a computer-readable storage medium is disclosed, which stores instructions, and when the instructions are executed, the above-mentioned surface-mounted permanent magnet synchronous motor torque pulsation modeling method can be implemented. More specifically, the instructions can be a computer-readable language. The above-mentioned computer can be a general-purpose computer device or a special-purpose computer device. In a specific implementation, the computer can be a desktop, a portable computer, a network server, a PDA (Personal Digital Assistant), a mobile phone, a tablet computer, a wireless terminal device, a communication device or an embedded device. The storage medium can be any available medium that can be accessed by the computer or a data storage device such as a server or a data center that includes one or more available media integrated. For example, the storage medium is, for example, but not limited to, a magnetic medium (for example, a floppy disk, a hard disk, a tape), an optical medium (for example, a digital versatile disc (DigitalVersatile Disc, DVD)), or a semiconductor medium (for example, a solid-state drive (SSD)), etc.

[0062] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0063] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for modeling torque ripple of a surface mounted permanent magnet synchronous motor, characterized in that: include: The source excitation magnetic field generated by the surface-mounted permanent magnet is asynchronously modulated by the stator salient pole reluctance modulator, and the source armature magnetic field generated by the energized armature winding is synchronously modulated to obtain a synthetic magnetic field; the total torque pulsation is further calculated; The expression of total torque ripple is: Where R s , R r are the stator inner diameter and rotor outer diameter of the motor respectively, l stk is the effective axial length of the motor, μ0 is the vacuum magnetic permeability, ο is a positive integer, is the amplitude of the armature field harmonics of the ο-pole pair, are the fundamental amplitude and nth harmonic amplitude of o-pole excitation field harmonics, δ and ξ are the spatial rotation speed coefficients of o-pole armature field harmonics and excitation field harmonics, Γ is the least common multiple of the number of stator and rotor poles, p is the number of stator pole pairs, ω is the speed of the motor, and t is time.

2. The method for modeling torque ripple of a surface-mounted permanent magnet synchronous motor according to claim 1, characterized in that: The torque pulsation includes: the torque pulsation generated by the excitation magnetic field alone, and the torque pulsation generated by the interaction between the armature magnetic field and the excitation magnetic field.

3. The method for modeling torque ripple of a surface-mounted permanent magnet synchronous motor according to claim 1, characterized in that: The motor contains only a cogging torque component when running at no load, and contains a cogging torque component and a modulation torque pulsation component when running with load.

4. A computer-readable storage medium storing instructions, which, when executed, can implement the surface-mounted permanent magnet synchronous motor torque pulsation modeling method described in any one of claims 1 to 3.

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