A highly efficient and accurate method for separating instantaneous torque of permanent magnet motors

Abstract

The present invention discloses a method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy. The method comprises: establishing a finite element model for a target permanent magnet motor for simulation analysis, and solving the cogging torque under the load condition. Then, using the frozen permeability technology, finite element models in which only the permanent magnet and the armature current act alone are obtained, and the permanent magnet torque and the reluctance torque are solved respectively. At this point, the torque of the permanent magnet motor is completely separated into permanent magnet torque, reluctance torque and cogging torque. The method is written into a program in MATLAB to control the open source finite element software FEMM for modeling and analysis, and can flexibly perform post-processing and complete torque separation efficiently in one go. By completely separating the instantaneous torque, the method can analyze the influence of permanent magnet torque, reluctance torque and cogging torque on torque pulsation under different load conditions.

Description

Technical Field

[0001] The present invention provides a method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy, belonging to the technical field of permanent magnet motors. Background Art

[0002] Permanent magnet motors (PMMs) are widely used in electric vehicles, aerospace, and other fields due to their high power density and high torque density. Torque is a key parameter reflecting the load performance of PMMs. High average torque and low torque ripple are ideal design goals for PMM torque performance. From the perspective of torque sources, PMM torque is composed of permanent magnet torque, reluctance torque, and cogging torque. Accurately separating the components of a PMM's instantaneous torque facilitates torque performance evaluation and optimization. However, few methods or plug-ins exist that can efficiently and accurately separate the instantaneous torque of a motor in a single, efficient manner. Summary of the Invention

[0003] The purpose of the present invention is to propose a method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy based on the consideration of the saturation and cross-coupling effects of the permanent magnet motor.

[0004] The technical solution of the present invention is: a method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy, comprising the following steps:

[0005] Step 1: Establish and initialize a finite element model for the target motor;

[0006] Step 2: Set the load current for the motor winding, solve the finite element model under the motor load, and use the virtual displacement method to solve the cogging torque;

[0007] Step 3: Using the frozen permeability technique based on the load finite element model solved in step 2, after retaining the permeabilities of all ferrous materials in step 2, the finite element model at this point is solved by setting the load current of the motor to 0 to obtain the permanent magnet torque;

[0008] Step 4: After retaining the magnetic permeability of all ferrous materials in step 2, set the remanent magnetic density of the permanent magnet of the motor to 0, and solve the model with only the quadrature-axis current or the direct-axis current, respectively, to obtain the self-inductance and mutual inductance of the quadrature and direct axes of the permanent magnet motor. Then, solve the model with the same load current as in step 2 to obtain the reluctance torque considering the cross-mutual inductance effect.

[0009] Step 5. Combining the permanent magnet torque, reluctance torque and cogging torque obtained in steps 2-4, it can be analyzed that the superposition of the instantaneous waveforms of the three is the instantaneous waveform of the load torque. At the same time, the load current is changed. By analyzing the instantaneous waveforms of the permanent magnet torque, reluctance torque and cogging torque, their influence on the instantaneous torque pulsation can be analyzed.

[0010] Furthermore, the establishment of the finite element model in step 1 is based on the open source finite element software FEMM combined with MATLAB software programming, and the initialization content includes relevant simulation parameters such as the motor speed and simulation step size.

[0011] Furthermore, the setting of the load current in step 2 is accomplished by simulating one electrical cycle of the motor by establishing an expression for the n-phase current through MATLAB. After completing the finite element analysis, the magnetic field energy storage of all finite element units of the entire motor is calculated, and the calculation expression is:

[0012]

[0013] Where W m is the magnetic field energy storage of the entire motor, that is, the sum of the magnetic field energy storage of all N finite element units, B i is the magnetic induction intensity of the i-th finite element, V i is the volume of the i-th finite element unit, μ0 is the vacuum permeability, μ r is the relative permeability of the finite element to the permeability of vacuum.

[0014] Furthermore, the solution formula for the cogging torque in step 2 is:

[0015]

[0016] The solution to the cogging torque is the negative derivative of the magnetic field energy storage with respect to the mechanical angle of rotation, where T cog is the cogging torque to be solved, W m is the magnetic field energy storage of the motor, θ m Refers to the mechanical angle of the motor rotation, W m (k) and W m (k-1) is the energy storage of the entire motor magnetic field at the k-th simulation step and the k-1-th simulation step, and n is the total number of steps in one electrical cycle simulation of the motor.

[0017] Furthermore, the solution formula for the permanent magnet torque in step 3 is:

[0018]

[0019] Where T pm is the permanent magnet torque of the motor, m is the number of phases of the motor, p is the number of pole pairs of the motor, ψ d(PM) With ψ q(PM) They are the d-axis and q-axis flux linkages of the finite element model after using frozen permeability when only permanent magnets are acting, i d and i q The currents of the motor’s d-axis and q-axis are solved respectively, and θe is the electrical angle through which the motor has rotated.

[0020] Furthermore, in step 4, the method for solving the self-inductance and mutual inductance of the DC axis of the permanent magnet motor is to solve them according to the following set of equations:

[0021]

[0022] where ψ d(I) With ψ q(I) They are the d-axis and q-axis flux linkages of the finite element model after solving the frozen magnetic permeability when only the armature current acts alone, L dd , L qq are the d-axis self-inductance and the q-axis self-inductance, L dq , L qd The mutual inductance of the d-axis and q-axis is obtained by setting the DC-axis currents id and iq to 0 in turn, and then using the Clarke-Parker inverse transform to obtain the current and bring it into the finite element simulation to obtain the flux linkage ψ d(I) With ψ q(I) , after substituting into the above equations, we can obtain the self-inductance and mutual inductance.

[0023] Furthermore, the formula for solving the reluctance torque of 4 is:

[0024]

[0025] Where T r Is to solve the reluctance torque of the motor, L dd , L qq are the d-axis self-inductance and the q-axis self-inductance, L dq , L qd is the mutual inductance between the d-axis and the q-axis, ψ d(I) With ψ q(I) The d-axis and q-axis flux linkages of the finite element model after using frozen permeability are solved when only the same armature current as in step 2 acts alone.

[0026] Furthermore, in steps 2-4, the composite torque of the permanent magnet torque, the reluctance torque and the cogging torque completely coincides with the simulated load torque.

[0027] Furthermore, in step 5, by changing the load current amplitude, the permanent magnet torque of the permanent magnet motor under different load conditions can be obtained, and the amplitude phase angle relationship between the reluctance torque and the cogging torque waveform can be obtained. It can be concluded that the phase of the cogging torque is always opposite to the electromagnetic torque synthesized by the permanent magnet torque and the reluctance torque, which has the effect of offsetting the torque pulsation. As the load current increases, the load torque pulsation will show a period of decline. This is caused by the pulsation of the reluctance torque gradually exceeding the pulsation of the permanent magnet torque.

[0028] The beneficial effects of the present invention are:

[0029] Taking saturation and cross-coupling into account, the instantaneous torque of a permanent magnet motor is efficiently and accurately separated into permanent magnet torque, reluctance torque, and cogging torque. By combining MATLAB scripts with the open-source finite element software FEMM, the electromagnetic field under different excitation conditions can be rapidly and in parallel after freezing the magnetic permeability. Simultaneously, the transient field parameter calculation, which requires calling the static electromagnetic field parameters of two adjacent simulation steps, can be automatically processed using MATLAB script programming, thereby achieving a one-time, highly efficient separation of the instantaneous torque of a permanent magnet motor. As a script, the program implementing this method can be redeveloped for other applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart for implementing the method for accurate instantaneous torque separation of a permanent magnet motor in the present invention.

[0031] Figure 2 This is a finite element model diagram of the permanent magnet motor selected as an embodiment of the present invention.

[0032] Figure 3 This is the solved quadrature and direct axis inductance diagram of the motor according to the embodiment of the present invention.

[0033] Figure 4 Graph showing the separation of permanent magnet torque, reluctance torque and cogging torque of the motor according to an embodiment of the present invention.

[0034] Figure 5 It is a verification comparison diagram of the separation torque synthesis and simulation torque of the motor in the embodiment of the present invention.

[0035] Figure 6 Graphs showing average torque and peak-to-peak torque of the motor under different load conditions according to an embodiment of the present invention.

[0036] Figure 7 1 is a comparison diagram of the peak-to-peak torque of the separation torque part of the motor in the embodiment of the present invention.

[0037] Figure 8 4 is a comparison diagram of the instantaneous waveforms of the permanent magnet torque and reluctance torque of the motor according to the embodiment of the present invention.

[0038] Figure 9 4 is a comparison diagram of the instantaneous waveforms of the electromagnetic torque and the cogging torque of the motor according to the embodiment of the present invention. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0040] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0041] The present invention proposes a method for analyzing torque pulsation under load after completely separating the instantaneous torque of a permanent magnet motor under load conditions, taking into account motor saturation, cross-coupling and other conditions.

[0042] like Figure 1 As shown in the figure, the process for accurately determining instantaneous torque is as follows: First, a finite element model of the permanent magnet motor is created using FEMM software. After setting the load current, this finite element model is simulated and solved. This allows the magnetic field energy storage to be solved and the cogging torque to be calculated. Simultaneously, the magnetic permeability of all the motor core materials is saved via a command. Second, the finite element model saved in the first step is simulated in parallel under four different excitation conditions, solving for the quadrature and direct axis self-inductance and mutual inductance, permanent magnet torque, and reluctance torque, respectively. This completes the separation of the permanent magnet motor's instantaneous torque.

[0043] like Figure 2 As shown in the figure, a 12-slot 10-pole three-phase spoke permanent magnet synchronous motor is selected as the example motor to establish the finite element model diagram, using MATLAB according to Figure 1 The prepared post-processing program completes accurate instantaneous torque separation. The simulation time is one electrical cycle, divided into 128 simulation steps. The load current of the example is set to 3A, and the current angle is 0.

[0044] Figure 3 To determine the AC and DC axis inductances, the frozen permeability technique is used to account for the motor's saturation. The results are accurate. Under the influence of the AC and DC axis currents, both the self-inductance and mutual inductance of the AC and DC axes are determined, allowing for cross-coupling effects when calculating the reluctance torque.

[0045] Figure 4 The instantaneous waveforms of permanent magnet torque, reluctance torque and cogging torque are solved in parallel. They are obtained by superimposing the three waveforms, such as Figure 5 As shown, it can be concluded that the separation method fully coincides with the simulated torque by the traditional Maxwell stress tensor method.

[0046] By changing the amplitude of the load current, the torque characteristics of the permanent magnet motor under different load conditions can be simulated. In the embodiment, the load current of the motor is increased from 0A to 9.5A in intervals of 0.5A to complete the instantaneous torque separation under different load conditions. Figure 6 As shown, the motor of the embodiment will experience a period of peak-to-peak torque drop (torque ripple) when the load current reaches about 8 A. This phenomenon is common in permanent magnet motors and can be analyzed and explained by separating the instantaneous torque of permanent magnet motors.

[0047] like Figure 7As shown in the figure, when the load current is small, the peak-to-peak value of the permanent magnet torque will be greater than the peak-to-peak value of the reluctance torque; as the load current exceeds 6A, the peak-to-peak value of the reluctance torque will gradually exceed the peak-to-peak value of the permanent magnet torque. Figure 8 As shown in , the phase relationship between the permanent magnet torque and the reluctance torque is in a mutually canceling relationship. Figure 9 As shown, the phase relationship between cogging torque and electromagnetic torque (permanent magnet torque + reluctance torque) is also mutually canceling. The peak-to-peak value of the three increases fastest with the reluctance torque. Therefore, after the peak-to-peak value of the reluctance torque equals the peak-to-peak value of the permanent magnet torque, there must be a point where the reluctance torque, permanent magnet torque, and cogging torque cancel each other out, resulting in a peak-to-peak torque drop.

[0048] In summary, the present invention discloses a method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy. By calling the FEMM software through MATLAB, the accurate separation of the instantaneous torque can be completed in one go and with high efficiency on the basis of considering the saturation and cross-coupling effects of the permanent magnet motor. The instantaneous torque finally formed by the superposition of the separated permanent magnet torque, reluctance torque and cogging torque completely coincides with the torque obtained by the finite element software using the Maxwell stress tensor method. This torque method is applicable to all permanent magnet motors. While being able to separate the average torque, it can also be used as a tool to explore the factors affecting torque pulsation. Due to the MATLAB script used, it can be flexibly combined with other script plug-ins and can be applied to secondary development occasions such as motor optimization design.

[0049] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative uses of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0050] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy, characterized in that: The following steps are included: Step 1: Establish and initialize a finite element model for the target motor; Step 2: Set the load current for the motor winding, solve the finite element model under the motor load, and use the virtual displacement method to solve the cogging torque; Step 3: Using the frozen permeability technique based on the load finite element model solved in step 2, after retaining the permeabilities of all ferrous materials in step 2, the finite element model at this point is solved by setting the load current of the motor to 0 to obtain the permanent magnet torque; Step 4: After retaining the magnetic permeability of all ferrous materials in step 2, set the remanent magnetic density of the permanent magnet of the motor to 0, and solve the model with only the quadrature-axis current or the direct-axis current to obtain the self-inductance and mutual inductance of the quadrature and direct axes of the permanent magnet motor. Then, solve the model with the same load current as in step 2 to obtain the reluctance torque considering the cross-mutual inductance effect. Step 5: Combine the permanent magnet torque, reluctance torque, and cogging torque obtained in steps 2-4, and analyze that the superposition of the instantaneous waveforms of the three is the instantaneous waveform of the load torque. At the same time, change the load current and analyze their effects on the instantaneous torque ripple by analyzing the instantaneous waveforms of the permanent magnet torque, reluctance torque, and cogging torque. The load current in step 2 is set by setting the expression of n-phase current in MATLAB to complete the simulation of one electrical cycle of the motor. After completing the finite element analysis, the magnetic field energy storage of all finite element units of the entire motor is calculated, and the calculation expression is: Where W m is the magnetic field energy storage of the entire motor, that is, the sum of the magnetic field energy storage of all N finite element units, B i is the magnetic induction intensity of the i-th finite element, V i is the volume of the i-th finite element unit, μ0 is the vacuum permeability, μ r is the relative permeability of the finite element unit to the vacuum permeability; The solution formula for the cogging torque in step 2 is: The solution to the cogging torque is the negative derivative of the magnetic field energy storage with respect to the mechanical angle of rotation, where T cog is the cogging torque to be solved, W m is the magnetic field energy storage of the motor, θ m Refers to the mechanical angle of the motor rotation, W m (k) and W m (k-1) is the energy storage of the entire motor magnetic field at the k-th simulation step and the k-1-th simulation step, respectively, and n is the total number of steps in one electrical cycle simulation of the motor; The solution formula for the permanent magnet torque in step 3 is: Where T pm is the permanent magnet torque of the motor, m is the number of phases of the motor, p is the number of pole pairs of the motor, ψ d(PM) With ψ q(PM) They are the d-axis and q-axis flux linkages of the finite element model after using frozen permeability when only permanent magnets are acting, i d and i q The currents of the motor’s d-axis and q-axis are solved respectively, and θe is the electrical angle through which the motor has rotated.

2. The method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy according to claim 1 is characterized in that: The establishment of the finite element model in step 1 is based on the open source finite element software FEMM combined with MATLAB software programming. The initialization content includes the motor speed and simulation parameters related to the simulation step.

3. The method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy according to claim 1 is characterized in that: In step 4, the method for solving the self-inductance and mutual inductance of the DC axis of the permanent magnet motor is to solve them according to the following equations: where ψ d(I) With ψ q(I) They are the d-axis and q-axis flux linkages of the finite element model after solving the frozen magnetic permeability when only the armature current acts alone, L dd , L qq are the d-axis self-inductance and the q-axis self-inductance, L dq , L qd The mutual inductance of the d-axis and q-axis is obtained by setting the DC-axis currents id and iq to 0 in turn, and then using the Clarke-Parker inverse transform to obtain the current and bring it into the finite element simulation to obtain the flux linkage ψ d(I) With ψ q(I) , after substituting into the above equations, we can obtain the self-inductance and mutual inductance.

4. The method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy according to claim 1 is characterized in that: The formula for solving the reluctance torque of 4 is: Where T r Is to solve the reluctance torque of the motor, L dd , L qq are the d-axis self-inductance and the q-axis self-inductance, L dq , L qd is the mutual inductance between the d-axis and the q-axis, ψ d(I) With ψ q(I) The d-axis and q-axis flux linkages of the finite element model after using frozen permeability are solved when only the same armature current as in step 2 acts alone.

5. The method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy according to claim 1 is characterized in that: In steps 2-4, the composite torque of the permanent magnet torque, the reluctance torque and the cogging torque completely coincides with the simulated load torque.

6. The method for separating the instantaneous torque of a permanent magnet motor with high efficiency and accuracy according to claim 1, characterized in that: In step 5, changing the load current amplitude can obtain the permanent magnet torque of the permanent magnet motor under different load conditions, the amplitude phase angle relationship between the reluctance torque and the cogging torque waveform, and obtain that the phase of the cogging torque is always opposite to the electromagnetic torque synthesized by the permanent magnet torque and the reluctance torque, which has the effect of offsetting the torque pulsation. As the load current increases, the load torque pulsation will show a period of decline, which is caused by the pulsation of the reluctance torque gradually exceeding the pulsation of the permanent magnet torque.

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