A measurement and calculation method for the shaft center locus of a permanent magnet motor based on the back electromotive force change

Abstract

The present invention discloses a method for measuring and calculating the shaft center locus of a permanent magnet motor based on the back electromotive force change. First, the relationship between the back electromotive force and the rotor displacement is analyzed, and it is obtained that when the rotor displacement is small, there is an approximately linear relationship between the amplitude change of the back electromotive force and the rotor displacement. Then, a finite element model of a multi-unit motor is established to obtain the amplitude change of the back electromotive force at different eccentric distances, and the least squares method is used for linear fitting to calibrate the proportional coefficient between the amplitude change of the back electromotive force and the rotor displacement. The non-driving unit motors in the multi-driving unit motor are tested under no-load to obtain the no-load back electromotive force of the non-driving unit motors. The back electromotive force waveform of the non-driving unit obtained from the no-load test is extracted, and the amplitude change of the back electromotive force is calculated. The rotor displacement corresponding to the non-driving unit is calculated by combining the amplitude change of the back electromotive force with the calibrated proportional coefficient. The method of the present invention does not require additional physical sensors for measurement and is not affected by the driving inverter, and is simple and easy to implement.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control and regulation, and particularly relates to a method for measuring and calculating the shaft center trajectory of a permanent magnet motor based on the change of back electromotive force. Background Technique

[0002] Multi-unit motors integrate multiple independent electromagnetic units, combining the advantages of redundancy and fault tolerance, flexible regulation, and high-precision monitoring. Their modular design supports power grading regulation and compact layout, and can maintain more than 70% of the rated power after isolating the faulty unit, significantly improving the system reliability. It is particularly suitable for high-reliability demand scenarios such as new energy vehicles and aerospace. However, during the operation of the motor, the rotor shaft center may shift due to factors such as mechanical imbalance, load fluctuation, or bearing wear, forming a complex shaft center trajectory. The real-time monitoring of the shaft center trajectory is of great significance for the assessment of the motor health status, fault warning, and control optimization.

[0003] Currently, the detection of the shaft center trajectory mainly relies on physical measurement devices such as eddy current sensors or laser displacement sensors, and additional hardware needs to be installed on the motor shaft or end cover. For example, in the invention patent CN109145505B, an eddy current sensor is used to obtain the shaft center trajectory of the generator shaft, and in the invention patent CN112504658B, a Doppler laser rangefinder is used to measure the shaft center trajectory. However, these methods have the following significant limitations in practical applications:

[0004] 1. The installation of the sensor requires reserved mechanical space, which is prone to cause structural interference in compact motors (such as new energy vehicle drive motors), and even requires customized design of the housing, resulting in increased costs. The supporting signal processing circuit also increases the hardware complexity;

[0005] 2. The calibration of the sensor depends on off-line calibration. The laser sensor is easily interfered by the oil stain or vibration on the rotor surface, which will greatly reduce the signal-to-noise ratio;

[0006] 3. In industrial sites with high temperature, high humidity, or strong vibration (such as mining machinery and ship propulsion motors), the service life of the sensor is shortened, and maintenance and replacement are required, affecting the production efficiency.

[0007] The back electromotive force is an important parameter of the permanent magnet motor. The existing back electromotive force measurement is mostly used for motor control. For example, the patent CN119093799A proposes to estimate the back electromotive force through an inverter model, which is easily interfered by the inverter signal, the calculation is complex, and there are few patents mentioning the relationship between the back electromotive force and the shaft center trajectory.

[0008] In summary, how to calculate and measure the shaft center trajectory of a multi-unit permanent magnet motor quickly and accurately without relying on sensors is a major problem that needs to be solved in the current shaft center trajectory detection. Summary of the Invention

[0009] The purpose of the present invention is to provide a method for measuring and calculating the shaft center locus of a permanent magnet motor based on the back electromotive force change. Combining the structural advantages of a multi-unit motor, according to the approximate linear relationship between the back electromotive force change and the rotor displacement, the shaft center locus is obtained by measuring and calculating the amplitude change of the back electromotive force. There is no need to add physical sensors for measurement, and it is not affected by the drive inverter, which is simple and easy to implement.

[0010] To achieve the above object, the present invention provides a method for measuring and calculating the shaft center locus of a permanent magnet motor based on the back electromotive force change, including the following steps:

[0011] S1. Analyze the relationship between the back electromotive force and the rotor displacement, and obtain that when the ratio of the rotor displacement to the original air gap length ≤ 0.1, the amplitude change of the back electromotive force and the rotor displacement are approximately linearly related. Analyzing the relationship between the back electromotive force and the rotor displacement includes:

[0012] The air gap magnetic flux density of the permanent magnet motor is inversely proportional to the air gap length as:

[0013]

[0014] where, is the vacuum permeability, is the equivalent magnetization intensity of the permanent magnet. When the rotor has a radial displacement , the local air gap length becomes:

[0015]

[0016] where, is the original air gap length, is the rotor position angle;

[0017] When , perform a Taylor expansion on the magnetic flux density and retain the first-order term as:

[0018]

[0019] At this time, the change in the air gap magnetic flux density and the displacement are approximately linearly related:

[0020]

[0021] And the back electromotive force is determined by the magnetic flux change rate. For the stator winding, the back electromotive force amplitude is proportional to the fundamental component of the air gap magnetic flux as:

[0022]

[0023] where, is the number of winding turns, is the angular velocity of the rotor. When the rotor displacement causes a change in the fundamental component of the magnetic flux , the change in the back electromotive force amplitude is:

[0024]

[0025] The fundamental component of the magnetic flux is expressed as:

[0026]

[0027] Substituting into , and integrating gives:

[0028]

[0029] Therefore, when , the change in the back electromotive force amplitude and the rotor displacement show a linear relationship:

[0030] ;

[0031] S2. Perform finite element modeling on the multi-unit motor to obtain the change in the back electromotive force amplitude at different eccentric distances, and use the least squares method for linear fitting to calibrate the proportional coefficient between the change in the back electromotive force amplitude and the rotor displacement;

[0032] S3. Divide the multi-drive unit motor into several drive unit motors and non-drive unit motors, connect the drive unit motors to the driver to drive the motor to rotate, and conduct no-load tests on the non-drive unit motors to obtain the no-load back electromotive force of the non-drive unit motors;

[0033] S4. Extract the back electromotive force waveform of the non-drive unit obtained from the no-load test, and calculate the change in the back electromotive force amplitude;

[0034] S5. Combine the change in the back electromotive force amplitude obtained in step S3 with the proportional coefficient calibrated in step S2 to calculate the rotor displacement corresponding to the non-drive unit, and then combine the eccentric direction of the rotor corresponding to the non-drive unit to synthesize the axis trajectory of the motor rotor.

[0035] Further, in step S2, a finite element model of the multi-unit motor is established. The operating condition of the multi-unit motor is set to no-load, that is, the winding input current is set to 0, and the no-load back electromotive force without eccentricity distance is solved. Then, the range of rotor eccentricity is set, and the no-load back electromotive forces at different eccentricity distances are calculated respectively. The amplitude change of the back electromotive force compared with that without eccentricity is recorded and analyzed. There are n data points for the calculated back electromotive force amplitude change, n≥2. Linear fitting is performed by the least squares method. Let the linearity between the back electromotive force amplitude change and the rotor displacement be defined by the formula The calculation formula for the slope b obtained by the least squares method is:

[0036]

[0037] The calculation formula for the intercept a is:

[0038] 。

[0039] Further, in step S2, a finite element model of the four-unit motor is established. The rated speed of the four-unit motor is set to 300 rpm, and the air gap width is set to 0.1 mm. The no-load back electromotive force without eccentricity distance is solved. Then, the rotor eccentricity is set from 0.01 mm to 0.1 mm with a step size of 0.01 mm, and the no-load back electromotive forces at different eccentricity distances are calculated respectively. The amplitude change of the back electromotive force compared with that without eccentricity is recorded and analyzed. There are 10 data points for the calculated back electromotive force amplitude change. Linear fitting is performed by the least squares method. The calculation formula for the slope b obtained is:

[0040]

[0041] The calculation formula for the intercept a is:

[0042]

[0043] The calculated slope b is 7.407, the intercept a is 0.0014, and the fitting mean absolute error is 0.0015. Ignoring the intercept, the relationship between the electromotive force amplitude change and the rotor displacement satisfies: =7.407 。

[0044] Further, in step S3, the multi-unit motor is a four-unit motor, which is divided into two driving unit motors and two non-driving unit motors. The two driving unit motors are connected to the driver to drive the motor to rotate. The motor speed for no-load test is set to 300 rpm, and the two non-driving unit motors are open-circuited to measure the voltage, and the no-load back electromotive forces of the two non-driving unit motors are measured.

[0045] Further, in step S4, the two non-driving unit motors are naturally orthogonal, so the eccentric directions of the rotors corresponding to the two non-driving units are perpendicular to each other, which are in the X-axis and Y-axis directions. Combining the rotor displacements of the two non-driving unit motors, the center locus of the motor rotor is synthesized.

[0046] Further, in step S5, if the two non-driving unit motors are not orthogonal, orthogonal basis coordinate correction is performed.

[0047] Further, after step S5, the calculated center locus is input into the finite element model for simulation and solution, and the back electromotive force of the motor under no-load is extracted. It is observed that the amplitude fluctuations of the back electromotive force obtained by testing and simulation are consistent, which proves that there is no obvious error between the center locus obtained by testing and the actual center locus.

[0048] After adopting the above scheme, the beneficial effects of the present invention are as follows:

[0049] 1. The present invention uses the natural back electromotive force signal of the open-circuit unit in the multi-unit motor as the displacement sensing carrier, calculates the rotor displacement by measuring the back electromotive force of the non-driving unit motor, without additional physical sensors, avoiding the installation space limitation and electromagnetic interference problems, and reducing the cost.

[0050] 2. The present invention analyzes that there is a linear relationship between the back electromotive force and the rotor displacement. Through finite element modeling and analysis, the proportional coefficient between the back electromotive force and the rotor displacement can be calculated. Thus, the rotor displacement can be obtained from the change in the amplitude of the back electromotive force measured by no-load testing, and then the center locus is synthesized. Therefore, based on the spatial layout of multiple units, the present invention extracts two-dimensional displacement components through independent back electromotive force, realizing the decoupling of the rotor center locus, which is simple and easy to implement.

[0051] 3. The present invention can synchronously complete the back electromotive force acquisition and trajectory calculation during the operation of the motor without stopping the machine or external dragging, and measures the back electromotive force when the non-driving unit motor is open-circuited, without setting a driving inverter, and the back electromotive force signal is not interfered by the driving inverter. Description of the Drawings

[0052] Figure 1 is the flowchart of the method of the present invention;

[0053] Figure 2 is the mesh division diagram of the four-unit motor structure of the present invention;

[0054] Figure 3 is the solution result of the back electromotive force under no-load without eccentricity of the present invention;

[0055] Figure 4 is the scatter diagram of the change in the amplitude of the back electromotive force under different eccentric distances of the present invention;

[0056] Figure 5Schematic diagram of the unit division of the four-unit permanent magnet motor of the present invention;

[0057] Figure 6 Test results of the no-load back electromotive force of the motors of Unit 3 and Unit 4 of the present invention;

[0058] Figure 7 Amplitude change diagram of the no-load back electromotive force of the motors of Unit 3 and Unit 4 of the present invention;

[0059] Figure 8 Synthetic diagram of the axis locus of the motor rotor of the present invention;

[0060] Figure 9 Comparison diagram of the no-load back electromotive force test and simulation of the present invention. Specific embodiments

[0061] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] The present invention provides a method for measuring and calculating the axis locus of a permanent magnet motor based on the change of back electromotive force, as Figure 1 shown, including the following steps:

[0063] S1. Analyze the relationship between the back electromotive force and the rotor displacement, including the following steps:

[0064] According to Ohm's law of magnetic circuit and the magnetic flux density formula, the air-gap magnetic flux density of the permanent magnet motor is inversely proportional to the air-gap length as:

[0065]

[0066] where, is the vacuum permeability, is the equivalent magnetization intensity of the permanent magnet. When the rotor has a radial displacement , the local air-gap length becomes:

[0067]

[0068] where, is the original air-gap length, is the rotor position angle;

[0069] When the rotor displacement is extremely small, specifically when , perform Taylor expansion on the magnetic flux density and retain the first-order term as:

[0070]

[0071] At this time, the change amount of the air-gap magnetic flux density is approximately linearly related to the displacement as:

[0072]

[0073] The back electromotive force is determined by the rate of change of magnetic flux. For the stator winding, the amplitude of the back electromotive force is proportional to the fundamental component of the air-gap magnetic flux as follows:

[0074]

[0075] where is the number of turns of the winding, is the angular velocity of the rotor. When the rotor displacement causes a change in the fundamental component of the magnetic flux , the change in the amplitude of the back electromotive force is:

[0076]

[0077] The fundamental component of the magnetic flux is expressed as:

[0078]

[0079] Substituting into , and integrating gives:

[0080]

[0081] Therefore, when , the change in the amplitude of the back electromotive force has a linear relationship with the rotor displacement as follows:

[0082]

[0083] Through the above formula derivation, it is obtained that when the ratio of the rotor displacement to the original air-gap length ≤ 0.1, the change in the amplitude of the back electromotive force has an approximately linear relationship with the rotor displacement. Thus, when the rotor displacement is small, the change in the amplitude of the back electromotive force can reflect the change in the rotor displacement. Therefore, in the subsequent steps of the present invention, the rotor displacement can be calculated by measuring the back electromotive force obtained during no-load testing, and then the axis locus of the rotor can be obtained, without relying on physical measurement devices such as eddy current sensors or laser displacement sensors, nor using an inverter.

[0084] S2. Perform finite element modeling on the multi-unit motor to obtain the change in the amplitude of the back electromotive force at different eccentric distances, and use the least squares method for linear fitting to calibrate the proportional coefficient between the change in the amplitude of the back electromotive force and the rotor displacement.

[0085] Specifically, the Maxwell model is used to perform finite element analysis on the multi-unit motor. The operating condition of the motor is set to no-load, that is, the input current of the winding is 0, and the no-load back electromotive force without eccentric distance is solved. Then, the range of rotor eccentricity is set, and the no-load back electromotive forces at different eccentric distances (i.e., rotor displacements) are calculated respectively. Record and analyze the change in the amplitude of the back electromotive force compared to that without eccentric distance. There are n data points for the calculated electromotive force amplitude, where n≥2. Linear fitting is performed by the least squares method. Let the linearity between the change in the amplitude of the back electromotive force and the rotor displacement be defined by the formula Then, the calibrated proportionality coefficient includes the slope b and the intercept a. The calculation formula for the slope b obtained by the least squares method is:

[0086]

[0087] The calculation formula for the intercept a is:

[0088]

[0089] Through the calculated a and b, the relationship between the change in the amplitude of the electromotive force and the rotor displacement can be obtained as ΔE = a + bΔx. Subsequently, the rotor displacement can be calculated from the change in the amplitude of the back electromotive force measured through no-load testing.

[0090] Specifically, taking the finite element analysis of a four-unit motor as an example, the mesh division of the four-unit motor structure is as Figure 2 shown. The rated speed of the four-unit motor is set to 300 rpm, and the air gap width is 0.1 mm. The no-load back electromotive force without eccentric distance is solved, and the solution result is as Figure 3 shown. Figure 3 The three curves in Figure 4 respectively represent the changes in the back electromotive forces of the three-phase windings of the motor under this operating condition. It can be seen from the figure that the peak and valley values of each curve reflect the maximum and minimum values of the back electromotive force, and the change trends of the three curves are similar, showing periodic fluctuations, indicating that the back electromotive force changes periodically with time, and the change period of the back electromotive force changes with the speed. Therefore, the amplitude of the back electromotive force changes with the magnitude of the magnetic field at the winding. Since the rotor displacement causes changes in the magnetic field, the amplitude changes, and thus the axis locus can be calculated from the back electromotive force. Then, the rotor eccentricity is set from 0.01 mm to 0.1 mm with a step size of 0.01 mm, and the no-load back electromotive forces at different eccentric distances are calculated respectively. Record and analyze the change in the amplitude of the back electromotive force compared to that without eccentric distance. The result is as

[0091]

[0092] shown. There are 10 data points for the calculated electromotive force amplitude. Linear fitting is performed by the least squares method, and the calculation formula for the slope b obtained is:

[0093]

[0094] The calculated slope b is 7.407, the intercept a is 0.0014, and the fitting mean absolute error is 0.0015. Since the value of the calculated intercept a is extremely small and can be ignored, the change in the potential amplitude and the rotor displacement are in a direct proportional relationship and satisfy: = 7.407 , that is, when the back electromotive force amplitude changes by 1 V, the rotor displacement is 0.135 mm.

[0095] S3. Divide the multi-drive unit motor into several drive unit motors and non-drive unit motors. The drive unit motors are used to connect to the driver to drive the motor to rotate, while the non-drive unit motors are used for no-load testing. Open the non-drive unit motors to measure the voltage, and the measured voltage is the no-load back electromotive force of the non-drive unit motors.

[0096] As Figure 5 shown, taking a four-drive unit motor as an example, the four-drive unit motor is divided into four unit motors: No. 1, No. 2, No. 3, and No. 4. Among them, No. 1 and No. 2 unit motors are drive unit motors, and No. 3 and No. 4 unit motors are non-drive unit motors. No. 1 and No. 3 unit motors are parallel, and No. 2 and No. 4 unit motors are parallel. Then, No. 3 and No. 4 unit motors are naturally orthogonal, that is, perpendicular to each other. During no-load testing, connect No. 1 and No. 2 unit motors to the driver to drive the motor to rotate. Set the motor speed for no-load testing to 300 rpm. Open No. 3 and No. 4 unit motors to measure the voltage, and measure the no-load back electromotive force of No. 3 and No. 4 unit motors. After the rotor rotates two circles, the no-load back electromotive force of No. 3 and No. 4 unit motors is as Figure 6 shown.

[0097] S4. Extract the back electromotive force waveform of the non-drive unit obtained from no-load testing and calculate the change amount of the back electromotive force amplitude. In addition, since the change trend of the back electromotive force amplitude cannot be clearly observed from Figure 6 , adjust the display range of the vertical axis in Figure 6 and mark the amplitude of the no-load back electromotive force in each electrical cycle. As Figure 7 shown, it can be seen that the amplitude of the motor no-load back electromotive force changes periodically as the motor rotor rotates.

[0098] S5. By combining the back electromotive force amplitude change obtained in step S3 with the intercept a and slope b calibrated in step S2, the rotor displacement corresponding to the non-driving unit can be obtained. Since the intercept a obtained in step S2 is negligible, the rotor displacement corresponding to the non-driving unit is obtained by dividing the back electromotive force amplitude change by the slope b. Then, by combining the eccentricity direction of the rotor corresponding to the non-driving unit, the axis locus of the motor rotor can be synthesized.

[0099] In the embodiment taking a four-unit drive motor as an example, since the two non-driving unit motors are naturally orthogonal, it can be considered that the eccentricity directions of the rotors corresponding to them are orthogonal directions. The eccentricity directions of the rotors corresponding to the two non-driving units are the X-axis and Y-axis directions. By combining the rotor displacements of the two non-driving unit motors, the axis locus of the motor rotor is synthesized as Figure 8 shown. In other embodiments, if the two non-driving unit motors are not orthogonal, the eccentricity direction of the rotor corresponding to the driving unit motor can be corrected by using trigonometric functions in the orthogonal basis coordinates, and the axis locus represented by the X-axis and Y-axis coordinates as shown in Figure 8 can also be obtained.

[0100] To further verify the correctness of the method of the present invention, after step S5, the calculated axis locus is input into the finite element model for simulation and solution, and the back electromotive force of the motor under no-load is extracted to observe the fluctuation of the back electromotive force amplitude obtained by testing and simulation, as shown in Figure 9 shown. The fluctuation of the back electromotive force amplitude obtained by testing and simulation is consistent, which proves that there is no obvious error between the axis locus obtained by testing and the actual axis locus.

[0101] The above are only the preferred embodiments of the present invention, and do not limit the design of this case. All equivalent changes made according to the key design of this case fall within the protection scope of this case.

Claims

1. A method for measuring and calculating the shaft center locus of a permanent magnet motor based on the back electromotive force change, characterized in that, The method includes the following steps: S1. Analyze the relationship between the back electromotive force and the rotor displacement. When the ratio of the rotor displacement to the original air-gap length ≤ 0.1, an approximately linear relationship exists between the amplitude change of the back electromotive force and the rotor displacement. Analyzing the relationship between the back electromotive force and the rotor displacement includes: Air-gap flux density of permanent magnet motor is inversely proportional to the air-gap length as follows: Wherein, is the vacuum permeability, is the equivalent magnetization intensity of the permanent magnet. When the rotor undergoes a radial displacement , the local air-gap length becomes: Among them, is the original air gap length, is the rotor position angle; When the Taylor expansion of the magnetic flux density is carried out and the first-order term is retained as: At this time, the change in air-gap flux density and displacement are approximately linearly related: The back electromotive force is determined by the rate of change of magnetic flux. For the stator winding, the back electromotive force amplitude is proportional to the fundamental component of the air-gap magnetic flux as follows: Among them, is the number of turns of the winding, is the angular velocity of the rotor. When the rotor displacement causes a change in the fundamental component of the magnetic flux the change in the back electromotive force amplitude is: Fundamental flux component Expressed as: Substitute , and integrate to obtain: Therefore, when the variation in the back electromotive force amplitude is linearly related to the rotor displacement as follows: ； S2. Perform finite element modeling on the multi-unit motor to obtain the amplitude change of the back electromotive force at different eccentric distances. Use the least squares method for linear fitting to calibrate the proportional coefficient between the amplitude change of the back electromotive force and the rotor displacement; S3. Divide the multi-drive unit motor into several drive unit motors and non-drive unit motors. Connect the drive unit motors to the driver to drive the motor to rotate, and conduct no-load tests on the non-drive unit motors to obtain the no-load back electromotive force of the non-drive unit motors; S4. Extract the back electromotive force waveform of the non-drive unit obtained from the no-load test, and calculate the amplitude change of the back electromotive force; S5. Combine the amplitude change of the back electromotive force obtained in step S3 with the proportional coefficient calibrated in step S2 to calculate the rotor displacement corresponding to the non-drive unit, and then combine the eccentric direction of the rotor corresponding to the non-drive unit to synthesize the axis locus of the motor rotor.

2. The measurement and calculation method of the permanent magnet motor shaft center locus based on the back electromotive force change according to claim 1, characterized in that: In step S2, a finite element model of the multi-unit motor is established. The operating condition of the multi-unit motor is set to no-load, that is, the input current of the winding is set to 0, and the no-load back electromotive force without eccentricity distance is solved. Then, the range of the rotor eccentricity is set, and the no-load back electromotive force at different eccentricity distances is calculated respectively. The amplitude change of the back electromotive force with the no-eccentricity case is recorded and analyzed. There are n data points for the calculated amplitude change of the back electromotive force, where n≥2. Linear fitting is performed by the least squares method. Let the linearity between the amplitude change of the back electromotive force and the rotor displacement be defined by the formula The calculation formula for the slope b obtained by the least squares method is: The calculation formula for the intercept a is: 。 3. A method for measuring and calculating the axis trajectory of a permanent magnet motor based on the change of back electromotive force according to claim 2, characterized in that: In step S2, perform finite element modeling on the four-unit motor. Set the rated speed of the four-unit motor to 300 rpm and the air-gap width to 0.1 mm. Solve the no-load back electromotive force without eccentric distance. Then set the rotor eccentricity to 0.01 mm to 0.1 mm with a step size of 0.01 mm, and calculate the no-load back electromotive force at different eccentric distances respectively. Record and analyze the amplitude change of the back electromotive force compared with the back electromotive force without eccentricity. There are 10 data points for the calculated amplitude change of the back electromotive force. Use the least squares method for linear fitting, and the calculation formula for the slope b is: The calculation formula for the intercept a is: The calculated slope b is 7.407, the intercept a is 0.0014, and the fitting mean absolute error is 0.0015. Ignoring the intercept, the change in potential amplitude and the rotor displacement The linear relationship between them satisfies: = 7.407 .

4. The measurement and calculation method of the permanent magnet motor shaft center locus based on the back electromotive force change according to claim 3, wherein: In step S3, the multi-unit motor is a four-unit motor, which is divided into two drive unit motors and two non-drive unit motors. Connect the two drive unit motors to the driver to drive the motor to rotate. Set the motor speed of the no-load test to 300 rpm, and measure the voltage of the two non-drive unit motors when they are open-circuited to obtain the no-load back electromotive force of the two non-drive unit motors.

5. A method for measuring and calculating the shaft center locus of a permanent magnet motor based on the change of back electromotive force as described in claim 4, characterized in that: In step S4, the two non-drive unit motors are naturally orthogonal, so the eccentric directions of the rotors corresponding to the two non-drive units are perpendicular to each other, which are in the X-axis and Y-axis directions. Combine the rotor displacements of the two non-drive unit motors to synthesize the axis locus of the motor rotor.

6. A method for measuring and calculating the axis trajectory of a permanent magnet motor based on the back electromotive force change, characterized in that: In step S5, if the two non-drive unit motors are not orthogonal, orthogonal basis coordinate correction is performed.

7. A method for measuring and calculating the axis trajectory of a permanent magnet motor based on the change of back electromotive force according to claim 1, characterized in that: After step S5, input the calculated axis locus into the finite element model for simulation and solution, extract the no-load back electromotive force of the motor, and observe that the amplitude fluctuations of the no-load back electromotive force obtained from the test and the simulation are consistent, proving that there is no obvious error between the axis locus obtained from the test and the actual axis locus.

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