Permanent magnet synchronous motor for new energy vehicle and optimization method thereof

By adding an asymmetric arc-shaped second permanent magnet to the built-in permanent magnet synchronous motor and optimizing its angle and position, combined with sensitivity analysis and multi-objective optimization algorithms, the electromagnetic vibration and noise problem of the built-in permanent magnet synchronous motor was solved, improving the ride comfort and motor stability of new energy vehicles.

CN120955944BActive Publication Date: 2026-02-10EAST CHINA JIAOTONG UNIVERSITY +1
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Patent Information

Application Number
CN202511476574.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-10-16
Publication Date
2026-02-10
Estimated Expiration
2045-10-16

AI Technical Summary

Technical Problem

Existing built-in permanent magnet synchronous motors in new energy vehicles suffer from electromagnetic vibration and noise problems, affecting ride comfort.

Method used

In a traditional built-in permanent magnet synchronous motor, an asymmetric arc-shaped second permanent magnet is added. By optimizing its sweep angle and position, combined with sensitivity analysis and multi-objective optimization algorithm, an objective function is constructed to optimize the magnetic field distribution and reduce vibration noise.

Benefits of technology

It effectively reduces the vibration and noise of permanent magnet synchronous motors, improves ride comfort, enhances electromagnetic performance, reduces mechanical shock and torque fluctuations, and improves the stable operation of the motor.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application provides a permanent magnet synchronous motor for a new energy vehicle and an optimization method thereof. The permanent magnet synchronous motor comprises a stator and a rotor. The stator comprises a stator yoke and a stator winding. A plurality of stator teeth are arranged in the inner circle of the stator yoke. The rotor comprises first permanent magnets arranged in a symmetrically embedded manner, second permanent magnets in a non-symmetric circular arc shape, and a magnetic bridge. The number of the first permanent magnets is equal to that of the second permanent magnets. The thickness of the two ends of the second permanent magnets is not equal. For two adjacent second permanent magnets, the distance between one of the second permanent magnets and the center line of the stator winding is not equal to the distance between the other second permanent magnet and the center line of the stator winding. The driving motor is optimized by optimizing the sweep angle and position of the second permanent magnets. The application can reduce electromagnetic vibration noise, thereby improving the riding comfort.
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Description

Technical Field

[0001] This invention relates to the technical field of new energy vehicles, and more specifically to a permanent magnet synchronous motor for new energy vehicles and its optimization method. Background Technology

[0002] A permanent magnet synchronous motor (PMSM) is a type of motor that uses permanent magnets to generate a magnetic field and rotate synchronously with the stator magnetic field. Due to its high efficiency, high power density, and good dynamic performance, it is widely used. PMSMs are divided into two types: embedded and surface-mounted. In an embedded PMSM, the permanent magnets are embedded inside the rotor core, while in a surface-mounted PMSM, the permanent magnets are attached to the rotor surface. Compared to surface-mounted PMSMs, embedded PMSMs overcome the disadvantages of surface-mounted PMSMs, such as susceptibility to demagnetization due to high temperatures or strong magnetic fields and lower rotor structural strength. They are suitable for high-speed applications and are therefore widely used in new energy vehicles.

[0003] Vibration and noise studies on built-in permanent magnet synchronous motors can optimize mechanical structures, reduce mechanical wear caused by vibration, and extend product life.

[0004] With the rapid development of new energy vehicles, passengers have increasingly higher requirements for the comfort of these vehicles. However, existing research indicates that slotting in the stator and rotor weakens their structural strength, easily leading to electromagnetic vibration and noise, thus affecting ride comfort. Summary of the Invention

[0005] In view of this, the present invention provides a permanent magnet synchronous motor for new energy vehicles and an optimization method thereof to reduce electromagnetic vibration noise, thereby improving ride comfort.

[0006] One aspect of the present invention provides a permanent magnet synchronous motor for new energy vehicles, comprising:

[0007] The stator includes a stator yoke and a stator winding, wherein the inner ring of the stator yoke is provided with a plurality of axially arranged stator teeth;

[0008] The rotor includes an embedded symmetrically arranged first permanent magnet, an asymmetrical arc-shaped second permanent magnet, and a magnetic isolation bridge, wherein the number of the first permanent magnet and the second permanent magnet are equal.

[0009] The thicknesses at both ends of the second permanent magnet are not equal;

[0010] For two adjacent second permanent magnets, the distance between one second permanent magnet and the center line of the stator winding is not equal to the distance between the other second permanent magnet and the center line of the stator winding.

[0011] The drive motor is optimized by optimizing the sweep angle and position of the second permanent magnet.

[0012] Another aspect of the present invention provides an optimization method for a permanent magnet synchronous motor for new energy vehicles, comprising the following steps:

[0013] Step S1: Determine the basic parameter information of the permanent magnet synchronous motor based on its operating conditions. The basic parameter information includes the size of the stator, the size of the rotor, the size and arrangement of the first permanent magnet, and the size and arrangement of the second permanent magnet.

[0014] Step S2: Based on the determined basic parameter information of the permanent magnet synchronous motor, perform finite element modeling of the permanent magnet synchronous motor in Maxwell, and simultaneously perform parametric scanning of the sweep angle and position of the second permanent magnet to obtain the electromagnetic performance parameters of the permanent magnet synchronous motor. The electromagnetic performance parameters include the maximum cogging torque, the maximum radial electromagnetic force density, and the three-phase no-load back electromotive force.

[0015] Step S3: Based on the maximum cogging torque and the maximum radial electromagnetic force density, calculate the sensitivity dynamic weight corresponding to the normalized cogging torque and the sensitivity dynamic weight corresponding to the normalized maximum radial electromagnetic force density.

[0016] Step S4: Based on the three-phase no-load back EMF, construct a multi-interval back EMF penalty function;

[0017] Step S5: Based on the normalized cogging torque corresponding to the sensitivity dynamic weight, the normalized maximum radial electromagnetic force density corresponding to the sensitivity dynamic weight, and the multi-interval back electromotive force penalty function, construct the objective function of the multi-objective optimization algorithm.

[0018] Step S6: Solve the objective function to obtain the optimal sweep angle and optimal position of the second permanent magnet.

[0019] The permanent magnet synchronous motor and its optimization method for new energy vehicles provided by the present invention have the following beneficial effects:

[0020] (1) Based on the traditional permanent magnet synchronous motor, the present invention adds an asymmetric arc-shaped second permanent magnet to optimize the magnetic field distribution between the rotor and the stator. By optimizing the sweep angle and position of the second permanent magnet, the effective drive motor can be optimized.

[0021] (2) Based on the normalized cogging torque corresponding to the sensitivity dynamic weight, the normalized maximum radial electromagnetic force density corresponding to the sensitivity dynamic weight, and the multi-interval back EMF penalty function, the present invention constructs the objective function of the multi-objective optimization algorithm, which can effectively reduce the vibration noise of the permanent magnet synchronous motor, thereby improving the ride comfort. In addition, it can take into account the improvement of electromagnetic performance, change the radial electromagnetic force density, weaken the harmonic amplitude of magnetomotive force and magnetic permeability, reduce the torque fluctuation amplitude, reduce mechanical shock, and improve the sinusoidal waveform of air gap magnetic flux density. Thus, while ensuring that the three-phase no-load back EMF remains basically unchanged, the cogging torque of the permanent magnet synchronous motor is greatly reduced, thereby improving the stable operation capability of the permanent magnet synchronous motor.

[0022] (3) This invention introduces a sensitivity analysis weighting mechanism, which can dynamically adjust the weights according to the sensitivity of the objective function to parameter changes. In addition, the constructed multi-interval back electromotive force penalty function can dynamically adjust the solutions that violate the constraints through nonlinear penalties, thereby expanding the convergence speed of the feasible region. This invention also adopts an adaptive normalization method to avoid the neglect of small-order-of-magnitude targets due to huge differences in the order of magnitude of different targets, making the weight adjustment more fair and effective. Attached Figure Description

[0023] Figure 1 A schematic diagram of the structure of a permanent magnet synchronous motor for new energy vehicles provided in an embodiment of the present invention;

[0024] Figure 2 A schematic diagram of the dimensional parameters of a permanent magnet synchronous motor for new energy vehicles provided in an embodiment of the present invention;

[0025] Figure 3 A flowchart illustrating an optimization method for a permanent magnet synchronous motor for new energy vehicles, provided in an embodiment of the present invention.

[0026] Figure 4 A comparison diagram of the cogging torque of a permanent magnet synchronous motor for new energy vehicles and the original motor under no-load conditions, provided for an embodiment of the present invention.

[0027] Figure 5 A comparison diagram of the cogging torque of a permanent magnet synchronous motor for new energy vehicles and the original motor under load, provided for an embodiment of the present invention.

[0028] Figure 6 A comparison diagram of radial electromagnetic force density between a permanent magnet synchronous motor for new energy vehicles and the original motor, provided for an embodiment of the present invention. Detailed Implementation

[0029] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0030] Please see Figure 1 An embodiment of the present invention provides a permanent magnet synchronous motor for new energy vehicles, including a stator 3 and a rotor 5.

[0031] The stator 3 includes a stator yoke 1 and a stator winding 2. The inner ring of the stator yoke 1 is provided with a plurality of axially arranged stator teeth 4.

[0032] The rotor 5 includes an embedded, symmetrically arranged first permanent magnet 8, an asymmetrical, arc-shaped second permanent magnet 6, and a magnetic isolation bridge 7. The number of the first permanent magnet 8 and the second permanent magnet 6 are equal. Specifically, in this embodiment, there are 8 pairs of both the first permanent magnet 8 and the second permanent magnet 6.

[0033] The thicknesses at both ends of the second permanent magnet 6 are unequal. For details in this embodiment, please refer to [link / reference needed]. Figure 2 The thickness W1 at one end of the second permanent magnet 6 is 3.251 mm, and the thickness W2 at the other end of the second permanent magnet 6 is 3.176 mm.

[0034] For two adjacent second permanent magnets 6, the distance between one second permanent magnet and the center line of the stator winding is not equal to the distance between the other second permanent magnet and the center line of the stator winding. For details in this embodiment, please refer to... Figure 2 One of the second permanent magnets 6 is 2.067 mm away from the center line L of the stator winding 2, and the other second permanent magnet 6 is 4.589 mm away from the center line L of the stator winding 2.

[0035] The drive motor is optimized by optimizing the sweep angle and position of the second permanent magnet 6. (See also...) Figure 2 The sweep angle of the second permanent magnet 6 is The position of the second permanent magnet 6 is determined by the angle of rotation of one end of the second permanent magnet 6 from the X-axis. The angle of rotation of the other end of the second permanent magnet 6 from the X-axis Decide.

[0036] Please see Figure 3 The embodiments of the present invention also provide an optimization method for the above-mentioned permanent magnet synchronous motor, including steps S1-S6:

[0037] Step S1: Determine the basic parameter information of the permanent magnet synchronous motor based on its operating conditions. The basic parameter information includes the size of the stator, the size of the rotor, the size and arrangement of the first permanent magnet, and the size and arrangement of the second permanent magnet.

[0038] In this embodiment, the outer diameter of the stator 3 core is 260mm, the inner diameter of the stator 3 core is 168mm, the outer diameter of the rotor 5 core is 166mm, and the inner diameter of the rotor 5 core is 55mm. The stator has 48 slots, and the rotor has 8 poles. Both the first permanent magnet 8 and the second permanent magnet 6 are built-in.

[0039] The basic parameter information also includes: the stator 3 and rotor 5 are both made of M19_29G material, the first permanent magnet 8 and the second permanent magnet 6 are both made of NdFe35N material, and the stator windings are made of copper wire. After assigning material properties to each component, the electromagnetic performance and radial electromagnetic force parameters of the permanent magnet synchronous motor can be simulated.

[0040] Step S2: Based on the determined basic parameter information of the permanent magnet synchronous motor, perform finite element modeling of the permanent magnet synchronous motor in Maxwell, and simultaneously perform parametric scanning of the sweep angle and position of the second permanent magnet to obtain the electromagnetic performance parameters of the permanent magnet synchronous motor. The electromagnetic performance parameters include the maximum cogging torque, the maximum radial electromagnetic force density, and the three-phase no-load back electromotive force.

[0041] In this embodiment, parametric scanning is performed using the finite element simulation software Maxwell, and the parametric scanning range is set to the scanning angle of the second permanent magnet 6. For angles ranging from 3° to 15°, linear optimization was employed, with a 0.01 interval between every two sets of parameters, to obtain the corresponding electromagnetic performance data of the motor. Each sweep angle... For multiple cogging torques and radial electromagnetic force densities at different times, the sweep angle can be found from the cogging torques at multiple times. The sweep angle can be found from the radial electromagnetic force density at multiple times corresponding to the maximum cogging torque. The corresponding maximum radial electromagnetic force density.

[0042] Step S3: Based on the maximum cogging torque and the maximum radial electromagnetic force density, calculate the sensitivity dynamic weights corresponding to the normalized cogging torque and the normalized maximum radial electromagnetic force density.

[0043] In this invention, sensitivity is used to assign dynamic weights to each data point, and the gradient of cogging torque and force density at each point is calculated as a sensitivity index, so that optimization has higher weight in the region of high sensitivity.

[0044] Specifically, the sensitivity dynamic weight corresponding to the normalized cogging torque is calculated using the following formula:

[0045]

[0046] in, This represents the dynamic sensitivity weight corresponding to the normalized cogging torque. Indicates the sweep angle of the second permanent magnet; The sweep angle of the second permanent magnet is . At that time, the corresponding maximum cogging torque; This indicates taking the maximum value. This represents the partial derivative.

[0047] The sensitivity dynamic weight corresponding to the maximum radial electromagnetic force density after normalization is given by the following formula:

[0048]

[0049] in, This represents the dynamic sensitivity weight corresponding to the maximum radial electromagnetic force density after normalization. The sweep angle of the second permanent magnet is . At that time, the corresponding maximum radial electromagnetic force density.

[0050] Step S4: Based on the three-phase no-load back EMF, construct a multi-interval back EMF penalty function.

[0051] In this process, a multi-interval back EMF penalty function is constructed. If the no-load back EMF of any phase is outside the specified range, it enters the penalty region.

[0052] Specifically, the expression for the constructed multi-interval back EMF penalty function is as follows:

[0053]

[0054] in, Denotes the multi-interval back electromotive force penalty function. For the three-phase index of the motor, Three-phase index for motor The corresponding penalty factor, Three-phase index for motor The corresponding no-load back electromotive force, Three-phase index for motor The center value of the corresponding allowable range of back electromotive force, Three-phase index for motor The minimum value in the corresponding allowable range of back electromotive force. Three-phase index for motor The maximum value within the corresponding allowable range of back electromotive force. This represents the allowable range of back electromotive force corresponding to motor A. This represents the allowable range of back electromotive force corresponding to motor B. This represents the allowable range of back electromotive force corresponding to motor C. In this embodiment, The value is [106, 111]. The value is [106, 111]. [109, 114].

[0055] Step S5: Based on the normalized cogging torque corresponding to the sensitivity dynamic weight, the normalized maximum radial electromagnetic force density corresponding to the sensitivity dynamic weight, and the multi-interval back electromotive force penalty function, construct the objective function of the multi-objective optimization algorithm.

[0056] It should be noted that the axial electromagnetic force originates from the interaction of the permanent magnetic field, and the amplitudes of the electromagnetic forces from the armature reaction field and stator slots vary periodically with time and space. Resonance only occurs when the spatial order and frequency of the electromagnetic force are consistent with the inherent characteristics of the stator. Therefore, the influence of electromagnetic forces must be considered simultaneously when analyzing the vibration and noise of an electric motor.

[0057] Specifically, in this embodiment, the sweep arc and position of the added second permanent magnet 6 are used as optimization variables for the multi-objective optimization algorithm. The optimization objective is to significantly reduce the cogging torque of the permanent magnet synchronous motor without sacrificing the no-load back electromotive force and ensuring the output torque, while reducing the radial electromagnetic force and improving the sinusoidal nature of the air gap magnetic flux density.

[0058] The objective function of the constructed multi-objective optimization algorithm is expressed as follows:

[0059]

[0060] in, Describe the objective function. The sweep angle of the second permanent magnet is . At that time, the corresponding normalized cogging torque; The sweep angle of the second permanent magnet is . At that time, the corresponding normalized radial electromagnetic force density.

[0061] Step S6: Solve the objective function to obtain the optimal sweep angle and optimal position of the second permanent magnet.

[0062] The motor's current excitation was set to both no-load and load states and simulations were performed. The electromagnetic performance and radial electromagnetic force parameters of the optimized motor were compared with those of the original motor (specifically, a traditional built-in V-type permanent magnet synchronous motor). The results are as follows: Figures 4 to 6 As shown.

[0063] from Figure 4 It can be seen that the maximum no-load cogging torque of the motor after optimization by this invention is 574.497. The original motor's cogging torque was 866.181. Therefore, it can be seen that the present invention optimizes the cogging torque by 33% under no-load conditions, which is a good optimization effect. The peak value of the cogging torque is reduced, which can reduce torque pulsation. Since torque pulsation is the main source of electromagnetic noise, the reduction of the peak value reduces the motor noise and makes the operation more stable.

[0064] from Figure 5 It can be seen that, under load, the average output torque of the original motor is 179.12. The average output torque of the motor after optimization according to this invention is 177.16. The average output torque of the motor remained essentially unchanged before and after optimization, ensuring the motor's output power. Meanwhile, the maximum cogging torque of the original motor under load was 192.78. The optimized maximum cogging torque of the motor under load, as determined by this invention, is 179.12. The cogging torque under load is reduced by 7%. This demonstrates that while maintaining output power under load, the optimized motor of this invention achieves a significant reduction in cogging torque, resulting in smoother motor operation and preventing "creeping" phenomena.

[0065] from Figure 6 As can be seen, compared with the original motor, the maximum radial electromagnetic force density under load of the optimized motor of this invention decreased from 706202 Pa to 584611 Pa. The optimized motor of this invention reduces the amplitude of the radial electromagnetic force density, and radial electromagnetic force is a key factor causing motor structural vibration and noise radiation. Reducing the peak value can decrease the deformation of the stator core and housing, reduce high-frequency noise, and decrease motor vibration noise. Simultaneously, compared with the original motor, the optimized motor of this invention reduces the amplitude of the air gap magnetic flux density and improves the sinusoidal nature of the air gap magnetic flux density, which is beneficial for weakening electromagnetic vibration noise.

[0066] In summary, the permanent magnet synchronous motor and its optimization method for new energy vehicles according to the above embodiments have the following beneficial effects:

[0067] (1) Based on the traditional permanent magnet synchronous motor, the present invention adds an asymmetric arc-shaped second permanent magnet to optimize the magnetic field distribution between the rotor and the stator. By optimizing the sweep angle and position of the second permanent magnet, the effective drive motor can be optimized.

[0068] (2) Based on the normalized cogging torque corresponding to the sensitivity dynamic weight, the normalized maximum radial electromagnetic force density corresponding to the sensitivity dynamic weight, and the multi-interval back EMF penalty function, the present invention constructs the objective function of the multi-objective optimization algorithm, which can effectively reduce the vibration noise of the permanent magnet synchronous motor, thereby improving the ride comfort. In addition, it can take into account the improvement of electromagnetic performance, change the radial electromagnetic force density, weaken the harmonic amplitude of magnetomotive force and magnetic permeability, reduce the torque fluctuation amplitude, reduce mechanical shock, and improve the sinusoidal waveform of air gap magnetic flux density. Thus, while ensuring that the three-phase no-load back EMF remains basically unchanged, the cogging torque of the permanent magnet synchronous motor is greatly reduced, thereby improving the stable operation capability of the permanent magnet synchronous motor.

[0069] (3) This invention introduces a sensitivity analysis weighting mechanism, which can dynamically adjust the weights according to the sensitivity of the objective function to parameter changes. In addition, the constructed multi-interval back electromotive force penalty function can dynamically adjust the solutions that violate the constraints through nonlinear penalties, thereby expanding the convergence speed of the feasible region. This invention also adopts an adaptive normalization method to avoid the neglect of small-order-of-magnitude targets due to huge differences in the order of magnitude of different targets, making the weight adjustment more fair and effective.

[0070] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A permanent magnet synchronous motor for new energy vehicles, characterized in that, include: The stator includes a stator yoke and a stator winding, wherein the inner ring of the stator yoke is provided with a plurality of axially arranged stator teeth; The rotor includes an embedded symmetrically arranged first permanent magnet, an asymmetrical arc-shaped second permanent magnet, and a magnetic isolation bridge, wherein the number of the first permanent magnet and the second permanent magnet are equal. The thicknesses at both ends of the second permanent magnet are not equal; For two adjacent second permanent magnets, the distance between one second permanent magnet and the center line of the stator winding is not equal to the distance between the other second permanent magnet and the center line of the stator winding. The drive motor can be optimized by optimizing the sweep angle and position of the second permanent magnet; The optimization method for the permanent magnet synchronous motor includes the following steps: Step S1: Determine the basic parameter information of the permanent magnet synchronous motor based on its operating conditions. The basic parameter information includes the size of the stator, the size of the rotor, the size and arrangement of the first permanent magnet, and the size and arrangement of the second permanent magnet. Step S2: Based on the determined basic parameter information of the permanent magnet synchronous motor, perform finite element modeling of the permanent magnet synchronous motor in Maxwell, and simultaneously perform parametric scanning of the sweep angle and position of the second permanent magnet to obtain the electromagnetic performance parameters of the permanent magnet synchronous motor. The electromagnetic performance parameters include the maximum cogging torque, the maximum radial electromagnetic force density, and the three-phase no-load back electromotive force. Step S3: Based on the maximum cogging torque and the maximum radial electromagnetic force density, calculate the sensitivity dynamic weight corresponding to the normalized cogging torque and the sensitivity dynamic weight corresponding to the normalized maximum radial electromagnetic force density. Step S4: Based on the three-phase no-load back EMF, construct a multi-interval back EMF penalty function; Step S5: Based on the normalized cogging torque corresponding to the sensitivity dynamic weight, the normalized maximum radial electromagnetic force density corresponding to the sensitivity dynamic weight, and the multi-interval back electromotive force penalty function, construct the objective function of the multi-objective optimization algorithm. Step S6: Solve the objective function to obtain the optimal sweep angle and optimal position of the second permanent magnet; In step S5, the expression for the objective function of the constructed multi-objective optimization algorithm is: in, Describe the objective function. The sweep angle of the second permanent magnet is . At that time, the corresponding normalized cogging torque; The sweep angle of the second permanent magnet is . At that time, the corresponding normalized radial electromagnetic force density, This represents the dynamic sensitivity weight corresponding to the normalized cogging torque. This indicates the sweep angle of the second permanent magnet. This represents the dynamic sensitivity weight corresponding to the maximum radial electromagnetic force density after normalization. This represents the multi-interval back electromotive force penalty function.

2. The permanent magnet synchronous motor according to claim 1, characterized in that, In step S3, the sensitivity dynamic weight corresponding to the normalized cogging torque is calculated using the following formula: in, The sweep angle of the second permanent magnet is . At that time, the corresponding maximum cogging torque; This indicates taking the maximum value. This represents the partial derivative.

3. The permanent magnet synchronous motor according to claim 2, characterized in that, In step S3, the sensitivity dynamic weight corresponding to the maximum radial electromagnetic force density after normalization is adopted using the following formula: in, The sweep angle of the second permanent magnet is . At that time, the corresponding maximum radial electromagnetic force density.

4. The permanent magnet synchronous motor according to claim 3, characterized in that, In step S4, the expression for the constructed multi-interval back electromotive force penalty function is: in, For the three-phase index of the motor, Three-phase index for motor The corresponding penalty factor, Three-phase index for motor The corresponding no-load back electromotive force, Three-phase index for motor The center value of the corresponding allowable range of back electromotive force, Three-phase index for motor The minimum value in the corresponding allowable range of back electromotive force. Three-phase index for motor The maximum value within the corresponding allowable range of back electromotive force. This represents the allowable range of back electromotive force corresponding to motor A. This represents the allowable range of back electromotive force corresponding to motor B. This represents the allowable range of back electromotive force corresponding to motor C.

Citation Information

Patent Citations

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