A cogging torque suppression method that changes air gap length

Abstract

The application relates to the motor technical field and is a method for changing the slot torque of a permanent magnet synchronous motor. First, a slot torque expression based on an energy method is established, and a distribution function relationship expression before and after the change of the air gap length is derived; second, a motor model is established, the tooth crest height is changed, the air gap length is increased, and the slot torque is weakened; finally, the air gap length of the motor is further optimized through arc cutting of the tooth tip, and the slot torque is further weakened. Since the motor also affects other performances during optimization, the output torque and loss before and after optimization are compared and analyzed, the output torque is reduced, the loss is increased by less than 0.5%, and the efficiency and power of the motor are ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the motor technical field, specifically relates to a kind of change air gap length's slot torque suppression method. BACKGROUND

[0002] With the continuous development of power electronics technology and permanent magnet material, permanent magnet synchronous motor is widely applied with its high efficiency, power factor, small size, stable operation performance and other advantages.But permanent magnet motor has an inherent defect: slot torque even in the case of no power supply, almost impossible to eliminate completely, can only weaken.

[0003] Slot torque directly affects the operation performance of motor, causes the vibration and noise of output torque, is an important factor influencing control accuracy, and is one of the research hotspots of permanent magnet synchronous motor.Some methods for weakening slot torque are difficult to implement or have greater impact on other performance of motor, especially for high-speed permanent magnet synchronous motor, high speed, centrifugal force, involves the strength of rotor, loss and temperature problems, once the structure of motor is changed, the stress field, temperature field, electromagnetic field of motor may be reanalyzed, and calculation is complicated, so various factors should be considered, and the method for weakening slot torque with less impact on motor temperature, loss and torque is selected. SUMMARY

[0004] For the above problems, the present application adopts the method of changing the structure of stator to weaken slot torque, in order to ensure the efficiency and output of optimized motor, the motor is optimized to ensure that the reduction of slot torque and the decrease of output torque and the increase of loss are within 0.5% range;

[0005] In order to achieve the above purpose, the specific operation steps are as follows:

[0006] Step one:

[0007] Establish the expression of slot torque based on energy method, and derive the function relationship of air gap length distribution before and after tooth top eccentricity;

[0008] The slot torque expression is as follows:

[0009]

[0010] In the formula, z is the number of stator slots, L a is the length of stator core, R2 and R1 are the inner diameter and outer diameter of stator core respectively, B rn is the Fourier decomposition coefficient of air gap flux density square.

[0011] As shown in formula (1), slot torque is related to the harmonic amplitude of air gap flux density, and slot torque can be reduced by weakening the harmonic of air gap flux density, and the air gap flux density distribution function can be expressed as:

[0012] B(θ,α)=f(θ,α)Λ(θ,α) (2)

[0013] In the formula, f(θ,α) is air-gap magnetic motive force, and Λ(θ,α) is air-gap permeance.

[0014] It can be seen from formula (2) that the air-gap magnetic density is related to air-gap magnetic motive force and air-gap permeance distribution, but the air-gap length of the motor stator tooth changes very little relative to the whole air gap before and after the structure is changed, the air-gap magnetic motive force has little influence, and the air-gap permeance has great influence, and the air-gap permeance can be expressed as:

[0015]

[0016] In the formula, δ(θ) is a distribution function of air-gap length, and it can be seen from formula (1), (2) and (3) that the distribution function of the reciprocal of the air-gap length reduces the corresponding harmonic amplitude, reduces the corresponding air-gap magnetic density harmonic, and further reduces the cogging torque.

[0017] Step two:

[0018] A motor model is established, the positions of two end points of a top circular arc of a stator tooth are kept unchanged, a parameterized modeling of the motor is carried out by taking the distance L from the center of the outer circle of the motor stator to the center of the top of the stator tooth as a variable, and the results of the cogging torque, the output torque, the air-gap magnetic density and the loss of the motor are obtained;

[0019] Step three:

[0020] The parameterized modeling results obtained in step two are compared and analyzed, and the optimal matching parameters are selected, and the selection principle is that the cogging torque is reduced, and the reduction of the output torque and the increase of the loss are less than 0.5%;

[0021] Step four:

[0022] The shape of the tooth is further changed, the tooth tip of the stator is arc cut, and the results of the cogging torque, the output torque and the loss before and after the cutting are compared, the cogging torque is further reduced, the reduction of the output torque and the increase of the loss are less than 0.5%, otherwise the arc cutting radius is changed until the requirements are met.

[0023] Compared with the prior art, the beneficial effects of the present application are:

[0024] 1. The present application analyzes the relationship between the cogging torque and the air-gap magnetic density and the air-gap length distribution function, and provides a good idea for excellent motor workers to propose other methods for changing the air-gap length to weaken the cogging torque.

[0025] 2. The present application proposes to weaken the cogging torque while ensuring that the reduction of the output torque and the increase of the loss are less than 0.5%, which is more comprehensive compared with the prior art.

[0026] 3. The cogging torque weakening method of the present application has a wide application range, and is not only suitable for high-speed permanent magnet synchronous motors with more restrictions, but also suitable for other types of speed-regulating permanent magnet synchronous motors. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to facilitate the use of this method, the present application is described in detail by the following specific embodiments and drawings.

[0028] Figure 1 Flow chart for weakening cogging torque of the present application;

[0029] Figure 2 Optimized stator tooth shape of a high-speed permanent magnet synchronous motor before tooth tip eccentricity;

[0030] Figure 3 Stator tooth shape of a high-speed permanent magnet synchronous motor after tooth tip eccentricity;

[0031] Figure 4 Stator tooth shape of a high-speed permanent magnet synchronous motor after tooth tip cutting;

[0032] Figure 5 Cogging torque waveform diagram of parameterized modeling;

[0033] Figure 6 Fourier decomposition diagram of front and rear air gap magnetic density after tooth tip eccentricity;

[0034] Figure 7 Cogging torque waveform diagram before and after tooth tip cutting;

[0035] Figure 8 Stator tooth tip eccentricity after air gap length diagram; DETAILED DESCRIPTION

[0036] In order to make the purpose, technical scheme and advantages of the present application patent clearer and more intelligible, the method described in the present application patent will be described in detail through specific embodiments shown in the drawings, but it should be understood that these descriptions are exemplary and are not intended to limit the scope of the present application patent.

[0037] Implementation example:

[0038] The present application takes a 150kW, 30000r / min high-speed permanent magnet synchronous motor as an example, and operates according to the flow chart of the present application: Figure 1

[0039] Step one: according to the present application Figure 8 Establishes the air gap length distribution function relationship.

[0040] The expressions of the distribution functions δ1(θ), δ2(θ) of the air gap length before and after tooth tip eccentricity are:​

[0041]

[0042]

[0043] In the formula, δ0 is the air gap length between the stator tooth crown and the rotor surface before the structure is changed, R is the radius of the tooth tip arc after the structure is changed, L is the increase in distance of the stator tooth crown relative to the original structure, h0 is the stator slot height, b0 is the stator slot opening width, b1 is the stator tooth width, l is the center distance between two adjacent stator teeth, and k takes values ​​of 0, 1, 2, ...

[0044] The distribution functions g1(θ) and g2(θ) of the reciprocal of the air gap length are expressed as follows:

[0045]

[0046]

[0047] Expand equations (6) and (7) into Fourier series:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] In the formula, g 10 With g 20 These are the constant components of the Fourier series, g 1n With g 2n Let n = 1, 2, ..., and n = 1, 2, ... From equations (1) to (13), it can be seen that the amplitude of the corresponding harmonic of the distribution function of the reciprocal of the air gap length decreases, which will reduce the corresponding air gap magnetic flux density harmonic, and thus reduce the cogging torque.

[0055] Step 2: Keeping the positions of the two ends of the stator tooth tip arc unchanged, the distance L from the center of the outer circle of the motor stator to the center of the stator tooth tip is used as a variable, with a step size of 1mm. The starting distance is the inner circle radius of the stator, which is 59mm, and the ending distance is 62mm. Parametric modeling of the motor is performed to obtain the motor cogging torque, output torque, air gap magnetic flux density, and loss results.

[0056] Step 3: Compare and analyze the results of parametric modeling. For example... Figure 5The tooth slot torque parameterization modeling results are shown. As shown in the figure, before the motor optimization, that is, when L is 59 mm, the tooth slot torque is 270.29 mN·m, when L is 60 mm, 61 mm and 62 mm, the tooth slot torque is 97.18 mN·m, 262.43 mN·m and 372.58 mN·m respectively. In terms of reducing the tooth slot torque, the best parameter is 60 mm, the tooth slot torque is reduced by 64.05%, and the output torque, iron loss, copper loss and rotor eddy current loss are continuously compared and analyzed. The average output torque and average loss data of the motor in the stable state are shown in Table 1:

[0057] Table 1

[0058] Iron loss / W Copper loss / W Eddy current loss / W Output torque / N-m 59 mm 1195.23 696.01 1523.54 46.09 60 mm 1196.38 718.45 1431.10 45.62 61 mm 1189.58 747.67 1455.08 45.17 62 mm 1196.13 784.35 1508.21 44.99

[0059] As shown in Table 1, with the increase of L, the copper loss gradually increases, the output torque gradually decreases, the iron loss is almost unchanged, and the eddy current loss changes greatly. The purpose of the present application is to ensure that the reduction of the output torque and the increase of the loss are less than 0.5%. When L is 60 mm, the increase of the copper loss and the iron loss and the reduction of the output torque are all within the range of 0.5%, and the eddy current loss is reduced by 92.44 W. From the above tooth slot torque comparison and analysis, when L is 60 mm, the tooth slot torque also decreases the most, so 60 mm is selected as the best matching parameter. As Figure 2 , 3 respectively, are schematic diagrams of the stator tooth shape of the high-speed permanent magnet synchronous motor before optimization and after tooth tip eccentricity.

[0060] Figure 6 are Fourier decomposition schematic diagrams of the air gap magnetic flux density before optimization and when L is 60 mm. As shown in the figure, the air gap magnetic flux density fundamental wave amplitude before and after optimization is 0.543 T and 0.542 T respectively, and the air gap magnetic flux density fundamental wave amplitude is reduced by 0.18%, which is an acceptable solution. In addition, the 5th, 7th, 9th, 11th and 17th harmonic amplitudes of the air gap magnetic flux density are reduced, which is the same as the calculation result of step one.

[0061] Step four: further change the shape of the tooth, cut the tooth tip of the stator in an arc shape, take points equidistantly along the two sides with the tooth tip vertex as the reference, draw an internal circular arc with the two points as the cutting points, and compare the tooth slot torque, output torque and loss results before and after cutting. The purpose of this method is to further reduce the tooth slot torque after the tooth tip of the stator is eccentric, and to ensure that the reduction of the output torque and the increase of the loss are less than 0.5%. The size of the tooth slot torque before the tooth tip is eccentric and after cutting is compared, as shown in Figure 7 .

[0062] As shown in Figure 7 , the tooth slot torque after cutting is 82.35 mN·m, the tooth slot torque is further reduced by 15.26%, and the total tooth slot torque is reduced by 70%.

[0063] The average output torque of the high-speed permanent magnet synchronous motor after tooth tip cutting is 45.6867 N·m, which is improved compared with the tooth top eccentricity, the average iron loss is 1191.94 W, the copper loss is 728.31 W, the reduction is within 5%, the eddy current loss is 1427.19 W, which is slightly reduced, and the requirements can be met. From the above analysis, it can be seen that the method provided by the application can significantly reduce the cogging torque under the condition that the output torque is reduced and the loss is increased by less than 0.5%, and the cogging torque is reduced by 70%.

Claims

1. A cogging torque suppression method that changes an air gap length, characterized by: The motor is a high-speed permanent magnet synchronous motor, and the method comprises the following steps: Step 1: establishing a tooth slot torque expression based on energy method, and deducing a function relationship expression of tooth tip eccentric pre-post air gap length distribution; Step 2: keeping the positions of two end points of the stator tooth tip arc unchanged, changing the length from the center of the motor stator outer circle to the center of the stator tooth tip to change the stator tooth tip height, and further changing the air gap length; Step 3: performing arc cutting on the stator tooth tip, taking points equidistantly along two sides with the tooth tip vertex as a reference, and drawing an inscribed circular arc with the two points as cutting points; In step 1, the tooth slot torque expression based on energy method is as follows: where z is the number of slots of the stator, L a is the length of the stator core, R2 and R1 are the inner diameter and the outer diameter of the stator core, respectively, B rn is the Fourier decomposition coefficient of the square of the air-gap flux density, and the air-gap flux density distribution function can be expressed as: B(θ,α)=f(θ,α)Λ(θ,α)(2) In the formula, f(θ,α) is air gap magnetic motive force, Λ(θ,α) is air gap permeance, and the air gap permeance can be expressed as: In the formula, δ(θ) is a distribution function of air gap length, The expression of the distribution functions g1(θ) and g2(θ) of the reciprocals of the air gap lengths before and after tooth tip eccentricity is as follows: In the formula, δ0 is the air gap length between the stator tooth crown and the rotor surface before the structure is changed, R is the radius of the tooth tip arc after the structure is changed, L is the distance increased relative to the stator tooth crown before the structure is changed, h0 is the stator slot height, b0 is the stator slot opening width, b1 is the stator tooth width, l is the center distance of two adjacent stator teeth, and k takes values of 0, 1, 2, …; The formula (4) (5) is expanded into Fourier series: where g 10 and g 20 are the constant components of the Fourier series, g 1n and g 2n are the amplitudes of the fundamental and the harmonics, n = 1, 2, …, the harmonic amplitudes of the distribution function of the reciprocal of the air gap length are reduced, the cogging torque is reduced.

2. A cogging torque suppression method of varying air gap length according to claim 1, characterized by: The motor is a 150kW, 30000r / min high-speed permanent magnet synchronous motor, and the length from the center of the motor stator outer circle to the center of the stator tooth tip after being changed in step 2 is 60mm.

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