A method for calculating rotor harmonic eddy current losses of solid rotor induction motor

Abstract

The invention discloses a method for calculating the rotor harmonic eddy current loss of a solid rotor induction motor. A two-dimensional electromagnetic field analysis finite element model of the solid rotor induction motor is constructed. A transient field time-step finite element simulation calculation method is adopted to obtain the spatiotemporal distribution of the steady-state air gap magnetic field of the motor. Two-dimensional Fourier decomposition is adopted to quantitatively extract the air gap harmonic magnetic field characteristics of the motor. Boundary conditions are constructed to simulate the air gap magnetic field characteristics to excite the solid rotor. The material properties of the solid rotor under load conditions are considered in combination with a frozen permeability method to realize high-precision rapid separation calculation of the rotor harmonic eddy current loss of the solid rotor induction motor. The invention can effectively improve the calculation accuracy, reduce the calculation scale, and accelerate the calculation speed.

Description

Technical Field

[0001] The present invention relates to a method for rapidly calculating rotor harmonic eddy current losses of a solid rotor induction motor based on a two-dimensional finite element analysis and calculation method, which adopts two-dimensional Fourier decomposition to quantitatively extract the air gap harmonic magnetic field of a motor, utilizes boundary conditions to reversely construct the extracted air gap harmonic magnetic field to excite a solid rotor, and combines a frozen permeability method to consider the material properties of the solid rotor under load conditions, thereby realizing a method for rapidly calculating rotor harmonic eddy current losses of a solid rotor induction motor. Background Art

[0002] Compared with other types of motors, induction motors have the advantages of low cost, simple structure, and high reliability. Their application scenarios cover various speeds and power levels. The rotor of the solid rotor induction motor is made of steel and its alloy materials. It has the characteristics of high mechanical strength, strong corrosion resistance and good reliability. It can challenge higher speeds, higher power levels and more severe operating environments. It is suitable for frequent heavy-load starting or long-term operation in a braking state.

[0003] Different from the traditional squirrel cage rotor induction motor, the rotor of the solid rotor induction motor is both a part of the motor magnetic circuit and a carrier of the rotor induced eddy current flow. This feature leads to large rotor eddy current loss and low power factor. At the same time, the solid rotor will lead to a strong end effect, causing the rotor induced eddy current to surge radially toward the shaft at both ends of the rotor, shortening the effective length of the solid rotor and increasing the rotor loss, which will eventually further deteriorate the efficiency index of the motor.

[0004] Therefore, the analysis and calculation of the rotor eddy current loss of the solid rotor induction motor is the premise for its effective suppression and the top priority for improving the efficiency of the solid rotor induction motor. Generally speaking, the academic community mainly uses analytical methods to analyze and calculate the air gap harmonic magnetic field characteristics and the harmonic eddy current loss caused on the solid rotor surface, and uses current sheet excitation to simulate harmonics to excite the solid rotor, thereby realizing the separation and calculation of the induced eddy current loss on the rotor surface.

[0005] However, the above methods generally have difficulty in considering the influence of factors such as nonlinear material properties, distortion of air gap permeability caused by stator and rotor slotting, and load changes, resulting in large errors in the extraction of motor air gap harmonic magnetic field characteristics and the separation and calculation of rotor eddy current losses. Therefore, it is necessary to explore a calculation method for high-precision, rapid and quantitative separation of solid rotor induction motor rotor harmonic eddy current losses in response to a series of problems existing in the existing technical methods, so as to provide a theoretical basis for reducing solid rotor induction motor rotor eddy current losses. Summary of the invention

[0006] The technology of the present invention solves the problem: in view of the fact that it is difficult to accurately consider the influence of factors such as nonlinear material characteristics, air gap magnetic permeability distortion caused by stator and rotor slotting, and load changes in the process of separating rotor harmonic eddy current losses of a solid rotor induction motor, a method for calculating the rotor harmonic eddy current losses of a solid rotor induction motor is provided, which has the advantages of being able to consider material nonlinearity and fast convergence speed.

[0007] The present invention achieves the above object through the following technical scheme, comprising the following steps:

[0008] The present invention provides a method for calculating the harmonic eddy current loss of a solid rotor induction motor rotor, comprising the following steps:

[0009] (1) Establish a two-dimensional finite element model of a solid rotor induction motor based on material nonlinearity and load conditions, which mainly includes two parts: the stator side model and the solid rotor side model;

[0010] (2) performing time-step finite element simulation on the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1), and after the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions reaches a stable state, extracting the air gap magnetic flux time-space distribution B(θ, t) at the center of the stator and rotor air gap in the last electrical cycle after the simulation model reaches a stable state, where θ is the rotor position angle and t is time;

[0011] (3) Extract the relative permeability distribution μ of each node in the solid rotor region at the last moment of the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1) r (x, y), where x and y are the horizontal and vertical coordinates in the rectangular coordinate system;

[0012] (4) Extracting the harmonic characteristics of the air gap magnetic flux B(θ,t) in step (2), including: harmonic order ν, νth harmonic amplitude B ν ,ν harmonic frequency f ν ;

[0013] (5) The stator side model is deleted from the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1), and only the solid rotor side model is retained to form a separate rotor model, and the relative permeability distribution μ extracted in step (3) is converted into r (x, y) is assigned to each node in the retained solid rotor region, thereby retaining the material properties of each node in the solid rotor region in step (3);

[0014] (6) In step (5), a constant magnetic field boundary condition is established at the outer edge of the air gap of the separate rotor model to achieve the reverse construction of the air gap magnetic flux harmonic characteristics in step (4) to excite the solid rotor and form a solid rotor model of harmonic excitation. The parameter equation of the constant magnetic field boundary in the rectangular coordinate system of x and y can be expressed as:

[0015]

[0016] Where: ν is the electrical angular frequency corresponding to the νth harmonic, ω ν =2πf ν ;

[0017] (7) Based on the harmonic excitation solid rotor model established in step (6), the air gap magnetic flux density ν subharmonic excitation is used to simulate and calculate the solid rotor model to be harmonically excited to reach a stable state, and obtain the average value P of the eddy current loss of the solid rotor in the last electrical cycle. ν , which is the harmonic eddy current loss of the solid rotor induction motor rotor caused by the νth harmonic of the air gap magnetic density.

[0018] As a further optimized solution of the present invention, in the step (1), the material nonlinearity is determined by a magnetic induction intensity-magnetic field intensity curve, namely a BH curve, to ensure that the influence of the nonlinear material on the electromagnetic performance of the motor is taken into account.

[0019] As a further optimized solution of the present invention, in step (2), a two-dimensional finite element model of a solid rotor induction motor based on material nonlinearity and load conditions is solved and calculated using a transient field solver, and the simulation step size can be selected according to specific engineering actual needs to ensure calculation accuracy and fully take into account the influence of air gap magnetic field harmonics.

[0020] As a further optimized solution of the present invention, in step (2), the criterion for the stable state is that the difference in the fundamental amplitude of the three-phase current in the last electrical cycle of the simulation does not exceed 0.5%, thereby reducing the calculation error caused by the unbalanced three-phase current.

[0021] As a further optimized solution of the present invention, in step (3), the relative permeability distribution μ of each node in the solid rotor region is extracted by using the frozen permeability method. r (x,y), reducing the number of nonlinear iterations of the model material properties in subsequent calculations of the individual rotor models.

[0022] As a further optimized solution of the present invention, in step (4), two-dimensional Fourier decomposition is used to extract the harmonic characteristics of the air gap magnetic flux B(θ, t), thereby improving the accuracy of harmonic separation and reducing the aliasing effect caused by using traditional one-dimensional Fourier decomposition in time or space.

[0023] As a further optimization scheme of the present invention, in step (6), the outer edge radius of the air gap of the separate rotor model is the rotor radius plus 1 / 2 of the air gap length between the stator and the rotor, thereby improving the accuracy of the air gap magnetic flux waveform to be extracted subsequently.

[0024] As a further optimized solution of the present invention, in step (7), the model simulation runs for 2 to 5 electrical cycles to reach a steady state, ensuring that the calculation can fully reach a steady state while reducing the calculation time.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0026] The present invention not only ensures the calculation accuracy of the eddy current loss of the solid rotor induction motor rotor, but also reduces the model calculation scale and shortens the time for the model to reach a stable state. Compared with the prior art, the present invention mainly improves the use of two-dimensional Fourier decomposition method to trace the air gap magnetic field, improves the accuracy of spectrum analysis and reduces the aliasing effect caused by the use of traditional time or space one-dimensional Fourier decomposition; at the same time, compared with the analysis technology using constant magnetic permeability, the use of frozen magnetic permeability can further fully consider the influence of load conditions and saturation effects on the distribution of rotor induced eddy currents; in addition, the present invention can not only quantitatively calculate the size of the harmonic eddy current loss of the solid rotor induction motor rotor, but also obtain the distribution of induced eddy currents, providing an effective basis for the subsequent reduction of eddy current losses. In summary, the present invention provides a complete system idea solution for the calculation of the harmonic eddy current loss of the solid rotor induction motor rotor.

[0027] The conceptual mechanism is as follows: first, a two-dimensional finite element analysis model of a solid rotor induction motor is established considering material nonlinearity and load conditions; the air gap harmonic magnetic field is traced and quantitatively analyzed in combination with the two-dimensional Fourier decomposition method; the relative permeability distribution of each node in the solid rotor area is extracted using frozen permeability, and the geometric model scale is further reduced to retain only the solid rotor side model, thereby reducing the nonlinear iterative solution step size in the finite element calculation process; a constant magnetic field boundary condition is established at the outer edge of the air gap of the rotor model after the geometric scale is reduced, and the air gap harmonic magnetic field is constructed in reverse to excite the solid rotor, and the simulation calculation reaches a steady state, thereby realizing the quantitative extraction of the harmonic eddy current loss of the solid rotor. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A schematic diagram of a flow chart of a method for calculating rotor harmonic eddy current losses of a solid rotor induction motor according to the present invention;

[0029] Figure 2 It is a schematic diagram of a two-dimensional electromagnetic field finite element single rotor model of the present invention;

[0030] Figure 3 The size distribution diagram of the eddy current loss of the solid rotor is simulated and calculated by the present invention;

[0031] Figure 4 The present invention simulates and calculates the distribution diagram of the induced eddy current caused by the -5th stator winding harmonic on the surface of the solid rotor.

[0032] The numbers in the figure are: 1 is the solid rotor, 2 is the air, and 3 is the model boundary. DETAILED DESCRIPTION

[0033] In order to clearly describe the purpose, technical solutions and advantages of the embodiments of the present invention, the present invention is described in full and clearly below in conjunction with the drawings in the embodiments of the present invention. However, the embodiments described in the present invention are only part of the embodiments of the present invention, not all the embodiments, and the description of the embodiments is only used to help understand the core idea of ​​the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work should be included in the scope of protection required by the present invention.

[0034] like Figure 1 As shown, an embodiment of a method for calculating harmonic eddy current loss of a solid rotor induction motor rotor of the present invention comprises the following steps:

[0035] (1) A two-dimensional finite element model of a 660V, 200Hz, 1MW, 12000r / min solid rotor induction motor based on material nonlinearity and load conditions is established. It mainly includes two parts: the stator side model and the solid rotor side model. The stator material is M270-35A, the rotor material is S355, the load condition is determined by the slip rate of 0.0038, the stator inner diameter is 240mm, the stator outer diameter is 560mm, the rotor outer diameter is 230mm, the stator has 36 slots, and the rotor has 44 slots.

[0036] (2) Using transient field, a time-step finite element simulation is performed on the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions established in step (1); the simulation step size is 5×10 -5 s, when the simulation time reaches 0.9s, a total of 18000 steps are taken to reach a stable state; the last electrical cycle after the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions reaches a steady state is extracted along the center of the stator and rotor air gap, that is, the air gap magnetic density spatiotemporal distribution B(θ, t) of the center of the stator and rotor air gap in the time period from 0.9s to 0.895s, where θ is the rotor position angle and t is time.

[0037] (3) Extract the relative permeability distribution μ of each node in the solid rotor region at the last moment, i.e., 0.9 s, of the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1). r (x, y), where x and y are the horizontal and vertical coordinates in the rectangular coordinate system.

[0038] (4) Extracting the harmonic characteristics of the air gap magnetic flux B(θ,t) in step (2), including: harmonic order ν, νth harmonic amplitude B ν ,ν harmonic frequency f ν ; Among them, the stator winding harmonics can cause harmonic eddy current losses in the solid rotor, and the quantitatively extracted stator winding harmonic characteristics are shown in Table 1.

[0039] Table 1

[0040] Order Frequency (Hz) Amplitude(T) 1 200 0.8555 -5 200 0.0048 7 200 0.0038 -11 200 0.0077 13 200 0.0065 -17 200 0.0015 19 200 0.0010 -23 200 0.0034 25 200 0.0035 -29 200 0.0014 31 200 0.0013 -35 200 0.0260 37 200 0.0070

[0041] (5) The stator side model is deleted from the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1), and only the solid rotor side model is retained to form the following Figure 2 The single rotor model is shown in the figure. The key parameters in the figure are 1 for the solid rotor, 2 for the air, and 3 for the model boundary. After the single rotor model is constructed, the relative permeability distribution μ extracted in step (3) is r (x,y) is assigned to each node within the retained solid rotor region.

[0042] (6) In step (5), a constant magnetic field boundary condition is established at the outer edge of the air gap of the separate rotor model, that is, at a radius of 117 mm from the center of the rotor, to achieve the reverse construction of the air gap harmonic magnetic field in step (4) to excite the solid rotor. The parametric equation of the constant magnetic field boundary in the rectangular coordinate system of x and y can be expressed as:

[0043]

[0044] Where: ν is the electrical angular frequency corresponding to the νth harmonic, ω ν =2πf ν .

[0045] (7) According to the model established in step (6), the νth harmonic excitation is used, and the simulation calculation is performed until 0.04s reaches a stable state, with a total of 800 steps, to obtain the average value P of the eddy current loss of the solid rotor in the last electrical cycle, that is, the time period from 0.04s to 0.035s. ν ; Figure 3 The present invention simulates and calculates the size distribution diagram of the eddy current loss of the solid rotor, realizes the quantitative separation and source tracing of the harmonic eddy current loss, and provides a calculation basis for adopting targeted technical means to suppress it; Figure 4 The present invention simulates and calculates the distribution diagram of the induced eddy current caused by the -5th stator winding harmonic on the surface of the solid rotor, which can intuitively reflect the depth of the induced eddy current penetrating into the solid rotor, and provides a theoretical basis for suppressing the harmonic eddy current by changing the rotor structure topology.

[0046] Wherein, in step (1), the material nonlinearity is determined by the magnetic induction intensity-magnetic field intensity curve, namely the BH curve, to ensure that the influence of the nonlinear material on the electromagnetic performance of the motor is taken into account. In the embodiment, the stator material is M270-35A and the rotor material is S355.

[0047] In step (2), the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions is solved and calculated using a transient field solver. The simulation step size can be selected according to the actual needs of the specific project to ensure the calculation accuracy and fully consider the influence of the air gap magnetic field harmonics. In the embodiment, the simulation step size is 5×10 -5 s.

[0048] Wherein, in step (2), the criterion of the stable state is that the difference between the fundamental amplitudes of the three-phase currents in the last electrical cycle of the simulation does not exceed 0.5%, thereby reducing the calculation error caused by the unbalanced three-phase current. In the embodiment, the last electrical cycle is 0.9s to 0.895s, and the corresponding maximum error of the fundamental amplitude of the three-phase current is 0.22%.

[0049] In step (3), the relative permeability distribution μ of each node in the solid rotor region is extracted by using the frozen permeability method. r (x,y), reducing the number of nonlinear iterations of the model material properties in subsequent calculations of the individual rotor models.

[0050] Wherein, in step (4), two-dimensional Fourier decomposition is used to extract the harmonic characteristics of the air gap magnetic flux B(θ, t), thereby improving the accuracy of harmonic separation and reducing the aliasing effect caused by using traditional time or space one-dimensional Fourier decomposition.

[0051] Wherein, in step (6), the outer radius of the air gap of the single rotor model is the rotor radius plus 1 / 2 of the air gap length between the stator and the rotor, so as to improve the accuracy of the air gap magnetic flux waveform to be extracted later. In the embodiment, the outer radius of the air gap of the single rotor model is 117 mm.

[0052] Among them, in step (7), the model simulation runs for 2 to 5 electrical cycles to reach a steady state, ensuring that the calculation can fully reach a steady state while reducing the calculation time. In the embodiment, the simulation calculation reaches a steady state in 0.04s, with a total of 800 steps.

Claims

1. A method for calculating the harmonic eddy current loss of a solid rotor induction motor rotor, characterized in that: The steps include: (1) Establish a two-dimensional finite element model of a solid rotor induction motor based on material nonlinearity and load conditions, including a stator side model and a solid rotor side model; (2) performing a time-step finite element simulation on the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1), and after the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions reaches a stable state, extracting the air gap magnetic flux space-time distribution B(θ, t) at the center of the stator and rotor air gap in the last electrical cycle after the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions reaches a steady state, where θ is the rotor position angle and t is time; (3) Extract the relative permeability distribution μ of each node in the solid rotor region at the last moment of the two-dimensional finite element model of the solid rotor induction motor based on material nonlinearity and load conditions in step (1) r (x, y), where x and y are the horizontal and vertical coordinates in the rectangular coordinate system; (4) Extracting the harmonic characteristics of the air gap magnetic flux B(θ,t) in step (2), including: harmonic order ν, νth harmonic amplitude B ν ,ν harmonic frequency f ν ; (5) The solid rotor induction motor two-dimensional finite element model based on material nonlinearity and load conditions in step (1) is only retained to form a separate rotor model, and the relative permeability distribution μ extracted in step (3) is converted into r (x, y) is assigned to each node in the retained solid rotor region, thereby retaining the material properties of each node in the solid rotor region in step (3); (6) In step (5), a constant magnetic field boundary condition is established at the outer edge of the air gap of the separate rotor model to achieve the reverse construction of the air gap magnetic flux harmonic characteristics in step (4) to excite the solid rotor and form a solid rotor model of harmonic excitation. The parameter equation of the constant magnetic field boundary in the rectangular coordinate system of x and y is expressed as: Where: ν is the electrical angular frequency corresponding to the νth harmonic, ω ν =2πf ν ; (7) Based on the harmonic excitation solid rotor model established in step (6), the air gap magnetic flux density ν subharmonic excitation is used to simulate and calculate the solid rotor model to be harmonically excited to reach a stable state, and obtain the average value P of the eddy current loss of the solid rotor in the last electrical cycle. ν , which is the harmonic eddy current loss of the solid rotor induction motor rotor caused by the νth harmonic of the air gap magnetic density.

2. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In step (1), the material nonlinearity is determined by a magnetic induction intensity-magnetic field intensity curve, namely a BH curve, to ensure that the influence of the nonlinear material on the electromagnetic performance of the motor is taken into account.

3. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In the step (2), a two-dimensional finite element model of a solid rotor induction motor based on material nonlinearity and load conditions is solved and calculated using a transient field solver. The simulation step size can be selected according to the actual needs of the specific project to ensure the calculation accuracy and fully consider the influence of the air gap magnetic field harmonics.

4. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In the step (2), the criterion for the stable state is that the difference in the fundamental amplitude of the three-phase current in the last electrical cycle of the simulation does not exceed 0.5%, thereby reducing the calculation error caused by the unbalanced three-phase current, providing a criterion for the stable state, and making the definition of the stable state more accurate.

5. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In step (3), the relative permeability distribution μ of each node in the solid rotor region is extracted by using the frozen permeability method. r (x,y), reducing the number of nonlinear iterations of the model material properties in subsequent calculations of the individual rotor models.

6. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In the step (4), two-dimensional Fourier decomposition is used to extract the harmonic characteristics of the air gap magnetic flux B(θ, t), thereby improving the accuracy of harmonic separation and reducing the aliasing effect caused by using traditional one-dimensional Fourier decomposition in time or space.

7. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In step (6), the air gap outer edge radius of the separate rotor model is the rotor radius plus 1 / 2 of the air gap length between the stator and the rotor, thereby improving the accuracy of the air gap magnetic flux waveform to be extracted subsequently.

8. The method for calculating the harmonic eddy current loss of a solid rotor induction motor according to claim 1, characterized in that: In the step (7), the steady state is achieved after the model simulation runs for 2 to 5 electrical cycles, ensuring that the steady state can be fully achieved while reducing the computational time.

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