Rapid calculation method and system for inherent frequency of stator core

Abstract

The invention discloses a method and a system for quickly calculating the inherent frequency of a stator core. The method comprises the following steps: constructing a five-degree-of-freedom cylindrical shell theoretical model, and converting five degrees of freedom of a cylindrical shell into a single-variable function through a variable separation method; calculating strain energy and kinetic energy of the orthotropic cylindrical shell without the reinforcing ribs and the reinforcing ribs; in combination with a Lagrange interpolation function and a GLL integral point, axially segmenting the stator, and performing matrix expression on energy equations of the cylindrical shell and the stator teeth to obtain a stiffness matrix and a mass matrix corresponding to the discrete cylindrical shell and stator teeth; and respectively adding the stiffness matrixes and the mass matrixes corresponding to the cylindrical shell and the stator teeth to obtain a total stiffness matrix and a total mass matrix, carrying out eigenvalue solution on the total stiffness matrix and the total mass matrix to obtain the square of the inherent angular frequency of the stator core and a displacement fitting function in each direction, and converting to generate the inherent frequency of the stator core. According to the method, the inherent frequency of the stator core under each boundary condition can be quickly calculated.

Description

Technical Field

[0001] The present invention belongs to the technical field of combining motors with structural mechanics, and in particular relates to a method and system for quickly calculating the natural frequency of a stator core. Background Art

[0002] Manufacturing is the main body of the national economy, the foundation of the country, the tool for the country's prosperity, and the basis for the country's strength. In the eight major fields of high-end CNC machine tools and robots, aerospace equipment, marine engineering equipment and high-tech ships, advanced rail transportation equipment, energy-saving and new energy vehicles, power equipment, agricultural machinery equipment, biomedicine and high-performance medical equipment, and high-performance electric drive systems, the motor is the most important component of the electric drive system, and its working reliability directly affects the overall performance of the electric drive system. With the continuous increase in motor power levels and the continuous improvement of motor performance, people's requirements for the comprehensive performance of motors are also getting higher and higher. In high-power applications, vibration and noise problems are a major problem to be solved. In order to prevent resonance and reduce electromagnetic noise, it is necessary to perform modal analysis on the stator. The modal analysis of the stator is of great significance for reducing motor noise and diagnosing motor faults. An accurate analytical model is conducive to establishing the relationship between the motor stator parameters and the natural frequency, which in turn helps to optimize the motor design.

[0003] At present, the mainstream analysis method of the stator natural frequency is to use commercial software for calculation or conduct experimental tests. However, the use of software for calculation has certain requirements on the computing power of the computer and the calculation time is long. Experiments require obtaining physical models and purchasing experimental equipment, which has disadvantages in manpower and economic costs. The mainstream calculation method is to simplify the stator core into a cylindrical shell, which affects the accuracy of the results. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a calculation method that can quickly and accurately calculate the natural frequency of the actual stator core. Based on the actual structure of the stator core, it is simplified into a combination of a cylindrical shell and reinforcing ribs, and the calculation accuracy is guaranteed by combining the energy method and the quadrature unit method.

[0005] In order to achieve the aforementioned object of the invention, the present invention adopts the following scheme:

[0006] One aspect of the present invention provides a method for quickly calculating the natural frequency of a stator core, wherein the stator core is composed of a stator yoke and stator teeth uniformly distributed inside; the calculation method comprises:

[0007] Step S1: simplifying the stator yoke into an orthotropic cylindrical shell, and simplifying the stator teeth into reinforcing ribs uniformly distributed along the circumferential direction; constructing a five-degree-of-freedom cylindrical shell theoretical model, and converting the five degrees of freedom of the cylindrical shell into a single variable function by using a variable separation method;

[0008] Step S2: Calculate the strain energy and kinetic energy of the orthotropic cylindrical shell without stiffeners; Calculate the strain energy and kinetic energy of the stiffeners;

[0009] Step S3: combining the Lagrange interpolation function and the GLL integration point, dividing the stator axially into segments, and expressing the energy equations of the cylindrical shell and the stator teeth in matrix form, so as to obtain the stiffness matrix and mass matrix corresponding to the discretized cylindrical shell, and the stiffness matrix and mass matrix corresponding to the discretized stator teeth;

[0010] Step S4: Add the stiffness matrix and mass matrix corresponding to the cylindrical shell and the stator teeth respectively to obtain the total stiffness matrix and the total mass matrix, solve the eigenvalues ​​of the total stiffness matrix and the total mass matrix, obtain the square of the natural angular frequency of the stator core and the fitting function of the displacement in all directions, and convert them to generate the natural frequency of the stator core.

[0011] Another aspect of the present invention provides a fast calculation system for the natural frequency of a stator core, wherein the stator core is composed of a stator yoke and stator teeth uniformly distributed inside; the system comprises:

[0012] A stator core model building module is used to simplify the stator yoke into an orthotropic cylindrical shell and the stator teeth into reinforcing ribs uniformly distributed along the circumference; a five-degree-of-freedom cylindrical shell theoretical model is built, and the five degrees of freedom of the cylindrical shell are converted into a single variable function by using a variable separation method;

[0013] Strain energy and kinetic energy calculation module, used to calculate the strain energy and kinetic energy of orthotropic cylindrical shells without stiffeners; calculate the strain energy and kinetic energy of stiffeners;

[0014] The stiffness matrix and mass matrix calculation module is used to combine the Lagrange interpolation function and the GLL integration point to segment the stator axially, express the energy equations of the cylindrical shell and the stator teeth in a matrix form, and obtain the stiffness matrix and mass matrix corresponding to the discretized cylindrical shell, as well as the stiffness matrix and mass matrix corresponding to the discretized stator teeth;

[0015] The natural frequency calculation module is used to add the stiffness matrix and mass matrix corresponding to the cylindrical shell and the stator teeth respectively to obtain the total stiffness matrix and the total mass matrix, solve the eigenvalues ​​of the total stiffness matrix and the total mass matrix, obtain the square of the natural angular frequency of the stator core and the fitting function of the displacement in all directions, and convert them to generate the natural frequency of the stator core.

[0016] Compared with the prior art, the present invention has at least the following advantages: (1) The calculation method proposed in the present invention fully considers the actual structure of the stator core, and comprehensively analyzes the energy of the stator core. Through the quadrature unit method, only a few integral points are needed to accurately fit the displacement function and the natural frequency. The modal vibration shape of the corresponding frequency can be obtained by simple post-processing of the obtained data. (2) Compared with mainstream commercial software, this method significantly reduces computer calculation time and releases computer computing power. (3) This method can play an important role in the motor design process, guiding motor design engineers to optimize the analysis of the important issue of vibration noise. There is no need to obtain the natural frequency and mode through prototype experiments, which shortens the design time and saves economic costs. (4) This method can impose changes on the rows and columns of the matrix corresponding to the discrete points at both ends, and can calculate the natural frequencies under various classical boundary conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 It is a schematic diagram of a calculation process provided by a typical implementation case of the present invention;

[0019] Figure 2 It is a simplified schematic diagram of the actual structure of the motor stator provided by a typical implementation case of the present invention;

[0020] Figure 3 It is a cross-sectional view of a stator and teeth provided in a typical implementation case of the present invention;

[0021] Figure 4 is a reference stator core parameter table provided by a typical implementation case of the present invention;

[0022] Figure 5 It is a comparison diagram of the calculation results and finite element simulation results of a reference core under a free boundary provided by a typical implementation case of the present invention;

[0023] Figure 6 It is a comparison diagram of the calculation results and finite element simulation results of a reference core under a simply supported boundary provided by a typical implementation case of the present invention;

[0024] Figure 7 It is a comparison diagram of the calculation results of the reference core under the fixed support boundary and the finite element simulation results provided by a typical implementation case of the present invention;

[0025] Figure 8It is a modal vibration shape diagram provided by a typical implementation case of the present invention, which is drawn based on the characteristic vector solved when the circumferential half-wave number of the reference core is 2 and the axial half-wave number is 1 under the simply supported boundary;

[0026] Fig. 9 It is a modal vibration diagram of a reference iron core drawn according to the finite element simulation results provided in a typical implementation case of the present invention when the circumferential half-wave number is 2 and the axial half-wave number is 1 under a simply supported boundary. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical scheme and advantages of the present invention clearer, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. Examples of these preferred embodiments are illustrated in the accompanying drawings. The embodiments of the present invention shown in the accompanying drawings and described according to the accompanying drawings are merely exemplary, and the present invention is not limited to these embodiments.

[0028] The stator core is composed of a stator yoke and stator teeth uniformly distributed inside. The stator yoke can be regarded as an orthotropic cylindrical shell, and the stator teeth can be regarded as reinforcing ribs. The natural frequency is calculated according to the energy method, including: step (1) according to the first-order shear deformation theory and the separation of variables method, the axial variables of the five variables of the cylindrical shell are decomposed to obtain the displacement coordination equation of the stator teeth and the yoke; step (2): substituting the displacement equation into the calculation of the strain energy and kinetic energy of the yoke and the stator teeth; step (3) combining the Lagrange interpolation function and the GLL integral point, the stator is axially segmented, and the energy expression is converted into a matrix; (4) by deleting the corresponding rows and columns of the matrix, the boundary constraints are imposed without introducing additional spring stiffness, the eigenvalues ​​of the processed matrix are solved, and the natural frequency is calculated. This method can be applied to various classical boundary conditions, and the natural frequency of the stator core can be obtained quickly and accurately. It can guide engineers in design and play an important role in solving the hot issue of motor vibration noise.

[0029] One aspect of the present invention provides a method for quickly calculating the natural frequency of a stator core, wherein the stator core is composed of a stator yoke and stator teeth uniformly distributed inside; the calculation method comprises:

[0030] Step S1: simplifying the stator yoke into an orthotropic cylindrical shell, and simplifying the stator teeth into reinforcing ribs uniformly distributed along the circumferential direction; constructing a five-degree-of-freedom cylindrical shell theoretical model, and converting the five degrees of freedom of the cylindrical shell into a single variable function by using a variable separation method;

[0031] Step S2: Calculate the strain energy and kinetic energy of the orthotropic cylindrical shell without stiffeners; Calculate the strain energy and kinetic energy of the stiffeners;

[0032] Step S3: combining the Lagrange interpolation function and the GLL integration point, dividing the stator axially into segments, and expressing the energy equations of the cylindrical shell and the stator teeth in matrix form, so as to obtain the stiffness matrix and mass matrix corresponding to the discretized cylindrical shell, and the stiffness matrix and mass matrix corresponding to the discretized stator teeth;

[0033] Step S4: Add the stiffness matrix and mass matrix corresponding to the cylindrical shell and the stator teeth respectively to obtain the total stiffness matrix and the total mass matrix, solve the eigenvalues ​​of the total stiffness matrix and the total mass matrix, obtain the square of the natural angular frequency of the stator core and the fitting function of the displacement in all directions, and convert them to generate the natural frequency of the stator core.

[0034] In one embodiment, in step S1, the deformation of the cylindrical shell is expressed as:

[0035] u(x,θ,z,t)=u 0 (x,θ,z,t)+zΨ x (x, θ, z, t)

[0036] v(x,θ,z,t)=v 0 (x,θ,z,t)+zΨ θ (x, θ, z, t)

[0037] w(x,θ,z,t)=w 0 (x,θ,z,t)

[0038] Among them, u, v, and w are the displacements of the cylindrical shell in the x, θ, and z directions respectively. 0 , v 0 , w 0 are the displacements of the neutral surface in the x, θ, and z directions, ψ x , ψ θ is the rotation of the normal around the x and θ axes, and z is the radial coordinate;

[0039] The strain of the cylindrical shell is expressed as:

[0040]

[0041]

[0042] Among them, ε is the strain symbol, γ is the shear strain symbol, the subscript represents the strain direction, and R is the neutral surface radius.

[0043] In one embodiment, in step S1, the stator teeth are regarded as Euler beams, and the displacement equation of the stator teeth is obtained by the deformation coordination equation:

[0044] u t =ue s Ψ x

[0045] v t =ve s Ψ θ

[0046] w t =w

[0047] Among them, u t , v t , w t is the displacement of the tooth in the x, y, and z directions of its own coordinate system, e s is the eccentricity between the neutral plane of the cylindrical shell and the center of the tooth.

[0048] In one embodiment, in step S2, the calculation process of the strain energy of the cylindrical shell is:

[0049]

[0050] in, is the strain energy of the cylindrical shell, σ is the stress symbol, the subscript represents the direction, E and G are the elastic modulus and shear modulus, the subscript represents the direction, and κ is the shear correction factor of the cylindrical shell. In this example,

[0051] The calculation process of the kinetic energy of a cylindrical shell is:

[0052]

[0053] in, is the strain energy of the cylindrical shell, and ω is the natural angular frequency.

[0054] In one embodiment, step S4 includes: using the formula The square of the natural angular frequency of the core and the fitting function of the displacement in all directions are obtained by solving the stiffness matrix and the coefficient matrix. After the transformation of ω=2πf, the natural frequency f of the stator core is obtained.

[0055] Another aspect of the present invention provides a fast calculation system for the natural frequency of a stator core, comprising: the stator core is composed of a stator yoke and stator teeth uniformly distributed inside; the system comprises:

[0056] A stator core model building module is used to simplify the stator yoke into an orthotropic cylindrical shell and the stator teeth into reinforcing ribs uniformly distributed along the circumference; a five-degree-of-freedom cylindrical shell theoretical model is built, and the five degrees of freedom of the cylindrical shell are converted into a single variable function by using a variable separation method;

[0057] Strain energy and kinetic energy calculation module, used to calculate the strain energy and kinetic energy of orthotropic cylindrical shells without stiffeners; calculate the strain energy and kinetic energy of stiffeners;

[0058] The stiffness matrix and mass matrix calculation module is used to combine the Lagrange interpolation function and the GLL integration point to segment the stator axially, express the energy equations of the cylindrical shell and the stator teeth in a matrix form, and obtain the stiffness matrix and mass matrix corresponding to the discretized cylindrical shell, as well as the stiffness matrix and mass matrix corresponding to the discretized stator teeth;

[0059] The natural frequency calculation module is used to add the stiffness matrix and mass matrix corresponding to the cylindrical shell and the stator teeth respectively to obtain the total stiffness matrix and the total mass matrix, solve the eigenvalues ​​of the total stiffness matrix and the total mass matrix, obtain the square of the natural angular frequency of the stator core and the fitting function of the displacement in all directions, and convert them to generate the natural frequency of the stator core.

[0060] In one embodiment, in the stator core model building module, the deformation of the cylindrical shell is expressed as:

[0061] u(x,θ,z,t)=u 0 (x,θ,z,t)+zΨ x (x, θ, z, t)

[0062] v(x,θ,z,t)=v 0 (x,θ,z,t)+zΨ θ (x, θ, z, t)

[0063] w(x,θ,z,t)=w 0 (x,θ,z,t)

[0064] Among them, u 0 , v 0 , w 0 are the displacements of the neutral surface in the x, θ, and z directions, ψ x , ψ θ is the rotation of the normal around the x and θ axes;

[0065] The strain of the cylindrical shell is expressed as:

[0066]

[0067] In one embodiment, in the stator core model building module, the stator teeth are regarded as Euler beams, and the displacement equation of the stator teeth is obtained through the deformation coordination equation:

[0068] u t =ue s Ψ x

[0069] v t =ve s Ψ θ

[0070] wt =w.

[0071] In one embodiment, in the strain energy and kinetic energy calculation module, the calculation process of the strain energy of the cylindrical shell is:

[0072]

[0073] Among them, E and G are elastic modulus and shear modulus, and the subscript represents the direction;

[0074] The calculation process of the kinetic energy of a cylindrical shell is:

[0075]

[0076] Where ω is the natural angular frequency.

[0077] In one embodiment, the natural frequency calculation module includes: using the formula The square of the natural angular frequency of the core and the fitting function of the displacement in all directions are obtained by solving the stiffness matrix and the coefficient matrix. The natural frequency of the stator core is obtained after the transformation of ω=2πf.

[0078] like Figure 1 As shown in the figure, a calculation method for calculating the natural frequency of the stator core proposed by the present invention can quickly calculate the natural frequency of the stator core under various boundary conditions. The important structural parameters of the calculation method include the axial length L of the stator core, the thickness h of the yoke, the radius R of the mid-surface of the yoke, the height h of the stator tooth section, and the thickness h of the yoke. t , width b t The required material parameters are the stator core's isotropic elastic modulus, bending modulus and Poisson's ratio.

[0079] This application constructs a five-degree-of-freedom cylindrical shell theoretical model based on the first-order shear deformation theory (FSDT), in which the five degrees of freedom of the cylindrical shell are converted into a single variable function through the separation of variables method; then the stator teeth are regarded as uniformly distributed reinforcement ribs, and the cylindrical shell and the reinforcement ribs are stacked by silicon steel sheets, which are regarded as orthotropic materials to obtain the physical parameters of the material.

[0080] Step 1: Convert the stator core displacement u(x, θ, r, t) into u(x)u(θ)u(r)u(t) by separation of variables. Except for the axial variable, the remaining variables can be eliminated, and only the axial variable x remains. The axial function can be replaced by the cosine function due to the structural symmetry. The radial function is considered to be independent of z in FSDT and can be eliminated in the integration process.

[0081] Step 2: Consider the stator teeth and simplify them into reinforcing ribs evenly distributed along the circumference. Take the displacement of the neutral plane of the yoke as the reference to obtain the displacement coordination equation of the teeth. Then, through the deformation coordination equation, the displacement equation of the teeth is obtained.

[0082] u t =u-eΨ x

[0083] v t =v-eΨ θ

[0084] Step 3: Determine the strain energy and kinetic energy of the stator yoke in the motor stator core, where:

[0085]

[0086] Using the equation from step 1, we get the energy equation for a single variable x.

[0087] Step 4: Use step 2 and the strain energy and kinetic energy equations of the beam to obtain the energy expression of each tooth.

[0088] Step 5: Introduce the Lagrange interpolation function and the GLL integration point, perform the axial discrete fitting of the five-degree-of-freedom displacement of the shell, substitute it into the energy equation, and obtain the energy of the stator core yoke. The usage steps are as follows: Discretize the displacement function through the Lagrange interpolation function. Derivate the obtained function to obtain the first-order derivative expression of the function, and so on to obtain higher-order derivatives. Using the GLL integration point, substitute the corresponding discrete points into the discretized equation to obtain the stiffness matrix and mass matrix. Specifically:

[0089] (i) Use the Lagrangian function and GLL integral points to fit the displacement function, substitute it into the energy equation, and discretize the displacement function through the Lagrangian interpolation function.

[0090] (ii) Differentiate the obtained function to obtain the first-order derivative expression of the function, and so on to obtain higher-order derivatives.

[0091] (iii) Using the GLL integration points, substitute the corresponding discrete points into the discretized equations to obtain the stiffness matrix and mass matrix.

[0092] Step 6: Referring to step 5, discretize the energy equation of the tooth in the axial direction to obtain the stiffness matrix and mass matrix.

[0093] Step 7: Add the energy of the yoke and the teeth to obtain the energy of the entire stator core, that is, add the stiffness matrix (mass matrix) of the yoke and the teeth respectively.

[0094] Step 8: Use the formula to find Solve the eigenvalues ​​of the stiffness matrix and the coefficient matrix to obtain the square of the natural angular frequency of the core and the fitting function of the displacement in all directions, and then convert them to get the natural frequency.

[0095] The following is a detailed introduction to this implementation method:

[0096] The deformation of the shell can be expressed as:

[0097] u(x,θ,z,t)=u 0 (x,θ,z,t)+zΨ x (x, θ, z, t)

[0098] v(x,θ,z,t)=v 0 (x,θ,z,t)+zΨ θ (x, θ, z, t)

[0099] w(x,θ,z,t)=w 0 (x, θ, z, t)

[0100] where u 0 , v 0 , w 0 are the displacements of the neutral plane in the x, θ, and z directions respectively. x , ψ θ is the rotation of the normal around the x and θ axes. The strain can be expressed by:

[0101]

[0102] The additional stator teeth are regarded as Euler beams, and the displacement equation of the teeth can be obtained through the deformation coordination equation:

[0103] u t =ue s Ψ x

[0104] v t =ve s Ψ θ

[0105] w t =w

[0106] First, calculate the strain energy of the shell, and calculate the strain energy of the orthotropic cylindrical shell without stiffeners; the strain energy formula of the orthotropic cylindrical shell without stiffeners is:

[0107]

[0108] Where σ and ε represent stress and strain respectively, and the subscripts represent the corresponding directions.

[0109] The strain is known, and since the stator is considered as an orthotropic material, its stress should be:

[0110]

[0111] Among them, E and G are elastic modulus and shear modulus, and the subscript represents the direction. After simplification, it can become a function of a single variable x.

[0112] Then calculate the kinetic energy of the shell and the kinetic energy of the orthotropic cylindrical shell without stiffeners; the kinetic energy formula of the orthotropic cylindrical shell without stiffeners is:

[0113]

[0114] Where ω is the natural angular frequency.

[0115] According to the displacement coordination equation, the strain energy and kinetic energy of the reinforcement are calculated. According to the displacement equation of the beam obtained above, it is substituted into the strain energy formula and kinetic energy formula of the Euler beam to obtain its strain energy:

[0116]

[0117] Among them, A t is the cross-sectional area, I θ , I z are the moments of inertia of the cross section relative to the θ and z axes, J t is the torsion coefficient of the beam, which is related to the cross-sectional shape, and ρ is the material density.

[0118] Its kinetic energy is:

[0119]

[0120] Where ρ is the material density, N t is the number of teeth.

[0121] According to Hamilton's principle

[0122]

[0123] The solution to the natural frequency is the solution of the function when δΠ is 0.

[0124] Next, combining the Lagrange interpolation function and the GLL integration point, we first use the Lagrange interpolation function to fit the displacement function, and the discretized strain energy and kinetic energy are obtained in the form of:

[0125]

[0126] u represents the displacement variable u={u,v,w,ψ x , ψ θ}, the point represents the time derivative. By this method, the analytical solution is converted into a matrix expression to obtain the stiffness matrix K and the mass matrix M. The problem is transformed into a characteristic root problem, that is:

[0127] K-ω 2 M=0

[0128] The stiffness matrix and mass matrix obtained using QEM are in the form of:

[0129]

[0130]

[0131] According to the above steps, the stiffness and mass matrices of the shell and the tooth can be obtained respectively, and the sum is the total stiffness and total mass matrix.

[0132] K G =K s +K t

[0133] M G =M s +M t

[0134] The eigenvalue of the corresponding mode is solved to obtain the natural angular frequency, and the natural frequency can be obtained by converting ω=2πf.

[0135] It should be understood that although this specification is described according to implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions of each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for quickly calculating the natural frequency of a stator core, characterized in that: The stator core is composed of a stator yoke and stator teeth uniformly distributed inside; the calculation method includes: Step S1: simplifying the stator yoke into an orthotropic cylindrical shell, and simplifying the stator teeth into reinforcing ribs uniformly distributed along the circumferential direction; constructing a five-degree-of-freedom cylindrical shell theoretical model, and converting the five degrees of freedom of the cylindrical shell into a single variable function by using a variable separation method; Step S2: Calculate the strain energy and kinetic energy of the orthotropic cylindrical shell without stiffeners; Calculate the strain energy and kinetic energy of the stiffeners; Step S3: combining the Lagrange interpolation function and the GLL integration point, dividing the stator axially into segments, and expressing the energy equations of the cylindrical shell and the stator teeth in matrix form, so as to obtain the stiffness matrix and mass matrix corresponding to the discretized cylindrical shell, and the stiffness matrix and mass matrix corresponding to the discretized stator teeth; Step S4: Add the stiffness matrix and mass matrix corresponding to the cylindrical shell and the stator teeth respectively to obtain the total stiffness matrix and the total mass matrix, solve the eigenvalues ​​of the total stiffness matrix and the total mass matrix, obtain the square of the natural angular frequency of the stator core and the fitting function of the displacement in all directions, and convert them to generate the natural frequency of the stator core.

2. The method for quickly calculating the natural frequency of the stator core according to claim 1, characterized in that: In step S1, the deformation of the cylindrical shell is expressed as: u(x,θ,z,t)=u0(x,θ,z,t)+zΨ x (x,θ,z,t) v(x,θ,z,t)=v0(x,θ,z,t)+zΨ θ (x,θ,z,t) w(x,θ,z,t)=w0(x,θ,z,t) Among them, u, v, w are the displacements of the cylindrical shell in the x, θ, and z directions respectively, u0, v0, w0 are the displacements of the neutral surface in the x, θ, and z directions respectively, ψ x , ψ θ is the rotation of the normal around the x and θ axes, and z is the radial coordinate; The strain of the cylindrical shell is expressed as: Among them, ε is the strain symbol, γ is the shear strain symbol, the subscript represents the strain direction, and R is the neutral surface radius.

3. The method for quickly calculating the natural frequency of the stator core according to claim 2, characterized in that: In step S1, the stator teeth are regarded as Euler beams, and the displacement equation of the stator teeth is obtained by the deformation coordination equation: in t =you s Ψ x v t =ve s Ψ θ In t =in Among them, u t , v t , w t is the displacement of the tooth in the x, y, and z directions of its own coordinate system, e s is the eccentricity between the neutral plane of the cylindrical shell and the center of the tooth.

4. The method for quickly calculating the natural frequency of the stator core according to claim 3, characterized in that: In step S2, the calculation process of the strain energy of the cylindrical shell is: in, is the strain energy of the cylindrical shell, σ is the stress symbol, the subscript represents the direction, E, G are the elastic modulus and shear modulus, the subscript represents the direction, and κ is the shear correction factor of the cylindrical shell; The calculation process of the kinetic energy of a cylindrical shell is: in, is the strain energy of the cylindrical shell, and ω is the natural angular frequency.

5. The method for quickly calculating the natural frequency of the stator core according to claim 4, characterized in that: Step S4 includes: using the formula The square of the natural angular frequency of the core and the fitting function of the displacement in all directions are obtained by solving the stiffness matrix and the coefficient matrix. After the transformation of ω=2πf, the natural frequency f of the stator core is obtained.

6. A fast calculation system for the natural frequency of a stator core, characterized in that: The stator core is composed of a stator yoke and stator teeth evenly distributed inside; the system includes: A stator core model building module is used to simplify the stator yoke into an orthotropic cylindrical shell and the stator teeth into reinforcing ribs uniformly distributed along the circumference; a five-degree-of-freedom cylindrical shell theoretical model is built, and the five degrees of freedom of the cylindrical shell are converted into a single variable function by using a variable separation method; Strain energy and kinetic energy calculation module, used to calculate the strain energy and kinetic energy of orthotropic cylindrical shells without stiffeners; calculate the strain energy and kinetic energy of stiffeners; The stiffness matrix and mass matrix calculation module is used to combine the Lagrange interpolation function and the GLL integration point to segment the stator axially, express the energy equations of the cylindrical shell and the stator teeth in a matrix form, and obtain the stiffness matrix and mass matrix corresponding to the discretized cylindrical shell, as well as the stiffness matrix and mass matrix corresponding to the discretized stator teeth; The natural frequency calculation module is used to add the stiffness matrix and mass matrix corresponding to the cylindrical shell and the stator teeth respectively to obtain the total stiffness matrix and the total mass matrix, solve the eigenvalues ​​of the total stiffness matrix and the total mass matrix, obtain the square of the natural angular frequency of the stator core and the fitting function of the displacement in all directions, and convert them to generate the natural frequency of the stator core.

7. The fast calculation system of the natural frequency of the stator core according to claim 6, characterized in that: In the stator core model building module, the deformation of the cylindrical shell is expressed as: u(x,θ,z,t)=u0(x,θ,z,t)+zΨ x (x,θ,z,t) v(x,θ,z,t)=v0(x,θ,z,t)+zΨ θ (x,θ,z,t) w(x,θ,z,t)=w0(x,θ,z,t) Among them, u, v, w are the displacements of the cylindrical shell in the x, θ, and z directions respectively, u0, v0, w0 are the displacements of the neutral surface in the x, θ, and z directions respectively, ψ x , ψ θ is the rotation of the normal around the x and θ axes, and z is the radial coordinate; The strain of the cylindrical shell is expressed as: Where ε is the symbol of strain, γ is the symbol of shear strain, the subscript represents the strain direction, and R is the radius of the neutral surface.

8. The fast calculation system of the natural frequency of the stator core according to claim 7, characterized in that: In the stator core model building module, the stator teeth are regarded as Euler beams, and the displacement equation of the stator teeth is obtained through the deformation coordination equation: in t =you s Ψ x v t =ve s Ψ θ In t =in Among them, u t , v t , w t is the displacement of the tooth in the x, y, and z directions of its own coordinate system, e s is the eccentricity between the neutral plane of the cylindrical shell and the center of the tooth.

9. The fast calculation system of the natural frequency of the stator core according to claim 8, characterized in that: In the strain energy and kinetic energy calculation module, the calculation process of the strain energy of the cylindrical shell is: in, is the strain energy of the cylindrical shell, σ is the stress symbol, the subscript represents the direction, E, G are the elastic modulus and shear modulus, the subscript represents the direction, and k is the shear correction factor of the cylindrical shell; The calculation process of the kinetic energy of a cylindrical shell is: Where ω is the natural angular frequency.

10. The fast calculation system of the natural frequency of the stator core according to claim 9, characterized in that: The natural frequency calculation module includes: using the formula The square of the natural angular frequency of the core and the fitting function of the displacement in all directions are obtained by solving the stiffness matrix and the coefficient matrix. After the transformation of ω=2πf, the natural frequency f of the stator core is obtained.

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