CN114547946B - Method for calculating orthogonal anisotropic material parameters of motor - Google Patents

Method for calculating orthogonal anisotropic material parameters of motor Download PDF

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CN114547946B
CN114547946B CN202210210340.1A CN202210210340A CN114547946B CN 114547946 B CN114547946 B CN 114547946B CN 202210210340 A CN202210210340 A CN 202210210340A CN 114547946 B CN114547946 B CN 114547946B
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谢颖
李道璐
蔡蔚
陈鹏
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Harbin University of Science and Technology
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Abstract

A method for calculating the parameters of orthotropic materials of a motor belongs to the field of motors. The invention aims to solve the problem that the existing method is difficult to calculate when the motor modal analysis is carried out. According to the method for calculating the parameter of the motor orthotropic material, the orthotropic analysis model taking the shell theory as the core is utilized, the easily measured low-order radial natural frequency and the corresponding order thereof are used as input conditions, and the parameter of the motor orthotropic material can be simply and quickly calculated. Meanwhile, the motor stator core lamination structure is considered, and errors caused by neglecting the reduction of axial rigidity are avoided; the low-order radial natural frequency and the corresponding order are used as input conditions, and the method is simple, accurate and easy to obtain.

Description

Method for calculating orthogonal anisotropic material parameters of motor
Technical Field
The invention belongs to the field of motors.
Background
The motor noise mainly comes from the electromagnetic vibration excited by the radial electromagnetic force wave of the motor, when the spatial distribution of the electromagnetic force wave is consistent with the vibration mode of the structural mode, and the frequency of the electromagnetic force wave is close to the modal frequency, the more obvious electromagnetic vibration noise can be generated, so the radial electromagnetic force wave and the structural mode are two important factors causing the motor vibration noise.
The calculation of the natural frequency is the key point in the structural modal research, the existing calculation methods are three, namely experimental test, simulation analysis and analytic calculation, and compared with the former two methods, the analytic calculation is simple and quick, and does not need experimental equipment and a large amount of simulation resources.
When an analytical method is applied to modal analysis, the stator core is mostly equivalent to an isotropic entity in the existing method. This method, however, ignores the problem of the reduction of axial stiffness caused by the lamination of the stator core and is therefore not accurate. Some methods consider the characteristic of the orthogonal anisotropy of the stator core, but the solution of the orthogonal anisotropy material is based on a method combining finite element simulation and experiments, and the method needs multiple attempts and is relatively time-consuming; meanwhile, for parts with high simulation modeling difficulty, such as end windings, accurate finite element calculation is difficult to achieve.
Disclosure of Invention
The invention provides a method for calculating parameters of an orthotropic material of a motor, aiming at solving the problem that the conventional method is difficult to calculate in the process of motor modal analysis.
A method for calculating the parameters of orthotropic materials of a motor comprises the following steps:
the method comprises the following steps: the method comprises the following steps that a shell, a stator core and a winding of a motor are equivalent to be of a tubular structure, a cylindrical coordinate system is established by taking the circle center of one end face of the tubular structure as an origin O, the X-axis direction of the cylindrical coordinate system is the axial direction of the tubular structure, the Z-axis direction of the cylindrical coordinate system is the radial direction of the tubular structure, and the Y-axis direction of the cylindrical coordinate system is the circumferential direction of the tubular structure;
step two: establishing a motion equation of the tubular structure while neglecting the moment of inertia:
Figure BDA0003530738560000011
Figure BDA0003530738560000012
Figure BDA0003530738560000013
wherein N isxAnd NyInternal force per unit length, N, of the tubular construction material in axial and circumferential directions, respectivelyxyIs the unit length force, q, of the tubular structural material in the XY cambered surfacex、qyAnd q iszAxial, circumferential and radial external pressure, u, v and w being any reference point on the tubular structureAxial, circumferential and radial displacement, ρ is the density of the tubular structure, h is the wall thickness of the tubular structure, QxAnd QyThe shear force is respectively axial and circumferential, R is the radius of the tubular structure, x is the displacement variable of the tubular structure along the axial direction, y is the displacement variable of the tubular structure along the circumferential direction, and t is time;
step three: according to the theory of shell vibration, Q is obtainedx、Qy、Nx、NxyAnd NyThe expression of (c):
Figure BDA0003530738560000021
Figure BDA0003530738560000022
wherein M isxAnd MyBending moments per unit length, M, in axial and circumferential directions, respectivelyxyBending moment per unit length, E, inside XY cambered surface of tubular structureyIs the modulus of elasticity in the circumferential direction,
Figure BDA0003530738560000023
and
Figure BDA0003530738560000024
axial and circumferential stresses, respectively,
Figure BDA0003530738560000025
is the stress in the XY cambered surface of the tubular structure, K is the rigidity of the motor, vxyV and vyxPrimary and secondary Poisson's ratios, G, of XY cambered surfaces respectivelyxyIs the shear modulus of the XY arc;
step four: assuming that the natural frequency, the expressions of the axial, circumferential and radial displacements u, v and w of any reference point on the tubular structure are:
Figure BDA0003530738560000026
wherein A, B and C are both axial, circumferential and radial amplitudes, m is an axial modal order, n is a radial modal order, and l is the axial length of the tubular structure;
step five: q obtained in the third stepx、Qy、Nx、NxyAnd NyAnd substituting u, v and w obtained in the fourth step into the motion equation in the second step to obtain a result matrix:
Figure BDA0003530738560000027
wherein the content of the first and second substances,
Figure BDA0003530738560000028
Figure BDA0003530738560000029
Figure BDA00035307385600000210
Figure BDA0003530738560000031
Figure BDA0003530738560000032
Figure BDA0003530738560000033
Exthe axial elastic modulus is shown, and the angular frequency is shown as omega-2 pi f;
step six: let m be 0, obtain n and f through the experiment, arrange the result matrix as:
Figure BDA0003530738560000034
Figure BDA0003530738560000035
Figure BDA0003530738560000036
Figure BDA0003530738560000037
Figure BDA0003530738560000038
step seven: making [ AB C ] in the result matrix after the arrangement in the sixth step]TWith a non-zero solution, then:
S′11(S′22S′33-S′23S′23)＝0，
step eight: since the tubular structure exists in the case where f/n is not constant:
S′11not equal to 0 and S'22S′33-S′23S′23＝0，
The elastic modulus E in the circumferential direction and the radial direction can be obtainedyAnd EzExpression (c):
Figure BDA0003530738560000039
step nine: dividing the tubular structure into a structure 1 and a structure 2 along the axial direction according to different stator core materials, and respectively obtaining Poisson ratios v of the structure 1 and the structure 21And v2，
Step ten: v obtained by step nine1And v2The Poisson's ratio v of the ZOY plane is obtained according to the following formulazyPrincipal Poisson's ratio of XY cambered surfaceνxyAnd Poisson's ratio v of XOZ planexz：
vzy＝v1α+v2(1-α)，
νyx＝0.03νxy＝0.03νxz＝νzy，
Wherein alpha is the ratio of the volume of the structure 1 in the total volume of the tubular structure;
step eleven: the primary and secondary Poisson's ratio v of XY cambered surfacexyV and vyxSubstituting E obtained in the step eightyAnd EzIn the expression (2), the modulus of elasticity E in the circumferential direction and the radial direction is obtainedyAnd EzThen E is addedyAnd EzSubstituting the formula to obtain the axial elastic modulus E of the tubular structurex：
Figure BDA0003530738560000041
Step twelve: will EyAnd vzySubstituting the following formula to obtain the shear modulus G of the ZOY planezy：
Figure BDA0003530738560000042
Step thirteen: the shear modulus G of the XY cambered surface was obtained according to the following formulaxyAnd shear modulus G in the XOZ planexz：
Figure BDA0003530738560000043
Wherein E is1And E2The modulus of elasticity for structure 1 and structure 2, respectively.
Further, bending moment M per unit length in the third stepx、MxyAnd MyRespectively as follows:
Figure BDA0003530738560000044
Figure BDA0003530738560000045
Figure BDA0003530738560000046
wherein D is the bending rigidity of the motor,
Figure BDA0003530738560000047
further, the motor bending stiffness D is expressed as follows:
Figure BDA0003530738560000048
further, the stress in the third step
Figure BDA0003530738560000049
And
Figure BDA00035307385600000410
are respectively:
Figure BDA00035307385600000411
Figure BDA0003530738560000051
Figure BDA0003530738560000052
further, the expression of the motor stiffness K in the third step is as follows:
Figure BDA0003530738560000053
further, in the fourth step, there is a hypothetical solution of the axial, circumferential and radial displacements u, v and w of any reference point on the tubular structure at the natural frequency:
u＝U(x,y)ejωt，v＝V(x,y)ejωt，w＝W(x,y)ejωt，
wherein U (x, y), V (x, y) and W (x, y) are the mode shapes of U, V and W respectively,
there is support at both ends of the tubular structure, then there is:
Figure BDA0003530738560000054
Figure BDA0003530738560000055
Figure BDA0003530738560000056
Figure BDA0003530738560000057
further, S 'in the eighth step'22S′33-S′23S′230 is expanded to:
Figure BDA0003530738560000058
wherein Z is 1-vxyνyx，
Figure BDA0003530738560000059
Further, the main Poisson ratio v of the XY cambered surfacexyThe unit tension or the tension strain in the X-axis direction is caused by the unit tension or the tension strain in the Y direction, and the sub-Poisson's ratio v of the XY cambered surfaceyxIs a unit pull in the Y-axis directionOr compressive strain induced compressive or tensile strain in the X direction.
Further, the stator core is a laminated structure formed by silicon steel sheets and epoxy resin sheets which are axially stacked, the silicon steel sheets in the tubular structure, the external windings and the casing of the silicon steel sheets are jointly used as a structure 1, the epoxy resin sheets in the tubular structure, the external windings and the casing of the epoxy resin sheets in the tubular structure are jointly used as a structure 2, the windings and the coils are in close contact, each structure in the structure 1 and the structure 2 is isotropic, and the Poisson ratio v of the structure 1 is V1The Poisson ratio v of the structure 1 is the average value of the Poisson ratio of the silicon steel sheet and the Poisson ratio of the winding outside the silicon steel sheet and the Poisson ratio of the shell2The epoxy poisson ratio and the average of the winding poisson ratio and the chassis poisson ratio outside the epoxy poisson ratio.
Further, the elastic modulus E of the above-described structures 1 and 21And E2Are respectively:
Figure BDA0003530738560000061
Figure BDA0003530738560000062
wherein, Eenc、Este、Ewin、EepoThe elastic modulus, V, of the case, the silicon steel sheet, the winding and the epoxy resin sheet respectivelyenc、Vste、VwinAnd VepoThe volumes of the shell, the silicon steel sheet, the winding and the epoxy resin sheet are respectively.
According to the method for calculating the parameter of the motor orthotropic material, the orthotropic analysis model taking the shell theory as the core is utilized, the easily measured low-order radial natural frequency and the corresponding order are used as input conditions, and the parameter of the motor orthotropic material is simply and quickly calculated. Meanwhile, the motor stator core lamination structure is considered, and errors caused by neglecting the reduction of axial rigidity are avoided; the low-order radial natural frequency and the corresponding order thereof are used as input conditions, and the method is simple, accurate and easy to obtain.
Drawings
FIG. 1 is a flow chart of a method of calculating orthotropic material parameters of a motor according to the present invention;
FIG. 2 is an equivalent model diagram of a tubular structure;
FIG. 3 is a schematic view of a stator core lamination stack;
fig. 4 is a graph of natural frequency experiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. It should be noted that the embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
The first embodiment is as follows: the present embodiment will be described in detail with reference to fig. 1 to 4, and in the method for calculating the parameters of the orthotropic material of the motor according to the present embodiment, since the rotor and the rotating shaft have little influence on the natural frequency, the present embodiment is only directed to the housing, the stator core, the winding, and the end cap. Therefore, based on the orthotropic analysis model with the shell theory as the core, the research object needs to be subjected to cylindrical shell equivalence first, that is, the shell, the stator core and the winding are equivalent to the shell, and the end covers at the two ends are used as the supporting structures, that is: the shell, the stator core and the winding of the motor are equivalent to a tubular structure.
For the convenience of analysis, a cylindrical coordinate system is established by using the center of a circle of one end face of the tubular structure as an origin O, the X-axis direction of the cylindrical coordinate system is the axial direction of the tubular structure, the Z-axis direction of the cylindrical coordinate system is the radial direction of the tubular structure, and the Y-axis direction of the cylindrical coordinate system is the circumferential direction of the tubular structure, as shown in fig. 2
The total number of the quantities to be solved in the coordinates is 9, which are respectively: modulus of elasticity E in the axial, circumferential and radial directionsx、EyAnd EzShear modulus G of ZOY planezyShear modulus G of XY cambered surfacexyAnd shear modulus G in the XOZ planexzPoisson ratio v of ZOY planezyAnd main Poisson ratio v of XY cambered surfacexyAnd Poisson's ratio v of the XOZ planexz。
In this embodiment, the stator core having a tubular structure is a laminated structure in which silicon steel sheets and epoxy resin sheets are stacked in an axial direction. So the materials of the XOZ plane and the XY cambered surface are orthotropic, and are orthotropic in the ZOY plane, the relationship of the material parameters is as follows: ey＝Ez≠Ex、Gxy＝Gxz≠Gzy、νxy＝νxz≠vzy。
Neglecting the moment of inertia, establishing a motion equation of the tubular structure in a cylindrical coordinate system:
Figure BDA0003530738560000071
wherein, NxAnd NyInternal force per unit length, N, in axial and circumferential directions, respectively, of the material of the tubular structurexyThe internal unit length force of the tubular structural material on the XY cambered surface; q. q.sx、qyAnd q iszAxial, circumferential and radial external pressures, respectively; u, v and w are the axial, circumferential and radial displacements of any reference point on the tubular structure, respectively; ρ is the density of the tubular structure; h is the wall thickness of the tubular structure, QxAnd QyAxial and circumferential shear forces, respectively; r is the radius of the tubular structure; x is the displacement variable of the tubular structure along the axial direction, and y is the displacement variable of the tubular structure along the circumferential direction; t is time.
According to the theory of shell vibration, Q is obtainedx、Qy、Nx、NxyAnd NyThe expression of (c):
Figure BDA0003530738560000072
Figure BDA0003530738560000073
in the above formula, MxAnd MyBending moments per unit length, M, in axial and circumferential directions, respectivelyxyThe bending moment per unit length in the XY cambered surface of the tubular structure is expressed as follows:
Figure BDA0003530738560000081
Figure BDA0003530738560000082
and
Figure BDA0003530738560000083
axial and circumferential stresses, respectively,
Figure BDA0003530738560000084
the stress inside the XY cambered surface of the tubular structure is expressed as follows:
Figure BDA0003530738560000085
d is the bending rigidity of the motor, and the expression is as follows:
Figure BDA0003530738560000086
k is the rigidity of the motor, and the expression is as follows:
Figure BDA0003530738560000087
in the above formula, vxyV and vyxRespectively the primary and secondary Poisson ratios of XY cambered surfaces, wherein v is the primary Poisson ratio of the XY cambered surfacesxyIn the Y direction by unit tensile or compressive strain in the X-axis directionPoisson's ratio v of compressive or tensile strain, XY camberyxIs the compressive or tensile strain in the X direction caused by the unit tensile or compressive strain in the Y-axis direction.
EyIs the modulus of elasticity in the circumferential direction, GxyIs the shear modulus of the XY arc,
Figure BDA0003530738560000088
assuming a natural frequency f, there exists a hypothetical solution for the axial, circumferential and radial displacements u, v and w of any reference point on the tubular structure:
Figure BDA0003530738560000089
wherein, U (x, y), V (x, y) and W (x, y) are the mode shapes of U, V and W respectively.
Since in the actual structure of the motor, the two ends of the casing are respectively fixed by the end covers, that is, there are supports along the axial directions x-0 and x-l, which means that there is no displacement of the tubular structure at these two points, then there are:
Figure BDA0003530738560000091
u (x, y), V (x, y) and W (x, y) are expressed as follows:
Figure BDA0003530738560000092
substituting (10) into (8), the axial, circumferential and radial displacements u, v and w of any reference point on the tubular structure are expressed as:
Figure BDA0003530738560000093
wherein A, B and C are both axial, circumferential and radial amplitudes, m is the axial modal order, n is the radial modal order, and l is the axial length of the tubular structure.
Since the housing is free to vibrate, the external pressure in the axial direction, the tangential direction and the radial direction are all 0, and the result matrix is obtained by substituting (2), (3) and (11) into the motion equation of the formula (1):
Figure BDA0003530738560000094
the elements in the above matrix are as follows:
Figure BDA0003530738560000095
Figure BDA0003530738560000096
Figure BDA0003530738560000097
Figure BDA0003530738560000098
Figure BDA0003530738560000099
Figure BDA0003530738560000101
in the above formula, ω ═ 2 pi f is an angular frequency.
Let m be 0, n and f be obtained by experiment, and (13) to (18) are collated to obtain:
Figure BDA0003530738560000102
Figure BDA0003530738560000103
Figure BDA0003530738560000104
Figure BDA0003530738560000105
S′12＝S′21＝0 (23)，
S′13＝S′31＝0 (24)。
therefore (12) can be arranged as:
Figure BDA0003530738560000106
[A B C]Tthe conditions with non-zero solutions are:
Figure BDA0003530738560000107
namely: s'11(S′22S′33-S′23S′23)＝0 (27)。
There are three conditions that can satisfy the above equation (27):
(a)S′110 and S'22S′33-S′23S′23＝0，
(b)S′110 and S'22S′33-S′23S′23≠0，
(c)S′11Not equal to 0 and S'22S′33-S′23S′23＝0。
In the above conditions (a) and (b), there is S'11If 0, substituting (19) then:
Figure BDA0003530738560000108
p, G due to tubular structurexyAnd R is constant, then there is:
Figure BDA0003530738560000111
wherein h is1Is a constant greater than 0.
As can be seen from equation (29), the conditions (a) and (b) are used under the following conditions: the ratio of any natural frequency f to its corresponding radial mode order n remains constant, i.e., f/n is constant. However, in most of the configurations, if f/n is not constant, that is, if the condition (c) is satisfied, then substituting (20) to (22) into the condition (c) includes:
S′22S′33-S′23S′23when 0, the formula is expanded to yield:
Figure BDA0003530738560000112
wherein Z is 1-vxyνyx，
Figure BDA0003530738560000113
E in the formula (30)yThe modulus of elasticity E in the circumferential and radial directions can be determined as unknownsyAnd EzExpression (c):
Figure BDA0003530738560000114
the silicon steel sheet in the tubular structure and the winding and the case outside the silicon steel sheet are taken together as a structure 1, and the epoxy resin sheet in the tubular structure and the winding and the case outside the silicon steel sheet are taken together as a structure 2, as shown in fig. 3. The winding coils are in intimate contact and each of the structures 1 and 2 is isotropic. Poisson ratio v of structure 11Is the Poisson's ratio of the silicon steel sheet and the outside thereofThe winding poisson's ratio of (a) and the case poisson's ratio; poisson ratio v of Structure 12Is the epoxy sheet poisson's ratio and the average of the winding poisson's ratio and the chassis poisson's ratio outside it.
Using v1And v2The Poisson's ratio v of the ZOY plane is obtained according to the following formulazyAnd the main Poisson's ratio v of the XY cambered surfacexyAnd Poisson's ratio v of the XOZ planexz：
vzy＝v1α+v2(1-α)，
νyx＝0.03νxy＝0.03νxz＝νzy，
Where α is the ratio of the volume of structure 1 to the total volume of the tubular structure.
The primary and secondary Poisson's ratio v of XY cambered surfacexyV and vyxSubstitution of formula (31) to obtain EyAnd Ez.
Then E isyAnd EzSubstituting the formula to obtain the axial elastic modulus E of the tubular structurex：
Figure BDA0003530738560000115
Then E is mixedyAnd vzySubstituting the following equation to obtain shear modulus G of ZOY planezy：
Figure BDA0003530738560000121
Further obtaining the shear modulus G of the XY cambered surface according to the following formulaxyAnd shear modulus G in the XOZ planexz：
Figure BDA0003530738560000122
Wherein, E1And E2The modulus of elasticity for structure 1 and structure 2, respectively.
At this point, the elastic modulus E of the orthotropic material parameter of the motor is finishedx、EyAnd EzShear modulus Gzy、GxyAnd GxzPoisson ratio vzy、νxyV and vxz。
In the above formula E1And E2Are respectively:
Figure BDA0003530738560000123
Figure BDA0003530738560000124
wherein, Eenc、Este、Ewin、EepoThe elastic modulus, V, of the case, the silicon steel sheet, the winding and the epoxy resin sheet respectivelyenc、Vste、VwinAnd VepoThe volumes of the shell, the silicon steel sheet, the winding and the epoxy resin sheet are respectively.
The elastic modulus E of the winding in the above formula is obtained because the winding is composed of copper wire and insulating materialwinThe following expression is given:
Ewin＝Ecopξ+Eins(1-ξ)，
wherein, EcopAnd EinsThe elastic modulus of the copper and the insulating material respectively, and xi is the groove filling rate of the copper.
In the case where m ≠ 0, equations (13), (16), and (18) can be rewritten into the following form:
Figure BDA0003530738560000125
Figure BDA0003530738560000126
Figure BDA0003530738560000127
further, the formula (12) is rewritten as follows:
Figure BDA0003530738560000128
due to [ A B C]TWith a non-zero solution, equation (35) can be simplified to a linear homogeneous equation:
ω6+k1ω4+k2ω2+k3＝0 (36)，
Figure BDA0003530738560000131
Figure BDA0003530738560000132
Figure BDA0003530738560000133
by solving ω in equation (36) as an unknown quantity, it is possible to obtain:
Figure BDA0003530738560000134
where i ═ 1,2,3, β is the phase, the expression is as follows:
Figure BDA0003530738560000135
then, the natural frequency f can be obtained according to the following formulai：
Figure BDA0003530738560000136
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
This embodiment selectsA three-phase permanent magnet synchronous motor with the model number YT-3000-8 is selected as an experimental motor, a rotor, a bearing and the like are removed, only an assembly structure of a shell, a stator core, a winding and two end cover supports is selected as an experimental prototype, the experimental prototype is suspended by a soft rope, and the experimental prototype is ensured to be in a free state as much as possible. The method is characterized in that an excitation point is selected along a prototype body, a hammering method is adopted to measure low-order natural frequency, and in order to improve the correlation between an acceleration signal and a force hammer signal and reduce errors caused by interference signals. Obtaining accurate experimental data (m, n, f) by adopting a method of knocking the same point for multiple times and averaging the transfer functionsExperiment of). Due to the limitation of experimental equipment, only two cases of 0 and 1 can be measured for the axial order m, and the radial order is not limited, and 2,3,4 and 5 are selected for the embodiment.
Will be (0, n, f)Experiment of) In several cases, the medium radial order n is 2,3,4,5, and 9 material parameters (0, n, f) are obtained by analytical calculation according to the method in the specific embodimentExperiment of)＝(0,n,fParse)。
Establishing a shell model with the same size as a prototype for finite element analysis, and calculating (0, n, f) by taking 9 material parameters as input conditionsFinite element)。
Comparing the natural frequencies of the same radial order n, when fExperiment ofAnd fFinite elementWhen the error is less than 5%, the rationality of the material solving method and the finite element model is indicated, otherwise, the finite element model needs to be tested or adjusted for many times, and the operation is repeated until the error is less than 5%.
When the material solving method and the finite element model are determined to be reasonable, the obtained 9 parameters are used as known conditions, and the natural frequency (m) is respectively calculated by an experimental method, a finite element method and a natural frequency analytic prediction method,n,f1)、(m,n,f2)、(m,n,f3) When m and n are the same, f1、f2And f3The basic consistency (the error is less than 5 percent) further illustrates the rationality of the natural frequency analysis prediction method. And if the error of the three is more than 5%, the analysis calculation needs to be carried out again until the requirement is met.
Reasonable analysis, finite element and experimental results are compared, error ratio is calculated, accurate material parameters, finite element models, high-order radial inherent frequency and each-order axial inherent frequency are obtained,
to verify the feasibility of the embodiment, simulation and experimental analysis are performed on the method of the embodiment, and the feasibility of the embodiment is further described in detail with reference to the simulation and experimental result table.
In the present embodiment, a prototype with h being 0.035m and R being 0.09055m was selected, and the results of the obtained 9 material parameters are shown in table 1, and the results of the analysis, simulation and comparison of the natural frequencies of the experiment are shown in table 2:
TABLE 1 Material parameters of prototype
Figure BDA0003530738560000141
TABLE 2 comparison of analytic, simulated and experimental natural frequencies
Figure BDA0003530738560000142
Figure BDA0003530738560000151
Wherein: a represents an analytical scheme, E represents an experimental scheme, S represents a simulation scheme, and the maximum error refers to the maximum value of the errors of AE, ES and AS in different radial orders.
Table 2 shows the comparison results of the natural frequencies obtained by the analysis, simulation and experiment methods, wherein the analysis results are calculated by applying the material parameters in table 1 to the above embodiment; the simulation result also takes the material parameters in table 1 as known conditions, and inputs the parameters into the finite element model to obtain (m, n, f), wherein m is 0,1, n is 2,3,4, 5; the experimental results are shown in fig. 4, but due to the limitation of the experimental equipment, only two cases of m being 0 and 1 can be measured.
As can be seen from table 2, when m is 0 and 1, the maximum errors of the analysis and experimental comparison are 0.31% and 1.44%, respectively, the maximum errors of the experimental and simulation comparison are 1.70% and 4.28%, respectively, and the maximum errors of the analysis and experimental, experimental and simulation do not exceed 5%, which verifies the correctness of the material parameter analysis method and the finite element model. When m is 2,3,4,5, the maximum error of the analytic calculation and the finite element simulation does not exceed 5%, and the rationality of the natural frequency method for predicting the shell m is not equal to 0 by using the material parameter obtained when m is 0 as the input condition is verified.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that various dependent claims and the features described herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (10)

1. A method for calculating the parameters of orthotropic materials of a motor is characterized by comprising the following steps:
the method comprises the following steps: the method comprises the following steps of equivalently forming a casing, a stator core and a winding of the motor into a tubular structure, establishing a cylindrical coordinate system by taking the circle center of one end face of the tubular structure as an origin O, wherein the X-axis direction of the cylindrical coordinate system is the axial direction of the tubular structure, the Z-axis direction of the cylindrical coordinate system is the radial direction of the tubular structure, and the Y-axis direction of the cylindrical coordinate system is the circumferential direction of the tubular structure;
step two: establishing a motion equation of the tubular structure while neglecting the moment of inertia:
Figure FDA0003530738550000011
wherein N isxAnd NyInternal force per unit length, N, in axial and circumferential directions, respectively, of the material of the tubular structurexyIs the internal unit length force of the tubular structural material in the XY cambered surface qx、qyAnd q iszAxial, circumferential and radial external pressure, u, v and w axial, circumferential and radial displacement of any reference point on the tubular structure, p is the density of the tubular structure, h is the thickness of the tubular structure wall, QxAnd QyThe shear force is respectively axial and circumferential, R is the radius of the tubular structure, x is the displacement variable of the tubular structure along the axial direction, y is the displacement variable of the tubular structure along the circumferential direction, and t is time;
step three: according to the theory of shell vibration, Q is obtainedx、Qy、Nx、NxyAnd NyExpression (c):
Figure FDA0003530738550000012
Figure FDA0003530738550000013
wherein M isxAnd MyBending moments per unit length, M, in axial and circumferential directions, respectivelyxyBending moment per unit length in the XY arc surface of the tubular structure, EyIs the modulus of elasticity in the circumferential direction,
Figure FDA0003530738550000014
and
Figure FDA0003530738550000015
axial and circumferential stresses, respectively,
Figure FDA0003530738550000016
stress in the XY cambered surface of the tubular structure, K is motor rigidity, vxyV and vyxPrimary and secondary Poisson's ratios, G, of XY cambered surfaces, respectivelyxyIs the shear modulus of the XY arc;
step four: assuming a natural frequency f, the expressions for the axial, circumferential and radial displacements u, v and w of any reference point on the tubular structure are:
Figure FDA0003530738550000017
Figure FDA0003530738550000021
Figure FDA0003530738550000022
wherein A, B and C are both axial, circumferential and radial amplitudes, m is the axial modal order, n is the radial modal order, l is the axial length of the tubular structure;
step five: q obtained in the third stepx、Qy、Nx、NxyAnd NyAnd substituting u, v and w obtained in the fourth step into the motion equation in the second step to obtain a result matrix:
Figure FDA0003530738550000023
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003530738550000024
Figure FDA0003530738550000025
Figure FDA0003530738550000026
Figure FDA0003530738550000027
Figure FDA0003530738550000028
Figure FDA0003530738550000029
Exis the elastic modulus in the axial direction, ω is the angular frequency and ω is 2 π f;
step six: let m be 0, obtain n and f through the experiment, arrange the result matrix as:
Figure FDA00035307385500000210
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00035307385500000211
Figure FDA00035307385500000212
Figure FDA0003530738550000031
Figure FDA0003530738550000032
step seven: making [ AB C ] in the result matrix after the arrangement in the sixth step]TWith a non-zero solution, then:
S′11(S′22S′33-S′23S′23)＝0；
step eight: since the tubular structure exists in the case where f/n is not constant:
S′11not equal to 0 and S'22S′33-S′23S′23＝0，
The elastic modulus E in the circumferential direction and the radial direction can be obtainedyAnd EzExpression (c):
Figure FDA0003530738550000033
step nine: dividing the tubular structure into a structure 1 and a structure 2 along the axial direction according to different stator core materials, and respectively obtaining Poisson ratios v of the structure 1 and the structure 21And v2；
Step ten: v obtained by step nine1And v2The Poisson's ratio v of the ZOY plane is obtained according to the following formulazyMain poisson ratio v of XY cambered surfacexyAnd Poisson's ratio v of XOZ planexz：
vzy＝v1α+v2(1-α)，
vyx＝0.03vxy＝0.03vxz＝vzy，
Wherein alpha is the ratio of the volume of the structure 1 in the total volume of the tubular structure;
step eleven: the primary and secondary Poisson's ratio v of XY cambered surfacexyV and vyxSubstituting E obtained in the step eightyAnd EzIn the expression (2), the modulus of elasticity E in the circumferential direction and the radial direction is obtainedyAnd EzThen E isyAnd EzSubstituting the formula to obtain the axial elastic modulus E of the tubular structurex：
Figure FDA0003530738550000034
Step twelve: will EyAnd vzySubstituting the following formula to obtain the shear modulus G of the ZOY planezy：
Figure FDA0003530738550000035
Step thirteen: obtaining the shear modulus G of the XY cambered surface according to the following formula under the condition that the winding coils are in close contactxyAnd shear modulus G in the XOZ planexz：
Figure FDA0003530738550000041
Wherein E is1And E2The modulus of elasticity of the material of structure 1 and the material of structure 2, respectively.
2. The method for calculating the parameters of orthotropic material of motor of claim 1, wherein the bending moment M per unit length in step threex、MxyAnd MyRespectively as follows:
Figure FDA0003530738550000042
Figure FDA0003530738550000043
Figure FDA0003530738550000044
wherein D is the bending rigidity of the motor,
Figure FDA0003530738550000045
3. the method for calculating the orthotropic material parameter of the motor according to claim 2, wherein the bending stiffness D of the motor is expressed as follows:
Figure FDA0003530738550000046
4. the method for calculating the parameters of orthotropic material of motor of claim 1, wherein the stress in step three is
Figure FDA0003530738550000047
And
Figure FDA0003530738550000048
are respectively:
Figure FDA0003530738550000049
Figure FDA00035307385500000410
Figure FDA00035307385500000411
5. the method for calculating the orthotropic material parameter of the motor as claimed in claim 1, wherein the motor stiffness K in the step three is expressed as:
Figure FDA00035307385500000412
6. the method for calculating the parameters of the orthotropic material of the motor of claim 1, wherein in step four, there are hypothetical solutions to the axial, circumferential and radial displacements u, v and w of any reference point on the tubular structure at the natural frequency:
u＝U(x,y)ejωt，v＝V(x,y)ejωt，w＝W(x,y)ejωt，
wherein U (x, y), V (x, y) and W (x, y) are the mode shapes of U, V and W respectively,
there is a support at both ends of the tubular structure, then there are:
Figure FDA0003530738550000051
Figure FDA0003530738550000052
Figure FDA0003530738550000053
Figure FDA0003530738550000054
7. the method for calculating the orthotropic material parameter of the motor as claimed in claim 1, wherein S 'in step eight'22S′33-S′23S′230 expansion is:
Figure FDA0003530738550000055
wherein Z is 1-vxyνyx，
Figure FDA0003530738550000056
8. The method of calculating orthotropic material parameters of an electrical machine according to claim 1,
main poisson ratio v of XY cambered surfacexyIs the compressive or tensile strain in the Y direction caused by the unit tensile or compressive strain in the X axis direction,
poisson ratio v of XY cambered surfaceyxIs the compressive or tensile strain in the X direction caused by the unit tensile or compressive strain in the Y-axis direction.
9. The method of claim 1, wherein the parameters of the orthotropic material of the motor are calculated,
the stator iron core is a laminated structure formed by laminating silicon steel sheets and epoxy resin sheets along the axial direction,
the silicon steel sheet in the tubular structure and the winding and the machine shell outside the silicon steel sheet are taken as a structure 1, the epoxy resin sheet in the tubular structure and the winding and the machine shell outside the silicon steel sheet are taken as a structure 2, wherein the winding coils are in close contact, and each structure in the structure 1 and the structure 2 is isotropic,
poisson ratio v of structure 11Is the average value of the poisson ratio of the silicon steel sheet and the poisson ratio of the winding outside the silicon steel sheet and the poisson ratio of the shell,
poisson ratio v of Structure 12The epoxy poisson ratio and the average of the winding poisson ratio and the chassis poisson ratio outside the epoxy poisson ratio.
10. The method for calculating orthotropic material parameters of motor of claim 9, wherein the elastic modulus E of structure 1 and structure 21And E2Are respectively:
Figure FDA0003530738550000057
Figure FDA0003530738550000061
wherein E isenc、Este、Ewin、EepoBullet of casing, silicon steel sheet, winding and epoxy resin sheet respectivelyModulus of elasticity, Venc、Vste、VwinAnd VepoThe volumes of the shell, the silicon steel sheet, the winding and the epoxy resin sheet are respectively.
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