CN111666642A - Micro-vibration analysis method for flywheel rotor system - Google Patents

Micro-vibration analysis method for flywheel rotor system Download PDF

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CN111666642A
CN111666642A CN202010459229.7A CN202010459229A CN111666642A CN 111666642 A CN111666642 A CN 111666642A CN 202010459229 A CN202010459229 A CN 202010459229A CN 111666642 A CN111666642 A CN 111666642A
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韩勤锴
褚福磊
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Abstract

The invention discloses a micro-vibration analysis method of a flywheel rotor system, which comprises the following steps: aiming at four subsystems of a high-speed rotor, a bearing assembly, a flexible support and a vibration isolation device, a system rigid-flexible coupling nonlinear micro-vibration model is established, and an analysis method for inherent characteristics of the whole system is provided. On the basis of the analysis method of the inherent characteristics of the whole machine system, the mathematical description of the complex frequency response function of the system is deduced to quantitatively represent the vibration isolation performance of the whole machine, the influence rule of the unbalanced mass of the flywheel, the bearing waviness, the axial preload, the gravity of the flywheel, the flexible support rigidity, the rigidity and the damping of the vibration isolator on the micro-vibration of the whole machine is given, and the action mechanism of the rigidity and the damping parameters of the vibration isolation device and the flexibility of the mounting bracket on the vibration isolation performance of the whole machine is given. The analysis method clears up the mechanical characteristics of disturbance vibration of the flywheel, solves the key technical problems related to micro-vibration suppression of the whole machine, and has important guiding significance for micro-vibration control and vibration isolation device design of an actual flywheel rotor system.

Description

Micro-vibration analysis method for flywheel rotor system
Technical Field
The invention relates to the technical field of micro-vibration of a flywheel, in particular to a micro-vibration analysis method of a flywheel rotor system.
Background
The micro-vibration of the flywheel is one of the key problems restricting the development of high-precision and high-performance spacecrafts. At present, a mode of additionally arranging a vibration isolation device on a transmission path from a flywheel to a spacecraft is generally adopted, so that the influence of micro-vibration on the payload of the spacecraft is reduced, but the problem of the micro-vibration of the flywheel is solved only by mastering a micro-vibration mechanism of the flywheel and starting from the micro-vibration to suppress the micro-vibration.
At present, research work aiming at the micro-vibration mechanism of a high-speed flywheel has been carried out at home and abroad, but some key technical requirements are still not met: (1) no quantitative modeling method is available for the micro mechanical disturbance source of the flywheel structure; (2) the disturbance vibration mechanics model of the high-speed rotor is inaccurate; (3) the coupling transfer characteristics of the flywheel and the flexible support are not clear.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, the invention aims to provide a micro-vibration analysis method for a flywheel rotor system, which clears up the mechanical characteristics of disturbance vibration of a flywheel and solves the key technical problems related to the suppression of the vibration of the whole machine.
In order to achieve the above object, an embodiment of the present invention provides a method for analyzing micro-vibration of a flywheel rotor system, including the following steps: step S1, dividing the flywheel rotor system into four subsystems, including a high-speed rotor, a bearing assembly, a flexible support and a vibration isolation device, and establishing a complete machine nonlinear spring-mass centralized parameter analysis model of the flywheel rotor system; step S2, constructing a disturbance vibration equation set of the high-speed rotor according to load balance conditions based on a complete machine nonlinear spring-mass concentration parameter analysis model of the flywheel rotor system; step S3, carrying out load analysis on the bearing assembly based on the Hertz contact theory and the elastohydrodynamic lubrication theory to obtain contact deformation and contact angles between a rolling body and inner and outer raceways in the bearing assembly and a deformation position vector of an outer ring under the preloading action so as to construct a nonlinear supporting force vector of the bearing assembly; step S4, coupling the main shaft in the bearing assembly with five-direction freedom degree motion of the high-speed rotor through the bearing nonlinear supporting force vector to obtain a flexible support motion differential equation set, and calculating the coupling of the vibration isolation device with three-direction freedom degree motion of the flexible support to obtain a vibration isolation device motion differential equation set; and S5, sorting the high-speed rotor disturbance vibration equation set, the bearing assembly nonlinear supporting force vector, the flexible support motion differential equation set and the vibration isolation device motion differential equation set to obtain a complete machine system micro-vibration analysis model, and solving the complete machine system micro-vibration analysis model through a numerical method to obtain a flywheel rotor system micro-vibration response.
According to the method for analyzing the micro-vibration of the flywheel rotor system, the inherent characteristics of the whole system are analyzed, the vibration isolation performance of the whole system is quantitatively represented, the influence rule of relevant parameters on the micro-vibration of the whole system and the action mechanism of the vibration isolation performance are given, the mechanical characteristics of the disturbance vibration of the flywheel are cleared, the key technical problems related to the suppression of the vibration of the whole system are solved, and the method has important guiding significance for the design of the micro-vibration control and vibration isolation device of the actual flywheel rotor system.
In addition, the method for analyzing the micro-vibration of the flywheel rotor system according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the bearing assembly includes a bearing mounting housing, a left bearing, a main shaft, a right bearing, a bearing inner loading sleeve, and a bearing outer loading sleeve.
Further, in an embodiment of the present invention, the structural relationship of the flywheel rotor system is: the high-speed rotor is fixed with the outer ring of the angular contact ball bearing through the bearing mounting shell, one end of the main shaft is connected with the vibration isolation device, and the other end of the main shaft is supported on the deck plate shell.
Further, in an embodiment of the present invention, the step S2 further includes: neglecting the self structural vibration of the high-speed rotor, regarding the high-speed rotor as a concentrated mass, and establishing a grouping coordinate system X on the nonlinear spring-mass concentrated parameter analysis model of the complete machinefw-Yfw-Zfw(ii) a In the minuteGroup coordinate system Xfw-Yfw-ZfwMaking the high-speed rotor along Xfw，Yfw，ZfwThree-directional translation (u)fw，vfw，wfw) Winding Xfw，YfwOscillation of the shaft
Figure BDA0002510401900000021
Figure BDA0002510401900000022
And around ZfwTorsion of shafts
Figure BDA0002510401900000023
According to the balance relation of the forces, obtaining a disturbance equation set of the high-speed rotor:
Figure BDA0002510401900000024
Figure BDA0002510401900000025
Figure BDA0002510401900000026
Figure BDA0002510401900000027
Figure BDA0002510401900000028
Figure BDA0002510401900000029
wherein m isfw，Idfw，IpfwMass, diameter moment of inertia and pole moment of inertia, f, of the high speed rotorbLi，fbRi(i 1, 2., 5) represents the nonlinear disturbance vibration force and moment of the left and right angular contact bearings respectively,fu1，fu2，Tu1，Tu2for the excitation forces and moments caused by the unbalanced mass of the flywheel, Ω denotes the high-speed rotor speed.
Further, in one embodiment of the invention, the excitation force f caused by said flywheel unbalanced mass resulting from the static imbalance between the spokes and hub of the actual high speed rotoru1，fu2The calculation formula is as follows:
Figure BDA00025104019000000210
Figure BDA0002510401900000031
wherein, Us＝msrmsRepresenting excitation of static unbalance, msRepresenting the static unbalance mass, rmsThe eccentricity is represented by the distance between the two elements,
Figure BDA00025104019000000313
an initial phase angle representing the amount of static unbalance.
Further, in one embodiment of the invention, the excitation torque T caused by the flywheel imbalance mass resulting from the dynamic imbalance between the spokes and hub of the actual high speed rotoru1，Tu2The calculation formula is as follows:
Figure BDA0002510401900000032
Figure BDA0002510401900000033
wherein, Ud＝mdrmdhfRepresenting dynamic unbalance excitation, mdRepresenting the dynamic unbalance mass, rmdRepresenting radial eccentricity, hfThe axial eccentricity is represented by the axial eccentricity,
Figure BDA0002510401900000034
an initial phase angle representing the amount of dynamic unbalance.
Further, in an embodiment of the present invention, the step S4 further includes: reducing a spindle in the bearing assembly to a concentrated mass; in a grouped coordinate system Xfw-Yfw-ZfwOne end of the main shaft is connected through the vibration isolation device, the other end of the main shaft is supported through the flexible support, and a motion differential equation set of the flexible support is obtained according to a force balance relation:
Figure BDA0002510401900000035
Figure BDA0002510401900000036
Figure BDA0002510401900000037
Figure BDA0002510401900000038
Figure BDA0002510401900000039
Figure BDA00025104019000000310
wherein k isx1，ky1，kz1Coupling stiffness, k, of the vibration isolation device in three directions, respectivelysxz，ksyzRespectively the coupling stiffness, k, of the transverse and axial movements of the spindlex2，ky2For the coupling stiffness of the deck housing, IsdIs the transverse moment of inertia of the main shaft, cspFor damping torsional vibrations of the main shaft, kspAs torsional stiffness of the main shaft, us，vs，wsThe three-dimensional translation direction is adopted,
Figure BDA00025104019000000311
Figure BDA00025104019000000312
in three swing directions, msFor statically unbalanced masses uf，vf，wfFreedom of movement of the vibration-isolating device in three spatial directions,/1，l2The distance between the high-speed rotor and the left and right bearings, fbLi，fbRi(i ═ 1, 2., 5) represents the nonlinear disturbance forces and moments of the left and right angular contact bearings, respectively.
Further, in an embodiment of the present invention, the step S4 further includes: simplifying the vibration isolation device into a centralized mass; in a grouped coordinate system Xfw-Yfw-ZfwAnd the vibration isolation device is connected with the satellite body through the flexible support, and a motion differential equation set of the vibration isolation device is obtained according to the force balance relation:
Figure BDA0002510401900000041
Figure BDA0002510401900000042
Figure BDA0002510401900000043
Figure BDA0002510401900000044
wherein k isfx，kfy，kfzRespectively the connection stiffness m of the flexible support in three directionsfIs the collective mass of the vibration isolation device, uf，vf，wfFreedom of movement of the vibration-isolating device in three spatial directions, IpfTo be the moment of inertia of the vibration-isolating device, cpfIs a rotation resistance of the vibration isolation device, kpfIn order to provide the vibration isolating device with torsional rigidity,
Figure BDA0002510401900000045
respectively shows the swing angular displacement of the fixed main shaft around three spatial directions,
Figure BDA0002510401900000046
for oscillatory displacement of the vibration-isolating device, /)1，l2Is the distance between the high-speed rotor and the left and right bearings, us，vs，wsRespectively representing the spatial three-directional displacement of the fixed main axis, thetasIndicating the rotational angle of the fixed spindle.
Further, in an embodiment of the present invention, the overall system micro-vibration analysis model is:
Figure BDA0002510401900000047
wherein the content of the first and second substances,
Figure BDA0002510401900000048
representing the system degree of freedom vector, M, K1，C1G is the mass, stiffness, damping and gyro matrix of the system, respectively, Fe，FgRepresenting excitation of unbalanced masses and excitation of self-gravity, FbRepresenting the non-linear disturbance force vector caused by the left and right bearings.
Further, in an embodiment of the present invention, the step S5 further includes: solving the contact deformation and the contact angle of the outer ring under the preset preload; inputting the contact deformation and the contact angle into a nonlinear algebraic equation, and iteratively solving to obtain the nonlinear vibration disturbing force of the left and right axes; substituting the nonlinear disturbance vibration force of the left shaft and the right shaft into the complete machine system micro-vibration analysis model, calculating the nonlinear disturbance vibration force of the bearing at the current moment by adopting a differential equation solver in MATLAB, judging whether the calculation moment exceeds a preset time, outputting the nonlinear disturbance vibration force of the bearing if the calculation moment exceeds the preset time, and otherwise, iterating the solving process.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a method for analyzing micro-vibration of a flywheel rotor system according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a flywheel overall system according to an embodiment of the invention;
FIG. 3 is a schematic diagram of a model for a non-linear spring-mass lumped parameter analysis of a whole machine in accordance with one embodiment of the invention;
FIG. 4 is a schematic view of an analytical degree of freedom of a flywheel rotor according to an embodiment of the present invention;
FIG. 5 is a schematic view of a flywheel rotor mass imbalance in which (a) is a static imbalance and (b) is a dynamic imbalance, according to one embodiment of the present invention;
FIG. 6 is an angular contact ball bearing analytical coordinate system in accordance with one embodiment of the present invention;
FIG. 7 is a schematic view showing waviness of inner and outer races and rolling elements of a bearing according to an embodiment of the present invention;
FIG. 8 is a schematic view of the loaded fore-aft raceway groove center of curvature and ball center according to one embodiment of the present invention;
FIG. 9 is a schematic diagram of rolling element forces and moments under load according to one embodiment of the present invention;
FIG. 10 is a bearing assembly analysis coordinate system according to one embodiment of the present invention;
FIG. 11 is a flowchart illustrating a complete machine system micro-vibration analysis model according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of a flywheel vibration test testing system according to one embodiment of the present invention;
FIG. 13 is a physical diagram of a test flywheel system according to one embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The following describes a micro-vibration analysis method of a flywheel rotor system according to an embodiment of the present invention with reference to the accompanying drawings.
FIG. 1 is a flow chart of a method for analyzing micro-vibration of a flywheel rotor system according to an embodiment of the present invention.
As shown in fig. 1, the method for analyzing the micro-vibration of the flywheel rotor system comprises the following steps:
in step S1, the flywheel rotor system is divided into four subsystems, including a high-speed rotor, a bearing assembly, a flexible support and a vibration isolation device, and a complete machine nonlinear spring-mass lumped parameter analysis model of the flywheel rotor system is established.
It should be noted that, as shown in fig. 2, the flywheel rotor system mainly includes a high-speed rotor, a bearing assembly, a deck plate housing, a mounting bracket, and the like, where the flexible support is equivalent to the mounting bracket and the deck plate bracket, and the bearing assembly includes a bearing mounting shell, a left bearing, a main shaft, a right bearing, a bearing inner loading sleeve, and a bearing outer loading sleeve. The structural relationship of the flywheel rotor system is as follows: the high-speed rotor is fixed with the outer ring of the angular contact ball bearing through a bearing mounting shell, one end of the main shaft is connected with the vibration isolation device, the vibration isolation device is connected with the mounting support, and the other end of the main shaft is supported on the deck plate shell. The mounting bracket is used for connecting the high-speed rotor and the satellite body. The flywheel rotor system is a complex rigid-flexible coupling system. As shown in fig. 3, during micro-vibration modeling, a non-linear spring-mass centralized parameter analysis model of the whole machine is established for four subsystems, namely a high-speed rotor, a bearing assembly, a deck plate support and a vibration isolation device, respectively, respective disturbance vibration analysis equations are given for the subsystems, and finally a micro-vibration analysis model of the whole machine system is obtained through equation set.
In step S2, a high-speed rotor disturbance equation set of the high-speed rotor is constructed according to a load balance condition based on a complete machine nonlinear spring-mass lumped parameter analysis model of the flywheel rotor system.
Specifically, as shown in fig. 4, the high-speed rotor is a complex spoke-type structure, structural vibration of the high-speed rotor itself needs to be ignored, the high-speed rotor is regarded as a concentrated mass, and a grouping coordinate system X is established on a nonlinear spring-mass concentrated parameter analysis model of the whole machinefw-Yfw-Zfw；
In a grouped coordinate system Xfw-Yfw-ZfwIn the following, considering six-freedom-degree motion of flywheel rotor system space, the high-speed rotor is enabled to move along Xfw，Yfw，ZfwThree-directional translation (u)fw，vfw，wfw) Winding Xfw，YfwOscillation of the shaft
Figure BDA0002510401900000061
Figure BDA0002510401900000062
And around ZfwTorsion of shafts
Figure BDA0002510401900000063
According to the balance relation of the forces, obtaining a disturbance equation set of the high-speed rotor:
Figure BDA0002510401900000064
wherein m isfw，Idfw，IpfwMass, diameter moment of inertia and pole moment of inertia, f, of the flywheel rotor, respectivelybLi，fbRi(i ═ 1, 2.., 5) represents the nonlinear disturbance forces and moments of the left and right angular contact bearings, respectively, fu1，fu2，Tu1，Tu2For the excitation forces and moments caused by the unbalanced mass of the flywheel, Ω denotes the high-speed rotor speed.
Further, the spokes and the hub of the actual flywheel are assembled by machining and assembling, so that an inevitable mass unbalance exists. As shown in fig. 5, two types of unbalanced excitation are considered in the embodiment of the present invention: static imbalance and dynamic imbalance.
For static imbalance, a time-varying force excitation will be induced, along Xfw，YfwComponent of the axis fu1，fu2The calculation formula is as follows:
Figure BDA0002510401900000065
Figure BDA0002510401900000066
wherein, Us＝msrmsRepresenting excitation of static unbalance, msRepresenting the static unbalance mass, rmsThe eccentricity is represented by the distance between the two elements,
Figure BDA0002510401900000067
an initial phase angle representing the amount of static unbalance.
For dynamic imbalances, a time-varying moment excitation will be induced, also along Xfw，YfwComponent of axis Tu1，Tu2The calculation formula is as follows:
Figure BDA0002510401900000071
Figure BDA0002510401900000072
wherein, Ud＝mdrmdhfRepresenting dynamic unbalance excitation, mdRepresenting the dynamic unbalance mass, rmdRepresenting radial eccentricity, hfThe axial eccentricity is represented by the axial eccentricity,
Figure BDA0002510401900000073
an initial phase angle representing the amount of dynamic unbalance.
In step S3, based on Hertz' contact theory and elastohydrodynamic lubrication theory, load analysis is performed on the bearing assembly to obtain contact deformation and contact angle between the rolling elements and the inner and outer raceways in the bearing assembly and a deformation position vector of the outer ring under preload, so as to construct a bearing assembly nonlinear bearing force vector.
Further, firstly, based on the Hertz contact theory and the elastohydrodynamic lubrication theory, the bearing load under preload is analyzed, specifically as follows:
the outer ring rotates at a constant speed with omega as the rotating speed. As shown in FIG. 6, the bearing global coordinate system (X-Y-Z) and the jth rolling element local coordinate system (X)j-yj-zj) Wherein, the center of X-Y-Z is fixed at the axle center of the bearing, Xj-yj-zjThen by ω about the Z axiscjRotation (omega)cjRepresenting the revolution speed of the rolling elements) regardless of the torsion of the bearing outer ring around the Z-axis, the vectors of the degrees of freedom in the remaining five directions of the outer ring are u ═ u, v, w, αu，θv]T. Accordingly, the preload vectors in the five directions are: f. ofp＝[fu，fv，fw，mu，mv]TWherein f isu，fv，fwForce loads in three directions, respectively, mu，mvThen the torque applied to the X, Y axes.
At a certain time, the position angle of the jth rolling element
Figure BDA0002510401900000074
Wherein phi is0Initial position angle, NbThe number of rolling elements. Without loss of generality, let phi00. At this moment, the load makes the outer ring move, and then the groove curvature center of the outer ring at the jth rolling element translates along the y and z axes and the swing displacement vector around the x axis is respectively:j＝[ξj，ηj，θj]T. Under the condition of small deformation, the deformation of the steel pipe is reduced,jcan be obtained by coordinate transformation of outer ring displacement u
j＝Tju+Δwj(4)
In the formula TjFor transforming the matrix, can be expressed as
Figure BDA0002510401900000075
Wherein R iso＝0.5de-(rgo-0.5db)cosβ0The distance from the bearing rotation axis to the curvature center of the outer ring raceway is shown. deIndicates the bearing pitch circle diameter, rgoDenotes the outer ring groove curvature radius, dbDenotes the ball diameter, β0Representing the bearing nominal contact angle.
Δ w in formula (4)jShowing additional displacement vectors due to the waviness of the inner and outer rings and the rolling elements of the bearing. As shown in FIG. 7, pij，pojRepresents the waviness of the inner and outer races in contact with the rolling elements j in the circumferential direction of the raceways, and qij，qojThe waviness in the axial direction is indicated. w is aij，wojRespectively showing the waviness of the rolling element j when contacting the inner raceway and the outer raceway. The waviness is a periodic function of time, and can be described as follows by using a harmonic function:
pij＝∑Aincos(ninωcjt+2π(j-1)/Nb+ψin)
Figure BDA0002510401900000081
poj＝∑Aoutcos(nout(Ω-ωcj)t+2π(j-1)/Nb+ψout)
Figure BDA0002510401900000082
Figure BDA0002510401900000086
Figure BDA0002510401900000087
wherein A isin，Bin，Aout，Bout，Cn，nin，nout，nbaAnd psiin，
Figure BDA0002510401900000088
ψout，
Figure BDA0002510401900000089
Respectively representing the amplitude, order and phase, omega, of the waviness of the various parts of the bearingsjIs the rolling body spin speed. Under pure rolling conditions, considering the structural form of fixed inner ring and rotating outer ring, the revolution speed of the rolling elements can be expressed as follows:
Figure BDA0002510401900000083
the rotation speed is as follows:
Figure BDA0002510401900000084
the geometrical relationships shown in fig. 6 and 7 are combined to see that:
Figure BDA0002510401900000085
when the bearing is unloaded, the rolling body is only contacted with the inner raceway and the outer raceway, but deformation does not occur, the mass center of the rolling body is collinear with the curvature centers of the inner raceway and the outer raceway, and as shown by a dotted line in FIG. 8, the contact angle is a nominal contact angle β0Once the outer ring is loaded, firstly the outer ring is moved, the rolling bodies are contacted with the inner and outer raceways to deform, so that the mass center of the rolling bodies is moved, and the three parts reach balance again, as shown by a solid line in fig. 8, the curvature center of the inner ring groove is always kept unchanged due to the fixation of the inner ring, and the displacement of the curvature center of the outer ring groove can be (ξ) from formula (4)j，ηj). The position of the center of the ball is to be quantified in (v)jy，vjz) Shows that the contact angle of the inner and the outer raceways is reduced to β due to the load effectojAnd the inner raceway contact angle increases to βij。
As shown in FIG. 8, before deformation, the center of curvature of the inner ring groove is spaced from the center of the ball by a distance LijAfter deformation the distance becomes lij. For the distance between the center of curvature of the outer ring groove and the center of the ball, similarly, from L before deformationojChange to loj. If the curvature radius of the inner and outer raceway grooves is rgi，rgoIn consideration of waviness of the respective parts of the bearing, there are
Lij＝rgi+pij-hci-(0.5db+wij) (10)
Loj＝rgo+poj-hco-(0.5db+woj) (11)
Wherein h isci，hcoThe thicknesses of the lubricating oil films between the rolling bodies and the inner and outer raceways are respectively shown. According to Hamrock and Dowson's results, the lubricating film thickness can be calculated from the following empirical formula:
hc＝2.69RxU0.67G0.53W-0.067(1-0.61e-0.73κ) (12)
in the formula (12)
Figure BDA0002510401900000091
Representing dimensionless speed, wherein η0Which represents the viscosity of the lubricating oil at atmospheric pressure and at a temperature of 200C,
Figure BDA0002510401900000092
the equivalent radius of the rolling direction of the rolling body is shown, the outer raceway contact is shown as "+", the inner raceway contact is shown as "-",
Figure BDA0002510401900000093
is an equivalent rotational speed, and dro，driThe diameters of the bearing outer raceway and the bearing inner raceway are respectively. G ═ E' cηpDenotes a dimensionless elastic modulus, wherein cηpIs a viscosity coefficient, E' ═ E/(1-v)2) Denotes the effective modulus of elasticity (E is the modulus of elasticity of the materialAnd v is the poisson's ratio).
Figure BDA0002510401900000094
Representing a dimensionless load, wherein QjIs the contact load between the rolling bodies and the raceways.
From the geometric relationship of FIG. 8, it can be obtained
Figure BDA0002510401900000095
Figure BDA0002510401900000096
Figure BDA0002510401900000097
Figure BDA0002510401900000098
The above formula is a geometric equation that needs to be satisfied in the load analysis. In addition to the geometrical conditions, load balancing conditions have to be met, respectively for the rolling elements and the bearing outer ring. Fig. 9 shows the stress situation of the jth rolling element. In the figure FcjAnd MgjThe centrifugal force and gyro moment to which the rolling elements rotate are shown
Figure BDA0002510401900000099
And Mgj＝IbωsjωcjsinαjWherein m isb，IbRespectively rolling body mass and moment of inertia, αjIs the included angle between the rotation axis and the z axis. Under pure rolling condition, can obtain
Figure BDA0002510401900000101
The contact force between the rolling body and the inner and outer raceways is respectively Qij，QojAnd (4) showing. According to the Hertz contact theory, it is possible to obtain:
Figure BDA0002510401900000102
wherein, Ki，KoAndij，ojthe contact rigidity coefficient and the contact deformation of the rolling body and the inner and outer raceways are respectively. As can be seen from the above-described geometric analysis,ij＝lij-Lijandoj＝loj-Loj. When in useij，ojWhen greater than 0, χij＝1，χoj1 is ═ 1; when in useij，ojWhen the concentration is less than or equal to 0, χij＝0，χoj0. For the contact stiffness coefficient, it is determined by the geometric dimension of the contact area, the elasticity of the material, etc., there are
Figure BDA0002510401900000103
Wherein
Figure BDA0002510401900000104
The equivalent curvature radius and ellipticity corresponding to the rolling element and the inner raceway, and the rolling element and the outer raceway can be respectively calculated according to Harris' monograph, and further the contact stiffness coefficient K of the inner raceway and the outer raceway can be obtainedi，Ko。
In the force analysis, out-of-plane friction is ignored, assuming the gyro moment is exactly balanced by the moment created by the friction in the y-z plane, as shown in FIG. 9. Lambda [ alpha ]ij，λojThe coefficient of friction of the rolling elements in contact with the inner and outer raceways is shown as lambdaij，＝λoj1. From the force relationship of the rolling element given in FIG. 9, the following force balance equation of the rolling element can be obtained
Figure BDA0002510401900000105
Figure BDA0002510401900000106
Equations (17) and (18) are a pair of nonlinear algebraic equations. For each rolling element, a similar force balance equation exists.
In the load analysis, the load balance of the outer ring needs to be considered in addition to the stress balance of the rolling body. The magnitude of the load applied to the outer ring by the jth rolling body is QojAnd
Figure BDA0002510401900000107
the direction is opposite to that shown in fig. 9. These loads are converted to the center of curvature of the groove in the outer ring at the jth rolling element, with
Figure BDA0002510401900000108
The resultant force of all the rolling bodies acting on the outer ring
Figure BDA0002510401900000111
Wherein f isb＝[fbu，fbv，fbw，mbu，mbv]TThe vector of the resultant force of all rolling bodies acting on the outer ring, namely the nonlinear bearing force vector of the bearing is shown. For the bearing outer ring, there is the following force balance equation
fp-fb＝0 (21)
Simultaneous equations (17), (18) and (21) are used for solving the nonlinear algebraic equation system by iteration through a Newton-Raphson method. Obviously, the dimensions of the system of equations are: 2Nb+5. Further, according to the formulas (13) to (16), contact deformation between the rolling elements and the inner and outer raceways can be obtainedij，ojAnd contact angle βij，βoj. At the same time, the deformation displacement vector u of the outer ring under given preload can be obtainedo。
Then, the deformation displacement vector u of the outer ring under the given preload is obtained according to the aboveoAnd (3) solving the micro-amplitude disturbance vibration force of the bearing, specifically as follows:
as shown in FIG. 10, Xfw-Yfw-ZfwRepresenting a flywheel coordinate system, and XbL-YbL-ZbLAnd XbR-YbR-ZbRIndividual watchShowing the left and right bearing analysis coordinate system. The distance between the left and right support bearings and the center of mass of the flywheel is l1，l2. Flywheel at Xfw-Yfw-ZfwThe displacement vector in the coordinate system is:
Figure BDA0002510401900000112
the principal axis displacement vector is:
Figure BDA0002510401900000113
because the left and right bearing inner rings are fixedly connected with the main shaft, the bearing inner ring displacement can be obtained through the main shaft displacement through coordinate conversion.
According to FIG. 10, the pre-deformation u caused by the pre-load is taken into account by a coordinate transformationoThe relative deformation vector of the left bearing outer ring and the right bearing outer ring can be respectively obtained as
Figure BDA0002510401900000114
Figure BDA0002510401900000115
Wherein the content of the first and second substances,
Figure BDA0002510401900000121
and
Figure BDA0002510401900000122
respectively, the displacement vectors of the left and right bearing outer races, and TLAnd TRRepresenting the corresponding transformation matrix, as can be seen from the definition of the three coordinate systems in fig. 10:
Figure BDA0002510401900000123
and after the vibration displacement at the rotating body is converted into the displacement of the outer ring of the bearing, the nonlinear disturbance vibration force of the bearing is accurately solved through the previous nonlinear iterative equation. A calculation method of the nonlinear bearing force of the bearing is described by taking a left bearing as an example:
left bearingOuter ring displacement vector
Figure BDA0002510401900000124
Substituting the equation (4) to obtain the disturbance vibration displacement vector at the jth rolling body of the outer ring of the left bearingjL. Similarly, the force balance equation satisfied by each rolling element of the left bearing can also be obtained, as shown in equations (17) and (18). Simultaneous equations (17) and (18) are adopted, and a Newton-Raphson method is adopted to iteratively solve the nonlinear algebraic equation system (the dimension is 2N)b) And solving to obtain the displacement of each rolling element in the random coordinate system, and further obtaining the load vector applied by the jth rolling element to the bearing outer ring according to the equations (13) - (15) and the equation (19) as follows: [ Q ]yjL，QzjL，QθxjL]T. Therefore, under the overall coordinate system, the resultant force of all the rolling bodies acting on the outer ring (i.e. the disturbance force of the left bearing on the fixed main shaft) can be expressed as
Figure BDA0002510401900000125
Similarly, the same disturbance force vector can be obtained for the right bearing as follows:
Figure BDA0002510401900000126
due to the Hertz contact nonlinearity, the lubricating oil film, and the unidirectional contact between the rolling elements and the raceways (only compression and no tension), there is a nonlinear relationship between bearing perturbation force and displacement.
In step S4, the main shaft in the bearing assembly is coupled to the five-directional degree-of-freedom motion of the high-speed rotor by the bearing nonlinear supporting force vector to obtain a flexible support motion differential equation set, and the coupling of the vibration isolation device to the three-directional degree-of-freedom motion of the flexible support is calculated to obtain a vibration isolation device motion differential equation set.
In particular, the spindle in the bearing assembly is first simplified to a lumped mass msWith six degrees of freedom, including three-directional translation us，vs，wsAnd swinging in three directions
Figure BDA0002510401900000131
In a grouped coordinate system Xfw-Yfw-ZfwAnd the fixed main shaft and the high-speed rotor are coupled by the nonlinear vibration disturbing force of the bearing to realize the movement in five directions. One end of the fixed main shaft is connected through the vibration isolation device, the other end of the fixed main shaft is supported through the cabin plate shell, and a flexible support motion differential equation set is obtained according to the force balance relation:
Figure BDA0002510401900000132
wherein k isx1，ky1，kz1Coupling stiffness, k, in each of three directions of the vibration isolation devicesxz，ksyzCoupled stiffness, k, of transverse and axial movement of the spindle, respectivelyx2，ky2For the coupling stiffness of the deck housing, IsdIs the transverse moment of inertia of the main shaft, cspFor damping torsional vibrations of the main shaft, kspAs torsional stiffness of the main shaft, us，vs，wsThe three-dimensional translation direction is adopted,
Figure BDA0002510401900000133
in three swing directions, uf，vf，wfFor freedom of movement of the vibration-isolating device in three spatial directions, msFor statically unbalanced masses, /)1，l2The distance between the high-speed rotor and the left and right bearings, fbLi，fbRi(i ═ 1, 2., 5) represents the nonlinear disturbance forces and moments of the left and right angular contact bearings, respectively.
Next, the vibration isolation device is simplified to a lumped mass mfBesides being coupled with the fixed main shaft through rigidity, the flexible support is connected with the satellite body through the flexible support. In a grouped coordinate system Xfw-Yfw-ZfwAnd (3) obtaining a motion differential equation set of the vibration isolation device according to the balance relation of the forces:
Figure BDA0002510401900000134
wherein k isfx，kfy，kfzConnection stiffness m in three directions of the flexible support, respectivelyfFor the central mass of the vibration-isolating device, uf，vf，wfFreedom of movement of the vibration-isolating device in three spatial directions, IpfTo be the moment of inertia of the vibration-isolating device, cpfFor rotational damping of vibration-isolating devices, kpfIn order to provide the vibration isolating device with torsional rigidity,
Figure BDA0002510401900000135
respectively shows the swing angular displacement of the fixed main shaft around three spatial directions,
Figure BDA0002510401900000141
for oscillatory displacement of the vibration-isolating device, /)1，l2Is the distance between the high-speed rotor and the left and right bearings, us，vs，wsRespectively representing the spatial three-directional displacement of the fixed main axis, thetasIndicating the rotational angle of the fixed spindle.
That is, the flexibility and mass inertia of the fixed main shaft, the vibration isolation device and the cabin plate bracket are respectively considered, and respective motion differential equations are established, wherein the fixed main shaft and the high-speed rotor exert nonlinear force coupling action through the rolling bearing.
In step S5, the high-speed rotor disturbance vibration equation set, the bearing assembly nonlinear support force vector, the flexible support motion differential equation set, and the vibration isolation device motion differential equation set are sorted to obtain a complete machine system micro-vibration analysis model, and the complete machine system micro-vibration analysis model is solved by a numerical method to obtain a flywheel rotor system micro-vibration response.
Wherein, the whole system micro-vibration analysis model is as follows:
Figure BDA0002510401900000142
in the formula
Figure BDA0002510401900000143
Representing the system degree of freedom vector, M, K1，C1G is the mass, stiffness, damping and gyro matrix of the system, respectively, Fe，FgRepresenting excitation of unbalanced masses and excitation of self-gravity, FbRepresenting the non-linear disturbance force vector caused by the left and right bearings. The specific expression is as follows:
M＝diag([mfw，mfw，mfw，Idfw，Idfw，Ipfw，ms，ms，ms，Isd，Isd，Isp，mf，mf，mf，If]) (30)
Figure BDA0002510401900000144
Figure BDA0002510401900000145
G＝diag([ΩGfw，0]) (33)
Figure BDA0002510401900000151
because the coupling of the vibration disturbing force between the high-speed rotor and the main shaft concentrated mass through the nonlinear bearing is considered, the rigidity matrix K1The sub-matrix Kfw in (1) is 0,
Figure BDA0002510401900000152
the remainder of the submatrix is:
Figure BDA0002510401900000153
Figure BDA0002510401900000154
Kf＝diag([(kx1+kfx) (ky1+kfy) (kz1+kfz)]) (37)
the sub-matrices of the gyro matrix G may be represented as:
Figure BDA0002510401900000155
as the nonlinear disturbance vibration force of the bearing is considered, the differential equation set is a nonlinear coupling equation set and needs to be solved through a numerical method. As shown in FIG. 11, the solving process first solves for the contact deformation of the outer race at a given preloadojAnd contact angle βoj(ii) a Respectively obtaining the nonlinear disturbance vibration force of the left bearing and the right bearing by iteratively solving a nonlinear algebraic equation; substituting the system disturbance response into a complete machine system micro-vibration differential equation set formula (29), and calculating the system disturbance response at the current moment by adopting a differential equation solver (such as ODE45) in MATLAB. At each calculation time step, nonlinear iterative analysis is required to solve the accurate nonlinear disturbance vibration force of the bearing. If the calculation time does not exceed the set time length, the solving process is repeated until the calculation time is equal to the set calculation time length, and a calculation result is output.
Further, according to the method for analyzing the micro-vibration of the flywheel rotor system in the embodiment of the present invention, the intrinsic characteristics of the whole system of the micro-vibration system of the flywheel rotor system can be analyzed, including:
since the bearing perturbation force is non-linear, embodiments of the present invention linearize it. The linear stiffness springs in five directions are adopted to simulate the bearing function of the bearing, the influence of cross stiffness is ignored, namely the translation stiffness k along three axes is consideredb1，kb2，kb3And a rotational stiffness k about two axesb4，kb5. By definition, the bearing linear stiffness can be approximated by
Figure BDA0002510401900000161
The respective stiffness of the bearing can be calculated as
Figure BDA0002510401900000162
Figure BDA0002510401900000163
Wherein f isbu1，fbu2Respectively for solving kb1Given two preload values, ub1，ub2The bearing outer ring deformation amount is obtained. Similarly, fbv1，fbv2、fbw1，fbw2、mbu1，mbu2And mbv1，mbv2Respectively for solving kb2，kb3，kb4，kb5Respectively, and a pre-load value, vb1，vb2、wb1，wb2、
Figure BDA0002510401900000165
And
Figure BDA0002510401900000166
the corresponding deformation of the outer ring.
And preload values respectively set for solving, and corresponding outer ring deformation amounts. Below with kb1The solving process is specifically explained for the example. First of all a given preload fbu1The displacement u of the outer coil under the load can be obtained by simultaneously and iteratively solving equations (17), (18) and (21)b1(ii) a Changing the preload to fbu2(in general f will bebu1By adding a small amount fbu2) By a similar process, the linear displacement u under new load can be obtainedb2. The stiffness k along the X-axis can be obtained using equation (40)b1. Similarly, k can be determined separatelyb2，kb3，kb4，kb5。
After the equivalent linear stiffness of the bearing is obtained, a linearized complete machine system micro-vibration equation set is obtained by derivation according to the force balance principle
Figure BDA0002510401900000164
Wherein, the vector q of degree of freedom, mass, damping, gyro matrix M, C1G and an excitation vector Fe，FgThe same as in formula (29). Because the linearization treatment is carried out in advance, the nonlinear disturbance vibration force vector F of the bearing does not existbWhile the stiffness matrix K is required1Is updated to reflect the effect of the bearing linear stiffness. The specific expression is as follows:
Figure BDA0002510401900000171
Kfws＝Ksfw T＝-Kfw(43)
Figure BDA0002510401900000172
the inherent characteristics of the system include: natural frequency and mode shape. The mathematical result is a solution to the eigenvalue problem of the linear system shown in equation (41). If the influence of damping is neglected, the natural frequency and the mode shape of the system can be solved by the following characteristic value problem:
[ω2M+ωΩG+K1]d＝0 (45)
where ω denotes the system natural frequency and d denotes the corresponding eigenvector, i.e., mode shape. Equation (45) is a polynomial eigenvalue problem that can be solved using poieig in MATLAB. Due to the influence of the gyro term, the natural frequency of the system also changes (dynamic frequency) corresponding to different high-speed rotor rotating speeds.
Further, according to the method for analyzing the micro-vibration of the flywheel rotor system in the embodiment of the invention, a method for evaluating the vibration isolation performance of the whole micro-vibration system of the flywheel rotor system can be provided, which specifically comprises the following steps:
the vibration isolation device is additionally arranged between the flywheel complete machine and the satellite support, so that the transmission of the micro-vibration of the flywheel to the satellite body can be effectively reduced. How to evaluate the vibration isolation performance of the vibration isolation device is the key point for guiding the vibration isolation device with reasonable design. The embodiment of the invention aims at a linear whole machine flywheel system (shown as a formula (41)), and omits the gyro effect, so that the evaluation index of the vibration isolation performance is determined. When the system is subjected to any excitation action, laplace transform can be firstly carried out on two sides of the formula (41), and the initial condition is set to be zero, so that:
(s2M+sC+K1)x(s)＝P(s) (46)
wherein s represents a complex variable, x(s), and P(s) is q (t), (F)e(t)+Fg(t)) in the same manner. G(s) is a transfer function of the system, which is defined as
G(s)＝(s2M+sC+K1)-1(47)
The output of the system is then related to the input by equation (46) as follows:
x(s)＝G(s)P(s) (48)
from the equation (47), the transfer function matrix depends only on the physical properties of the system itself, such as mass, stiffness, and damping, and it can also be expressed as:
Figure BDA0002510401900000181
this formula is referred to as the modal expansion of G(s). Similarly to the single degree of freedom system, let s be i ω in equation (47), the complex frequency response function matrix H (ω) of the system is obtained, which is defined as
H(ω)＝(K1-ω2M+iωC)-1(50)
From equation (48), the output to input relationship in the frequency domain is given by
x(ω)＝H(ω)P(ω) (51)
Wherein x (ω) and P (ω) are q (t), (F)e(t)+Fg(t)) Fourier transform. From equation (49), the modal expansion of H (ω) can be found as:
Figure BDA0002510401900000182
its row r and column s elements are:
Figure BDA0002510401900000191
like the transfer function matrix, the complex frequency response function matrix depends only on the physical properties of the system itself. The application discloses the transmission characteristics of the micro-vibration of the whole machine under different vibration isolation rigidity and damping conditions according to the formulas (52) to (53).
Further, according to the method for analyzing the micro-vibration of the flywheel rotor system in the embodiment of the present invention, a method for verifying a model of the micro-vibration system of the flywheel rotor system and a method for analyzing a parameter influence may be further provided, including:
as shown in fig. 12 to 13, mainly includes: flywheel driving system equipment, micro-vibration test system equipment (including 9253B force measuring platform, charge amplifier, OR35 data acquisition instrument, test computer, etc.), and flywheel support frock. In the test, the coordinate is defined by the calibration direction of the force measuring table, the X direction is the horizontal width direction of the force measuring table, the Z direction is the direction vertical to the force measuring table, and the Y direction is the horizontal length direction of the force measuring table. In the test, the X direction is the direction of the air suction nozzle, and the Z direction is the direction of the H vector.
For testing parameters of a momentum wheel system, the embodiment of the invention provides that the waviness amplitude of the inner and outer raceways along the circumferential direction and the axial direction is 0.1 micron, and the order is twice of the number of rolling bodies, namely Nb24, the phases are all set to zero. According to theoretical analysis results, the characteristic frequencies caused by the waviness of the inner and outer raceways are different. For the inner raceway waviness, the characteristic frequency is:
Figure BDA0002510401900000192
for the waviness of the outer race, its characteristic frequency is
Figure BDA0002510401900000193
And after the parameters of the momentum wheel system are tested, drawing a three-dimensional waterfall layout of X-direction dynamic force and bending moment spectral lines according to the result measured by the force measuring platform, and obtaining a natural frequency curve of the whole flywheel system, the frequency related to the bearing waviness, the higher-order waviness frequency and the like. On the basis of inherent characteristic analysis, a numerical integration method is adopted to calculate the results of the dynamic force and the bending moment in the X direction of the system. Comparing the drawn three-dimensional waterfall graph, and judging whether the theoretical model basically reflects the frequency conversion, the natural frequency and the characteristic frequency of each order of the waviness of the inner circle and the outer circle according to the frequency components; from the amplitude, whether the frequency amplitude of the theory and the measured result is basically equivalent or not is judged. And analyzing from a quantitative angle, and obtaining the frequency spectrum results of the X-direction dynamic force and the dynamic moment of the flywheel system at a given rotating speed.
Finally, analyzing the influence of different parameters on different devices, specifically as follows:
(1) flywheel horizontal placement
And analyzing the influence of the unbalance amount of the flywheel, the amplitude of the bearing waviness and the influence of axial preload.
(2) T-shaped bracket flywheel
And analyzing the influence of the gravity of the flywheel and the influence of the rigidity of the flexible support.
(3) Flywheel with vibration isolation device on T-shaped support
Analyzing the vibration isolation performance of the whole machine: the complex frequency response function is adopted to represent the vibration isolation performance of the whole machine, and the influence rule of the rigidity and the damping of the vibration isolation device and the flexibility of the support on the vibration isolation performance of the whole machine is analyzed aiming at a test flywheel whole machine system; under the given vibration isolation device, the influence of the change of the flexibility of the support on the vibration isolation performance of the whole machine is analyzed.
The influence of the rigidity and the damping of the vibration isolator: and analyzing the change rule of the dynamic load of the system when the rigidity and the damping of different vibration isolators are analyzed.
In summary, the method for analyzing the micro-vibration of the flywheel rotor system provided by the embodiment of the invention establishes a dynamic model of static and dynamic unbalance disturbance vibration of the flywheel, and quantitatively describes the unbalance excitation force and couple; the coupling mechanism of the flexible vibration and the micromechanical disturbance vibration of the internal structure of the flywheel is determined, and the influence rule of the coupling mechanism on the output characteristic of the flywheel is analyzed; revealing the coupling mechanism of the internal structure of the flywheel and the gyro effect of the rotor and the influence rule of the coupling mechanism on the output characteristic, and verifying the rationality of the analysis result through tests; the mounting support and the deck plate are equivalent to a flexible support, the influence rule of the flexible support on the micro-vibration output characteristic of the flywheel is revealed aiming at the dynamic coupling phenomenon caused by the mode of the flywheel and the flexible support, and the effectiveness of the model can be verified through tests; and a dynamic parameter description method of the vibration isolation device is also provided, a flywheel-flexible support-vibration isolation device transmission analysis model is established, the micro-vibration transmission characteristics of the whole flywheel are revealed, and the effectiveness of the model can be verified through tests.
The method comprises the steps of firstly analyzing inherent characteristics of a whole machine system, then quantitatively representing vibration isolation performance of the whole machine, finally giving a rule of influence of relevant parameters on micro-vibration of the whole machine and an action mechanism of the vibration isolation performance, clearing mechanical characteristics of disturbance vibration of a flywheel, solving key technical problems related to suppression of vibration of the whole machine, and having important guiding significance for micro-vibration control and vibration isolation device design of an actual flywheel rotor system.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (10)

1. A micro-vibration analysis method of a flywheel rotor system is characterized by comprising the following steps:
step S1, dividing the flywheel rotor system into four subsystems, including a high-speed rotor, a bearing assembly, a flexible support and a vibration isolation device, and establishing a complete machine nonlinear spring-mass centralized parameter analysis model of the flywheel rotor system;
step S2, constructing a disturbance vibration equation set of the high-speed rotor according to load balance conditions based on a complete machine nonlinear spring-mass concentration parameter analysis model of the flywheel rotor system;
step S3, carrying out load analysis on the bearing assembly based on the Hertz contact theory and the elastohydrodynamic lubrication theory to obtain contact deformation and contact angles between a rolling body and inner and outer raceways in the bearing assembly and a deformation position vector of an outer ring under the preloading action so as to construct a nonlinear supporting force vector of the bearing assembly;
step S4, coupling the main shaft in the bearing assembly with five-direction freedom degree motion of the high-speed rotor through the bearing nonlinear supporting force vector to obtain a flexible support motion differential equation set, and calculating the coupling of the vibration isolation device with three-direction freedom degree motion of the flexible support to obtain a vibration isolation device motion differential equation set;
and S5, sorting the high-speed rotor disturbance vibration equation set, the bearing assembly nonlinear supporting force vector, the flexible support motion differential equation set and the vibration isolation device motion differential equation set to obtain a complete machine system micro-vibration analysis model, and solving the complete machine system micro-vibration analysis model through a numerical method to obtain a flywheel rotor system micro-vibration response.
2. The method of claim 1, wherein the bearing assembly of the flywheel rotor system comprises a bearing mounting housing, a left bearing, a main shaft, a right bearing, an inner bearing loading sleeve, and an outer bearing loading sleeve.
3. The method of claim 2, wherein the flywheel rotor system has a structural relationship of:
the high-speed rotor is fixed with the outer ring of the angular contact ball bearing through the bearing mounting shell, one end of the main shaft is connected with the vibration isolation device, and the other end of the main shaft is supported on the deck plate shell.
4. The method for analyzing micro-vibration of a flywheel rotor system as claimed in claim 1, wherein the step S2 further comprises:
neglecting the self structural vibration of the high-speed rotor, regarding the high-speed rotor as a concentrated mass, and establishing a grouping coordinate system X on the nonlinear spring-mass concentrated parameter analysis model of the complete machinefw-Yfw-Zfw；
In the grouped coordinate system Xfw-Yfw-ZfwMaking the high-speed rotor along Xfw，Yfw，ZfwThree-directional translation (u)fw，vfw，wfw) Winding Xfw，YfwOscillation of the shaft
Figure FDA0002510401890000011
And around ZfwTorsion of shafts
Figure FDA0002510401890000012
According to the balance relation of the forces, obtaining a disturbance equation set of the high-speed rotor:
Figure FDA0002510401890000021
Figure FDA0002510401890000022
Figure FDA0002510401890000023
Figure FDA0002510401890000024
Figure FDA0002510401890000025
Figure FDA0002510401890000026
wherein m isfw，Idfw，IpfwMass, diameter moment of inertia and pole moment of inertia, f, of the high speed rotorbLi，fbRi(i ═ 1, 2.., 5) represents the nonlinear disturbance forces and moments of the left and right angular contact bearings, respectively, fu1，fu2，Tu1，Tu2For the excitation forces and moments caused by the unbalanced mass of the flywheel, Ω denotes the high-speed rotor speed.
5. The method of claim 4, wherein the excitation force f caused by the mass of the flywheel imbalance resulting from the static imbalance between the spokes and hub of the actual high speed rotor is the excitation force f caused by the mass of the flywheel imbalanceu1，fu2The calculation formula is as follows:
Figure FDA0002510401890000027
Figure FDA0002510401890000028
wherein, Us＝msrmsRepresenting excitation of static unbalance, msRepresenting the static unbalance mass, rmsThe eccentricity is represented by the distance between the two elements,
Figure FDA0002510401890000029
an initial phase angle representing the amount of static unbalance.
6. The method of claim 4, wherein the excitation torque T is generated by a flywheel imbalance mass generated by a dynamic imbalance between the spokes and hub of the actual high speed rotoru1，Tu2The calculation formula is as follows:
Figure FDA00025104018900000210
Figure FDA00025104018900000211
wherein, Ud＝mdrmdhfRepresenting dynamic unbalance excitation, mdRepresenting the dynamic unbalance mass, rmdRepresenting radial eccentricity, hfThe axial eccentricity is represented by the axial eccentricity,
Figure FDA00025104018900000212
an initial phase angle representing the amount of dynamic unbalance.
7. The method for analyzing micro-vibration of a flywheel rotor system as claimed in claim 1, wherein the step S4 further comprises:
reducing a spindle in the bearing assembly to a concentrated mass;
in a grouped coordinate system Xfw-Yfw-ZfwOne end of the main shaft is connected through the vibration isolation device, and the other end of the main shaft is supported through the flexible support and is balanced according to forceAnd (3) obtaining a motion differential equation system of the flexible support:
Figure FDA0002510401890000031
Figure FDA0002510401890000032
Figure FDA0002510401890000033
Figure FDA0002510401890000034
Figure FDA0002510401890000035
Figure FDA0002510401890000036
wherein k isx1，ky1，kz1Coupling stiffness, k, of the vibration isolation device in three directions, respectivelysxz，ksyzRespectively the coupling stiffness, k, of the transverse and axial movements of the spindlex2，ky2For the coupling stiffness of the deck housing, IspIs the transverse moment of inertia of the main shaft, cspFor damping torsional vibrations of the main shaft, kspAs torsional stiffness of the main shaft, us，vs，wsThe three-dimensional translation direction is adopted,
Figure FDA0002510401890000037
Figure FDA0002510401890000038
in three swing directions, uf，vf，wfFor freedom of movement of the vibration-isolating device in three spatial directions, msFor statically unbalanced masses, /)1，l2The distance between the high-speed rotor and the left and right bearings, fbLi，fbRi(i ═ 1, 2., 5) represents the nonlinear disturbance forces and moments of the left and right angular contact bearings, respectively.
8. The method for analyzing micro-vibration of a flywheel rotor system as claimed in claim 1, wherein the step S4 further comprises:
simplifying the vibration isolation device into a centralized mass;
in a grouped coordinate system Xfw-Yfw-ZfwAnd the vibration isolation device is connected with the satellite body through the flexible support, and a motion differential equation set of the vibration isolation device is obtained according to the force balance relation:
Figure FDA0002510401890000039
Figure FDA00025104018900000310
Figure FDA00025104018900000311
Figure FDA00025104018900000312
wherein m isfFor the central mass of the vibration-isolating device, kfx，kfy，kfzRespectively the stiffness of the flexible support in three directions, uf，vf，wfFreedom of movement of the vibration-isolating device in three spatial directions, IpfMoment of inertia of the vibration isolation device, cpfFor rotational damping of vibration-isolating devices, kpfIn order to provide the vibration isolating device with torsional rigidity,
Figure FDA00025104018900000313
are respectively provided withRepresenting the swing angular displacement of the fixed main shaft around three spatial directions,
Figure FDA00025104018900000314
for oscillatory displacement of the vibration-isolating device, /)1，l2Is the distance between the high-speed rotor and the left and right bearings, us，vs，wsRespectively representing the spatial three-directional displacement of the fixed main axis, thetasIndicating the rotational angle of the fixed spindle.
9. The method for analyzing the micro-vibration of the flywheel rotor system according to claim 1, wherein the overall system micro-vibration analysis model is as follows:
Figure FDA0002510401890000041
wherein the content of the first and second substances,
Figure FDA0002510401890000042
representing the system degree of freedom vector, M, K1，C1G is the mass, stiffness, damping and gyro matrix of the system, respectively, Fe，FgRepresenting excitation of unbalanced masses and excitation of self-gravity, FbRepresenting the non-linear disturbance force vector caused by the left and right bearings.
10. The method for analyzing micro-vibration of a flywheel rotor system as claimed in claim 1, wherein the step S5 further comprises:
solving the contact deformation and the contact angle of the outer ring under the preset preload;
respectively obtaining the nonlinear disturbance vibration force of the left bearing and the right bearing by iteratively solving a nonlinear algebraic equation;
substituting the nonlinear disturbance vibration force of the left shaft and the right shaft into the complete machine system micro-vibration analysis model, calculating the micro-vibration response of the flywheel rotor system at the current moment by adopting a differential equation solver in MATLAB, if the calculation moment does not exceed the preset calculation time, iterating the solving process until the calculation moment is equal to the preset calculation time, and outputting a calculation result.
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