CN116702470A - Method and system for determining supporting rigidity by considering simultaneous rotation of inner ring and outer ring of intermediate bearing - Google Patents

Method and system for determining supporting rigidity by considering simultaneous rotation of inner ring and outer ring of intermediate bearing Download PDF

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CN116702470A
CN116702470A CN202310671607.1A CN202310671607A CN116702470A CN 116702470 A CN116702470 A CN 116702470A CN 202310671607 A CN202310671607 A CN 202310671607A CN 116702470 A CN116702470 A CN 116702470A
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inner ring
bearing
outer ring
center
deformation
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孔程程
余文念
章朝栋
许晋
张玉东
余永波
何志祥
彭一真
黄文彬
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Chongqing University
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Chongqing University
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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Abstract

The invention discloses a method and a system for determining supporting rigidity by considering simultaneous rotation of an inner ring and an outer ring of an intermediate bearing, wherein the method is based on basic parameters of a bearing assembly and obtains the center O of a channel of the inner ring of the bearing ij Center O of outer ring channel oj Deformation delta in the contact plane ij 、δ oj Inner ring deformation u in fixed coordinate system with bearing inner ring i And outer ring deformation u o Is established with respect to the contact angle beta ij 、β oj And contact deformation delta ij 、δ oj Respectively establishing a static equilibrium equation and an outer ring of the inner ring in the direction of 5 degrees of freedom on a V axis and a W axis of a rotating coordinate systemStatic equilibrium equations in the 5 degrees of freedom direction, for the deformations u i And u o And deriving to obtain an analytic solution of the supporting rigidity matrix. By adopting the technical scheme, the supporting force of the inner ring and the outer ring of the bearing and the coupling effect of the deformation of the inner ring and the outer ring of the bearing are considered, so that more accurate supporting rigidity is obtained.

Description

Method and system for determining supporting rigidity by considering simultaneous rotation of inner ring and outer ring of intermediate bearing
Technical Field
The invention belongs to the technical field of bearing systems, and relates to a method and a system for determining supporting rigidity by considering simultaneous rotation of inner and outer rings of an intermediate bearing.
Background
As a key part bearing load in a rotating system, the rolling bearing has the advantages of small starting moment, vibration and noise reduction, easy replacement and the like, and is widely applied to the fields of automobiles, aerospace and the like. Modern aeroengines widely adopt a double-rotor structure, and a rolling bearing is generally adopted between an inner rotor and an outer rotor as an intermediate bearing for supporting the high-speed rotation of the inner rotor and the outer rotor. The rolling bearing connects the inner rotor and the outer rotor, so that the dynamic behaviors of the inner rotor and the outer rotor are coupled through the rolling bearing, and complex vibration behaviors are generated.
The rolling bearing has the function of supporting load and the function of motion connection in the rotating mechanism, and the rigidity change of the rolling bearing has an important influence on the working performance of the rotating system. Bearing support stiffness refers to the ability of a bearing to resist deformation under load, and stiffness characteristics are the primary factors affecting the dynamics of the engine rotor support system and coupled vibration characteristics. Under high-speed and heavy-load conditions, the supporting rigidity of the intermediate bearing changes nonlinearly with the born load and the rotating speed, so that the rigidity and the performance of the whole rotating system are influenced. Therefore, research on the method for calculating the supporting rigidity of the intermediate bearing is conducted, and the method has important significance for analyzing the dynamic characteristics of the rotating system and reducing vibration.
Because the equation related to the bearing quasi-static model is a nonlinear equation with high degree, the number of solved unknowns is large, and the conditions of non-convergence, low solving speed and the like are frequently encountered during solving. The relevant scholars therefore set forth empirical formulas for calculating the stiffness values of the bearings. However, the empirical formula only can roughly estimate the rigidity, and the calculated result has deviation in theory and practice. In addition, the conventional rolling bearing stiffness calculation method can only estimate translational stiffness in different directions under a static condition, but in a practical situation, bending deformation and coupling deformation in all directions generated under a dynamic running condition of the bearing can also directly influence the performance of the bearing. On the other hand, the existing bearing rigidity calculation method does not consider the coupling effect of the supporting force of the inner ring and the outer ring of the bearing and the deformation of the inner ring and the outer ring of the bearing. In the prior art, accurate and reasonable supporting rigidity is not obtained, dynamic modeling is carried out on a bearing system, dynamic characteristics cannot be accurately reflected, and vibration and usability of the bearing cannot be accurately analyzed.
Disclosure of Invention
The invention aims to provide a method and a system for determining supporting rigidity by considering simultaneous rotation of an inner ring and an outer ring of an intermediate bearing, so as to solve the problem that the existing method for calculating the bearing rigidity does not consider the coupling effect of supporting force of the inner ring and the outer ring of the bearing and deformation of the inner ring and the outer ring of the bearing, and cannot obtain accurate and reasonable supporting rigidity.
In order to achieve the above purpose, the basic scheme of the invention is as follows: a method for determining the supporting rigidity by considering the simultaneous rotation of the inner ring and the outer ring of an intermediate bearing comprises the following steps:
s1, acquiring basic parameters of a bearing assembly;
s2, based on small deformation hypothesis conditions, acquiring a center O of a groove of the inner ring of the bearing ij Center O of outer ring channel oj Deformation delta in the contact plane ij 、δ oj Inner ring deformation u in fixed coordinate system with bearing inner ring i And outer ring deformation u o Is a transformation relation of (2);
s3, according toInner ring channel curvature center I of bearing before and after deformation of inner ring and outer ring j And the outer ring channel curvature center O j Geometric relationship in contact plane, established with respect to contact angle beta ij 、β oj And contact deformation delta ij 、δ oj Is a deformation coordination equation of (1);
s4, respectively establishing a static equilibrium equation of the inner ring in the 5-degree-of-freedom direction and a static equilibrium equation of the outer ring in the 5-degree-of-freedom direction on a V axis and a W axis of a rotating coordinate system according to external force and external moment vectors of the given inner ring and outer ring in the 5-degree-of-freedom direction;
s5, supporting forces f of the inner ring and the outer ring of the bearing in the static balance equation of the inner ring and the outer ring according to the step S4 i and fo For the deformation u i and uo And deriving to obtain an analytic solution of the supporting rigidity matrix.
The working principle and the beneficial effects of the basic scheme are as follows: according to the technical scheme, the analytical calculation method for the bearing loading and deformation displacement is researched, an accurate mathematical model of the rigidity of the bearing under the given speed and load boundary conditions is established according to the basic principle of the rolling bearing kinematics and the Hertz contact theory, an analytical formula of a complete supporting rigidity matrix of the bearing is deduced, and the nonlinearity and time-varying characteristics of the supporting rigidity of the bearing during high-speed rotation of the rotating mechanism are fully considered.
The coupling elements of the bearing support stiffness matrix on the off-diagonal first are deduced through the method, and the influence of bending deformation and coupling deformation in different directions on stress is fully reflected. The invention not only calculates the supporting force f of the bearing inner ring i Supporting rigidity matrix caused by deformation of inner ring and supporting force f of outer ring of bearing o The supporting rigidity matrix caused by deformation of the outer ring is generated, and the supporting force f of the outer ring is calculated o Support rigidity matrix caused by deformation of inner ring and inner ring support force f i And generating a supporting rigidity matrix caused by deformation on the outer ring, and obtaining an accurate analytic solution of the supporting rigidity matrix. The bearings or the research objects are designed through the optimal parameters, so that the vibration of the system is reduced, and the running performance of the system is improved.
Further, the bearing assembly comprises rolling bodies, a bearing outer ring and a bearing inner ring;
basic parameters of the bearing assembly include nominal inner diameter, radial clearance, initial contact angle, number of rollers, inner raceway radius of curvature, outer raceway radius of curvature, radial and axial loads, bending moment, rotational speed, rotor eccentricity, bearing waviness, and support type.
Corresponding parameters are obtained, and subsequent use is facilitated.
Further, the method for obtaining the transformation relation in step S2 is as follows:
defining a fixed coordinate system X-Y-Z and a rotating coordinate system U-V-W, wherein the origin of the fixed coordinate system is positioned at the rotation center O of the inner ring and the outer ring; the origin of the rotating coordinate system is positioned at the geometric center O of the jth ball j The method comprises the steps of carrying out a first treatment on the surface of the For the bearing with both inner and outer rings rotating, the 5 degree of freedom vectors u of the inner and outer rings are defined i ＝{x i ,y i ,z i ,θ xi ,θ yi } T and uo ＝{x o ,y o ,z o ,θ xo ,θ yo } T ；x i The translational degree of freedom of the inner ring in the x direction; y is i The translational degree of freedom of the inner ring in the y direction; z i The translational degree of freedom of the inner ring in the z direction; θ xi The rotational freedom degree of the inner ring around the x axis is adopted; θ yi The rotational freedom degree of the inner ring around the y axis is set; x is x o The translational degree of freedom of the outer ring in the x direction; y is o The translational degree of freedom of the outer ring in the y direction; z o The translational degree of freedom of the outer ring in the z direction; θ xo The degree of freedom of rotation of the outer ring around the x axis is provided; θ yo The degree of freedom of rotation of the outer ring around the y axis is provided; the superscript T denotes the transpose of the matrix;
for the j-th ball, define the center O of the inner and outer ring channels ij ,O oj 3 degree of freedom vector delta in the contact plane ij ＝{v ij ,w ij ,θ uij } T and δoj ＝{v oj ,w oj ,θ uoj } T The method comprises the steps of carrying out a first treatment on the surface of the V in the rotation coordinate system U-V-W of the jth ball ij Translational degree of freedom of the center of the inner ring raceway in the v-axis direction; w (w) ij Is centered on the inner ring racewayTranslational degree of freedom in the w-axis direction; θ uij The rotational freedom degree of the center of the inner ring raceway in the u-axis direction is set; v oj The translational degree of freedom of the center of the outer ring raceway in the v-axis direction is set; w (w) oj The translational degree of freedom of the center of the outer ring raceway in the w-axis direction is set; θ uoj The rotational freedom degree of the center of the outer ring raceway in the u-axis direction is set;
deformation is generated under the action of external force and external moment, and the center O of a groove of the inner ring of the bearing oj Deformation delta in the contact plane oj Under the assumption of small deformation, the transformation relation is satisfied, and the relation expression is as follows:
δ oj ＝T oj u o
wherein ,Toj Is a bearing coordinate change matrix.
The operation is simple, and the use is facilitated.
Further, in step S3, a contact angle beta is established ij 、β oj And contact deformation delta between the jth ball and the inner and outer rings respectively ij 、δ oj The deformation coordination equation of (2) is as follows:
according to the geometrical relationship of the centers in the contact plane before and after the deformation of the inner ring and the outer ring, after the bearing inner ring and the outer ring are deformed under the stress, the center of the inner ring channel is formed by I j Move to I j ' the center of the outer ring raceway is formed by O j Move to O j ' the center of the ball is denoted by B j Move to B j '；
According to the contact angle beta ij 、β oj And contact deformation delta of the jth ball and the inner ring and the outer ring ij 、δ oj Is obtained by the geometric relationship:
and obtaining a deformation coordination equation after simplification:
wherein ,Awj and Avj Is available according to the geometric relationship;
A wj ＝(L oj +L ij )sinβ 0 +(w ij -w oj )
A vj ＝(L oj +L ij )cosβ 0 +(v ij -v oj )-r L
l ij ＝L ij +δ ij
l oj ＝L oj +δ oj
wherein ,rL Is the radial clearance of the bearing; l (L) oj and Lij Respectively an outer ring channel center Oj and an inner ring channel center I j From the center B of the ball j A distance; delta ij and δoj The contact deformation of the jth ball and the inner ring and the outer ring is realized; w (w) ij and vij Is deformation u of the inner ring under the action of external force and external moment i Resulting inner race channel center of curvature I j Displacement in the axial and radial directions; w (w) oj and voj Is deformation u of the outer ring under the action of external force and external moment o Resulting in an inner race channel center of curvature O j Displacement in the axial and radial directions; beta 0 Is the j-th ball center B j And a curvature center O of a bearing outer ring channel j The angle between a straight line formed in the contact plane and the radial straight line of the bearing is the nominal contact angle of the bearing; x is X wj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; x is X vj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system; a is that wj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; a is that vj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system.
Build-up of the contact angle beta ij 、β oj And contact deformation delta ij 、δ oj Is convenient to use.
Further, the method for establishing the static balance equation of the inner ring in the 5 degrees of freedom direction and the static balance equation of the outer ring in the 5 degrees of freedom direction in the step S4 is as follows:
according to the external force and external moment vector f of the inner ring and the outer ring in the 5 degrees of freedom direction i ＝{f xi ,f yi ,f zi ,M xi ,M yi } T and fo ＝{f xo ,f yo ,f zo ,M xo ,M yo } T ，f xi External force is applied to the inner ring in the X direction in a fixed coordinate system X-Y-Z; f (f) yi External force is applied to the inner ring in the Y direction in a fixed coordinate system X-Y-Z; f (f) zi External force is applied to the inner ring in the Z direction in a fixed coordinate system X-Y-Z; m is M xi The outer moment of the inner ring in the X direction in a fixed coordinate system X-Y-Z is applied to the inner ring; m is M yi The outer moment of the inner ring in the Y direction in a fixed coordinate system X-Y-Z is applied to the inner ring; f (f) xo External force applied to the outer ring in the X direction in a fixed coordinate system X-Y-Z; f (f) yo External force applied to the outer ring in the Y direction in a fixed coordinate system X-Y-Z; f (f) zo External force is applied to the outer ring in the Z direction in a fixed coordinate system X-Y-Z; m is M xo The outer ring is subjected to external moment in the X direction in a fixed coordinate system X-Y-Z; m is M yo The outer ring is subjected to external moment in the Y direction in a fixed coordinate system X-Y-Z;
establishing a static equilibrium equation of the inner ring and the outer ring in the 5-degree-of-freedom directions:
wherein ,Tij A bearing coordinate change matrix about the center of the inner ring channel; t (T) oj A bearing coordinate change matrix about the center of the outer ring channel; nb is the number of balls; psi phi type ij ＝{Q ij cosβ ij +f ij sinβ ij ,Q ij sinβ ij -f ij cosβ ij ,f ij r gi } T and ψoj ＝{-Q oj cosβ oj -f oj sinβ oj ,-Q oj sinβ oj +f oj cosβ oj ,f oj r go } T The j-th ball B is respectively arranged on the inner ring and the outer ring j The contact force and moment vectors in three directions in the contact plane are obtained by carrying out stress analysis on the inner ring and the outer ring:
to the inner ring
To the outer ring
wherein ,Φj Is the angular position of the jth roller in the circumferential direction from the X axis, R i For the inner ring rotation center O to the inner ring channel curvature center I j Distance in V direction, R o For the outer ring rotation center O to the outer ring channel curvature center O j Distance in V direction, r gi Is the curvature radius of the inner ring channel of the bearing, r go The curvature radius of the outer ring channel of the bearing is the curvature radius; q (Q) ij 、Q oj The outer ring and the inner ring are respectively contacted with the jth ball in the Hertz; beta ij 、β oj Contact angles of the balls with the inner ring channel and the outer ring channel are respectively; f (f) ij 、f oj Respectively by ball turning moment M gj The equivalent friction force of the inner ring and the outer ring on the balls in the contact plane is caused.
And a static equilibrium equation is established, so that the use is facilitated.
Further, in step S5, the deformation u i and uo The method for obtaining the supporting rigidity matrix is as follows:
according to the supporting force f of the bearing inner ring in the step S4 i The static equilibrium equation is constructed, and the deformation u of the bearing inner ring is calculated i Deriving to obtain a supporting bearing rigidity matrix K ii ：
And is also provided with
wherein ,
wherein ,Loj and Lij Respectively an outer ring channel center Oj and an inner ring channel center I j From the center B of the ball j A distance; delta ij and δoj The contact deformation of the jth ball and the inner ring and the outer ring is realized; k (K) ij and Koj The jth roller Hertz contact stiffness of the inner ring and the outer ring can be calculated by a contact stiffness formula; x-shaped articles ij and χoj Respectively corresponding to the contact coefficient, when the contact deformation delta ij Or delta oj When the X is greater than 0, X is ij Or χ oj Taking 1, otherwise taking 0; a is that wj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; a is that vj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system; x is X wj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; x is X vj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system;
according to the supporting force f of the bearing inner ring i The static equilibrium equation is constructed, and the deformation u of the outer ring of the bearing is calculated o Deriving to obtain a supporting bearing rigidity matrix K io ：
And is also provided with
wherein ,
according to the supporting force f of the outer ring of the bearing o The static equilibrium equation is constructed, and the deformation u of the outer ring of the bearing is calculated o Deriving to obtain a supporting bearing rigidity matrix K oo ：
And is also provided with
wherein ,
according to the supporting force f of the outer ring of the bearing o The static equilibrium equation is constructed, and the deformation u of the bearing inner ring is calculated i Deriving to obtain a supporting bearing rigidity matrix K oi ：
And is also provided with
wherein ,
from solved K ii 、K io 、K oo and Koi Obtaining a supporting rigidity matrix K of the intermediate bearing with the inner ring and the outer ring rotating simultaneously B ：
The comprehensive consideration is that an accurate and reasonable supporting rigidity matrix is obtained, and guidance is provided for dynamic characteristic analysis and high-reliability design of intermediate bearings in double-rotor structures of aeroengines, vehicle transmission systems and the like.
The invention also provides a system for determining the supporting rigidity by considering the simultaneous rotation of the inner ring and the outer ring of the intermediate bearing, which comprises a data acquisition module and a processing module, wherein the data acquisition module is used for acquiring basic parameters of a bearing assembly, the output end of the data acquisition module is connected with the input end of the processing module, and the processing module executes the method of the invention to acquire the supporting rigidity by considering the simultaneous rotation of the inner ring and the outer ring of the intermediate bearing.
The system is utilized to obtain the supporting rigidity of the inner ring and the outer ring of the intermediate bearing, which is simultaneously rotated, and the system is simple to operate and convenient to use.
Drawings
FIG. 1 is a flow chart of a method for determining the supporting rigidity by considering simultaneous rotation of inner and outer rings of an intermediate bearing according to the present invention;
FIG. 2 is a plan geometry diagram of the V-axis and W-axis of a rotational coordinate system of the method of determining support stiffness considering simultaneous rotation of inner and outer races of an intermediate bearing according to the present invention;
FIG. 3 is a diagram of the force applied to the j-th ball in the contact plane in consideration of the method for determining the supporting rigidity of the inner and outer rings of the intermediate bearing rotating simultaneously in the present invention;
FIG. 4 is an axial schematic view of a bearing in accordance with the present invention which contemplates a method of determining the support stiffness for simultaneous rotation of the inner and outer races of the intermediate bearing;
fig. 5 is a radial schematic view of a bearing in consideration of a method of determining support rigidity by which inner and outer rings of the bearing are simultaneously rotated.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
In the description of the present invention, it should be understood that the terms "longitudinal," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientation or positional relationships shown in the drawings, merely to facilitate describing the present invention and simplify the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the present invention.
In the description of the present invention, unless otherwise specified and defined, it should be noted that the terms "mounted," "connected," and "coupled" are to be construed broadly, and may be, for example, mechanical or electrical, or may be in communication with each other between two elements, directly or indirectly through intermediaries, as would be understood by those skilled in the art, in view of the specific meaning of the terms described above.
The invention discloses a method for determining supporting rigidity by considering simultaneous rotation of an inner ring and an outer ring of an intermediate bearing, which comprises the steps of establishing a rolling bearing quasi-static model under the condition of simultaneous rotation of the inner ring and the outer ring, calculating contact deformation and contact angle of each ball of the bearing with the inner ring and the outer ring under the boundary conditions of given speed and load, calculating a time-varying nonlinear bearing supporting rigidity matrix, calculating bending rigidity of the bearing and coupling rigidity in different directions, and calculating supporting forces f of the inner ring and the outer ring of the bearing under the boundary conditions of given speed and load i and fo The resulting intermediate bearing supports the stiffness matrix.
As shown in fig. 1, the support rigidity determination method includes the steps of:
s1, as shown in fig. 4 and 5, acquiring basic parameters of a bearing assembly, wherein the bearing assembly comprises rolling bodies, a bearing outer ring and a bearing inner ring; basic parameters of the bearing assembly include nominal inner diameter, radial clearance, initial contact angle, number of rollers, inner raceway radius of curvature, outer raceway radius of curvature, radial and axial loads, bending moments, rotational speed, rotor eccentricity, bearing waviness, and support type.
S2, based on small deformation hypothesis conditions, acquiring a center O of a groove of the inner ring of the bearing ij Center O of outer ring channel oj Deformation delta in the contact plane ij 、δ oj Inner ring deformation u in fixed coordinate system with bearing inner ring i And outer ring deformation u o Is a transformation relation of (2);
s3, as shown in FIG. 2, according to the curvature center I of the inner ring channel and the rear ring channel of the bearing before and after the deformation of the inner ring and the outer ring j Center of curvature O of outer ring channel j And the jth roller center B j Geometric relationship in contact plane, established with respect to contact angle beta ij 、β oj And contact deformation delta ij 、δ oj Is a deformation coordination equation of (1);
s4, respectively establishing a static equilibrium equation of the inner ring in the 5-degree-of-freedom direction and a static equilibrium equation of the outer ring in the 5-degree-of-freedom direction on a V axis and a W axis of a rotating coordinate system according to external force and external moment vectors of the given inner ring and outer ring in the 5-degree-of-freedom direction;
s5, supporting forces f of the inner ring and the outer ring of the bearing in the static balance equation of the inner ring and the outer ring according to the step S4 i and fo For the deformation u i and uo And deriving to obtain an analytic solution of the supporting rigidity matrix. The support stiffness of the bearing has an important influence on the dynamics of the rotating system, which influences the bearing to the overall natural frequency and frequency response. And accurately calculating a supporting rigidity matrix of the supporting bearing, and determining the mapping rule of non-deterministic factors (radial clearance, initial contact angle, number of rollers, radial and axial loads, bending moment, rotating speed, rotor eccentricity, bearing waviness and supporting type) and supporting rigidity of the supporting bearing. For example, the values of the rotating speed omega and the initial contact angle beta of the inner ring are changed, and the change curve of the time-varying support rigidity mean value of the support bearing is studied. And researching the relation between the uncertain parameters and the rigidity, obtaining the most suitable rigidity value or rigidity change by changing the uncertain parameters, and designing a bearing or a research object by the optimal parameters so as to reduce the vibration of the system and improve the running performance of the system. In addition, by analyzing the supporting rigidity of each part of the bearing, the distribution of the load can be analyzed by q=χk (δ), so that measures related to the suppression of the internal load can be taken.
In a preferred embodiment of the present invention, the method for obtaining the transformation relationship in step S2 includes:
defining a fixed coordinate system X-Y-Z and a rotating coordinate system U-V-W, wherein the origin of the fixed coordinate system is positioned at the rotation center O of the inner ring and the outer ring; the origin of the rotating coordinate system is positioned at the geometric center O of the jth ball j The method comprises the steps of carrying out a first treatment on the surface of the For the bearing with both inner and outer rings rotating, the 5 degree of freedom vectors u of the inner and outer rings are defined i ＝{x i ,y i ,z i ,θ xi ,θ yi } T and uo ＝{x o ,y o ,z o ,θ xo ,θ yo } T ；x i The translational degree of freedom of the inner ring in the x direction; y is i The translational degree of freedom of the inner ring in the y direction; z i The translational degree of freedom of the inner ring in the z direction; θ xi The rotational freedom degree of the inner ring around the x axis is adopted; θ yi The rotational freedom degree of the inner ring around the y axis is set; x is x o The translational degree of freedom of the outer ring in the x direction; y is o The translational degree of freedom of the outer ring in the y direction; z o The translational degree of freedom of the outer ring in the z direction; θ xo The degree of freedom of rotation of the outer ring around the x axis is provided; θ yo The degree of freedom of rotation of the outer ring around the y axis is provided; the superscript T denotes the transpose of the matrix;
as shown in FIG. 3, for the jth ball, the inner and outer ring channel centers O are defined respectively ij ,O oj A 3-degree-of-freedom vector delta in the plane of contact (i.e., V-W plane) ij ＝{v ij ,w ij ,θ uij } T and δoj ＝{v oj ,w oj ,θ uoj } T The method comprises the steps of carrying out a first treatment on the surface of the V in the rotation coordinate system U-V-W of the jth ball ij Translational degree of freedom of the center of the inner ring raceway in the v-axis direction; w (w) ij Translational degree of freedom of the center of the inner ring raceway in the w-axis direction; θ uij The rotational freedom degree of the center of the inner ring raceway in the u-axis direction is set; v oj The translational degree of freedom of the center of the outer ring raceway in the v-axis direction is set; w (w) oj The translational degree of freedom of the center of the outer ring raceway in the w-axis direction is set; θ uoj The rotational freedom degree of the center of the outer ring raceway in the u-axis direction is set;
deformation is generated under the action of external force and external moment, and the center O of a groove of the inner ring of the bearing oj Deformation delta in the contact plane oj Assumption of small deformationUnder the condition, the transformation relation is satisfied, and the relation expression is as follows:
δ oj ＝T oj u o
wherein ,Toj Is a bearing coordinate change matrix.
In a preferred embodiment of the invention, the contact angle β is established in step S3 ij 、β oj And contact deformation delta between the jth ball and the inner and outer rings respectively ij 、δ oj The deformation coordination equation of (2) is as follows:
according to the geometrical relationship of the centers in the contact plane before and after the deformation of the inner ring and the outer ring, after the bearing inner ring and the outer ring are deformed under the stress, the center of the inner ring channel is formed by I j Move to I j ' the center of the outer ring raceway is formed by O j Move to O j ' the center of the ball is denoted by B j Move to B j '；
According to the contact angle beta ij 、β oj And contact deformation delta of the jth ball and the inner ring and the outer ring ij 、δ oj Is obtained by the geometric relationship:
and obtaining a deformation coordination equation after simplification:
wherein ,Awj and Avj Is available according to the geometric relationship;
A wj ＝(L oj +L ij )sinβ 0 +(w ij -w oj )
A vj ＝(L oj +L ij )cosβ 0 +(v ij -v oj )-r L
l ij ＝L ij +δ ij
l oj ＝L oj +δ oj
wherein ,rL Is the radial clearance of the bearing; l (L) oj and Lij Respectively an outer ring channel center Oj and an inner ring channel center I j From the center B of the ball j A distance; delta ij and δoj The contact deformation of the jth ball and the inner ring and the outer ring is realized; w (w) ij and vij Is deformation u of the inner ring under the action of external force and external moment i Resulting inner race channel center of curvature I j Displacement in the axial and radial directions; w (w) oj and voj Is deformation u of the outer ring under the action of external force and external moment o Resulting in an inner race channel center of curvature O j Displacement in the axial direction (W) and the radial direction (V); beta 0 Is the j-th ball center B j And a curvature center O of a bearing outer ring channel j The angle between a straight line formed in the contact plane and the radial straight line of the bearing is the nominal contact angle of the bearing; x is X wj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; x is X vj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system; a is that wj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; a is that vj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system.
In a preferred embodiment of the present invention, the method for establishing the static equilibrium equation of the inner ring in the 5 degrees of freedom direction and the static equilibrium equation of the outer ring in the 5 degrees of freedom direction in step S4 is as follows:
according to the external force and external moment vector f of the inner ring and the outer ring in the 5 degrees of freedom direction i ＝{f xi ,f yi ,f zi ,M xi ,M yi } T and fo ＝{f xo ,f yo ,f zo ,M xo ,M yo } T ，f xi External force is applied to the inner ring in the X direction in a fixed coordinate system X-Y-Z; f (f) yi Is fixed on the inner ringExternal force is applied to the coordinate system X-Y-Z in the Y direction; f (f) zi External force is applied to the inner ring in the Z direction in a fixed coordinate system X-Y-Z; m is M xi The outer moment of the inner ring in the X direction in a fixed coordinate system X-Y-Z is applied to the inner ring; m is M yi The outer moment of the inner ring in the Y direction in a fixed coordinate system X-Y-Z is applied to the inner ring; f (f) xo External force applied to the outer ring in the X direction in a fixed coordinate system X-Y-Z; f (f) yo External force applied to the outer ring in the Y direction in a fixed coordinate system X-Y-Z; f (f) zo External force is applied to the outer ring in the Z direction in a fixed coordinate system X-Y-Z; m is M xo The outer ring is subjected to external moment in the X direction in a fixed coordinate system X-Y-Z; m is M yo The outer ring is subjected to external moment in the Y direction in a fixed coordinate system X-Y-Z;
establishing a static equilibrium equation of the inner ring and the outer ring in the 5-degree-of-freedom directions:
wherein ,Tij A bearing coordinate change matrix about the center of the inner ring channel; t (T) oj A bearing coordinate change matrix about the center of the outer ring channel; nb is the number of balls; psi phi type ij ＝{Q ij cosβ ij +f ij sinβ ij ,Q ij sinβ ij -f ij cosβ ij ,f ij r gi } T and ψoj ＝{-Q oj cosβ oj -f oj sinβ oj ,-Q oj sinβ oj +f oj cosβ oj ,f oj r go } T The j-th ball B is respectively arranged on the inner ring and the outer ring j The contact force and moment vectors in three directions in the contact plane are obtained by carrying out stress analysis on the inner ring and the outer ring:
to the inner ring
To the outer ring
wherein ,Φj Is the angular position of the jth roller in the circumferential direction from the X axis, R i For the inner ring rotation center O to the inner ring channel curvature center I j Distance in V direction, R o For the outer ring rotation center O to the outer ring channel curvature center O j Distance in V direction, r gi Is the curvature radius of the inner ring channel of the bearing, r go The curvature radius of the outer ring channel of the bearing is the curvature radius; q (Q) ij 、Q oj The outer ring and the inner ring are respectively contacted with the jth ball in the Hertz; beta ij 、β oj Contact angles of the balls with the inner ring channel and the outer ring channel are respectively; f (f) ij 、f oj Respectively by ball turning moment M gj The equivalent friction force of the inner ring and the outer ring on the balls in the contact plane is caused.
In a preferred embodiment of the invention, the deformation u is set in step S5 i and uo The method for obtaining the supporting rigidity matrix is as follows:
according to the supporting force f of the bearing inner ring in the step S4 i The static equilibrium equation is constructed, and the deformation u of the bearing inner ring is calculated i Deriving to obtain a supporting bearing rigidity matrix K ii ：
And is also provided with
wherein ,
wherein ,Loj and Lij Respectively an outer ring channel center Oj and an inner ring channel center I j From the center B of the ball j A distance; delta ij and δoj The contact deformation of the jth ball and the inner ring and the outer ring is realized; k (K) ij and Koj The jth roller Hertz contact stiffness of the inner ring and the outer ring can be calculated by a contact stiffness formula; x-shaped articles ij and χoj Respectively corresponding to the contact coefficient, when the contact deformation delta ij Or delta oj When the X is greater than 0, X is ij Or χ oj Taking 1, otherwise taking 0; a is that wj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; a is that vj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system; x is X wj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; x is X vj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system;
according to the supporting force f of the bearing inner ring i The static equilibrium equation is constructed, and the deformation u of the outer ring of the bearing is calculated o Deriving to obtain a supporting bearing rigidity matrix K io ：
And is also provided with
wherein ,
according to the supporting force f of the outer ring of the bearing o The static equilibrium equation is constructed, and the deformation u of the outer ring of the bearing is calculated o Deriving to obtain a supporting bearing rigidity matrix K oo ：
And is also provided with
wherein ,
according to the supporting force f of the outer ring of the bearing o The static equilibrium equation is constructed, and the deformation u of the bearing inner ring is calculated i Deriving to obtain a supporting bearing rigidity matrix K oi ：
And is also provided with
wherein ,
from solved K ii 、K io 、K oo and Koi Obtaining a supporting rigidity matrix K of the intermediate bearing with the inner ring and the outer ring rotating simultaneously B ：
The invention also provides a system for determining the supporting rigidity by considering the simultaneous rotation of the inner ring and the outer ring of the intermediate bearing, which comprises a data acquisition module and a processing module, wherein the data acquisition module is used for acquiring basic parameters of the bearing assembly (the specific data acquisition module can be connected with the man-machine interaction module and is used for inputting the basic parameters of the bearing assembly through the man-machine interaction module, and/or can also be connected with a sensor, the basic parameters of the bearing assembly can be acquired through the sensor, for example, the nominal inner diameter, the radial gap and the like are acquired through a distance sensor, the rotating speed is acquired through a rotating speed sensor), the output end of the data acquisition module is electrically connected with the input end of the processing module, and the processing module executes the method of the invention to acquire the supporting rigidity by simultaneously rotating the inner ring and the outer ring of the intermediate bearing. The system is utilized to obtain the supporting rigidity of the inner ring and the outer ring of the intermediate bearing, which is simultaneously rotated, and the system is simple to operate and convenient to use.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means 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 present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.

Claims (7)

1. A method for determining the supporting rigidity by considering the simultaneous rotation of the inner ring and the outer ring of an intermediate bearing is characterized by comprising the following steps:
s1, acquiring basic parameters of a bearing assembly;
s2, based on small deformation hypothesis conditions, acquiring a center O of a groove of the inner ring of the bearing ij Center O of outer ring channel oj Deformation delta in the contact plane ij 、δ oj Inner ring deformation u in fixed coordinate system with bearing inner ring i And outer ring deformation u o Is a transformation relation of (2);
s3, according to the curvature center I of the inner ring channel of the bearing before and after deformation of the inner ring and the outer ring j And the outer ring channel curvature center O j Geometric relationship in contact plane, established with respect to contact angle beta ij 、β oj And contact deformation delta ij 、δ oj Is a deformation coordination equation of (1);
s4, respectively establishing a static equilibrium equation of the inner ring in the 5-degree-of-freedom direction and a static equilibrium equation of the outer ring in the 5-degree-of-freedom direction on a V axis and a W axis of a rotating coordinate system according to external force and external moment vectors of the given inner ring and outer ring in the 5-degree-of-freedom direction;
s5, according to the inner bearing, the outer bearing and the inner bearing in the static balance equation in the step S4,Outer ring supporting force f i and fo For the deformation u i and uo And deriving to obtain an analytic solution of the supporting rigidity matrix.
2. The method for obtaining support determination considering simultaneous rotation of inner and outer rings of an intermediate bearing according to claim 1, wherein the bearing assembly comprises rolling elements, an outer ring of the bearing, and an inner ring of the bearing;
basic parameters of the bearing assembly include nominal inner diameter, radial clearance, initial contact angle, number of rollers, inner raceway radius of curvature, outer raceway radius of curvature, radial and axial loads, bending moment, rotational speed, rotor eccentricity, bearing waviness, and support type.
3. The method for determining the supporting rigidity considering simultaneous rotation of the inner ring and the outer ring of the intermediate bearing according to claim 1, wherein the method for obtaining the transformation relationship in step S2 is as follows:
defining a fixed coordinate system X-Y-Z and a rotating coordinate system U-V-W, wherein the origin of the fixed coordinate system is positioned at the rotation center O of the inner ring and the outer ring; the origin of the rotating coordinate system is positioned at the geometric center O of the jth ball j The method comprises the steps of carrying out a first treatment on the surface of the For the bearing with both inner and outer rings rotating, the 5 degree of freedom vectors u of the inner and outer rings are defined i ＝{x i ,y i ,z i ,θ xi ,θ yi } T and uo ＝{x o ,y o ,z o ,θ xo ,θ yo } T ；x i The translational degree of freedom of the inner ring in the x direction; y is i The translational degree of freedom of the inner ring in the y direction; z i The translational degree of freedom of the inner ring in the z direction; θ xi The rotational freedom degree of the inner ring around the x axis is adopted; θ yi The rotational freedom degree of the inner ring around the y axis is set; x is x o The translational degree of freedom of the outer ring in the x direction; y is o The translational degree of freedom of the outer ring in the y direction; z o The translational degree of freedom of the outer ring in the z direction; θ xo The degree of freedom of rotation of the outer ring around the x axis is provided; θ yo The degree of freedom of rotation of the outer ring around the y axis is provided; the superscript T denotes the transpose of the matrix;
for the followingThe j-th ball respectively defines the center O of the inner and outer ring channels ij ,O oj 3 degree of freedom vector delta in the contact plane ij ＝{v ij ,w ij ,θ uij } T and δoj ＝{v oj ,w oj ,θ uoj } T The method comprises the steps of carrying out a first treatment on the surface of the V in the rotation coordinate system U-V-W of the jth ball ij Translational degree of freedom of the center of the inner ring raceway in the v-axis direction; w (w) ij Translational degree of freedom of the center of the inner ring raceway in the w-axis direction; θ uij The rotational freedom degree of the center of the inner ring raceway in the u-axis direction is set; v oj The translational degree of freedom of the center of the outer ring raceway in the v-axis direction is set; w (w) oj The translational degree of freedom of the center of the outer ring raceway in the w-axis direction is set; θ uoj The rotational freedom degree of the center of the outer ring raceway in the u-axis direction is set;
deformation is generated under the action of external force and external moment, and the center O of a groove of the inner ring of the bearing oj Deformation delta in the contact plane oj Under the assumption of small deformation, the transformation relation is satisfied, and the relation expression is as follows:
δ oj ＝T oj u o
wherein ,Toj Is a bearing coordinate change matrix.
4. The method for determining supporting rigidity considering simultaneous rotation of inner and outer rings of intermediate bearing according to claim 1, wherein the method for determining supporting rigidity regarding contact angle β is established in step S3 ij 、β oj And contact deformation delta between the jth ball and the inner and outer rings respectively ij 、δ oj The deformation coordination equation of (2) is as follows:
according to the geometrical relationship of the centers in the contact plane before and after the deformation of the inner ring and the outer ring, after the bearing inner ring and the outer ring are deformed under the stress, the center of the inner ring channel is formed by I j Move to I j ' the center of the outer ring raceway is formed by O j Move to O j ' the center of the ball is denoted by B j Move to B j '；
According to the contact angle beta ij 、β oj And contact deformation delta of the jth ball and the inner ring and the outer ring ij 、δ oj Is obtained by the geometric relationship:
and obtaining a deformation coordination equation after simplification:
wherein ,Awj and Avj Is available according to the geometric relationship;
A wj ＝(L oj +L ij )sinβ 0 +(w ij -w oj )
A vj ＝(L oj +L ij )cosβ 0 +(v ij -v oj )-r L
l ij ＝L ij +δ ij
l oj ＝L oj +δ oj
wherein ,rL Is the radial clearance of the bearing; l (L) oj and Lij Respectively an outer ring channel center Oj and an inner ring channel center I j From the center B of the ball j A distance; delta ij and δoj The contact deformation of the jth ball and the inner ring and the outer ring is realized; w (w) ij and vij Is deformation u of the inner ring under the action of external force and external moment i Resulting inner race channel center of curvature I j Displacement in the axial and radial directions; w (w) oj and voj Is deformation u of the outer ring under the action of external force and external moment o Resulting in an inner race channel center of curvature O j Displacement in the axial and radial directions; beta 0 Is the j-th ball center B j And a curvature center O of a bearing outer ring channel j The angle between a straight line formed in the contact plane and the radial straight line of the bearing is the nominal contact angle of the bearing; x is X wj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; x is X vj Is the center B of the j-th ball after deformation j ' with outer race channelCenter of curvature O j ' distance on the V-axis in the rotational coordinate system; a is that wj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; a is that vj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system.
5. The method for determining the supporting rigidity considering simultaneous rotation of the inner ring and the outer ring of the intermediate bearing according to claim 1, wherein the method for establishing the static equilibrium equation of the inner ring in the 5-degree-of-freedom direction and the static equilibrium equation of the outer ring in the 5-degree-of-freedom direction in step S4 is as follows:
according to the external force and external moment vector f of the inner ring and the outer ring in the 5 degrees of freedom direction i ＝{f xi ,f yi ,f zi ,M xi ,M yi } T and fo ＝{f xo ,f yo ,f zo ,M xo ,M yo } T ，f xi External force is applied to the inner ring in the X direction in a fixed coordinate system X-Y-Z; f (f) yi External force is applied to the inner ring in the Y direction in a fixed coordinate system X-Y-Z; f (f) zi External force is applied to the inner ring in the Z direction in a fixed coordinate system X-Y-Z; m is M xi The outer moment of the inner ring in the X direction in a fixed coordinate system X-Y-Z is applied to the inner ring; m is M yi The outer moment of the inner ring in the Y direction in a fixed coordinate system X-Y-Z is applied to the inner ring; f (f) xo External force applied to the outer ring in the X direction in a fixed coordinate system X-Y-Z; f (f) yo External force applied to the outer ring in the Y direction in a fixed coordinate system X-Y-Z; f (f) zo External force is applied to the outer ring in the Z direction in a fixed coordinate system X-Y-Z; m is M xo The outer ring is subjected to external moment in the X direction in a fixed coordinate system X-Y-Z; m is M yo The outer ring is subjected to external moment in the Y direction in a fixed coordinate system X-Y-Z;
establishing a static equilibrium equation of the inner ring and the outer ring in the 5-degree-of-freedom directions:
wherein ,Tij A bearing coordinate change matrix about the center of the inner ring channel; t (T) oj A bearing coordinate change matrix about the center of the outer ring channel; nb is the number of balls; psi phi type ij ＝{Q ij cosβ ij +f ij sinβ ij ,Q ij sinβ ij -f ij cosβ ij ,f ij r gi } T and ψoj ＝{-Q oj cosβ oj -f oj sinβ oj ,-Q oj sinβ oj +f oj cosβ oj ,f oj r go } T The j-th ball B is respectively arranged on the inner ring and the outer ring j The contact force and moment vectors in three directions in the contact plane are obtained by carrying out stress analysis on the inner ring and the outer ring:
to the inner ring
To the outer ring
wherein ,Φj Is the angular position of the jth roller in the circumferential direction from the X axis, R i For the inner ring rotation center O to the inner ring channel curvature center I j Distance in V direction, R o For the outer ring rotation center O to the outer ring channel curvature center O j Distance in V direction, r gi Is the curvature radius of the inner ring channel of the bearing, r go The curvature radius of the outer ring channel of the bearing is the curvature radius; q (Q) ij 、Q oj The outer ring and the inner ring are respectively contacted with the jth ball in the Hertz; beta ij 、β oj Contact angles of the balls with the inner ring channel and the outer ring channel are respectively; f (f) ij 、f oj Respectively by ball turning moment M gj The inner and outer rings are caused to rollEquivalent friction of the beads in the contact plane.
6. The method for determining supporting rigidity considering simultaneous rotation of inner and outer rings of intermediate bearing according to claim 5, characterized in that the deformation u is set in step S5 i and uo The method for obtaining the supporting rigidity matrix is as follows:
according to the supporting force f of the bearing inner ring in the step S4 i The static equilibrium equation is constructed, and the deformation u of the bearing inner ring is calculated i Deriving to obtain a supporting bearing rigidity matrix K ii ：
And is also provided with
wherein ,
wherein ,Loj and Lij Respectively an outer ring channel center Oj and an inner ring channel center I j From the center B of the ball j A distance; delta ij and δoj The contact deformation of the jth ball and the inner ring and the outer ring is realized; k (K) ij and Koj The jth roller Hertz contact stiffness of the inner ring and the outer ring can be calculated by a contact stiffness formula; x-shaped articles ij and χoj Respectively corresponding to the contact coefficient, when the contact deformation delta ij Or delta oj When the X is greater than 0, X is ij Or χ oj Taking 1, otherwise taking 0; a is that wj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the W axis in the rotational coordinate system; a is that vj The curvature center I of the inner ring channel of the support bearing is formed after the inner ring and the outer ring are deformed j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system; x is X wj Is the center B of the j-th ball after deformation j ' and outer raceCenter of curvature O of channel j ' distance on the W axis in the rotational coordinate system; x is X vj Is the center B of the j-th ball after deformation j ' and outer race channel center of curvature O j ' distance on the V-axis in the rotational coordinate system;
according to the supporting force f of the bearing inner ring i The static equilibrium equation is constructed, and the deformation u of the outer ring of the bearing is calculated o Deriving to obtain a supporting bearing rigidity matrix K io ：
And is also provided with
wherein ,
according to the supporting force f of the outer ring of the bearing o The static equilibrium equation is constructed, and the deformation u of the outer ring of the bearing is calculated o Deriving to obtain a supporting bearing rigidity matrix K oo ：
And is also provided with
wherein ,
according to the supporting force f of the outer ring of the bearing o The static equilibrium equation is constructed, and the deformation u of the bearing inner ring is calculated i Deriving to obtain a supporting bearing rigidity matrix K oi ：
And is also provided with
wherein ,
from solved K ii 、K io 、K oo and Koi Obtaining a supporting rigidity matrix K of the intermediate bearing with the inner ring and the outer ring rotating simultaneously B ：
7. A system for determining the supporting rigidity by considering the simultaneous rotation of the inner ring and the outer ring of an intermediate bearing, which is characterized by comprising a data acquisition module and a processing module, wherein the data acquisition module is used for acquiring basic parameters of a bearing assembly, the output end of the data acquisition module is connected with the input end of the processing module, and the processing module executes the method of any one of claims 1-6 to acquire the supporting rigidity by the simultaneous rotation of the inner ring and the outer ring of the intermediate bearing.
CN202310671607.1A 2023-06-07 2023-06-07 Method and system for determining supporting rigidity by considering simultaneous rotation of inner ring and outer ring of intermediate bearing Pending CN116702470A (en)

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