CN112326242B - Contact rigidity measuring method and system for angular contact ball bearing - Google Patents

Contact rigidity measuring method and system for angular contact ball bearing Download PDF

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CN112326242B
CN112326242B CN202011209663.6A CN202011209663A CN112326242B CN 112326242 B CN112326242 B CN 112326242B CN 202011209663 A CN202011209663 A CN 202011209663A CN 112326242 B CN112326242 B CN 112326242B
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contact
rolling
rolling body
stiffness
rigidity
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CN112326242A (en
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陆凤霞
赵志强
王涛
鲍和云
靳广虎
朱如鹏
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0041—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress

Abstract

The invention relates to a method and a system for measuring contact rigidity of an angular contact ball bearing, belonging to the field of bearing rigidity measurement.

Description

Contact rigidity measuring method and system for angular contact ball bearing
Technical Field
The invention relates to the field of bearing rigidity measurement, in particular to a method and a system for measuring contact rigidity of an angular contact ball bearing.
Background
The angular contact ball bearing is a core supporting part in an aero-engine transmission system and a lubricating oil system, an oil film is formed between a rolling body and an inner ring/outer ring under the lubricating action, if a traditional Hertz contact rigidity calculation model based on dry friction is adopted, the influence of the lubricating effect on a contact angle and contact rigidity cannot be considered, larger deviation can be brought to the calculation of the contact rigidity of the bearing and the analysis of dynamic behavior, and accurate bearing load distribution and service life prediction cannot be obtained.
Disclosure of Invention
The invention aims to provide a method and a system for measuring contact rigidity of an angular contact ball bearing, which consider the lubricating effect, improve the measurement accuracy and provide more accurate technical parameters for bearing parameter design and service life estimation.
In order to achieve the purpose, the invention provides the following scheme:
an angular contact ball bearing contact stiffness measurement method, comprising:
acquiring coefficients, geometric parameters, mechanical parameters, speed parameters, materials and lubricating oil parameters of the angular contact ball bearing; the coefficients include: a first drag coefficient, a second drag coefficient, an oil film stiffness coefficient and a load-deformation coefficient; the geometric parameters include: the diameter of the rolling element, the diameter of a bearing pitch circle, the azimuth angle of the rolling element, the curvature radius of the inner and outer ring channels and the major semiaxis of the contact ellipse of the rolling element and the inner and outer rings; the mechanical parameters include: the centrifugal force of the rolling body, the gyro moment of the rolling body, the axial load of the inner ring and the radial load of the inner ring; the speed parameters include: the rotating speed of the inner ring, the revolution speed of the rolling body and the rotation speed of the rolling body; the material and oil parameters include: the comprehensive elastic modulus of the rolling body and the ferrule and the environmental viscosity of lubricating oil;
according to the coefficient, the geometric parameter, the mechanical parameter, the speed parameter, the material and lubricating oil parameters, obtaining a contact angle between the rolling body and the inner ring and a contact angle between the rolling body and the outer ring by using a rolling body contact angle calculation model, obtaining a comprehensive curvature radius of the rolling body in a rolling direction by using a rolling body contact micro-area geometric model, and obtaining a entrainment speed of the rolling body in the rolling direction by using a rolling body contact micro-area speed model; the comprehensive curvature radius of the rolling body in the rolling direction comprises: the comprehensive curvature radius of the rolling body and the inner ring in the rolling direction and the comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; the entrainment speed of the rolling bodies in the rolling direction comprises: the entrainment speed of the rolling body and the inner ring in the rolling direction and the entrainment speed of the rolling body and the outer ring in the rolling direction;
obtaining the contact rigidity of the rolling body by utilizing a rolling body contact rigidity calculation model according to the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction; the contact stiffness of the rolling bodies includes: the contact rigidity of the rolling body and the inner ring and the contact rigidity of the rolling body and the outer ring;
judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is yes, then
Obtaining the total contact rigidity of the rolling body by utilizing a rolling body total contact rigidity calculation model according to the contact angle between the rolling body and the inner ring and the contact angle between the rolling body and the outer ring; the total contact stiffness of the rolling elements comprises: axial contact stiffness of the rolling bodies and radial contact stiffness of the rolling bodies;
obtaining the rigidity of the bearing by utilizing a bearing rigidity calculation model according to the total contact rigidity of the rolling body; the stiffness of the bearing includes: the axial stiffness of the bearing and the radial stiffness of the bearing.
Optionally, the rolling element contact angle calculation model is as follows:
Figure GDA0003205634260000021
wherein alpha isijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle of the rolling body and the outer ring is shown; qijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; lambda [ alpha ]ijIs a first drag coefficient, λojIs the second drag coefficient; d is the diameter of the rolling body; fcjIs the centrifugal force of the rolling body; mgjA gyroscopic moment for the rolling elements; faThe axial load of the inner ring is taken; frIs the radial load of the inner ring; psijIs the azimuth angle of the rolling body;
the rolling element contact micro-area geometric model is as follows:
Figure GDA0003205634260000031
wherein R isbiyjIs the combined curvature radius of the rolling body and the inner ring in the rolling direction, RboyjThe comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; dmThe bearing pitch circle diameter;
the rolling element contact micro-area speed model is as follows:
Figure GDA0003205634260000032
wherein: u. ofbiyjIs the entrainment velocity u of the rolling body and the inner ring in the rolling directionboyjThe entrainment speed of the rolling body and the outer ring in the rolling direction; omegaiThe rotating speed of the inner ring; omegamThe revolution speed of the rolling body; omegaxbjComponent of rolling body rotation speed on x-axis, ωzbjComponent of rolling element rotation speed in z-axis, CRijThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the inner ring, CRojThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the outer ring is expressed as follows:
Figure GDA0003205634260000033
wherein: rijRadius of curvature of inner race channel, RojThe curvature radius of the outer ring channel is shown; a isijMajor semi-axis of ellipse of contact of rolling body with inner ring, aojThe long semi-axis of the ellipse is contacted by the rolling body and the outer ring.
Optionally, the rolling element contact stiffness calculation model is as follows:
Figure GDA0003205634260000034
wherein k iscjHertz contact stiffness, k, for the rolling body in contact with the Hertz contact regionfjThe oil film rigidity of the rolling body and the Hertz contact area is obtained; k is a radical ofefjThe oil film rigidity of the rolling body and the contact micro-area lubricating oil inlet is obtained; k is a radical ofjThe contact rigidity of the rolling body, namely the combined rigidity of the Hertz contact rigidity and the oil film rigidity; k is a radical ofnjIs the load-deflection coefficient; deltaejIs the elastic deformation of the rolling body; cjIs the oil film stiffness coefficient; e'jThe comprehensive elastic modulus of the rolling body and the ferrule; ryjThe comprehensive curvature radius of the rolling body in the rolling direction; u shapejIs a dimensionless speed parameter; gjIs a dimensionless material parameter; eta0Is the ambient viscosity of the lubricating oil; a isjThe long half shaft is a contact ellipse of the rolling body; h isminjThe minimum oil film thickness of the rolling body contact micro-area; u. ofyjThe rolling speed of the rolling body in the rolling direction is shown.
Optionally, the calculation model of the total contact stiffness of the rolling element is as follows:
Figure GDA0003205634260000041
wherein k isijContact stiffness of the rolling elements with the inner ring, kojContact stiffness of the rolling elements with the outer ring, kij、kojRespectively calculating the contact micro-areas of the rolling body and the inner ring/the outer ring by using a rolling body contact rigidity calculation model; k is a radical ofajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies, alphaijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle between the rolling body and the outer ring is shown.
Optionally, the bearing stiffness calculation model is as follows:
Figure GDA0003205634260000042
wherein, KaFor axial stiffness of the bearing, KrFor radial stiffness of the bearing, kajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies,. psijThe azimuth angle of the rolling elements.
Optionally, the angular contact ball bearing contact stiffness measuring method further includes:
judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is no, then
According to the contact rigidity of the rolling body, obtaining the contact load of the rolling body by utilizing a rolling body contact load calculation model; the contact load of the rolling bodies includes: the contact load of the rolling body and the inner ring and the contact load of the rolling body and the outer ring;
and updating the contact load of the rolling body contact angle calculation model, and recalculating the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring, the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction.
Optionally, the rolling element contact load calculation model is as follows:
Figure GDA0003205634260000051
wherein k isijContact stiffness of the rolling elements with the inner ring, kojThe contact rigidity of the rolling body and the outer ring is obtained; deltaeijIs the amount of elastic deformation, δ, of the rolling elements and the inner raceeojThe elastic deformation of the rolling body and the outer ring; h isminijIs the minimum oil film thickness of the rolling body and the inner ring, hminojThe minimum oil film thickness between the rolling body and the outer ring.
An angular contact ball bearing contact stiffness measurement system, the measurement system comprising:
the data acquisition module is used for acquiring the coefficient, the geometric parameter, the mechanical parameter, the speed parameter and the material and lubricating oil parameter of the angular contact ball bearing; the coefficients include: a first drag coefficient, a second drag coefficient, an oil film stiffness coefficient and a load-deformation coefficient; the geometric parameters include: the diameter of the rolling element, the diameter of a bearing pitch circle, the azimuth angle of the rolling element, the curvature radius of the inner and outer ring channels and the major semiaxis of the contact ellipse of the rolling element and the inner and outer rings; the mechanical parameters include: the centrifugal force of the rolling body, the gyro moment of the rolling body, the axial load of the inner ring and the radial load of the inner ring; the speed parameters include: the rotating speed of the inner ring, the revolution speed of the rolling body and the rotation speed of the rolling body; the material and oil parameters include: the comprehensive elastic modulus of the rolling body and the ferrule and the environmental viscosity of lubricating oil;
the contact angle, geometric parameter and speed parameter calculation module is used for obtaining a contact angle between the rolling body and the inner ring and a contact angle between the rolling body and the outer ring by utilizing a rolling body contact angle calculation model according to the coefficient, the geometric parameter, the mechanical parameter, the speed parameter, the material and the lubricating oil parameter, obtaining a comprehensive curvature radius of the rolling body in the rolling direction by utilizing a rolling body contact micro-area geometric model, and obtaining the entrainment speed of the rolling body in the rolling direction by utilizing a rolling body contact micro-area speed model; the comprehensive curvature radius of the rolling body in the rolling direction comprises: the comprehensive curvature radius of the rolling body and the inner ring in the rolling direction and the comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; the entrainment speed of the rolling bodies in the rolling direction comprises: the entrainment speed of the rolling body and the inner ring in the rolling direction and the entrainment speed of the rolling body and the outer ring in the rolling direction;
the contact rigidity calculation module of the rolling body is used for obtaining the contact rigidity of the rolling body by utilizing a rolling body contact rigidity calculation model according to the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction; the contact stiffness of the rolling bodies includes: the contact rigidity of the rolling body and the inner ring and the contact rigidity of the rolling body and the outer ring;
the judging module is used for judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is yes, then
The total contact rigidity calculation module of the rolling body is used for obtaining the total contact rigidity of the rolling body by utilizing a rolling body total contact rigidity calculation model according to the contact angle between the rolling body and the inner ring and the contact angle between the rolling body and the outer ring; the total contact stiffness of the rolling elements comprises: axial contact stiffness of the rolling bodies and radial contact stiffness of the rolling bodies;
the rigidity calculation module of the bearing is used for obtaining the rigidity of the bearing by utilizing a bearing rigidity calculation model according to the total contact rigidity of the rolling body; the stiffness of the bearing includes: the axial stiffness of the bearing and the radial stiffness of the bearing.
Optionally, the rolling element contact angle calculation model is as follows:
Figure GDA0003205634260000061
wherein alpha isijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle of the rolling body and the outer ring is shown; qijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; lambda [ alpha ]ijIs a first drag coefficient, λojIs the second drag coefficient; d is the diameter of the rolling body; fcjIs the centrifugal force of the rolling body; mgjA gyroscopic moment for the rolling elements; faThe axial load of the inner ring is taken; frIs the radial load of the inner ring; psijIs the azimuth angle of the rolling body;
the rolling element contact micro-area geometric model is as follows:
Figure GDA0003205634260000062
wherein R isbiyjIs the combined curvature radius of the rolling body and the inner ring in the rolling direction, RboyjThe comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; dmThe bearing pitch circle diameter;
the rolling element contact micro-area speed model is as follows:
Figure GDA0003205634260000063
wherein: u. ofbiyjIs the entrainment velocity u of the rolling body and the inner ring in the rolling directionboyjThe entrainment speed of the rolling body and the outer ring in the rolling direction; omegaiThe rotating speed of the inner ring; omegamThe revolution speed of the rolling body; omegaxbjComponent of rolling body rotation speed on x-axis, ωzbjComponent of rolling element rotation speed in z-axis, CRijThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the inner ring, CRojIn the geometry of rolling bodiesThe distance from the center to the contact elliptical surface of the rolling body and the outer ring is expressed as follows:
Figure GDA0003205634260000071
wherein: rijRadius of curvature of inner race channel, RojThe curvature radius of the outer ring channel is shown; a isijMajor semi-axis of ellipse of contact of rolling body with inner ring, aojA long semi-axis of an ellipse in which the rolling body is contacted with the outer ring;
the rolling body contact rigidity calculation model is as follows:
Figure GDA0003205634260000072
wherein k iscjHertz contact stiffness, k, for the rolling body in contact with the Hertz contact regionfjThe oil film rigidity of the rolling body and the Hertz contact area is obtained; k is a radical ofefjThe oil film rigidity of the rolling body and the contact micro-area lubricating oil inlet is obtained; k is a radical ofjThe contact rigidity of the rolling body, namely the combined rigidity of the Hertz contact rigidity and the oil film rigidity; k is a radical ofnjIs the load-deflection coefficient; deltaejIs the elastic deformation of the rolling body; cjIs the oil film stiffness coefficient; e'jThe comprehensive elastic modulus of the rolling body and the ferrule; ryjThe comprehensive curvature radius of the rolling body in the rolling direction; u shapejIs a dimensionless speed parameter; gjIs a dimensionless material parameter; eta0Is the ambient viscosity of the lubricating oil; a isjThe long half shaft is a contact ellipse of the rolling body; h isminjThe minimum oil film thickness of the rolling body contact micro-area; u. ofyjThe entrainment speed of the rolling body in the rolling direction;
the calculation model of the total contact stiffness of the rolling body is as follows:
Figure GDA0003205634260000073
wherein k isijContact stiffness of the rolling elements with the inner ring, kojContact stiffness of the rolling elements with the outer ring, kij、kojRespectively calculating the contact micro-areas of the rolling body and the inner ring/the outer ring by using a rolling body contact rigidity calculation model; k is a radical ofajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies, alphaijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle between the rolling body and the outer ring is shown;
the bearing rigidity calculation model is as follows:
Figure GDA0003205634260000081
wherein, KaFor axial stiffness of the bearing, KrFor radial stiffness of the bearing, kajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies,. psijThe azimuth angle of the rolling elements.
Optionally, the judging module is further configured to, when the judging result is negative,
according to the contact rigidity of the rolling body, obtaining the contact load of the rolling body by utilizing a rolling body contact load calculation model; the contact load of the rolling bodies includes: the contact load of the rolling body and the inner ring and the contact load of the rolling body and the outer ring;
updating the contact load of the rolling body contact angle calculation model, and recalculating the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring, the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction;
the rolling body contact load calculation model is as follows:
Figure GDA0003205634260000082
wherein k isijContact stiffness of the rolling elements with the inner ring, kojThe contact rigidity of the rolling body and the outer ring is obtained; deltaeijIs the amount of elastic deformation, δ, of the rolling elements and the inner raceeojAre rolling bodies andthe elastic deformation amount of the outer ring; h isminijIs the minimum oil film thickness of the rolling body and the inner ring, hminojThe minimum oil film thickness between the rolling body and the outer ring.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a method and a system for measuring contact rigidity of an angular contact ball bearing, which consider the lubricating effect, improve the measurement accuracy and provide more accurate technical parameters for bearing parameter design and service life estimation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a contact stiffness measuring method of an angular contact ball bearing provided by the invention;
FIG. 2 is a schematic diagram of a model of contact stiffness of a single friction pair taking into account lubrication effects;
FIG. 3 is a diagram illustrating the total contact stiffness of the rolling elements;
FIG. 4 is a schematic view of a bearing radial stiffness distribution;
FIG. 5 is a schematic view of the contact stiffness of the rolling elements;
FIG. 6 is a schematic view of a contact stiffness measuring system of an angular contact ball bearing provided by the invention;
FIG. 7 is a graph showing the comparison of contact angle between a Hertz contact stiffness model and a lubricated contact stiffness model;
FIG. 8 is a schematic diagram showing the comparison result of the axial stiffness of the bearing under the Hertz contact stiffness model and the lubricating contact stiffness model;
FIG. 9 is a graph showing the comparison of radial stiffness of a bearing in a Hertz contact stiffness model and a lubricated contact stiffness model;
FIG. 10 is a graph showing the comparison of contact load between a Hertz contact stiffness model and a lubricated contact stiffness model.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The terms "first," "second," "third," and the like in the description and in the claims, as well as in the drawings, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the objects so described are interchangeable under appropriate circumstances. Furthermore, the terms "comprising" and "having," as well as any variations thereof, are intended to cover non-exclusive inclusions.
In this patent document, the drawings discussed below and the embodiments used to describe the principles of the present disclosure are by way of illustration only and should not be construed in any way to limit the scope of the present disclosure. Those skilled in the art will understand that the principles of the present invention may be implemented in any suitably arranged system. Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. Further, a terminal according to an exemplary embodiment will be described in detail with reference to the accompanying drawings. Like reference symbols in the various drawings indicate like elements.
The terms used in the description of the present invention are only used to describe specific embodiments, and are not intended to show the concept of the present invention. Unless the context clearly dictates otherwise, expressions used in the singular form encompass expressions in the plural form. In the present specification, it is to be understood that terms such as "comprising," "having," and "containing" are intended to specify the presence of stated features, integers, steps, acts, or combinations thereof, as taught in the present specification, and are not intended to preclude the presence or addition of one or more other features, integers, steps, acts, or combinations thereof. Like reference symbols in the various drawings indicate like elements.
The invention aims to provide a method and a system for measuring contact rigidity of an angular contact ball bearing, which are used for obtaining more accurate contact angles of a rolling element and an inner ring and contact angles of the rolling element and an outer ring by considering a lubricating effect and utilizing coupling iterative calculation of the lubricating contact rigidity and the contact angles of the angular contact ball bearing, improving the accuracy of measuring the contact rigidity of the angular contact ball bearing and providing more accurate technical parameters for bearing parameter design and service life estimation.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, a schematic flow chart of a method for measuring contact stiffness of an angular contact ball bearing is provided, and the method for measuring contact stiffness of an angular contact ball bearing includes:
step 101: acquiring coefficients, geometric parameters, mechanical parameters, speed parameters, materials and lubricating oil parameters of the angular contact ball bearing; the coefficients include: a first drag coefficient, a second drag coefficient, an oil film stiffness coefficient and a load-deformation coefficient; the geometric parameters include: the diameter of the rolling element, the diameter of a bearing pitch circle, the azimuth angle of the rolling element, the curvature radius of the inner and outer ring channels and the major semiaxis of the contact ellipse of the rolling element and the inner and outer rings; the mechanical parameters include: the centrifugal force of the rolling body, the gyro moment of the rolling body, the axial load of the inner ring and the radial load of the inner ring; the speed parameters include: the rotating speed of the inner ring, the revolution speed of the rolling body and the rotation speed of the rolling body; the material and oil parameters include: the comprehensive elastic modulus of the rolling body and the ferrule and the environmental viscosity of lubricating oil.
Step 102: according to the coefficient, the geometric parameter, the mechanical parameter, the speed parameter, the material and lubricating oil parameters, obtaining a contact angle between the rolling body and the inner ring and a contact angle between the rolling body and the outer ring by using a rolling body contact angle calculation model, obtaining a comprehensive curvature radius of the rolling body in a rolling direction by using a rolling body contact micro-area geometric model, and obtaining a entrainment speed of the rolling body in the rolling direction by using a rolling body contact micro-area speed model; the comprehensive curvature radius of the rolling body in the rolling direction comprises: the comprehensive curvature radius of the rolling body and the inner ring in the rolling direction and the comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; the entrainment speed of the rolling bodies in the rolling direction comprises: the rolling speed of the rolling body and the inner ring in the rolling direction and the rolling speed of the rolling body and the outer ring in the rolling direction.
Step 103: obtaining the contact rigidity of the rolling body by utilizing a rolling body contact rigidity calculation model according to the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction; the contact stiffness of the rolling bodies includes: the contact rigidity of the rolling body and the inner ring and the contact rigidity of the rolling body and the outer ring.
Step 104: judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is yes, then
Step 105: obtaining the total contact rigidity of the rolling body by utilizing a rolling body total contact rigidity calculation model according to the contact angle between the rolling body and the inner ring and the contact angle between the rolling body and the outer ring; the total contact stiffness of the rolling elements comprises: axial contact stiffness of the rolling elements and radial contact stiffness of the rolling elements.
Step 106: obtaining the rigidity of the bearing by utilizing a bearing rigidity calculation model according to the total contact rigidity of the rolling body; the stiffness of the bearing includes: the axial stiffness of the bearing and the radial stiffness of the bearing.
The contact angle calculation model of the rolling element is obtained according to the equilibrium equation of the force of the rolling element of the angular contact ball bearing by the inner ring and the outer ring, the force of the rolling element of the inner ring and the equilibrium equation of the external load:
Figure GDA0003205634260000111
wherein alpha isijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle of the rolling body and the outer ring is shown; qijFor contact load of rolling bodies with inner rings, QojOf rolling bodies and outer racesA contact load; lambda [ alpha ]ijIs a first drag coefficient, λojThe second dragging coefficient can be obtained according to the outer ring raceway control theory, and the two coefficients can be taken as lambda ij0 and λ oj2; d is the diameter of the rolling body; fcjIs the centrifugal force of the rolling body; mgjA gyroscopic moment for the rolling elements; faThe axial load of the inner ring is taken; frIs the radial load of the inner ring; psijThe azimuth angle of the rolling elements.
Obtaining the contact angle alpha of the rolling body and the inner ring through a rolling body contact angle calculation modelijAnd the contact angle alpha of the rolling body with the outer ringoj。
The rolling element contact micro-area geometric model is as follows:
Figure GDA0003205634260000121
wherein R isbiyjIs the combined curvature radius of the rolling body and the inner ring in the rolling direction, RboyjThe comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; dmIs the bearing pitch circle diameter.
The rolling element contact micro-area speed model is as follows:
Figure GDA0003205634260000122
wherein: u. ofbiyjIs the entrainment velocity u of the rolling body and the inner ring in the rolling directionboyjThe entrainment speed of the rolling body and the outer ring in the rolling direction; omegaiThe rotating speed of the inner ring; omegamThe revolution speed of the rolling body; omegaxbjComponent of rolling body rotation speed on x-axis, ωzbjComponent of rolling element rotation speed in z-axis, CRijThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the inner ring, CRojThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the outer ring is expressed as follows:
Figure GDA0003205634260000123
wherein: rijRadius of curvature of inner race channel, RojThe curvature radius of the outer ring channel is shown; a isijMajor semi-axis of ellipse of contact of rolling body with inner ring, aojThe long semi-axis of the ellipse is contacted by the rolling body and the outer ring.
The Hertz contact model considers that a friction contact pair between a rolling body and an inner ring/an outer ring is a uniform isotropic linear elastomer and is in a small deformation state under the action of an external load; however, after the lubrication effect between the rolling element and the inner/outer ring is considered, not only the contact deformation of the rolling element and the elliptical contact surface of the inner/outer ring changes, but also the contact stiffness of the friction contact pair is influenced by the entrainment and squeezing effects of the lubricating oil, the contact stiffness of the friction contact pair is composed of Hertz contact stiffness and oil film stiffness, and the schematic diagram of the contact stiffness model of the single friction pair after the lubrication effect is considered is shown in fig. 2.
The calculation model of the contact stiffness of the rolling body after considering the lubrication effect is as follows:
Figure GDA0003205634260000131
wherein k iscjHertz contact stiffness, k, for the rolling body in contact with the Hertz contact regionfjThe oil film rigidity of the rolling body and the Hertz contact area is obtained; k is a radical ofefjThe oil film rigidity of the rolling body and the contact micro-area lubricating oil inlet is obtained; k is a radical ofjThe contact rigidity of the rolling body, namely the combined rigidity of the Hertz contact rigidity and the oil film rigidity; k is a radical ofnjIs the load-deflection coefficient; deltaejIs the elastic deformation of the rolling body; cjIs the oil film stiffness coefficient; e'jThe comprehensive elastic modulus of the rolling body and the ferrule; ryjThe comprehensive curvature radius of the rolling body in the rolling direction; u shapejIs a dimensionless speed parameter; gjIs a dimensionless material parameter; eta0Is the ambient viscosity of the lubricating oil; a isjThe long half shaft is a contact ellipse of the rolling body; h isminjThe minimum oil film thickness of the rolling body contact micro-area; u. ofyjFor the rolling bodies in the rolling directionThe entrainment speed of (1).
Two contact pairs exist between the rolling body and the inner/outer ring raceway, the two contact pairs have contact rigidity components in the axial direction and the radial direction, the total contact rigidity of the rolling body and the inner/outer ring is not only influenced by the contact rigidity of the rolling body and the inner ring, the rolling body and the outer ring, but also influenced by the contact angle of the rolling body and the inner ring/the outer ring, the schematic diagram is shown in fig. 3, and the calculation model of the total contact rigidity of the rolling body is as follows:
Figure GDA0003205634260000132
wherein k isijContact stiffness of the rolling elements with the inner ring, kojContact stiffness of the rolling elements with the outer ring, kij、kojRespectively calculating the contact micro-areas of the rolling body and the inner ring/the outer ring by using a rolling body contact rigidity calculation model; k is a radical ofajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies, alphaijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle between the rolling body and the outer ring is shown.
The radial stiffness distribution schematic diagram of the bearing is shown in fig. 4, and the bearing stiffness calculation model is as follows:
Figure GDA0003205634260000133
wherein, KaFor axial stiffness of the bearing, KrFor radial stiffness of the bearing, kajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies,. psijThe azimuth angle of the rolling elements.
The contact rigidity measurement and calculation method of the angular contact ball bearing further comprises the following steps:
judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is no, then
According to the contact rigidity of the rolling body, obtaining the contact load of the rolling body by utilizing a rolling body contact load calculation model; the contact load of the rolling bodies includes: the contact load of the rolling body and the inner ring and the contact load of the rolling body and the outer ring.
And updating the contact load of the rolling body contact angle calculation model, and recalculating the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring, the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction.
As can be seen from the schematic diagram of the contact stiffness between the rolling elements and the inner/outer rings in fig. 5, in the coupled iteration of the bearing dynamics model and the friction pair contact stiffness model considering the lubrication effect, the contact angle α between the rolling elements and the inner/outer ringsij、αojThe change of (2) causes the contact micro-area position, the contact load, the geometric parameters and the speed parameters to change, thereby leading the contact rigidity k of the rolling body and the inner and outer ringsij、kojAnd the equivalent axial/radial contact stiffness is changed, while the contact stiffness k of the rolling body and the inner/outer ring is changedij、kojThe change of the contact angle and the contact load in turn influence parameters such as the contact angle and the contact load, so that the contact angle alpha between the rolling body and the inner and outer rings is adoptedij、αojAnd contact stiffness kij、kojAs a feature quantity characterizing the coupling iteration of the two models.
Firstly, substituting the contact stiffness of the single friction contact pair obtained in the step 2 into a replacement parameter k in a rolling body contact load calculation modelij、kojObtaining the contact load of the rolling element and the inner and outer rings considering the lubrication effect, substituting the contact load into a rolling element contact angle calculation model to obtain a new contact angle between the rolling element and the inner and outer rings, wherein the change of the contact angle can change the elastic deformation deltaejMinimum oil film thickness hminjGeometric parameter RyjAnd a speed parameter uyjAccording to the rolling body contact load calculation model, the rolling body contact micro-area geometric model and the rolling body contact micro-area speed model, the comprehensive curvature of the rolling body in the rolling direction and the entrainment speed parameter of the rolling body in the rolling direction are obtained, then the rolling body contact rigidity calculation model is utilized to obtain new contact rigidity, and the method is againstAnd repeating coupling iteration until the precision requirement is met, and acquiring the contact rigidity between the rolling body and the inner/outer ring under the working condition of meeting the given rotating speed and the axial/radial load.
The rolling body contact load calculation model is as follows:
Figure GDA0003205634260000141
wherein k isijContact stiffness of the rolling elements with the inner ring, kojThe contact rigidity of the rolling body and the outer ring is obtained; deltaeijIs the amount of elastic deformation, δ, of the rolling elements and the inner raceojThe elastic deformation of the rolling body and the outer ring; h isminijIs the minimum oil film thickness of the rolling body and the inner ring, hminojThe minimum oil film thickness between the rolling body and the outer ring.
The invention provides a method and a system for measuring contact rigidity of an angular contact ball bearing, which consider a lubrication effect, obtain a contact angle between a rolling body and an inner ring and a contact angle between the rolling body and an outer ring which meet a precision threshold value through coupled iterative calculation of the lubrication contact rigidity and the contact angle of the angular contact ball bearing, improve the measurement accuracy, and provide more accurate technical parameters for bearing parameter design and service life estimation.
As shown in fig. 6, for the system corresponding to the method for measuring contact stiffness of angular contact ball bearing provided by the present invention, the system comprises: the device comprises a data acquisition module 201, a contact angle, geometric parameter and speed parameter calculation module 202, a contact rigidity calculation module 203 of the rolling body, a judgment module 204, a total contact rigidity calculation module 205 of the rolling body and a rigidity calculation module 206 of the bearing.
The data acquisition module 201 is used for acquiring coefficients, geometric parameters, mechanical parameters, speed parameters, and material and lubricating oil parameters of the angular contact ball bearing; the coefficients include: a first drag coefficient, a second drag coefficient, an oil film stiffness coefficient and a load-deformation coefficient; the geometric parameters include: the diameter of the rolling element, the diameter of a bearing pitch circle, the azimuth angle of the rolling element, the curvature radius of the inner and outer ring channels and the major semiaxis of the contact ellipse of the rolling element and the inner and outer rings; the mechanical parameters include: the centrifugal force of the rolling body, the gyro moment of the rolling body, the axial load of the inner ring and the radial load of the inner ring; the speed parameters include: the rotating speed of the inner ring, the revolution speed of the rolling body and the rotation speed of the rolling body; the material and oil parameters include: the comprehensive elastic modulus of the rolling body and the ferrule and the environmental viscosity of lubricating oil.
The contact angle, geometric parameter and speed parameter calculation module 202 is configured to obtain a contact angle between the rolling element and the inner ring and a contact angle between the rolling element and the outer ring according to the coefficient, the geometric parameter, the mechanical parameter, the speed parameter, and the material and lubricating oil parameter by using a rolling element contact angle calculation model, obtain a comprehensive curvature radius of the rolling element in the rolling direction by using a rolling element contact micro-area geometric model, and obtain a entrainment speed of the rolling element in the rolling direction by using a rolling element contact micro-area speed model; the comprehensive curvature radius of the rolling body in the rolling direction comprises: the comprehensive curvature radius of the rolling body and the inner ring in the rolling direction and the comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; the entrainment speed of the rolling bodies in the rolling direction comprises: the rolling speed of the rolling body and the inner ring in the rolling direction and the rolling speed of the rolling body and the outer ring in the rolling direction.
The contact rigidity calculation module 203 of the rolling body is used for obtaining the contact rigidity of the rolling body by utilizing a rolling body contact rigidity calculation model according to the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction; the contact stiffness of the rolling bodies includes: the contact rigidity of the rolling body and the inner ring and the contact rigidity of the rolling body and the outer ring.
The judging module 204 is configured to judge whether a contact angle between the rolling element and the inner ring, a contact angle between the rolling element and the outer ring, and a contact stiffness of the rolling element satisfy a precision threshold; if the judgment result is yes, then
The total contact rigidity calculation module 205 of the rolling element is used for obtaining the total contact rigidity of the rolling element by utilizing a total contact rigidity calculation model of the rolling element according to the contact angle between the rolling element and the inner ring and the contact angle between the rolling element and the outer ring; the total contact stiffness of the rolling elements comprises: axial contact stiffness of the rolling elements and radial contact stiffness of the rolling elements.
The bearing rigidity calculation module 206 is configured to obtain the rigidity of the bearing by using a bearing rigidity calculation model according to the total contact rigidity of the rolling elements; the stiffness of the bearing includes: the axial stiffness of the bearing and the radial stiffness of the bearing.
The rolling element contact angle calculation model is as follows:
Figure GDA0003205634260000161
wherein alpha isijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle of the rolling body and the outer ring is shown; qijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; lambda [ alpha ]ijIs a first drag coefficient, λojIs the second drag coefficient; d is the diameter of the rolling body; fcjIs the centrifugal force of the rolling body; mgjA gyroscopic moment for the rolling elements; faThe axial load of the inner ring is taken; frIs the radial load of the inner ring; psijThe azimuth angle of the rolling elements.
The rolling element contact micro-area geometric model is as follows:
Figure GDA0003205634260000162
wherein R isbiyjIs the combined curvature radius of the rolling body and the inner ring in the rolling direction, RboyjThe comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; dmIs the bearing pitch circle diameter.
The rolling element contact micro-area speed model is as follows:
Figure GDA0003205634260000171
wherein: u. ofbiyjIs the entrainment velocity u of the rolling body and the inner ring in the rolling directionboyjThe rolling body and the outer ring are in a rolling directionThe speed of the inward entrainment; omegaiThe rotating speed of the inner ring; omegamThe revolution speed of the rolling body; omegaxbjComponent of rolling body rotation speed on x-axis, ωzbjComponent of rolling element rotation speed in z-axis, CRijThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the inner ring, CRojThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the outer ring is expressed as follows:
Figure GDA0003205634260000172
wherein: rijRadius of curvature of inner race channel, RojThe curvature radius of the outer ring channel is shown; a isijMajor semi-axis of ellipse of contact of rolling body with inner ring, aojThe long semi-axis of the ellipse is contacted by the rolling body and the outer ring.
The rolling body contact rigidity calculation model is as follows:
Figure GDA0003205634260000173
wherein k iscjHertz contact stiffness, k, for the rolling body in contact with the Hertz contact regionfjThe oil film rigidity of the rolling body and the Hertz contact area is obtained; k is a radical ofefjThe oil film rigidity of the rolling body and the contact micro-area lubricating oil inlet is obtained; k is a radical ofjThe contact rigidity of the rolling body, namely the combined rigidity of the Hertz contact rigidity and the oil film rigidity; k is a radical ofnjIs the load-deflection coefficient; deltaejIs the elastic deformation of the rolling body; cjIs the oil film stiffness coefficient; e'jThe comprehensive elastic modulus of the rolling body and the ferrule; ryjThe comprehensive curvature radius of the rolling body in the rolling direction; u shapejIs a dimensionless speed parameter; gjIs a dimensionless material parameter; eta0Is the ambient viscosity of the lubricating oil; a isjThe long half shaft is a contact ellipse of the rolling body; h isminjThe minimum oil film thickness of the rolling body contact micro-area; u. ofyjThe rolling speed of the rolling body in the rolling direction is shown.
The calculation model of the total contact stiffness of the rolling body is as follows:
Figure GDA0003205634260000181
wherein k isijContact stiffness of the rolling elements with the inner ring, kojContact stiffness of the rolling elements with the outer ring, kij、kojRespectively calculating the contact micro-areas of the rolling body and the inner ring/the outer ring by using a rolling body contact rigidity calculation model; k is a radical ofajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies, alphaijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle between the rolling body and the outer ring is shown.
The bearing rigidity calculation model is as follows:
Figure GDA0003205634260000182
wherein, KaFor axial stiffness of the bearing, KrFor radial stiffness of the bearing, kajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies,. psijThe azimuth angle of the rolling elements.
The decision block 204 is further configured to, when the decision result is negative,
according to the contact rigidity of the rolling body, obtaining the contact load of the rolling body by utilizing a rolling body contact load calculation model; the contact load of the rolling bodies includes: the contact load of the rolling body and the inner ring and the contact load of the rolling body and the outer ring.
And updating the contact load of the rolling body contact angle calculation model, and recalculating the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring, the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction.
The rolling body contact load calculation model is as follows:
Figure GDA0003205634260000183
wherein k isijContact stiffness of the rolling elements with the inner ring, kojThe contact rigidity of the rolling body and the outer ring is obtained; deltaeijIs the amount of elastic deformation, δ, of the rolling elements and the inner raceeojThe elastic deformation of the rolling body and the outer ring; h isminijIs the minimum oil film thickness of the rolling body and the inner ring, hminojThe minimum oil film thickness between the rolling body and the outer ring.
The contact rigidity measuring method and the system of the angular contact ball bearing claimed by the invention are applied to the angular contact ball bearing 7012C, and the structure and the material parameters are shown in table 1; selecting 4109 aviation lubricating oil as the lubricating oil, wherein the performance parameters are shown in table 2; axial load Fa5000N, radial load Fr＝1500N。
Table 17012C angular contact ball bearing parameters
Figure GDA0003205634260000191
TABLE 24109 aviation lubricating oil Performance parameters
Figure GDA0003205634260000192
And (3) programming a solving program by using the matlab, and obtaining a numerical solution of the contact rigidity of the high-speed angular contact ball bearing according to the given rotating speed, the axial/radial load and the lubricating parameters. Under a Hertz contact stiffness model and a lubrication contact stiffness model considering a lubrication effect, a schematic diagram of a comparison result of contact angles of a rolling body and an inner ring and an outer ring is shown in FIG. 6, a hollow point corresponds to the Hertz contact stiffness model, and a solid point corresponds to the lubrication contact stiffness model. As can be seen from FIG. 6, the contact angle between the rolling element and the inner ring increases with the rotating speed in the two models, and the contact angle between the rolling element and the outer ring decreases with the rotating speed; the contact angles of the inner ring and the outer ring of the lubricating contact stiffness model are smaller than those of the Hertz contact stiffness model, because the contact deformation and the contact stiffness are increased due to the addition of the oil film, the smaller contact angle can meet the stress balance equation of the rolling element and the inner ring.
The graph of the comparison result of the axial/radial stiffness of the bearing under the Hertz contact stiffness model and the lubrication contact stiffness model is shown in FIG. 7 and FIG. 8.
As shown in fig. 7, the axial stiffness of the Hertz contact stiffness model is in a nonlinear gradual increase trend with the increase of the rotation speed, and the lubricating contact stiffness model has higher axial stiffness and larger growth curvature compared with the Hertz contact stiffness model, which indicates that the oil film increases the axial stiffness of the bearing and is greatly influenced by the rotation speed.
As shown in fig. 8, the radial stiffness of the lubricated contact stiffness model is significantly increased compared to the Hertz contact stiffness model, and the curvature of the radial stiffness decreases as the rotation speed increases, indicating that the bearing radial stiffness is more affected by the lubricant as the rotation speed increases.
The results of comparing the contact load of the rolling element and the inner/outer ring in the Hertz contact stiffness model and the lubrication contact stiffness model considering the lubrication effect at the rotation speed of 14000r/min are shown in fig. 9. Therefore, the contact load of the lubricating contact stiffness model is larger than that of the Hertz contact stiffness model, and the contact deformation and the contact stiffness between the rolling element and the inner ring and the outer ring are increased due to the existence of the oil film, so that the contact load of the lubricating contact stiffness model is increased.
The conclusions that can be drawn from fig. 7-9 are:
the contact angle between the rolling body and the inner ring/outer ring is obtained through coupling iterative calculation of the lubrication contact rigidity and the contact angle of the angular contact ball bearing, according to analysis results, the contact angle between the rolling body and the inner ring is increased along with the increase of the rotating speed, the contact angle between the rolling body and the outer ring is reduced, and the contact angle obtained by a lubrication contact rigidity model is smaller compared with a Hertz contact rigidity model.
According to the method and the system for measuring the contact rigidity of the angular contact ball bearing, the lubricating effect is considered, the contact rigidity is obviously increased compared with a Hertz contact rigidity model, and the change along with the increase of the rotating speed is more obvious; the contact load of the rolling body and the inner ring/outer ring under different azimuth angles is increased compared with that of a Hertz contact rigidity model; the actual lubrication effect is considered in the angular contact ball bearing contact stiffness calculation model, and more accurate technical parameters and a calculation method are provided for bearing parameter design and service life estimation.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. The contact rigidity measuring method of the angular contact ball bearing is characterized by comprising the following steps:
acquiring coefficients, geometric parameters, mechanical parameters, speed parameters, materials and lubricating oil parameters of the angular contact ball bearing; the coefficients include: a first drag coefficient, a second drag coefficient, an oil film stiffness coefficient and a load-deformation coefficient; the geometric parameters include: the diameter of the rolling element, the diameter of a bearing pitch circle, the azimuth angle of the rolling element, the curvature radius of the inner and outer ring channels and the major semiaxis of the contact ellipse of the rolling element and the inner and outer rings; the mechanical parameters include: the centrifugal force of the rolling body, the gyro moment of the rolling body, the axial load of the inner ring and the radial load of the inner ring; the speed parameters include: the rotating speed of the inner ring, the revolution speed of the rolling body and the rotation speed of the rolling body; the material and oil parameters include: the comprehensive elastic modulus of the rolling body and the ferrule and the environmental viscosity of lubricating oil;
according to the coefficient, the geometric parameter, the mechanical parameter, the speed parameter, the material and lubricating oil parameters, obtaining a contact angle between the rolling body and the inner ring and a contact angle between the rolling body and the outer ring by using a rolling body contact angle calculation model, obtaining a comprehensive curvature radius of the rolling body in a rolling direction by using a rolling body contact micro-area geometric model, and obtaining a entrainment speed of the rolling body in the rolling direction by using a rolling body contact micro-area speed model; the comprehensive curvature radius of the rolling body in the rolling direction comprises: the comprehensive curvature radius of the rolling body and the inner ring in the rolling direction and the comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; the entrainment speed of the rolling bodies in the rolling direction comprises: the entrainment speed of the rolling body and the inner ring in the rolling direction and the entrainment speed of the rolling body and the outer ring in the rolling direction;
obtaining the contact rigidity of the rolling body by utilizing a rolling body contact rigidity calculation model according to the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction; the contact stiffness of the rolling bodies includes: the contact rigidity of the rolling body and the inner ring and the contact rigidity of the rolling body and the outer ring;
judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is yes, then
Obtaining the total contact rigidity of the rolling body by utilizing a rolling body total contact rigidity calculation model according to the contact angle between the rolling body and the inner ring and the contact angle between the rolling body and the outer ring; the total contact stiffness of the rolling elements comprises: axial contact stiffness of the rolling bodies and radial contact stiffness of the rolling bodies;
obtaining the rigidity of the bearing by utilizing a bearing rigidity calculation model according to the total contact rigidity of the rolling body; the stiffness of the bearing includes: the axial stiffness of the bearing and the radial stiffness of the bearing.
2. The angular contact ball bearing contact stiffness measurement method according to claim 1, wherein the rolling element contact angle calculation model is:
Figure FDA0003205634250000021
wherein alpha isijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle of the rolling body and the outer ring is shown; qijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; lambda [ alpha ]ijIs a first drag coefficient, λojIs the second drag coefficient; d is the diameter of the rolling body; fcjIs the centrifugal force of the rolling body; mgjA gyroscopic moment for the rolling elements; faThe axial load of the inner ring is taken; frIs the radial load of the inner ring; psijIs the azimuth angle of the rolling body;
the rolling element contact micro-area geometric model is as follows:
Figure FDA0003205634250000022
wherein R isbiyjIs the combined curvature radius of the rolling body and the inner ring in the rolling direction, RboyjThe comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; dmThe bearing pitch circle diameter;
the rolling element contact micro-area speed model is as follows:
Figure FDA0003205634250000023
wherein: u. ofbiyjIs the entrainment velocity u of the rolling body and the inner ring in the rolling directionboyjThe entrainment speed of the rolling body and the outer ring in the rolling direction; omegaiThe rotating speed of the inner ring; omegamThe revolution speed of the rolling body; omegaxbjComponent of rolling body rotation speed on x-axis, ωzbjComponent of rolling element rotation speed in z-axis, CRijThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the inner ring, CRojThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the outer ring is expressed as follows:
Figure FDA0003205634250000031
wherein: rijRadius of curvature of inner race channel, RojThe curvature radius of the outer ring channel is shown; a isijMajor semi-axis of ellipse of contact of rolling body with inner ring, aojThe long semi-axis of the ellipse is contacted by the rolling body and the outer ring.
3. The angular contact ball bearing contact stiffness measurement method according to claim 1, wherein the rolling element contact stiffness calculation model is:
Figure FDA0003205634250000032
wherein k iscjHertz contact stiffness, k, for the rolling body in contact with the Hertz contact regionfjThe oil film rigidity of the rolling body and the Hertz contact area is obtained; k is a radical ofefjThe oil film rigidity of the rolling body and the contact micro-area lubricating oil inlet is obtained; k is a radical ofjThe contact rigidity of the rolling body, namely the combined rigidity of the Hertz contact rigidity and the oil film rigidity; k is a radical ofnjIs the load-deflection coefficient; deltaejIs the elastic deformation of the rolling body; cjIs the oil film stiffness coefficient; e'jThe comprehensive elastic modulus of the rolling body and the ferrule; ryjThe comprehensive curvature radius of the rolling body in the rolling direction; u shapejIs a dimensionless speed parameter; gjIs a dimensionless material parameter; eta0Is the ambient viscosity of the lubricating oil; a isjThe long half shaft is a contact ellipse of the rolling body; h isminjThe minimum oil film thickness of the rolling body contact micro-area; u. ofyjThe rolling speed of the rolling body in the rolling direction is shown.
4. The angular contact ball bearing contact stiffness measurement method according to claim 1, wherein the rolling element total contact stiffness calculation model is:
Figure FDA0003205634250000033
wherein k isijContact stiffness of the rolling elements with the inner ring, kojContact stiffness of the rolling elements with the outer ring, kij、kojRespectively calculating the contact micro-areas of the rolling body and the inner ring/the outer ring by using a rolling body contact rigidity calculation model; k is a radical ofajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies, alphaijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle between the rolling body and the outer ring is shown.
5. The angular contact ball bearing contact stiffness measurement method according to claim 1, wherein the bearing stiffness calculation model is:
Figure FDA0003205634250000041
wherein, KaFor axial stiffness of the bearing, KrFor radial stiffness of the bearing, kajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies,. psijThe azimuth angle of the rolling elements.
6. The angular contact ball bearing contact stiffness measurement method of claim 1, further comprising:
judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is no, then
According to the contact rigidity of the rolling body, obtaining the contact load of the rolling body by utilizing a rolling body contact load calculation model; the contact load of the rolling bodies includes: the contact load of the rolling body and the inner ring and the contact load of the rolling body and the outer ring;
and updating the contact load of the rolling body contact angle calculation model, and recalculating the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring, the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction.
7. The angular contact ball bearing contact stiffness measurement method according to claim 6, wherein the rolling element contact load calculation model is:
Figure FDA0003205634250000042
wherein Q isijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; k is a radical ofijContact stiffness of the rolling elements with the inner ring, kojThe contact rigidity of the rolling body and the outer ring is obtained; deltaeijIs the amount of elastic deformation, δ, of the rolling elements and the inner raceeojThe elastic deformation of the rolling body and the outer ring; h isminijIs the minimum oil film thickness of the rolling body and the inner ring, hminojThe minimum oil film thickness between the rolling body and the outer ring.
8. An angular contact ball bearing contact stiffness measurement system, the measurement system comprising:
the data acquisition module is used for acquiring the coefficient, the geometric parameter, the mechanical parameter, the speed parameter and the material and lubricating oil parameter of the angular contact ball bearing; the coefficients include: a first drag coefficient, a second drag coefficient, an oil film stiffness coefficient and a load-deformation coefficient; the geometric parameters include: the diameter of the rolling element, the diameter of a bearing pitch circle, the azimuth angle of the rolling element, the curvature radius of the inner and outer ring channels and the major semiaxis of the contact ellipse of the rolling element and the inner and outer rings; the mechanical parameters include: the centrifugal force of the rolling body, the gyro moment of the rolling body, the axial load of the inner ring and the radial load of the inner ring; the speed parameters include: the rotating speed of the inner ring, the revolution speed of the rolling body and the rotation speed of the rolling body; the material and oil parameters include: the comprehensive elastic modulus of the rolling body and the ferrule and the environmental viscosity of lubricating oil;
the contact angle, geometric parameter and speed parameter calculation module is used for obtaining a contact angle between the rolling body and the inner ring and a contact angle between the rolling body and the outer ring by utilizing a rolling body contact angle calculation model according to the coefficient, the geometric parameter, the mechanical parameter, the speed parameter, the material and the lubricating oil parameter, obtaining a comprehensive curvature radius of the rolling body in the rolling direction by utilizing a rolling body contact micro-area geometric model, and obtaining the entrainment speed of the rolling body in the rolling direction by utilizing a rolling body contact micro-area speed model; the comprehensive curvature radius of the rolling body in the rolling direction comprises: the comprehensive curvature radius of the rolling body and the inner ring in the rolling direction and the comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; the entrainment speed of the rolling bodies in the rolling direction comprises: the entrainment speed of the rolling body and the inner ring in the rolling direction and the entrainment speed of the rolling body and the outer ring in the rolling direction;
the contact rigidity calculation module of the rolling body is used for obtaining the contact rigidity of the rolling body by utilizing a rolling body contact rigidity calculation model according to the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction; the contact stiffness of the rolling bodies includes: the contact rigidity of the rolling body and the inner ring and the contact rigidity of the rolling body and the outer ring;
the judging module is used for judging whether the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring and the contact rigidity of the rolling body meet a precision threshold value or not; if the judgment result is yes, then
The total contact rigidity calculation module of the rolling body is used for obtaining the total contact rigidity of the rolling body by utilizing a rolling body total contact rigidity calculation model according to the contact angle between the rolling body and the inner ring and the contact angle between the rolling body and the outer ring; the total contact stiffness of the rolling elements comprises: axial contact stiffness of the rolling bodies and radial contact stiffness of the rolling bodies;
the rigidity calculation module of the bearing is used for obtaining the rigidity of the bearing by utilizing a bearing rigidity calculation model according to the total contact rigidity of the rolling body; the stiffness of the bearing includes: the axial stiffness of the bearing and the radial stiffness of the bearing.
9. The angular contact ball bearing contact stiffness measurement system of claim 8, wherein the rolling element contact angle calculation model is:
Figure FDA0003205634250000061
wherein alpha isijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle of the rolling body and the outer ring is shown; qijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; lambda [ alpha ]ijIs a first drag coefficient, λojIs the second drag coefficient; d is the diameter of the rolling body; fcjIs the centrifugal force of the rolling body; mgjA gyroscopic moment for the rolling elements; faThe axial load of the inner ring is taken; frIs the radial load of the inner ring; psijIs the azimuth angle of the rolling body;
the rolling element contact micro-area geometric model is as follows:
Figure FDA0003205634250000062
wherein R isbiyjIs the combined curvature radius of the rolling body and the inner ring in the rolling direction, RboyjThe comprehensive curvature radius of the rolling body and the outer ring in the rolling direction; dmThe bearing pitch circle diameter;
the rolling element contact micro-area speed model is as follows:
Figure FDA0003205634250000063
wherein: u. ofbiyjIs the entrainment velocity u of the rolling body and the inner ring in the rolling directionboyjThe entrainment speed of the rolling body and the outer ring in the rolling direction; omegaiThe rotating speed of the inner ring; omegamThe revolution speed of the rolling body; omegaxbjThe rotation speed of the rolling bodies is on the x axisComponent of (a) omegazbjComponent of rolling element rotation speed in z-axis, CRijThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the inner ring, CRojThe distance from the geometric center of the rolling body to the contact elliptical surface of the rolling body and the outer ring is expressed as follows:
Figure FDA0003205634250000071
wherein: rijRadius of curvature of inner race channel, RojThe curvature radius of the outer ring channel is shown; a isijMajor semi-axis of ellipse of contact of rolling body with inner ring, aojA long semi-axis of an ellipse in which the rolling body is contacted with the outer ring;
the rolling body contact rigidity calculation model is as follows:
Figure FDA0003205634250000072
wherein k iscjHertz contact stiffness, k, for the rolling body in contact with the Hertz contact regionfjThe oil film rigidity of the rolling body and the Hertz contact area is obtained; k is a radical ofefjThe oil film rigidity of the rolling body and the contact micro-area lubricating oil inlet is obtained; k is a radical ofjThe contact rigidity of the rolling body, namely the combined rigidity of the Hertz contact rigidity and the oil film rigidity; k is a radical ofnjIs the load-deflection coefficient; deltaejIs the elastic deformation of the rolling body; cjIs the oil film stiffness coefficient; e'jThe comprehensive elastic modulus of the rolling body and the ferrule; ryjThe comprehensive curvature radius of the rolling body in the rolling direction; u shapejIs a dimensionless speed parameter; gjIs a dimensionless material parameter; eta0Is the ambient viscosity of the lubricating oil; a isjThe long half shaft is a contact ellipse of the rolling body; h isminjThe minimum oil film thickness of the rolling body contact micro-area; u. ofyjThe entrainment speed of the rolling body in the rolling direction;
the calculation model of the total contact stiffness of the rolling body is as follows:
Figure FDA0003205634250000073
wherein k isijContact stiffness of the rolling elements with the inner ring, kojContact stiffness of the rolling elements with the outer ring, kij、kojRespectively calculating the contact micro-areas of the rolling body and the inner ring/the outer ring by using a rolling body contact rigidity calculation model; k is a radical ofajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies, alphaijIs the contact angle of the rolling body with the inner ring, alphaojThe contact angle between the rolling body and the outer ring is shown;
the bearing rigidity calculation model is as follows:
Figure FDA0003205634250000081
wherein, KaFor axial stiffness of the bearing, KrFor radial stiffness of the bearing, kajFor axial contact stiffness of the rolling bodies, krjIs the radial contact stiffness of the rolling bodies,. psijThe azimuth angle of the rolling elements.
10. The angular contact ball bearing contact stiffness measuring system according to claim 8 or 9, wherein the determining module is further configured to, when the determination result is negative,
according to the contact rigidity of the rolling body, obtaining the contact load of the rolling body by utilizing a rolling body contact load calculation model; the contact load of the rolling bodies includes: the contact load of the rolling body and the inner ring and the contact load of the rolling body and the outer ring;
updating the contact load of the rolling body contact angle calculation model, and recalculating the contact angle between the rolling body and the inner ring, the contact angle between the rolling body and the outer ring, the comprehensive curvature radius of the rolling body in the rolling direction and the entrainment speed of the rolling body in the rolling direction;
the rolling body contact load calculation model is as follows:
Figure FDA0003205634250000082
wherein Q isijFor contact load of rolling bodies with inner rings, QojThe contact load of the rolling body and the outer ring is obtained; k is a radical ofijContact stiffness of the rolling elements with the inner ring, kojThe contact rigidity of the rolling body and the outer ring is obtained; deltaeijIs the amount of elastic deformation, δ, of the rolling elements and the inner raceeojThe elastic deformation of the rolling body and the outer ring; h isminijIs the minimum oil film thickness of the rolling body and the inner ring, hminojThe minimum oil film thickness between the rolling body and the outer ring.
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