CN112855755A - Method for selecting use condition of high-speed four-point contact ball bearing - Google Patents
Method for selecting use condition of high-speed four-point contact ball bearing Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
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- F16C19/00—Bearings with rolling contact, for exclusively rotary movement
- F16C19/02—Bearings with rolling contact, for exclusively rotary movement with bearing balls essentially of the same size in one or more circular rows
- F16C19/14—Bearings with rolling contact, for exclusively rotary movement with bearing balls essentially of the same size in one or more circular rows for both radial and axial load
- F16C19/16—Bearings with rolling contact, for exclusively rotary movement with bearing balls essentially of the same size in one or more circular rows for both radial and axial load with a single row of balls
- F16C19/163—Bearings with rolling contact, for exclusively rotary movement with bearing balls essentially of the same size in one or more circular rows for both radial and axial load with a single row of balls with angular contact
- F16C19/166—Four-point-contact ball bearings
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Abstract
The invention discloses a method for selecting the use condition of a high-speed four-point contact ball bearing, which is to establish a relation between the rotating speed and load condition and the dynamic contact state of a rolling body/raceway so as to select the rotating speed and load range applied in the use process of the bearing according to the required normal contact state of the rolling body/raceway, namely two-point contact. The invention utilizes the contact tracks left on the inner raceway and the outer raceway of the rolling element in the operation process to visually represent the contact state in the high-speed four-point contact ball bearing, including several point contacts and at what positions, thereby establishing visual relation between the rotating speed and load working condition parameters and the contact state, being used for standardizing the selection of the rotating speed and load working condition when the bearing is used, and overcoming the defect that the dynamic contact state of the rolling element/the raceway under the complex working condition can not be accurately judged in the prior art; according to the invention, the two, three or four-point dynamic contact state of the rolling ball and the inner and outer raceways within a period of operation time can be predicted according to the rotating speed and the load working condition.
Description
Technical Field
The invention relates to a method for selecting the use condition of a contact ball bearing, in particular to a method for selecting the use condition of a high-speed four-point contact ball bearing.
Background
The inner and outer ring rolling paths of the four-point contact ball bearing are peach-shaped sections, the inner ring is generally in a separated double-half form, and when the ball bearing is not loaded or under pure radial load, the rolling ball is in four-point contact with the rolling paths. The four-point contact ball bearing mainly comprises a turntable bearing and a high-speed four-point contact ball bearing. A rotating disc type supporting bearing is commonly used in occasions such as engineering machinery slewing bearings and wind power variable pitch blades, and the like, while a high-speed four-point contact ball bearing is a rolling bearing commonly used in the field of aerospace, and has relatively small size and relatively high rotating speed, and the operating technical index of the high-speed four-point contact ball bearing can reach million dmn is more than or equal to n, and can bear radial and axial loads and overturning moment, such as a rear supporting point bearing of a low-pressure compressor of a main shaft of the jet engine and a rear supporting point bearing of a high-pressure compressor, and the running performance of the rear supporting point bearing has a critical influence on the reliability of the engine and even the whole machine.
When the four-point contact ball bearing works, compared with a common angular contact ball bearing, the four-point contact ball bearing can bear the action of bidirectional axial load, can keep bearing capacity under the conditions of axial and radial combined load, overturning moment and rotating speed change, and simultaneously reduces the movement of a ball body and the displacement of an inner ring caused by rotating speed change through the two-point contact of the ball body and an inner raceway and an outer raceway, thereby improving the rigidity and the running precision of a rotor system. However, in order to avoid the phenomenon that the rolling bodies are in contact with the roller paths to generate larger sliding friction and reduce the service life, the high-speed four-point contact ball bearing only allows two points of four contact points to be in contact for a long time, so that the variation range of the rotating speed and the load working condition can be selected and regulated according to the contact state of the rolling bodies and the roller paths, the possibility of three-point and four-point contact is reduced, and the service life and the matching efficiency of the four-point contact ball bearing are obviously improved. In addition, parameters such as moment, wear failure and fatigue life of the bearing can be calculated according to different contact states, so that the evaluation and judgment of the contact state are important for the four-point contact ball bearing. However, the high-speed four-point contact ball bearing generates a large centrifugal force when the rolling body is in a high-speed state, and meanwhile, the bearing bears a complex external combined load, and the judgment and the evaluation of the contact state become abnormal and difficult, and a dynamic and kinematic model or experiment capable of reflecting the dynamic running state of the bearing needs to be used.
The invention patent CN102725545B of NTN company adopts an empirical formula to distinguish the two-point contact state from the four-point contact state, does not consider the action of speed working condition and complex load working condition, does not count the situation of three-point contact, and obviously is not accurate enough. The static model of the four-point contact ball bearing established by the Weanzhang (Weianzhang, Zhao soldier, four-point contact ball bearing contact angle to the contact stress is initially detected [ J ] university report of traffic university, 2015(4): 51-53.) and the Lilihao and the like (Pinlihao, Wangtongwu, Lijiangjun, four-point contact ball bearing contact problem research [ J ] Nanjing university of science and technology (Natural science edition), 2007, 31(4): 458-461) can calculate the contact state of the rolling element and the raceway under the load condition, but the actual dynamic contact state of the high-speed four-point contact ball bearing under the operation state cannot be reflected because the huge influence of high rotation speed and the dynamic interaction among components are not counted. In addition, the numerical solving algorithm [ J ] of the high-speed Four-Point Contact Ball Bearing mechanical Model (Nature science edition), 2016, 44(001):123-, but because it is still essentially a balanced model of the forces and moments experienced by the components, it is not possible to take into account the true three-dimensional motion of the components of the bearing and their dynamic interactions. The invention of Cao hong Rui et al, patent CN110008555B and journal article (Cao H, Wang D, Zhu Y, et al, Dynamic modification and anti-normal contact analysis of rolling ball bearings with double halo-inner rings [ J ]. Mechanical Systems and Signal Processing, 2021, 147: 107075.) can establish the link between the working condition parameters and the three-point Dynamic contact state, but the disadvantages are mainly: firstly, the structural characteristics and the dynamic interaction among components of the four-point contact ball bearing are more complex than those of a three-point contact ball bearing, so that a three-point contact ball bearing dynamic model cannot be directly used for the analysis of the four-point contact ball bearing; the method for judging the contact state by utilizing the contact angle and the contact load cannot intuitively reflect the change of the contact state in a certain operation time interval; and thirdly, the real-time contact position on the raceway of the ferrule cannot be obtained, and subsequent wear failure and fatigue life calculation are not facilitated.
Disclosure of Invention
The invention provides a method for selecting the use condition of a high-speed four-point contact ball bearing in order to make up the defects of the prior art.
The invention is realized by the following technical scheme: a method for selecting the use condition of a high-speed four-point contact ball bearing comprises the following steps:
the method comprises the following steps: establishing a dynamic coordinate system of the four-point contact ball bearing, wherein the dynamic coordinate system comprises an inertial coordinate system, a component connected body coordinate system, a contact coordinate system and an orientation coordinate system, the inertial coordinate system comprises a Cartesian rectangular coordinate system O-XYZ, namely the inertial rectangular coordinate system O-XYZ and an inertial cylindrical coordinate system, the component connected body coordinate system comprises an outer ring connected body coordinate system and an inner ring connected body coordinate system, the orientation coordinate system comprises a spherical orientation coordinate system, and the connected body coordinate system comprises an outer ring connected body coordinate system and an inner ring connected body coordinate system;
step two: establishing a four-point contact ball bearing multi-body motion dynamics model, and solving a component motion mechanics model; the differential equations for the contact ball and inner race motion are set forth in terms of the general motion dynamics of the assembly, wherein,min order to be of a mass,Jin order to be the moment of inertia,ωin order to be the angular velocity of the object,Fin order to have a resultant force,Min order to obtain the resultant moment,Nthe number of contact ball bodies; r isb（x b , r b , θ b ) Is the vector of the center O of the contact ball with respect to the origin of the inertial coordinate O, rr（x r , y r , z r ) Is the geometric center o of the inner ringrA vector relative to an inertial coordinate origin O;F r for external radial forces acting on the inner ring,F a as axial force, Mr(M xr , M yr , M zr ) For external torque acting on the inner ring, when the inner ring rotates at a constant speed
， 
The superscript letters all represent coordinate systems where the variables are located; the equation of motion is specifically as follows;
the three-dimensional mass center motion equation of the sphere in an inertial cylindrical coordinate system O-xr theta is as follows:
sphere in azimuth coordinate system o-xayazaThe three-dimensional rotational equation of motion in (1) is:
the three-dimensional mass center motion equation of the inner ring in the inertial rectangular coordinate system O-XYZ is as follows:
coordinate system o with inner ring and inner ring connectedr-xryrzrThe three-dimensional rotational equation of motion in (1) is:
step three: performing coordinate conversion and contact point position calculation, specifically, performing coordinate conversion of variables in different coordinate systems, and calculating contact point position vectors in an inner and outer ring connected body coordinate system through the coordinate conversion to represent the contact state of the rolling body/raceway;
to obtain attitude parameters of the inner ring(η,β,γ)Simultaneously solving an attitude kinematics equation:
conversion matrix A between inner circle connected coordinate system and inertia rectangular coordinate systemirExpressed by the following matrix:
the conversion matrix between the sphere azimuth coordinate system and the inertia rectangular coordinate system is as follows:
four contact coordinate systems o1-xc1yc1zc1、o2-xc2yc2zc2、o3-xc3yc3zc3、o4-xc4yc4zc4And the sphere orientation coordinate system is as follows:
wherein the content of the first and second substances,jdenotes a contact coordinate system o when =1, 2, 3, 41-xc1yc1zc1、o2-xc2yc2zc2、o3-xc3yc3zc3、o4-xc4yc4zc4Four cases of (1);
spatial contact angles at four contact pointsα 1 Andα 2 obtained by the following method:
the vector of the center of the ball relative to the curvature center of the half ferrule where a certain contact point is located is as follows:
wherein r isrcjThe position vector of the curvature center of the half ferrule where the contact point is located relative to the geometric center of the ferrule;
defining a unit vector e based on the position vectorj(e 1j ,e 2j ,e 3j ) Comprises the following steps:
there is an indirect antenna:
step four: whether the four contact points contact or not is continuously judged according to the distance between the edge of the ball and the raceway:
wherein the content of the first and second substances,R j the radius of curvature of the half ferrule where the contact point is located,Dis the diameter of a sphere; when in useΔ j If the ball body is not contacted with the roller path, continuing the next time variable step length integration iteration, when the time variable step length integration iteration is finishedΔ j If the contact deformation is larger than 0, the normal contact load, the tangential friction force and the resultant moment are calculated, and meanwhile, the raceway contact position is calculated;
step five: and calculating the contact position of the roller path, wherein in a contact coordinate system where the four contact points are located, the vector of the contact point relative to the center of the ball is expressed as:
the contact point position vector is expressed in the outer circle connected coordinate system as:
the position vector of the contact point is expressed in an inner circle connected coordinate system as follows:
wherein the content of the first and second substances,
and
respectively recording the contact positions of the contact points on the outer raceway and the inner raceway at each integration moment, and then connecting the contact position results in a given time interval of the dynamic model to form the running track of the contact points; through the output of the contact locus, whether the four contact areas are in contact or not and whether two-point contact, three-point contact or four-point contact exists or not are visually reflected on the raceways of the inner ring and the outer ring;
step six: by varying the speed of rotation of the inner ringωOr external load, to obtain the normal two-point contact state of the high-speed four-point contact ball bearing, so as to obtain the rotating speed and load working condition parameters.
Further, the external load includes a radial forceF r Axial forceF a And overturning momentM yr 、M zr 。
Compared with the prior art, the invention has the advantages that:
1. the contact state inside the high-speed four-point contact ball bearing is visually represented by utilizing the contact tracks left on the inner raceway and the outer raceway of the rolling body in the operation process, including several point contacts and at which positions, so that the visual relation is established between the rotating speed and load working condition parameters and the contact state, and the visual relation is used for standardizing the rotating speed and load working condition selection when the bearing is used;
2. the invention provides a dynamic contact model and a dynamic contact method for selecting the use working condition of a high-speed four-point contact ball bearing by intuitively utilizing a raceway contact track, which overcome the defect that the dynamic contact state of a rolling body/raceway under the condition of complex working conditions cannot be accurately judged in the prior art;
2. on the basis of a Gupta dynamics method, a gyroscopic moment, a centrifugal force and a dynamic interaction of components are considered, a dynamics model of six degrees of freedom of a rolling ball, six degrees of freedom of an inner ring and a fixed outer ring of a high-speed four-point contact ball bearing is established, all contact point information of a roller path of the inner ring and a roller path of the outer ring in a considered time interval is obtained through solving, the contact point information comprises whether four contact surfaces are in contact or not and at what positions, and further the rotating speed working condition and the load working condition range of the high-speed four-point contact ball bearing during assembly and use can be selected according to the.
Drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of a coordinate system of a high-speed four-point contact ball bearing according to the present invention;
FIG. 2 is a schematic diagram of four quasi-contact points of the high-speed four-point contact ball bearing of the present invention;
FIG. 3 is a block diagram of the selection process of the operating condition of the high-speed four-point contact ball bearing of the present invention;
FIG. 4 is a schematic diagram of a two-point contact trajectory of the high-speed four-point contact ball bearing of the present invention;
FIG. 5 is a schematic diagram of a three-point contact trace of the high-speed four-point contact ball bearing of the present invention;
FIG. 6 is a diagram of four-point contact traces of the high-speed four-point contact ball bearing according to the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
A method for selecting the use condition of a high-speed four-point contact ball bearing is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: as shown in fig. 1, establishing a dynamic coordinate system of a four-point contact ball bearing, which comprises an inertial coordinate system, a component connected body coordinate system, a contact coordinate system and an orientation coordinate system, wherein the inertial coordinate system comprises a cartesian rectangular coordinate system O-XYZ, namely an inertial rectangular coordinate system O-XYZ, and an inertial cylindrical coordinate system, the component connected body coordinate system comprises an outer ring connected body coordinate system and an inner ring connected body coordinate system, the orientation coordinate system comprises a sphere orientation coordinate system, and the connected body coordinate system comprises an outer ring connected body coordinate system and an inner ring connected body coordinate system;
the process of establishing the coordinate system is explained as follows:
the inertial frame is the basic frame of reference in space. The inertia coordinate system is divided into two, one is a Cartesian rectangular coordinate system O-XYZ, namely the inertia rectangular coordinate system O-XYZ, because the outer ring is fixed, the original point O is fixed at the geometric center of the outer ring, the X axis is consistent with the direction of the axial force, the Z axis is consistent with the direction of the radial force, and the Y axis is determined by the right-hand rule. The translational motion of the inner ring is considered in an inertial rectangular coordinate system, the translational motion of the sphere is considered in an inertial cylindrical coordinate system O-xr theta, the X axis of the inertial cylindrical coordinate system is coincident with the X axis, r is the projection of a vector on a YOZ plane, and theta is the included angle between the projection of the inertial cylindrical coordinate system on the YOZ plane and the Z axis.
The assembly integrated coordinate system is fixedly connected in the assembly and performs spatial translation and rotation motion along with the assembly. And the outer ring connected coordinate system is superposed with the inertia rectangular coordinate system O-XYZ. The inner rings of the two halves are inseparable after mounting on the shaft and are therefore considered as one integral inner ring. Inner circle integrated coordinate system or-xryrzrThe origin of coordinates is its centroid, the axis of the initial positionThe direction is consistent with the inertial rectangular coordinate system O-XYZ.
The four-point contact ball bearing has two contact points respectively between the ball and the outer ring and between the ball and the inner ring, as shown in fig. 2. Defining a contact coordinate system on each contact point, i.e. a ball/outer ring contact coordinate system o1-xc1yc1zc1And o2-xc2yc2zc2Ball/inner circle contact coordinate system o3-xc3yc3zc3And o4-xc4yc4zc4. The origin of the contact coordinate system is set at the central position of the contact ellipse, zcAxis aligned with the contact normal, xcThe axis is aligned with the major axis of the contact ellipse.
Sphere orientation coordinate system o-xayazaWith the origin of coordinates in the center of the sphere, xaThe axis is consistent with the X-axis direction of the inertial rectangular coordinate system, and the vector of the ball center O relative to the inertial coordinate origin O is rb，zaShaft and rbAre aligned in the radial component direction. The following table is a description of the coordinate system type, name and coordinate system notation:
step two: establishing a four-point contact ball bearing multi-body motion dynamics model so as to realize the solution of inner ring attitude parameters and express a conversion matrix between an inner ring connected coordinate system and an inertia rectangular coordinate system
. The following dynamic contact model derivation is based on a fixed outer ring and a free inner ring, and the method is still applicable when the inner ring is fixed and the outer ring is free.
The differential equations for the contact ball and inner race motion are set forth in terms of the general motion dynamics of the assembly, wherein,min order to be of a mass,Jin order to be the moment of inertia,ωin order to be the angular velocity of the object,Fin order to have a resultant force,Min order to obtain the resultant moment,Nthe number of contact ball bodies; r isb（x b , r b , θ b ) Is the vector of the center O of the contact ball with respect to the origin of the inertial coordinate O, rr（x r , y r , z r ) Is the geometric center o of the inner ringrA vector relative to an inertial coordinate origin O;F r for external radial forces acting on the inner ring,F a as axial force, Mr(M xr , M yr , M zr ) For external torque acting on the inner ring, when the inner ring rotates at a constant speed
， 
The upper letters all represent coordinate systems where the variables are located, and the same is applied below; the equation of motion is specifically as follows;
the three-dimensional mass center motion equation of the contact sphere in an inertial cylindrical coordinate system O-xr theta is as follows:
contact ball body in ball orientation coordinate system o-xayazaThe three-dimensional rotational equation of motion in (1) is:
the three-dimensional mass center motion equation of the inner ring in the inertial rectangular coordinate system O-XYZ is as follows:
coordinate system o with inner ring and inner ring connectedr-xryrzrThe three-dimensional rotational equation of motion in (1) is:
step three: coordinate conversion and contact point position calculation are carried out, specifically, a four-order variable step length Runge-Kutta method is adopted to solve a general kinematic equation of the ball and the inner ring and an inner ring attitude kinematic equation, then coordinate conversion of variables in different coordinate systems can be carried out, and a contact point position vector in an inner and outer ring connected coordinate system is calculated through the coordinate conversion so as to represent the contact state of the rolling body/raceway;
to obtain attitude parameters of the inner ring(η,β,γ)Simultaneously solving an attitude kinematics equation:
conversion matrix A between inner circle connected coordinate system and inertia rectangular coordinate systemirExpressed by the following matrix:
the conversion matrix between the sphere azimuth coordinate system and the inertia rectangular coordinate system is as follows:
four contact coordinate systems o1-xc1yc1zc1、o2-xc2yc2zc2、o3-xc3yc3zc3、o4-xc4yc4zc4And the sphere orientation coordinate system is as follows:
wherein the content of the first and second substances,jdenotes a contact coordinate system o when =1, 2, 3, 41-xc1yc1zc1、o2-xc2yc2zc2、o3-xc3yc3zc3、o4-xc4yc4zc4Four cases of (1);
spatial contact angles at four contact pointsα 1 Andα 2 obtained by the following method:
the vector of the center of the ball relative to the curvature center of the half ferrule where a certain contact point is located is as follows:
wherein r isrcjThe position vector of the curvature center of the half ferrule where the contact point is located relative to the geometric center of the ferrule;
defining a unit vector e based on the position vectorj(e 1j ,e 2j ,e 3j ) Comprises the following steps:
there is an indirect antenna:
step four: the positions of the rolling body/raceway contact points in the four contact coordinate systems are respectively converted into an inertia rectangular coordinate system (outer ring connected coordinate system) and an inner ring connected coordinate system, so that whether the sphere is in contact with the inner ring and the outer ring at the considered moment or not and the contact position results on the inner ring and the outer ring can be respectively obtained, and then working condition parameters are adjusted according to the contact conditions, and a process block diagram is shown in fig. 3. Whether the four contact points are in contact or not is a contact state result which is finally obtained, and is also a precondition for calculating a normal contact load, a tangential friction force, the contact points and a contact position in the dynamic contact model, and the judgment is performed in the whole process of dynamic iterative calculation, so that whether the four contact points are in contact or not is continuously judged according to the distance between the edge of the ball and the raceway:
wherein the content of the first and second substances,R j the radius of curvature of the half ferrule where the contact point is located,Dis the diameter of a sphere; when in useΔ j If the ball body is not contacted with the roller path, continuing the next time variable step length integration iteration, when the time variable step length integration iteration is finishedΔ j If the contact deformation is larger than 0, the normal contact load, the tangential friction force and the resultant moment are calculated, and meanwhile, the raceway contact position is calculated;
step five: and calculating the contact position of the roller path, wherein in a contact coordinate system where the four contact points are located, the vector of the contact point relative to the center of the ball is expressed as:
the contact point position vector is expressed in the outer circle connected coordinate system as:
the position vector of the contact point is expressed in an inner circle connected coordinate system as follows:
wherein the content of the first and second substances,
and
respectively at the outer race andrecording the contact point position once at each integration moment on the contact position on the inner raceway, and then connecting the contact point position results in a given time interval of the dynamic model to form the running track of the contact point, wherein the given time interval is more than one step length; through the output of the contact locus, whether the four contact areas are in contact or not and whether two-point contact, three-point contact or four-point contact exists or not are intuitively reflected on the raceways of the inner ring and the outer ring, as shown in fig. 4-6, the number of contact points and the contact positions thereof can be intuitively seen;
step six: by varying the speed of rotation of the inner ringωOr external loads, e.g. radial forcesF r Axial forceF a And overturning momentM yr 、M zr And obtaining the normal two-point contact state of the high-speed four-point contact ball bearing, thereby obtaining the rotating speed and the load working condition parameters.
The invention provides a method for selecting the use condition of a high-speed four-point contact ball bearing, namely, a relation is established between the rotating speed and load condition and the dynamic contact state of a rolling body/raceway, so that the rotating speed and load range applied in the use process of the bearing is selected according to the required normal contact state of the rolling body/raceway, namely two-point contact. In the invention, the relation between the use working condition and the dynamic contact state of the rolling body/raceway is realized by solving the established high-speed four-point contact ball bearing dynamic contact model, and the two, three or four-point dynamic contact state of the rolling ball and the inner and outer raceways within a period of operation time can be predicted by solving the model according to the rotating speed and the load working condition. The prediction of the dynamic contact state of the rolling ball and the inner and outer raceways is intuitively expressed by outputting the contact trajectory distribution on the inner and outer raceways, and not only can a few point contacts be seen, but also the contact point position within a period of time can be obtained. In specific implementation, in order to calculate the contact point positions on the inner raceway and the outer raceway, a set of coordinate conversion method for describing the contact position vectors in the corresponding ferrule connected coordinate system is provided, so that the visual expression of the contact position and the contact track on the half ferrule raceway is realized; in order to obtain attitude parameters required in coordinate conversion, a four-order variable step length Runge Kutta method is utilized to solve a four-point contact ball bearing dynamic model which comprises a general motion differential equation of a sphere and an inner ring and an attitude kinematic differential equation of the inner ring; and in the iteration process, the normal distance between the edge of the ball body and the peach-shaped raceway is judged in real time, the acting force and the position of the contact point are calculated and output when the normal distance is larger than zero, and the condition of other contact points is judged or the next iteration is carried out when the normal distance is smaller than or equal to zero.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A method for selecting the use condition of a high-speed four-point contact ball bearing is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a dynamic coordinate system of the four-point contact ball bearing, wherein the dynamic coordinate system comprises an inertial coordinate system, a component connected body coordinate system, a contact coordinate system and an orientation coordinate system, the inertial coordinate system comprises a Cartesian rectangular coordinate system O-XYZ, namely the inertial rectangular coordinate system O-XYZ and an inertial cylindrical coordinate system, the component connected body coordinate system comprises an outer ring connected body coordinate system and an inner ring connected body coordinate system, the orientation coordinate system comprises a spherical orientation coordinate system, and the connected body coordinate system comprises an outer ring connected body coordinate system and an inner ring connected body coordinate system;
step two: establishing a four-point contact ball bearing multi-body motion dynamics model, and solving a component motion mechanics model; the differential equations for the contact ball and inner race motion are set forth in terms of the general motion dynamics of the assembly, wherein,min order to be of a mass,Jin order to be the moment of inertia,ωin order to be the angular velocity of the object,Fin order to have a resultant force,Min order to obtain the resultant moment,Nthe number of contact ball bodies; r isb（x b , r b , θ b ) Is the vector of the center O of the contact ball with respect to the origin of the inertial coordinate O, rr（x r , y r , z r ) As a geometry of the inner circleCenter orA vector relative to an inertial coordinate origin O;F r for external radial forces acting on the inner ring,F a as axial force, Mr(M xr , M yr , M zr ) For external torque acting on the inner ring, when the inner ring rotates at a constant speed
，
The superscript letters all represent coordinate systems where the variables are located; the equation of motion is specifically as follows;
the three-dimensional mass center motion equation of the sphere in an inertial cylindrical coordinate system O-xr theta is as follows:
sphere in azimuth coordinate system o-xayazaThe three-dimensional rotational equation of motion in (1) is:
the three-dimensional mass center motion equation of the inner ring in the inertial rectangular coordinate system O-XYZ is as follows:
coordinate system o with inner ring and inner ring connectedr-xryrzrThe three-dimensional rotational equation of motion in (1) is:
step three: performing coordinate conversion and contact point position calculation, specifically, performing coordinate conversion of variables in different coordinate systems, and calculating contact point position vectors in an inner and outer ring connected body coordinate system through the coordinate conversion to represent the contact state of the rolling body/raceway;
to obtain attitude parameters of the inner ring(η,β,γ)Simultaneously solving an attitude kinematics equation:
conversion matrix A between inner circle connected coordinate system and inertia rectangular coordinate systemirExpressed by the following matrix:
the conversion matrix between the sphere azimuth coordinate system and the inertia rectangular coordinate system is as follows:
four contact coordinate systems o1-xc1yc1zc1、o2-xc2yc2zc2、o3-xc3yc3zc3、o4-xc4yc4zc4And the sphere orientation coordinate system is as follows:
wherein the content of the first and second substances,jdenotes a contact coordinate system o when =1, 2, 3, 41-xc1yc1zc1、o2-xc2yc2zc2、o3-xc3yc3zc3、o4-xc4yc4zc4Four cases of (1);
spatial contact angles at four contact pointsα 1 Andα 2 obtained by the following method:
the vector of the center of the ball relative to the curvature center of the half ferrule where a certain contact point is located is as follows:
wherein r isrcjThe position vector of the curvature center of the half ferrule where the contact point is located relative to the geometric center of the ferrule;
defining a unit vector e based on the position vectorj(e 1j ,e 2j ,e 3j ) Comprises the following steps:
there is an indirect antenna:
step four: whether the four contact points contact or not is continuously judged according to the distance between the edge of the ball and the raceway:
wherein the content of the first and second substances,R j the radius of curvature of the half ferrule where the contact point is located,Dis the diameter of a sphere; when in useΔ j If the ball body is not contacted with the roller path, continuing the next time variable step length integration iteration, when the time variable step length integration iteration is finishedΔ j If the contact deformation is larger than 0, the normal contact load, the tangential friction force and the resultant moment are calculatedCalculating the contact position of the roller path;
step five: and calculating the contact position of the roller path, wherein in a contact coordinate system where the four contact points are located, the vector of the contact point relative to the center of the ball is expressed as:
the contact point position vector is expressed in the outer circle connected coordinate system as:
the position vector of the contact point is expressed in an inner circle connected coordinate system as follows:
wherein
And
respectively recording the contact positions of the contact points on the outer raceway and the inner raceway at each integration moment, and then connecting the contact position results in a given time interval of the dynamic model to form the running track of the contact points; through the output of the contact locus, whether the four contact areas are in contact or not and whether two-point contact, three-point contact or four-point contact exists or not are visually reflected on the raceways of the inner ring and the outer ring;
step six: by varying the speed of rotation of the inner ringωOr external load, to obtain the normal two-point contact state of the high-speed four-point contact ball bearing, so as to obtain the rotating speed and load working condition parameters.
2. According to claim1 the method for selecting the use condition of the high-speed four-point contact ball bearing is characterized in that: the external load comprising a radial forceF r Axial forceF a And overturning momentM yr 、M zr 。
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH1113750A (en) * | 1997-06-30 | 1999-01-22 | Nippon Seiko Kk | Three-point contact ball bearing |
| JP2000170753A (en) * | 1998-12-04 | 2000-06-20 | Ntn Corp | Ball bearing |
| DE102007024253A1 (en) * | 2007-05-16 | 2008-11-20 | Werkzeugmaschinenlabor WZL-RWTH Aachen Lehrstuhl für Werkzeugmaschinen | Ball bearing, particularly high accuracy angular ball bearing, has external and internal ring, which has running groove, in which rolling body engages |
| CN103500268A (en) * | 2013-09-06 | 2014-01-08 | 西安交通大学 | High-speed angular contact ball bearing damage fault dynamic analysis method |
| CN105822661A (en) * | 2016-06-01 | 2016-08-03 | 河南科技大学 | Design method and device of structural parameters of major and minor semi axes of elliptical race ball bearing |
| CN110008555A (en) * | 2019-03-27 | 2019-07-12 | 西安交通大学 | A kind of three-point contact ball bearing exception contact scratch quantitative evaluating method |
| CN110059408A (en) * | 2019-04-18 | 2019-07-26 | 重庆交通大学 | Flexible thin-walled bearing fatigue life calculation method in harmonic speed reducer |
-
2021
- 2021-02-23 CN CN202110200034.5A patent/CN112855755B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH1113750A (en) * | 1997-06-30 | 1999-01-22 | Nippon Seiko Kk | Three-point contact ball bearing |
| JP2000170753A (en) * | 1998-12-04 | 2000-06-20 | Ntn Corp | Ball bearing |
| DE102007024253A1 (en) * | 2007-05-16 | 2008-11-20 | Werkzeugmaschinenlabor WZL-RWTH Aachen Lehrstuhl für Werkzeugmaschinen | Ball bearing, particularly high accuracy angular ball bearing, has external and internal ring, which has running groove, in which rolling body engages |
| CN103500268A (en) * | 2013-09-06 | 2014-01-08 | 西安交通大学 | High-speed angular contact ball bearing damage fault dynamic analysis method |
| CN105822661A (en) * | 2016-06-01 | 2016-08-03 | 河南科技大学 | Design method and device of structural parameters of major and minor semi axes of elliptical race ball bearing |
| CN110008555A (en) * | 2019-03-27 | 2019-07-12 | 西安交通大学 | A kind of three-point contact ball bearing exception contact scratch quantitative evaluating method |
| CN110059408A (en) * | 2019-04-18 | 2019-07-26 | 重庆交通大学 | Flexible thin-walled bearing fatigue life calculation method in harmonic speed reducer |
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