CN113884266A - Equivalent high-speed bearing flow field parameter measuring method - Google Patents

Equivalent high-speed bearing flow field parameter measuring method Download PDF

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CN113884266A
CN113884266A CN202111153636.6A CN202111153636A CN113884266A CN 113884266 A CN113884266 A CN 113884266A CN 202111153636 A CN202111153636 A CN 202111153636A CN 113884266 A CN113884266 A CN 113884266A
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bearing
flow field
coordinate system
equivalent
simulation
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高羡明
华梦怡
郭宁波
张功学
赵逸飞
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Shaanxi University of Science and Technology
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Shaanxi University of Science and Technology
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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
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • G01M9/08—Aerodynamic models

Abstract

The invention discloses a method for measuring flow field parameters of an equivalent high-speed bearing, which comprises the steps of planning and designing a scheme of a simulation cavity, an equivalent bearing, a simulation heat source and other structures through theoretical numerical calculation, comparing and optimizing the design scheme with the flow field distribution condition of the original bearing under the high-speed rotation working condition through a simulation technology to obtain an equivalent flow field consistent with the flow change, the flow field distribution and the heat field distribution of the original high-speed bearing, and acquiring data of the flow field, the pressure, the temperature and other parameters of the equivalent flow field through reasonable layout of measuring points of a test sensor, thereby completing equivalent measurement of the flow field distribution parameters of the original high-speed bearing. The invention is convenient for designers to measure the parameters of the high-speed bearing such as flow, temperature, pressure and the like under any complex working conditions, can help the designers to find weak links in the design process of the high-speed bearing structure, and provides data reference for the optimal design of the high-speed bearing and an application carrier thereof.

Description

Equivalent high-speed bearing flow field parameter measuring method
Technical Field
The invention belongs to the technical field of high-speed bearings, and particularly relates to a method for measuring flow field parameters of an equivalent high-speed bearing.
Background
The bearing is a key element for realizing high-speed rotation, the bearing is arranged in a liquid flow field through a rotating main shaft, and the bearing has the working condition characteristics of high thrust, high rotating speed and extreme temperature, so that the bearing is blackened, scratched or even damaged in the operation process. The essential reason is that the bearing heating under high-speed rotation can not conduct heat in time, and heat diffusion is difficult to conduct. The working environment of the bearing is extremely complex, heat generated by friction of parts of the bearing is diffused, heat generated by friction of peripheral fluid is diffused, and under the complex working condition, the research on heat exchange is more complex. Due to the characteristic of high-speed working condition of the bearing, the flow field parameter data of the bearing is difficult to measure directly by the prior art means.
In view of the background that real-time and effective monitoring of data cannot be realized, theoretical calculation and numerical simulation are combined, an equivalent high-speed bearing flow field parameter measuring method is provided, the distribution and change conditions of complex flow, pressure and temperature parameters of a high-speed bearing are measured and analyzed, influence factors of the high-speed bearing are explored, and the method has important practical significance on structural design and improvement of the high-speed bearing and an application carrier of the high-speed bearing.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide the equivalent high-speed bearing flow field parameter measuring method, which can be used for more comprehensively analyzing the temperature flow field influence factors of the bearing in the flow field and improving the analysis efficiency.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for measuring equivalent high-speed bearing flow field parameters comprises the following steps;
the method comprises the following steps: constructing a simulation cavity 15, enabling the equivalent bearing 10 to be installed in the simulation cavity 15, determining the structural design of the simulation cavity 15 through a finite element simulation technology, and obtaining the same flow change as the original bearing working environment;
step two: constructing an equivalent bearing 10 with low rotating speed, determining the geometric dimension and the structural configuration of the equivalent bearing, and ensuring that the equivalent bearing can obtain a flow field distribution state similar to that of an actual high-speed rotating bearing through simulation comparison analysis of the flow field of the actual original bearing;
step three: determining the installation position of the equivalent bearing 10 in the simulation cavity 15, and obtaining a flow field distribution state similar to the actual working condition;
step four: constructing a simulated heat source 9, and enabling the calorific value of the simulated heat source 9 to be the same as the calorific value generated when the original bearing rotates at a high speed through calculation;
step five: determining the installation position of the simulated heat source 9 in the simulated cavity 15, so that the simulated heat source can equivalently simulate the distribution state of a peripheral heat flow field when the original bearing rotates at a high speed;
step six: constructing a simulation power source 17, enabling the simulation power source to drive the rotating main shaft 1 and the equivalent bearing 10 to rotate, simulating the high-speed rotation movement of the original bearing in the turbo pump, firstly analyzing the load direction and the service life of the equivalent bearing 10 in the flow field simulation process, calculating the friction power consumption of a supporting bearing, determining the type selection of the supporting bearing between the simulation power source 17 and the rotating main shaft 1, and determining the configuration mode of the supporting bearing;
step seven: comprehensively analyzing the velocity flow field trace diagram, the flow field distribution axial section diagram and the heat flow field distribution axial section diagram of the equivalent flow field obtained in the third step;
determining a monitoring key point of flow and pressure parameters at the fluid inlet pipeline 4 according to the requirement that the inlet flow and pressure of the simulation cavity 15 meet the simulation conditions of the equivalent bearing 10; determining a monitoring key point of flow and pressure parameters at a fluid outlet pipeline 11 according to the condition that a pressure release phenomenon can be generated at a flow outlet of the simulation cavity; in addition, the cavity area with the pressure most value, the pressure sudden change and the constant pressure change amplitude also serves as a monitoring key point of the pressure parameter;
determining a monitoring key point of a temperature parameter at the fluid inlet pipeline 4 according to the requirement of conveniently checking the internal heating condition of the equivalent bearing 10; by comparing the temperature parameters of the flow field near the front end surface and the flow field near the rear end surface of the equivalent bearing 10, the heating efficiency of the equivalent bearing 10 during working can be accurately calculated, and therefore the flow fields near the front end surface and the rear end surface of the equivalent bearing 10 are also determined as monitoring key points of the temperature parameters; analyzing the heat dissipation condition of the equivalent flow field by comparing the temperature parameters of the flow field near the rear end surface of the equivalent bearing 10 and the fluid outlet pipeline 11, so that the fluid outlet pipeline 11 is a monitoring key point of the temperature parameters; in addition, the sudden temperature change part is also a monitoring key point of the temperature parameter;
and (3) assembling the simulation cavity 15, the equivalent bearing 10, the simulation heat source 9 and the simulation power source 17 determined in the first step to the sixth step according to the obtained ideal positions, and installing corresponding sensors at key points of flow, pressure and temperature monitoring obtained by analysis, so that data acquisition can be carried out on parameters of the flow field, pressure, temperature and the like of the equivalent flow field, and therefore equivalent measurement on the distribution parameters of the original high-speed bearing flow field is completed.
The first step is specifically as follows:
1-1) referring to the working environment, structural characteristics and geometric dimensions of the original bearing, preliminarily designing the structure of the simulation cavity 15 to be a cylindrical shell, wherein the simulation cavity 15 can synchronously rotate along with the rotating main shaft 1, and the left simulation cavity end cover 5 and the right simulation cavity end cover 5 are respectively provided with a fluid inlet pipeline 4 and a fluid outlet pipeline 1 which are distributed in a circumferential row along with the rotating main shaft 15;
1-2) establishing a plurality of groups of three-dimensional models of different-diameter simulation cavity 15 structures in three-dimensional computer aided design software Solidworks by taking the diameter of the simulation cavity 15 as a variable;
1-3) respectively importing the three-dimensional models of the plurality of simulation cavity 15 structures established in the step 1-2) into finite element commercial software Ansys workbench in a format of an intermediate file, setting the same boundary conditions, respectively carrying out simulation calculation on flow fields of the models, solving to obtain flow field distribution cloud maps of the models, importing the flow field distribution cloud maps into post-processing software Tecplot for post-processing to obtain axial sectional maps of the models;
respectively selecting 5 position measuring points near a rotating main shaft 1 in the axial section of the flow field distribution cloud picture of each scheme, respectively determining the flow field resultant velocity numerical value of each position measuring point, and drawing a flow field resultant velocity curve chart simulating each diameter size scheme of the cavity 15;
1-4) comparing and analyzing the flow field resultant velocity curve diagrams of the measuring points of the simulation cavity 15 with different diameter size schemes obtained in the step 1-3), and comprehensively determining the design diameter of the cavity structure with larger flow velocity of the flow field by combining the diameter of the measured bearing in the cavity;
1-5) establishing a plurality of groups of three-dimensional models of simulation cavity 15 structures with different lengths in three-dimensional computer aided design software Solidworks by taking the length of the simulation cavity 15 as a variable;
1-6) respectively importing the three-dimensional models of the simulation cavity 15 structures established in the step 1-5) into finite element commercial software Ansys workbench in a format of an intermediate file, setting the same boundary conditions, performing simulation calculation on the flow field, and solving to obtain a velocity flow field trace diagram and a flow field distribution cloud diagram of the flow field;
guiding the obtained flow field distribution cloud charts of each scheme into post-processing software Tecplot for post-processing to obtain an axial sectional view of the flow field distribution cloud charts, selecting 5 position measuring points near a main rotating shaft 1, respectively determining flow field resultant velocity numerical values of the position measuring points, and drawing a flow field resultant velocity line graph simulating each length scheme of a cavity 15;
1-7) comparing and analyzing the flow field resultant velocity line graphs of the simulation cavity 15 with different length schemes obtained in the step 1-6) and the obtained velocity flow field trace graph, and comprehensively determining the scheme that the flow field change in the trace graph is more obvious and the speed numerical value fluctuation of the flow field in the line graph is larger to design the length for the cavity structure;
the second step is specifically as follows:
2-1) according to the geometrical structure characteristics of the original bearing, the cross section area and the pore area of the bearing jointly form the total area of a medium in the original flow field passing through the bearing, and the cross section area and the pore area of the original bearing are respectively calculated;
designing a plurality of groups of equivalent bearing 10 structure configuration schemes with different diameters, pores and thickness sizes, enabling the cross-sectional area of the equivalent bearing to be equal to the calculated maximum cross-sectional area of the original bearing, and enabling the pore area of the equivalent bearing 10 to be equal to the calculated pore area of the original bearing;
according to the mass flow calculation formula, the mass flow is equal to the product of the volume flow and the medium density, and according to the volume flow calculation formula, the volume flow is equal to the product of the average flow velocity and the total cross-sectional area through which the medium passes, so that when the cross-sectional area and the pore area of the equivalent bearing 10 are equal to the maximum cross-sectional area and the pore area of the original bearing, the equivalent bearing 10 can pass the flow which is approximately the same as the original bearing;
2-2) respectively establishing 2-1) three-dimensional models of the equivalent bearings 10, the original bearings and the simulation cavity 15 in different configuration schemes in three-dimensional computer aided design software Solidworks, and respectively installing the three-dimensional models of the equivalent bearings 10 and the original bearings in different schemes at the same installation positions of the three-dimensional models of the simulation cavity 15 to obtain assembly bodies of the equivalent bearings 10 and the original bearings in different configuration schemes;
2-3) repeating the steps 1-6) to obtain three-dimensional models of the assembly body with different configuration schemes, and a velocity flow field trace diagram, a flow field distribution axial section diagram and a flow field resultant velocity broken line diagram of a position measuring point of the three-dimensional model of the original bearing assembly body;
respectively carrying out accurate region division on the feasible structure configuration, the axial section flow field distribution cloud chart and the speed flow field trace chart of the original bearing by using the flow field resultant velocity numerical value of the position measuring point;
and 2-4) comparing and analyzing the flow field combination velocity numerical value, the flow field combination velocity broken line diagram, the accurately partitioned axial cross-section flow field distribution cloud chart and the velocity flow field trace diagram of the position measuring point obtained in the step 2-3), and if the configuration of a certain equivalent bearing 10 simultaneously meets the condition that the flow field combination velocity numerical value of the position measuring point is similar to the flow field combination velocity numerical value of the position measuring point obtained by the simulation of the original bearing, the flow field distribution condition near a rotating shaft in the flow field distribution cloud chart of the axial cross-section is similar to the flow field distribution condition near the rotating shaft of the original bearing, the velocity flow field trace diagram is basically similar to the original bearing velocity flow field trace diagram, and the combination velocity broken line diagram is basically superposed with the original bearing combination velocity broken line diagram, the configuration bearing is proved to be equivalent to the original bearing, namely the feasible structure configuration is the ideal structure configuration of the equivalent bearing 10.
The third step is specifically as follows:
3-1) taking the assembly distance between the mounting point of the equivalent bearing 10 and the left end face of the inner cavity of the simulation cavity 15 as a variable, mounting the three-dimensional model of the equivalent bearing 10 at different positions in the three-dimensional model of the simulation cavity 15 in three-dimensional computer aided design software Solidworks, and obtaining a plurality of assembly bodies with different mounting schemes of the equivalent bearing 10;
3-2) repeating the steps 1-6) to obtain velocity flow field trace graphs, flow field distribution axial section graphs and flow field resultant velocity broken line graphs of position measuring points of the equivalent bearing 10 assembly body with different installation schemes;
3-3) comprehensively determining that the flow field trace graphs of a plurality of different installation schemes obtained in the step 3-2) and the flow field resultant velocity broken line graphs thereof have obvious flow field steps and no vortex phenomenon, the gradient change near a rotating shaft is slow, the gradient change of the inner wall of the inner cavity of the tester and the inlet and outlet is obvious, and the installation scheme with obvious gradient distribution in the flow field resultant velocity broken line graphs is an ideal installation scheme of the equivalent bearing 10 in the simulation cavity 15.
The fourth step is specifically as follows:
4-1) defining a coordinate system by referring to the matching relation among all parts of the original bearing: an inertial coordinate system OXYZ, a fixed body coordinate system BXBYbZb of a rolling body, a rolling body azimuth coordinate system AXaYaZa, a ferrule fixed body coordinate system RXRYrZr and other local coordinate systems;
wherein, the inertial coordinate system is fixed in the space, the origin O is established at the center of the outer ring, and the X axis is along the central line of the bearing; the rolling body azimuth coordinate system is used for describing the track position of the rolling body center on the bearing, and the origin A of the rolling body azimuth coordinate system is positioned at the rolling body center; in an initial state, an Xa axis is parallel to an X axis, a Za axis passes through the center of the rolling body and is vertically intersected with the central line of the bearing, and a Ya axis is determined according to the right-hand spiral rule; the ferrule fixed body coordinate system is fixedly connected on the ferrule and moves along with the ferrule, the origin R of the ferrule fixed body coordinate system is positioned at the center of the ferrule, the direction of a coordinate axis Xr is parallel to an X axis in an initial state, the direction of a Zr axis is the same as a Z axis, and a Yr axis is determined according to a right-hand spiral rule;
4-2) the vector of the central position of the ball in the inertial cylindrical coordinate system is
Figure BDA0003287884300000071
The moving velocity vector is
Figure BDA0003287884300000072
The spherical position vector in the rectangular coordinate system is
Figure BDA0003287884300000073
The velocity vector is
Figure BDA0003287884300000074
Roller attitude angle of
Figure BDA0003287884300000075
The vector of the rotation speed of the ball in the fixed body coordinate system is
Figure BDA0003287884300000076
The position vector of the ferrule in the inertial rectangular coordinate system is
Figure BDA0003287884300000077
The velocity vector is
Figure BDA0003287884300000078
The attitude angle in the coordinate system of the ferrule stator is
Figure BDA0003287884300000079
The rotating speed in a sleeve ring fixed body coordinate system is
Figure BDA00032878843000000710
The conversion matrix from the sphere fixed body coordinate system to the inertial coordinate system is
Figure BDA00032878843000000711
The transformation matrix from the inner circle fixed body coordinate system to the inertial coordinate system is
Figure BDA0003287884300000081
The transformation matrix from the inertial coordinate system to the spherical orientation coordinate system is
Figure BDA0003287884300000082
The vector of the center of the ball relative to the center of the ferrule in the inertial rectangular coordinate system is
Figure BDA0003287884300000083
Conversion into an azimuth coordinate system of
Figure BDA0003287884300000084
And is converted into a ferrule fixed body coordinate system
Figure BDA0003287884300000085
Further obtaining the azimuth angle theta of the ball in the ferrule coordinate systembrThen the vector of the curvature center of the raceway of the orientation of the ball in the ferrule fixed body coordinate system is
Figure BDA0003287884300000086
Wherein r isfThe radius of the track circle of the curvature center of the ferrule is expressed, and the position vector of the center of the ball relative to the curvature center of the ferrule in the ball orientation coordinate system can be expressed according to the formula
Figure BDA0003287884300000087
And calculating to obtain the contact angle expression as follows:
Figure BDA0003287884300000088
then, a conversion matrix from the spherical orientation coordinate system to the contact coordinate system can be obtained as Tap＝T(αc1,αc20) and the contact deformation between the ball and the raceway can be according to formula
Figure BDA0003287884300000089
Is calculated to obtain f in the formularsDenotes the coefficient of the radius of curvature of the groove, dbRepresents the diameter of the sphere;
after contact deformation is obtained, an elliptical contact area is generated at the contact position of the ball and the raceway, and the major semi-axis a, the minor semi-axis b and the minor semi-axis b of the contact area can be calculated and obtained according to the Hertz point contact theoryContact stress ph(ii) a As the lubricating condition of the bearing of the turbopump is severe and belongs to the solid lubricating working condition, the traction force between the ball and the ferrule needs to be subjected to two-bit numerical integration solution, firstly, the contact ellipse is converted into a unit circle by utilizing a normalization variable (x, y), and the incremental force of the contact between the ball and the ferrule in unit area can be written into a polar coordinate system
Figure BDA00032878843000000810
After the contact load of unit area is obtained, the friction coefficient between the ball and the ferrule is determined according to materials, and two-dimensional numerical integration is carried out by utilizing a Chebyshev polynomial, so that the traction force and the traction torque can be obtained;
4-3) the position vector of the retainer in the inertial rectangular coordinate system is
Figure BDA0003287884300000091
The velocity vector is
Figure BDA0003287884300000092
An attitude angle of
Figure BDA0003287884300000093
Can obtain a conversion matrix from an inner ring stator coordinate system to an inertial coordinate system as
Figure BDA0003287884300000094
Rotation speed in holder fixed body coordinate system
Figure BDA0003287884300000095
And the position vector from the coordinate pocket center to the cage center in the cage fixed body coordinate system can be expressed as
Figure BDA0003287884300000096
The conversion matrix from the fixed body coordinate of the retainer to the pocket coordinate is Tcd(θd0,0), where θdThe azimuth of the center of the pocket is shown;
inertia rectangular seatThe position vector of the center of the ball in the marker system relative to the center of the retainer is
Figure BDA0003287884300000097
The position vector of the center of the ball relative to the center of the pocket in the pocket coordinate system can be expressed in terms of
Figure BDA0003287884300000098
The calculation is carried out to obtain the result,
Figure BDA0003287884300000099
x in pocket coordinate systemdYdProjection and X of planedThe included angle of the shaft can be according to the formula
Figure BDA00032878843000000910
Calculated so that the transformation matrix from the pocket coordinate system to the contact coordinate system PXpYpZp is
Figure BDA00032878843000000911
The minimum clearance between the ball and the pocket wall can be set by
Figure BDA00032878843000000912
Finding the position vector of the minimum clearance point relative to the center of the sphere in the contact coordinate system as
Figure BDA00032878843000000913
And the position vector relative to the center of the retainer can be expressed by
Figure BDA00032878843000000914
Calculated to obtain the vector of the relative speed between the ball and the retainer as
Figure BDA00032878843000000915
Contact coordinate system XpYpIn-plane relative velocity vector and ZpThe included angle of the shaft can be according to the formula
Figure BDA00032878843000000916
Calculating to obtain;
with the surface and pocket of the ballComprehensive roughness sigma between hole surfacesbdOn the basis of hbc≥σbdWhen the cage is used, the normal contact force between the ball and the cage pocket is 0; when h is generatedbc＜σbdWhen the contact deformation between the ball and the pocket is determined by the formula deltabd＝σbd-hbcCalculating to obtain; in view of the hysteresis damping effect, the contact force may be represented by
Figure BDA0003287884300000101
Calculated to obtain, wherein KbcRepresenting Hertz point contact stiffness, cnRepresents contact damping (N · s/m); traction force of Fμ＝μbc|FdbI, in the formula mubcExpressing the traction coefficient (calculated according to the coefficient of dynamic friction between materials);
the cage may have force and moment vectors on the ball that are:
Figure BDA0003287884300000102
the force and moment vector of the ball on the retainer are as follows:
Figure BDA0003287884300000103
4-4) the vector of the position of the center of the retainer relative to the center of the ferrule in the inertia seat right-angle system is
Figure BDA0003287884300000104
The vector from the acting edge point of the retainer and the guide ring to the center position of the retainer in the retainer fixed body coordinate system is
Figure BDA0003287884300000105
In the formula BcageRepresenting the width of the cage, plus representing the left end acting edge point, minus representing the right end acting edge point, when the outer ring is guided, dcIs the diameter d of the outer ring of the retainercoWhen guided by the inner ring, dcIs the diameter d of the inner ring of the cageci，φcThe azimuth angle of the upper contact point of the retainer;the position vector from the edge point to the center point of the ferrule in the ferrule body coordinate system is
Figure BDA0003287884300000106
Considering that the projection on the YrZr plane in the ferrule fixed body coordinate system is maximum when the outer ring guides and minimum when the inner ring guides, the phi is aligned at the momentcThe partial derivative is evaluated to obtain two values: phi is ac1And phic2(ii) a When the outer ring is guiding, phicTaking the maximum value, and when the inner ring is guided, phicTaking the minimum value; the retainer can generate deflection and tilt movement in the operation process, the flange is not completely contacted with the guide surface of the retainer, so that the action length of the retainer and the guide ring is divided into n pieces, and the coordinate of the center of the t-th piece in the center of the retainer is xtThen the vector of the position from the slice action point of the retainer to the center point of the ferrule in the coordinate system of the ferrule is
Figure BDA0003287884300000111
The distance from the edge point of the retainer to the guide surface of the ferrule can be determined
Figure BDA0003287884300000112
Calculating, wherein a plus sign represents an outer ring guide, and a minus sign represents an inner ring guide; with combined roughness σ of cage surface and guide ringcrOn the basis of hm＜σcrWhile the contact deformation between the edge point of the retainer segment and the surface of the guide ring is deltacr＝σcr-hm；
After contact deformation is obtained, contact force Q can be calculated according to the Hertz line contact formulaL(ii) a Then, a contact coordinate system EXpYpZp is established, and the conversion matrix from the ferrule fixed body coordinate system to the contact coordinate system is
Figure BDA0003287884300000113
The expression of the sliding speed of the retainer relative to the ferrule in the contact coordinate system is as follows:
Figure BDA0003287884300000114
calculating the traction coefficient mucrThe expression of the vector of the acting force of the retainer in the contact coordinate system is determined according to the contact material as follows:
Figure BDA0003287884300000115
in the formula, a plus sign represents outer ring guide, and a minus sign represents inner ring guide; when h is generatedm>σcrIn the process, because the viscosity of liquid nitrogen is low, a hydrodynamic film is difficult to form, and the normal contact force is 0, the vector of the acting force of the guide ferrule on the retainer slice in the contact coordinate system is
Figure BDA0003287884300000116
Coordinate conversion is carried out to obtain the acting force vector of the left end of the retainer in the inertial rectangular coordinate system
Figure BDA0003287884300000117
And right end force vector
Figure BDA0003287884300000118
Subsequent force direction changes to obtain corresponding guide ring force vector
Figure BDA0003287884300000119
And
Figure BDA00032878843000001110
then, the slice action torque vector at the two ends of the retainer in the retainer fixed body coordinate system is as follows:
Figure BDA00032878843000001111
the force and moment vectors of the guide ring on the retainer are as follows:
Figure BDA0003287884300000121
the force and moment vectors of the retainer on the guide ring are as follows:
Figure BDA0003287884300000122
4-5) obtaining the acting force and moment of the bearing component, constructing a kinetic equation through a Newton Euler equation, firstly, decomposing the motion of the bearing component into translation and rotation, and then establishing a rolling bearing kinetic model according to a corresponding centroid translation differential equation and a rotation differential equation, namely, the translation differential equation of the ring and the retainer can be established in an inertial rectangular coordinate system, wherein the expression is as follows:
Figure BDA0003287884300000123
in the formula mr/cRepresenting ferrule or cage mass, x, y, z representing part centroid position, Fx、Fy、FzThe total load borne by the three main shaft directions of the component is shown;
the translation differential equation of the rolling body is established in an inertial cylindrical coordinate system, and the expression is as follows:
Figure BDA0003287884300000124
in the formula mbDenotes the mass of the rolling elements, Fx、Fr、FθThe axial, radial and circumferential bearing loads of the rolling body under an azimuth coordinate system are represented;
all the part rotation differential equations can be established in a fixed body coordinate system, and the expression is as follows:
Figure BDA0003287884300000131
in the formula G1、G2、G3Representing the total applied moment, I, in a coordinate system of the stationary body of the component1、I2、I3Representing the moment of inertia of the part;
4-6) solving a dynamic model, firstly, giving structure and working condition parameters as input conditions, and bringing in the space positions and kinematic parameters of the rolling body, the ferrule and the retainer obtained by calculation to provide initial values for dynamic calculation; respectively bringing the initial values into a component interaction model to obtain the force and the moment acting on the component under the corresponding coordinate system; the obtained acting force and moment are brought into a dynamic equation established by a Newton Euler equation, calculation time, initial step length and calculation error are determined, then the model is solved according to a variable step length Ruge-Kutta integral method, a component interaction model is combined, a bearing component kinematic result (component displacement and speed) and a dynamic result (component acceleration, acting force and moment) at the moment are obtained, and the dynamic modeling and solving of the rolling bearing are completed;
4-7) the heat generated by the high-speed rotation motion of the original bearing is mainly caused by the power consumption of the bearing, and the heat mainly comprises the following components: rolling friction power consumption between the rolling body and the roller path, sliding power consumption between the rolling body and the pocket hole and sliding friction power consumption between the retainer and the guide ring, so that the original bearing power loss PtotalThe expression of (a) is:
Figure BDA0003287884300000132
wherein, PxnjRepresenting the frictional power loss, P, caused by the movement of the spherical gyro (along the long axis X of the ellipse)ynjRepresenting the loss of relative sliding power between ball and race, PsnjRepresenting the loss of spin friction power of the ball, PbcjRepresents the friction power loss (W), P, between the ball and the pocketclRepresenting the friction power loss between the cage and the guide ferrule;
the heat Q generated by the high-speed rotation of the original bearingtotalFor bearing power loss PtotalProduct of time and duration of operation;
4-8) because the resistance wire heating has the advantages of controllable temperature, rapid temperature rise, simple structure, convenient maintenance and the like, the resistance wire is selected as the material of the simulated heat source 9 to heat the flow field,the heat generation amount can be represented by the formula Qequal＝I2Rt is obtained by calculation, wherein I is passing current, R is resistance wire thermal resistance, and t is working time; the heat generation quantity Q of the simulated heat source 9 in the same time is adjusted by adjusting the passing currentequalHeat value Q generated by high-speed rotation of original bearingtotalKeeping the same, namely equivalently simulating the heating effect of the bearing.
The fifth step is specifically as follows:
5-1) analyzing the heating reason and the heating position of the original high-speed rolling bearing, determining that friction power consumption is generated by friction between a rolling body and a raceway when the original bearing moves, and sliding power consumption is generated between the rolling body and a pocket, so that a large amount of heat is brought; determining the position of a simulated heat source 9 by referring to the installation position of the original bearing rolling element, and determining the structural shape of the simulated heat source 9 by referring to the motion area of the rolling element in the crude oil bearing;
5-2) determining that the geometric structure of the simulated heat source 9 is circular according to the analysis result of 5-1), wherein the geometric dimension is the same as the dimension of the motion area of the rolling body of the original bearing, and the installation position is the middle part of the equivalent bearing 10;
5-3) constructing a three-dimensional model of a simulated heat source 9 in three-dimensional computer aided design software Solidworks, and respectively assembling the three-dimensional model with an equivalent bearing 10, a simulated cavity 15, an original bearing and the simulated cavity 15 to obtain an assembly body of the three-dimensional model;
5-4) respectively importing the two three-dimensional models of the assembly body established in the step 5-3) into finite element commercial software Ansys workbench in a format of an intermediate file, setting the same boundary conditions, and carrying out heat flow coupling simulation calculation on the two three-dimensional models to obtain a heat flow field distribution cloud chart;
importing the two groups of simulation results obtained by solving into post-processing software Tecplot for post-processing to obtain an axial sectional view of the post-processing software Tecplot;
respectively selecting 5 position measuring points near a rotating shaft in two groups of axial section heat flow field distribution cloud pictures, and respectively determining the temperature field of each position measuring point;
5-5) comparing and analyzing the temperature fields of the measuring points of the equivalent bearing 10 and the original bearing obtained in the step 5-4), and determining that when the temperature field of the measuring point at the position in the scheme of the equivalent bearing 10 is approximately the same as the temperature field of the measuring point at the position in the scheme of the original bearing, the simulated heat source 9 can equivalently simulate the heating effect of the original bearing due to self friction and fluid friction when rotating at high speed.
Sixthly, determining and calculating selected parameters according to the model of the support bearing of the rotating main shaft 1 obtained by analysis, and calculating the simulation power source 17 to meet the main shaft driving torque and the power source total driving torque; calculating the power of the motor according to a calculation formula of the torque and the power of the motor and the total driving torque obtained by calculation;
and determining the detailed type selection of the power source motor according to the calculated motor power and the working required rotating speed of the support bearing, and completing the construction of the simulation power source 17.
The invention has the beneficial effects that:
(1) the invention provides a method for measuring equivalent high-speed bearing flow field parameters. When the bearing rotates at a high speed, the bearing has the working condition characteristics of high thrust, high rotating speed, extreme temperature conditions and the like, so that the traditional method is difficult to measure the flow field parameters of the working environment of the bearing; the method of the invention carries out equivalent replacement on the high-speed rotating bearing by introducing an equivalent principle and a technical means of simulation analysis, and can more comprehensively measure and collect the flow field parameter data of the high-speed bearing.
(2) And the flow field parameters of the high-speed bearing can be obtained conveniently. The method solves the problem that the existing test conditions can not meet the measurement of the flow field parameters of the bearing under the complex working conditions by equivalently simulating the distribution conditions of the flow field and the thermal field of the high-speed rotating bearing, is convenient for designers to measure the parameters of the flow, the temperature, the pressure and the like of the high-speed bearing under any complex working conditions, and improves the analysis efficiency.
(3) The method can help designers to find weak links in the design process of the high-speed bearing and the application carrier structure thereof. The method measures and collects parameters such as flow, temperature, pressure and the like near the bearing under the working conditions of high thrust, high rotating speed and extreme temperature, and can intuitively know the influence factors of the bearing temperature flow field by analyzing data, thereby discovering weak links in the aspects of bearing structure design, heat diffusion research and the like and providing data reference for the optimized design of a high-speed bearing and an application carrier thereof in the future.
Drawings
FIG. 1 is a schematic structural diagram of an equivalent bearing flow field simulation device constructed by using the method of the invention.
Fig. 2 is an overall appearance diagram of an equivalent bearing flow field simulation device built by using the method of the invention.
Fig. 3 is a schematic diagram of the theoretical structure of an equivalent bearing.
Fig. 4 is an axial cross-sectional view of a flow field distribution.
FIG. 5 is a velocity flow field trace diagram, where 5-a is the velocity flow field trace diagram of the original bearing and 5-b is the equivalent bearing flow field trace diagram.
FIG. 6 is a plot of the flow field resultant velocity for position measurement points.
The specific reference numbers in the figures are as follows: the device comprises a rotating main shaft 1, a bearing end cover 2, a bearing end cover set screw 3, a fluid inlet pipeline 4, a simulation cavity end cover 5, a cavity set screw 6, a pressure sensor 7, a temperature sensor 8, a simulation heat source 9, an equivalent bearing 10, a fluid outlet pipeline 11, a support bearing 12, a mechanical sealing device 13, a flow sensor 14, a simulation cavity 15, a support frame 16 and a simulation power source 17, wherein the rotating main shaft is a rotating main shaft; A. b, C, D, E are the 5 selected position points.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1 to fig. 3, the equivalent bearing flow field simulation device constructed according to the method of the present invention uses a high-speed bearing produced by a certain bearing enterprise in China as an equivalent object, the equivalent bearing is installed in a simulation cavity, and a simulation power source drives the equivalent bearing to rotate through a rotating main shaft, so as to simulate the motion state of the original bearing rotating at a high speed in a turbo pump.
FIG. 3 is a schematic diagram of a theoretical structure of an equivalent bearing, wherein the equivalent bearing has an outer diameter of 215mm, an inner diameter of 120mm, a length of 40mm, a rim thickness of 10mm, and 12 rectangular flow passage holes of 21 × 25mm distributed in an array on the rim.
As shown in fig. 4, the position measuring points are respectively selected from positions from the inlet of the simulation cavity, the front and the rear of the equivalent bearing, the rear flow field of the rotating part to the outlet of the cavity of the tester, and a flow field resultant velocity broken line graph can be drawn according to the flow field resultant velocity numerical value at the position measuring points so as to reflect the velocity change trend of the flow field.
As shown in fig. 5-b, the flow field change in the velocity flow field trace diagram of the equivalent bearing is obvious, the flow field step in the flow field trace diagram is obvious, no vortex phenomenon occurs, the gradient change near the rotating shaft is slow, the gradient change of the inner wall of the inner cavity of the tester and the inlet and outlet is obvious, and is basically similar to the original bearing velocity flow field trace diagram of 5-a, and as shown in fig. 6, the obvious gradient distribution exists in the flow field resultant velocity broken line diagram, the structural configuration of the equivalent bearing is proved to be an ideal structural configuration, and the installation position of the equivalent bearing is an ideal installation position, namely, the flow field distribution state similar to the actual original bearing rotating at high speed can be obtained through the equivalent bearing.
The heat productivity of the simulated heat source is the same as the heat produced by the original bearing when rotating at a high speed, and the temperature field is approximately the same as the temperature field distribution of the original bearing, so that the simulated heat source can equivalently simulate the heating effect of the original bearing when rotating at a high speed due to self friction and fluid friction.
The invention has been described in connection with the accompanying drawings, and it is to be understood that the invention is not limited to the disclosed embodiments, but is intended to cover various modifications, equivalent arrangements, improvements, and adaptations of the invention using its general principles and techniques.

Claims (7)

1. A method for measuring equivalent high-speed bearing flow field parameters is characterized by comprising the following steps;
the method comprises the following steps: constructing a simulation cavity (15), installing the equivalent bearing (10) in the simulation cavity (15), determining the structural design of the simulation cavity (15) through a finite element simulation technology, and obtaining the same flow change as the original bearing working environment;
step two: constructing an equivalent bearing (10) with low rotating speed, determining the geometric dimension and the structural configuration of the equivalent bearing, and ensuring that the equivalent bearing can obtain a flow field distribution state similar to that of an actual high-speed rotating bearing through simulation comparison analysis of the flow field of the actual original bearing;
step three: determining the installation position of the equivalent bearing (10) in the simulation cavity (15) to obtain a flow field distribution state similar to the actual working condition;
step four: constructing a simulated heat source (9), and enabling the calorific value of the simulated heat source (9) to be the same as the calorific value generated when the original bearing rotates at a high speed through calculation;
step five: determining the installation position of a simulated heat source (9) in a simulated cavity (15) so that the simulated heat source can equivalently simulate the distribution state of a peripheral heat flow field when an original bearing rotates at a high speed;
step six: constructing a simulation power source (17) to drive a rotating main shaft (1) and an equivalent bearing (10) to rotate, simulating the high-speed rotation movement of the original bearing in a turbine pump, firstly analyzing the load direction and the service life of the equivalent bearing (10) in the flow field simulation process, calculating the friction power consumption of a supporting bearing, determining the type selection of the supporting bearing between the simulation power source (17) and the rotating main shaft (1), and determining the configuration mode of the supporting bearing;
step seven: comprehensively analyzing the velocity flow field trace diagram, the flow field distribution axial section diagram and the heat flow field distribution axial section diagram of the equivalent flow field obtained in the third step;
determining a monitoring key point of flow and pressure parameters at a fluid inlet pipeline (4) according to the requirement that the inlet flow and pressure of the simulation cavity (15) meet the simulation condition of the equivalent bearing (10); determining a monitoring key point of flow and pressure parameters at a fluid outlet pipeline (11) according to the condition that a pressure release phenomenon can be generated at a flow outlet of the simulation cavity; in addition, the cavity area with the pressure most value, the pressure sudden change and the constant pressure change amplitude also serves as a monitoring key point of the pressure parameter;
determining a monitoring key point of a temperature parameter at the position of the fluid inlet pipeline (4) according to the requirement of conveniently checking the internal heating condition of the equivalent bearing (10); by comparing the temperature parameters of the flow field near the front end surface and the flow field near the rear end surface of the equivalent bearing (10), the heating efficiency of the equivalent bearing (10) during working can be accurately calculated, so that the flow fields near the front end surface and the rear end surface of the equivalent bearing (10) are also determined as monitoring key points of the temperature parameters; analyzing the heat dissipation condition of the equivalent flow field by comparing the temperature parameters of the flow field near the rear end surface of the equivalent bearing (10) and the fluid outlet pipeline (11), so that the fluid outlet pipeline (11) is a monitoring key point of the temperature parameters; in addition, the sudden temperature change part is also a monitoring key point of the temperature parameter;
and (3) assembling the simulation cavity (15), the equivalent bearing (10), the simulation heat source (9) and the simulation power source (17) determined in the first step to the sixth step according to the obtained ideal positions, and installing corresponding sensors at key points of flow, pressure and temperature monitoring obtained by analysis, so that data acquisition can be carried out on parameters such as the flow field, the pressure and the temperature of the equivalent flow field, and the equivalent measurement on the distribution parameters of the original high-speed bearing flow field is completed.
2. The method for measuring the parameters of the equivalent high-speed bearing flow field according to claim 1, wherein the first step is specifically as follows:
1-1) referring to the working environment, structural characteristics and geometric dimensions of an original bearing, preliminarily designing a simulation cavity (15) to be a cylindrical shell, wherein the simulation cavity (15) can synchronously rotate along with a rotating main shaft (1), and a fluid inlet pipeline (4) and a fluid outlet pipeline (1) are respectively arranged on a left simulation cavity end cover (5) and a right simulation cavity end cover (5) and are distributed along with the rotating main shaft (15) in a circumferential manner;
1-2) establishing a plurality of groups of three-dimensional models of different-diameter simulation cavity (15) structures in three-dimensional computer aided design software Solidworks by taking the diameter of the simulation cavity (15) as a variable;
1-3) respectively importing the three-dimensional models of the structures of the plurality of simulation cavities (15) established in the step 1-2) into finite element commercial software Ansys workbench in a format of an intermediate file, setting the same boundary conditions, respectively carrying out simulation calculation on flow fields of the models, solving to obtain flow field distribution cloud maps of the models, importing the flow field distribution cloud maps into post-processing software Tecplot for post-processing to obtain axial sectional maps of the models;
selecting 5 position measuring points near a rotating main shaft (1) in the axial section of the flow field distribution cloud picture of each scheme, respectively determining the flow field resultant velocity numerical value of each position measuring point, and drawing a flow field resultant velocity broken line graph simulating each diameter size scheme of the cavity (15);
1-4) comparing and analyzing the resultant velocity curve diagrams of the flow fields of the measuring points of the simulation cavity (15) with different diameter size schemes obtained in the step 1-3), and comprehensively determining the design diameter of the cavity structure with larger flow velocity of the flow field by combining the diameter of the measured bearing in the cavity;
1-5) establishing a plurality of groups of three-dimensional models of simulation cavity (15) structures with different lengths in three-dimensional computer aided design software Solidworks by taking the length of the simulation cavity (15) as a variable;
1-6) respectively importing the three-dimensional models of the structure of the simulation cavities (15) established in the step 1-5) into finite element commercial software Ansys workbench in a format of an intermediate file, setting the same boundary conditions, carrying out simulation calculation on the flow field, and solving to obtain a velocity flow field trace diagram and a flow field distribution cloud diagram of the flow field;
guiding the obtained flow field distribution cloud charts of each scheme into post-processing software Tecplot for post-processing to obtain an axial sectional view of the flow field distribution cloud charts, selecting 5 position measuring points near a rotating main shaft (1), respectively determining flow field resultant velocity numerical values of the position measuring points, and drawing flow field resultant velocity curve charts of each length scheme of a simulation cavity (15);
1-7) comparing and analyzing the flow field resultant velocity line graphs of the simulation cavity (15) obtained in the step 1-6) in different length schemes and the obtained velocity flow field trace graph, and comprehensively determining the scheme that the flow field change in the trace graph is more obvious and the speed numerical value fluctuation of the flow field in the line graph is larger to design the length for the cavity structure.
3. The method for measuring the parameters of the equivalent high-speed bearing flow field according to claim 1, wherein the second step is specifically as follows:
2-1) according to the geometrical structure characteristics of the original bearing, the cross section area and the pore area of the bearing jointly form the total area of a medium in the original flow field passing through the bearing, and the cross section area and the pore area of the original bearing are respectively calculated;
designing a plurality of groups of equivalent bearing (10) structure configuration schemes with different diameters, pores and thickness sizes, enabling the cross-sectional area of the equivalent bearing to be equal to the calculated maximum cross-sectional area of the original bearing, and enabling the pore area of the equivalent bearing (10) to be equal to the calculated pore area of the original bearing;
according to the mass flow calculation formula, the mass flow is equal to the product of the volume flow and the medium density, and according to the volume flow calculation formula, the volume flow is equal to the product of the average flow velocity and the total cross-sectional area through which the medium passes, so that when the cross-sectional area and the pore area of the equivalent bearing (10) are equal to the maximum cross-sectional area and the pore area of the original bearing, the equivalent bearing (10) can pass the flow which is approximately the same as that of the original bearing;
2-2) respectively establishing 2-1) three-dimensional models of the equivalent bearings (10), the original bearings and the simulation cavity (15) in different configuration schemes in three-dimensional computer aided design software Solidworks, and respectively installing the three-dimensional models of the equivalent bearings (10) and the original bearings in different schemes at the same installation positions of the three-dimensional models of the simulation cavity (15) to obtain assembly bodies of the equivalent bearings (10) in different configuration schemes and the assembly bodies of the original bearings;
2-3) repeating the steps 1-6) to obtain three-dimensional models of the assembly body with different configuration schemes, and a velocity flow field trace diagram, a flow field distribution axial section diagram and a flow field resultant velocity broken line diagram of a position measuring point of the three-dimensional model of the original bearing assembly body;
respectively carrying out accurate region division on the feasible structure configuration, the axial section flow field distribution cloud chart and the speed flow field trace chart of the original bearing by using the flow field resultant velocity numerical value of the position measuring point;
and 2-4) comparing and analyzing the flow field resultant velocity numerical value, the flow field resultant velocity broken line diagram, the accurately partitioned axial cross-section flow field distribution cloud chart and the velocity flow field trace diagram of the position measuring point obtained in the step 2-3), and if the configuration of a certain equivalent bearing (10) simultaneously meets the condition that the flow field resultant velocity numerical value of the position measuring point is similar to the flow field resultant velocity numerical value of the position measuring point obtained by the simulation of the original bearing, the flow field distribution condition near a rotating shaft in the flow field distribution cloud chart of the axial cross-section is similar to the flow field distribution condition near the rotating shaft of the original bearing, the velocity flow field trace diagram is basically similar to the original bearing velocity flow field trace diagram, and the resultant velocity broken line diagram is basically superposed with the original bearing resultant velocity broken line diagram, the configured bearing is equivalent to the original bearing, namely the feasible structure configuration is the ideal structure configuration of the equivalent bearing (10).
4. The method for measuring the parameters of the equivalent high-speed bearing flow field according to claim 1, wherein the third step is specifically as follows:
3-1) taking the assembly distance between the mounting point of the equivalent bearing (10) and the left end face of the inner cavity of the simulation cavity (15) as a variable, and mounting the three-dimensional model of the equivalent bearing (10) at different positions in the three-dimensional model of the simulation cavity (15) in three-dimensional computer aided design software Solidworks to obtain an assembly body with a plurality of different mounting schemes of the equivalent bearing (10);
3-2) repeating the steps 1-6) to obtain velocity flow field trace graphs, flow field distribution axial section graphs and flow field resultant velocity broken line graphs of position measuring points of the equivalent bearing (10) assembly bodies with different installation schemes;
3-3) comprehensively determining that the flow field trace graphs of a plurality of different installation schemes obtained in the step 3-2) and the flow field resultant velocity broken line graphs thereof have obvious flow field steps and no vortex phenomenon, the gradient change near a rotating shaft is slow, the gradient change of the inner wall of the inner cavity of the tester and the inlet and outlet is obvious, and the installation scheme with obvious gradient distribution in the flow field resultant velocity broken line graphs is an ideal installation scheme of the equivalent bearing (10) in the simulation cavity (15).
5. The method for measuring the parameters of the equivalent high-speed bearing flow field according to claim 1, wherein the step four is specifically as follows:
4-1) defining a coordinate system by referring to the matching relation among all parts of the original bearing: an inertial coordinate system OXYZ, a fixed body coordinate system BXBYbZb of a rolling body, a rolling body azimuth coordinate system AXaYaZa, a ferrule fixed body coordinate system RXRYrZr and other local coordinate systems;
wherein, the inertial coordinate system is fixed in the space, the origin O is established at the center of the outer ring, and the X axis is along the central line of the bearing; the rolling body azimuth coordinate system is used for describing the track position of the rolling body center on the bearing, and the origin A of the rolling body azimuth coordinate system is positioned at the rolling body center; in an initial state, an Xa axis is parallel to an X axis, a Za axis passes through the center of the rolling body and is vertically intersected with the central line of the bearing, and a Ya axis is determined according to the right-hand spiral rule; the ferrule fixed body coordinate system is fixedly connected on the ferrule and moves along with the ferrule, the origin R of the ferrule fixed body coordinate system is positioned at the center of the ferrule, the direction of a coordinate axis Xr is parallel to an X axis in an initial state, the direction of a Zr axis is the same as a Z axis, and a Yr axis is determined according to a right-hand spiral rule;
4-2) the vector of the central position of the ball in the inertial cylindrical coordinate system is
Figure FDA0003287884290000071
The moving velocity vector is
Figure FDA0003287884290000072
The spherical position vector in the rectangular coordinate system is
Figure FDA0003287884290000073
The velocity vector is
Figure FDA0003287884290000074
Roller attitude angle of
Figure FDA0003287884290000075
The vector of the rotation speed of the ball in the fixed body coordinate system is
Figure FDA0003287884290000076
The position vector of the ferrule in the inertial rectangular coordinate system is
Figure FDA0003287884290000077
The velocity vector is
Figure FDA0003287884290000078
The attitude angle in the coordinate system of the ferrule stator is
Figure FDA0003287884290000079
The rotating speed in a sleeve ring fixed body coordinate system is
Figure FDA00032878842900000710
The conversion matrix from the sphere fixed body coordinate system to the inertial coordinate system is
Figure FDA00032878842900000711
The transformation matrix from the inner circle fixed body coordinate system to the inertial coordinate system is
Figure FDA00032878842900000712
The transformation matrix from the inertial coordinate system to the spherical orientation coordinate system is
Figure FDA00032878842900000713
The vector of the center of the ball relative to the center of the ferrule in the inertial rectangular coordinate system is
Figure FDA00032878842900000714
Conversion into an azimuth coordinate system of
Figure FDA00032878842900000715
And is converted into a ferrule fixed body coordinate system
Figure FDA00032878842900000716
Further obtaining the azimuth angle theta of the ball in the ferrule coordinate systembrThen the vector of the curvature center of the raceway of the orientation of the ball in the ferrule fixed body coordinate system is
Figure FDA00032878842900000717
Wherein r isfThe radius of the track circle of the curvature center of the ferrule is expressed, and the position vector of the center of the ball relative to the curvature center of the ferrule in the ball orientation coordinate system can be expressed according to the formula
Figure FDA00032878842900000718
Calculated to obtain a contact angle tableThe expression is as follows:
Figure FDA00032878842900000719
then, a conversion matrix from the spherical orientation coordinate system to the contact coordinate system can be obtained as Tap＝T(αc1,αc20) and the contact deformation between the ball and the raceway can be according to formula
Figure FDA00032878842900000720
Is calculated to obtain f in the formularsDenotes the coefficient of the radius of curvature of the groove, dbRepresents the diameter of the sphere;
after contact deformation is obtained, an elliptical contact area is generated at the contact position of the ball and the raceway, and the contact area major semi-axis a, minor semi-axis b and contact stress p can be calculated and obtained according to the Hertz point contact theoryh(ii) a As the lubricating condition of the bearing of the turbopump is severe and belongs to the solid lubricating working condition, the traction force between the ball and the ferrule needs to be subjected to two-bit numerical integration solution, firstly, the contact ellipse is converted into a unit circle by utilizing a normalization variable (x, y), and the incremental force of the contact between the ball and the ferrule in unit area can be written into a polar coordinate system
Figure FDA0003287884290000081
After the contact load of unit area is obtained, the friction coefficient between the ball and the ferrule is determined according to materials, and two-dimensional numerical integration is carried out by utilizing a Chebyshev polynomial, so that the traction force and the traction torque can be obtained;
4-3) the position vector of the retainer in the inertial rectangular coordinate system is
Figure FDA0003287884290000082
The velocity vector is
Figure FDA0003287884290000083
An attitude angle of
Figure FDA0003287884290000084
Can obtain a conversion matrix from an inner ring stator coordinate system to an inertial coordinate system as
Figure FDA0003287884290000085
Rotation speed in holder fixed body coordinate system
Figure FDA0003287884290000086
And the position vector from the coordinate pocket center to the cage center in the cage fixed body coordinate system can be expressed as
Figure FDA0003287884290000087
The conversion matrix from the fixed body coordinate of the retainer to the pocket coordinate is Tcd(θd0,0), where θdThe azimuth of the center of the pocket is shown;
the position vector of the center of the ball relative to the center of the retainer in the inertial rectangular coordinate system is
Figure FDA0003287884290000088
The position vector of the center of the ball relative to the center of the pocket in the pocket coordinate system can be expressed in terms of
Figure FDA0003287884290000089
The calculation is carried out to obtain the result,
Figure FDA00032878842900000810
x in pocket coordinate systemdYdProjection and X of planedThe included angle of the shaft can be according to the formula
Figure FDA00032878842900000811
Calculated so that the transformation matrix from the pocket coordinate system to the contact coordinate system PXpYpZp is
Figure FDA00032878842900000812
The minimum clearance between the ball and the pocket wall can be set by
Figure FDA00032878842900000813
Finding the position vector of the minimum clearance point relative to the center of the sphere in the contact coordinate system as
Figure FDA00032878842900000814
And the position vector relative to the center of the retainer can be expressed by
Figure FDA0003287884290000091
Calculated to obtain the vector of the relative speed between the ball and the retainer as
Figure FDA0003287884290000092
Contact coordinate system XpYpIn-plane relative velocity vector and ZpThe included angle of the shaft can be according to the formula
Figure FDA0003287884290000093
Calculating to obtain;
by the comprehensive roughness sigma between the ball surface and the pocket surfacebdOn the basis of hbc≥σbdWhen the cage is used, the normal contact force between the ball and the cage pocket is 0; when h is generatedbc＜σbdWhen the contact deformation between the ball and the pocket is determined by the formula deltabd＝σbd-hbcCalculating to obtain; in view of the hysteresis damping effect, the contact force may be represented by
Figure FDA0003287884290000094
Calculated to obtain, wherein KbcRepresenting Hertz point contact stiffness, cnRepresents contact damping (N · s/m); traction force of Fμ＝μbc|FdbI, in the formula mubcExpressing the traction coefficient (calculated according to the coefficient of dynamic friction between materials);
the cage may have force and moment vectors on the ball that are:
Figure FDA0003287884290000095
the force and moment vector of the ball on the retainer are as follows:
Figure FDA0003287884290000096
4-4) the vector of the position of the center of the retainer relative to the center of the ferrule in the inertia seat right-angle system is
Figure FDA0003287884290000097
The vector from the acting edge point of the retainer and the guide ring to the center position of the retainer in the retainer fixed body coordinate system is
Figure FDA0003287884290000098
In the formula BcageRepresenting the width of the cage, plus representing the left end acting edge point, minus representing the right end acting edge point, when the outer ring is guided, dcIs the diameter d of the outer ring of the retainercoWhen guided by the inner ring, dcIs the diameter d of the inner ring of the cageci，φcThe azimuth angle of the upper contact point of the retainer; the position vector from the edge point to the center point of the ferrule in the ferrule body coordinate system is
Figure FDA0003287884290000101
Considering that the projection on the YrZr plane in the ferrule fixed body coordinate system is maximum when the outer ring guides and minimum when the inner ring guides, the phi is aligned at the momentcThe partial derivative is evaluated to obtain two values: phi is ac1And phic2(ii) a When the outer ring is guiding, phicTaking the maximum value, and when the inner ring is guided, phicTaking the minimum value; the retainer can generate deflection and tilt movement in the operation process, the flange is not completely contacted with the guide surface of the retainer, so that the action length of the retainer and the guide ring is divided into n pieces, and the coordinate of the center of the t-th piece in the center of the retainer is xtThen the vector of the position from the slice action point of the retainer to the center point of the ferrule in the coordinate system of the ferrule is
Figure FDA0003287884290000102
The distance from the edge point of the retainer to the guide surface of the ferrule can be determined
Figure FDA0003287884290000103
Calculating, wherein a plus sign represents an outer ring guide, and a minus sign represents an inner ring guide; with combined roughness σ of cage surface and guide ringcrOn the basis of hm＜σcrWhile the contact deformation between the edge point of the retainer segment and the surface of the guide ring is deltacr＝σcr-hm；
After contact deformation is obtained, contact force Q can be calculated according to the Hertz line contact formulaL(ii) a Then, a contact coordinate system EXpYpZp is established, and the conversion matrix from the ferrule fixed body coordinate system to the contact coordinate system is
Figure FDA0003287884290000104
The expression of the sliding speed of the retainer relative to the ferrule in the contact coordinate system is as follows:
Figure FDA0003287884290000105
calculating the traction coefficient mucrThe expression of the vector of the acting force of the retainer in the contact coordinate system is determined according to the contact material as follows:
Figure FDA0003287884290000106
in the formula, a plus sign represents outer ring guide, and a minus sign represents inner ring guide; when h is generatedm>σcrIn the process, because the viscosity of liquid nitrogen is low, a hydrodynamic film is difficult to form, and the normal contact force is 0, the vector of the acting force of the guide ferrule on the retainer slice in the contact coordinate system is
Figure FDA0003287884290000111
Coordinate conversion is carried out to obtain an inertial rectangular seatLeft end force vector of retainer in the system
Figure FDA0003287884290000112
And right end force vector
Figure FDA0003287884290000113
Subsequent force direction changes to obtain corresponding guide ring force vector
Figure FDA0003287884290000114
And
Figure FDA0003287884290000115
then, the slice action torque vector at the two ends of the retainer in the retainer fixed body coordinate system is as follows:
Figure FDA0003287884290000116
the force and moment vectors of the guide ring on the retainer are as follows:
Figure FDA0003287884290000117
the force and moment vectors of the retainer on the guide ring are as follows:
Figure FDA0003287884290000118
4-5) obtaining the acting force and moment of the bearing component, constructing a kinetic equation through a Newton Euler equation, firstly, decomposing the motion of the bearing component into translation and rotation, and then establishing a rolling bearing kinetic model according to a corresponding centroid translation differential equation and a rotation differential equation, namely, the translation differential equation of the ring and the retainer can be established in an inertial rectangular coordinate system, wherein the expression is as follows:
Figure FDA0003287884290000119
in the formula mr/cRepresenting ferrule or cage mass, x, y, z representing part centroid position, Fx、Fy、FzThe total load borne by the three main shaft directions of the component is shown;
the translation differential equation of the rolling body is established in an inertial cylindrical coordinate system, and the expression is as follows:
Figure FDA0003287884290000121
in the formula mbDenotes the mass of the rolling elements, Fx、Fr、FθThe axial, radial and circumferential bearing loads of the rolling body under an azimuth coordinate system are represented;
all the part rotation differential equations can be established in a fixed body coordinate system, and the expression is as follows:
Figure FDA0003287884290000122
in the formula G1、G2、G3Representing the total applied moment, I, in a coordinate system of the stationary body of the component1、I2、I3Representing the moment of inertia of the part;
4-6) solving a dynamic model, firstly, giving structure and working condition parameters as input conditions, and bringing in the space positions and kinematic parameters of the rolling body, the ferrule and the retainer obtained by calculation to provide initial values for dynamic calculation; respectively bringing the initial values into a component interaction model to obtain the force and the moment acting on the component under the corresponding coordinate system; the obtained acting force and moment are brought into a dynamic equation established by a Newton Euler equation, calculation time, initial step length and calculation error are determined, then the model is solved according to a variable step length Ruge-Kutta integral method, a component interaction model is combined, a bearing component kinematic result (component displacement and speed) and a dynamic result (component acceleration, acting force and moment) at the moment are obtained, and the dynamic modeling and solving of the rolling bearing are completed;
4-7) the heat generated by the high-speed rotation motion of the original bearing is mainly caused by the power consumption of the bearing, and the heat mainly comprises the following components: rolling friction power consumption between the rolling body and the roller path, sliding power consumption between the rolling body and the pocket hole and sliding friction power consumption between the retainer and the guide ring, so that the original bearing power loss PtotalThe expression of (a) is:
Figure FDA0003287884290000131
wherein, PxnjRepresenting the frictional power loss, P, caused by the movement of the spherical gyro (along the long axis X of the ellipse)ynjRepresenting the loss of relative sliding power between ball and race, PsnjRepresenting the loss of spin friction power of the ball, PbcjRepresents the friction power loss (W), P, between the ball and the pocketclRepresenting the friction power loss between the cage and the guide ferrule;
the heat Q generated by the high-speed rotation of the original bearingtotalFor bearing power loss PtotalProduct of time and duration of operation;
4-8) because the resistance wire heating has the advantages of controllable temperature, rapid temperature rise, simple structure, convenient maintenance and the like, the resistance wire is selected as the material of the simulated heat source 9 to heat the flow field, and the heat productivity can be represented by the formula Qequal＝I2Rt is obtained by calculation, wherein I is passing current, R is resistance wire thermal resistance, and t is working time; the heat generation quantity Q of the simulated heat source 9 in the same time is adjusted by adjusting the passing currentequalHeat value Q generated by high-speed rotation of original bearingtotalKeeping the same, namely equivalently simulating the heating effect of the bearing.
6. The method for measuring the parameters of the equivalent high-speed bearing flow field according to claim 1, wherein the step five is specifically as follows:
5-1) analyzing the heating reason and the heating position of the original high-speed rolling bearing, determining that friction power consumption is generated by friction between a rolling body and a raceway when the original bearing moves, and sliding power consumption is generated between the rolling body and a pocket, so that a large amount of heat is brought; determining the position of a simulated heat source (9) according to the original bearing rolling element installation position, and determining the structural shape of the simulated heat source (9) according to the rolling element motion area in the crude oil bearing;
5-2) determining that the geometric structure of the simulated heat source (9) is circular according to the analysis result of 5-1), wherein the geometric dimension of the simulated heat source is the same as the dimension of the motion area of the original bearing rolling body, and the installation position is the middle part of the equivalent bearing (10);
5-3) constructing a three-dimensional model of a simulated heat source (9) in three-dimensional computer aided design software Solidworks, and respectively assembling the three-dimensional model with an equivalent bearing (10), a simulated cavity (15), an original bearing and the simulated cavity (15) to obtain an assembly body of the three-dimensional computer aided design software Solidworks;
5-4) respectively importing the two three-dimensional models of the assembly body established in the step 5-3) into finite element commercial software Ansys workbench in a format of an intermediate file, setting the same boundary conditions, and carrying out heat flow coupling simulation calculation on the two three-dimensional models to obtain a heat flow field distribution cloud chart;
importing the two groups of simulation results obtained by solving into post-processing software Tecplot for post-processing to obtain an axial sectional view of the post-processing software Tecplot;
respectively selecting 5 position measuring points near a rotating shaft in two groups of axial section heat flow field distribution cloud pictures, and respectively determining the temperature field of each position measuring point;
5-5) comparing and analyzing the temperature fields of the measuring points of the equivalent bearing (10) and the original bearing obtained in the step 5-4), and determining that when the temperature field of the measuring point at the position in the scheme of the equivalent bearing (10) is approximately the same as the temperature field of the measuring point at the position in the scheme of the original bearing, the simulated heat source (9) can equivalently simulate the heating effect of the original bearing due to self friction and fluid friction during high-speed rotation.
7. The method for measuring the flow field parameters of the equivalent high-speed bearing according to claim 1, wherein the sixth step is to determine and calculate selected parameters according to the model of the support bearing of the rotating main shaft (1) obtained by analysis, and calculate that the simulated power source (17) should meet the main shaft driving torque and the total driving torque of the power source; calculating the power of the motor according to a calculation formula of the torque and the power of the motor and the total driving torque obtained by calculation;
and determining the detailed type selection of the power source motor according to the calculated motor power and the working required rotating speed of the support bearing, and completing the construction of the simulation power source (17).
CN202111153636.6A 2021-09-29 2021-09-29 Equivalent high-speed bearing flow field parameter measuring method Withdrawn CN113884266A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116502340A (en) * 2023-06-25 2023-07-28 江铃汽车股份有限公司 Thermal boundary data processing method, system, computer and readable storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116502340A (en) * 2023-06-25 2023-07-28 江铃汽车股份有限公司 Thermal boundary data processing method, system, computer and readable storage medium
CN116502340B (en) * 2023-06-25 2023-11-21 江铃汽车股份有限公司 Thermal boundary data processing method, system, computer and readable storage medium

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