An optimized design method for angular contact ball bearings

Abstract

The application relates to the technical field of mechanical engineering, and discloses a kind of angular contact ball bearing optimization design method, according to the load of rotor system and bearing installation structure space, the load of double half inner ring angular contact ball bearing is calculated, and the structure parameters of double half inner ring angular contact ball bearing are designed;The load actually borne by angular contact ball bearing under the working state of rotor is analyzed, the three-point contact, climbing, contact stress of rolling body and sleeve ring are calculated, the bearing structure parameters meeting the requirement of bearing steady-state performance are determined by adjustment;Then, through carrying out bearing dynamic performance analysis, according to bearing film thickness ratio and motion stability, the cage parameters or bearing roughness are optimized, so that the steady-state and transient performance of the bearing meet the design requirements.The application comprehensively considers the load transmission relationship between the bearing and the rotor, and on the basis of fully considering the change law of the dynamic performance of the bearing, such as contact fatigue, slip, three-point contact and cage motion stability, the structure parameters of the double half inner ring angular contact ball bearing are optimized.

Description

Technical Field

[0001] This invention relates to the field of mechanical engineering technology and discloses an optimized design method for angular contact ball bearings. Background Technology

[0002] Double-half inner ring angular contact ball bearings are widely used in various rotating machinery such as aero engines, gas turbines, and rocket engines. Their function is to support the stable rotation of the rotor system. Numerous design and testing processes have revealed that unreasonable double-half inner ring angular contact ball bearing designs can increase the bearing failure rate and seriously threaten the operational safety of the rotor system.

[0003] To improve the service life of double-half inner ring angular contact ball bearings in conjunction with rotor systems, it is necessary to establish a comprehensive ball bearing optimization design method to mitigate various potential failure risks, such as abnormal wear caused by three-point contact, rolling element damage caused by incline, accelerated fatigue failure caused by excessive contact stress, and abnormal cage wear or even fracture caused by cage motion instability. This will enhance the reliability of the bearing-rotor system. Scholars have conducted research on related issues. Literature review shows that previous publications and patents on the design of double-half inner ring angular contact ball bearings are scarce. Most research focuses on optimizing general-purpose angular contact ball bearings. Currently, there is a lack of systematic structural optimization design methods specifically for double-half inner ring angular contact ball bearings. The design often employs a successor-based, trial-and-error, and screening approach, failing to consider the rotor system level and the bearing's usage origins. This results in incomplete design considerations, a lack of scientific and reasonable optimization design processes, low design efficiency, and a high probability of design iterations. For high-speed double-half inner ring angular contact ball bearings, inadequate design considerations can pose certain safety hazards.

[0004] To ensure that the performance of the designed double-ring angular contact ball bearing is well matched with the rotor system it supports, it is necessary to establish an optimization design method for double-ring angular contact ball bearings based on the rotor system and comprehensively considering the bearing contact state and dynamic performance state. This requires establishing corresponding scientific and reasonable analysis and optimization design methods and processes for double-ring angular contact ball bearings, reducing bearing failure rate, extending bearing service life, and ensuring stable operation of the rotor system. Summary of the Invention

[0005] The purpose of this invention is to provide an optimized design method for angular contact ball bearings. This method can comprehensively consider the load transmission relationship between the bearing and the rotor during the design and analysis of rolling bearings. Based on a full consideration of the dynamic performance of the bearing, such as contact fatigue, slippage, and the changing laws of cage motion stability, the structural parameters of double-half inner ring angular contact ball bearings can be optimized in a targeted manner. This helps to improve the design efficiency and quality of double-half inner ring angular contact ball bearings and extend their service life.

[0006] To achieve the above-mentioned technical effects, the technical solution adopted by the present invention is as follows:

[0007] An optimization design method for angular contact ball bearings includes the following steps:

[0008] S1. Based on the external load of the rotor system and the bearing installation space, calculate the load distributed to the double-half inner ring angular contact ball bearing and design the structural parameters of the double-half inner ring angular contact ball bearing.

[0009] S2. Establish the force balance equation of the bearing-rotor-bearing housing system, and calculate the load transmitted to the bearing under rotor deformation conditions based on the system force balance equation.

[0010] S3. Calculate the bearing contact stress, three-point contact condition, and ramp condition based on the load transmitted to the bearing under rotor deformation conditions to determine whether the steady-state performance meets the requirements; if not, adjust the structural parameters of the double-half inner ring angular contact ball bearing to make the steady-state performance meet the requirements.

[0011] S4. Calculate the transient performance of the bearing to determine whether the transient performance meets the requirements. If it does not meet the requirements, adjust the bearing roughness or cage parameters according to the motion stability and bearing film thickness ratio until the transient performance fully meets the design requirements.

[0012] Furthermore, the structural parameters of the double-half inner ring angular contact ball bearing in step S1 include the bearing outer diameter D, the bearing inner diameter d, the bearing width B, and the bearing material.

[0013] Furthermore, in step S1, the radial load F distributed to the j-th bearing is calculated based on the force balance relationship between the fulcrum and the external load. rj and axial load F aj , where 1≤j≤n, and n is the number of bearings on the rotor.

[0014] Furthermore, in step S1, the maximum axial force on the double-half inner ring angular contact ball bearing to be designed is determined according to its operating conditions. Minimum axial force and maximum radial force Minimum radial force and the maximum operating rotational speed ω of the bearing rings max and minimum rotational speed ω min The preliminary design of the structural parameters of the double-half inner ring angular contact ball bearing includes the diameter and number of rolling elements, as well as the bearing shim angle, groove curvature coefficient, inner and outer diameters of the cage, and pocket diameter.

[0015] Furthermore, in step S2, based on the variational principle, a finite element model of the rotor and a finite element model of the bearing housing are established, and the rotor stiffness matrix K is calculated. rbearing housing stiffness matrix K sq Simultaneously, taking the system composed of the bearing rolling elements and bearing housing as a unit, the force balance equation of the bearing-rotor-bearing housing system is established. The magnitude of the rotor load transmitted to the double-half inner ring angular contact ball bearing under rotor deformation conditions is calculated, and the forces acting on the bearing from the rotor in various directions are obtained. The established equation set is as follows: F h F is the vector of the external load on the rotor. B G is the force exerted by the bearing on the rotor. h Given the gravity vector acting on the rotor, the system of equations is solved using a globally convergent nonlinear numerical method to obtain the rotor displacement, bearing displacement, and bearing seat displacement. The results are then substituted into the quasi-static model F of the support system. quasi The load F acting on the double-half inner ring angular contact ball bearing can then be obtained. B .

[0016] Furthermore, the steady-state performance evaluation method for the bearing in step S3 is as follows:

[0017] Calculate the contact load between the rolling elements and the raceway of the double-half inner ring angular contact ball bearing, and the contact angle between each rolling element and the raceway; calculate the contact stress between the rolling elements and the raceway according to Hertz contact theory, and calculate the contact mark between the rolling elements and the raceway by combining the contact angle between each rolling element and the raceway; if the bearing does not show three-point contact, ramping, or contact stress exceeding the limit according to the calculation results, proceed to step S4; otherwise, adjust the structural parameters of the double-half inner ring angular contact ball bearing and re-enter steps S2 and S3.

[0018] Furthermore, the method for determining three-point contact in step S3 is as follows: For the j-th rolling element, three-point contact occurs if the following conditions are met:

[0019]

[0020] In the formula, OO r2nonF Let OO be the vector from the bearing center to the center of curvature of the non-main load-bearing half-circle groove. bj Let O be the vector from the bearing center to the center of the j-th rolling element. r2nonF O bj O is the vector from the curvature center of the non-main bearing half-circle groove to the center of the j-th rolling element. r2nonF O bj (m) represents the m-th component of the vector;

[0021] The method for determining whether rolling elements will not climb is as follows: Based on the results of the quasi-static analysis, calculate the contact angle of each rolling element in the bearing, find the rolling element with the largest contact angle, and let its contact angle be α. maxjUsing Hertzian contact theory, the major axis of the contact ellipse of the rolling element is calculated, and the minimum contact angle occupied by the contact ellipse is also calculated. and maximum contact angle Simultaneously calculate the shoulder angle. Specifically:

[0022]

[0023] Simultaneously, calculate the inner ring shoulder angle based on the bearing raceway geometry. Specifically:

[0024]

[0025] The condition under which the rolling elements of a bearing do not climb is:

[0026] In the formula, R x R is the reciprocal of the sum of the principal curvatures of the rolling element and the raceway along the minor axis of the contact ellipse. y ρ is the reciprocal of the sum of the principal curvatures of the rolling element and the raceway along the major axis of the contact ellipse; sum It is the sum of the curvatures of the rolling elements and the rings along the major and minor axes of the contact ellipse.

[0027] Furthermore, in step S3, under the condition that the rolling element neither engages in three-point contact nor experiences climbing, the upper limit of the calculated initial contact angle range is... and lower limit Lower limit of the gasket angle and upper limit Calculate the four combinations of initial contact angle and gasket angle, i.e., the combinations of initial contact angle and gasket angle are respectively Under these conditions, the maximum contact stress between the rolling elements and the inner and outer rings of the double-half inner ring angular contact ball bearing is... and like and None of them exceeded the infinite cycle life limit σ that the bearing rings or rolling element materials can withstand. s If the contact stress meets the requirements, then the contact stress is satisfactory.

[0028] Further, in step S4, based on the elastohydrodynamic lubrication force, hydrodynamic pressure, and resistance to the movement of the components, the differential equations of motion for the bearing rolling elements, outer ring, main load-bearing inner ring, and non-main load-bearing inner ring are established. These equations are then solved using numerical integration to obtain data on the three-dimensional spatial motion of the cage and the spin and revolution motion of the rolling elements. Next, the contact film thickness ratio between the bearing rolling elements and the raceways is calculated to adjust the surface roughness of the rolling elements and raceways. Based on the cage's center of mass, rotation, and yaw motion, the cage motion stability index β is calculated, and the cage pocket clearance and guide clearance are adjusted accordingly. This ensures that the contact film thickness ratio between the rolling elements and the raceways meets the requirements for complete elastohydrodynamic lubrication, and that the cage motion stability index β meets the ideal motion stability index.

[0029] Furthermore, the calculation method for the cage motion stability in step S4 is as follows:

[0030]

[0031] In the formula, v represents the average values ​​of the rotational acceleration of the cage around the x-axis, y-axis, and z-axis at each time point. i To maintain the velocity of the frame's center of mass at each time point, To maintain the average value of the frame's center of mass motion, n represents the number of all time points counted.

[0032] Compared with the prior art, the beneficial effects of the present invention are: the present invention can comprehensively consider the load transmission relationship between the bearing and the rotor when designing and analyzing rolling bearings, and on the basis of fully considering the changing laws of bearing dynamic performance such as contact fatigue, slippage, and cage motion stability, the structural parameters of double-half inner ring angular contact ball bearings can be optimized in a targeted manner, which helps to improve the design efficiency and quality of double-half inner ring angular contact ball bearings and extend their service life. Attached Figure Description

[0033] Figure 1 This is a flowchart of the optimized design method for angular contact ball bearings in Example 2;

[0034] Figure 2 This is a simplified assembly diagram of the bearing-rotor-bearing housing system in Example 2;

[0035] Among them, 1. elastic support; 2. rotor; 3. double-half inner ring angular contact ball bearing; 4. cylindrical roller bearing. Detailed Implementation

[0036] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0037] Example 1

[0038] See Figure 1 and Figure 2 An optimization design method for angular contact ball bearings includes the following steps:

[0039] S1. Based on the external load of the rotor 2 system and the bearing installation space, calculate the load distributed to the double-half inner ring angular contact ball bearing 3, and design the structural parameters of the double-half inner ring angular contact ball bearing 3.

[0040] S2. Establish the force balance equation of the bearing-rotor-bearing housing system, and calculate the load transmitted to the bearing under the deformation condition of rotor 2 based on the system force balance equation.

[0041] S3. Calculate the bearing contact stress, three-point contact condition, and ramp condition based on the load transmitted to the bearing under the deformation condition of rotor 2, and determine whether the steady-state performance meets the requirements; if not, adjust the structural parameters of the double-half inner ring angular contact ball bearing 3 to make the steady-state performance meet the requirements.

[0042] S4. Calculate the transient performance of the bearing to determine whether the transient performance meets the requirements. If it does not meet the requirements, adjust the bearing roughness or cage parameters according to the internal film thickness ratio and motion stability of the bearing until the transient performance fully meets the design requirements.

[0043] In this embodiment, by analyzing the external load of the rotor 2 system supported by the double-half inner ring angular contact ball bearing 3 and the bearing load, as well as the structural space of the angular contact ball bearing, the initial structural parameters of the angular contact ball bearing are designed. Combining the force balance relationship of the bearing-rotor-bearing housing system, the actual load borne by the angular contact ball bearing is calculated. Based on this, the three-point contact, creepage, and contact stress of the rolling elements and the raceway are calculated. The bearing structural parameters that meet the steady-state performance requirements of the bearing are determined through adjustment. Then, by conducting dynamic performance analysis of the bearing, the cage parameters or bearing roughness are optimized based on the cage force and motion stability until the steady-state and transient performance of the bearing fully meets the design requirements. The angular contact ball bearing optimization design method in this embodiment can comprehensively consider the load transmission relationship between the bearing and rotor 2 during the design and analysis of rolling bearings. Based on fully considering the changing laws of bearing dynamic performance such as contact fatigue, slippage, and cage motion stability, the structural parameters of the double-half inner ring angular contact ball bearing 3 are specifically optimized, helping to improve the design efficiency and quality of the double-half inner ring angular contact ball bearing 3 and extend its service life.

[0044] The parameters collected in this embodiment include the structural and material parameters of the bearing housing and rotor 2 system. The structural parameters include the specific dimensions of the rotor 2 system and the bearing housing. The material parameters include the elastic modulus, Poisson's ratio, and density of the rotor 2 and the bearing housing material (in this embodiment, the bearing housing uses elastic support 1). This lays the foundation for subsequently establishing the finite element model of rotor 2 and the bearing. The bearing outer diameter D is determined based on the dimensions of the bearing housing where the double-ring inner ring angular contact ball bearing 3 is installed. The bearing inner diameter d and bearing width B are determined based on the dimensions of the rotor 2 where the double-ring inner ring angular contact ball bearing 3 is installed. The bearing material is selected according to the working requirements of rotor 2.

[0045] Example 2

[0046] This embodiment takes the design of a certain type of double-half inner ring angular contact ball bearing 3 of a certain aero-engine rotor 2 as an example to explain the design method of the present invention in detail, and at the same time illustrate the effectiveness of the method of the present invention.

[0047] The design process is as follows:

[0048] 1) Collect and obtain the structural and material parameters of the bearing housing and rotor 2 system. The structural parameters include the specific dimensions of the rolling rotor 2 and the bearing housing, and the material parameters include the elastic modulus, Poisson's ratio, and density of the rotor 2 and bearing housing materials. Determine the bearing outer diameter D based on the bearing housing dimensions at the location where the double-half inner ring angular contact ball bearing 3 is installed. Determine the bearing inner diameter d and bearing width B based on the rotor 2 dimensions at the location where the double-half inner ring angular contact ball bearing 3 is installed. Select the bearing material based on the working requirements of rotor 2.

[0049] 2) Based on the number W of angular contact ball bearings on rotor 2 and the resultant force of the axial force borne by rotor 2 Calculate the axial load on the double-half inner ring angular contact ball bearing 3 to be designed. Calculate the radial load F distributed to the j-th bearing by the force balance relationship between the rotor's two support points and the external load. Bj (1≤j≤n), thus the radial load borne by the double-half inner ring ball bearing to be designed can be calculated. The specific solution method is as follows:

[0050]

[0051] In the formula, D ij Let be the axial distance between the i-th bearing and the j-th bearing (1≤i,j≤n). This is the kth radial load borne by rotor 2. Let N be the axial distance from the k-th radial load to the j-th bearing, and N be the total number of radial loads borne by rotor 2. Based on the above relationship and considering a series of external loads on the rotor 2 system, the set of radial loads borne by the double-half inner ring angular contact ball bearing 3 when rotor 2 is subjected to different external loads can be calculated. and axial load set

[0052] 3) Based on the radial load set and axial load set of the angular contact ball bearing obtained from the above analysis, further screen the load set to find the maximum axial force experienced by the double-half inner ring angular contact ball bearing 3. Minimum axial force and maximum radial force Minimum radial force And based on the operating conditions of rotor 2, obtain the maximum operating rotational speed ω of the bearing rings. max and minimum rotational speed ω min The preliminary design parameters of the bearing structure are as follows:

[0053] The pitch circle diameter of the rolling element is D m = (D+d) / 2;

[0054] The initial selection of the rolling element diameter is as follows: Select the closest standard diameter based on the bearing design manual;

[0055] The initial contact angle of the rolling element is

[0056] Inner ring washer angle is

[0057] The number of rolling elements is

[0058] Inner groove curvature coefficient f i and the outer groove curvature coefficient f o All are taken as

[0059] The diameter of the cage pocket is taken as The corresponding cage pocket clearance dD p =D p -D w ;

[0060] The cage guiding method is determined by the lubrication method. If side-spray lubrication is used, an external guiding method is selected, with a guide clearance dD. c for At this time, the outer diameter of the cage The inner diameter of the cage is If ring-type oil supply lubrication is used, then an internal guiding method is employed. In this case, the inner diameter of the cage... The outer diameter of the cage is

[0061] 4) Based on the variational principle, establish the finite element model of rotor 2 and the finite element model of bearing housing, and calculate the stiffness matrix K of rotor 2. r bearing housing stiffness matrix Ksq Simultaneously, taking the system composed of the bearing rolling elements and bearing housing as the unit, a corresponding quasi-static model F of the support system is established. quasi Based on the load and speed conditions of rotor 2, and combined with the force balance relationship of the bearing-rotor-bearing housing system, the force balance equation of the bearing-rotor-bearing housing system is established. The magnitude of the load transmitted from rotor 2 to the double-half inner ring angular contact ball bearing 3 under the deformation condition of rotor 2 is calculated, and the forces acting on the bearing from rotor 2 in various directions are obtained. The specific set of equations is as follows: In the formula, F h Let F be the vector of the external load acting on rotor 2. B G is the force exerted by the bearing on rotor 2. h Given the gravity vector acting on rotor 2, the equation system is solved using a globally convergent nonlinear numerical solution method to obtain the rotor 2 displacement, bearing displacement, and bearing seat displacement. The results are then substituted into the quasi-static model F of the support system. quasi The load F acting on the double-half inner ring angular contact ball bearing 3 can then be obtained. B .

[0062] 5) Based on the load F on the bearing B Steady-state performance evaluation of the bearing was conducted. The contact load between the rolling elements and the raceway of the double-half inner ring angular contact ball bearing 3 was calculated. Based on Hertzian contact theory, the contact stress was calculated. Combining the contact angle and contact ellipse size of each rolling element and raceway, the three-point contact condition and creepage condition between the rolling elements and raceway were calculated. Based on the calculation results, the bearing structural parameters were adjusted. The specific adjustment method is as follows:

[0063] 5-1) Analyze whether three-point contact occurs between the bearing rolling elements and the raceway. For the j-th rolling element, three-point contact occurs if the following conditions are met:

[0064]

[0065] In the formula, OO r2nonF Let OO be the vector from the bearing center to the center of curvature of the non-main load-bearing half-circle groove. bj Let O be the vector from the bearing center to the center of the j-th rolling element. r2nonF O bj O is the vector from the curvature center of the non-main bearing half-circle groove to the center of the j-th rolling element. r2nonF O bj (m) represents the m-th component of the vector.

[0066] 5-2) Based on the results of the quasi-static analysis, calculate the contact angle of each rolling element in the bearing, find the rolling element with the largest contact angle, and let its contact angle be α. maxjUsing Hertzian contact theory, the major axis of the contact ellipse of the rolling element is calculated, and the minimum contact angle occupied by the contact ellipse is also calculated. and maximum contact angle Simultaneously calculate the shoulder angle. Specifically:

[0067]

[0068] Simultaneously, calculate the inner ring shoulder angle based on the bearing raceway geometry. Specifically:

[0069]

[0070] The condition under which the rolling elements of a bearing do not climb is:

[0071] In the formula, R x R is the reciprocal of the sum of the principal curvatures of the rolling element and the raceway along the minor axis of the contact ellipse. y ρ is the reciprocal of the sum of the principal curvatures of the rolling element and the raceway along the major axis of the contact ellipse. sum It is the sum of the curvatures of the rolling elements and the rings along the major and minor axes of the contact ellipse.

[0072] If the rolling elements do not achieve three-point contact or climb, proceed to the next step. Otherwise, return to 5-1) to adjust the initial bearing contact angle and shim angle. The adjustment iteration format is as follows:

[0073]

[0074] Adjust the bearing structural parameters as described above. After each adjustment, return to step 4) to perform a force balance analysis on the bearing-rotor-bearing housing system, update the load on the double-half inner ring angular contact ball bearing 3, and calculate the bearing's three-point contact and ramp conditions based on the newly updated load to find the initial contact angle range where three-point contact and ramp do not occur. and gasket angle range

[0075] 5-3) The upper limit of the initial contact angle range calculated in 5-2). and lower limit Lower limit of the gasket angle and upper limit Calculate the four combinations of initial contact angle and gasket angle, i.e., the combinations of initial contact angle and gasket angle are respectively Under these conditions, the maximum contact stress between the rolling elements and the inner and outer rings of the double-half inner ring angular contact ball bearing is... and like and None of them exceeded the infinite cycle life limit σ that the bearing rings or rolling element materials can withstand. s If the condition is met, proceed to the next step; otherwise, adjust the groove curvature coefficient using the following formula. The specific adjustment method is as follows:

[0076]

[0077] The bearing structural parameters are adjusted in the manner described above. Each adjustment involves calculating the bearing contact stress, three-point contact, and creepage conditions under the four combinations of initial contact angles and shim angles. The goal is to find the inner ring groove curvature range where three-point contact and creepage do not occur, and where the contact stress meets the requirements. Outer groove curvature range By selecting the upper and lower limits of the groove curvature, 16 combinations of structural parameters can be obtained that meet the contact stress requirements and do not result in three-point contact or slope climbing.

[0078] 6) For the 16 selected structural parameter combinations, a bearing dynamics model is established, considering the internal elastohydrodynamic lubrication force, hydrodynamic pressure, and resistance to component movement. Motion differential equations for the rolling elements, outer ring, main load-bearing inner ring, and non-main load-bearing inner ring are established. These equations are solved using numerical integration to obtain the three-dimensional spatial motion of the cage and the spin and revolution motion of the rolling elements under each structural parameter combination. Based on this, the average sliding velocity of the j-th rolling element in contact with the inner ring is calculated.

[0079]

[0080] In the formula, T icn2 T is the transformation matrix between the inertial frame and the contact coordinate system between the rolling element and the inner ring. r2i T is the transformation matrix between the inner coordinate system and the inertial coordinate system. acn2 For the transformation between the rolling element orientation coordinate system and the rolling element-inner ring contact coordinate system, T ia v1 is the transformation matrix between the inertial frame and the rolling body orientation coordinate system, and v2 is the translational velocity vector of the inner ring. O' is the rotational speed of the inner ring. r2 O' p2 Let O2O be the vector from the center of curvature of the inner groove to the contact point. r2 ) r2 Let be the position vector from the center of the inner circle to the center of the groove curvature, described in the inner circle's fixed-body coordinate system. Let be the velocity of the j-th rolling element along the bearing axis in cylindrical coordinates, and let be the velocity of the j-th rolling element in cylindrical coordinates. Let be the orbital speed of the j-th rolling element in cylindrical coordinates.

[0081] The average sliding velocity of the j-th rolling element in contact with the outer ring is calculated as follows:

[0082]

[0083] The ratio of the contact film thickness of the j-th rolling element to that of the outer ring is calculated as follows:

[0084]

[0085] The ratio of the contact film thickness between the j-th rolling element and the inner ring is calculated as follows:

[0086]

[0087] In the formula, Q j Let K be the contact load between the j-th rolling element and the raceway, K be the ellipticity of the contact ellipse, e be the base of the natural logarithm, η0 be the dynamic viscosity of the lubricating oil, E0 be the equivalent elastic modulus of the contact between the rolling element and the raceway, and σ be the contact load between the rolling element and the raceway. ball and σ race These refer to the surface roughness of the rolling elements and the rings, respectively.

[0088] If the calculated λ 1j or λ 2j If the roughness is less than 3, adjust the roughness of the rolling elements and the raceway. The specific adjustment method is as follows:

[0089]

[0090] Based on the bearing dynamics model, and considering the cage's center of mass, rotation, and yaw motion, the cage's motion stability β is calculated.

[0091]

[0092] In the formula, v represents the average values ​​of the rotational acceleration of the cage around the x-axis, y-axis, and z-axis at each time point. i To maintain the velocity of the frame's center of mass at each time point, To maintain the average value of the frame's center of mass motion, n represents the number of all time points counted.

[0093] If the calculated cage motion stability exceeds the ideal stability value β u Then adjust the cage pocket clearance dD p With guide gap dD c The adjustment method is as follows:

[0094]

[0095] By following the steps above, the bearing surface roughness, cage pocket clearance, and guide clearance that meet the design requirements under 16 combined structural parameters are selected, thus obtaining the bearing structural parameters that meet the usage requirements.

[0096] Figure 2 A simplified assembly diagram of the bearing-rotor-bearing housing system in this embodiment is provided. In this structure, the outer rings of both the angular contact ball bearing and the cylindrical roller bearing 4 are mounted on the bearing housing. One end of the rotor 2 is fitted with a newly designed double-half inner ring angular contact ball bearing 3, and the other end is fitted with the selected cylindrical roller bearing 4. Table 1 shows the main parameters of the rotor 2 and the bearing housing; Table 2 shows the structural parameters of the cylindrical roller bearing 4 mounted on the rotor 2; Table 3 shows the operating conditions of the rotor 2; Table 4 shows the equivalent load borne by the double-half inner ring angular contact ball bearing 3 calculated based on the force balance and deformation coordination relationship of the rotor-bearing system; and Table 5 shows the structural parameters of the designed double-half inner ring angular contact ball bearing 3.

[0097] Table 1 Main parameters of rotor and bearing housing

[0098] symbol illustrate value unit Dr1 Rotor outer diameter 100 mm Dr2 Rotor inner diameter 0 mm Lr Rotor length 300 mm Mre Rotor imbalance 1e-7 Kg·m <![CDATA[D Z ]]> The inner diameter of the bearing housing where the double-half inner ring angular contact balls are installed... 180 mm Jl Distance of ball bearing position from the left end of rotor 50 mm Jr Distance of roller bearing position from the left end of rotor 250 mm

[0099] Table 2 Main Parameters of Cylindrical Roller Bearings

[0100] symbol illustrate value unit <![CDATA[D w ]]> Rolling element diameter 10 mm <![CDATA[d i ]]> bearing inner diameter 100 mm <![CDATA[d o ]]> bearing outer diameter 140 mm Z Number of rolling elements 26 ddi Bearing inner ring groove bottom diameter 110 mm ddo Bearing outer ring groove bottom diameter 130 mm Dm Pitch circle diameter 120 mm L Roller length 10 mm Pd bearing operating clearance 0.01 mm B bearing width 20 mm DC cage inner diameter 116.8 mm Dc cage outer diameter 129 mm Cg cage guide clearance 0.9 mm B cage width 18 mm DDp Circumferential clearance of cage pocket 0.1 mm Dpp Axial clearance of cage pocket 0.1 mm / Bearing material type GCr15 /

[0101] Table 3 Rotor operating parameters

[0102] Serial Number Rotor speed / r / min Axial load / N Radial load / N Distance from radial load application point to the left end of rotor / mm 1 18000 10000 800 200 2 20000 500 6000 200 3 10000 50000 100 200

[0103] Table 4 shows the calculated loads of the double-half inner ring angular contact ball bearing.

[0104]

[0105]

[0106] Table 5 Structural parameters of a certain type of angular contact ball bearing after design.

[0107] symbol illustrate value unit <![CDATA[D w ]]> Rolling element diameter 19.05 mm <![CDATA[d i ]]> bearing inner diameter 100 mm <![CDATA[d o ]]> bearing outer diameter 180 mm Z Number of rolling elements 18 / <![CDATA[a0]]> Initial contact angle 23 ° B bearing width 26 mm Dc cage outer diameter 148.8 mm DC cage inner diameter 129 mm Dp cage pocket diameter 10.3 mm L cage guide surface width 5 mm Cg cage guide clearance 1.7 mm <![CDATA[f1]]> Outer groove curvature coefficient 0.515 <![CDATA[f2]]> Inner groove curvature coefficient 0.535 Bearing material type GCr15

[0108] As can be seen, this embodiment, by comprehensively considering bearing contact stress, three-point contact, ramp conditions, bearing cage movement stability, and oil film thickness, efficiently and comprehensively optimizes the bearing structural parameters, which can reduce the probability of abnormal failure of the double-half inner ring angular contact ball bearing 3, and at the same time improve the reliability of the bearing and rotor 2 system working together.

[0109] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the design of angular contact ball bearings, characterized in that: Includes the following steps: S1. Based on the external load of the rotor system and the bearing installation space, calculate the load distributed to the double-half inner ring angular contact ball bearing and design the structural parameters of the double-half inner ring angular contact ball bearing. S2. Establish the force balance equation of the bearing-rotor-bearing housing system, and calculate the load transmitted to the bearing under rotor deformation conditions based on the system force balance equation. S3. Calculate the bearing contact stress, three-point contact condition, and ramp condition based on the load transmitted to the bearing under rotor deformation conditions to determine whether the steady-state performance meets the requirements. If not, adjust the structural parameters of the double-half inner ring angular contact ball bearing to make the steady-state performance meet the requirements. The steps for evaluating the steady-state performance of the bearing are as follows: Calculate the contact load between the rolling elements and the raceway of the double-half inner ring angular contact ball bearing, and the contact angle between each rolling element and the raceway; calculate the contact stress between the rolling elements and the raceway according to Hertz contact theory, and calculate the contact mark between the rolling elements and the raceway by combining the contact angle between each rolling element and the raceway; if the bearing does not show three-point contact, ramping, or contact stress exceeding the limit according to the calculation results, proceed to step S4; otherwise, adjust the structural parameters of the double-half inner ring angular contact ball bearing and re-enter steps S2 and S3. The method for determining three-point contact is as follows: For the j-th rolling element, three-point contact occurs if the following conditions are met: In the formula, , This is the vector from the bearing center to the curvature center of the non-main load-bearing half-circle groove. From the bearing center to the first j The vector of the center of each rolling element From the center of curvature of the non-primary load-bearing semi-circular groove to the first j The vector of the center of each rolling element This represents the m-th component of the vector. The inner groove curvature coefficient. Where Z is the diameter of the rolling element and Z is the number of rolling elements. For the inner ring washer angle; The method for determining whether rolling elements will not climb is as follows: Based on the results of the quasi-static analysis, calculate the contact angle of each rolling element in the bearing, find the rolling element with the largest contact angle, and let its contact angle be θ. Using Hertzian contact theory, the major axis of the contact ellipse of the rolling element is calculated, and the minimum contact angle occupied by the contact ellipse is also calculated. and maximum contact angle Simultaneously calculate the shoulder angle Specifically: Simultaneously, calculate the inner ring shoulder angle based on the bearing raceway geometry. Specifically: ； The condition under which the rolling elements of a bearing do not climb is: ; In the formula, , The sum of the principal curvatures of the rolling element and the raceway along the minor axis of the contact ellipse is the reciprocal of the sum of their principal curvatures. It is the reciprocal of the sum of the principal curvatures of the rolling element and the ring along the major axis of the contact ellipse; It is the sum of the curvatures of the rolling elements and the rings along the major and minor axes of the contact ellipse; The upper limit of the calculated initial contact angle range under conditions where the rolling element neither makes three-point contact nor climbs an incline. and lower limit , and the lower limit of the gasket angle and upper limit Calculate the four combinations of initial contact angle and gasket angle, i.e., the combinations of initial contact angle and gasket angle are respectively , , , Under these conditions, the maximum contact stress between the rolling elements and the inner and outer rings of the double-half inner ring angular contact ball bearing is... and ,like and None of them exceeded the infinite cycle life limit that the bearing rings or rolling element materials can withstand. If the contact stress meets the requirements, then the contact stress is satisfactory. S4. Calculate the transient performance of the bearing to determine whether the transient performance meets the requirements. If it does not meet the requirements, adjust the bearing roughness or cage parameters according to the motion stability and bearing film thickness ratio until the transient performance fully meets the design requirements.

2. The optimized design method for angular contact ball bearings according to claim 1, characterized in that, The structural parameters of the double-half inner ring angular contact ball bearing in step S1 include the bearing outer diameter. Bearing inner diameter and bearing width and bearing materials.

3. The optimized design method for angular contact ball bearings according to claim 1, characterized in that, In step S1, the rotor load is distributed to the first load by using the force balance relationship between the fulcrum and the external load. j Radial load F on each bearing rj and axial load F aj ,in , n This represents the number of bearings on the rotor.

4. The optimized design method for angular contact ball bearings according to claim 3, characterized in that, In step S1, the maximum axial force on the double-half inner ring angular contact ball bearing to be designed is determined according to its operating conditions. Minimum axial force and maximum radial force Minimum radial force and the maximum operating rotational speed of the bearing rings and minimum rotational speed The preliminary design of the structural parameters of the double-half inner ring angular contact ball bearing includes the diameter and number of rolling elements, as well as the bearing shim angle, groove curvature coefficient, inner and outer diameters of the cage, and pocket diameter.

5. The optimized design method for angular contact ball bearings according to claim 1, characterized in that, In step S2, based on the variational principle, a finite element model of the rotor and a finite element model of the bearing housing are established, and the rotor stiffness matrix is ​​calculated. bearing housing stiffness matrix Simultaneously, taking the system composed of the bearing rolling elements and bearing housing as a unit, the force balance equation of the bearing-rotor-bearing housing system is established. The magnitude of the rotor load transmitted to the double-half inner ring angular contact ball bearing under rotor deformation conditions is calculated, and the forces acting on the bearing from the rotor in various directions are obtained. The established equation set is as follows: F h F is the vector of the external load on the rotor. B G is the force exerted by the bearing on the rotor. h Given the gravity vector acting on the rotor, the system of equations is solved using a globally convergent nonlinear numerical method to obtain the rotor displacement, bearing displacement, and bearing seat displacement. The results are then substituted into the quasi-static model of the support system. The load on the double-half inner ring angular contact ball bearing can then be obtained. .

6. The optimized design method for angular contact ball bearings according to claim 1, characterized in that, In step S4, based on the elastohydrodynamic lubrication force, hydrodynamic pressure, and resistance to the movement of the components within the bearing, the differential equations of motion for the bearing rolling elements, outer ring, main load-bearing inner ring, and non-main load-bearing inner ring are established. These equations are then solved using numerical integration to obtain data on the three-dimensional spatial motion of the cage and the spin and revolution motions of the rolling elements. Next, the contact film thickness ratio between the bearing rolling elements and the raceways is calculated to adjust the surface roughness of the rolling elements and raceways. Finally, based on the cage's center of mass, rotation, and yaw motion, the cage's motion stability index is calculated. Based on this, the cage pocket clearance and guide clearance are adjusted to ensure that the film thickness ratio between the rolling elements and the raceways meets the requirements for complete elastohydrodynamic lubrication, and that the cage's motion stability index is maintained. It meets the ideal motion stability index.

7. The optimized design method for angular contact ball bearings according to claim 6, characterized in that, The calculation method for cage motion stability in step S4 is as follows: In the formula, , , These represent the average values ​​of the rotational acceleration of the cage around the x-axis, y-axis, and z-axis at each time point. To maintain the velocity of the frame's center of mass at each time point, To maintain the average value of the frame's center of mass motion, This represents the total number of times recorded.

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