Structural parameter design method of thermally constrained high-speed mixed ceramic angular contact ball bearing

Abstract

The invention belongs to the field of structural design of high-speed and high-precision mixed ceramic angular contact ball bearings, and particularly relates to a structural parameter design method of a thermally constrained high-speed mixed ceramic angular contact ball bearing. According to the method, aiming at the characteristics of light load and high speed of the mixed ceramic angular contact ball bearing, the diameters of rolling bodies, the number of the rolling bodies, curvature radius coefficients of inner and outer raceway grooves, a cage pocket gap and a cage lintel width are used as design target parameters; on the basis of considering factors such as mechanical conditions, operation rotating speed, material performance, bearing capacity and fatigue life, heating conditions influencing bearing service performance are introduced and considered, and a structural parameter design method of multivariable constraint conditions and multi-objective functions is established. According to the method, verification is carried out in multiple sets of foreign bearings, a calculation design result is matched with a surveying and mapping numerical value, in addition, the performance of the designed 7008 bearing is more excellent after a rack test, and the structural calculation design of the mixed ceramic angular contact ball bearing is scientific and reliable according to the actual working condition proposed by the method.

Description

Technical Field

[0001] The invention belongs to the field of high-speed and high-precision angular contact ball bearing structure design, and in particular relates to a structural parameter design method for a thermally constrained high-speed hybrid ceramic angular contact ball bearing. Background Art

[0002] At present, my country is showing a good trend of rapid development in various fields such as aerospace, rail transportation, and high-end manufacturing, which has led to an increasing demand for high-end equipment in various fields. Among them, high-end bearings, as one of the key components of high-precision equipment, play an indispensable supporting and promoting role in the sustainable and healthy development of my country's industry. After decades of hard work, my country has become a major bearing country in the world, occupying a large share in both the export and import of bearings. However, the bearings produced by my country's bearing companies are currently mainly concentrated in the mid- and low-end markets, and there are still major shortcomings in the field of high-end and high-precision bearings, which cannot compete with world-renowned bearing companies such as SKF and FAG. This has led to the fact that high-end bearings used in various fields in my country still rely mainly on large-scale imports, which has become a major problem that my country urgently needs to solve. One of the key reasons for this situation is that we lack a systematic understanding of the characteristics of current high-end bearings, lack the corresponding underlying physical understanding, and are relatively weak in the concepts, methods, and procedures of structural design. This leads to a gap between theoretical design and bench testing and mass production in practical applications, which ultimately forces us to rely on foreign companies to provide design and continuous supply.

[0003] Different from steel angular contact ball bearings, the inner and outer rings of hybrid ceramic angular contact ball bearings are made of bearing steel or stainless steel, and the rolling elements are made of ceramic balls. The ceramic balls can be made of materials such as ZrO2, Si3N4 or SiC, forming a high-speed, high-precision and long-life steel-ceramic hybrid bearing with the following characteristics:

[0004] (1) High temperature resistance. Ceramic balls have a small thermal expansion coefficient and will not expand due to temperature in a high temperature environment. This greatly increases the operating temperature of the entire bearing. The temperature of ordinary bearings is around 160°C, while that of ceramic balls can reach over 220°C.

[0005] (2) High speed. Ceramic balls have oil-free self-lubricating properties and a low friction coefficient, so hybrid ceramic angular contact ball bearings have a very high speed. The speed of bearings using ceramic balls is more than 1.5 times that of ordinary bearings.

[0006] (3) Long life. Ceramic balls do not require any grease, which means that even if the grease dries up, the bearing can still operate. This avoids the premature damage of ordinary bearings caused by grease drying up. The service life of bearings using ceramic balls is 2 to 3 times that of ordinary bearings.

[0007] (4) Insulation. Bearings with ceramic balls can insulate the inner and outer rings of the bearings. Ceramic balls are insulators. Using ceramic balls between the inner and outer rings of the bearings can achieve insulation, allowing the bearings to be used in a conductive environment.

[0008] Current research has found that high-speed and high-precision machine tool bearings will fail and retire due to reduced precision long before reaching their fatigue life. This shows that the key factor affecting the service performance of high-speed and high-precision machine tool bearings is no longer fatigue, but the stability of their precision. Therefore, the previous design concept of excessive pursuit of the longest fatigue life is no longer applicable. For high-speed and high-precision machine tool bearings, their operating speed has been greatly increased, making the bearings more prone to frictional heating and thus causing precision failure. The frictional heating phenomenon is difficult to observe directly, but it can be converted into the calculation of the bearing roll ratio. The so-called roll ratio refers to the ratio of the angular velocity of the rolling element's rotation around the normal of the contact surface to the angular velocity of its revolution. It can be used to study the degree of sliding and heating of the rolling element. The larger the value, the more severe the frictional heating, that is, the worse the precision stability. In addition, the introduction of the PV value, an important indicator for measuring bearing wear power consumption and heat generation, can achieve effective regulation of the heat generation of the inner and outer raceways of high-speed rotating bearings, thereby further ensuring the precision stability of the bearings under high-speed operation. In view of this, we propose to comprehensively consider various important factors that affect the precision and stability of bearings, introduce the PV value of the bearing to measure the heat generation of the inner and outer raceways, and use the spin-to-roll ratio of the bearing as the final constraint objective function, so as to establish a structural parameter calculation and design scheme for high-speed hybrid ceramic angular contact ball bearings. We hope that this work can play a positive role in promoting the independent design and manufacturing of high-end bearings in my country. Summary of the invention

[0009] In view of the shortcomings of the current high-speed angular contact ball bearing structure designed according to actual working conditions, the purpose of the present invention is to provide a structural parameter design method for a thermally constrained high-speed hybrid ceramic angular contact ball bearing to solve the problem of difficulty in high-speed angular contact ball bearing structure design.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is:

[0011] A method for designing structural parameters of a thermally constrained high-speed hybrid ceramic angular contact ball bearing comprises the following steps:

[0012] Step S1: Establishing the objective function of structural design;

[0013] Step S2: Establish multivariable constraints;

[0014] Step S3: Propose a structural calculation design method for a hybrid ceramic angular contact ball bearing taking heating conditions into consideration.

[0015] The structural parameter design method of the thermally constrained high-speed hybrid ceramic angular contact ball bearing, in step S1, establish X = (x1, x2, f e ,f i ,g,B)’s objective function:

[0016] Take X=(x1,x2,f e ,f i ,g,B) as design variables, x1 is the rolling element diameter, x2 is the number of rolling elements, f e is the outer raceway groove curvature radius coefficient, f i is the inner raceway groove curvature radius coefficient, g is the cage pocket clearance, and B is the cage beam width. According to the design requirements of high running stability of hybrid ceramic angular contact ball bearings, the following objective function is constructed:

[0017] minf1(x)=(1-rcosu)tan(ut)+rsinu (1)

[0018] In the above formula (1), minf1(x) represents the minimum roll ratio, r=x1 / D0, D0 is the pitch circle diameter, u is the working contact angle, and t is the deflection angle.

[0019] The structural parameter design method of the thermally constrained high-speed hybrid ceramic angular contact ball bearing, in step S2, constructs X=(x1, x2, f e ,f i ,g,B)’s multivariate constraints:

[0020] (1) Multivariable constraints on carrying capacity

[0021] Hybrid ceramic angular contact ball bearings need to meet specific load requirements according to actual working conditions. They must meet both the required static load rating and the dynamic load rating. The following static load rating and dynamic load rating constraints are constructed:

[0022] R1(x)=C or >[C or ] (2)

[0023] R2(x)=C r >[C r ] (3)

[0024] In the above formulas (2) and (3), C or and C r They are the rated static load and rated dynamic load, [C or ] and [C r ] are the rated static load and rated dynamic load required under actual working conditions;

[0025] (2) Multivariable constraints on safety factor

[0026] Hybrid ceramic angular contact ball bearings need to withstand the combined effects of radial force and axial force during operation and must meet certain force safety requirements:

[0027] R3(x)=C oa / F a >S a (4)

[0028] R4(x)=C 0r / F r >S r (5)

[0029] In the above formulas (4) and (5), C oa and C or is the static load rating of the axial and radial directions, F a and F r are the axial force and radial force, S a and S r are the axial and radial safety factors;

[0030] (3) Structural association multivariate constraints

[0031] In hybrid ceramic angular contact ball bearings, the rolling elements need to be separated by a cage. The width of the cage beam is B. The circumference of the rolling element pitch is represented by (g+B+x1)x2, where g is the cage pocket clearance and the circumference of the rolling element pitch is also represented by πD0, so the following relationship is obtained:

[0032] πD0=(x1+B+g)x2 (6)

[0033] For hybrid ceramic angular contact ball bearings, the requirements for the width of the beam B are usually: B>1mm and B>0.1x1, thus establishing the following constraints:

[0034] R5(x)=πD0 / x2-g-x1≥1.0 (7)

[0035] R6(x)=πD0 / x2-g-x1≥0.1x1 (8)

[0036] Among them, the cage pocket clearance g = 0.004x1 + 0.12;

[0037] (4) Rated life constraints

[0038] Rated life is an important criterion for evaluating the service performance of bearings. This life is associated with 90% reliability, commonly used high-quality materials, good processing quality and normal operating conditions. The rated life calculation formula is as follows:

[0039]

[0040] In the above formula, L 10 is the rated life, a1 is the reliability life correction factor, a ISO is the life correction factor based on the life calculation system method, n is the bearing speed, C0 is the rated dynamic load, and P0 is the equivalent dynamic load;

[0041] The following fatigue life constraints are established:

[0042]

[0043] In the above formula (10), L0 is the fatigue life value required to be achieved;

[0044] (5) Friction torque constraint condition

[0045] The rotational motion of the bearing is hindered by the friction torque. In order to ensure the stable operation of the hybrid ceramic angular contact ball bearing, the friction torque is calculated using the following formula:

[0046]

[0047] In the above formula (11), M is the friction torque, f0 is a coefficient related to the bearing type and lubrication method, v0 is the lubricant viscosity, n is the bearing speed, f1 is a coefficient related to the bearing structure, equivalent static load and rated static load, and F β is the load related to the bearing type and external load;

[0048] The following friction torque constraint condition is established:

[0049]

[0050] In the above formula (12), M max It is the upper limit of the friction torque allowed for the bearing operation;

[0051] (6) Stiffness requirement constraints

[0052] The structure of the hybrid ceramic angular contact ball bearing must meet the stiffness requirements of the service environment, and the following stiffness requirements constraints are established:

[0053]

[0054] In the above formulas (13) and (14), δ a and δ r are the axial and radial deformations, α is the contact angle, G amin and G rmin are the required stiffness values ​​in the axial and radial directions respectively;

[0055] (7) Lubrication constraints

[0056] Based on the research results proposed by Hamrock B J and Dowson D, the following lubrication constraint conditions are established:

[0057]

[0058] In the above formula (15), U, W, G, R x , E0, K are the speed parameter, load parameter, viscosity-pressure index, equivalent curvature radius, equivalent elastic modulus, and ellipticity respectively, and h min is the required minimum oil film thickness value;

[0059] (8) Thermal constraint conditions of the inner and outer raceways of the bearing

[0060] The service condition of the hybrid ceramic angular contact ball bearing is light load and high speed, and the temperature rise is an important factor affecting the service performance of the bearing; the PV value is an important indicator to measure the friction power consumption and heat generation of the bearing. P is the contact stress between the rolling element and the raceway, and V is the rolling linear speed of the contact area. The PV value of the bearing is introduced to represent the heat generation of the bearing. Under other unchanged conditions, the higher the PV value, the higher the temperature rise of the bearing. In order to limit the excessive heating of the bearing, the PV value of the bearing must be constrained. Therefore, the following constraint conditions are established:

[0061] R 12 (x) = P i V i ≤ [PV] i (16)

[0062] R 13 (x) = P e V e ≤ [PV] e (17)

[0063] In the above formulas (16) and (17), P i and V i are the contact stress and contact linear speed between the rolling element and the inner raceway, P e and V e are the contact stress and contact linear speed between the rolling element and the outer raceway, [PV] i and [PV] e are the allowable PV values of the inner and outer raceways of the bearing;

[0064] During the operation of the hybrid ceramic angular contact ball bearing, it is necessary to make the temperature rises of the inner and outer raceways as close as possible, which is beneficial to maintaining the high stability of the bearing operation. The ratio of the heat generation of the inner and outer raceways of the bearing must be limited within a certain range (a, b), and a < b. Therefore, the following heat generation constraint conditions are constructed:

[0065] R 14 (x) = P iV i / P e V e ≥a (18)

[0066] R 15 (x) = P i V i / P e V e ≤b (19)

[0067] a and b in the above formula are determined according to the corresponding actual working conditions;

[0068] In addition, in hybrid ceramic angular contact ball bearings, the groove curvature radius coefficient of the inner and outer raceways is required to be between 0.510 and 0.600. Due to the high-speed operation of hybrid ceramic angular contact ball bearings and the lower heat dissipation efficiency of the inner raceway than that of the outer raceway, it is necessary to consider increasing the inner raceway groove curvature radius coefficient during design, thereby establishing the following constraints:

[0069] R 16 (x) = f i -0.600<0 (20)

[0070] R 17 (x) = f i -0.510>0 (21)

[0071] R 18 (x) = f e -0.600<0 (22)

[0072] R 19 (x) = f e -0.510>0 (23)

[0073] R 20 (x) = f i -f e >0 (24).

[0074] The structural parameter design method of the thermally constrained high-speed hybrid ceramic angular contact ball bearing, in step S3, the structural calculation design method of the hybrid ceramic angular contact ball bearing comprises the following steps:

[0075] (1) The rated dynamic load, rated static load and inner and outer diameters of the bearing under actual working conditions are used as initial input data;

[0076] (2) Calculate and filter through multivariable constraint formulas (2)-(24) to obtain a set of values ​​X1=(x1, x2, f e ,f i ,g,B);

[0077] (3) Using the objective function formula (1), the value set X1 = (x1, x2, f e ,f i ,g,B) to screen and determine the optimal value that satisfies the objective function, and finally obtain the optimal structural parameters.

[0078] The design idea of ​​the present invention is:

[0079] The present invention discloses a method for designing the structural parameters of a high-speed hybrid ceramic angular contact ball bearing with thermal constraints. Starting from the actual service working conditions of the bearing, the structural parameters of the bearing are coupled and comprehensively considered. Through the requirements of load distribution, material properties, load-bearing capacity, fatigue life, and operation stability, the actual production and processing conditions and the accumulated relevant experience are integrated, and the heating conditions of the high-speed operation of the bearing are introduced to establish a design framework of a multi-objective function under multivariable constraints, so as to realize the accurate design of the structural parameters of the high-speed hybrid ceramic angular contact ball bearing. The design method is derived from the thermodynamic physical principles of high-speed bearings, which is completely different from the current empirical design. The method is scientific and universal, and can design the structural parameters of the high-speed hybrid ceramic angular contact ball bearing that meet the requirements according to the given actual working conditions.

[0080] The advantages and beneficial effects of the present invention are:

[0081] The present invention proposes a method for designing the structural parameters of a high-speed hybrid ceramic angular contact ball bearing with thermal constraints. The method takes the rolling element diameter, the number of rolling elements, the outer raceway groove curvature radius coefficient, the inner raceway groove curvature radius coefficient, the cage pocket clearance, and the cage crossbar width as design target parameters for the light-load and high-speed characteristics of the hybrid ceramic angular contact ball bearing. On the basis of considering factors such as mechanical conditions, operating speed, material properties, load-bearing capacity, and fatigue life, the heating conditions of the inner and outer raceways that affect the service performance of the bearing are introduced, and multivariable constraints and multi-objective functions are established, thereby forming a multivariable coupled structural parameter design method. The method can realize the calculation and design of the structural parameters of the hybrid ceramic angular contact ball bearing that meets the working conditions according to the actual given working conditions, and will have a positive role in promoting the independent structural design and production of high-speed and high-precision hybrid ceramic angular contact ball bearings in my country. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 This is the temperature change diagram of the bench test for bearing No. 1 and bearing No. 2.

[0083] Figure 2 The vibration change diagram of bearing No. 1 at 26000rpm. Among them, (a) is the time domain analysis of the vibration stable data after startup, (b) is the time domain analysis of the vibration data after temperature stabilization, the horizontal axis time is time (s), the vertical axis is magnitude represents the frequency amplitude (m / s2 ); (c) is the frequency domain analysis of the vibration data after startup, (d) is the frequency domain analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the frequency intensity (dB); (e) is the envelope analysis of the vibration data after startup, (f) is the envelope analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the signal intensity (dimensionless).

[0084] Figure 3 The vibration change diagram of bearing No. 1 at 30000rpm. Among them, (a) is the time domain analysis of the vibration stable data after startup, (b) is the time domain analysis of the vibration data after temperature stabilization, the horizontal axis time is time (s), the vertical axis is magnitude represents the frequency amplitude (m / s 2 ); (c) is the frequency domain analysis of the vibration data after startup, (d) is the frequency domain analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the frequency intensity (dB); (e) is the envelope analysis of the vibration data after startup, (f) is the envelope analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the signal intensity (dimensionless).

[0085] Figure 4 The vibration change diagram of bearing No. 2 at 26000rpm. Among them, (a) is the time domain analysis of the vibration stable data after startup, (b) is the time domain analysis of the vibration data after temperature stabilization, the horizontal axis time is time (s), the vertical axis is magnitude represents the frequency amplitude (m / s 2 ); (c) is the frequency domain analysis of the vibration data after startup, (d) is the frequency domain analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the frequency intensity (dB); (e) is the envelope analysis of the vibration data after startup, (f) is the envelope analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the signal intensity (dimensionless).

[0086] Figure 5 The vibration change diagram of bearing No. 2 at 30000rpm. Among them, (a) is the time domain analysis of the vibration stable data after startup, (b) is the time domain analysis of the vibration data after temperature stabilization, the horizontal axis time is time (s), the vertical axis is magnitude represents the frequency amplitude (m / s 2); (c) is the frequency domain analysis of the vibration data after startup, (d) is the frequency domain analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the frequency intensity (dB); (e) is the envelope analysis of the vibration data after startup, (f) is the envelope analysis of the vibration data after temperature stabilization, the horizontal axis frequency is the frequency (Hz), and the vertical axis magnitude represents the signal intensity (dimensionless). DETAILED DESCRIPTION

[0087] In the specific implementation process, the present invention proposes a structural parameter design method for a thermally constrained high-speed hybrid ceramic angular contact ball bearing, which couples the structural parameters of the bearing together and comprehensively considers to determine the optimal value of each structural parameter, including the following steps:

[0088] Step S1: Establish X = (x1, x2, f e ,f i ,g,B)

[0089] Take X=(x1,x2,f e ,f i ,g,B) as design variables, x1 is the rolling element diameter (mm), x2 is the number of rolling elements (pieces), f e is the outer raceway groove curvature radius coefficient, f i is the inner raceway groove curvature radius coefficient, g is the cage pocket clearance (mm), and B is the cage beam width (mm); in the embodiment, the rolling elements of the hybrid ceramic angular contact ball bearing are Si3N4 ceramic balls, and the inner and outer rings are rare earth bearing steel.

[0090] According to the design requirements of high running stability of hybrid ceramic angular contact ball bearings, the following objective function is constructed:

[0091] min f1(x)=(1-rcosu)tan(ut)+rsinu (1)

[0092] In the above formula (1), minf1(x) represents the minimum spin-to-roll ratio, r=x1 / D0, D0 is the pitch circle diameter (mm), u is the working contact angle (°), and t is the deflection angle (°).

[0093] Step S2: construct X = (x1, x2, f e ,f i ,g,B) multivariate constraints

[0094] (1) Multivariable constraints on carrying capacity

[0095] Hybrid ceramic angular contact ball bearings need to meet specific load requirements according to actual working conditions. They must meet both the required static load rating and the dynamic load rating. The following static load rating and dynamic load rating constraints are constructed:

[0096] R1(x)=C or >[C or ] (2)

[0097] R2(x)=C r >[C r ] (3)

[0098] In the above formulas (2) and (3), C or and C r They are the rated static load (N) and the rated dynamic load (N), [C or ] and [C r ] are the rated static load (N) and rated dynamic load (N) required under actual working conditions;

[0099] (2) Multivariable constraints on safety factor

[0100] Hybrid ceramic angular contact ball bearings need to withstand the combined effects of radial force and axial force during operation and must meet certain force safety requirements:

[0101] R3(x)=C oa / F a >S a (4)

[0102] R4(x)=C 0r / F r >S r (5)

[0103] In the above formulas (4) and (5), C oa and C or is the static load rating of the axial and radial directions (N), F a and F r is the axial force (N) and radial force (N), S a and S r are the axial and radial safety factors (selected according to the working conditions);

[0104] (3) Structural association multivariate constraints

[0105] In hybrid ceramic angular contact ball bearings, the rolling elements need to be separated by a cage. The width of the cage beam is B. The circumference of the rolling element pitch circle can be expressed as (g+B+x1)x2, where g is the cage pocket clearance and the circumference of the rolling element pitch circle can also be expressed as πD0, so the following relationship is obtained:

[0106] πD0=(x1+B+g)x2 (6)

[0107] For hybrid ceramic angular contact ball bearings, the requirements for the width of the beam B are usually: B>1mm and B>0.1x1, thus establishing the following constraints:

[0108] R5(x)=πD0 / x2-g-x1≥1.0 (7)

[0109] R6(x)=πD0 / x2-g-x1≥0.1x1 (8)

[0110] Among them, the cage pocket clearance g = 0.004x1 + 0.12.

[0111] (4) Rated life constraints

[0112] Rated life is an important criterion for evaluating the service performance of bearings. This life is associated with 90% reliability, commonly used high-quality materials, good processing quality and normal operating conditions. The rated life calculation formula is as follows:

[0113]

[0114] In the above formula, L 10 is the rated life (h), a1 is the reliability life correction factor (a1 in the embodiment is 1), a ISO is the life correction factor based on the life calculation system method (a in the embodiment ISO Take value 1), n ​​is the bearing speed (rpm), C0 is the rated dynamic load (N), P0 is the equivalent dynamic load (N);

[0115] The following fatigue life constraints are established:

[0116]

[0117] In the above formula (10), L0 is the fatigue life value required to be achieved (h);

[0118] (5) Friction torque constraint condition

[0119] The rotational motion of the bearing is hindered by the friction torque. In order to ensure the stable operation of the hybrid ceramic angular contact ball bearing, the friction torque is calculated using the following formula:

[0120]

[0121] In the above formula (11), M is the friction torque (N*mm), f0 is a coefficient related to the bearing type and lubrication method (the value of f0 in the embodiment is 2), and v0 is the viscosity of the lubricant (mm 2 / s), n is the bearing speed (rpm), f1 is a coefficient related to the bearing structure, equivalent static load and rated static load (f1 in the embodiment refers to GB / T24609-2023), F β is the load related to the bearing type and external load (N);

[0122] The following friction torque constraint condition is established:

[0123]

[0124] In the above formula (12), M max is the upper limit of the friction torque allowed for the bearing operation (N*mm);

[0125] (6) Stiffness requirement constraints

[0126] The structure of the hybrid ceramic angular contact ball bearing must meet the stiffness requirements of the service environment, and the following stiffness requirements constraints are established:

[0127]

[0128] In the above formulas (13) and (14), δ a and δ r are the axial and radial deformations (mm), α is the contact angle (°), G amin and G rmin are the required stiffness values ​​in the axial and radial directions (N / mm);

[0129] (7) Lubrication constraints

[0130] According to the research results proposed by Hamrock B J and Dowson D, the following lubrication constraints are established:

[0131]

[0132] In the above formula (15), U, W, G, R x , E0, and K are speed parameter, load parameter, viscosity pressure index (depending on the properties of the lubricant), equivalent radius of curvature (mm), equivalent elastic modulus (Pa), and ellipticity (ratio of the contact semi-minor axis to the semi-major axis), respectively. min is the required minimum oil film thickness value (mm);

[0133] (8) Thermal constraints of the inner and outer raceways of bearings

[0134] The service condition of hybrid ceramic angular contact ball bearings is light load and high speed (dn value greater than 10 6For high speed, where: d is the inner diameter of the bearing in mm; n is the rotational speed in rpm), the temperature rise is an important factor affecting the service performance of the bearing. The PV value is an important indicator for measuring the frictional power consumption and heat generation of the bearing, where P is the contact stress (MPa) between the rolling elements and the raceway, and V is the rolling linear velocity (mm / s) of the contact area. The PV value of the bearing is introduced to represent the heat generation of the bearing. Under the condition that other conditions remain unchanged, the higher the PV value, the higher the temperature rise of the bearing. In order to limit the excessive heating of the bearing, the PV value of the bearing must be restricted, and the following constraint conditions are established:

[0135] R 12 (x) = P i V i ≤ [PV] i (16)

[0136] R 13 (x) = P e V e ≤ [PV] e (17)

[0137] In the above formulas (16) and (17), P i and V i are the contact stress (MPa) and the contact linear velocity (mm / s) between the rolling elements and the inner raceway, P e and V e are the contact stress (MPa) and the contact linear velocity (mm / s) between the rolling elements and the outer raceway, [PV] i and [PV] e are the allowable PV values of the inner and outer raceways of the bearing;

[0138] During the operation of the hybrid ceramic angular contact ball bearing, it is necessary to make the temperature rises of the inner and outer raceways as close as possible, which is beneficial to maintaining the high stability of the bearing operation. The ratio of the heat generation of the inner and outer raceways of the bearing must be restricted within a certain range (a, b), and a < b. Therefore, the following heat generation constraint conditions are constructed:

[0139] R 14 (x) = P i V i / P e V e ≥ a (18)

[0140] R 15 (x) = P i V i / P e V e ≤ b (19)

[0141] a and b in the above formula are determined according to the corresponding actual working conditions;

[0142] In addition, in hybrid ceramic angular contact ball bearings, the groove curvature radius coefficient of the inner and outer raceways is required to be between 0.510 and 0.600. Due to the high-speed operation of hybrid ceramic angular contact ball bearings and the lower heat dissipation efficiency of the inner raceway than that of the outer raceway, it is necessary to consider increasing the inner raceway groove curvature radius coefficient during design, thereby establishing the following constraints:

[0143] R 16 (x) = f i -0.600<0 (20)

[0144] R 17 (x) = f i -0.510>0 (21)

[0145] R 18 (x) = f e -0.600<0 (22)

[0146] R 19 (x) = f e -0.510>0 (23)

[0147] R 20 (x) = f i -f e >0 (24)

[0148] Step S3: Propose a structural parameter design method for a high-speed hybrid ceramic angular contact ball bearing with thermal constraints, comprising the following steps:

[0149] (1) The rated static load, rated dynamic load and inner and outer diameters of the bearing under actual working conditions are used as initial input data;

[0150] (2) Calculate and filter through multivariable constraint formulas (2)-(24) to obtain a set of values ​​X1=(x1, x2, f e ,f i ,g,B);

[0151] (3) Using the objective function formula (1), the value set X1 = (x1, x2, f e ,f i ,g,B) to screen and determine the optimal value that satisfies the objective function, and finally obtain the optimal structural parameters.

[0152] Implementation calculation case:

[0153] For several sets of imported high-speed hybrid ceramic angular contact ball bearings from a certain country, the structural parameters are calculated and designed according to their respective service conditions (rated dynamic load, rated static load, fatigue life and stiffness, etc.), and compared and verified with the actual surveying values. The results of the calculation and design using the present invention and the actual surveying data are shown in Table 1. By comparison, it is found that the calculation results of the design method proposed by the present invention are very consistent with the actual measured values.

[0154] Table 1 Comparison of the calculated values ​​of a certain imported high-speed hybrid ceramic angular contact ball bearing by this method and the actual surveyed values

[0155]

[0156] Case study of bench test:

[0157] A certain brand of 7008 bearing was selected for recalculation and design. The new bearing and the original bearing were tested on a bench to obtain the temperature rise and vibration data of the bearing. Bearing No. 1 represents the original bearing, and bearing No. 2 represents the bearing designed by this method. The results are shown in Figure 1 to Figure 5 .from Figure 1 to Figure 5 It can be found that at 26000rpm and 30000rpm, the outer ring temperature and temperature rise of bearing No. 2 are lower than those of bearing No. 1; moreover, the vibration of bearing No. 2 is also lower than that of bearing No. 1.

[0158] From the bench test cases, it can be seen that the bearing structure designed by the present invention performs better in terms of temperature rise and vibration. The method has been verified in multiple sets of foreign bearings, and the calculation and design results are very consistent with the surveying and mapping values. In addition, a certain brand of 7008 bearing was redesigned. After bench testing, it was found that the new structure was lower than the original structure in terms of temperature rise and vibration, which shows that the design method of the present invention is scientific and reliable. This method will have a positive role in promoting the independent structural design and production of high-speed and high-precision bearings in my country.

Claims

1. A method for designing structural parameters of a thermally constrained high-speed hybrid ceramic angular contact ball bearing, characterized in that: The following steps are involved: Step S1: Establishing the objective function of structural design; Step S2: Establish multivariable constraints; Step S3: Propose a structural calculation design method for a hybrid ceramic angular contact ball bearing taking heating conditions into consideration.

2. The structural parameter design method of the thermally constrained high-speed hybrid ceramic angular contact ball bearing according to claim 1 is characterized in that: In step S1, establish X=(x1,x2,f e ,f i ,g,B)’s objective function: Take X=(x1,x2,f e ,f i ,g,B) as design variables, x1 is the rolling element diameter, x2 is the number of rolling elements, f e is the outer raceway groove curvature radius coefficient, f i is the inner raceway groove curvature radius coefficient, g is the cage pocket clearance, and B is the cage beam width. According to the design requirements of high running stability of hybrid ceramic angular contact ball bearings, the following objective function is constructed: min f1(x)=(1-rcosu)tan(ut)+rsinu (1) In the above formula (1), minf1(x) represents the minimum roll ratio, r = x1 / D0, D0 is the pitch circle diameter, u is the working contact angle, and t is the deflection angle.

3. The structural parameter design method of the thermally constrained high-speed hybrid ceramic angular contact ball bearing according to claim 1 or 2, characterized in that: In step S2, construct X=(x1,x2,f e ,f i ,g,B)’s multivariate constraints: (1) Multivariable constraints on carrying capacity Hybrid ceramic angular contact ball bearings need to meet specific load requirements according to actual working conditions. They must meet both the required static load rating and the dynamic load rating. The following static load rating and dynamic load rating constraints are constructed: R1(x)=C or >[C or ] (2) R2(x)=C r >[C r ] (3) In the above formulas (2) and (3), C or and C r They are the rated static load and rated dynamic load, [C or ] and [C r ] are the rated static load and rated dynamic load required under actual working conditions; (2) Multivariable constraints on safety factor Hybrid ceramic angular contact ball bearings need to withstand the combined effects of radial force and axial force during operation and must meet certain force safety requirements: R3(x)=C oa / F a >S a (4) R4(x)=C 0r / F r >S r (5) In the above formulas (4) and (5), C oa and C or is the static load rating of the axial and radial directions, F a and F r are the axial force and radial force, S a and S r are the axial and radial safety factors; (3) Structural association multivariate constraints In hybrid ceramic angular contact ball bearings, the rolling elements need to be separated by a cage. The width of the cage beam is B. The circumference of the rolling element pitch is represented by (g+B+x1)x2, where g is the cage pocket clearance and the circumference of the rolling element pitch is also represented by πD0, so the following relationship is obtained: πD0=(x1+B+g)x2 (6) For hybrid ceramic angular contact ball bearings, the requirements for the width of the beam B are usually: B>1mm and B>0.1x1, thus establishing the following constraints: R5(x)=πD0 / x2-g-x1≥1.0 (7) R6(x)=πD0 / x2-g-x1≥0.1x1 (8) Among them, the cage pocket clearance g = 0.004x1 + 0.12; (4) Rated life constraints Rated life is an important criterion for evaluating the service performance of bearings. This life is associated with 90% reliability, commonly used high-quality materials, good processing quality and normal operating conditions. The rated life calculation formula is as follows: In the above formula, L 10 is the rated life, a1 is the reliability life correction factor, a ISO is the life correction factor based on the life calculation system method, n is the bearing speed, C0 is the rated dynamic load, and P0 is the equivalent dynamic load; The following fatigue life constraints are established: In the above formula (10), L0 is the fatigue life value required to be achieved; (5) Friction torque constraint condition The rotational motion of the bearing is hindered by the friction torque. In order to ensure the stable operation of the hybrid ceramic angular contact ball bearing, the friction torque is calculated using the following formula: In the above formula (11), M is the friction torque, f0 is a coefficient related to the bearing type and lubrication method, v0 is the lubricant viscosity, n is the bearing speed, f1 is a coefficient related to the bearing structure, equivalent static load and rated static load, and F β is the load related to the bearing type and external load; The following friction torque constraint condition is established: In the above formula (12), M max It is the upper limit of the friction torque allowed for the bearing operation; (6) Stiffness requirement constraints The structure of the hybrid ceramic angular contact ball bearing must meet the stiffness requirements of the service environment, and the following stiffness requirements constraints are established: In the above formulas (13) and (14), δ a and δ r are the axial and radial deformations, α is the contact angle, G amin and G rmin are the required stiffness values ​​in the axial and radial directions respectively; (7) Lubrication constraints According to the research results proposed by Hamrock B J and Dowson D, the following lubrication constraints are established: In the above formula (15), U, W, G, R x , E0, K are velocity parameter, load parameter, viscosity pressure index, equivalent curvature radius, equivalent elastic modulus and ellipticity, respectively, h min is the required minimum oil film thickness value; (8) Thermal constraints of the inner and outer raceways of bearings The service conditions of hybrid ceramic angular contact ball bearings are light load and high speed, and the temperature rise is an important factor affecting the service performance of the bearings; the PV value is an important indicator to measure the friction power consumption and heat generation of the bearings. P is the contact stress between the rolling elements and the raceways, and V is the rolling linear speed of the contact area. The PV value introduced into the bearings represents the heat generation of the bearings. Under the condition that other conditions remain unchanged, the higher the PV value, the higher the temperature rise of the bearings. In order to limit the excessive heating of the bearings, the PV value of the bearings must be restricted. Thus, the following constraint conditions are established: R 12 (x)=P i V i ≤[PV] i (16) R 13 (x)=P e V e ≤[PV] e (17) In the above formulas (16) and (17), P i and V i is the contact stress and contact line velocity between the rolling element and the inner ring, P e and V e is the contact stress and contact line velocity between the rolling element and the outer ring, [PV] i and [PV] e It is the allowable PV value of the inner and outer rings of the bearing; During the operation of hybrid ceramic angular contact ball bearings, it is necessary to make the temperature rises of the inner and outer raceways as close as possible, which is conducive to maintaining high stability of the bearing operation. The ratio of the heat generation of the inner and outer raceways of the bearing must be restricted within a certain range (a, b), and a < b. Thus, the following heat generation constraint conditions are constructed: R 14 (x)=P i V i / P e V e ≥a (18) R 15 (x)=P i V i / P e V e ≤b (19) The values of a and b in the above formula are determined according to the corresponding actual working conditions; In addition, in hybrid ceramic angular contact ball bearings, the groove curvature radius coefficients of their inner and outer raceways are required to be between 0.510 and 0.

600. Considering the high-speed operation of hybrid ceramic angular contact ball bearings and the characteristic that the heat dissipation efficiency of the inner raceway is lower than that of the outer raceway, it is necessary to consider increasing the groove curvature radius coefficient of the inner raceway during design. Thus, the following constraint conditions are established: R 16 (x)=f i -0.600<0 (20) R 17 (x)=f i -0.510>0 (21) R 18 (x)=f e -0.600<0 (22) R 19 (x)=f e -0.510>0 (23) R 20 (x)=f i -f e >0 (24)。 4. The structural parameter design method of the thermally constrained high-speed hybrid ceramic angular contact ball bearing according to claim 3 is characterized in that: In step S3, the structural calculation and design method of hybrid ceramic angular contact ball bearings includes the following steps: (1) Take the rated dynamic load, rated static load of the actual working conditions of the bearing and the inner and outer diameters of the bearing as the initial input data; (2) Calculate and filter through multivariable constraint formulas (2)-(24) to obtain a set of values ​​X1=(x1, x2, f e ,f i ,g,B); (3) Using the objective function formula (1), the value set X1 = (x1, x2, f e ,f i ,g,B) to screen and determine the optimal value that satisfies the objective function, and finally obtain the optimal structural parameters.

Images