Design method of high-rigidity small-vibration low-power-consumption bearing structure

Abstract

The invention relates to a design method for a high-rigidity small-vibration low-power-consumption bearing structure. The design method comprises the following steps that S1, structure parameters, working condition parameters and lubrication parameters of a bearing system are obtained; s2, acting an external force vector on the inner ring, respectively establishing kinetic equations of the retainer, the rolling body and the inner ring according to a moment balance principle and a force balance principle, and establishing a bearing kinetic model; s3, solving the bearing model by using a variable-step Runge-Kutta method, and obtaining bearing dynamic behavior data at the same time; s4, determining the important size type of the bearing, changing the structure size of the type, calculating the vibration, power consumption and rigidity of the bearing according to the dynamic behavior of the bearing, and comprehensively analyzing the vibration, power consumption and rigidity of the bearing; and S5, determining the structural size of the high-rigidity small-vibration low-power-consumption angular contact ball bearing according to the comprehensive analysis of the vibration, the power consumption and the rigidity of the bearing. The structural size of the bearing can be designed more reasonably to obtain the high-rigidity, small-vibration and low-power-consumption bearing performance.

Description

Technical Field

[0001] The invention relates to the field of rolling bearing structure design, and more specifically to a method for designing a bearing structure with high rigidity, small vibration and low power consumption. Background Art

[0002] Angular contact ball bearings are widely used in rotating machinery. Their stiffness, power consumption, vibration and other properties have an important impact on the accuracy, reliability and life of the entire mechanical system. At present, bearing companies mainly use experimental methods to design high-stiffness, low-vibration, and low-power angular contact ball bearings. The experimental scheme is very arbitrary, the experimental cycle is long and the cost is high. Therefore, predicting the stiffness, power consumption and vibration of the bearing through the bearing dynamics model to design the key structural dimensions of the bearing can provide basic theoretical common technical support, shorten the experimental cycle and reduce the experimental cost.

[0003] It can be seen from the existing literature that the vibration, power consumption and stiffness of bearings have always attracted the attention of many scholars. Wang et al. (Wang PF, Yang Y, Ma Het al. Vibration characteristics of rotor-bearing system with angular misalignment and cage fracture: Simulation and Experiment. Mechanical Systems and Signal Processing, 2023, 182: 109545) analyzed the influence of bearing misassembly and cage fracture on bearing vibration, and how it affects the dynamic characteristics of the rotor. However, the cage in this analysis model only has rotational freedom. Yun Xialun et al. (Yun Xialun, Mei Xuesong, Jiang Gedong, et al. Dynamic stiffness analysis and test method of high-speed spindle angular contact ball bearings. Vibration, Testing and Diagnosis, 2019, 39 (4): 892-912) studied the angular relationship between residual vibration displacement and excitation response displacement, derived the dynamic support stiffness test principle, and accurately tested the dynamic support stiffness of high-speed electric spindle angular contact ball bearings, but the experimental cycle is long and the cost is high. Chen Yue et al. (Chen Yue, Qiu Ming, Du Hui, et al. Factors affecting the rotation accuracy of four-point contact ball bearings for robots. China Mechanical Engineering, 2020, 31(14): 1678-1685) considered the influence of the roundness error of the inner and outer ring grooves of the bearing on the rotation accuracy of the bearing, but the quasi-static model of the bearing ignores many dynamic influencing factors.

[0004] It can be seen from the above literature search that the existing bearing performance design is to predict the bearing vibration, stiffness and power consumption performance separately according to the specific bearing structure size. There is no comprehensive prediction of bearing vibration, stiffness and power consumption to design a reasonable bearing structure size. The design of a certain structure size will reduce vibration while deteriorating other performances. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for designing a bearing structure with high stiffness, low vibration and low power consumption, which can more reasonably design the bearing structure dimensions to obtain bearing performance with high stiffness, low vibration and low power consumption.

[0006] The technical solution adopted by the present invention to solve the technical problem is: constructing a high-rigidity, low-vibration and low-power consumption bearing structure design method, comprising the following steps:

[0007] S1. Obtaining structural parameters, operating parameters and lubrication parameters of the bearing system;

[0008] S2. Apply an external force vector to the inner ring, and establish the dynamic equations of the cage, rolling element and inner ring respectively according to the principles of moment balance and force balance, and establish a bearing dynamics model;

[0009] S3, using the variable step-size Runge-Kutta method to solve the bearing model and obtain the bearing dynamic behavior data;

[0010] S4. Determine the important dimension type of the bearing, change the structural dimension of this type, calculate the bearing vibration, power consumption and stiffness according to the bearing dynamic behavior, and comprehensively analyze the bearing vibration, power consumption and stiffness;

[0011] S5. Based on the comprehensive analysis of bearing vibration, power consumption and stiffness, the structural dimensions of the angular contact ball bearing with high stiffness, low vibration and low power consumption are determined.

[0012] According to the above scheme, the structural parameters include the structural parameters of the bearing inner ring, outer ring, rolling element and retaining cage, as well as material parameters and initial position parameters of the inner ring, outer ring, retaining cage and rolling element; the operating condition parameters include rotational speed and external force vector.

[0013] According to the above scheme, the bearing dynamics model in step S2 is expressed by the following formula:

[0014]

[0015] Solving the above nonlinear equations simultaneously, we can get the initial value of the dynamic model calculation: a , δ r ,θ,X 1j , X 2j , δ ij , δ oj ;

[0016] In the formula, F a is the axial force on the bearing, F r is the radial force on the bearing, K oj is the load displacement constant of the outer ring, Kij is the load displacement constant of the inner ring, M gj is the ball gyro torque, δ r is the total radial deformation of the bearing, δ a is the total axial deformation of the bearing, θ is the angular deformation of the bearing, and f i is the curvature coefficient of the inner circle, f o is the curvature coefficient of the outer ring, δ ij The contact deformation between the jth rolling element and the inner ring, δ oj is the contact deformation between the jth rolling element and the outer ring, B is the total curvature, α ij The contact angle between the jth rolling element and the inner ring, α oj is the contact angle between the jth rolling element and the outer ring, α0 is the initial contact angle, D is the rolling element diameter, m is the rolling element mass, w is the angular velocity of the inner ring, w m is the rolling element revolution speed, w R is the rolling element rotation speed, M′ is the torque on the bearing, Δ c is the radial clearance reduction, β i is the ball attitude angle.

[0017] According to the above scheme, in step S2, the dynamic equilibrium equation of the cage, rolling element and inner ring is established by analyzing the forces acting on the cage, rolling element and inner ring;

[0018] The rolling element dynamics differential equation is:

[0019]

[0020] The cage dynamics differential equation is:

[0021]

[0022] The differential equation for the inner ring dynamics is:

[0023]

[0024] According to the above scheme, Runge-Kutta method is used in step S3 to jointly solve the differential equations of rolling element dynamics, cage dynamics and inner ring dynamics. The initial displacement in the x direction is 10 -6 The initial values ​​of velocity, angular displacement and angular velocity are 0, and the initial value of angular velocity around the x direction is the angular velocity of bearing rotation.

[0025] According to the above scheme, in step S4, the method for calculating the bearing stiffness according to the bearing dynamic behavior includes:

[0026] Calculate the five-dimensional stiffness matrix K:

[0027]

[0028] The elements in the stiffness matrix K are expressed as follows:

[0029]

[0030] in,

[0031]

[0032]

[0033] in,

[0034]

[0035] In formula (6), the remaining unknown quantities are The partial differential expression of is as follows:

[0036]

[0037] According to the above scheme, in step S4, the power consumption calculation method is as follows:

[0038] The elastic hysteresis power consumption caused by the friction generated by the elastic deformation of the rolling elements and raceways is:

[0039]

[0040] The sliding friction power consumption caused by differential sliding of the rolling elements on the inner and outer raceways is:

[0041]

[0042] The spin friction power consumption caused by the spin friction torque is:

[0043]

[0044] The oil film shear friction power consumption generated by the lubrication shear action when the rolling element moves is:

[0045]

[0046] The power loss caused by the friction torque between the cage and the guide ring during rotation is:

[0047] P cg =ω c (|M cg |+|M ce |) (16)

[0048] The power loss caused by the viscous friction resistance generated by the lubricant on the rolling element surface during the movement of the rolling element is:

[0049] P vj =0.5ω bj d m πC D ρ e D b 2 (0.5d m ω i (1-D b cosα o / d m )) 1.95 / (32g) (17)

[0050] In the formula, α o is the initial contact angle, d m is the pitch diameter of the bearing, ρ e is the effective density of the lubricant, C D is the drag torque coefficient, ω i is the inner circle angular velocity.

[0051] The total power consumption is:

[0052]

[0053] According to the above scheme, in step S4, the vibration data is used to obtain the inner ring acceleration through the inner ring dynamics differential equation.

[0054] The high-rigidity, low-vibration, and low-power-consumption bearing structure design method of the present invention has the following beneficial effects:

[0055] 1. The method of the present invention comprehensively considers the contact load generated by the Hertzian contact between the rolling element and the inner and outer raceways, the centrifugal force generated by the orbital motion of the rolling element, the gyroscopic torque generated by the rotational motion, the viscous friction and blocking torque of the lubricating oil, the traction force and torque generated between the rolling element and the raceway, and the real-time changes of the force and friction between the rolling element and the cage. The obtained dynamic behavior is more in line with engineering practice, and the predicted bearing vibration, power consumption and stiffness are more accurate.

[0056] 2. The present invention accurately predicts bearing vibration, power consumption and stiffness through a bearing dynamics model, and then comprehensively analyzes bearing vibration, power consumption and stiffness to reasonably design the bearing structure size, thereby forming a high-rigidity, low-vibration, low-power angular contact ball bearing structure design method. This method can also determine reasonable working conditions by comprehensively analyzing bearing vibration, power consumption and stiffness, and can also be used for comprehensive analysis of vibration, power consumption and stiffness of different working conditions and specific bearing objects, and then select bearings that meet the working conditions. In addition, the same or similar applications are within the scope of protection of this patent. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which: Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 This is a simplified diagram of the bearing-rotor system; Figure 3 (a) Contact load Q i , (b) Contact load Q o , (c) Contact deformation δ i , (d) Contact deformation δ o , (e) contact angle α i , (f) contact angle α o , (g) Inner ring offset distance ( A 1j - X 1j ), (h) inner ring offset distance ( A 2j - X 2j ), (i) major axis of the elliptical contact area a o , (j) minor axis of the elliptical contact area b o , (k) Center oil film thickness h o , (l) sliding speed v o , (m) friction coefficient μ bo , (n) spin angular velocity ω so ; Figure 4 The acceleration fluctuation of the inner ring under different combinations of inner and outer raceway curvature radii: (a) (b) (c) (d) (e) ; Figure 5 are (a) axial stiffness, (b) angular stiffness, and (c) radial stiffness; Figure 6 is the total friction power consumption P T . DETAILED DESCRIPTION

[0064] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0065] like Figure 1-6 As shown, in the high-rigidity, low-vibration, low-power consumption bearing structure design method of the present invention, the present invention provides a high-rigidity, low-vibration, low-power consumption angular contact ball bearing structure design method, comprising the following steps:

[0066] S1. According to the bearing parts, simplify the bearing into Figure 2 The mathematical model shown in the figure establishes a bearing coordinate system to describe the dynamic behavior of the bearing inner ring, outer ring, rolling element and cage, and sets the structural parameters, operating parameters and lubrication parameters of the bearing system. The structural parameters include the structural parameters of the bearing inner ring, outer ring, rolling element and cage, material parameters, and the initial position parameters of the inner ring, outer ring, cage and rolling element.

[0067] S2. Apply the external force vector to the inner ring, and establish the dynamic equations of the cage, rolling element and inner ring respectively according to the principles of moment balance and force balance, and establish the bearing dynamics model, considering the contact load Q generated by the Hertzian contact between the rolling element and the inner and outer raceways. i and Q o , the rolling element's orbital motion generates centrifugal force The rotation motion generates a gyroscopic torque M q , the viscous friction force F of the lubricating oil v and the blocking torque M e , the traction force F is generated between the rolling element and the raceway to and F ti , and the moment M to 、M ti , the force F between the rolling element and the cage bc and friction F τbc The kinetic model can be expressed by the following formula:

[0068]

[0069]

[0070] Solving the above nonlinear equations simultaneously, we can get the initial value of the dynamic model calculation (δ a , δ r ,θ,X 1j , X 2j , δ ij , δ oj );where F a is the axial force on the bearing, F r is the radial force on the bearing, Koj is the load displacement constant of the outer ring, K ij is the load displacement constant of the inner ring, M gj is the ball gyro torque, δ r is the total radial deformation of the bearing, δ a is the total axial deformation of the bearing, θ is the angular deformation of the bearing, and f i is the curvature coefficient of the inner circle, f o is the curvature coefficient of the outer ring, δ ij The contact deformation between the jth rolling element and the inner ring, δ oj is the contact deformation between the jth rolling element and the outer ring, B is the total curvature, α ij The contact angle between the jth rolling element and the inner ring, α oj is the contact angle between the jth rolling element and the outer ring, α0 is the initial contact angle, λ oj =2,λ ij =0, D is the rolling element diameter, m is the rolling element mass, w is the inner ring angular velocity, w m is the rolling element revolution speed, w R is the rolling element rotation speed, M′ is the torque on the bearing, Δ c is the radial clearance reduction, β i is the ball attitude angle.

[0071] S3. Through the force analysis of the cage, rolling element and inner ring, the dynamic equilibrium equation of the cage, rolling element and inner ring is established:

[0072] Differential equation for rolling element dynamics:

[0073]

[0074] Differential equation of cage dynamics:

[0075]

[0076] Inner ring dynamics differential equation:

[0077]

[0078] S4. Use the Runge-Kutta method to solve the dynamic equations (3-5). The initial value of the x-direction displacement is 10 -6 The initial values ​​of velocity, angular displacement and angular velocity are 0, and the initial value of angular velocity around the x direction is the angular velocity of bearing rotation.

[0079] S5. Calculate bearing stiffness based on bearing dynamic behavior:

[0080] Five-dimensional stiffness matrix K:

[0081]

[0082] The elements in the stiffness matrix K are expressed as follows:

[0083]

[0084] in,

[0085]

[0086] in,

[0087]

[0088] In expression (6), the remaining unknown quantities are The partial differential expression of is as follows:

[0089]

[0090] S6, power consumption calculation equation is as follows:

[0091] The elastic hysteresis power consumption caused by the friction generated by the elastic deformation of the rolling elements and raceways is:

[0092]

[0093] The sliding friction power consumption caused by differential sliding of the rolling elements on the inner and outer raceways is:

[0094]

[0095] The spin friction power consumption caused by the spin friction torque is:

[0096]

[0097] The oil film shear friction power consumption generated by the lubrication shear action when the rolling element moves is:

[0098]

[0099] The power loss caused by the friction torque between the cage and the guide ring during rotation is:

[0100] P cg =ω c (|M cg |+|M ce |) (16)

[0101] The power loss caused by the viscous friction resistance generated by the lubricant on the rolling element surface during the movement of the rolling element is:

[0102] P vj =0.5ω bj d m πC Dρ e D b 2 (0.5d m ω i (1-D b cosα o / d m )) 1.95 / (32g) (17)

[0103] In the formula, α o is the initial contact angle, d m is the pitch diameter of the bearing, ρ e is the effective density of the lubricant, C D is the drag torque coefficient, ω i is the inner circle angular velocity.

[0104] The total power consumption is:

[0105]

[0106] To facilitate understanding and avoid omissions, all formula parameters involved in this embodiment are as follows:

[0107] F is the combined load vector; d is the inner ring displacement vector; δ x , δ y and δ z are the inner ring translation displacements respectively; θ y and θ z is the angular displacement of the inner ring; δ i / o is the elastic deformation between the rolling element and the raceway; X 1j X is the axial distance between the center of curvature of the outer raceway and the center of the ball after force is applied; 2j A is the radial distance between the center of curvature of the outer raceway and the center of the ball after force is applied; 1j A is the axial distance between the center of curvature of the inner raceway and the center of the ball after force is applied; 2j is the radial distance between the center of curvature of the inner raceway and the center of the ball after force is applied; Q is the contact load; α is the contact angle; is the centrifugal force of the rolling element; m b is the mass of the rolling element; ω m F is the rolling element revolution speed; v is the viscous resistance of the lubricating oil; M e M is the retardation torque of the lubricating oil on the rolling element; q I is the gyroscopic torque generated by the rolling body rotating around its own axis; b F is the moment of inertia of the rolling element; ti / o and M ti / o They are the oil film traction and torque of the rolling element in the inner and outer raceway contact areas; ω x′ ,ω y′ and ω z′are the component speeds of the rolling element's rotation; ω s F is the rolling element rotation speed; bc F is the contact force between rolling element and cage; τbc F is the friction between rolling element and cage; cgyc F is the collision force between the cage and the guide surface; χ M is the balancing force when the cage rotates irregularly; ce is the resistance torque of the cage caused by the oil and gas shear force; K is the five-dimensional stiffness matrix; k is an element in the stiffness matrix.

[0108] The following is a detailed description of the structural design method of the high-rigidity, low-vibration, and low-power angular contact ball bearing of the present invention in conjunction with an example, which is not intended to limit the present invention. The steps are:

[0109] 1) Get Figure 2 The structural parameters, operating parameters and lubrication parameters of the bearing system shown in Table 1 are as follows:

[0110] Table 1 Angular contact ball bearing structure, operating conditions and lubricating oil parameters

[0111]

[0112] 2) According to the parameters in step 1), the quasi-static method is used to obtain the initial value (δ a , δ r ,θ,X 1j , X 2j , δ ij , δ oj ).

[0113] 3) According to the initial value calculated in step 2), the bearing dynamics model is calculated, and the variable step-length Runge-Kutta method is used to solve the step dynamics equations 3-5, and the dynamic behavior is output, as shown in Figure (3).

[0114] Figure 3 Given the dynamic behavior, (a) is the internal contact load Q under the change of the inner raceway radius i , (b) is the external contact load Q o , (c) is the internal elastic deformation δ i , (d) is the external elastic deformation δ o , (e) is the internal contact angle α i , (f) is the external contact angle α o , (g) is the axial offset distance (A 1j -X 1j ), (h) is the radial offset distance (A 2j -X 2j ), (i) is the major axis a of the elliptical contact area o , (j) is the minor axis b of the elliptical contact areao , (k) is the center oil film thickness h o , (l) is the sliding velocity v o , (m) is the friction coefficient μ bo , (n) is the spin angular velocity ω so .

[0115] 4) According to the dynamic behavior, the bearing vibration data under different combinations of inner and outer raceway curvature radii are obtained, as shown in Figure (4). (a)r o =3.302mm,(b)r o =3.366mm,(c)r o =3.429mm,(d)r o =3.493mm,(e)r o =3.556mm.

[0116] 5) According to the dynamic behavior in step 3), the stiffness calculation matrix in step 5) is used to obtain the bearing stiffness data under different combinations of inner and outer raceway curvature radii, as shown in Figure (5), (a) axial stiffness, (b) angular stiffness, (c) radial stiffness.

[0117] 6) The dynamic behavior in step 3) is used, and the power consumption calculation equation in step 6) is used to obtain the bearing power consumption data under different combinations of inner and outer raceway curvature radii, as shown in Figure (6). It can be seen from Figure (4) that r i =3.493mm, the bearing vibration is small and gradually decreases with the increase of the outer raceway curvature radius; it can be seen from Figure (5) that r o =3.302mm, a larger radial and axial stiffness can be obtained, while r i =3.493mm, a higher angular stiffness can be obtained; from Figure (6), we can get r i =3.493mm, the bearing power consumption is small, and as the inner raceway curvature radius increases, the bearing power consumption decreases slightly. Comprehensive analysis shows that r i =3.493mm and r o =3.302mm, the bearing can achieve reasonable high stiffness, low power consumption and low vibration performance, which also guides the structural design of high stiffness, low power consumption and low vibration bearings.

[0118] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for designing a bearing structure with high rigidity, low vibration and low power consumption, characterized in that: The following steps are involved: S1. Obtaining structural parameters, operating parameters and lubrication parameters of the bearing system; S2. Apply an external force vector to the inner ring, and establish the dynamic equations of the cage, rolling element and inner ring respectively according to the principles of moment balance and force balance, and establish a bearing dynamics model; S3, using the variable step-size Runge-Kutta method to solve the bearing model and obtain the bearing dynamic behavior data; S4. Determine the important dimension type of the bearing, change the structural dimension of this type, calculate the bearing vibration, power consumption and stiffness according to the bearing dynamic behavior, and comprehensively analyze the bearing vibration, power consumption and stiffness; S5. Based on the comprehensive analysis of bearing vibration, power consumption and stiffness, the structural dimensions of the angular contact ball bearing with high stiffness, low vibration and low power consumption are determined.

2. The high-rigidity, low-vibration, and low-power-consumption bearing structure design method according to claim 1 is characterized in that: The structural parameters include structural parameters of the bearing inner ring, outer ring, rolling element and cage, material parameters, and initial position parameters of the inner ring, outer ring, cage and rolling element; the operating condition parameters include rotation speed and external force vector.

3. The high-rigidity, low-vibration, and low-power-consumption bearing structure design method according to claim 1 is characterized in that: The bearing dynamics model in step S2 is expressed by the following formula: Solving the above nonlinear equations simultaneously, we can get the initial value of the dynamic model calculation: a , δ r ,θ,X 1j , X 2j , δ ij , δ oj ; In the formula, F a is the axial force on the bearing, F r is the radial force on the bearing, K oj is the load displacement constant of the outer ring, K ij is the load displacement constant of the inner ring, M gj is the ball gyro torque, δ r is the total radial deformation of the bearing, δ a is the total axial deformation of the bearing, θ is the angular deformation of the bearing, and f i is the curvature coefficient of the inner circle, f o is the curvature coefficient of the outer ring, δ ij The contact deformation between the jth rolling element and the inner ring, δ oj is the contact deformation between the jth rolling element and the outer ring, B is the total curvature, α ij The contact angle between the jth rolling element and the inner ring, α oj is the contact angle between the jth rolling element and the outer ring, α0 is the initial contact angle, D is the rolling element diameter, m is the rolling element mass, w is the angular velocity of the inner ring, w m is the rolling element revolution speed, w R is the rolling element rotation speed, M′ is the torque on the bearing, Δ c is the radial clearance reduction, β j is the ball attitude angle.

4. The high-rigidity, low-vibration, and low-power-consumption bearing structure design method according to claim 3 is characterized in that: In step S2, a dynamic equilibrium equation of the cage, rolling elements and inner ring is established by analyzing the forces acting on the cage, rolling elements and inner ring; The differential equation of rolling element dynamics is: The cage dynamics differential equation is: The differential equation for the inner ring dynamics is:

5. The high-rigidity, low-vibration, low-power-consumption bearing structure design method according to claim 4 is characterized in that: In step S3, the Runge-Kutta method is used to jointly solve the rolling element dynamics differential equation, the cage dynamics differential equation, and the inner ring dynamics differential equation. The initial value of the x-direction displacement is 10 -6 The initial values ​​of velocity, angular displacement and angular velocity are 0, and the initial value of angular velocity around the x direction is the angular velocity of bearing rotation.

6. The high-rigidity, low-vibration, low-power-consumption bearing structure design method according to claim 5 is characterized in that: In step S4, the method for calculating the bearing stiffness according to the bearing dynamic behavior includes: Calculate the five-dimensional stiffness matrix K: The elements in the stiffness matrix K are expressed as follows: in, in, In formula (6), the remaining unknown quantities are The partial differential expression of is as follows:

7. The method for designing a bearing structure with high rigidity, low vibration and low power consumption according to claim 6 is characterized in that: In step S4, the power consumption calculation method is as follows: The elastic hysteresis power consumption caused by the friction generated by the elastic deformation of the rolling elements and raceways is: The sliding friction power consumption caused by differential sliding of the rolling elements on the inner and outer raceways is: The spin friction power consumption caused by the spin friction torque is: The oil film shear friction power consumption generated by the lubrication shear action when the rolling element moves is: The power loss caused by the friction torque between the cage and the guide ring during rotation is: P cg =ω c (|M cg |+|M ce |) (16) The power loss caused by the viscous friction resistance generated by the lubricant on the rolling element surface during the movement of the rolling element is: P vj =0.5h bj d m BC D r e D b 2 (0.5d m oh i (1-D b thing o / d m )) 1.95 / (32g) (17) In the formula, α o is the initial contact angle, d m is the pitch diameter of the bearing, ρ e is the effective density of the lubricant, C D is the drag torque coefficient, ω i is the inner circle angular velocity. The total power consumption is:

8. The method for designing a high-rigidity, low-vibration, and low-power bearing structure according to claim 7 is characterized in that: In step S4, the vibration data is used to obtain the inner ring acceleration through the inner ring dynamics differential equation.

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