High-speed bearing structure matching design method driven by bearing digital twin model

Abstract

The invention relates to a high-speed bearing structure matching design method driven by a bearing digital twin model. The method comprises the following steps that S1, structure parameters meeting the bearing capacity, the service life and the reliability of a main bearing are designed according to constraint conditions; s2, combining the structure size according to the structure size type, predicting vibration, rotation precision, power consumption and rigidity in combination with bearing-rotor dynamics, and realizing correlation of structure-dynamics-performance; and S3, according to the performance demand priority, determining a priority combination sequence of various types of structure sizes. The experiment cost can be remarkably reduced, and the experiment period can be shortened. According to the high-speed bearing structure matching design method driven by the bearing digital twin model, the bearing vibration, rotation precision, power consumption and rigidity can be predicted according to the bearing rotor dynamical model to match and design the structural size of the angular contact ball bearing, the cost can be effectively reduced, and the experimental period is shortened.

Description

Technical Field

[0001] This invention relates to the field of high-performance bearing design, and more specifically, to a high-speed bearing structure matching design method driven by a digital twin model of a bearing. Background Technology

[0002] Rolling bearings are crucial supporting components of rotor systems in rotating machinery. Their vibration, rotational accuracy, power consumption, and stiffness significantly impact the operating accuracy, temperature rise, and lifespan of the machinery. Currently, the design of optimal angular contact ball bearings relies primarily on theoretical calculations and simulation analysis, combined with extensive experimental testing, lacking effective design methods. Existing design methods mainly focus on optimizing the structural dimensions of bearing assemblies by considering the influence of single dimensional factors such as inconsistent ball diameters, unevenly distributed pocket diameters, guide clearance, pocket clearance, free play, lubricant viscosity and temperature, and macroscopic geometric defects in the bearing assembly on a specific mechanical property. However, bearing assembly dimensions are numerous. The contact angle and free play are determined by the outer raceway diameter, inner raceway diameter, outer raceway radius of curvature, inner raceway radius of curvature, and ball diameter; the pocket clearance is determined by the ball diameter and pocket diameter; and the guide clearance is determined by the outer ring guide ring diameter and cage outer diameter or the inner ring guide ring diameter and cage inner diameter. Therefore, how to match the structural dimensions of the bearing assembly to design an optimal angular contact ball bearing remains unclear. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a high-speed bearing structure matching design method driven by a digital twin model of the bearing. This method can predict the bearing vibration, rotational accuracy, power consumption and stiffness based on the bearing rotor dynamics model to match and design the structural dimensions of the angular contact ball bearing, which can effectively reduce costs and shorten the experimental cycle.

[0004] The technical solution adopted by this invention to solve its technical problem is: to construct a high-speed bearing structure matching design method driven by a digital twin model of a bearing, including the following steps:

[0005] S1. Design structural parameters that meet the load-bearing capacity, lifespan, and reliability of the main bearing according to the constraints.

[0006] S2. Combine structural dimensions according to structural size type, and combine bearing-rotor dynamics to predict vibration, rotational accuracy, power consumption, and stiffness, so as to realize the correlation between structure-dynamics-performance;

[0007] S3. Determine the priority combination order of structural dimensions for each type based on performance requirements.

[0008] According to the above scheme, in step S1, the structural parameters, operating parameters and lubrication conditions of the bearing rotor system are obtained.

[0009] According to the above scheme, the structural parameters include bearing parameters, material parameters, rotor geometric parameters, and bearing and rotor position parameters.

[0010] According to the above scheme, the operating parameters include rotational speed and external force vector; the lubrication conditions include lubrication viscosity and lubrication density.

[0011] According to the above scheme, in step S2, the external force vector is applied to the rotor, and the rotor is subjected to the load vector F. s ={F sx ,F sy ,F sz M sy M sz The function of} is to generate the displacement vector d of the inner raceway. s ={δ sx ,δ sy ,δ sz ,θ sy ,θ sz The left bearing generates a nonlinear force vector F. L ={F L x ,F L y ,F L z M L y M L z} and displacement vector d L ={δ L x ,δ L y ,δ L z ,θ L y ,θ L z}, while the right bearing is F R ={F R x ,F R y ,F R z M R y M R z} and d R ={δ R x ,δ R y ,δ R z ,θ R y ,θ Rz The outer raceway is fixed inside the bearing housing, and the rotor moves at an angular velocity ω. i Rotation; Based on the principles of torque balance and force balance, establish the dynamic equations of the bearing rotor system:

[0012]

[0013] In the formula, m r The rotor mass, bearing contact force, and torque are respectively expressed as F. ix ,F iy ,F iz M iy and M iz l0 represents the distance from the point of force application to the left bearing, and l1 and l2 represent the distances from the left and right bearings to the rotor's center of mass, respectively; the rotor rotation accuracy and vibration data are output based on the rotor system dynamic equations.

[0014] According to the above scheme, in step S2, the dynamic equation of the bearing inner ring is as follows:

[0015]

[0016] According to the above scheme, in step S2, the relevant dynamic behavior is output based on the bearing-rotor system dynamic equation, combined with the five-dimensional stiffness matrix K:

[0017]

[0018] The elements of the stiffness matrix K are expressed as follows:

[0019] in,

[0020]

[0021]

[0022] in,

[0023]

[0024] The partial differential expression is as follows:

[0025]

[0026] According to the above scheme, in step S2, the relevant dynamic behavior is output based on the bearing-rotor system dynamic equation, combined with the power consumption calculation equation:

[0027] The power consumption of elastic hysteresis is:

[0028]

[0029] The power consumption of sliding friction is:

[0030]

[0031] According to the above scheme, in step S2, the spin friction power consumption is:

[0032]

[0033] The oil film shear friction power consumption is:

[0034]

[0035] The cage friction power consumption is:

[0036] P cg =ω c (|M cg |+|M ce |)(13)

[0037] The viscous friction power consumption of the ball is:

[0038] 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) (14)

[0039] In the formula, α o Let d be the initial contact angle. m ρ is the pitch circle diameter of the machine tool spindle bearing. e C is the effective density of the lubricant. D ω is the drag torque coefficient. i The inner angular velocity;

[0040] Total power consumption is:

[0041]

[0042] According to the above scheme, in step S3, the inner and outer raceway curvature radii, inner and outer raceway diameters, ball diameters and number, pocket diameter, cage outer diameter, and guide surface diameter are classified and combined with the same type of structural parameters to calculate the changes in vibration, rotational accuracy, power consumption, and stiffness of the angular contact ball bearing. The priority combination order of each type of structural dimension is determined according to the degree of influence of each type of structural dimension combination on the comprehensive performance of the bearing, thereby obtaining the bearing assembly structural dimension combination data.

[0043] The bearing digital twin-driven high-speed bearing structure matching design method of the present invention has the following advantages:

[0044] The method of this invention first designs structural dimension parameters that meet the basic performance indicators such as load-bearing capacity, life and reliability of the main bearing based on the constraints of existing design methods. Then, it combines structural dimensions according to structural dimension types, and combines bearing-rotor dynamics to predict vibration, rotational accuracy, power consumption and stiffness, so as to realize the correlation between structure-dynamics-performance. According to the priority of performance requirements, the priority combination order of each type of structural dimension is determined, forming a high-speed bearing structure matching design method driven by bearing digital twin model, which can significantly reduce experimental costs and shorten the experimental cycle. Attached Figure Description

[0045] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 A simplified diagram of the bearing rotor system; Figure 2 The rotor runout is the combined curvature radii of the inner and outer raceways of the right bearing. Figures 3(a)-3(e) show the acceleration spectra of the inner raceway when there are different combinations of inner and outer raceway curvature radii: (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; Figures 4(a)-4(g) show the average frictional power consumption under different combinations of inner and outer groove curvature radii: (a) Sliding frictional power consumption P d (b) Spin triboelectric power consumption P s (c) Oil film shear friction power consumption P t (d) Elastic hysteresis friction power consumption Pe (e) Viscous friction power consumption P v (f) Cage friction power consumption P cg (g) Total frictional power consumption P T ; Figures 5(a)-5(c) show the bearing stiffness variation under different combinations of inner and outer raceway curvature radii: (a) axial stiffness, (b) angular stiffness, (c) radial stiffness; Figure 6 Dimension matching process for various structural types. Detailed Implementation

[0052] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0053] This invention provides a high-speed bearing structure matching design method driven by a digital twin model of the bearing, comprising the following steps:

[0054] (1) Based on a certain electric spindle, establish a dynamic model of the bearing-rotor system, such as... Figure 1 As shown.

[0055] (2) Obtain the structural parameters, operating parameters and lubrication parameters of the bearing rotor system. The structural parameters mainly include bearing parameters, material parameters, rotor geometric parameters, and bearing and rotor position parameters. The operating parameters include rotational speed and external force vector. The lubrication parameters include lubrication viscosity and lubrication density.

[0056] (3) When the external force vector is applied to the rotor, the rotor is subjected to the load vector F. s ={F sx ,F sy ,F sz M sy M sz The function of} is to generate the displacement vector d of the inner raceway. s ={δ sx ,δ sy ,δ sz ,θ sy ,θ sz Therefore, the left bearing generates a nonlinear force vector F. L ={F L x ,F L y ,F Lz M L y M L z} and displacement vector d L ={δ L x ,δ L y ,δ L z ,θ L y ,θ L z}, while the right bearing is F R ={F R x ,F R y ,F R z M R y M R z} and d R ={δ R x ,δ R y ,δ R z ,θ R y ,θ R z The outer raceway is fixed inside the bearing housing, and the rotor moves at an angular velocity ω. i Rotation. Based on the principles of torque balance and force balance, the dynamic equations of the bearing rotor system are established:

[0057]

[0058] In the formula, m r The rotor mass, bearing contact force, and torque are respectively expressed as F. ix ,F iy ,F iz M iy and M iz l0 represents the distance from the point of force application to the left bearing, and l1 and l2 represent the distances from the left and right bearings to the rotor's center of mass, respectively. The rotor rotation accuracy and vibration data are output based on the rotor system dynamics equations.

[0059] (4) The dynamic balance of the rotor is inseparable from the force action of the inner rings of the left and right bearings. The dynamic equation of the inner rings of the bearings is as follows:

[0060] (5) Output the relevant dynamic behavior based on the dynamic equations of the bearing-rotor system, combined with the five-dimensional stiffness matrix K:

[0061]

[0062] The elements of the stiffness matrix K are expressed as follows:

[0063]

[0064] in,

[0065]

[0066] in,

[0067]

[0068] Other unknowns The partial differential expression is as follows:

[0069] (6) Output the relevant dynamic behavior based on the bearing-rotor system dynamic equations, and combine it with the power consumption calculation equations:

[0070] The power consumption of elastic hysteresis is:

[0071]

[0072] The power consumption of sliding friction is:

[0073]

[0074] The spin triboelectric power consumption is:

[0075]

[0076] The oil film shear friction power consumption is:

[0077]

[0078] The cage friction power consumption is:

[0079] P cg =ω c (|M cg |+|M ce |)(13)

[0080] The viscous friction power consumption of the ball is:

[0081] P vj =0.5ω bj d m πC D ρ e Db 2 (0.5d m ω i (1-D b cosα° / d m )) 1.95 / (32g) (14)

[0082] In the formula, α° is the initial contact angle, and d m ρ is the pitch circle diameter of the machine tool spindle bearing. e C is the effective density of the lubricant. D ω is the drag torque coefficient. i This represents the inner angular velocity.

[0083] Total power consumption is:

[0084]

[0085] (7) Classify the structural dimensions such as inner and outer raceway curvature radius, inner and outer raceway diameter, ball diameter and number, pocket diameter, cage outer diameter, and guide surface diameter, and combine the same type of structural dimensions to calculate the changes in vibration, rotational accuracy, power consumption, and stiffness of the angular contact ball bearing. Determine the priority combination order of each type of structural dimension according to the degree of influence of the combination of each type of structural dimension on the comprehensive performance of the bearing, and then obtain the structural dimension combination data of the bearing assembly. Analyze and establish a high-speed bearing structure matching design method driven by a digital twin model of the bearing.

[0086] (8) In the above scheme, the Runge-Kutta method is used to solve the dynamic equations, and the initial value of the 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 the angular velocity around the x-direction is the rotational angular velocity of the angular contact ball bearing.

[0087] The following example further illustrates the structural design method of the angular contact ball bearing with low vibration and high rotational accuracy according to the present invention. This example is not intended to limit the invention. The steps are as follows:

[0088] (1) Obtain as follows Figure 1 The structural parameters, operating parameters, and lubrication parameters of the bearing rotor system are shown in Tables 1 and 2:

[0089] Table 1 Rotor Parameters

[0090]

[0091] Table 2 Parameters for Bearing B7008C and Lubrication

[0092]

[0093] (2) Using the bearing rotor dynamics model established in steps 2) to 7) based on the parameters in step (1), the variable step size Runge-Kutta method in step 8) is used to calculate the vibration, rotational accuracy, power consumption and stiffness of the bearing rotor system.

[0094] Figure 2 As shown, in (r i ,r o In the combination of (3.493, 3.302), (3.493, 3.429), (3.336, 3.493)}, the runout value is relatively small. As shown in Figure 3, when the inner raceway curvature radius remains constant, the difference between the outer raceway curvature radius and the ball radius gradually increases, resulting in a gradual decrease in low-frequency peak values ​​and a very small high-frequency peak value. The same variation can be observed when the difference between the ball radius and the inner raceway curvature radius gradually increases. Furthermore, when the inner raceway curvature radius and the outer raceway curvature radius are very close, the high-frequency vibration becomes more intense. Therefore, (r i r o The combination of {(3.493, 3.302), (3.336, 3.493)} mm can achieve optimal vibration for the inner ring. As shown in Figure 4, the average sliding friction power consumption and the average spin friction power consumption gradually decrease with the increase of the inner ring raceway curvature radius, while they do not change significantly at the large outer ring raceway curvature radius, but gradually decrease with the increase of the outer ring raceway curvature radius. For the oil film shear friction power consumption, it decreases sharply when the outer ring raceway curvature radius is close to the radius of the rolling element, and then gradually decreases with the increase of the inner ring raceway curvature radius. This is due to the intense sliding of the rolling element. The opposite is true when the outer ring raceway curvature radius is significantly larger than the radius of the rolling element. This is attributed to the oil film thickness, and there is no significant change when the outer ring raceway curvature radius is 3.429 mm. For elastic hysteresis frictional power consumption, it generally increases with the increase of the outer ring raceway radius of curvature under small inner ring raceway curvature radius, while the opposite is true under large inner ring raceway radius of curvature radius, and gradually increases with the increase of the inner ring raceway radius of curvature radius. This is related to the difference between the raceway radius of curvature and the radius of the rolling element. Viscous frictional power consumption remains almost unchanged. For the frictional power consumption of the cage, its significant increase is caused by the irregular movement of the cage's center of mass trajectory, which depends on the dynamic stability of the cage. The total bearing frictional power consumption is larger under the combination of small outer ring raceway radius of curvature radius and small inner ring raceway radius of curvature radius. Besides the combination of large outer ring raceway radius of curvature radius and large inner ring raceway radius of curvature radius, low total frictional power consumption can also be obtained when the raceway radius of one ring is close to the radius of the rolling element, and the raceway radius of the other ring is larger than the radius of the rolling element. In particular, when the inner and outer ring raceway radii of curvature are close to the radii of the rolling element, low total frictional power consumption can always be achieved, i.e., r0. i=3.493mm can achieve low total frictional power consumption. As shown in Figure 5, when the inner raceway curvature radius remains constant, the axial stiffness and angular stiffness increase with the outer raceway curvature radius (r). o As the radius of curvature of the outer raceway increases, the axial stiffness gradually decreases. Similarly, when the radius of curvature of the outer raceway remains constant, an increase in the radius of curvature of the inner raceway reduces both axial and angular stiffness. For radial stiffness, when the radius of curvature of the inner raceway is close to the radius of the small ball, its strength gradually increases with the increase of the radius of curvature of the outer raceway. However, when the radius of curvature of the inner raceway significantly exceeds the radius of curvature of the small ball, the trend reverses. In particular, when the radius of curvature of the inner raceway reaches 3.493 mm, the radial stiffness does not change significantly. Furthermore, the radial stiffness is lower when the radius of curvature of the inner raceway is smaller than when it is larger. These trends indicate that bearing stiffness varies with (r)... i r o When ) = (3.493, 3.302) mm, it is relatively ideal. Comprehensive analysis shows that (r) = (3.493, 3.302) mm. i r o When the radius of curvature of the bearing raceway is (3.493, 3.302) mm, high rotational accuracy, low vibration, low power consumption, and high stiffness can be achieved. Based on this method, combined with... Figure 6 The process of matching the dimensions of various structural types can achieve the optimal design of various structural dimensions for bearings with the best overall performance.

[0095] This invention first designs structural dimensional parameters that meet the basic performance indicators of the main bearing, such as load-bearing capacity, lifespan, and reliability, based on the constraints of existing design methods. It then combines structural dimensions according to their types, and combines bearing-rotor dynamics to predict vibration, rotational accuracy, power consumption, and stiffness, thus achieving a correlation between structure, dynamics, and performance. Based on performance requirements, it determines the priority combination order of various structural dimensions, forming a high-speed bearing structure matching design method driven by a bearing digital twin model. This significantly reduces experimental costs and shortens the experimental cycle. Furthermore, this method can also be used to determine reasonable assembly and operating conditions based on bearing-rotor performance requirements; similar or identical applications are within the scope of this patent.

[0096] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A bearing digital twin model driven high-speed bearing structure matching design method, characterized in that, The method comprises the following steps: S1, designing structure parameters meeting the load capacity, service life and reliability of the main bearing according to constraint conditions; S2, combining structure sizes according to structure size types, and combining bearing-rotor dynamics to predict vibration, rotation accuracy, power consumption and stiffness, so as to realize the association of structure-dynamics-performance; S3, determining the priority combination order of each type of structure size according to the priority of performance requirements.

2. The bearing digital twin model driven high-speed bearing structure matching design method according to claim 1, characterized in that, In the step S1, the structure parameters, working condition parameters and lubrication conditions of the bearing-rotor system are obtained.

3. The bearing digital twin model driven high-speed bearing structure matching design method according to claim 2, characterized in that, The structure parameters include bearing parameters, material parameters, rotor geometric parameters and position parameters of the bearing and the rotor.

4. The bearing digital twin model driven high-speed bearing structure matching design method according to claim 2, characterized in that, The working condition parameters include rotating speed and external force vector; and the lubrication conditions include lubrication viscosity and lubrication density.

5. The bearing digital twin model driven high-speed bearing structure matching design method of claim 1, wherein, In the step S2, an external force vector acts on the rotor, the rotor is subjected to a load vector F s sx sy sz sy sz and generates an inner raceway displacement vector d s sx sy sz sy sz ; the left bearing generates a nonlinear force vector F L L x L y L z L y L z and a displacement vector d L L x L y L z L y L z , while the right bearing is F R R x R y R z R y R z and d R R x R y R z R y R z ; the outer raceway is fixed in the bearing seat, and the rotor rotates at an angular velocity ω i ; the bearing-rotor system dynamics equation is established according to the principle of torque balance and force balance:​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ where m r The contact force and moment of the bearing are represented as F ix ,F iy ,F iz ,M iy and M iz , l0 represents the distance from the force application point to the left bearing, and l1 and l2 represent the distances from the left and right bearings to the mass center of the rotor, respectively; the rotor rotation accuracy and vibration data are output according to the rotor system dynamics equation.

6. The bearing digital twin model driven high-speed bearing structure matching design method of claim 1, wherein, In the step S2, the dynamics equation of the bearing inner ring is as follows:

7. The bearing digital twin model driven high-speed bearing structure matching design method of claim 1, wherein, In the step S2, the relevant dynamics behavior is output according to the bearing-rotor system dynamics equation, and the five-dimensional stiffness matrix K is combined: The elements in the stiffness matrix K are expressed as follows: Wherein, Wherein, The partial differentiation of the function f(x, y) with respect to x is given by:

8. The bearing digital twin model driven high-speed bearing structure matching design method of claim 1, wherein, In the step S2, the relevant dynamics behavior is output according to the bearing-rotor system dynamics equation, and the power consumption calculation equation is combined: The elastic hysteresis power consumption is: The sliding friction power consumption is:

9. The bearing digital twin model driven high-speed bearing structure matching design method according to claim 8, characterized in that, The self-rotation friction power consumption is: The oil film shear friction power consumption is: The cage friction power consumption is: P cg = ω c (|M cg |+|M ce |) (13) The ball viscous friction power consumption is: P vj = 0.5ω bj d m πC D ρ e D b 2 (0.5d m ω i (1-D b cosα° / d m )) 1.95 / (32g) (14) wherein a° is the initial contact angle, d m is the pitch diameter of the machine tool spindle bearing, p e is the effective density of the lubricant, C D is the resistance torque coefficient, w i is the angular velocity of the inner ring; The total power consumption is:

10. The bearing digital twin model driven high-speed bearing structure matching design method of claim 1, wherein, In the step S3, the curvature radii of the inner and outer raceways, the diameters of the inner and outer raceways, the diameters and number of balls, the diameters of pockets, the outer diameters of cages and the diameters of guide surfaces are classified, the same type of structure parameters are combined to calculate the change of vibration, rotation accuracy, power consumption and stiffness of the angular contact ball bearing, the priority combination order of each type of structure size is determined according to the influence degree of each type of structure size combination on the comprehensive performance of the bearing, and then the structure size combination data of the bearing assembly is obtained.

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