A vibration-damping design method for a rolling bearing with an odd number of rolling elements

Abstract

This invention relates to a vibration reduction design method for rolling bearings with an odd number of rolling elements, comprising: S1, obtaining bearing operating conditions and performance requirements, designing bearing structural parameters that meet basic performance indicators such as load capacity, lifespan, and reliability, and determining the parameter selection range; S2, within the range of structural parameters that meet the basic performance indicators, prioritizing the determination that the number of effective rolling elements is an odd prime number, and then determining other structural parameters to meet the low vibration performance requirements of the bearing. This invention can disperse vibration energy throughout the entire vibration frequency domain, reducing the enhancement and superposition of bearing vibration, and actively reducing bearing vibration by starting with the structural design of the bearing itself.

Description

Technical Field

[0001] This invention relates to the field of rolling bearing design, and more specifically, to a method for vibration reduction design of rolling bearings with an odd number of rolling elements. Background Technology

[0002] Rolling bearings are widely used in rotating machinery. Excessive vibration can reduce the accuracy, reliability, and lifespan of the entire mechanical system. Existing bearing design methods consider vibration performance in addition to meeting performance requirements such as load capacity, lifespan, and stiffness, generally believing that a full-ball bearing is better. Then, they try to reduce the vibration intensity of the bearing, without considering how to distribute the vibration energy across the entire vibration frequency domain.

[0003] There are many existing methods for bearing vibration reduction. Hua Lin et al. (Structural Design Method for Angular Contact Ball Bearing with Small Vibration and High Rotational Accuracy, ZL2024109748007) actively reduced the bearing vibration intensity by optimizing structural parameters; Wu Hongkai et al. (Wu Hongkai. Vibration Reduction Bearing Design and Analysis Based on Extrusion Oil Film Damper. Dalian University of Technology, 2022) reduced the bearing vibration intensity by adding a damper as a passive vibration reduction method.

[0004] The literature search results show that existing vibration reduction methods mainly focus on reducing vibration intensity or passive vibration reduction, without designing bearings for active vibration reduction from the perspective of vibration energy dispersion. Even if a bearing with dispersed vibration energy resonates, it will not have a large vibration intensity. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a vibration reduction design method for rolling bearings with an odd number of rolling elements, which can disperse vibration energy throughout the entire vibration frequency domain, reduce the enhancement and superposition of bearing vibration, and actively reduce bearing vibration by starting from the structural design of the bearing itself.

[0006] The technical solution adopted by this invention to solve its technical problem is: a method for constructing a vibration reduction design for a rolling bearing with an odd number of rolling elements, comprising: S1. Obtain bearing operating conditions and performance requirements, design bearing structural parameters that meet the basic performance indicators of load capacity, life and reliability, and determine the parameter selection range; S2. Within the range of structural parameters that meet the basic performance indicators, prioritize determining that the number of effective rolling elements is an odd prime number, and then determine other structural parameters to meet the low vibration performance requirements of the bearing.

[0007] According to the above scheme, the effective rolling element is the number of rolling elements in the bearing assembly that are loaded and excited.

[0008] According to the above scheme, when the rolling bearing is a bearing that bears axial load, the number of effective rolling elements is equal to the number of nominal rolling elements, and the number of nominal rolling elements is the total number of rolling elements installed in the bearing. According to the above scheme, the bearing that bears the axial load is an angular contact ball bearing or a tapered roller bearing.

[0009] According to the above scheme, when the rolling bearing is a bearing that bears axial load, the number of effective rolling elements ensures that all rolling elements excite the bearing assembly to form vibrations that are dispersed across non-integer multiples of frequency, thus avoiding vibration concentration at a specific frequency.

[0010] According to the above scheme, when the rolling bearing is a bearing that bears radial load, the number of effective rolling elements is less than the number of nominal rolling elements. The number of nominal rolling elements is the total number of rolling elements installed in the bearing. According to the above scheme, the bearing that bears the radial load is a deep groove ball bearing or a cylindrical roller bearing.

[0011] According to the above scheme, when the rolling bearing is a bearing that bears radial load, the number of effective rolling elements enables the effective rolling elements to excite the bearing assembly to form vibrations that are dispersed across non-integer multiples of frequency, thus avoiding vibration concentration at a specific frequency.

[0012] The rolling bearing vibration reduction design method for an odd number of rolling elements according to the present invention has the following beneficial effects: 1. The method of the present invention uses the vibration caused by the rolling body with prime number distribution to be dispersed in non-integer multiples of frequency, which avoids the vibration being concentrated on a specific frequency; the non-integer multiples of frequency vibration are difficult to couple with the system's natural frequency or other excitation frequency, which reduces the occurrence rate of system resonance.

[0013] 2. For angular contact ball bearings, tapered roller bearings, and other bearings that mainly bear axial loads, the vibration of the entire rolling element-excited bearing assembly is dispersed into non-integer multiples of frequency, avoiding vibration concentration at a specific frequency; non-integer multiples of frequency vibration are difficult to couple with the system's natural frequency or other excitation frequencies, reducing the occurrence rate of system resonance.

[0014] 3. For bearings such as deep groove ball bearings and cylindrical roller bearings that mainly bear radial loads, it is necessary to distinguish between the nominal number of rolling elements and the effective number of rolling elements that are excited by the load. The bearing should be designed with the number of effective rolling elements as an odd prime number as the core starting point, so that the vibration of the bearing assembly excited by the effective rolling elements is dispersed in non-integer multiples of frequency, avoiding the vibration from being concentrated on a specific frequency. Attached Figure Description

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 A schematic diagram of bearing I with 19 balls; Figure 2 A schematic diagram of bearing II with 22 balls; Figure 3 A schematic diagram of bearing III with 21 balls; Figure 4 Schematic diagram of the reconstructed acceleration spectrum of bearing I; Figure 5 Schematic diagram of the reconstructed acceleration spectrum of bearing II; Figure 6 Schematic diagram of the reconstructed acceleration spectrum of bearing III; Figure 7 A schematic diagram illustrating the differences in the spectral structure of vibration signals from bearings I, II, and III. Detailed Implementation

[0016] 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.

[0017] This invention provides a method for vibration reduction design of rolling bearings with an odd number of rolling elements, comprising the following steps: 1) Obtain bearing performance requirements, and use existing design technologies to design bearing structural parameters that meet basic performance indicators such as roll ratio, axial stiffness, and life, and determine the selection range of relevant parameters; the following is an example using the 7008C angular contact ball bearing: For a rolling ball bearing with a given life, its life L The calculation equation is as follows:

[0018] In the formula, C Indicates the rated dynamic load. F This indicates the service load; for ball bearings, a=3.

[0019] Using the rated dynamic load of the bearing as the objective function, the maximum rated dynamic load is obtained under the optimal bearing structure. The calculation equation for the maximum rated dynamic load of the angular contact ball bearing is as follows:

[0020]

[0021] , ,

[0022] For the inner raceway swirl ratio xgb:

[0023] For axial stiffness G s :

[0024] The bearing is designed based on the following constraints: Sphere diameter constraint K wmin ( D - d )≤ D b ≤ K wmax ( D - d ) Ball number constraints Z ≤π( D + d ) / (2 K z D b ) Sphere center circle constraint condition 0.49 ( D + d )≤ D wp ≤0.515(D+d) The constraint condition for the raceway curvature coefficient is 0.515 ≤ f o ≤0.54, 0.53≤ f i ≤0.58 Pocket clearance constraint condition 0.6 ( D p - D b )≤ C p ≤0.8( D p - D b ) Note: f c These are coefficients related to the geometry, manufacturing precision, and materials of the bearing components. α It is the contact angle. It is the initial contact angle. D o It is the outer raceway diameter. D i It is the inner raceway diameter. r o It is the outer raceway radius of curvature. r i It is the inner raceway radius of curvature. D b It is the diameter of the rolling element. D p It is the diameter of the pocket. D goIt is the diameter of the outer guide ring. D co It is the outer diameter of the cage. D ci It is the diameter of the inner guide ring. D gi It is the inner diameter of the cage. D It is the nominal outer diameter of the bearing. d It is the nominal inner diameter of the bearing. Z It is the number of rolling elements. n It's the inner ring speed. K w The constraint coefficient is 0.23≤ K w ≤0.32, K z It is a constraint coefficient. D wp It is the diameter of the center circle of the sphere. f o and f i It is the raceway curvature coefficient. It is the external axial load borne by the bearing.

[0025] 2) Based on the target dynamic load of 30kN, the target inner raceway roll ratio of 0.8, and the target axial stiffness of 5×10⁻⁶... 8 Within the range of structural parameters that meet the basic performance indicators, the number of rolling elements is preferentially determined to be an odd prime number. Then, parameters such as ball diameter, inner and outer raceway curvature radius, and inner and outer raceway diameter are determined. In order to compare and prove that an odd prime number of rolling elements can disperse vibration energy throughout the entire vibration frequency domain, and that a bearing with dispersed vibration energy will not have a large vibration intensity even if it resonates, the bearing structural parameters are also determined by an odd and even number of rolling elements, as shown in Table 1.

[0026] Table 1. Main structural parameters (mm) of bearing 7008C

[0027] 3) Bearings with an odd number of prime elements, an even number of prime elements, and an odd number of prime elements, such as... Figure 1 , Figure 2 and Figure 3 As shown, experimental tests were conducted.

[0028] 4) The reconstructed signal after experimental data processing is as follows: Figure 4 , Figure 5 and Figure 6 As shown. Figure 4 and Figure 5 and Figure 6Comparative analysis reveals observable vibration amplitudes in the broadband frequency domain of the acceleration spectra in the z and y directions (the z and y directions are the radial directions of the bearing) of bearing I. Significantly small vibration amplitudes exist near the larger amplitudes, indicating that the vibration energy of bearings using prime-number spheres is discretized and distributed over a broadband frequency domain. Bearings with dispersed vibration energy will not exhibit significant vibration intensity even if resonance occurs. Conversely, small vibration amplitudes are difficult to observe near the frequencies with larger vibration amplitudes in the z and y direction acceleration spectra of bearings II and III, making it impossible to clearly observe vibration in the broadband frequency domain. This suggests that the vibration energy of bearings using composite-number spheres is concentrated at specific frequencies, where parametric resonance can induce significant vibration intensity.

[0029] 5) Further quantitative evaluation Figure 4 , Figure 5 and Figure 6 The vibration signals of bearings with prime balls and composite balls were evaluated using bearing vibration spectrum structure evaluation indicators such as spectral spread σ, spectral kurtosis S, spectral entropy H, and spectral flatness FLAT. Figure 7 As shown, at different rotational speeds, the spectral spread, spectral entropy, and spectral flatness of bearing I are significantly higher than those of bearings II and III. This indicates that the vibrational energy of bearing I is more dispersed in the frequency domain than that of bearings II and III, and the spectral structure of bearing I is more complex, chaotic, random, and flat, closer to white noise. Furthermore, the spectral kurtosis of bearing I is significantly lower than that of bearings II and III, indicating that the vibration of bearing I is more stable and the spectrum is flatter. This demonstrates that the vibrational energy dispersion effect of bearing I is significantly better than that of bearings II and III; that is, the vibrational energy dispersion effect of bearings using a prime number of balls is significantly better than that of bearings using odd or even numbers of balls.

[0030] 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 method for vibration reduction design of rolling bearings with an odd number of rolling elements, characterized in that, include: S1. Obtain bearing operating conditions and performance requirements, design bearing structural parameters that meet the basic performance indicators of load capacity, life and reliability, and determine the parameter selection range; S2. Within the range of structural parameters that meet the basic performance indicators, prioritize determining that the number of effective rolling elements is an odd prime number, and then determine other structural parameters to meet the low vibration performance requirements of the bearing.

2. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 1, characterized in that, The effective rolling element is the number of rolling elements in the bearing assembly that are excited by a load.

3. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 2, characterized in that, When a rolling bearing is used to bear axial loads, the number of effective rolling elements is equal to the number of nominal rolling elements. The number of nominal rolling elements is the total number of rolling elements installed in the bearing.

4. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 3, characterized in that, The bearing that bears the axial load is an angular contact ball bearing or a tapered roller bearing.

5. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 3, characterized in that, When a rolling bearing is used to bear axial loads, the number of effective rolling elements ensures that all rolling elements excite the bearing assembly to generate vibrations that are dispersed across non-integer multiples of the frequency, thus avoiding vibration concentration at a specific frequency.

6. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 2, characterized in that, When a rolling bearing is used to bear radial loads, the number of effective rolling elements is less than the number of nominal rolling elements. The number of nominal rolling elements is the total number of rolling elements installed in the bearing.

7. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 6, characterized in that, The bearing that bears the radial load is a deep groove ball bearing or a cylindrical roller bearing.

8. The method for vibration reduction design of rolling bearings with an odd number of rolling elements according to claim 1, characterized in that, When the rolling bearing is a bearing that bears radial loads, the number of effective rolling elements ensures that the effective rolling elements excite the bearing assembly to form vibrations that are dispersed across non-integer multiples of the frequency, thus avoiding vibration concentration at a specific frequency.

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