| 摘要(英) |
Large-scale slewing bearings, typically with a diameter greater than 1 meter, and commonly combined with gears on the side of either the inner or outer ring, are used to drive rotary working equipment, e.g., turrets for civil engineering equipment of military weapons. In order to optimize the utilization of space, these bearings are often typically configured as a single unit and must demonstrate the capacity to withstand extremely high loads in all directions. It is therefore common to distinguish between cross roller bearings and four-point contact ball bearings as the two main types of bearing design. In applications where the rotational speeds are relatively slow, typically below 10 rpm, the load capacity of these slewing bearings is calculated under quasi-static conditions. The loading of the bearing rollers poses a statically indeterminate problem. Because of the influences of the clearance, the additional five deformation displacements make the load analysis more difficult.
This paper aims to establish design and load analysis method for the mentioned two types of large-scale slewing bearings, namely cross-roller bearing and four-point contact ball bearing. This method can be used to analyze the load distribution of all the rollers (or balls) and the contact characteristics of each roller (ball) with the inner and outer raceway when the bearings are subjected to different working loads with clearances. It is also used to compare the loading characteristics of crossed roller bearings with different roller profile modifications, as well as four-point contact ball bearings under the same loading conditions.
In this paper, the influence coefficient method will be used to establish a contact analysis model of the raceways and the rollers. The contact stiffness maps of the raceway and the rollers can also be obtained by this method. The stiffness map is then used to establish a complete analysis model of the bearing and to analyze the load distribution and bearing displacement. When there is clearance in the bearing, the convergence calculation is performed iteratively using the final position of the rotating ring under the load of the bearing as a variable. First, the interference between each roller (ball) and the raceway is solved based on the guessed value of the position of the rotating ring, and then the load of each contact roller (ball) is determined from the stiffness map, and then the load equilibrium of the loaded rotating ring is used as a convergence condition for the iterative calculation, so that the position of the rotating ring as well as the distribution of the load on each roller and the corresponding contact stress are finally determined.
In this study, two types of large slewing bearings, namely crossed roller bearing and four point contact ball bearing, are analyzed under the usual bearing clearances with a practical example. The roller profiles of the crossed roller bearings are studied in different profile modification, while the contact angle and the curvature radius of the raceway profile of the four point contact ball bearings are determined according to the loading conditions.
The results of the load distribution analysis demonstrate that when both types of bearings are subjected to axial loading only, the clearance has a negligible influence on the roller load distribution. Conversely, when the bearings are subjected to radial loading or tilting moments only, an increase in the clearance results in a reduction in the number of pairs of roller contacts. A reduction in the number of roller contacts results also in a corresponding decrease in bearing stiffness and an increase in the acting load on the rollers (balls). The same effect of bearing clearance can be also found when the outer ring is subjected to combined loading.
The results of the comparison between the two types of slewing bearings demonstrate that the bearing stiffness of crossed roller bearings is superior to that of four-point contact ball bearings. The roller profile of crossed roller bearings enhances the stress distribution, yet concurrently reduces the bearing stiffness.
Furthermore, the analysis indicates that as the clearance increases, the tilting angle of the outer ring also increases. This condition has an impact on the roller contact stresses in crossed roller bearings. A comparative analysis of various roller profiles reveals that the tilting of the outer ring results in unequal distribution of roller stresses. The application of logarithmic profile can effectively reduce stress concentration. Conversely, the standard profile will cause stress concentration at the edges. However, the implementation of large circular end relief is not optimal, as it tends to be overly expansive, leading to suboptimal stress size and distribution. Consequently, an adjustment of the parameters is needed. On the other hand, the tilting of the outer ring results in alterations to the contact angle of the balls in four-point contact ball bearings. With an increase in clearance, the maximum difference in contact angle change can reach approximately 10 degrees.
The results demonstrate that the analysis method proposed in this paper can be effectively and efficiently employed to analyze the load distribution of the rollers (balls) in the bearing as a whole and the contact stress distribution of the contact pairs for both types of rotary bearings, such as crossed rollers and four-point contact ball bearings, in the context of clearance.
Keywords: Larger-scaled slewing bearing, Cross-roller bearings, Four-point contact ball bearings, Contact load analysis, Influence coefficient method, Stiffness map method, Bearing clearance, Roller profile modification, Contact angle, Bearing stiffness, Roller load distribution, Roller contact stress and contact pattern. |
| 參考文獻 |
[1] 李雲峰，程亞兵，交叉圓柱滾子轉盤軸承的滾子偏載分析及修形，機械工程學報，第51卷，第1期，161-166頁，2015。
[2] Quagliato, L., et al., “Run-out Based Crossed Roller Bearing Life Prediction by Utilization of Accelerated Testing Approach and FE Numerical Models,” International Journal of Mechanical Sciences, Vol. 130, pp. 99-110, 2017.
[3] Van-Canh Tong,Seong-Wook Hong,“Stiffness Characteristics of Crossed Roller Bearings With Roller Roundness Deformation” Journal of Tribology, Vol144, pp. 1-23, 2021.
[4] 张钢,刘莹,刘汝卫,阮娟,殷庆振, “径向载荷作用下高速交叉滚子轴承的载荷分布” ISSN1000-3762轴承2010年4期. CN41-1148/TH Bearing 2010, No 4。
[5] Kania, L. and Krynke, M. “Computation of the General Carrying Capacity of Slewing Bearings,” Engineering Computations, Vol. 30, No. 7, pp. 1011-1028, 2013.
[6] He, P.Y., Wang, Y., Liu, H., Guo, E. & Wang, H., “Optimization design of structural parameters of single-row four‑point contact ball slewing bearing,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 42, No. 291, 2020.
[7] 傅林立，「大型薄壁四點接觸旋轉軸承之結構動態分析」，國立中央大學機械工程學系碩士論文，2021。
[8] Amasorrain, J.I., Sagartzazu, X. & Damian. J., “Load distribution in a four contact-point slewing bearing,” Mechanism and Machine Theory, Vol. 38, pp. 479–496, 2003.
[9] Srečko Glodež, Rok Potočnik, Jože Flašker “Computational model for calculation of static capacity and lifetime of large slewing bearing′s raceway” Mechanism and Machine Theory,Vol.47,pp16-30,2012.
[10] Hartnet, M.J., “General numerical solution for elastic body contact problems,” American Society of Mechanical Engineers, Applied Mechnics Dvision, AMD, Vol. 39, pp. 51-66, 1980.
[11] Hartnet, M.J., “General numerical solution for elastic body contact problems,” American Society of Mechanical Engineers, Applied Mechnics Dvision, AMD, Vol. 39, pp. 51-66, 1980.
[12] 吳思漢，「近似線接觸型態之歪斜軸漸開線錐形齒輪對齒面接觸強度之研究」，國立中央大學機械工程學系博士論文，2009。
[13] Huang, C.H. & Tsai, S.J., “A study on loaded tooth contact analysis of a cycloid planetary gear reducer considering friction and bearing roller stiffness,” Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol. 11, No. 6, pp. 213-230, 2017.
[14] 蘇威守，「交叉滾柱軸承負載分析」，國立中央大學機械工程學系碩士論文，2019。
[15] 連庭緯，「四點接觸滾珠軸承負載分析」，國立中央大學機械工程學系碩士論文，2021。
[16] ISO 1281-2 Rolling Bearings – Explanatory Notes on ISO 281 – Part2: Modified Rating Life Calculation, 2008.
[17] Torstenfelt, B. and Fredriksson, B., “Pressure Distribution in Crowned Roller Contacts,” Engineering Analysis, Vol. 1, No. 1, pp. 32-39, 1984. |
[Endnote RIS 格式]
[相關文章]
[文章引用]
[完整記錄]
[館藏目錄]
至系統瀏覽論文 ( 永不開放)
plurk
funp
live
udn
HD
myshare
netvibes
friend
youpush
delicious
baidu
Google bookmarks
del.icio.us
hemidemi
facebook
twitter
google
reddit