Analysis on Mechanical Properties of Linear Bearings Considering Dimensional Error of Rolling Elements and Radial Clearance
-
摘要: 以受横向载荷的滚珠直线轴承为研究对象，对直线轴承进行了力学分析，建立了直线轴承受横向载荷下的力学模型，结合赫兹接触理论和变形协调关系，构建了在考虑滚动体几何误差和轴承游隙条件下能对直线轴承的每一个滚动体受力、变形进行精确计算的力学模型。并以LM8UU型直线轴承为算例，深入研究了载荷大小和位置、径向游隙、单个滚动体出现的尺寸误差、每个滚动体都存在的尺寸误差等因素对直线轴承力学性能的影响规律。研究发现，横向载荷的大小和作用位置会改变直线轴承内部滚动体受力的大小和承载区的分布情况；单个滚动体尺寸正误差使其受力增大，负误差使其受力减小。Abstract: Taking the linear ball bearing subjected to transverse load as the research object, the relationship between the contact force and deformation of the balls was established based on mechanical analysis. Combined with the Hertz theory and deformation coordination relation, an accurate mechanical model for calculating the contact force and deformation of each ball in linear bearing was constructed, which considered the dimensional error of the balls and the clearance of the bearing. Using MATLAB software to develop the algorithm and taking the LM8UU linear bearing as an example, the factors affecting the contact force of the balls, such as the size and position of lateral load, the dimensional error and clearance between the balls, and raceways, were systematically studied. Finally, a series of regular relationship curves were obtained. The results showed that the contact force of each ball increased with the increase of transverse load. As the transverse load moved from the middle to the edge, the distribution of force on the balls started to become uneven, with more circular columns bearing the force, but less balls bearing in each column. Clearance made the contact force decrease among most of the balls, while a small part of the balls bore more with the increase of clearance. The negative dimensional error of one ball reduced its contact force and the positive one increased its contact force. When all the balls had dimensional error, the contact force exerted on each ball would be distinctly different from that without considering dimensional error. These conclusions provided a theoretical basis for further accurate calculation of the stress distribution, deformation and fatigue life of linear bearings.
-
Key words:
- linear bearing /
- force analysis /
- dimensional error of rolling elements /
- clearance
-
图 4 直线轴承滚动体受力计算流程图
Figure 4. Calculation flow chart of force on rolling elements of the linear bearing
图 5 不同载荷下直线轴承各列滚动体受力（x=1 mm）
Figure 5. Force on balls of linear bearing under different loads（x=1 mm）
图 6 不同载荷作用位置下各列滚动体受力（F=40 N）
Figure 6. Force on balls with different load positions (F=40 N)
图 7 不同游隙下的直线轴承滚动体受力（F=40 N; x=1 mm）
Figure 7. Force on balls of linear bearings with different clearances (F=40 N; x=1 mm)
图 8 1个滚动体存在3 μm负误差时各列滚动体受力（F=40 N; x=1 mm）
Figure 8. Force on balls with 3 μm negative error for a ball (F=40 N; x=1 mm)
图 9 1个滚动体存在3 μm正误差时各列滚动体受力（F=40 N; x=1 mm）
Figure 9. Force on balls with 3 μm positive error for a ball (F=40 N; x=1 mm)
图 11 每个滚动体存在随机尺寸误差时滚动体受力（F=40 N; x=1 mm）
Figure 11. Force on balls while each ball has random size error (F=40 N; x=1 mm)
图 12 每个滚动体存在随机误差时直线轴承滚动体受力（F=40 N; x=1 mm）
Figure 12. Force on balls of linear bearing while each ball has random size error (F=40 N; x=1 mm)
表 1 直线轴承参数
Table 1. Parameters of linear bearing
Dw/mm D0/mm n m φ β E1/Pa E2/Pa µ1 µ2 1.5 8 4 12 π/2 π/6 2.1×1011 2.1×1011 0.3 0.3 
下载: 导出CSV
-
[1] 孙健利. 直线滚动导轨机构承受垂直载荷时的刚度计算[J]. 华中科技大学学报(自然科学版), 1988,16(5): 35-40. [2] YOU H Y, ZHU C X, LI W X. Contact analysis on large negative clearance four-point contact ball bearing[J]. Procedia Engineering, 2012, 37: 174-178. [3] 田红亮, 余媛, 杜义贤. 重载下滚动直线导轨副的接触特性[J]. 西安交通大学学报, 2018, 52(9): 1-9. [4] 高飞. 直线滚动滚子导轨寿命分析[J]. 机床与液压, 2015, 43(11): 59-62. doi: 10.3969/j.issn.1001-3881.2015.11.017 [5] 周怡帆, 韩军, 欧屹, 等. 不同预紧等级下滚珠直线导轨副综合性能的试验研究[J]. 组合机床与自动化加工技术, 2018(2): 1-4. [6] 徐斌, 梁医, 赵义鹏, 等. 滚动直线导轨副精度保持性及磨损机理试验研究[J]. 组合机床与自动化加工技术, 2017(3): 1-5. [7] WU J S S, CHANG J C, TSAI G A, et al. The effect of bending loads on the dynamic behaviors of a rolling guide[J]. Journal of Mechanical Science and Technology, 2012, 26(3): 671-680. [8] KWON S W, TONG V C, HONG S W. Five-degrees-of-freedom model for static analysis of linear roller bearing subjected to external loading[J]. Proceedings of the Institution of Mechanical Engineers: Part C. Journal of Mechanical Engineering Science, 2019, 233(8): 2920-2938. [9] 毛宽民, 龚灿, 李斌, 等. 考虑波纹度的滚珠直线导轨动力学建模研究[J]. 华中科技大学学报(自然科学版), 2014, 42(6): 1-5. [10] 王会彬. 混合陶瓷滚珠直线导轨副接触特性与动力学分析[D]. 河北: 燕山大学, 2017. [11] TOMOVIĆ R. Calculation of the necessary level of external radial load for inner ring support on q rolling elements in a radial bearing with internal radial clearance[J]. International Journal of Mechanical Sciences, 2012, 60(1): 23-33. [12] TOMOVIĆ R. Calculation of the boundary values of rolling bearing deflection in relation to the number of active rolling elements[J]. Mechanism and Machine Theory, 2012, 47(1): 74-88. [13] 陈汀, 黄其柏. 一种计及滑块裙部变形的滚珠直线导轨副模态分析方法[J]. 中国机械工程, 2012, 23(2): 150-154. doi: 10.3969/j.issn.1004-132X.2012.02.007 [14] 徐起贺, 孙健利. 滚动直线导轨副一般载荷下额定寿命的计算[J]. 现代机械, 2002(1): 24-28. doi: 10.3969/j.issn.1002-6886.2002.01.009 [15] 粟爽格, 安琦. 内外圈装配过盈量对圆柱滚子轴承力学性能的影响[J]. 华东理工大学学报(自然科学版), 2020, 46(3): 436-444. [16] 陆俊杰, 吴晨, 安琦. 基于微观接触力学的旋塞阀密封面疲劳寿命数值研究[J]. 华东理工大学学报(自然科学版), 2020, 46(2): 284-292. [17] 甄妮, 安琦. 考虑滚珠尺寸误差时滚珠螺旋副的受力和寿命分析[J]. 华东理工大学学报(自然科学版), 2017, 43(5): 134-142. [18] HARRIS T A, CRECELIUS W J. Rolling bearing analysis[J]. Journal of Tribology, 1986, 108(1): 149-150. [19] 马方波, 纪鹏, 安琦. 双列球面滚子轴承力学分析及滚子受载计算方法[J]. 华东理工大学学报(自然科学版), 2015, 41(1): 111-117. doi: 10.3969/j.issn.1006-3080.2015.01.018 -
点击查看大图
计量
- 文章访问数: 455
- HTML全文浏览量: 252
- PDF下载量: 15
- 被引次数: 0
