Analysis on Mechanical Properties of Linear Bearings Considering the Dimensional Error of Rolling Elements and Radial Clearance
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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、滚动体与滚道之间的游隙、单个滚动体出现尺寸误差、每个滚动体都存在尺寸误差等因素对直线轴承力学性能的影响规律，得出一系列具有规律性的关系曲线。本文的研究对于进一步精确计算直线轴承受力、变形和疲劳寿命提供了理论依据。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 is established based on the 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 is constructed, which considers the dimensional error of the balls and the clearance of the bearing. Using MATLAB software to form the algorithm and taking the LM8UU linear bearing as an example, the factors affecting the contact force of balls such as the size and position of lateral load, the dimensional error and clearance between balls and raceways are deeply studied. Finally, a series of regular relationship curves are obtained. The result shows that the contact force of each ball increases with the increase of transverse load. As the transverse load moves from the middle to the edge, the distribution of force on the balls starts to become uneven, with more circular columns bearing the force, but less balls bearing in each column. Clearance makes the contact force decrease among most of the balls, while a small part of the balls bear more with the increase of clearance. The negative dimensional error of one ball reduces its contact force and the positive one increases its contact force. When all balls have dimensional error, the contact force exerted on each ball will be significantly different from that without considering dimensional error. These conclusions provide a theoretical basis for further accurate calculation of the stress distribution, deformation and fatigue life of linear bearings.
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Key words:
- Linear bearing /
- Force analysis /
- Dimensional error of rolling elements /
- Clearance
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图 6 载荷作用于不同位置时各列滚动体受力（F=40 N）
Figure 6. Force of 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 of balls 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 of balls with 3 μm negative error for a single 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 of balls with 3 μm positive error for a single 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 of balls with 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 of balls with 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、E2/MPa µ1、µ2 1.5 8 4 12 π/2 π/6 2.1×105 0.3 
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