直线运动滚动导轨副的法向接触力学模型
Normal Contact Mechanics Model of Linear Motion Rolling Guideway Pair

借助赫兹点接触形成椭圆接触区域的计算机制,考虑外加法向工作总载荷和法向预紧力,构建了直线运动滚动导轨副的运动结合部法向接触力学模型;采用第一类与第二类完全椭圆积分解算了椭圆离心率。给出一个滚珠斜向下压缩力与外加法向工作总载荷的隐函数方程,并重点推出了单个滚珠法向压缩量、滚珠法向接触刚度、滑块总压缩量、滑块整体法向接触刚度的解析解。数值仿真结果表明:单个滚珠的压缩量随着沟道曲率半径系数的增加而增加;滚珠的法向接触刚度随着单个滚珠压缩量的增大而向上凸弧式增大,但随着沟道曲率半径系数的增大而减小;滑块的总压缩量随着外加法向工作总载荷或沟道曲率半径系数的增大而增大,但随着预紧力、每列滚珠总数或接触角的增加而减小;当外加法向工作总载荷远远小于最大外加法向工作总载荷时,可视滑块整体法向接触刚度为常值;当外加法向工作总载荷接近最大外加法向工作总载荷时,外加法向工作总载荷对滑块整体法向接触刚度有显著影响,滑块整体法向接触刚度随着外加法向工作总载荷的增加而迅速减小;滑块整体法向接触刚度随着预紧力、每列滚珠总数或接触角的增加而提升,但随着外加法向工作总载荷或沟道曲率半径系数的增加而减小。结合部法向接触力学模型的建立将有助于分析直线运动滚动导轨副运动接触表面间的实际接触状态。
Based on the theory of Hertz point contact forming elliptic contact region, a movable joint interface’s normal contact mechanics model of linear motion rolling guideway pair is established considering the external normal total load and preload. The elliptic eccentricity is revolved using the first and second complete elliptic integrals. An implicit function equation relating a ball’s oblique low compression force with the external normal total working load is obtained. Particularly, some analytic expressions about one ball’s normal compression deformation, one ball’s normal contact rigidity, the carriage’s total compression deformation and overall normal contact rigidity are deduced. The digital simulation results show that one ball’s compression deformation increases with the groove curvature radius coefficient; the ball’s normal contact rigidity increases upwards protrusively with the ball’s compression deformation, but decreases with the groove curvature radius coefficient; and the carriage’s total compression deformation increases with the external normal total working load or groove curvature radius coefficient, but decreases with the increasing of the preload, the ball’s total number per column or contact angle. When the external normal total working load is much smaller than the maximum value, the carriage’s overall normal contact rigidity is constant. When the external normal total working load is close to the maximum, it has a notable impact on the carriage’s overall normal contact rigidity, i？？e？？, the latter decreases dramatically with the increase of the former. The carriage’s overall normal contact rigidity increases with the increase of the preload, the ball’s total number per column or contact angle, but declines with the external normal total working load or groove curvature radius coefficient. Constructing the normal contact mechanics model of joint interface helps analyze the actual contact states between movable contact surfaces of linear motion rolling guideway pair