重载下滚动直线导轨副的接触特性
Contact Characters of Rolling Linear Guide Way Pair Under Heavy Load

针对现有数控机床滚动直线导轨副的研究仅限于外力小于临界力时的情况,求解了当外力大于临界力时的静力学特性参数。假设在轻载下,滑块和直线导轨都给滚珠施加相等的压力,则滚珠的压缩变形量是传统结果的2倍,据此对外力小于临界力时的刚度公式进行了改进。考虑在重载下上滚珠受力但下滚珠不受力,建立了滚动直线导轨副的刚度公式,从而构建了外力小于临界力以及大于临界力时的完整刚度公式,并通过有限元法获得了滚珠与滚道之间的接触应力和接触变形量。理论分析表明:导轨副在轻载下,上滚珠力是外力的隐函数,但外力是上滚珠力的显函数;在轻载和重载的整个范围内,导轨副的所有静力学特性参数都是上滚珠力的显函数。仿真结果表明:当外力小于临界力时,上滚珠力和刚度均随预载荷等级的提高而增大;当外力大于临界力时,导轨副刚度随外力的增大而增大,上滚珠力和刚度都不依赖预载荷等级;上滚珠力随外力的增大而增大,下滚珠力随外力的增大或预载荷等级的降低而减小;上滚珠刚度随外力的增大而增大,下滚珠刚度随外力的增大而减小。推导的完整刚度公式可为分析数控机床滚动直线导轨副的接触特性提供参考。
The current researches about the rolling linear guide way pair of a CNC machine tool are usually set within the limit of outer force less than the critical force, thus the static characteristic parameters are solved for the case of outer force larger than the critical force. Provided that the carriage and linear guide way transfer the equivalent compressive force to the ball under light load, the ball’s compressive deformation is two times the traditional result, hence the stiffness formulas for the case of outer force less than the critical force are improved. The rolling linear guide way pair’s stiffness formulas are established considering that the upper ball bears force but no force on the lower ball under heavy load. As a result, the general stiffness formulas are set up for the outer force less than or larger than the critical force. The contact stress and contact deformation between the ball and race are attained through finite element method. Theoretical analysis shows that the upper ball force is an implicit function of the outer force, but the outer force is an explicit function of the upper ball force when the guide way pair is under light load. All static characteristic parameters of the guide way pair are explicit functions of the upper ball force within the whole ranges of light and heavy loads. Simulation shows that: 1) when the outer force is smaller than the critical force, the upper ball force and stiffness increase with the improvement of preload grade; 2) when the outer force is larger than the critical force, the guide way pair’s stiffness increases with the increase of outer force, and the upper ball force and stiffness are independent of preload grade; 3) the upper ball force increases with the increase of outer force, and the lower ball force decreases with the increase of outer force or with the reduction of preload grade; and 4) the upper ball stiffness increases and the lower ball stiffness decreases with the increase of outer force. These general stiffness formulas may be applied to the analysis of the contact characteristics of rolling linear guide way