To solve the deformations and stiffnesses changes of linear rolling guideway under different loads, and to provide reference for the structural design of the carriage, this paper presents an analytical model of three-degrees-of-freedom static stiffness for linear rolling guideway considering the structural deformations of the carriage. In this study, first, the contact loads and elastic deformations between balls and raceways caused by external loads and preload were obtained by Hertz contact theory. The elastic deformations between balls and raceways were described by the change of the curvature centers of the carriage raceways. Next, according to the constraints and loading conditions of the carriage, the elastic beam theory was introduced, and the structural deformations of the carriage under the contact loads were equivalent to the deformations of two cantilever beams. Then, the external loads and the displacements of the carriage were derived by the static equilibrium conditions of the carriage. At last, the proposed equivalent model of carriage structure deformations was validated by comparing the calculated deformations of the carriage with those from a commercial program under various loading conditions, and the accuracy of the static stiffness model proposed in this paper was further verified by the experimental results in the reference. The results show that the calculated structural deformations of carriage matched the deformations calculated by a commercial program well. Also, with relative errors of 4.4–17.5%, the calculated stiffnesses using the model proposed in this paper more closely matched the measured stiffnesses. Clearly, there is a better match between the calculated results of the proposed model and the measurements than with the conventional rigid model.

为解决直线滚动导轨在不同载荷下的变形和刚度变化问题，为滑块的结构设计提供参考，本文提出了一种考虑结构因素的直线滚动导轨三自由度静刚度分析模型。车厢变形。在本研究中，首先，通过赫兹接触理论获得了由外部载荷和预载荷引起的滚珠和滚道之间的接触载荷和弹性变形。滚珠与滚道之间的弹性变形通过滑座滚道曲率中心的变化来描述。接下来，根据车厢的约束条件和载荷条件，引入弹性梁理论，接触载荷作用下小车的结构变形相当于两根悬臂梁的变形。然后，通过小车的静平衡条件推导出小车的外部载荷和位移。最后，通过将计算得到的车厢变形与商业程序在各种载荷条件下的变形进行比较，验证了提出的车厢结构变形等效模型，并通过实验进一步验证了本文提出的静刚度模型的准确性。结果在参考中。结果表明，计算得到的车厢结构变形与商业程序计算得到的变形吻合较好。此外，相对误差为 4.4-17.5%，使用本文提出的模型计算出的刚度更接近于测量的刚度。显然，与传统的刚性模型相比，所提出模型的计算结果与测量结果之间存在更好的匹配。