Investigation of the Mechanical Characteristics of Linear Rolling Guides Considering Multiple Errors

Existing research on the linear rolling guide has predominantly focused on performance under ideal conditions or isolated error types, while systematic studies concerning multi-error coupling mechanisms and their impact on internal contact parameters remain limited. To address this, a comprehensive static model based on Hertz contact theory is proposed that simultaneously incorporates ball diameter, raceway radius, and raceway curvature center distance errors. This model is validated using finite element analysis (FEA) in ABAQUS, and the numerical results verify the feasibility and effectiveness of the proposed analytical model. Analysis of single, combined, and random errors indicates that geometric errors significantly influence vertical stiffness, load distribution, and critical load-carrying capacity. For example, as the ball diameter error varies from −2.5 to 2.5 μm, the vertical stiffness increases by a factor of 3.8, while a representative negative error combination reduces the critical load by nearly 40%. Additionally, random error analysis reveals that larger manufacturing tolerance ranges lead to increased fluctuation in ball contact forces, raising performance uncertainty. These findings establish the proposed model as a theoretical foundation for the precision design and load-bearing assessment of linear rolling guides under static conditions.