Real contact total length of linear motion roller guide without preload based on Greenwood–Williamson rough contact model

Abstract

In traditional studies of linear motion roller guide, the static stiffness is a main indicator to evaluate the mechanical behavior. However, the local contact profile between the roller and raceway surface, although very important to the precision maintenance, cannot be reflected in the measured value of static stiffness. In this article, a new indicator, named the real contact total length (RCTL), is proposed based on the Greenwood–Williamson model and the Hertz contact theory. In particular, an electric contact model is presented where the RCTL of linear motion roller guide without preload is expressed in terms of the measured electric resistances. To verify the model, an experiment is conducted to measure the electric resistances under different vertical loads by a designed load test bench and a digital, direct-current, high-resolution electric resistance meter (DRRM). The test results show good agreement with the model. Based on the electric contact model, the main parameters that affect the RCTL value are roughness Ra and the length of roller, which are directly related to the mechanical behavior of linear motion roller guide in the design and manufacture stages.

A multi-scale model of real contact area for linear guideway based on the fractal theory

“…In addition, the statistical parameters depend entirely on the sample length and instrument resolution. 12 Based on the GW model and the Hertz contact theory, Ke et al 15 proposed an electric contact model with the real contact total length (RCTL), aiming to evaluate the static stiffness of linear motion roller guide without preload. In Tomota et al, 16 using the GW model, an asperities distribution model considering skewness and kurtosis of non-Gaussian surface was proposed, which aimed to calculate the real contact area between smooth and rough surfaces.…”