By studying the effects of geometric precision on kinematic accuracy, an error mapping model has been established, based on the hypothesis that a motion pair and its installation surface are rigid. However, when using this assumption, there is a significant error induced in high-precision computer numerical control (CNC) machine tools as compared with reality. One of the most important reasons for this error is failing to consider the error averaging effect of motion pair elements. Therefore, this work examines a high-precision horizontal machining center as its research object, and analyzes the error averaging mechanism of a rolling guide pair under a deformation of the rolling elements. The carriage bearing forces caused by guideway straightness errors are obtained by constructing a geometric error model of a single carriage. The relationship between guideway straightness errors and carriage bearing forces is described by a transfer function in the spatial frequency domain, and its characteristics are analyzed. It quantifies the so-called error averaging effect of the rolling guide system and, on this basis, a static model for four carriages is established to reflect the error averaging effect of the rolling guide pair on the position and orientation errors of the motion pair. In addition, it is found that the wavelengths and phase differences of guideway errors affect this error averaging mechanism, but the amplitude and preload have little influence thereon. The experiment result shows that the kinematic straightness errors in the x- and y-directions were approximately 1/3 to 1/2 of the guideway straightness errors in the corresponding directions. The results can be used to guide the precision design and assembly of machine tools.
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