Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Abstract

Abstract:The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Variable Span Multistep Straightening Process for Long/Extra-Long Linear Guideways

“…If the deflection δ i > 0, the straightening step would generate in the tensile coordinate system {S S : O S − X S Y S }.The angle of rotation at the supporting points during single-step straightening process can be calculated as in [20]. (15) where, θ f = M x l/ (4EI ) is the angle of rotation during the elastic springback. M x is the applied straightening moment.…”

“…Sofuoğlu et al [14] investigated the springback behavior of the AA6082T6 tubes, including the springback level and acceleration in a three-point bending operation, considering indenter travel distance and wall thickness. Zhang et al [15] considered neutral axis deviation caused by asymmetrical factors in linear guideways with complex sectional features and improved the prediction accuracy of three-point pressure straightening model. Song [16] established the load-deflection model, as well as the straightening stroke-deflection model, for the three-point straightening process of T-section rail under lateral loads, using the elastic-plastic power-law hardening material model.…”

Billet Straightening by Three-Point Bending and Its Automation

“…The straightening process can be automated in accordance with the Industry 4.0 strategy, but this is a challenging task [ 17 , 18 ]. An automatic straightening machine can achieve optimal effectivity only if the straightening algorithm is adopted to the various profile curvatures of the billet (e.g., single-arc shape, “S” shape, or shape with multiple vertices [ 19 ]).…”

“…Figure18. Shape of the fourth exemplary billet before straightening (solid curve) and after straightening (dashed curve) in regime 4.…”