A Study on Hybrid Straightening Strategies for High-Speed Linear Guides with Hardened Layers Based on Inverse Finite Element Modeling

Abstract

High-frequency induction hardening enhances the surface wear resistance and contact fatigue life of high-speed linear guides, but simultaneously produces an inhomogeneous, layered cross-sectional structure comprising a high-strength, low-ductility outer hardened layer and a low-strength, high-ductility inner core. This structural heterogeneity renders conventional straightening stroke prediction models—predicated on homogeneous material assumptions—fundamentally inadequate. Moreover, the iterative trial-bending operations ubiquitous in industrial practice progressively accumulate plastic strain, causing guide rails to exhibit erratic positive-to-negative deflection reversal during sequential straightening passes. To address these critical challenges, this study proposes a novel two-stage hybrid straightening strategy based on inverse finite element analysis (FEA) and closed-loop experimental feedback. An equivalent hardened layer depth (HD0) is introduced as a parametric descriptor to construct a layered elastoplastic finite element model, and an inverse simulation strategy is developed to generate a comprehensive three-dimensional stroke–residual deflection prediction dataset encompassing both vertical and lateral straightening conditions across multiple support spans. Displacement-controlled three-point bending experiments validate the layered model and elucidate the mechanism by which cumulative plasticity progressively amplifies cross-sectional plastic sensitivity under repeated loading. Grounded in this physical insight, a hybrid straightening algorithm is formulated, combining dataset-driven initial stroke prediction for rapid large-deformation elimination with an upper-bound constraint and a measurement-feedback-driven sequential reduction compensation scheme for fine-tuning. Comparative experiments demonstrate that the proposed strategy effectively suppresses the oscillatory over-straightening characteristic of conventional empirical trial-and-error approaches, consistently reducing residual deflection below 0.05 mm within two to three loading cycles. This work bridges the gap between theoretical simulation and the complex physical state of actual machining, substantially improving both the efficiency and precision of straightening for guide rails with induction-hardened layers.