This article establishes an axial contact stiffness model of position preloaded ball screw mechanism based on Hertz contact theory. The analysis of dynamic axial contact stiffness is one of the foundations of the research on the dynamic characteristic of the ball screw feed drive system. The model takes into account the coupling relationship between the contact angle and the normal contact force, as well as the coupling relationship between the elastic deformation and the contact deformation coefficient. The static and dynamic axial contact stiffness characteristics of the preloaded ball screw mechanism are studied. The numerical analysis result shows that the static contact stiffness of the preloaded ball screw mechanism increases with the increase in the preload and decreases with the increase in the axial load. The dynamic contact stiffness of the preloaded ball screw mechanism increases with the increase in the screw’s rotational speed. The variation range of dynamic contact stiffness increases with the increase in axial load under the same preload. And the variation range of dynamic contact stiffness decreases with the increase in preload under the same axial load. The axial contact stiffness model established in this article can be used to analyze either static or dynamic contact stiffness of position preloaded ball screw mechanism.

As the critical performance index of ball screws, the contact characteristics have a significant influence on the lubricant properties, tribological properties, and wear properties of ball screws, which further directly affect the service life of ball screws. The non-uniform load distribution induced by geometric errors results in imbalances among balls along the nut, negatively impacting the service life of ball screws. This study focuses on the load distribution of single-nut ball screws under low-speed working conditions. This paper proposes a self-adjustable model of load distribution that considers the flexibility of the screw and nut with respect to the determination of the non-bearing ball. A refined model for axial stiffness is proposed to systematically analyze the influence of geometric errors on stiffness variations under various loading conditions. The results confirm the ability of the proposed model to reveal the static load distribution in view of geometric errors. The greatest discrepancy observed between the theoretical predictions and the experimental data was 9.22%. The numerical simulations demonstrate variation trends in the normal contact load, the loaded-ball number, and the axial deformation of a nut with geometric errors. Furthermore, the relationship between the axial stiffness of a single-nut ball screw and the geometric error is obtained. The self-adjustable model of load distribution is helpful for studying the carrying capacity of a single-nut ball screw. The findings of the study provide a definite reference for optimization of structural design and wear life prediction.

Purpose: This study aims to improve the calibration accuracy of triaxial magnetometers by developing a hierarchical collaborative dynamic particle swarm optimization (HCD-PSO) algorithm for error parameter estimation. Design/methodology/approach: An HCD-PSO algorithm is proposed for triaxial magnetometer error parameter estimation and calibration. The proposed method improves the standard particle swarm optimization (PSO) framework by incorporating an adaptive parameter collaborative regulation mechanism, a low-quality particle information source reconstruction mechanism, and a dual-population competitive collaborative evolution mechanism, thereby enhancing population diversity and improving convergence performance and parameter estimation accuracy. Findings: Simulation results demonstrate that HCD-PSO can achieve stable error estimation results with low calibration errors under different noise conditions. Comparative experiments further show that HCD-PSO outperforms PSO, two-Swarm learning particle Swarm optimization and Sand Cat Swarm Optimization in terms of parameter estimation accuracy and convergence efficiency. In addition, parameter sensitivity analysis confirms that the proposed algorithm maintains stable optimization performance under different parameter search range settings. Additional comparisons with two classical calibration methods, further show that HCD-PSO achieves lower magnitude MAE and RMSE. Real-sensor experiments further show that HCD-PSO reduces the magnitude MAE from 11.347 µT before calibration to 0.116 µT after calibration. Originality/value: The proposed method effectively improves the accuracy of triaxial magnetometer error parameter estimation and provides a reliable intelligent optimization approach for high-precision magnetometer calibration.

Particle Swarm Optimization (PSO) faces challenges such as premature convergence, insufficient population diversity, and limited search capability in complex optimization problems. To address these issues, a particle swarm optimization algorithm integrating reinforcement learning and an adaptive regeneration mechanism, termed RLARPSO, is developed. The proposed approach incorporates a neighborhood-best guidance mechanism based on a small-world topology, a reinforcement learning (RL)-driven dynamic acceleration factor adjustment strategy, and a Levy flight-based regeneration mechanism for inferior particles. Performance evaluation is conducted on the CEC2017 benchmark function suite, with comparisons against five representative PSO variants. Experimental results demonstrate that RLARPSO achieves superior convergence accuracy, solution stability, and capability of escaping local optima. Statistical significance tests confirm the reliability of the observed performance differences. Ablation studies further analyze the contribution of each key component to the overall optimization performance, supporting the effectiveness and rationality of the algorithmic design.