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Machines, Volume 13, Issue 7 (July 2025) – 2 articles

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19 pages, 886 KiB  
Article
A Novel Rapid Design Framework for Tooth Profile of Double- Circular-Arc Common-Tangent Flexspline in Harmonic Reducers
by Xueao Liu, Jianghao Zhang, Hui Wang, Xuecong Wang and Jianzhong Ding
Machines 2025, 13(7), 535; https://doi.org/10.3390/machines13070535 (registering DOI) - 20 Jun 2025
Abstract
Due to its small size, high transmission ratio and precision, the harmonic reducer is widely used. The design of the flexspline tooth profile is crucial for the transmission accuracy and service life of harmonic reducers. However, the numerous design parameters and the lack [...] Read more.
Due to its small size, high transmission ratio and precision, the harmonic reducer is widely used. The design of the flexspline tooth profile is crucial for the transmission accuracy and service life of harmonic reducers. However, the numerous design parameters and the lack of a unified design standard for the flexspline tooth profile make it challenging to accurately determine these parameters. This can lead to issues such as tooth profile interference and excessive stress on the gear teeth during transmission. To address these issues, we propose a novel rapid design framework for the tooth profile of a double-circular-arc common-tangent flexspline in harmonic reducers. Firstly, the mathematical formula for the flexspline tooth profile with a double-circular-arc common-tangent and its conjugate circular spline tooth profile is derived. Then, two-dimensional and three-dimensional parametric finite element models of the harmonic reducer are established, and radial and axial profile modifications of the flexspline are carried out. Based on the parametric two-dimensional finite element model of the harmonic reducer, the optimized Latin hypercube experimental design method is employed to determine the flexspline tooth profile parameters. The method proposed can be implemented using Python language code and integrated into the Abaqus 2019 software, offering the advantage of meeting the requirements for rapid engineering development. Finally, a case study is presented to verify the effectiveness of the proposed design method. Full article
(This article belongs to the Section Machine Design and Theory)
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21 pages, 7793 KiB  
Article
Studies on Vibration and Synchronization Characteristics of an Anti-Resonance System Driven by Triple-Frequency Excitation
by Duyu Hou, Zheng Liang, Zhuozhuang Zhang and Zihan Wang
Machines 2025, 13(7), 534; https://doi.org/10.3390/machines13070534 (registering DOI) - 20 Jun 2025
Abstract
In the continuous drilling process of oil wells, to achieve the efficient screening of drilling fluids by the vibrating screen while ensuring the safety of the screening operation, an anti-resonance system driven by two exciters with triple-frequency (denoted as 3:1 frequency ratio) is [...] Read more.
In the continuous drilling process of oil wells, to achieve the efficient screening of drilling fluids by the vibrating screen while ensuring the safety of the screening operation, an anti-resonance system driven by two exciters with triple-frequency (denoted as 3:1 frequency ratio) is proposed. Initially, differential motion equations are formulated utilizing Lagrange’s equation, followed by the definition of vibration isolation coefficients adopting ratios. Triple-frequency synchronization and stability criterion between two eccentric blocks are subsequently elucidated via the asymptotic method and Routh–Hurwitz criterion. Concurrently, the effects of structural parameters on vibration isolation capacity, steady-state trajectory, and the triple-frequency synchronization phase are investigated through numerical computation. Ultimately, the reliability of the theoretical study is corroborated by simulation analysis. Results indicate that under the allowable system parameters for the practical project, the amplitude of the vibration body can exceed three times that of the isolation body; the two solutions of the stable phase difference (SPD) are different by π, one of which is stable and the other is unstable, and the stability of phase difference is determined by the sign of the stability coefficient. This work is useful for developing new vibrating screens and other multi-frequency vibration machines. Full article
(This article belongs to the Section Machine Design and Theory)
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