A theoretical model of time-varying meshing stiffness for a spur-face gear drive according to its localized characteristics during point-contact

IF 2.1 3区工程技术 Q3 MECHANICS

Meccanica Pub Date : 2025-08-05 DOI:10.1007/s11012-025-02033-y

Bo Xu, Lingyun Zhu, Xiangfeng Gou, Qingfu Guo, Guoguang Jin, Chang Liu, Dong Liang, Xinhao Zhao, Guoliang Liu

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Abstract

The contact region is actually an ellipse during point-contact, as stated by Hertzian contact theory. The load in the contact ellipse (CE) gradually decays rather than uniformly distributes due to the varying curvature of contact surfaces. Spur-face gear drive (SFGD) is highly valued in modern machines due to its point-contact characteristics. An improved theoretical model of time-varying mesh stiffness (TVMS) for SFGD has been constructed by coupling tooth, contact and fillet-foundation stiffness. A novel thought named deformation suppression which there is a fixed effect on the CE by the area outside the CE due to the absence of force is proposed according to the local contact characteristics of point-contact. The coupling effect between the meshing teeth pairs and the fillet-foundation stiffness are both considered. The position, size and incompleteness of the CE are determined by the movement of the meshing tracks which are derived from the explicit equation and multi-state meshing regions of SFGD and the load distribution ratio (LDR) calculated based on them. The characteristics of point contact are qualitatively verified experimentally. The results show that LDR mutations of gear switching are reduced considering incomplete CE. TVMS of point-contact considering deformation suppression is improved by an order of magnitude compared to the one of line-contact which may be the cause for the high carrying capacity of point-contact. It can be the basis to investigate the characteristics of SFGD and the point-contact further. This method is applicable to the study of point-contact in other fields.

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根据直齿面齿轮传动点接触局部化特性，建立了直齿面齿轮传动时变啮合刚度的理论模型

在点接触过程中，接触区域实际上是一个椭圆，正如赫兹接触理论所述。由于接触面曲率的变化，接触椭圆中的载荷不是均匀分布的，而是逐渐衰减的。直齿齿轮传动（SFGD）由于其点接触特性在现代机械中受到高度重视。通过齿、接触和圆角基础刚度的耦合，建立了SFGD时变网格刚度的改进理论模型。根据点接触的局部接触特性，提出了一种变形抑制的新思想，即由于无力作用，接触面外的面积对接触面有固定的影响。同时考虑了啮合齿对与圆角基础刚度之间的耦合效应。由SFGD的显式方程和多状态网格区域推导出网格轨迹的运动轨迹，并在此基础上计算出负载分配比（LDR），从而确定CE的位置、大小和不完整程度。对点接触特性进行了实验定性验证。结果表明，考虑不完全CE，齿轮切换的LDR突变减小。考虑变形抑制的点接触的TVMS比线接触的TVMS提高了一个数量级，这可能是点接触承载能力高的原因。为进一步研究SFGD和点接触特性提供了依据。该方法适用于其他领域的点接触研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Meccanica 物理-力学

CiteScore

4.70

自引率

3.70%

发文量

151

审稿时长

7 months

期刊介绍： Meccanica focuses on the methodological framework shared by mechanical scientists when addressing theoretical or applied problems. Original papers address various aspects of mechanical and mathematical modeling, of solution, as well as of analysis of system behavior. The journal explores fundamental and applications issues in established areas of mechanics research as well as in emerging fields; contemporary research on general mechanics, solid and structural mechanics, fluid mechanics, and mechanics of machines; interdisciplinary fields between mechanics and other mathematical and engineering sciences; interaction of mechanics with dynamical systems, advanced materials, control and computation; electromechanics; biomechanics. Articles include full length papers; topical overviews; brief notes; discussions and comments on published papers; book reviews; and an international calendar of conferences. Meccanica, the official journal of the Italian Association of Theoretical and Applied Mechanics, was established in 1966.