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图1 Graphical abstract

1.采用双对数功率谱验证了齿面的微观粗糙形貌具有自相似分形特征，并计算了用于表征齿面粗糙形貌的分形维数和分形粗糙度；

1. Self-similar fractal characteristics of the tooth surface micro-roughness are verified by using double-logarithmic power spectrum, and the fractal dimension and fractal roughness featuring the tooth surface roughness are calculated.

齿轮机构的传动精度高，是机械传动系统的重要部件。齿面微观形貌特征对齿轮动态响应的影响已得到广泛研究。考虑到机加工的齿面微观形貌具有粗糙自相似特征，相较于统计学参数表征微观粗糙形貌，分形参数具有尺度独立的优势，因此，有必要研究齿面分形参数与振动响应之间的匹配关系。

为此，上海交通大学李鸿光教授和武汉大学孙韵韵博士在《国际机械系统动力学学报（英文）》（International Journal of Mechanical System Dynamics, IJMSD）发表题为“Experimental-based study of gear vibration characteristics incorporating the fractal topography of tooth surface”的研究论文。该文首先设计了齿轮传动试验台，并加工出具有不同微观粗糙度的齿轮；其次，采用双对数功率谱验证了齿面的微观粗糙形貌具有自相似分形特征，计算了用于表征齿面粗糙形貌的分形维数和分形粗糙度；最后，采集不同工况下的齿轮振动信号，揭示了齿面微观粗糙分形参数与振动响应量之间的映射关系。结果表明，转速和负载恒定时，齿面粗糙度越大，即分形维数越小或分形粗糙度越大，齿轮传动系统的振动幅值越大。此外，齿面微观粗糙形貌对齿轮振动幅值的影响程度随转速、负载等工况变化；在低速和轻载条件下，齿轮的振动响应量对分形维数和分形粗糙度更敏感，即，在该工况下，齿面微观形貌对系统振动特性的影响不可忽略。

Abstract: Microscopic roughness is inevitable on the gear meshing surface, which is also a key parameter affecting the dynamic response. The surface roughness exhibits self-affine characteristics across multiscales. To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads, an experimental setup of spur gear transmission is devised. The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method. The relationships between gear response and fractal parameters are revealed experimentally. Results indicate that a rougher tooth surface, that is, a smaller fractal dimension or larger fractal roughness, corresponds to an intense vibration amplitude. The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads. Under low speed and light load conditions, the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system. With the increase of speed and load, the macroworking conditions gradually become the main factor attributed to vibration amplitude.

Keywords:

spur gear, fractal roughness, vibration amplitude, surface morphology

DOI: 10.1002/msd2.12077

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https://onlinelibrary.wiley.com/doi/10.1002/msd2.12077（点击链接直达原文）

Cite this article: Lei Q, Yuan L, Yu X, Sun Y, Li H. Experimental-based study of gear vibration characteristics incorporating the fractal topography of tooth surface. Int J Mech Syst Dyn. 2023; 3: 173-182. doi:10.1002/msd2.12077

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作 者 简 介

雷淇奥   武汉大学动力与机械学院硕士研究生，主要从事齿轮动力学研究。

李鸿光   上海交通大学机械与动力工程学院振动、冲击、噪声研究所教授、博士生导师，主要从事机械系统动力学、信号处理与故障诊断的研究。曾任振动、冲击、噪声研究所副所长，机械系统与振动国家重点实验室副主任等职务，现任重点学科实验室副主任，兼任中国振动工程学会理事，转子动力学专业委员会主任委员等。撰写专著2部，发表学术论文200余篇，获授权或公开国家发明专利34项，软件著作权6项。

参考阅读

IJMSD | 武汉大学孙韵韵副研究员等：考虑齿面微观表面分形特征的正齿轮副动力学响应