试论弓网机械磨耗的数学模型

On the Mathematical Model of Mechanical Wear of Bow Net

摘要: 在城市轨道交通中，地铁电客车受电弓与接触线之间所产生的磨耗(简称弓网磨耗)，是常见的设备问题。而在弓网磨耗的类型中，机械磨耗占85%以上。本文以接触线的磨耗为研究对象，尝试将其机械磨耗现象纳入数学模型当中，对其进行规范化，以此建立一个规范的量化的理论系统。结合一般的量纲分析、分析力学、摩擦学理论，对弓网磨耗现象列出相关物理量，试推出量纲关系，揭示该磨耗类型的特征。通过模型的构造，可以对弓网磨耗现象的本质做出更深入的了解，对磨耗量的变化采取更有可控性的监测。

Abstract: In urban rail transit, the wear between the pantograph and the contact wire, known as the bow-net wear, is a common equipment issue. Among the types of bow-net wear, mechanical wear constitutes over 85%. This study focuses on the wear of the contact wire, aiming to integrate the mechanical wear phenomenon into a mathematical model, standardize it, and establish a standardized and quantified theoretical system. By combining dimensional analysis, analytical mechanics, and the theory of friction, relevant physical quantities related to bow-net wear are identified, dimensional relationships are derived, and the characteristics of this wear type are revealed. Through the construction of the model, a deeper understanding of the essence of bow-net wear phenomenon can be achieved, and a more controllable monitoring of wear variation can be implemented.