Contact Resistance Modeling Under Complex Wear Conditions Based on Fractal Theory

Changgeng Zhang¹,²*, Xiaoxiao Liu¹,², Liang Jin¹,², Rongge Yan¹,², Qingxin Yang¹,²

¹ State Key Lab of Intelligent Power Distribution Equipment and System, College of Electrical Engineering, Hebei University of Technology, Tianjin 300401, China
² Hebei Key Laboratory of Equipment and Technology Demonstration of Flexible DC Transmission, College of Electrical Engineering, Hebei University of Technology, Tianjin 300401, China

* Author to whom correspondence should be addressed

Materials 2025, 18(13), 3060; https://doi.org/10.3390/ma18133060
Submission received: 9 May 2025 / Revised: 17 June 2025 / Accepted: 19 June 2025 / Published: 27 June 2025
(This article belongs to the Section Mechanics of Materials)

Abstract

The muzzle velocity of electromagnetic rail launchers approaches 1550 m/s, exhibiting typical hypervelocity electrical contact characteristics. During the electromagnetic launching process, extreme conditions—high current density, rapid temperature rise, and strong strain—cause wear on the armature and rail surfaces. Electromagnetic launch tests were conducted to study rail‐surface wear and its effect on contact resistance. After hundreds of launches, the rail’s 2D surface profile and morphology were measured and analyzed. A static contact‐resistance model based on fractal theory was developed, and contact resistance was measured at various rail positions. Results show that, along the launch direction, rail wear transitions from mechanical to electrical, the 2D‐profile fluctuation smooths, and surface roughness decreases. Higher roughness yields greater sensitivity of contact resistance to external load.

Keywords: rail wear · contact resistance · fractal theory · surface profile

1. Introduction

Electromagnetic launchers have received significant attention because of their high launch kinetic energy, high energy efficiency, precise controllability, and extended range [1,2]. However, friction and wear are inevitable [3–8]. The coupling effects of electricity, magnetism, force, and heat cause composite mechanical and electrical wear on the contact surfaces of the armature and rail [9]. The influence of temperature on electrical resistivity varies across different materials. Thomas et al. investigated ceramic materials and found that their resistivity decreases with increasing temperature; however, the sensitivity of this change depends on the ceramic’s specific composition [10]. Kamila et al. reported a similar trend for nanocomposites, where the resistivity decreased as the temperature increased to 180 °C. Notably, the sensitivity of the resistivity to temperature changes was closely related to the release of free water from the pores of the cement matrix [11,12]. Liu et al. demonstrated that lubricant viscosity significantly affects the shear force, fluctuation duration, and friction‐induced vibration during the initial stage of friction. In particular, low‐viscosity lubricants are more effective in reducing the initial friction force and system fluctuations under low‐temperature conditions, thereby lowering the coefficient of friction and reducing wear [12]. The contact characteristics of ultra–high‐velocity sliding contact affect the reliability and stability of the operation of the equipment [13]. The wear behavior of the rail surface influences the contact characteristics between the armature and rail, affecting launch efficiency and reducing rail lifespan [14].

Currently, research on rail wear primarily focuses on numerical simulations and experimentation [15–19]. To study the internal damage mechanisms during electromagnetic launch, Dong et al. developed an internal profile detector. By comparing the measured actual surface profile with the ideal surface profile, they obtained the damage profile. Two‐ and three‐dimensional profile graphs are plotted to visually observe the extent of damage, providing more precise data for damage analysis [20]. Gao et al., to study the effects of electromagnetic force and preload on the contact characteristics and wear of the armature–rail interface, used ANSYS to establish a three‐dimensional simulation model based on the Archard model. They determined the impact of the armature’s interference and acceleration on wear [21]. Ren et al. used HyperMesh and ANSYS to predict wear based on the Archard wear model and found that the wear between the armature and rail is proportional to the load. Additionally, wear is significantly affected by the friction coefficient, which can be reduced by improving lubrication conditions [22].

Currently, the calculation of the contact resistance between the armature and rail mainly relies on numerical simulations and experiments to obtain the muzzle voltage, as well as laboratory static measurements to determine the static contact resistance between the armature and rail [23–27]. Zhu et al. established a numerical model for contact resistance and friction coefficient between the armature and rail. By analyzing the muzzle voltage, pulse current, and armature displacement velocity curves collected from electromagnetic launch tests, they calculated the contact resistance and friction coefficient, thereby verifying the accuracy of the model. They also analyzed the impact of rail surface wear on the reliability of the sliding contact between the armature and rail [28]. Ge et al., based on the kinematics and electromagnetics of electromagnetic launch, eliminated the influence of induced electromotive force in muzzle voltage on contact resistance. They established a contact resistance model, revealing the relationships among the contact resistance, muzzle voltage, armature velocity, and pulse current, and analyzed the contact state between the armature and rail during the actual launch process [29].

Most current research studies the wear mechanisms of rail and armature and the characterization of contact resistance separately, with limited research focusing on the impact of rail surface damage on contact resistance. To address this issue, this study scanned the rail after electromagnetic launch to observe the damage morphology of the rail surface at different locations. By extracting the two‐dimensional profile curves of the rail surface and measuring the static contact resistance at different positions using a resistance measuring instrument, we explored the relationship between rail surface wear and static contact resistance under different external loads.