# Derating of Electrical Contacts with Varying Surface Roughness
## 1 Introduction  
Derating is the process of intentionally reducing the maximum operating parameters of a device, component, or system to increase its reliability, durability, and safety. In the context of electrical, mechanical, and thermal engineering, derating refers to decreasing the current, voltage, thermal, mechanical, or other loads relative to the nominal values that a given component can theoretically withstand under laboratory conditions [1, 2]. The primary purpose of derating is to prevent overloading components in practical application scenarios, which are often more demanding and less predictable than laboratory conditions [3, 4]. In practice, derating accounts for factors such as temperature fluctuations, voltage variations, environmental conditions (e.g., humidity, contamination), and material aging [5, 6]. By doing so, derating minimizes the risk of failures that could occur due to the degradation of components during extended use [7]. In electrical systems, derating involves reducing the maximum current or voltage allowed for components such as wires, connectors, transistors, and resistors [8]. For example, an electrical wire may have a nominal current-carrying capacity of 10 A, but under higher ambient temperatures (e.g., 50 \({}^{\circ}\)C), its maximum load may be reduced to 8 A to prevent overheating [9]. Similarly, in transistors, derating may involve reducing the allowable power dissipation to avoid thermal damage [10]. In mechanical systems, derating entails reducing the maximum permissible load, torque, or speed to avoid mechanical failures such as material fatigue or breakage [11]. For example, in bearing design, applying a derating factor is recommended to adjustload capacity to real-world operating conditions, such as dynamic loads or irregular lubrication [12]. Derating in electrical contacts refers to reducing allowable operating parameters, such as maximum current, voltage, or temperature, below their nominal values to ensure the reliability, durability, and safety of the contacts in practical application scenarios [1; 3]. Electrical contacts are critical components in electrical circuits responsible for conducting current between elements. Their physical and electrical properties are crucial for the system's performance, and their durability depends on factors such as temperature, humidity, mechanical vibrations, and electrical loads [7; 13]. The main objective of derating in electrical contacts is to prevent overloading, potentially resulting in material degradation or failure. Operationally, this implies that a contact capable of conducting a specified maximum current under laboratory conditions (e.g., 6 A) is designed to handle a lower load in real operating conditions, such as 4 A [2; 8; 12]. This reduction incorporates a safety margin that protects the contact from overheating, surface damage, and reduced conduction efficiency [5]. A fundamental phenomenon justifying derating in electrical contacts is their susceptibility to changes in contact resistance due to operation [3; 6; 11]. Contact resistance depends on the quality of the contact, which is influenced by factors such as contact force, surface area, and surface condition (e.g., contamination, oxidation, or mechanical damage) [4; 7]. An increase in contact resistance leads to higher power losses in the form of heat, which can cause localized overheating, material degradation, and ultimately, failure [9; 14]. Derating also considers the effects of temperature on the materials used in contacts. High temperatures can soften metals, reduce the force of contact springs, and accelerate chemical processes such as oxidation and corrosion [10; 13; 15]. Moreover, in contacts with high resistance, micro-arcing can occur, further degrading the contact's condition [16]. Reducing the current flowing through the contact decreases heat generation and mitigates these negative effects [14]. Environmental factors, such as humidity, air contamination, or the presence of chemicals, also influence derating in electrical contacts.