Fractal Prediction Model During the Wear Process Based on Archard Formula

Abstract

Abstract. It is very important for the tribological design of the mechanical system to develop a mathematical model to predict the rate of wear depth in a wear process. Archard formula is the basement of wear calculation, it is very important to estimate the adhesive wear life. This paper uses the fractal parameters with scale-independence to characterize surface topography in the wear process by introducing the fractal theory, and takes into account the different shape of asperities during the running-in process and the stable wear process, the revised Archard wear calculation formula is developed. The numerical simulation results show that the rate of wear depth and the wear depth changing with time and the fractal parameters are consistent with that described by classical theories, it will provide a theoretical support for accurate prediction of the friction pairs' wear life. IntroductionThe development of tribology theory can be traced back to 1508, Da Vinci Leonado firstly proposed the basic concept of friction. Amontons [1] and Couloms [2] put forward the law of friction, that is, the friction force is proportional to contact pressure, it has been used as a scientific law. Tomlinson explained the phenomenon of friction by surface molecular force, and then deduced the coefficient of Amontons' wear formula [3]. Bowden and Tabor have established a relatively complete adhesive wear theory by experiment [4]. Holm deduced the wear volume of the unit sliding displacement according to the interaction between atoms in wear process [5]. In 1953, Archard [6] proposed the adhesive wear calculation formula, it shows that the wear volume is proportional to the load and the sliding distance, and is inversely proportional to the softer surface's yield strength. It is considered that only adhesive wear theory established by Bowden and Archard formula are scientific laws in these well-known wear calculation models. There are a lot of researches and applications based on the Archard formula, Zhang Jiasi deduced the simplified formula of material's wear rate with the condition of the middle and low temperature based on the concept of wear mechanisms [7]; Zhang Yishan established a mathematical model to characterize cylinder liner and piston ring during running-in process by using liner 's surface roughness and wear rate as two state parameters of the system [8]; Ting and Mayer proposed a wear analysis model which can calculate the wear on piston ring's thrust surface based on Archard theory [9].Archard model is widely used in the wear calculation, the model assumes that all the bonding points are the hemispherical asperities, it corrected the assumption by introducing adhesion wear constant [3], however, there aren't accurate calculation method for the adhesion wear constant, and the constant is determined by experiment which can range from 10