Mitigation of climate change has increasingly become a global consensus, in which reducing vehicle emissions and energy consumption is of great significance. According to the statistics, the transport of goods and people accounts for about 20% of the primary energy consumption and 23% of CO2
emissions globally, of which more than 99.9% are powered by internal combustion engines (ICEs) [1
]. With the extensive promotion of battery electric vehicles (BEVs), the market share of ICE vehicles is shrinking year by year. However, up to 2040, 75% of the automotive market will still rely upon the use of ICEs [2
]. In addition, researchers have pointed out that blind elimination of ICEs may bring adverse effects, considering the harmful substances produced in the production and discard of batteries used in BEVs and the pollutant emissions caused by electricity generation [3
]. Recently, a study demonstrated that the CO2
emissions of a Tesla Class 3 during its lifetime with the German energy mix ranged from 11% to 28% more than the modern Diesel E6d Temp engines [4
]. Therefore, the development of ICEs is still necessary to fight against global climate change. It is estimated that more than one-fifth of the fuel energy in passenger cars is used to overcome friction, of which about 15% is consumed in the valve train [5
]. As the core part of the valve train, the cam/tappet pair undergoes the highest loads in ICEs, and its friction loss accounts for about 85% of the whole valve train [6
]. Hence, the study of thermal and tribological inefficiencies of the cam/tappet pair is imperative to improve upon fuel economy and its service life.
There have been a fair number of theoretical and experimental studies of the cam/tappet pair. Theoretical models are important tools for a better understanding of multi-physics tribodynamics of cam/tappet pairs. The fundamental work in the theoretical analysis may date back to Dowson et al. [7
] in 1992, where the minimum oil film thickness of the whole cam cycle considering the influence of the squeeze film mechanism was analyzed by a numerical method and compared with the experimental results. However, it is known that the cam/tappet pair works in a mixed lubrication state. Thus, Chong et al. [8
] used a mixed thermo-elastohydrodynamic lubrication (TEHL) model for the cam/tappet conjunction, while the frictional behaviour was conducted under the North American emission testing city cycle. The results demonstrated that under the low-speed emission cycles, the highest power losses occurred mainly when the lubricant film viscous shear was below the limiting Eyring shear stress. Recently, Torabi et al. [9
] investigated the running-in behaviour of a cam-follower, and they pointed out that during the running-in period, the rate of flattening of surface roughness was a crucial factor. At the same time, experimental studies for cam/tappet pairs were conducted by researchers. To determine the friction loss of the cam/tappet pair in the whole valve train, Teodorescu et al. [10
] conducted experiments where the friction losses of the cam/tappet, valve stem/valve guide, and sliding bearing of rocker shaft are separately measured. Green et al. [11
] explored the wear condition of valve train in real engines with contaminated lubricating oil and obtained a group of wear data, which could be used in wear-prediction models.
To further improve the efficiency of the valve train, innovative technologies including new mechanical designs and surface modifications play a key role. Among these, surface coating using diamond-like carbon (DLC) by means of physical vapour deposition (PVD) and plasma-enhanced chemical vapour deposition (PECVD) are effective. High hardness, high resistance of wear and corrosion, chemical inertness, low friction characteristics, and thermal stability are factors that make DLC coatings the subject of many studies and seem suitable for use in engine parts [2
], hard disk [12
], and implantation of biomaterials [13
]. The essential subclasses of DLC are hydrogenated amorphous carbon (a-C:H) and hydrogen free tetrahedral amorphous carbon (ta-C). Basically, a-C:H is an amorphous network composed of carbon and hydrogen, which consists of strongly cross-linked carbon atoms with mainly sp2 (graphitic-like) and sp3 (diamond-like) bonds, and its properties depend closely on the deposition process. More details about the properties and the deposition process of a-C:H can be found in the review article [14
]. Another subclass, ta-C, are hydrogen free and are mostly (>80%) carbon, which is sp3 hybridized. The ta-C films are mainly produced from pure carbon targets by a filtered vacuum arc, as described in the review article [15
]. DLC coatings deposited on the valve train components are already used in series productions, and investigations were carried out to understand the effects of DLC coatings in the valve train applications on friction reduction and anti-wear. Kano [16
] in 2006 reported that super-low friction coefficients (below 0.01) in a cam and follower test-rig and friction reductions up to 45% in motor-driven valve train tests were observed while using ta-C coatings lubricated with the ester-containing PAO oil. Later, the influence of engine oil, additives, temperature, and camshaft speed on efficiency improvement using a-C:H:ZrC and a-C:H:X coatings was studied by Dobrenizki et al. [17
]. Since the surface coatings can alter the tribological and thermal behaviour of contacts [18
], Yu et al. [21
] investigated the effects of mechanical and thermal coating properties on the cam/tappet contact under a TEHL model using numerical simulations. They pointed out that the friction reduction could be attributed to “the thermal barrier effect”—the coating serves as a thermal barrier increasing the contact temperature in the lubricating gap and therefore changing the shear resistance of the oil. Marian et al. [22
] focused on the effect of DLC coatings with micro-texture. In their experiments, the solid and fluid friction force would be reduced in a wide range of lubrication regimes when using DLC-coatings, while micro-texturing may increase the fraction of fluid friction. The formation of the transfer film between DLC coating and the counterpart is crucial to protect the surface from further wear and high friction [23
]. In the experiments conducted by Gangopadhyay et al. [26
], the results showed that in the presence of engine oil, the friction coefficient between the DLC-coated cam/tappet conjunction was slightly higher than that observed in the absence of the engine oil, despite significant wear resistance. Nevertheless, studies have proved the great potential for application on components under challenging lubricating and loading conditions.
For cam/tappet pairs, the real friction and wear performance of the DLC coating is influenced by many factors, including friction coefficient, thermal properties, load conditions, and surface topography. In order to investigate these factors to further improve the fuel efficiency and durability of the cam/tappet pair, a comprehensive multi-physics analytical model should be built. However, this kind of model has not been reported hitherto. Therefore, in this paper the mechanical, thermal and tribological properties of DLC coatings will be simultaneously incorporated in a comprehensive model, in which the lubrication, contact, wear, thermal and roughness effects will be considered together. Moreover, as modern engines undergo increasingly severe thermal and mechanical conditions, a much heavier load is inevitably encountered due to compact structure, abnormal combustion and dynamic conditions during the cam/tappet’s service life. Therefore, the DLC coating’s effect on cam/tappet pairs under heavy loads (compared to the normal load in a gasoline engine) will also be discussed.