components (eg gears, shafts) made of steel to provide CALCULATION OF CARBON hardness and strength while maintaining a tough core. The tough core provides low carbon steel to about 0.2%. DIFFUSION However, the steel containing 0.2% C is not a guarantee to get the necessary amount of martensite. The theoretical amount of carbon for steel quenching (hardening) is 0.3%. FORCEMENTATION OF More favorable for quenching (hardening) is the carbon content - about 0.7 to 0.8%. Therefore, the surface of the GEAR WHEELS steel structural component must be saturated with carbon - cementing. However, the cementation would not produce JIRI MACHUTA, IVA NOVA, PAVEL SEVCIK the desired result without subsequent heat treatment, so Technical University of Liberec called quenching. E.g. thepresent thermal treatment of Department of Engineering Technology gears is accomplished by cementation in batch furnaces or Liberec, Czech Republic in vacuum, followed by martensitic hardening and low DOI: 10.17973/MMSJ.2018_10_201826 temperature tempering. The martensitic structure in the e-mail: [email protected] surface layer of the gear wheel increases the hardness and abrasion resistance of the surface. The paper deals with the determination of the precise calculation of carbon diffusion and carbon prediction in the Subsequently, attention is paid directly to carbon steeping, production of gear wheels cementation from steel by Czech i.e cementation, and subsequent heat treatment. The standard (steel CSN 14220, or ASTMA 506). In the research components must be quenched after carbon saturation part of the paper, considerable attention is paid to the itself to obtain a hard surface layer and a tough core, and determination of the necessary data for calculating the subsequently lowered to lower the residual austenite to cementation, especially the mass- the carbon-binding reduce internal stresses. In the experiment, the gears of the coefficients βC and the determination of the value of the same pitch, with the same chemical composition and carbon diffusion coefficient DC. A diffusion analysis was processing, were cemented to three given depths of performed with respect to its kinetics. At the same time, cementation. Subsequently, carbon saturation calculations the essence of diffusion in metals is described, and were made using carbon under different time conditions. attention is paid to the cementation of the selected steel, To demonstrate the influence of temperature on the i.e the diffusion conditions of its cementation. According to cementing process, an experiment was carried out at the industrial experience, three cementation times for steel conclusion of the diploma thesis, where the temperature of gears were chosen. The main attention was paid to cementation was reduced and the effects of this change on calculating the diffusion and distribution of carbon in the the other parameters of the process were examined. In wheel teeths under different conditions of cementation. In addition to the unique input quantities, the so-called addition to the definite input variables of the diffusion carbon-to-carbon transfer coefficient βC has to be taken process, the mass-carbon β determined on the basis of into account for a more precise calculation of diffusion. This WYSS recommendations [Wyss 1978]. This factor affects coefficient affects the thickness of the diffusion layer at the the thickness of the diffusion boundary layer at the interface of the metal atmosphere resulting from the heat interface of the metal atmosphere resulting from carbon transfer, and defines the amount of carbon atoms that transfer and defines the amount of carbon atoms that receives the surface of the steel from the atmosphere receives the surface of the steel from the carbonaceous [Hazlinger 2013]. atmosphere. Also, the significant diffusion coefficient D was determined based on the findings [Pisek 1974] and 2 CHARACTERIZATION OF CARBON DIFFUSION IN METALS [Brandes 1992]. Based on the diffusion production The mechanism of carbon diffusion in metals is based on parameters included in the calculation, experimental the introduction/movement of carbon atomsin the cementation of gears was performed under different crystalline metal lattice. conditions. The layer of overfilled carbon in wheel teeth, their measurement and statistical evaluation were The diffused carbon atoms settle into the position between monitored. The basis was to achieve 0.4 wt. % C in three the atoms of the crystalline iron grid. The rate of diffusion is types of diffusion layers (0.6 mm, 0.8 mm and 1.0 mm). governed by Fick's laws. The rate of diffusion of carbon is Gears after cementation were hardened and tempered. On the efficacy coefficient of DC. these technologically processed wheels, microhardness was The penetration of the atom of another element into the monitored, the CHD 550 value and the microstructure at crystalline lattice of the metal depends primarily on the various points of the teeth of the wheels were determined. dimensions of its crystalline lattice and the dimension of the atom of the penetrating element. An example is KEYWORDS diffusion of carbon and nitrogen in the iron, respectively in cementation, steel, carbon, diffusion, gear, wheels the steel. The size of radius of the carbon atom is 0.7710-10 [m] and the iron radius size is1.2810-10 [m]. To solve carbon 1 INTRODUCTION diffusion in metals, the Arrhenian´s equation, which can be Diffusion is a thermal-physical process that is applied in applied to determine the rate of diffusion of carbon atoms many engineering proceses. In mechanical engineering, in connection with activation energy and diffusion carbon diffusion is often used to heat-surface treatment conditions, is important. As the increasing activation energy steel parts - for example, cementation - for structural decreases, the rate of diffusion occurs. Rising temperature MM SCIENCE JOURNAL I 2018 I OCTOBER 2441 increases the mobility of carbon atoms - increases carbon of the steel and the carbon diffusion coefficient in the DC diffusion, [Pisek 1974], [Brandes 1992], [Totten 2006]. steel at austenitic temperatures. H D RT DC D0C e , (1) (1) Where: DC - diffusion coefficient of carbon atoms 2 -1 [m s ],D0C - frequency factor of diffusion of carbon atoms 2 -1 -1 [m s ],ΔHD - carbon diffusion activation energy [Jmol ],R - gas constant 8 314 [Jkmol-1K-1],T - absolute temperature of the carbon diffusion process [K]. Tab. 1 shows the values of the diffusion coefficient of carbon in the iron of the different elements in iron and the values for its calculation. Figure 1. Schematic representation of carbon transport in The process of carbon diffusion in metals (e.g. in-Fe, carburization proces [Dulcy 1999], [Karabelchtchikova 2007] -Fe) can be described by two Fick laws, which are dependent on the carbon diffusion coefficient D outside the Due to the process kinetics, the maximum carburettage carbon atom diffusion conditions. rate is reached when carbon transfer from the atmosphere Application of 1st Fick's law for calculating carbon diffusion is equal to or greater than the solid state carbon diffusion is determined for diffuser under constant conditions. This rate. Such a diffusion-controlled process has no carbon means that the concentration gradient c/x does not deficiency fed to the interface for its further transport to change over time. The diffusing carbon atoms move in the the solid; a constant surface carbon content can be direction of decreasing concentration. 1st Fick's law assumed. In practice, however, the transformation of the generally determines the diffusion flux of J atoms of the non-equilibrium carbon from the atmosphere into the diffusing substance. Diffusion flow J is given by the number solids boundary, including the surface reaction often of atoms that pass through the unit area perpendicular to referred to as the speed limiting factor [Dulcy 1999], [Stolar the direction of diffusion per unit of time. The diffusion flux 1984], especially at the beginning of the carburettage J (for carbon diffusion JC) is directly proportional to the process. Although the carbon transport mechanism is well diffusion coefficient D, resp. for DC carbon diffusion known, experimental results have shown[Stolar 1984], [Machuta 2014], [Calister 2003]. [Karabelchtchikova 2007], [Karabelchtchikova 2006] that c (x) for different carbonaceous atmospheres, carbon C concentration curves often deviate from those predicted. JC DC , (2a) x This suggests that knowledge of carbon potential and carburizing time is not sufficient for process control and cC (x) that β and D require attention [Karabelchtchikova 2006], (c c ) D (2b) C P S C x [Batz 1950]. These coefficients are important parameters of carbon diffusion processes for successful control of (2b)the gas -2 -1 Where: JC - diffusion flow of carbon atoms [kgm s ], carburization process [Karabelchtchikova 2006]. The 2 -1 DC - carbon diffusion coefficient [m s ], diffusion coefficient DC indicates the number of moles of a cC (x) - the concentration of the diffusing given component that passes the unit area per unit of time element at the location x, at the unit gradient of the component concentration – then x - instead of the observed carbon diffusion, carbon concentration.The partial derivative symbol -1 C – the carbonsharing factor [m⋅s ], indicates that concentration is variable not only in space CP - concentration of the carbon saturation but also in time [Karabelchtchikova 2007]. Carburization atmosphere [ wt. %C] occurs when the value