İçten yanmalı motorlarda krank mili ana yatağının hidrodinamik yağlama analizi
Hydrodynamic lubrication analysis of crank shaft main bearing in internal  combustion engines
Yazar: ÖNDER ÇAĞLAYAN
Danışman: DOÇ. DR. ÖZGEN AKALIN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Hidrodinamik yatak = Hydrodynamic bed ; Hidrodinamik yağlama = Hydrodynamic lubrication ; Mil yatak sistemleri = Shaft bearing systems ; İçten yanmalı motorlar = Internal combustion engines

Özet:
Son yıllarda, dünyada petrol ve türevi yakıtların rezervlerinin azalması ve dolayısıyla birim fiyatlarının artmasıyla en başta otomotiv sektöründe olmak üzere tüm sektörlerde özgül enerji harcanımının azaltılmasına yönelik çok sayıda araştırma ve çalışmalar yapılmaktadır. Bu araştırmaların başını haliyle en çok yakıt tüketiminin gerçekleştiği otomotiv sektörü çekmektedir. Otomotiv sektöründe enerji harcanımını azaltmaya yönelik bu çalışmalar farklı alt başlıklara ayrılmaktadır. Bunlar en genel haliyle; ağırlık azaltma çalışmaları, sürtünme azaltma çalışmaları ve ısıl verimi arttırma çalışmaları olarak sınıflandırılabilir. Ayrıca motor ömrü olarak 1 milyon kilometrenin hedeflendiği günümüzde dinamik motor komponentlerinin yağlanması ömür açısından da oldukça büyük önem taşımaktadır. Aşınmaların minimuma indirgenmesi ancak yağlamanın iyileştirmesi ile sağlanacak bu da motor ömrünü uzatacaktır. Bu bakımdam krank ana yatakları da oldukça büyük yükler altında çalışmakta ve yağlamanın sağlıklı olmadığı koşullarda aşınmalar ortaya çıkacak ve bu da yatak ömrünü ve takiben motor ömrünü önemli ölçüde etkileyecektir.
Bu çalışma kapsamında krank ana yatakları tribolojik olarak incelenmiş olup krank ana yataklarındaki tribolojik olayın yağlamaya etkisi hakkında fikir sahibi olunmuştur.  Daha detaylı şekliyle, krank ana yataklarındaki yağlama MATLAB yardımı ile hidrodinamik olarak  modellenmiş, elastik deformasyonlar ve sıcaklığa bağlı viskozite değişimi ise bu aşamada dikkate alınmamıştır. Kavitasyon modeli olarak Reynolds sınır koşulu kullanılmış ayrıca yüzey pürüzlülüğü hesaplamalarında Patir-Cheng yüzey pürüzlülüğü akış faktörleri kullanılmıştır. Çalışmanın başlangıcında Reynolds akış denklemi biri krank mili ana yatağı boyu doğrultusunda diğeri ise krank mili ana yatağı genişliği doğrultusunda olmak üzere iki eksende kurulmuş ve denklemin içerisindeki her bir terim kendi büyüklüğü doğrultusunda boyutsuzlaştırılarak diskritize edilmiştir. Boyutsuz hale getirilen Reynolds denklemi MATLAB'a girilerek başlangıç değerleri ile Gauss-Seidel metodu kullanılarak iterasyona sokulmuş ve üç boyutta bir basınç değişim, iki boyutta yağ filmi kalınlığı değişim eğrisi elde edilmiştir. Fakat bu adımda elde edilen basınç ve yağ film kalınlığı değerleri ilk aşamada doğru varsayılan başlangıç parametreleri ile hesaplandığından gerçek eksen kaçıklığı ve sınır koşullar ile tekrar iterasyona sokularak hesaplanmıştır. Bu adımlar bir ˚KMA için tamamlandığında 720 ˚KMA'lık tam bir çevrim için uygulanmıştır.
Çalışmanın sonuç kısmında her bir krank mili açısı için ilk başta elde edilen basınç değerlerinin mil dönme yönünde önce pozitif olduğu ve yağ filminin koptuğu bölgeden sonra basınçların negatife inerek kavitasyona uğradığı görülmüş, daha sonra Reynolds sınır koşulu uygulanarak negatif olan ve yük taşıma özelliği bulunmayan basınçlar atmosferik krank basıncına zorlanmış ve bu adım sonucunda pozitif basınçların az miktarda artış gösterdiğine tanık olunmuştur. Ayrıca yağ film basıncı değişimi ve yağ film kalınlığı grafikleri incelendiğinde maksimum yağ filmi basınçlarının seçilen 13 litre 6 silindirli diesel motor için 10 ˚KMA'ya karşılık gelen yanma fazında gerçekleştiği gözlemlenmiştir. Aynı zamanda bu aralıkta minimum yağ film kalınlıklarının en az olduğu gözlemlenmiştir. Düşey yöndeki krank mili eksen kaçıklığının ise yanma fazında maksimum halini aldığı sonucuna varılmıştır. Yanma odasından gelen basınç kuvvetlerinin ve piston ile biyelin atalet kuvvetlerinin x ve y yönündeki bileşenlerinin oranının tanjantını ifade eden atak açısı (φ) ise maksimum halini alarak 5,5˚ olarak gözlemlenmiştir.
Bu çalışma sonucunda, krank ana yatağındaki yağ filmi basınç dağılımı, yağ filmi kalınlığı, krank mili eksantirikliği ve ana yatağa gelen yükler yorumlanarak bu bölgedeki tribolojik olaya ışık tutmasına katkı sağlanmış ve çalışmanın bundan sonraki tribolojik çalışmalara da rehberlik etmesi amaçlanmıştır.

Abstract:
In recent years, decreasing of the petrolleum and petrolleum derived fuel reservoirs in the world and increasing the piece costs of the petrolleum fuels lead scientists to do so many investigations about decreasing of specific energy consumption for all industries. Naturally, automotive industry leads to these investigations due fuel consumption mostly occurs at that industry. We can classify these energy consumption decreasing investigations at three groups as; weight reduction, friction reduction and thermal efficiency increasing. Within the scope of this work, crank main bearing was investigated in point of tribology and it became possible to be able to have an idea about the effect of this tribologic phenomenon at the crank main bearing on specific fuel consumption. As detailed, the lubrication model at the crank main bearing was solved as hydrodynamically using MATLAB, elastic distortions and viscosity change due to temperatures were not considered. As boundary condition model, Reynolds cavitation model was used and surface roughness was considered by using Patir-Cheng flow factors. 
As initial step, modified Reynolds equation was written in cartesian coordinates for crank shaft main bearing. Fluid transport was considered two dimensional as one through bearing width (y) another one through bearing length (x). Bearing shell geometry was meshed as bearing length includes 360 nodes and bearing width includes 35 nodes. So there was occured 12.600 nodes where pressure values to be calculated on. Boundary conditions were determined as crank case pressure which is assumed as atmospheric pressure. Hence, the side rows of the bearing mesh, first column of the mesh geometry and the last column were forced to atmospheric pressure while there's done Gauss-Seidel iteration method. As this work planned to be done with numeric analysis method the Reynolds equation was needed to be discritisized. All terms which is used in Reynolds equation were non dimensionalised by dividing them with same dimensions. After that Reynolds main equation was introduced to MATLAB and boundary conditions were also entered as input. Accordingly, initial eccentricty, initial lubricant film thickness, clearance, surface roughness of crank shaft and crank shaft main bearing, angular velocity of crank shaft, average temperature, constant viscosity at average temperature and bearing geometry were also entered to MATLAB. Moreover, the first pressure iteration was created with Reynolds equation. After the first iteration as can be seen from results there occured a sinusoidal pressure curve which is including positive pressure values at the beginning of lubricant film thickness existence and negative pressure values at the rapture region of the lubricant film thickness. Lubricant film thickness is not able to provide any force to balance with the forces coming from combustion chamber and inertia forces of connecting rod and piston at negative pressure regions of the bearing. So these negative pressure regions were needed to be iterated as minimum crankcase pressure. Thus it means cavitation step.
At the cavitation step, these negative pressure values were equalised to crank case pressure while positive pressure values are left as it's own value. So, at the cavitation region there occured a half eliptic curve which shows the transition zone of the pressure from positive pressure to boundary condition which is atmospheric pressure. The section there's told is Reynolds boundary condition itself. During equalising negative pressures to crank case pressure which is atmospheric pressure the other positive pressure nodes are also effected by these new atmospheric pressure values. So, the lubricant film pressure graphic is changed as if it's squeezed with negative x (length) direction and peak pressure values are increased while considering cavitation phenomenon. These two iteration steps are applied for all degree crank angles and for each crank angle there naturally occurs different pressure values and cavitation boundary zone is moved according to angle of attack.
If these two iteration steps are applied once, there's seen pressure values for one degree crank angle. Thus at the outer iteration step is combined of pressure calculation, cavitation boundary zone determination steps for each degree crank angles. By applying that step for one degree crank angle, it is aimed that finding the right eccentricity values of crank shaft at x and y axials by equalising force values coming from lubricant film pressure and forces coming from combustion chamber and inertia forces of piston and connecting rod. During equalising forces if lubricant film pressure comes out smaller than the force comes from combustion and inertia the eccentricity at global vertical axial is increased to provide enough lubricant film pressure to balance forces. When this equation is done succesfully there comes out a right eccentricty value and all pressure curves and boundary conditions are updated according to right eccentricty value. While equalising forces, lubricant film pressure is calculated from Reynolds equation in code on the other hand forces coming from combustion and inertia of piston and connecting rod is provided from a random 11 liter heavy duty diesel engine's first main bearing's real forces at 2000 rpm. 
Following these steps for one degree crank angle, these iterations were done for all crank angles and real values of eccentricity for both x and y directions were found out and than there was existed a graphic which shows eccentricity at x direction and y direction. One of the main purpose of this work is getting the characteristic change of eccentricty. By this final step it was done successfully. At the final step, there was used an incremental magnitude as 10-9 at the outer iteration and initial eccentricty was assumed as 12 micron whereas the initial lubricant film thickness is 40 micron while clerance between crank shaft and crank shaft bearing is 20 micron, it means clearance was filled with lubricant. 
Moreover, engine speed was assumed as 2000 rpm during hydrodynamic analysis and average contact temperature is assumed as constant and 90 Celcius degree. Lubricant is assumed as 10W40 and bearing length is totally 36.75 cm, bearing width is totally 3.5 cm. Additionally surface roughness of crank shaft was considered as 0.1 micron and surface roughness of bearing surface is considered as 0.63 micron. As total surface roughness value, square root of these values' sums were calculated and than 0.637 micron total surface roughness value was used at the calculations.
At the end of this study, it was easily observed that, while eccentricity is increased the force which is coming from lubricant film pressure at vertical direction is also increased. Than, it becomes hard to balance forces in the condition of increasing eccentricity. Highest combustion forces are observed at the combustion region as can be guessed. So, in this situation there is required high lubricant film pressures to balance that high combustion force. High lubricant film pressures can only be provided while eccentricity is increased so much. So, there was seen maximum eccentricty values at the combustion region (around 10 ˚KMA) as can be expected. Hence, minimum oil film thickness is also existed at this region due to high combustion pressures.  This work is also showing that there's so sensitive line between lubricant film thickness pressure and pressure which is coming from combustion and inertia of piston and connecting rod. The reason is that if combustion forces are increased unexpectedly there will not be occured a continuous lubricant film and lubricant film will be raptured. Accordingly there will be seen tribological problems like bearing seizure and engine will work harsh so catastrophic failures will follow each others. At the automotive industry especially for diesel engines, this failure can be seen mostly and if we think this  failure's heavy damage to the engine and repairing costs of it exists so high these tribological optimisation work is definitely what industry needed. When the lubricant viscosity is changed a little, energy consumption and lubricant film thickness are changed so much. When the injected fuel amount was increased at the cylinders, lubricant film thickness is decreasing and lubrication regime is forced to be changed to mixed lubrication. Briefly, it is the best way to see what the lubricant viscosity, lubricant thickness, fuel injection amount per cylinder should be to optimise design parameters. On the other hand, engine manufacturer can determine optimum clearance value between bearings and crank shaft by applying this analysis at the basic design phase of engine projects. This is important due it would be so hard to change these basic design parameters at the next steps of the project. As the simplest example of this case can be given as, there's spent over million dollars as the repairing costs of engines due to bearing seizure problem for heavy duty diesel engines all around the world. Engine manufaturers mostly had to pay these repairing costs because the problems are mostly proved as it's not originated from customer usage conditions. But it should be also considered customer usage is also very significant factor that may be the root cause of the problem. So engine manufacturers always write the right usage conditions to vehicles' hand guides. Mainly there's a speed limit for the diesel engines and if it's been reached over by customer, hydrodynamic lubrication conditions are not provided due to overloads and there occurs bearing seizure. To come over that issue, some of engine manufacturers set break points to clutch system and when customer reaches over maximum speed while shifting gear or in maximum speed condition, system automatically prevents increasing speed.    As mentioned at the beginning, for this study elastic deformations of crank shaft and main bearing were neglected to simplify the phenomenon at the beginning of work. Temperature change according to engine speed and torqe were also neglected so there was assumed an average temperature for calculations and accordingly viscosity was also considered as constant. For the future studies elastic deformations of crank shaft and main bearing due to temperature changes and forces are also planned to be considered during pressure calculations. By this improvement it will be possible to have exact values which are closer to real life condition. Thereby this work was aimed to lighten further investigations on the lubrication of crank main bearings.