Stanislav Pehan

Numerical methods for determining stress intensity factors vs crack depth in gear tooth roots

The calculation of the strength of gears is usually carried out by standard procedures. The calculation of the service life of a gear with a crack in a tooth root, however, is possible only by numerical methods. The first step in determining the service life in such a case is the evaluation of the stress intensity factor as a function of crack shape and depth. Two-dimensional analysis is appropriate for this since it is fast and efficient. Here, the direction of crack propagation from the tip of the initial crack is determined using a special numerical algorithm, whereby the direction of maximum strain energy release rate G is sought. The procedure is repeated incrementally. In order to study the influence of realistic applied loads at the point of contact, the gear has to be treated three-dimensionally. Here, the propagation of each point along the crack tip profile is also assumed to be in the direction of the maximum strain energy release rate. The crack depth is determined in such a way that the stress intensity factor on the crack tip profile is constant. The result of such numerical calculations gives a diagram of the stress intensity factor as a function of crack depth. With known gear material properties it is then possible to calculate the service life of the gear by numerically integrating the Paris equation. This article describes two- and three-dimensional methods for monitoring the crack propagation for a particular gear geometry, including the effects of varying through-thickness load behaviour.

Experimental results of the fatigue crack growth in a gear tooth root

A spur gear pair from the first stage of an industrial vehicle gear box has been subjected to experimental testing. The effects of different load distributions along the gear tooth width on the fatigue crack growth in the gear tooth root are measured on an appropriate testing device. The recorded experimental results are represented using the methods of statistical analysis. Analysing the results proves that different load distributions along the tooth width have a significant influence on the crack growth and thus on the service-life of the gear. Since the experiments provide a three-dimensional experimental analysis of fatigue crack propagation in the tooth root, the results of such analysis can be used for calibrating the numerical simulation of similar problems.

Influence of biodiesel on injection, fuel spray, and engine characteristics

This paper discusses the influence of biodiesel on the injection, spray, and engine characteristics with the aim to reduce harmful emissions. The considered engine is a bus diesel engine with injection M system. The injection, fuel spray, and engine characteristics, obtained with biodiesel, are compared to those obtained with mineral diesel under peak torque and rated conditions. The considered fuel is neat biodiesel from rapeseed oil. Its density, viscosity, surface tension, and sound velocity are determined experimentally and compared to those of mineral diesel. The experimentally obtained results are used to analyze the most important injection, fuel spray, and engine characteristics. Furthermore, the influence of biodiesel usage on lubrication is presented briefly. The results indicate that, by using biodiesel, harmful emissions (NOx, CO, HC, smoke, and PM) can be reduced to some extent by adjusting the injection pump timing properly while keeping other engine characteristics within acceptable limits. Furthermore, the results indicate better lubrication conditions when biodiesel is used.

Guidelines for Improving Diesel Engine Characteristics

Diesel engine characteristics depend significantly on the engine type. But, even for a given engine type, the engine characteristics can still be varied in a wide range in dependence on engine management, exhaust gas after treatment, and usage of alternative fuels (Fino et al. 2003; Gray and Frost 1998; Maiboom et al. 2008; Peng et al. 2008; Stanislaus et al. 2010; Twigg 2007) (Fig. 3.1). Engine management and alternative fuels usage offer a possibility to reduce the formation of harmful emissions. On the other hand, exhaust gas after treatment techniques enable a reduction of harmful emissions already produced by the engine.

Biodiesel as Diesel Engine Fuel

In recent years, the interest to use biodiesel as a substitute for mineral diesel has been increasing steadily. Biodiesel is a renewable fuel, consisting of various fatty acid methyl esters with the exact composition depending on the feedstock. This is a distinctly different composition than the hydrocarbon content of mineral diesel. In spite of that, biodiesel has many properties very close to those of mineral diesel. Consequently, the required biodiesel-related modifications of the diesel engine are typically rather minor. On the other hand, because of its different chemical character, biodiesel has several properties, which differ from those of mineral diesel just enough to offer an opportunity to reduce harmful emissions without worsening other economy and engine performances. It should be noted, however, that biodiesel properties may depend heavily on its raw materials.

Diesel Engine Characteristics

Diesel engine is a compression ignition engine of a 2- or 4-stroke type. From the p − V diagrams (Fig. 2.1), it can be seen that the duration of the whole diesel cycle is 360°CA for the two-stroke engine and 720°CA for the four-stroke engine. The whole cycle consists of the following phases: intake of air, compression of air, fuel injection, mixture formation, ignition, combustion, expansion, and exhaust. The intake phase begins with the intake valve opening and lasts till the intake valve closing. After that the intake air is compressed to a level corresponding to compression ratios from 14:1 to 25:1 (Bauer 1999) or even more. The compression ratio e is a geometrical quantity, defined as

Efficient Velomobile Design

\varepsilon =\frac{V_{\max }}{V_{\min }}=\frac{V_{\mathrm{h}}+{V}_{\mathrm{c}}}{V_{\mathrm{c}}},