A series solution for three-dimensional Navier-Stokes equations of flow near an infinite rotating disk

In this paper, homotopy analysis method (HAM) and Padé approximant will be considered for finding analytical solution of three-dimensional viscous flow near an infinite rotating disk which is a well-known classical problem in fluid mechanics. The solution is compared to the numerical (fourth-order Runge-Kutta) solution and the convergence of the obtained series solution is carefully analyzed. The results illustrate that HAM-Padé is an appropriate method in solving the systems of nonlinear equations

The effect of cylinder de-activation on thermo-friction characteristics of the connecting rod bearing in the New European Drive Cycle (NEDC)

The over-riding objective in modern engine development is fuel efficiency. This has led to a host of pursued measures, including down-sizing (a lower number of cylinders), high output power-to-weight ratio, variable valve activation or cylinder de-activation (CDA) as well as a gradual trend towards mild or micro-hybrid technology. Furthermore, The main aim is to combine a suitable combination of the aforementioned methods with various driving conditions in order to reduce thermal and frictional losses as well as meeting the ever stringent emission directives as outlined in the NEDC. Another imperative is to ensure good NVH refinement which can be adversely affected by application of the above trends, such as light weight constructions and exacerbated power torque variations with CDA. The highlighted issues affect all the load bearing conjunctions in an engine. In particular, increased load fluctuations with CDA can also affect the whirl stability of big-end bearings. Therefore, the current paper concentrates on the issues that affect the big-end bearing thermo-frictional characteristics and dynamic stability in NEDC cycle. The predictive approach, which is critical in a multi-variate problem of this kind, includes determination of regime of lubrication under fluctuating loads and rictional characteristics contributed by both elastohydrodynamics of the bearing overlay as well as boundary friction as the result of asperity interactions. Predictive results include applied dynamics, contact kinematics, frictional power loss, maximum lubricant temperature and minimum film thickness variations during the NEDC. The difference between the CDA mode and the normal mode (all active cylinders). These show that the general benefits accrued through fuel efficiency do not necessarily conform to improved big end bearing frictional efficiency

Elastohydrodynamics of hypoid gears in axle whine conditions

This paper presents an investigation into Elastohydrodynamic (EHL) modeling of differential hypoid gears that can be used in coupling with Newtonian (or multibody) dynamics to study Noise, Vibration and Harshness (NVH) phenomena, such as axle whine. The latter is a noise of a tonal nature, emitted from differential axles, characterised by the gear meshing frequency and its multiples. It appears at a variety of operating conditions; during drive and coasting, high and low torque loading. Key design targets for differential hypoid gears are improved efficiency and reduced vibration, which depend critically on the formation of an EHL lubricant film. The stiffness and damping of the oil film and friction generated in the contact can have important effects and cannot be neglected when examining the NVH behaviour of hypoid gears. The operating conditions in hypoid gears are usually characterized by high load, relatively low speeds, angled flow and elliptical contact footprint of high aspect ratio. Some extrapolated/empirical equations to estimate friction and film thickness have been reported for moderate loads. However, their use in hypoid gears is questionable. Additionally, the majority of reported numerical models for film thickness and friction have not been applied under such operating conditions. In this paper a numerical model of EHL elliptical point contact has been presented to obtain the EHL film behaviour under the usual range of operating conditions of hypoid gears. Realistic engine torque-speed characteristics are used. For these conditions, the load share per teeth pair contact is in the region of 500-6000N. A suitable method of solution is applied to ease the convergence of the numerical method, namely the distributed line low relaxation effective influence Newton-Raphson method. As the result of the angled direction of the entraining flow in the contact of hypoid gear teeth pairs, this method has been found to be suitable, thus adopted. The geometric and kinematic input data for EHL calculations are calculated using Tooth Contact Analysis (TCA)

Optimisation of vehicle transmission and shifting strategy for minimum fuel consumption under EU and US legislated drive cycles

In recent years the importance of reducing fuel consumption and exhaust emissions from road vehicles has become paramount. This is because the exhaust gases contribute to global warming as well as adversely affect the quality of air. Emissions legislation is increasingly stringent and automobile manufacturers strive to mitigate these untoward effects and also improve fuel efficiency with new and innovative solutions. This paper shows that gearbox configuration and shifting strategy can be optimised to arrive at an optimum design, reducing fuel consumption and NOx emissions. Such solutions are based on performance enhancement under regulated test procedures embodied in specified drive cycles, both in Europe and in United States. It is shown that a combined dynamics analysis and multi-objective optimisation can yield optimum gearbox configurations for given vehicles/engines. Furthermore, the results of the analysis can be subjected to a trade-off routine in order to find a near optimal generic solution which would meet the requirement of global design and manufacture, and simultaneously comply well with the differing requirements of various drive cycles

A multi-physics, multi-scale investigation of the piston ring pack

It is essential for the automotive industry to improve efficiency and mitigate frictional losses in IC engines. About 20-25% of these frictional losses arise as a result of the piston ring pack-liner assembly. By reducing the friction, there is potential to improve fuel consumption and emissions. This paper conducts a multi-physics, multi-scale investigation for the piston ring to cylinder liner conjunction, analysing the fundamental tribology, asperity interactions and boundary conditions. A 2D hydrodynamic model has been created based on Reynolds equation for a piston ring – cylinder liner conjunction. The model uses a finite difference method, calculating friction and the minimum film thickness over a 4-stroke engine cycle

Elastohydrodynamic lubrication of hypoid gear pairs at high loads

Differential hypoid gear pairs have been the mechanism of choice for high torque capacity final drives in all forms of vehicles, at least since mid 19th century. Transmission efficiency as well noise and vibration concerns require combined elastohydrodynamic and tooth contact analysis of hypoid gear teeth pairs through mesh. Although such analyses have been reported for general cases of elliptical point contact conjunctions with angled flow entrainment, they do not comply with the prevailing load and kinematic conditions in differential gears. In particular, teeth pair contacts are subject to significant loads of order of several kN requiring solution to the EHL problem at such high loads. The current analysis reports solutions for rolling and sliding elastohydrodynamics of hypoid gear teeth pairs at realistic drive torques, not hitherto reported in literature

Interactions between tribology and dynamics of automotive differential hypoid gears considering thermal non-newtonian mixed lubrication effects

Interactions between tribology and dynamics of automotive differential hypoid gears considering thermal non-newtonian mixed lubrication effect

Analysis of lubricated contact in continuously variable transmissions (CVT)

This paper presents a tribological model for a toroidal CVT. The model predicts the lubricant film thickness, viscous and boundary generated friction and the spin power loss in the contact. This is in order to evaluate the effect of different parameters on the efficiency and durability of the CVT system. An optimisation study is carried out to ascertain the effect of contact surface materials, lubricant rheology and contact geometry upon power loss and maximum generated contact pressure. The results show that numerically, even if the contact pressure cannot be significantly reduced, the contact spin power loss can be reduced by as much as 24%., thus improving system efficienc

Thermal modelling of mixed non-Newtonian thermo-elastohydrodynamics in dry sump lubrication systems

Improved fuel efficiency is the primary objective in the optimization of modern drivetrain systems. Recently, the dry sump lubrication system is regarded as the lubrication system for high performance transmission systems. Dry sump lubrication enhances the system efficiency by reducing the churning losses, whilst providing sufficient lubrication for the tribological contacts. One of the most important aspects of any dry sump system is assessment of the thermal performance. The generated heat in the contacts should be dissipated through impinging jets and air-oil mist in the transmission casing in an efficient manner. The present work incorporates a tribological model and a 3D CFD model into a finite element model. The aim is to evaluate the quantity of generated heat in the lubricated gear pair contacts, as well as heat removal rate due to an impinging oil jet. Furthermore, the transient circumferential temperature distribution on gear surfaces is determined. This provides an accurate input temperature for the entrant lubricant in the gear teeth-pair contacts. Such an approach has not hitherto been reported in literature. To perform time-efficient system level analysis in the finite element model, extrapolated equations are obtained from a transient 3D CFD model using regression formulae

Influence of boundary conditions on starvation of piston ring conjunction

It is important to determine realistic inlet boundary conditions to correctly predict lubricant film thickness and generated frictional power losses in all tribological conjunctions. This is also true of piston compression ring as well. A 2D hydrodynamic solver using Reynolds equation is to analyse the differences between predicted conditions with a flooded inlet and that arising from a more realistic determined zero-reverse boundary condition for lubricant flow post inlet wedge stagnation point. The case of a cylinder of a 4-cylinder 4 stroke gasoline engine, running at the engine speed of 1500rpm is considered. The results show that with a more detailed and realistic inlet boundary a significant reduction in the minimum film thickness is predicted which leads to increased friction throughout the engine cycle