Stephanos Theodossiades

Periodic and chaotic dynamics of motor-driven gear-pair systems with backlash

Abstract Dynamics of gear-pair systems driven by motors and presenting speed-dependent moment resistance is investigated. First, a suitable mechanical model is developed, taking into account the gear mesh backlash and static transmission error as well as the essential non-linearities due to the bearing clearance and contact characteristics. In comparison with earlier related studies, the new element of the present work is that the model developed determines the system response by simply specifying the external loads, rather than by assuming an a priori value for the constant mean angular velocity of the gear shafts. In fact, models employed in earlier research studies are shown to be obtained as special cases of the present model. The study is completed by numerical results. First, classical response diagrams are presented, illustrating the effect of the most important parameters on the system response. Finally, direct integration of the equations of motion is also performed, demonstrating the existence of quasi-periodic and chaotic long time response for selected combinations of the system parameters.

Transient elastohydrodynamic lubrication of rough new or worn piston compression ring conjunction with an out-of-round cylinder bore

Real cylinder bores are out-of-round and axially asymmetrical. The top compression ring, nominally an incomplete circle, is subjected to ring tension and cyclic combustion force in order to conform to the bore surface. The bounding surfaces are rough and their conjunction is subject to a transient tribological state. Therefore, the ring–bore conjunction is only partially conforming for most of the engine cycle. The conjunction may be viewed as a problem of scale, depending on the analysis carried out at a certain bore order (out-of-roundness). Therefore, the contact may be viewed as a multi-lobed rough conjunction, where the regime of lubrication may vary from hydrodynamics to mix with dominant asperity friction at piston reversals. Measured bores and ring profiles are used to predict conjunctional power loss and percentage fuel energy consumed. Furthermore, lubricant’s flow through the ring is predicted throughout the engine cycle. These measures are key industrial design drivers for fuel efficiency and reduction of emissions. The results show that the effect of bore out-of-roundness can be even more significant than the surface topography.

Dynamic analysis of piecewise linear oscillators with time periodic coefficients

Abstract A new method is presented for locating periodic steady-state response of piecewise linear dynamical systems with time periodic coefficients. As an example mechanical model, a gear-pair system with backlash is examined, under the action of a constant torque. Originally, some useful insight is gained on the dynamics by investigating the response of a weakly non-linear Mathieu–Duffing oscillator, subjected to a constant external load. The information obtained is then used in seeking approximate periodic solutions of the piecewise linear system. These solutions are determined by developing a new analytical method, which combines elements from approaches applied to piecewise linear systems with constant coefficients as well as from classical perturbation techniques applied to systems with time varying coefficients. The existence analysis is complemented by appropriate stability analyses, for all the possible types of the located periodic motions. In the second part of the work, this analysis is employed and numerical results are obtained. Namely, a series of typical response diagrams is first presented, illustrating the effect of the variable stiffness, the damping and the constant load parameters on the gear-pair response. Moreover, results obtained by direct integration of the equation of motion are finally presented, showing that the system examined can also exhibit more complicated or irregular dynamics.

Mode identification in impact-induced high-frequency vehicular driveline vibrations using an elasto-multi-body dynamics approach

Abstract The paper describes a noise, vibration and harshness (NVH) phenomenon caused by impact of meshing gear teeth pairs, resulting in structural wave propagation and elastoacoustic coupling in the driveline system, referred to in industry as clonk. The numerical investigation combines multi-body dynamics analysis with flexible body oscillation behaviour predicted by finite element analysis (FEA) techniques. Particular attention is paid to local non-linearities such as the varying stiffness of meshing gear teeth and their normal backlash. The spectrum of vibration of lightly damped hollow driveshaft tubes shows good conformity with experimental results.

An investigation of manual transmission drive rattle

Abstract Manual transmission gear rattle is an NVH (noise, vibration, and harshness) concern in the automotive industry. It is induced by repetitive impacts on loose (unselected) gear wheel teeth by their corresponding driving pinions. This phenomenon occurs under various loading conditions and is classified accordingly, including ‘idle rattle’ when the transmission is in neutral and ‘creep and drive rattle’ when the transmission is in a gear with a widely open or a partially open throttle. The phenomenon is also present from drive to coast conditions, referred to as overrun rattle. Engine order fluctuations on the input shaft are considered to be the underlying cause for rattle of loose gears. However, the mechanism of transmission of vibration through lubricated contacts is not fundamentally understood. It is surmised that changes in lubricated contact conditions at different bulk oil temperatures may play a key role and, therefore, offer an opportunity to deal with rattle by a root-cause fundamental solution. This means that a detailed multi-physics approach (including dynamics, vibration, and tribology) is needed. This article provides detailed analytical models of lubricated conjunctions in a multi-body dynamics model of a transaxle seven-speed transmission system under creep rattle conditions. The results show the important role of the regime of lubrication in lightly loaded conjunctions, increasing the propensity to rattle at higher temperatures. It is also revealed that the effect of engine order vibration as an initiating source for rattle becomes significant with reduced hydrodynamic contact stiffness at rising temperatures.

Influence of In-Plane Dynamics of Thin Compression Rings on Friction in Internal Combustion Engines

The compression ring-bore conjunction accounts for significant frictional parasitic losses relative to its size. The prerequisite to improving the tribological performance of this contact is a fundamental understanding of ring dynamics within the prevailing transient nature of regime of lubrication. Studies reported thus far take into account ring-bore conformance, based on static fitment of the ring within an out-of-round bore, whose out-of-circularity is affected by manufacturing processes, surface treatment and assembly. The static fitment analyses presume quasi-static equilibrium between ring tension and gas pressure loading with generated conjunctional pressures. This is an implicit assumption of ring rigidity whilst in situ. The current analysis considers the global modal behaviour of the ring as an eigenvalue problem, thus including its dynamic in-plane behaviour in the tribological study of a mixed-hydrodynamic regime of lubrication. The results show that the contact transit time is shorter than that required for the ring to reach steady state condition. Hence, the conjunction is not only subject to transience on account of changing contact kinematics and varied combustion loading, but also subject to perpetual ring transient dynamics. This renders the ring-bore friction a more complex problem than usually assumed in idealised ring fitment analyses. An interesting finding of the analysis is increased ring-bore clearance at and in the vicinity of top dead centre, which reduces the ring sealing effect and suggests a possible increase in blow-by. The current analysis, integrating ring in-plane modal dynamics and mixed regime of lubrication includes salient features which are closer representation of practice, an approach which has not hitherto been reported in literature.

Axle whine phenomenon in light trucks: a combined numerical and experimental investigation:

Axle whine is a continuous, steady state tonal sound, emitted from the differential unit’s hypoid gears. It is essentially induced by torque variations. This can be as a result of resonant conditions or torque fluctuations caused by engine order vibrations, compounded by gear transmission error. The principal mechanism of gear whine noise generation is, therefore, through transmission of vibration from the gear shafts and bearings to the differential housing, which is radiated as noise. Furthermore, interactions between the differential unit, axles and driveshafts often generate excessive tonal noises, which are the result of coupled bending and torsional resonances of assembled components. These resonances induce a magnification effect upon the noise source itself through exciting the gear shafts and distorting the alignment of the gear sets. Axle whine noise has become an important noise, vibration and harshness (NVH) concern, because of the nature of the noise; further compounded by the human aural system, which is highly sensitive in tonal memory. The result is continuously increasing warranty costs or use of expensive palliatives to mitigate the phenomenon. In this paper, a combined experimental and numerical investigation of axle whine in a rear-wheel-drive light truck is presented. The aim is to reveal some root causes of the drivetrain’s NVH behaviour, which can be related to the amplification/reduction of axle whine vibration and noise. Correlation of the experimental results with the vibration modes of the drivetrain has shown that for vehicle coasting conditions a number of modes are excited, which can interact with the vibrations of the hypoid gear pair. Finally, some light is shed on the role that differential bulk oil temperature plays in the severity of the ensuing vibration.

Transmission efficiency and noise, vibration and harshness refinement of differential hypoid gear pairs

This article presents a combined multi-body dynamics and lubricated contact mechanics model of vehicular differential hypoid gear pairs, demonstrating the transient nature of transmission efficiency and noise, vibration and harshness performance under various driving conditions. The contact of differential hypoid gears is subjected to mixed thermo-elastohydrodynamic regime of lubrication. The coefficient of friction is obtained using an analytical approach for non-Newtonian lubricant shear and supplemented by boundary interactions for thin films. Additionally, road data and aerodynamic effects are used in the form of resisting torque applied to the output side of the gear pair. Sinusoidal engine torque variation is also included to represent engine order torsional input resident on the pinion gear. Analysis results are presented for New European Driving Cycle transience from low-speed city driving condition in second gear to steady-state cruising in fourth gear for a light truck. It is shown that the New European Driving Cycle captures the transmission efficiency characteristics of the differential hypoid gear pair under worst case scenario, with its underlying implications for fuel efficiency and emissions. However, it fails to address the other key attribute, being the noise, vibration and harshness performance. In the case of hypoid gears, the resultant noise, vibration and harshness characteristics can be particularly annoying. It is concluded that broader transient manoeuvres encompassing New European Driving Cycle are required for assessment, in order to obtain a balanced approach for transmission efficiency and noise, vibration and harshness performance. This approach is undertaken in this article, which is not hitherto reported in the literature.

Effect of a Dual-Mass Flywheel on the Impact-Induced Noise in Vehicular Powertrain Systems:

Abstract The appearance and persistence of impact-induced clonk noise in rear wheel drive light truck drivelines has led to an urgent need for remedial action. The pressure for delivering results within tight schedules and financial constraints has resulted in palliative actions rather than fundamental investigations. It has been speculated that the use of a dual-mass flywheel (DMF) can lead to attenuation of clonk metallic noise, even though its main purpose has been to counter transmission rattle by reducing the input torsional impulse. The present work investigates the effect of DMF on impact-induced clonk noise and its severity through experimentation. Sound measurements in the driveline only reveal a slight reduction in the overall levels of impact-induced noise, but a significant change in its quality - the sharpness associated with the typical metallic content of clonk is absent. The effect is also highlighted by the main frequency content of the response when DMF is employed. The duration of the clonk phenomenon is altered from the case where a traditional single solid-mass flywheel is employed.

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 requires 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 kilo Newtons requiring solution to the elastohydrodynamic lubrication 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.