Vibration energy harvester for variable speed rotor applications using passively self-tuned beams

A vibration energy harvester is proposed for rotating systems based on transverse vibrations of an assembly of thin beams and electromagnetic interaction of a carried magnet with a coil of wire. The harvester is designed in a way such that centrifugal forces are utilized to tune the system’s natural frequency to the expected frequency of torsional vibrations. In fact, a novel combination of a tuning mass positioned at the beam’s support and an applied preload are introduced to establish a tuning mechanism that is capable of maintaining resonance along a wide frequency range. The device’s tuning can cover relatively high rotor speeds, overcoming previous limitations on the size and the physics of tuning via axial loads. Moreover, exact expressions of the beams’ mode shapes are taken into account to improve the accuracy of the proposed tuning mechanism. Numerical simulations of the device’s response are carried out for case studies corresponding to different frequency orders. It is shown that the system can maintain a flat power output across a wide range of operating speeds, effectively leading to purely broadband energy harvesting

Vibration energy harvester for variable speed rotor applications using passively self-tuned beams

A vibration energy harvester is proposed for rotating systems based on transverse vibrations of an assembly of thin beams and electromagnetic interaction of a carried magnet with a coil of wire. The harvester is designed in a way such that centrifugal forces are utilized to tune the system’s natural frequency to the expected frequency of torsional vibrations. In fact, a novel combination of a tuning mass positioned at the beam’s support and an applied preload are introduced to establish a tuning mechanism that is capable of maintaining resonance along a wide frequency range. The device’s tuning can cover relatively high rotor speeds, overcoming previous limitations on the size and the physics of tuning via axial loads. Moreover, exact expressions of the beams’ mode shapes are taken into account to improve the accuracy of the proposed tuning mechanism. Numerical simulations of the device’s response are carried out for case studies corresponding to different frequency orders. It is shown that the system can maintain a flat power output across a wide range of operating speeds, effectively leading to purely broadband energy harvesting

Dynamic reduction technique for nonlinear analysis of spur gear pairs

In this study the dynamic response of a spur gear pair is analyzed using a novel nonlinear approach. The actual rolling motion and engagement of the system is simulated using a set of reduced order models obtained in a pre-processing phase using the minimal amount of master degrees of freedom without loss of accuracy or generality. The flexibility of the gear bodies is included by a refined finite element model, and no geometry simplification is introduced while also retaining all nonlinearity sources. To reduce the computational cost the time-varying mesh stiffness is also pre-computed and used depending on the instantaneous loading conditions. Contact loss is also taken into account, and reconnection events are treated as vibro impacts. The results are compared against high quality and demanding experimental results with a computational cost several orders of magnitude lower than models with similar accuracy. Different loading conditions are investigated during the sweep-up and down maneuvers. Mainly, the dynamic transmission error is analyzed, showing remarkable agreement with the test campaign’s results. Different nonlinear phenomena such as hysteretic jumps and sub- and super-harmonic resonances are correctly predicted by the proposed model in terms of both frequency and amplitude. This method allows quick and accurate nonlinear analyses overcoming current limitations and is open to further complications to include other components and effects

An alternative formulation of the dynamic transmission error to study the oscillations of automotive hypoid gears

A new modelling approach on the torsional dynamics of hypoid gear pairs is presented in this work. The current formulation is characterised by an alternative expression of the Dynamic Transmission Error (DTE), accounting for the variation of the effective mesh position. Speed dependent resistive torque is introduced on the gear wheel, enabling the system to reach dynamic equilibrium based on realistic vehicle operating conditions. The above are supplementing past research studies, where simplifications were introduced in the calculation of DTE, while the operating angular velocity was defined a priori. The analysis is accompanied by numerical results, indicating the rich dynamic behavior captured by the new formulation. The dynamic complexity of the system necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to follow the stable/unstable periodic response branches over the operating range of the differential under examination

Passive control of piston secondary motion using nonlinear energy absorbers

The impulsive behaviour of the piston in the cylinder liner plays a key role in the Noise, Vibration and Harshness (NVH) of internal combustion engines. There have been several studies on the identification and quantification of piston impact action under various operation conditions. In the current study, the dynamics of the piston secondary motion are initially explored in order to describe the aggressive oscillations, energy loss and noise generation. The control of piston secondary motion (and thus, impacts) is investigated using a new passive approach based on energy transfer of the highly transient oscillations to a nonlinear absorber. The effectiveness of this new method for improving the piston impact behaviour is discussed using a preliminary parametric study that leads to the conceptual design of a nonlinear energy absorber

Gear transmission rattle: assessment of meshing forces under hydrodynamic lubrication

The dynamic behavior of gear transmissions poses several challenges from the standpoint of design and requires the availability of more advanced models capable of simulating a wide range of operating conditions. In this paper, several formulations to represent efforts related to the lubricant in gear transmissions subjected to reduced torque levels has been assessed. Under these conditions, the lubrication regime is hydrodynamic and the dynamic behavior of the meshing contacts can happen in different scenarios depending on both the lubricant properties and operating conditions. Such problems are cumbersome in gear transmissions in which acoustic performance is a determining design factor, such as in car applications. In this regard, gear rattle is one of the subjects of concern by powertrain designers. In spite of several authors have approached this phenomena, the most recent interest is focused on the role played by the lubricant. The variety of fundamentals and aims of the developed models in this respect requires a better understanding of the effect taken into account by the different formulations in the accurate modeling of hydrodynamic lubrication in gears subjected to low torques. This is the reason why, in this work, several alternatives currently available in the literature to address the formulation of efforts in hydrodynamic regime was collected and presented. Such formulations were implemented in a transmission model previously developed by the authors which was used to simulate different operating conditions in order to assess the results obtained with each one of the considered formulations.This work has been supported by project DPI2013-44860 funded by the Spanish Ministry of Science and Technology and project PRX14/00451 funded by the Spanish Ministry of Education, Culture and Sports and COST Action TU 1105

On the dynamics of lubricated hypoid gears

The torsional dynamics of a vehicle differential hypoid gear pair is investigated. The model comprises applied torque, representing transmitted engine power, including engine order vibration. A number of gear teeth pairs transmit the applied torque through their lubricated conjunctions. Tooth contact analysis (TCA) is used to obtain the appropriate geometrical, kinematic and meshing parameters. These enable the evaluation of contact loads, film thickness and friction for conjugate teeth pairs, which are subject to mixed thermo-elastohydrodynamic regime of lubrication. It is shown that the lubricant undergoes non-Newtonian shear in line with the Eyring regime of traction. The inclusion of combined thermal non-Newtonian shear and boundary interactions has not hitherto been reported for the tribo-dynamics of hypoid gear pairs. When rate of change of gear teeth contact radii is included in the analysis more complex system dynamics (loss of teeth contact) result, particularly at higher speeds. The stated features constitute the main contributions of the current work, which have not hitherto been reported in literature. It is also shown that teeth contact separation ensues when resonant conditions are noted. This is regarded as the main root cause of a noise and vibration phenomenon, known as axle whine

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)

On the identification of piston slap events in internal combustion engines using tribodynamic analysis

Piston slap is a major source of vibration and noise in internal combustion engines. Therefore, better understanding of the conditions favouring piston slap can be beneficial for the reduction of engine Noise, Vibration and Harshness (NVH). Past research has attempted to determine the exact position of piston slap events during the engine cycle and correlate them to the engine block vibration response. Validated numerical/analytical models of the piston assembly can be very useful towards this aim, since extracting the relevant information from experimental measurements can be a tedious and complicated process.In the present work, a coupled simulation of piston dynamics and engine tribology (tribodynamics) has been performed using quasi-static and transient numerical codes. Thus, the inertia and reaction forces developed in the piston are calculated. The occurrence of piston slap events in the engine cycle is monitored by introducing six alternative concepts: (i) the quasi-static lateral force, (ii) the transient lateral force, (iii) the minimum film thickness occurrence, (iv) the maximum energy transfer, (v) the lubricant squeeze velocity and (vi) the piston-impact angular duration. The validation of the proposed methods is achieved using experimental measurements taken from a single cylinder petrol engine in laboratory conditions. The surface acceleration of the engine block is measured at the thrust- and anti-thrust side locations. The correlation between the theoretically predicted events and the measured acceleration signals has been satisfactory in determining piston slap incidents, using the aforementioned concepts. The results also exhibit good repeatability throughout the set of measurements obtained in terms of the number of events occurring and their locations during the engine cycle

An investigation on impact-induced oscillations and noise in lubricated conjunctions

Energy efficiency and Noise, Vibration and Harshness (NVH) have been in the centre of attention for automotive manufacturers during the last decades. Energy losses occur in different forms, such as friction, impacts and noise. Physical understanding of the mechanisms that lead to aggressive dynamics and noise generation is a key in order to design more efficient systems with better NVH performance. In the current study, impact energy is calculated at the lubricated piston-liner conjunctions combining dynamics and tribology. The vibration power at the engine block surface is converted into sound pressure level (SPL) at any desired location analytically. Then, a technique is presented to reduce the severity of impact dynamics by controlling piston's secondary motion, comprising vibration absorbers with nonlinear characteristics. The piston secondary motion dynamics are studied and the absorber effectiveness on vibration reduction is discussed