Development of analytical-numerical methods for dynamic analysis of geared transmission systems

The main objective of the present research activity is the study of geared transmission system dynamics, which is basically represented by a system of nonlinear differential equations. First of all, the different approaches to study the nonlinear dynamics of gears are qualitatively presented. Afterwards, the realization of a lumped parameter model is discussed by analyzing two different modeling strategies linked to two different numerical resolution techniques. The first modeling strategy is based on time integration techniques and enhances the employment of a commercial software to speed-up the modeling set-up phase. The proposed method rely on a block diagram technique and it is developed in Simcenter AMESim, a commercial software widely used in industries. By starting from the single gear pair model, detailed guidelines are given to construct any type of ordinary transmission layout by connecting some pre-programmed devices between them. In order to demonstrate the reliability of the approach, an experimental validation on industrial use case is proposed with excellent outcomes. The second modeling strategy rely on a frequency domain solution technique able to capture unstable solution branches in multi-valued frequency response regions. In particular, it proposes the Asymptotic Numerical Method combined to the Harmonic Balance Method as a valuable approach to solve the nonlinear dynamics of gear pairs. Thanks to a quadratic recast of the equation of motion, the Taylor and Fourier series can be computed in a very efficient way and each step produces a continuous representation of the solution branch making the continuation very robust. Effectiveness and reliability of the method are proved by comparing the numerical outcomes with that obtained from the Runge-Kutta time integration scheme. As a result, this technique provides for excellent computational performance despite additional time is needed for the quadratic recast of the equations system. Once a detailed analysis on the modeling strategy has been conducted, rattle noise and whine noise occurrence are investigated. Regarding the rattle noise, the research activity has conducted to the introduction of a new analytical parameter as a novelty to the current state of the art. A rattle index formulation is retrieved by starting from the classical 6-DOFs equation system defining the nonlinear dynamics of a gear pair. The proposed formulation may be applied to single or multiple branch geartrain, both in idle or loaded condions. The reliability of the analytical formulation is proved by numerical experiments which demonstrate the capability of the proposed index to instantaneously describe the vibro-impacts events related to any gear pair of the driveline. In addition its magnitude may be a measure of the tooth impact severity and it is shown to be a proper indicator of the potential presence of mutual interactions between different gear pairs pertaining to the same driveline. Finally, the investigation of whine noise occurrence addresses to an analytical formulation able to forecast the main overall direction and magnitude of bearing reaction forces on idler gear. By starting from the definition of meshing forces by means of Fourier series development, idler gear bearing forces are obtained under the hypothesis of quasi-static motion. This procedure demonstrates that the alternating component of bearing forces on idler gear describes an elliptical trajectory as the prime mover rotates over a pitch angle. The formulation directly links the bearing forces elliptical trajectory with the gear spatial position, the meshing phase and the amplitude of meshing forces. By properly setting the over-mentioned parameters one may be able to control the magnitude and direction of the overall idler bearing reaction forces. Numerical experiments were performed and the obtained results confirm the author intuitionL’obiettivo principale della presente attività di ricerca riguarda lo studio della dinamica non lineare degli ingranaggi che, di fatto, è rappresentata da un sistema di equazioni differenziali. Prima di tutto, viene presentata un ‘analisi qualitativa finalizzata a valutare i diversi approcci per studiare tale fenomeno. Successivamente, viene descritto lo sviluppo di un modello a parametri concentrati analizzando due diverse strategie di modellazione basate su metodi di risoluzione numerica diversi. Il primo approccio propone l’utilizzo di un software commerciale per velocizzare la fase di set-up del modello ed è basato su tecniche di integrazione temporale. Questa strategia di modellazione è sviluppata in Simcenter AMESim, un software commerciale distribuito da Siemens. Partendo dal modello di una singola coppia di ruote, viene dettagliata una procedura per costruire qualsiasi tipo di treno di ingranaggi grazie alla tecnica dei diagrammi a blocchi. Per dimostrare l’efficacia di tale tecnica, il metodo viene applicato ad un caso industriale ottenendo un’ottima correlazione numerico-sperimentale. Il secondo approccio si basa su tecniche di risoluzione numerica nel dominio della frequenza in grado di calcolare i rami instabili della risposta dinamica. Il metodo propone la combinazione del “Asymptotic Numerical Method” con il “Harmonic Balance Method” utilizzando una formulazione quadratica del sistema di equazioni differenziali. Grazie a tale formulazione, sia la serie di Taylor che quella di Fourier possono essere sviluppate in una maniera molto efficiente rendendo la continuazione della soluzione periodica molto robusta. L’affidabilità di questa tecnica è stata dimostrata confrontando i risultati con quelli ottenuti dal metodo di Runge-Kutta, basato sull’integrazione temporale. In più, tale tecnica garantisce performance computazionali eccellenti, anche se la riformulazione quadratica del sistema iniziale non è sempre facile da ottenere. Una volta analizzate le strategie di modellazione e le tecniche numeriche risolutive, lo studio si concentra su i fenomeni di rattle e whine noise. Riguardo il rattle noise, l’attività di ricerca ha portato all’introduzione di un nuovo parametro analitico come novità rispetto allo stato dell’arte. Partendo dal sistema di equazioni che governa il moto di una coppia di ruote dentate, è stato definito un indice analitico denominato “rattle index”. Tale indice può essere applicato a qualsiasi tipo di treno di ingranaggi, a uno o più rami, sia in condizioni di trasmissione di potenza che in folle. La sua affidabilità è supportata da simulazioni numeriche che dimostrano la capacità del “rattle index” di descrivere istantaneamente la perdita di contatto tra qualsiasi coppia di ruote di una trasmissione. Infine, la sua ampiezza è un indice della severità degli urti e permette di identificare l’esistenza di mutue interazioni tra le ruote della driveline. Infine, lo studio del whine noise ha portato ad una formulazione analitica capace di prevedere la direzione e l’ampiezza delle forze sui cuscinetti delle ruote oziose. Tale formulazione viene ottenuta partendo dalla definizione delle forze di ingranamento tramite lo sviluppo in serie di Fourier e ricavando le forze sui cuscinetti sotto l’ipotesi di moto quasi-statico. Questa procedura dimostra che le componenti alterne delle forze sui cuscinetti seguono una traiettoria ellittica quando il movente ruota di un passo angolare. La formulazione mette in relazione la traiettoria delle forze sui cuscinetti con la posizione delle ruote nel piano, la fase di ingranamento e l’ampiezza delle forze di ingranamento. Agendo sui parametri descritti, è possibile pilotare e controllare la direzione delle forze sui cuscinetti delle ruote oziose. La trattazione analitica è supportata da simulazioni numeriche con un ottimo riscontro

Experimental and Numerical Dynamic Investigation of an ORC System for Waste Heat Recovery Applications in Transportation Sector

ORC power units represent a promising technology for the recovery of waste heat in Internal Combustion Engines (ICEs), allowing to reduce emissions while keeping ICE performance close to expectations. However, the intrinsic transient nature of exhaust gases represents a challenge since it leads ORCs to often work in off-design conditions. It then becomes relevant to study their transient response to optimize performance and prevent main components from operating at inadequate conditions. To assess this aspect, an experimental dynamic analysis was carried out on an ORC-based power unit bottomed to a 3 L Diesel ICE. The adoption of a scroll expander and the control of the pump revolution speed allow a wide operability of the ORC. Indeed, the refrigerant mass flow rate can be adapted according to the exhaust gas thermal power availability in order to increase thermal power recovery from exhaust gases. The experimental data confirmed that when the expander speed is not regulated, it is possible to control the cycle maximum pressure by acting on the refrigerant flow rate. The experimental data have also been used to validate a model developed to extend the analysis beyond the experimental operating limits. It was seen that a 30% mass flow rate increase allowed to raise the plant power from 750 W to 830 W

Models for Flow Rate Simulation in Gear Pumps: A Review

Gear pumps represent the majority of the fixed displacement machines used for flow generation in fluid power systems. In this context, the paper presents a review of the different methodologies used in the last years for the simulation of the flow rates generated by gerotor, external gear and crescent pumps. As far as the lumped parameter models are concerned, different ways of selecting the control volumes into which the pump is split are analyzed and the main governing equations are presented. The principles and the applications of distributed models from 1D to 3D are reported. A specific section is dedicated to the methods for the evaluation of the necessary geometric quantities: analytic, numerical and Computer-Aided Design (CAD)-based. The more recent studies taking into account the influence on leakages of the interactions between the fluid and the mechanical parts are explained. Finally the models for the simulation of the fluid aeration are described. The review brings to evidence the increasing effort for improving the simulation models used for the design and the optimization of the gear machines

EXPERIMENTAL EVALUATION AND SIMULATION OF TORQUE TRANSMISSIBILITY FREQUENCY RESPONSE FUNCTIONS OF VIBRATION ISOLATORS AND ABSORBERS FOR DRIVETRAIN APPLICATIONS

Four studies involving torsional vibration isolation performance of automotive drivetrain components, make up this dissertation. One study features a prototype planetary torsional vibration absorber, a unique device that targets low frequency torsion modes in automotive drivetrains. Two studies feature experiments on several torque converters, clutch locked and open, to validate models of the hardware. The last study details experiments on a centrifugal pendulum absorber in a torque converter, to characterize the viscous friction while submerged in automatic transmission fluid (ATF). The enclosed studies improve the state of the art of drivetrain vibration absorbers and isolators, by introducing a new vibration absorber concept and increasing understanding of the underlying physics of torque converters, lock-up clutch dampers, and centrifugal pendulum absorbers. The design and test of the planetary torsional vibration absorber concept demonstrated the utility of a gear reduction in increasing the apparent inertia of the absorber. By increasing its apparent inertia, the device successfully attenuated a ~20 Hz mode of vibration, and used less packaging volume and mass than a traditional torsional vibration absorber of equivalent performance. Various lockup clutch designs were characterized with torque transmissibility frequency response function (TTFRF) measurements while spinning at simulated vehicle operating conditions. This in situ testing lent itself useful in characterizing the speed dependent friction in a lockup clutch damper, while also confirming other damper parameters—like stiffness and damping. The torque converters were also tested in open mode (lockup clutch not engaged). The open mode testing revealed that the hydrodynamic torque converter transmits enough torsional vibration to excite the damper mode for the turbine damper architectures. The open clutch testing contributes a complete data set—encompassing a wide range of speed ratios—to verify torque converter models with. When comparing the test TTFRFs to model TTFRFs, a discrepancy in the damper mode’s natural frequency was revealed, and it was hypothesized that this error resulted from a reflected inertia effect of the ATF undergoing toroidal flow. The locked clutch testing provoked some questions about the centrifugal pendulum absorber (CPA)—a component of one of the tested torque converter clutch dampers. To validate an existing CPA model, and to characterize the equivalent viscous damping of the CPA mechanism, TTFRFs of custom made torque converters were measured. The custom hardware included: pinned damper (CPA active), pinned CPA (damper active), and pinned straight spring (CPA and arc spring active). The torques due to friction and viscous damping of the damper were effectively eliminated from the CPA, and the equivalent viscous damping of the CPA characterized

Models for Flow Rate Simulation in Gear Pumps: A Review

Gear pumps represent the majority of the fixed displacement machines used for flow generation in fluid power systems. In this context, the paper presents a review of the different methodologies used in the last years for the simulation of the flow rates generated by gerotor, external gear and crescent pumps. As far as the lumped parameter models are concerned, different ways of selecting the control volumes into which the pump is split are analyzed and the main governing equations are presented. The principles and the applications of distributed models from 1D to 3D are reported. A specific section is dedicated to the methods for the evaluation of the necessary geometric quantities: analytic, numerical and Computer-Aided Design (CAD)-based. The more recent studies taking into account the influence on leakages of the interactions between the fluid and the mechanical parts are explained. Finally the models for the simulation of the fluid aeration are described. The review brings to evidence the increasing effort for improving the simulation models used for the design and the optimization of the gear machines

Applying thermophysics for wind turbine drivetrain fault diagnosis using SCADA data

Cost-effective wind turbine diagnosis using SCADA data is a promising technology for future intelligent wind farm operation and management. This paper presents a thermophysics based method for wind turbine drivetrain fault diagnosis. A synthesized thermal model is formed by incorporating thermal mechanisms of the drivetrain into a wind turbine system model. Applications of the model are demonstrated in case studies of the gearbox and generator comparing simulation results and SCADA data analysis. The results show nonlinearity of the gearbox oil temperature rise with wind speed/output power that can effectively indicate gearbox efficiency degradation, which may be attributed to gear transmission problems such as gear teeth wear. Electrical generator faults, such as ventilation failure and winding voltage unbalance will cause changes to heat transfer and result in temperature changes that can be used for diagnosis purposes. This is shown by different patterns of stator winding temperature associated with power generation, while the simulation reveals the thermal mechanism. The method can be applied to diagnose some failure modes which are hard to identify from vibration analysis. The developed thermal model can play a central role for the purpose of fault diagnosis, by deriving relationships between various SCADA signals and revealing changes in the thermophysics of wind turbine operation

Three-dimensional model of an external gear pump with an experimental evaluation of the flow ripple

A three-dimensional model of an external gear pump and a new application of an algorithm for the measurement of the unsteady flow rate in hydraulic pipes are presented. The experimental delivery flow ripple was compared with the outcomes of a simulation under different operating conditions. A comprehensive computational fluid dynamics model of the pump and of the high-pressure delivery circuit was developed in SimericsMP+. The pump model considers the clearances, which vary according to the shaft angle, between the tip of the tooth and the inner surface of the stator, as well as between the flanks of the teeth that are in contact. The pump delivery circuit is constituted by a straight pipe with a fixed orifice at the end to generate the load. The model of the entire system was preliminarily validated in terms of delivery pressure ripple. Subsequently, the simulated flow ripple was contrasted with the instantaneous flow rate, measured by means of an innovative flow meter. It was found that the proposed flow meter is reliable in assessing the flow oscillations under the various working conditions

DESIGN OF AN ANTI-JERK CONTROLLER FOR BOTH LOCKED AND SLIPPING TORQUE CONVERTER CONDITIONS IN A VEHICLE

With the advancement in the automotive technologies, the customer scrutiny on the ride comfort of automobiles has come to light. Vehicle drivability is one of the important aspects that defines the ride comfort for a vehicle. Drivability of a vehicle is a qualitative measure and may differ from person to person, however, researches have come up to highlight a few parameters that can categorize the drivability performance of a vehicle into good or bad for a majority of the targeted audience. One of those parameters include shuffle, which is defined as the longitudinal oscillations that occurs in the drivetrain when a sudden demand for torque rise or drop is made. Another such parameter is the sluggishness in the delivery of torque at wheels against the requested torque by the driver. This can exist due to the shift in the dynamics during the drivetrain operation from locked torque converter clutch to slipping torque converter clutch. This work addresses both the drivability related issues, namely, shuffle and torque lag mentioned in the preceding para. Initially, the shuffle oscillations generated in a vehicle are analyzed when subjected to a sudden positive to positive driver torque tip-in request. Further, a pre-compensator and feedback controller based control scheme is designed to damp those shuffle oscillations while keeping the torque delivery response fast. This control approach shapes the actuator torque (i.e., an engine or an e-motor) in such a way that the desired response is achieved. Next, the problem of sluggish torque response at wheels due to slipping of the torque converter clutch is addressed. Initially, a model-based feedforward and feedback controller is developed to control the actuator torque such that when the torque converter slips, an extra compensatory torque from the actuator is applied. This compensation torque ensures that the torque response at the turbine and succeeding driveline components up till the wheels is maintained as desired. However, the actuator has some physical limitations in terms of the maximum magnitude and rate of the torque delivery. So, at some instances, the torque request generated by the controller may not be feasible for the actuator to follow. This problem is addressed when another controller, based on model predictive control approach, is proposed. This controller is based on the approach that continuously updates the controller of the torque delivery of the actuator. The controller solves an optimisation problem over the defined constraints of the actuator and plant, and further finds the most feasible response for the actuator to follow within its defined operating range. Later, A comparison between the two controllers showed model predictive controller to be 15.3% better in terms of the propeller shaft torque response than the feedforward and feedback controller, for the problem under discussion

ADVANCED NUMERICAL METHODS FOR THE DYNAMIC OPTIMISATION OF MECHANICAL COMPONENTS

This PhD thesis concerns the development and assessment of innovative methodologies for simulating and improving the dynamic behaviour of mechanical components. In particular, two correlated issues are addressed herein: hybrid FE/LP gear pump modelling as a tool for foreseeing and optimising vibration behaviour in operational conditions; a new methodology for vibration reduction by applying damping patches in appropriate positions. In the field of positive displacement pump modelling, external gear pumps were analysed with the aim of developing ! ! "#! advanced methodologies which accurately predict of the dynamic behaviour of these components. Indeed, the first part of this thesis (PART A) is about external gear pumps for steering systems; the research activity concerning gear pumps was carried out in collaboration with the Dept. of Engineering at the University of Ferrara in co-operation with TRW Automotive Italia S.p.A – Divisione Automotive Pumps (Ostellato, Ferrara, Italy). This research pertains to the creation of a hybrid model, obtained through the integration of a nonlinear elastodynamic model with lumped parameters in relation to moving bodies, and an FE pump model. The model referred to bodies in motion takes into account the most important phenomena involved in pump operations, such as time-varying oil pressure distribution on gears, timevarying meshing stiffness, tooth profile errors, the possibility of tooth contact, bush displacement and hydrodynamic journal bearing reactions. Coupling the FE with the various parts which make up the pump, as well as coupling the lumped-parameter model and the FE model required the development of specific advanced techniques; thus several problems related to the combination of the different models employed in order to form a single hybrid LP/FE model were studied and resolved. Using particular techniques based on comparisons between simulations and experimental results concerning acceleration, forces and moments, the model was experimentally validated. Although this hybrid model is an excellent tool for improving the dynamic behaviour of gear pumps and for optimising the early stages of prototype design, some problems can still remain related to unwanted vibrations into precise frequency ranges. Thus, once the first part of the research was completed, it was decided to delve into the problem of structural optimisation. In particular, a methodology for surface damping treatment was created and applied. Indeed, the second part of the research activity (PART B) was about the optimisation of mechanical components and systems through the application of high damping material components known as patches; this research activity is being ! ! "! carried out by the Dept. of Mechanical Engineering (laboratoire vibrations acoustique) at the INSA institute (Institute National des Sciences Appliquées) in Lyon (France) where I spent thirteen months between the second and third year of my doctoral studies. Such treatment can be applied to existing structures and provides high damping capability over wide temperature and frequency ranges. In many practical plate and machinery casing structures, it is difficult to treat the whole surface with constrained layer viscoelastic material, due to reduced areas or inaccessible parts. Furthermore, it may indeed be desirable to selectively apply one or more damping patches to control certain resonances. Patch damping design is an efficient and cost effective concept for solving noise and vibration problems. As a result of these considerations, the research was focused on finding a general methodology, based on a purely energetic approach, to reduce the unwanted amplitude vibration level in mechanical components through the application of appropriate elements characterized by high damping properties. The methodology was enforced using IDEAS v7! software which makes it possible to address modelling in terms of energy distribution within a structure. Advanced methodologies were developed to reduce the vibration amplitude in components such as plate and bracket by applying patches. Specifically, potential energy estimations will precisely and accurately define the exact locations on the surface of the components which should be covered by the patches. As a result, these studies enable a reduction in vibration amplitude, in reference both to a single component and/or a complex system. In addition, this methodology makes it possible to improve the vibratory behaviour of a component in certain frequency ranges while reducing, at the same time, the effect of dangerous resonances, acting specifically on the location, extent and quantity of the patches to be applied on the surface of the base component. During this thesis, different fields were contemporarily studied: definition and identification of structural modification ! ! "#! methods, theoretical aspects of material damping characteristics, vibrational propagation methods and applicative aspects relating to the implementation of models for the vibratory optimisation of mechanical components. This thesis was developed within the LVA research and technology transfer laboratories at the INSA institute (Lyon, France) and InterMech (Division Acoustic and Vibrations – LAV); and was carried out with the contribution of the Emilia Romagna Region – Assessorato Attività Produttive, Sviluppo Economico, Piano telematico, PRRIITT misura 3.4 azione A

Development of an Integrated Virtual Engine Model to Simulate New Standard Testing Cycles

[EN] The combination of more strict regulation for pollutant and CO2 emissions and the new testing cycles, covering a wider range of transient conditions, makes very interesting the development of predictive tools for engine design and pre-calibration. This paper describes a new integrated Virtual Engine Model (VEMOD) that has been developed as a standalone tool to simulate new standard testing cycles. The VEMOD is based on a wave-action model that carries out the thermo-and fluid dynamics calculation of the gas in each part of the engine. In the model, the engine is represented by means of 1D ducts, while the volumes, such as cylinders and reservoirs, are considered as 0D elements. Different sub-models are included in the VEMOD to take into account all the relevant phenomena. Thus, the combustion process is calculated by the Apparent Combustion Time (ACT) 1D model, responsible for the prediction of the rate of heat release and NOx formation. Experimental correlations are used to determine the rest of pollutants. In order to predict tailpipe pollutant emissions to the ambient, different sub-models have been developed to reproduce the behavior of the aftertreatment devices (DOC and DPF) placed in the exhaust system. Dedicated friction and auxiliaries sub-models allow obtaining the brake power. The turbocharger consists of 0D compressor and turbine sub-models capable of extrapolating the available maps of both devices. The VEMOD includes coolant and lubricant circuits linked, on the one hand, with the engine block and the turbocharger through heat transfer lumped models; and on the other hand with the engine heat exchangers. A control system emulating the ECU along with vehicle and driver sub-models allow completing the engine simulation. The Virtual Engine Model has been validated with experimental tests in a 1.6 L Diesel engine using steady and transient tests in both hot and cold conditions. Engine torque was predicted with a mean error of 3 Nm and an error below 14 Nm for 90 % of the cycle duration. CO2 presented a mean error of 0.04 g/s, while during 80 % of the cycle, error was below 0.44 g/s.This research has been partially funded by the European Union’s Horizon 2020 Framework Programme for research, technological development and demonstration under grant agreement 723976 (“DiePeR”) and by the Spanish government under the grant agreement TRA2017-89894-R. The authors wish to thank Renault SAS, especially P. Mallet and E. Gaïffas, for supporting this research.Martín Díaz, J.; Arnau Martínez, FJ.; Piqueras, P.; Auñón-García, Á. (2018). Development of an Integrated Virtual Engine Model to Simulate New Standard Testing Cycles. SAE Technical Papers. https://doi.org/10.4271/2018-01-1413