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Viewing 1 to 30 of 185
2016-04-05
Technical Paper
2016-01-1051
Jeremy Walker, Josh Lierer, Riccardo Calza, Sundar Rajan Krishnan, Kalyan Srinivasan, Hossein Toghiani
This paper presents results from a GT-POWER engine model of a Weber 850 cc, two-cylinder spark ignition engine operating on E-85 and gasoline. The simulations utilizes a two-zone combustion model with the Woschni cylinder heat transfer model. Simulation results are compared to baseline experimental data of a naturally aspirated (NA) version of the two-cylinder Weber multipurpose engine (MPE). The turbocharged (TC) engine version was obtained from the manufacturer for the EcoCAR 3 advanced vehicular technology competition (AVTC). Experimental data and simulation results are used to develop and optimize a semi-predictive combustion model. Additionally, brake thermal efficiency data generated is being used to create a simplified, fast running model implemented in real time within the Mississippi State University (MSU) EcoCAR 3 team’s systems-level vehicle model for the turbocharged (TC) version of the MPE 850 engine operating on E-85.
2016-04-05
Technical Paper
2016-01-1127
Enrico Galvagno, Guido Ricardo Guercioni, Alessandro Vigliani
Abstract This paper presents a methodology for the assessment of the NVH (noise vibration and harshness) performance of Dual Clutch Transmissions (DCTs) depending on some transmission design parameters, e.g. torsional backlash in the synchronizers or clutch disc moment of inertia, during low speed maneuvers. A 21-DOFs nonlinear dynamic model of a C-segment passenger car equipped with a DCT is used to simulate the torsional behavior of the driveline and to estimate the forces at the bearings. The impacts between the teeth of two engaging components, e.g. gears and synchronizers, generate impulses in the forces, thus loading the bearings with force time-history characterized by rich frequency content. A broadband excitation is therefore applied to the gearbox case, generating noise and vibration issues.
2016-04-05
Technical Paper
2016-01-1124
Luca Castellazzi, Andrea Tonoli, Nicola Amati, Alessandro Piu, Enrico Galliera
Abstract The term driveability describes the driver's complex subjective perception of the interactions with the vehicle. One of them is associated to longitudinal acceleration aspects. A relevant contribution to the driveability optimization process is, nowadays, realized by means of track tests during which a considerable amount of driveline parameters are tuned in order to obtain a good compromise of longitudinal acceleration response. Unfortunately, this process is carried out at a development stage when a design iteration becomes too expensive. In addition, the actual trend of downsizing and supercharging the engines leads to higher vibrations that are transmitted to the vehicle. A large effort is therefore dedicated to develop, test and implement ignition strategies addressed to minimize the torque irregularities. Such strategies could penalize the engine maximum performance, efficiency and emissions. The introduction of the dual mass flywheel is beneficial to this end.
2016-04-05
Technical Paper
2016-01-1552
Renato Galluzzi, Andrea Tonoli, Nicola Amati, Gabriele Curcuruto, Piero Conti, Giordano Greco, Andrea Nepote
Abstract The development of suspension systems has seen substantial improvements in the last years due to the use of variable dampers. Furthermore, the efficiency increase in the subsystems within the automotive chassis has led to the use of regenerative solutions, in which electric machines can be employed as generators to recover part of the energy otherwise dissipated. However, the harvesting capability of regenerative suspensions is often limited by friction and inertial phenomena. The former ones waste mechanical energy into heat, while the latter ones hamper the shock absorption by locking the suspension when subject to dynamic excitation. Besides a suitable design and sizing of components, recent research works highlight the use of the so-called motion rectifier to improve energy recovery by constraining the motion of the electric motor to a single sense of rotation.
2016-04-05
Journal Article
2016-01-1662
Jyotishman Ghosh, Andrea Tonoli, Nicola Amati, Weitao Chen
Abstract A method for estimating the sideslip angle of a Formula SAE vehicle with torque vectoring is presented. Torque vectoring introduces large tire longitudinal forces which lead to a reduction of the tire lateral forces. A novel tire model is utilized to represent this reduction of the lateral forces. The estimation is realized using an extended Kalman filter which takes in standard sensor measurements. The developed algorithm is tested by simulating slalom and figure eight maneuvers on a validated VI-CarRealTime vehicle model. Results indicate that the algorithm is able to estimate the sideslip angle of the vehicle reliably on a high friction surface track.
2016-04-05
Technical Paper
2016-01-1654
Umair Hussain Syed, Alessandro Vigliani
Abstract Vehicle dynamics estimation has been the subject of study for some years now. If on-board vehicle control systems can be provided with information such as side slip angle, lateral force etc. then stability of the vehicle can be improved. To estimate these dynamic variables different observers have been used e.g., sliding mode, fuzzy logic, neural networks etc. In this article the authors propose an extended Kalman filter to estimate vehicle side slip angle. Roll angle is estimated using vertical loads as input. First, a linear Kalman filter is used to filter out the vertical forces and estimate roll angle. This information is then used to estimate the vehicle side slip angle. To take into account the nonlinearities concerning lateral vehicle dynamics, Pacejka magic formula is used to model lateral forces. Estimated results are then compared with simulations, showing good accuracy.
2016-04-05
Technical Paper
2016-01-0547
Andrea Piano, Federico Millo, Giulio Boccardo, Mahsa Rafigh, Alessandro Gallone, Marcello Rimondi
The predictive capabilities of an innovative multizone combustion model DIPulse, developed by Gamma Technologies, were assessed in this work for a last generation common rail automotive diesel engine. A detailed validation process, based on an extensive experimental data set, was carried out concerning the predicted heat release rate, the in-cylinder pressure trace, as well as NOx and soot emissions for several operating points including both part load and full load points. After a preliminary calibration of the model, the combustion model parameters were then optimized through a Latin Hypercube Design of Experiment (DoE), with the aim of minimizing the RMS error between the predicted and experimental burn rate of several engine operating points, thus achieving a satisfactory agreement between simulation and experimental engine combustion and emissions parameters.
2016-04-05
Technical Paper
2016-01-0557
Mohsen Mirzaeian, Federico Millo, Luciano Rolando
A 0D phenomenological turbulence model, based on the K-k and k- ɛ approaches, was coupled with a predictive turbulent combustion model using the commercial code GT-Suite, and its predictive capabilities were assessed for a downsized turbocharged SI engine. Differently from the 3D-CFD approach which is typically utilized to describe the evolution of the in-cylinder flow field, and which has very high computational requirements, the 0D phenomenological approach adopted in this work gives the opportunity to predict the evolution of the in-cylinder charge motion and the subsequent combustion process by means of a turbulent combustion model, with a significantly reduced computational effort, thus paving the way for the simulation of the whole engine operating map.
2016-04-05
Technical Paper
2016-01-0555
Federico Millo, Sabino Caputo, Claudio Cubito, Antonella Calamiello, Davide Mercuri, Marcello Rimondi
The target for future cooling systems is to control the fluid temperatures and flows through a demand oriented control of the engine cooling to minimize energy demand and to achieve comfort, emissions, or service life advantages. The scope of this work is to create a complete engine thermal model (including both cooling and lubrication circuits) able to reproduce engine warm up along the New European Driving Cycle in order to assess the impact of different thermal management concepts on fuel consumption. The engine cylinder structure was modeled through a finite element representation of cylinder liner, piston and head in order to simulate the cylinder heat exchange to coolant or oil flow circuits and to predict heat distribution during transient conditions. Heat exchanges with other components (EGR cooler, turbo cooler, oil cooler) were also taken into account.
2016-04-05
Journal Article
2016-01-0563
Andrea Piano, Federico Millo, Lucio Postrioti, Giulia Biscontini, Andrea Cavicchi, Francesco Concetto Pesce
The selection and tuning of the Fuel Injection System (FIS) are among the most critical tasks for the automotive diesel engine design engineers. In fact, the injection strongly affects the combustion phenomena through which controlling a wide range of related issues such as pollutant emissions, combustion noise and fuel efficiency becomes feasible. In the scope of the engine design optimization, the simulation is an efficient tool in order to both predict the key performance parameters of the FIS, and to reduce the amount of experiments needed to reach the final product configuration. In this work a complete characterization of a solenoid ballistic injector for a Light-Duty Common Rail system was therefore implemented in a commercially available one-dimensional computational software called GT-SUITE. The main phenomena governing the injector operation were simulated by means of three sub-models (electro-magnetic, hydraulic and mechanical).
2016-04-05
Journal Article
2016-01-1243
Roberto Finesso, Ezio Spessa, Mattia Venditti
Abstract An unsupervised machine-learning technique, aimed at the identification of the optimal rule-based control strategy, has been developed for parallel hybrid electric vehicles that feature a torque-coupling (TC) device, a speed-coupling (SC) device or a dual-mode system, which is able to realize both actions. The approach is based on the preliminary identification of the optimal control strategy, which is carried out by means of a benchmark optimizer, based on the deterministic dynamic programming technique, for different driving scenarios. The optimization is carried out by selecting the optimal values of the control variables (i.e., transmission gear and power flow) in order to minimize fuel consumption, while taking into account several constraints in terms of NOx emissions, battery state of charge and battery life consumption.
2016-01-15
Journal Article
2015-01-9044
Roberto Finesso, Ezio Spessa, Yixin Yang
Abstract A real-time mean-value engine model for the simulation of the HRR (heat release rate), in-cylinder pressure, brake torque and pollutant emissions, including NOx and soot, has been developed, calibrated and assessed at both steady-state and transient conditions for a Euro 6 1.6L GM diesel engine. The chemical energy release has been simulated using an improved version of a previously developed model that is based on the accumulated fuel mass approach. The in-cylinder pressure has been evaluated on the basis of the inversion of a single-zone model, using the net energy release as input. The latter quantity was derived starting from the simulated chemical energy release, and evaluating the heat transfer of the charge with the walls. NOx and soot emissions were simulated on the basis of semi-empirical correlations that take into account the in-cylinder thermodynamic properties, the chemical energy release and the main engine parameters.
2015-09-15
Technical Paper
2015-01-2453
Danilo Andreoli, Mario Cassaro, Manuela Battipede, Goodarz Ahmadi, Piergiovanni Marzocca
Abstract Flow control over aerodynamic shapes in order to achieve performance enhancements has been a lively research area for last two decades. Synthetic Jet Actuators (SJAs) are devices able to interact actively with the flow around their hosting structure by providing ejection and suction of fluid from the enclosed cavity containing a piezo-electric oscillating membrane through dedicated orifices. The research presented in this paper concerns the implementation of zero-net-mass-flux SJAs airflow control system on a NACA0015, low aspect ratio wing section prototype. Two arrays with each 10 custom-made SJAs, installed at 10% and 65% of the chord length, make up the actuation system. The sensing system consists of eleven acoustic pressure transducers distributed in the wing upper surface and on the flap, an accelerometer placed in proximity of the wing c.g. and a six-axis force balance for integral load measurement.
2015-09-15
Technical Paper
2015-01-2463
Giacomo Frulla, Enrico Cestino, Piero Gili, Michele Visone, Domenico Scozzola
Abstract The problem of wing shape modification under loads in order to enhance the aircraft performance and control is continuously improving by researchers. This requirement is in contrast to the airworthiness regulations that constraint stiffness and stress of the structure in order to maintain structural integrity under operative flight conditions. The lifting surface modification is more stringent in those cases, such as UAV configurations, where the installed power is limited but the variety of operative scenario is wider than in conventional aircraft. A possible solution for adaptive wing configuration can be found in the VENTURAS Project idea. The VENTURAS Project is a funded project with the aim of improve the wind turbine efficiency by means of introducing a twisting capability for the blade sections according to the best situation in any wind condition. The blade structure is composed by two parts: 1) internal supporting element, 2) external deformable envelope.
2015-09-15
Technical Paper
2015-01-2462
Claudia Bruni, Enrico Cestino, Giacomo Frulla, Piergiovanni Marzocca
Abstract The innovative highly flexible wings made of extremely light structures, yet still capable of carrying a considerable amount of non- structural weights, requires significant effort in structural simulations. The complexity involved in such design demands for simplified mathematical tools based on appropriate nonlinear structural schemes combined with reduced order models capable of predicting accurately their aero-structural behaviour. The model presented in this paper is based on a consistent nonlinear beam-wise scheme, capable of simulating the unconventional aeroelastic behaviour of flexible composite wings. The partial differential equations describing the wing dynamics are expanded up to the third order and can be used to explore the effect of static deflection imposed by external trim, the effect of gust loads and the one of nonlinear aerodynamic stall.
2015-09-15
Technical Paper
2015-01-2458
Giuseppe Sirigu, Manuela Battipede, Piero Gili, Mario Cassaro
Abstract The future revolution of the air traffic system imposes the development of a new class of Flight Management Systems (FMS), capable of providing the aircraft with real-time reference flight parameters, necessary to fly the aircraft through a predefined sequence of waypoints, while minimizing fuel consumption, noise and pollution emissions. The main goal is to guarantee safety operations while reducing the aircraft environmental impact, according to the main international research programs. This policy is expected to affect also the Unmanned Aerial Systems (UASs), as soon as they will be allowed to fly beyond the restricted portions of the aerospace where they are currently confined. In the future, in fact, UASs are expected to fly within the whole civilian airspace, under the same requirements deriving from the adoption of the Performance Based Navigation (PBN).
2015-09-06
Technical Paper
2015-24-2425
Mario Milanese, Ilario Gerlero, Carlo Novara, Giuseppe Conte, Maurizio Cisternino, Carmen Pedicini, Vincenzo Alfieri l, Stefano Mosca
Emission requirements for diesel engines are becoming increasingly strict, leading to the increase of engine architecture complexity. This evolution requires a more systematic approach in the development of control systems than presently adopted, in order to achieve improved performances and reduction of times and costs in design, implementation and calibration. To this end, large efforts have been devoted in recent years to the application of advanced Model-Based MIMO control systems. In the present paper a new MIMO nonlinear feedback control is proposed, based on an innovative data-driven method, which allows to design the control directly from the experimental data acquired on the plant to be controlled. Thus, the proposed control design does not need the intermediate step of a reliable plant model identification, as required by Model-Based methods.
2015-09-06
Technical Paper
2015-24-2467
Alessandro Ferrari, Federica Paolicelli
Abstract A challenging task that is required to modern injection systems is represented by the enhanced control of the injected quantities, especially when small injections are considered, such as, pilot and main shots in the context of multiple injections. The propagation of the pressure waves triggered by the nozzle opening and closure events through the high-pressure hydraulic circuit can influence and alter the performance of the injection apparatus. For this reason, an investigation of the injection system fluid dynamics in the frequency domain has been proposed. A complete lumped parameter model of the high-pressure hydraulic circuit has been applied to perform a modal analysis. The visualization of the main vibration modes of the apparatus allows a detailed and deep comprehension of the system dynamics. Furthermore, the possible resonances, which are induced by the action of the external forcing terms, have been identified.
2015-09-06
Journal Article
2015-24-2389
Mirko Baratta, Roberto Finesso, Daniela Misul, Ezio Spessa
Abstract The potential of internal EGR (iEGR) and external EGR (eEGR) in reducing the engine-out NOx emissions in a heavy-duty diesel engine has been investigated by means of a refined 1D fluid-dynamic engine model developed in the GT-Power environment. The engine is equipped with Variable Valve Actuation (VVA) and Variable Geometry Turbocharger (VGT) systems. The activity was carried out in the frame of the CORE Collaborative Project of the European Community, VII FP. The engine model integrates an innovative 0D predictive combustion algorithm for the simulation of the HRR (heat release rate) based on the accumulated fuel mass approach and a multi-zone thermodynamic model for the simulation of the in-cylinder temperatures. NOx emissions are calculated by means of the Zeldovich thermal and prompt mechanisms.
2015-09-06
Journal Article
2015-24-2426
Roberto Finesso, Ezio Spessa, Mattia Venditti, Yixin Yang
Abstract New methodologies have been developed to optimize EGR rate and injection timing in diesel engines, with the aim of minimizing fuel consumption (FC) and NOx engine-out emissions. The approach entails the application of a recently developed control-oriented engine model, which includes the simulation of the heat release rate, of the in-cylinder pressure and brake torque, as well as of the NOx emission levels. The engine model was coupled with a C-class vehicle model, in order to derive the engine speed and torque demand for several driving cycles, including the NEDC, FTP, AUDC, ARDC and AMDC. The optimization process was based on the minimization of a target function, which takes into account FC and NOx emission levels. The selected control variables of the problem are the injection timing of the main pulse and the position of the EGR valve, which have been considered as the most influential engine parameters on both fuel consumption and NOx emissions.
2015-09-06
Journal Article
2015-24-2416
Roberto Finesso, Ezio Spessa, Ezio Mancaruso, Luigi Sequino, Bianca Maria Vaglieco
Abstract An investigation has been carried out on the spray penetration and soot formation processes in a research diesel engine by means of a quasi-dimensional multizone combustion model. The model integrates a predictive non stationary 1D spray model developed by the Sandia National Laboratory, with a diagnostic multizone thermodynamic model, and is capable of predicting the spray formation, combustion and soot formation processes in the combustion chamber. The multizone model was used to analyze three operating conditions, i.e., a zero load point (BMEP = 0 bar at 1000 rpm), a medium load point (BMEP = 5 bar at 2000 rpm) and a medium-high load point (BMEP = 10 bar at 2000 rpm). These conditions were experimentally tested in an optical single cylinder engine with the combustion system configuration of a 2.0L Euro4 GM diesel engine for passenger car applications.
2015-04-14
Technical Paper
2015-01-0929
Petter Dahlander, Daniele Iemmolo, Yifei Tong
Abstract Time-resolved mass injection rates of an outward opening piezo-actuated and a solenoid actuated multi-hole GDI injector were measured to investigate (1) the influence of both hardware and software settings and (2) the influence on the injection rates from a wide range of operational parameters and (3) discuss limitations and issues with this measurement technique. The varied operating parameters were fuel pressure, back-pressure, electrical pulse width, single/double injection and injection frequency. The varied hardware/software parameters were injector protrusion, upstream fuel pressure condition and the cut-off frequency of the software's low-pass filter. Signal quality was found to be dependent on both hardware and software settings, especially the cut-off frequency of the low-pass filter. Measurements with high signal quality were not possible for back-pressures lower than 0.5 MPa.
2015-04-14
Technical Paper
2015-01-1533
Massimiliana Carello, Serra Andrea, Andrea Giancarlo Airale, Alessandro Ferraris
XAM is a two-seat city vehicle prototype developed at the Politecnico di Torino, equipped with a hybrid propulsion system to obtain low consumptions and reduced environmental impact. The design of this vehicle was guided by the requirements of weight reduction and aerodynamic optimization of the body, aimed at obtaining a reduction of resistance while guarantying roominess. The basic shape of the vehicle corresponding to the requirements of style, ergonomics and structure were deeply studied through CFD simulation in order to assess its aerodynamic performance (considering the vehicle as a whole or the influence of the various details and of their changes separately). The most critical areas of the body (underfloor, tail, spoiler, mirrors, A-pillar) were analyzed creating dedicated refinement volumes.
2015-04-14
Technical Paper
2015-01-0760
Sabino Luisi, Vittorio Doria, Andrea Stroppiana, Federico Millo, Mohsen Mirzaeian
Abstract The application of Miller cycle through Late Intake Valve Closure (LIVC) or Early Intake Valve Closure (EIVC) for knock mitigation at high load on a turbocharged downsized spark ignition engine was experimentally investigated. By reducing the effective compression ratio due to a shorter compression stroke and hence achieving lower charge temperatures inside the cylinder, significant mitigation of knock tendency could be obtained. As a consequence, the spark advance retard could be substantially decreased and the enrichment of the mixture could significantly be reduced, thus obtaining impressive efficiency improvements. In this research, both EIVC and LIVC strategies have been examined aiming to achieve possible improvements for knock mitigation and after some preliminary investigations confirmed LIVC being more effective than EIVC for this goal, the latter was discarded and the research activities were focused on LIVC only.
2015-04-14
Journal Article
2015-01-0879
Roberto Finesso, Ezio Spessa, Yixin Yang, Vincenzo Alfieri, Giuseppe Conte
Abstract The paper has the aim of assessing and applying control-oriented models capable of predicting HRR (Heat Release Rate) and MFB50 in DI diesel engines. To accomplish this, an existing combustion model, previously developed by the authors and based on the accumulated fuel mass approach, has been modified to enhance its physical background, and then calibrated and validated on a GM 1.6 L Euro 6 DI diesel engine. It has been verified that the accumulated fuel mass approach is capable of accurately simulating medium-low load operating conditions characterized by a dominant premixed combustion phase, while it resulted to be less accurate at higher loads. In the latter case, the prediction of the heat release has been enhanced by including an additional term, proportional to the fuel injection rate, in the model. The already existing and the enhanced combustion models have been calibrated on the basis of experimental tests carried out on a dynamic test bench at GMPT-E.
2015-04-14
Technical Paper
2015-01-1121
Enrico Galvagno, Mauro Velardocchia, Alessandro Vigliani, Antonio Tota
Abstract This paper investigates the torsional dynamic behaviour of a Dual Mass Flywheel (DMF) both numerically and experimentally. First, the experimental setup is described, followed by a mathematical description in the frequency domain of the mechanical system under test, using a lumped parameter model. An analytical expression for the frequency response function describing the rotational dynamics is derived and compared with experimental data. Sine sweep tests are used to characterise the system, imposing constant amplitude excitation, i.e. the torque applied to the engine side of the DMF. Moreover a method for enhancing the dynamic performance of the electric motor torque control is suggested in order to use it as a torsional shaker.
2014-10-13
Technical Paper
2014-01-2735
Alessandro Ferrari, Pietro Pizzo, Federica Paolicelli
Abstract A numerical-experimental analysis of a new generation Common Feeding (CF) fuel injection system, equipped with last generation solenoid injectors that feature pressure-balanced pilot-valves, has been developed. The main feature of the CF system is that it removes the accumulator from the high-pressure layout of the standard Common Rail (CR). In the CF apparatus, the high-pressure pump is connected directly to the injectors, and a small accumulation volume is integrated in the pump high-pressure circuit. The hydraulic performance of the CF system, including the injectors with the pressure-balanced pilot-valve, has been compared with that of the standard CR system in terms of injected masses, fuel leakages, high-pressure and injected flow-rate time histories. A previously developed advanced one-dimensional code for CR type systems has been adapted for the simulation of the CF high-pressure layout.
2014-05-05
Journal Article
2014-01-9046
Roberto Finesso, Ezio Spessa
Feed-forward low-throughput models have been developed to predict MFB50 and to control SOI in order to achieve a specific MFB50 target for diesel engines. The models have been assessed on a GMPT-E Euro 5 diesel engine, installed at the dynamic test bench at ICEAL-PT (Internal Combustion Engine Advanced Laboratory at the Politecnico di Torino) and applied to both steady state and transient engine operating conditions. MFB50 indicates the crank angle at which 50% of the fuel mass fraction has burned, and is currently used extensively in control algorithms to optimize combustion phasing in diesel engines in real-time. MFB50 is generally used in closed-loop combustion control applications, where it is calculated by the engine control unit, cycle-by-cycle and cylinder by-cylinder, on the basis of the measured in-cylinder pressure trace, and is adjusted in order to reduce the fuel consumption, combustion noise and engine-out emissions.
2014-04-01
Technical Paper
2014-01-1304
P.C. Bakker, J.E. De Abreu Goes, L.M.T. Somers, B.H. Johansson
The concept of Partially Premixed Combustion is known for reduced hazardous emissions and improved efficiency. Since a low-reactive fuel is required to extend the ignition delay at elevated loads, controllability and stability issues occur at the low-load end. In this investigation seven fuel blends are used, all having a Research Octane Number of around 70 and a distinct composition or boiling range. Four of them could be regarded as ‘viable refinery fuels’ since they are based on current refinery feedstocks. The latter three are based on primary reference fuels, being PRF70 and blends with ethanol and toluene respectively. Previous experiments revealed significant ignition differences, which asked for further understanding with an extended set of measurements. Experiments are conducted on a heavy duty diesel engine modified for single cylinder operation. In this investigation, emphasis is put on idling (600 rpm) and low load conditions.
2014-04-01
Technical Paper
2014-01-1798
Roberto Finesso, Ezio Spessa, Mattia Venditti
Abstract This paper describes the optimization of the layout and of the control strategy of through-the-road (TTR) parallel hybrid electric vehicles equipped with two compression-ignition engines that feature different values of maximum output power. First, a tool has been developed to define the optimal layout of each TTR vehicle. This is based on the minimization of the powertrain and fuel cost over a 10-year time span, taking into account the fuel consumption. Several performance requirements are guaranteed during the optimization, namely maximum vehicle velocity, 0-100 km/h acceleration time, gradeability and the all-electric range. A benchmark optimizer that is based on the dynamic programming theory has been developed to identify the optimal working mode and the gear number, which are the control variables of the problem. A mathematical technique, based on the pre-processing of a configuration matrix, has been developed in order to speed up the calculation time.
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