Vehicle gear shifting strategies co-simulations to optimize performance and fuel consumption at high speeds and accelerations. Jony Javorski Eckert Fabio Mazzariol Santiciolli Eduardo dos Santos Costa Heron JosĂŠ DionĂsio Franco Giuseppe Dedini State university of Campinas-UNICAMP
ABSTRACT The driver gear shifting strategy influences significantly in the vehicle dynamic behavior, performance and fuel consumption because it changes the transmission system inertia and the engine speed. In this paper was created an algorithm that can merge strategies that maximize vehicle acceleration performance with others that aim fuel economy according to the power demand. The analyses were performed through co-simulation between the multibody dynamics TM TM program Adams and Simulink/Matlab . The power demand was defined based on the motion resistance equations of the vehicle longitudinal dynamics and the standard driving cycle US06 which provides the speeds profile comparison of for simulations results.
INTRODUCTION The vehicle dynamics studies the interactions between the vehicle, the driver and the environment. The literature proposes to divide the vehicular dynamic into three areas: longitudinal, lateral and vertical. The longitudinal dynamics evaluates the vehicle power required for remain the desired speed, evaluating by means of equations the forces acting on the system. The power demand is a function of the aerodynamic drag, tire-ground interaction, climbing resistance, powertrain inertia and driving behavior. According to Wong (2001) the vehicle power is provided by the engine that can only be used with appropriate transmission because of its performance characteristics. The powertrain is usually composed by clutch, gearbox, drive shafts and differential. The gearbox provides a number of gear ratios selected to provide the: vehicle traction force to keep the speed closer to the ideal. The shift control governs the transmission behavior, during a shift event, in function of the resistance forces and vehicle speed. The top gear is selected to get a maximum speed and it is limited by the engine power, speed and the fuel economy (Singh et al., 2012). The longitudinal vehicle dynamics models proposed in the literature do not define a standard gear shifting, due because this factor is represented by the driver behavior, depending on road and traffic conditions. According to Kahlbau et al., (2013) efficiency and shift quality are determined by the shift strategy, defining at what time a shift event is executed, and presents significant effects over the vehicular performance and fuel consumption (Santiciolli et al., 2013). Vagg et al. (2012), describes that the use of gear shifting indicators, composed of light and/or sound alarms connected to management software installed in the Electronic Control Unit (ECU), results in 3.6% of fuel economy in a vehicle submitted to the New European Driving Cycle. Furthermore, Gao et al. (2011) optimized the gear shift time in heavy vehicles as a function of the engine torque and clutch performance. Guan and Frey (2012) developed a driving assistance system to help drivers giving them fuel efficiency guidelines that are suited for the current situation of the vehicle. With the same purpose of reduce fuel consumption Orfila et al. (2012) evaluated experimentally the variability of driver behaviors related, in relation with the engine speeds amplitude according to the driving style for 21 drivers. After that he reproduced the tests using ecodriving techniques to reduce the fuel consumption. The objective of this paper is evaluate the performance and fuel consumption of a 1.0L vehicle, based on US06 standard TM TM driving cycle, by co-simulations between Adams where is located the multibody vehicle model and Matlab/Simulink where is implemented the vehicle dynamics equations and the gear shifting control strategies used.
LONGITUDINAL VEHICLE DYNAMICS In this paper it will be used the longitudinal vehicle dynamics methodology proposed by Gillespie (1992) where the model is based on the acting forces on the vehicle travel direction as shown in Figure 1.
Figure 1 - Arbitrary forces acting on a vehicle (Gillespie, 1992)
AERODYNAMIC DRAG The aerodynamic load ( ) is the resistance imposed by the air during the vehicle passage. This effect is proportional to the square of the vehicle speed. According to Ehsani et al. (2009), a vehicle traveling at a particular speed in air, generates a resistance force of its motion. This force is known as aerodynamic drag and it is resultant from two components: shape drag and skin friction. Due to the complexity of the airflow outside the vehicle, this load is based on empirical constant and a term known as drag coefficient, as shown in Eq. (1). (1)
ROLLING RESISTANCE Rolling resistance is a result of energy loss in the tire, which can be traced back to the deformation of the area of tire contact and the damping properties of the rubber. These lead to the transformation of mechanical into thermal energy, contributing to warming of the tire (Reimpell and Stoll, 1996). At low speeds on hard pavement, rolling resistance ( ) is the primary resistance load caused essentially by: the tire deformation, the pavement and the tire adhesion on the ground. This paper will consider hard surfaces, such as asphalt and concrete. In these cases, the ground stiffness is higher than the tires, therefore the road can be considered undeformable. The rolling resistance is shown by the Eq. (2). (2) Where is the vehicle weight [ ] and of the vehicle speed . (
)
represents the rolling resistance coefficient calculated by the Eq. (3) in function
(3)
ROAD GRADE INFLUENCE This term refers to the weight force decomposition resulting from the road grade. In uphill, the weight force component acts retarding the vehicle movement, and in downhill, the weight force aids the movement. The grade angle also results in a component of weight parallel to the ground which, as in the case of accelerating or braking on flat ground, results in a longitudinal weight transfer. The effects of grade and longitudinal acceleration can be combined in finding the changes in
front and rear loads due to both (Milliken et al., 1995). The road grade is considered null in US06 cycle, therefore the terms relating to the climbing resistance will be removed from the vehicle longitudinal dynamics equationing proposed.
ACCELERATION PERFORMANCE The vehicle acceleration generates resistance forces as the vehicle longitudinal displacement as the powertrain rotational inertia. The available traction force ( ) in function of the engine torque and the transmission ratio is given by Eq. (4). (( •
)
)
= Available engine torque [
(4)
];
•
= Gearbox inertia [
];
•
= Total gear ratio;
•
= Differential inertia [
•
= Transmission overall efficiency;
•
= Wheels and tires inertia [
]; ];
•
= Tire external radius [ ];
•
= Gearbox transmission ratio;
•
= Gearbox inertia [
•
= Vehicle longitudinal acceleration [
];
The vehicle acceleration performance is given by the Eq. (5), where
is the vehicle mass [
] and
].
the road grade [rad].
( )
(5)
CO-SIMULATION The longitudinal dynamics simulation is normally used to compare the importance of energy balance characteristics for vehicles, without the need of building prototypes that can take much time and a high cost (Oliveira, 2005). The cosimulation technique is used in a development stage where the physical or mathematical mechatronic and control system are designed (Brezina et al., 2011). The simulations implemented in this paper were made via the multibody dynamic analysis program Adams™ (Automatic Dynamic Analysis of Mechanical Systems), where is implemented the vehicular model analyzed. The control of variables related to longitudinal dynamics, as described earlier, is done through the interface between Adams™ and MATLAB/Simulink™. The simulated vehicle was based on a compact hatchback equipped with 1.0L engine (Table 1). The implemented model was designed based on a dynamometer bench (Figure 2) to enable future experimental validations. The effects of vehicle suspension system were neglected to simplify the model. These factors are also disregarded by the current literature. Table 1 - Vehicle parameters
Components Engine inertia Transmission inertia Transmission ratio Diferencial inertia Diferencial ratio Wheels + tires inertia Vehicle mass Tires
Units
-
-
1st
2nd
0.0017 4.27
0.0022 2.35
Speed 3rd 0.1367 0.0029 1.48 9.22E-04 4.87 2 980 175/70 R13
4th
5th
0.0039 1.05
0.0054 0.8
Figure 2 - CAD model
The CAD model was exported to Adams™ where an appropriate revolution joints were created to allow the wheels movement and rotating masses. On the wheels were applied torques related to the powertrain and brake system in the rotating masses were applied a movement resistance torque. In the model, the vehicle chassis was connected to the base to prevent longitudinal movement so that the wheels remain aligned with the rollers. The rotational movement between the rollers and the wheels are done by means of a joint, transmitting torques and acting speeds. To facilitate the implementation of the vehicle dynamics equations, it was used a Simulink™/Adams™ interface, generating a block of data from the dynamic model as shown in Figure 3.
Figure 3 - Adams™ generated block
The Simulink™ programmed algorithm works together with the Adams™ solver. The Simulink™ provides for Adams™ torque values applied in the front wheels. The Adams™ generates a response from an angular velocity of the wheels, which supplies the Simulink™ algorithm to recalculate the required torque according to the new demand.
DRIVING CYCLE With the intention to establish a benchmark, standard cycles were utilized to determine the vehicle speed behavior, in a way that the mathematic model calculate the vehicle required power to follow the velocity profile predetermined by the cycle. A driving cycle represents the way the vehicle is driven during a trip and the road characteristics. In the simplest case, it is defined as a sequence of vehicle speed (and therefore acceleration) and road grade (CorrĂŞa et al., 2011). These driving cycles are designed to be representative of urban and extra-urban driving conditions, and reproduce measures of vehicle speed in real roads. Some of them and the test procedures have been recently updated to better suit modern vehicles, following criticism towards the previous regulation (Serrao et al., 2005). In the simulations was used the US06 (Figure 4) cycle that complements the U.S. test cycle FTP-75 because it represents high speeds and accelerations. This cycle represents a route of 12.8 , with an average speed of 77.9 , maximum speed of 129.2 and duration of 596 seconds. Therefore, this cycle allows a better analysis of the vehicle performance in acceleration condition, to evaluate a critical operation in the proposed model.
Figure 4 - Velocity profile US06
ENGINE PARAMETERS The simulated model considers the engine torque curves Figure 5(A) that is the previously described mathematic model compared with the available engine torque in function of the acceleration percentage and the engine speed. If the required torque exceeds the maximum torque available, there will be loss of performance. The fuel consumption is given by the map shown in Figure 5(B) as a function of torque and engine speed.
Figure 5 – (A) torque curve in function of the throttle. (B) Fuel consumption map
GEAR SHIFTING PARAMETERS For a correct representation of the vehicle behavior is necessary to define some specific parameters to avoid gear shifting instability. In the simulations performed was used a gear shifting time of 1 as proposed by Yin et al. (2007). Adwell time between two subsequent gear shifts is also important for stabilization. This is required to avoid chattering and to satisfy comfort conditions (Casavola et al., 2010). The downshift occurs at 5 km=h below the upshift speed, as proposed by Xi et al. (2009), to prevent gear shift instability
GEAR SHIFTING STRATEGIES Maximum power and torque strategies consist in optimize the vehicle acceleration performance, usually acting at engine higher speeds, thereby generating a fuel consumption increase. The fuel economy strategy is more difficult to define because it depends on a number of factors that vary from the engine behavior, available gear ratios, driver required acceleration and fuel type. Taking into in account these parameters, the tactics consist in keeping the engine running in higher efficiency regions. In this paper were used the gear shifting speeds proposed by GM (2013) for a similar vehicle that the simulated. First it was observed that the fuel economy strategy upshift occurred when the engine speed approached to 3000 , similarly the maximum torque strategy gear shifting close to the engine 5300 , and maximum power tactic in 6400 . Due to the high engine speed range available between the fuel economy strategy and the gear shifting at maximum engine torque, were included two intermediate strategies to make gear shifting at 3500 and 4500 engine .
RESULTS Primarily simulations for the gear shifting tactics mentioned above were performed, the results were compared with the standard US06 velocity profile, where it was observed that in high acceleration stretches, the vehicle did not have enough power to keep the required speed, staying at lower speeds until the cycle achieve braking sections or lower acceleration stretches.
LINEAR CORRELATION To evaluate the difference between the simulation results, we used the linear correlation between the velocity profile and the standard cycle adopted. The correlation coefficient is the intensity measure of the linear relationship between the two variables. The term is the square of the correlation coefficient, called determination coefficient, and consists of the sum of squares of prediction errors obtained as shown in Eq. (6), where and represent the curves values. ( ( (
̅ )( ̅)
(
̅)) ̅)
(6)
The regression measures the variability proportion between the two curves, therefore, is a direct correlation function between the variables, showing the variance percentage of the variables. A value of close to 1 indicates a strong relationship between the two variables.
SIMULATION RESULTS ANALYSIS Due to the vehicle remain at speeds lower that the required by the standard velocity profile, the total distance traveled is affected by the vehicle performance. This causes differences in the results, because in the simulations using fuel economy strategies travel a shorter distance because of the performance decrease in high acceleration stretches, than simulations using tactics focused on the vehicle acceleration performance, generating differences in the fuel consumption average by traveled.
The results obtained by simulations of the gear shifting tactics are shown in Table 2. As the simulation objective is follow the standard velocity profile imposed, correlations are always close to 1, and the differences were found in the third decimal place. Table 2 - Correlations and fuel consumption according to the gear shifting tactic
Gear Shifting Tactics
Linear Correlation
Fue lConsumption ( )
Traveled Distance ( )
Consumption Average ( )
Fuel economy
0.99298
798.5
12.82
16.05
Gear Shifting at 3500 rpm
0.99467
806.1
12.84
15.93
Gear Shifting at 4500 rpm
0.99608
828.7
12.88
15.54
Maximum torque
0.99665
883.3
12.89
14.60
Maximum power
0.99703
971.9
12.90
13.27
Figure 6 shows the performance difference between the fuel economy and the maximum power strategies. Using the fuel economy tactics the simulated vehicle does not follow the standard speeds on high acceleration stretches, because it has not enough power to fulfill the cycle, however this tactic present the best Consumption Average, even the vehicle traveled a lower distance in comparison with the standard velocity profile, because this strategy gives priority to engine better efficiency regions.
Figure 6 - Comparison between simulated tactics and the speed US06 profile.
For the vehicle follow the standard velocity profile was necessary to use the engine maximum power gear shifting strategy. This operation region is located at higher engine speeds, so the vehicle takes more time to reach the gear shifting speed, staying for a longer period using gears with greater transmission ratio, resulting in a higher torque in the wheels which increases the vehicle acceleration capacity. However this operation regime is located in an engine low efficiency region generating a significant fuel consumption increase.
HYBRID STRATEGY The driver does not keep a default strategy throughout all the route by simply adjusting the power required as needed (Yu et al. 2004), for example, in the fuel economy strategy simulation, the vehicle could keep the required performance in a large part of the cycle, only getting suboptimal performance in acceleration peaks. The gear shifting tactics in manual transmissions should be assisted by an intelligent interactive system, as proposed by Kang et al. (2012) using the gear shifting control to optimize the torque applied to the vehicle wheels. In order to maintain the performance and optimize fuel consumption compared to the maximum torque and power strategies was developed an adaptive algorithm that fits the gear shifting strategy as the power demand. This algorithm repeats the same simulation few times analyzing the stretches in which the vehicle fails to achieve the desired speed by changing the gear shifting strategy to achieve acceptable performance. The hybrid strategy achieved a similar performance to maximum power gear shifting tactic, however with a fuel consumption of 826.1 , representing 15% fuel economy compared to the maximum power strategy, and an increase of 3.45% over the fuel economy strategy, but with superior performance. The travelled distance was similar to the maximum power strategy, which achieved the best performance between the simulated tactics, totaling a fuel consumption average of 15.59 Figure 7 shows the engine speed in function of the gear shifting strategy used and the way that hybrid strategy operates by changing the default gear shifting speed according to the vehicle power demand.
Figure 7 - Gear shifting tactics utilized
Figure 8 shows the gear shifting strategy changes managed by the implemented algorithm. In the high acceleration stretches, is used the maximum power strategy to the vehicle reach the standard velocity profile the required performance. Already in low power demand situations fuel economy tactic is utilized. The intermediary strategies are used
in moderate acceleration stretches. The maximum torque strategy is used in shorts high acceleration stretches where the vehicle reachs the desired speed before the engine reaches maximum power strategy high speeds.
Figure 8 - Engine speed in function of the gear shifting tactic
In the Figure 9 and 10 can be observed the differences in the gear profiles used by the fuel economy and hybrid strategies. While in the simulations with fixed gear shifting strategies gear profiles are uniform due to upshifting and downshifting occur at specifics speeds stipulated by the gear shifting tactic used. The hybrid strategy possibility the downshift process even in acceleration stretches to increase the vehicle wheels torque, increasing the vehicle's performance and consequently the fuel consumption.
Figure 9 - Fuel economy tactic gear profiles
Figure 10 - Hybrid strategy gear profiles
CONCLUSION In this paper gear shifting strategy influence in the vehicle longitudinal calculation dynamics was evaluated. The results were obtained by co-simulations performed in the multibody dynamics analysis Adams TM with Simulink/MatlabTM. The calculation methodology was described in the book Fundamentals of Vehicle Dynamics, considering the vehicle geometry and powertrain inertias of a Compact Hatchback, equipped with 1.0L engine and also a gearbox with five ratios. After the first simulation, it was observed that the vehicle performance was lower than expected in some stretches where engine maximum power was required, due to high accelerations imposed by the US06 speed profile. With the purpose to extend the permanence time using the greatest reduction gear ratios (generating a higher available torque at the vehicle wheel) gear shifting strategies at higher engine speeds have been implemented. It was verified a gain in the vehicle performance and consequently an increase of fuel consumption due to new gear shifting strategies make the engine run in lower efficiency regions. Aiming to keep the maximum power strategy performance, and reducing the fuel consumption, was developed a hybrid strategy that combines the previously simulated gear shifting tactics applying them as required. The hybrid strategy resulted in a similar correlation of the maximum power tactic, but with lower fuel consumption close to the results found using the intermediary strategies. The hybrid strategy improves a better representation of the driver behavior in function of the required performance, which is provided by the US06 standard speeds profile. Finally is concluded that the knowledge of the gear shifting strategies is crucial in the vehicle dynamics calculation, because these influence the vehicle performance and consequently the fuel consumption.
ACKNOWLEDGMENTS The authors thank CNPq, CPFL, and ANEEL for financial support.
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CONTACT javorski@fem.unicamp.br, fabio@fem.unicamp.br, eduardo.costa@fem.unicamp.br, hjd_92@hotmail.com, dedini@fem. unicamp.br