Design of a Modular Swift-shift Multi-speed Transmission with Double Dual-clutch for Electric Vehicles

In this paper a novel concept of modular swift-shift multi-speed transmission with double dual clutches is proposed, with its architecture, simulation and control strategies discussed in detail. Due to its modularity, the desired number of gear ratios can be readily realized by adding the appropriate number of modules. Further, in this design, both the underdrive and the overdrive modes are combined within one single gear train, which reduces the overall volume and weight significantly. Due to its modularity and compactness, this transmission is suitable for electric vehicles, especially commercial fleets of mediumand heavy-duty electric trucks. A proof-of-concept testbed was developed; its preliminary simulation analysis is reported here.


INTRODUCTION
The idea of using electric and hybrid technologies for medium and heavy trucks in recent years became quite popular among automotive manufacturers; one of the potential sales categories for emerging hybrid and batterypowered vehicles includes commercial delivery fleets.
Currently the market of electrified trucks can be split into three categories of vehicles: delivery trucks, city (service) trucks, and e-buses.Generally, life-cycle vehicle cost consists of three main components: initial cost, ownership cost and recycling cost.High manufacturing cost of battery-motor systems is the main reason for the initial high cost of HEVs [1].On average, hybrid vehicles cost 15-20% higher than their identical gasoline counterparts.However, in terms of fuel economy, the mile per gallon (mpg) parameter for HEV can be two-three times bigger than that of conventional vehicles [2].Besides, battery replacement is the unique additional cost of HEVs, but with the development of the technology, the influence of this factor will obviously diminish.For delivery trucks the hybrid option is economically efficient only in low mileage and high stop-and-go driving cycles.Though the maintenance cost per km of a hybrid truck can be close to that in conventional trucks, the annual maintenance expenditure remains lower since fuel economy makes sense in these driving cycles only, the hybrid truck staying in service in such driving cycles.In turn, the gas truck in high stop-and-go usage costs more both in fuel and maintenance due to higher cost of brake service.Gas trucks do not have regeneration braking, while being subject to more intensive brake wear.All these issues, along with the longer oil change intervals in hybrids (due to the engine running less), make the benefits of hybrid delivery trucks apparent.For example, research undertaken between 2008 and 2011 for the Purolator delivery fleet showed that the average costs of maintenance per km for both gas and hybrid trucks are close to each other (both within the range of $0.15-$0.20/km),while the maintenance cost of a hybrid is nearly 30 percent lower than that of a gas unit (app.$2700 vs. $4000).
Series hybrid-diesel heavy trucks are being developed not only for commercial applications.As recently as 2002, Oshkosh Truck Corporation introduced the first in the world electric hybrid-drive Heavy Expanded Mobility Tactical Truck HEMTT-LHS featuring Oshkosh's ProPulse electric hybrid-drive propulsion system [3].According to the company expectations, fuel economy could reach 40%.Eventually, OSHKOSH Defence successfully implemented the ProPulse diesel electric drive system in the mass production of military Heavy Expanded Mobility Tactical Truck (HEMTT) A3 (first disclosed at CALSTART's Hybrid Truck Users Forum HTUF in Atlanta in October 2009).However, the actual improvement of fuel economy reaches only 20% [4], which is lower than the expected amount, but still quite good.
In a survey of medium and heavy hybrid trucks it is noteworthy that the biggest hybrid truck in the world [5] is developed for mining applications by Siemens and is powered by an electric drive system consisting of four electric motors, each of 1200 kW, capable of moving the total weight of a loaded truck of 800 ton.
After hybridization the next step in the application of electric technology to urban, delivery and service fleets is the development of all-electric, or battery-electric, commercial vehicles.Most recent research results [6] predict that battery-electric commercial vehicles in urban fleets will boom, and worldwide sales of electric drive and electricassisted commercial vehicles will grow tenfold between 2014 and 2023, reaching nearly 160,000 units per year.Lyden [7] analyzes the prospects of all-electric medium-duty (Class 3-7) trucks in modern business for the sake of elimination of fossil fuel and achieving zero direct emissions.This will happen due to the main advantages of all-electric trucks, namely, fuel cost savings, lower maintenance costs and increased productivity, which by 2020 will bring the number of e-trucks in the US market close to 50 percent of the total medium truck fleet.Needless to say, that, along with the hybrid versions of medium trucks, the total number of electrical commercial vehicles is expected to become the dominant majority in the market.
In the discussion of the current trends in the market of medium battery-electric trucks one can mention the series of prototypes developed by EMOSS Hybrid & Electric drive systems, such as 10-, 12-, 16-and 18-tonne electric trucks 1 .The biggest of them reaches a top speed of 85 km/h, with a range up to 230 km.
For medium electric trucks the most critical components are the batteries and the traction motors, which should have enough power to start and run the vehicle.For heavy trucks this problem is even more serious.
Regarding batteries, those that have enough power to drive a truck are quite heavy, which poses a real challenge for designers in selecting the appropriate batteries.In order to solve the foregoing problems, engineers suggest different creative solutions, e.g., the series of EMOSS trucks with configurable battery packs (40, 80, 120, 160, 200 and 300 kWh), with which the vehicles can achieve a range2 from 25 to 300 km.
Since the issue of battery size and weight is critical for the application in medium and heavy trucks, a related problem arises: packaging and space reduction.If the battery volume cannot be reduced, then other approaches should be used.One such approach is the reduction of the powertrain size, namely, transmission and final drive.The use of transmissions for electric vehicles is an important topic of modern research activities in the EV market.For example, in 2012, one of the world leaders in transmission technology, Oerlikon Graziano, in collaboration with Vocis Driveline Control, reported the results of a case study on a two-speed system for EVs [8].These results clearly demonstrated, as confirmed by many other research teams [9,10], the advantages of the two-speed transmission when compared to a single-speed model used in EVs via four main characteristics: acceleration time; maximum climbing grade; maximum speed; and energy consumption.However, most current developments explore the application of multi-speed (mostly, two-speed) transmissions only in the passenger-and sports-car EV segment, whereas the more powerful the powertrain, the larger the number of gears in the transmission should be.Among very few prototypes of e-trucks supplied with a transmission, the EMOSS 150 kW Powertrain can be mentioned with three transmission speeds: 1:6.4,1:8 and 1:10.2.
The authors of this paper conducted research on the use of two-speed transmissions in class-4 electric delivery medium-duty trucks [11], where they found that, contrary to small passenger cars, the use of a two-speed transmission in medium-duty e-trucks does not affect efficiency, but significantly improves performance, in comparison with direct drive battery e-trucks: gradeability and maximum speed are higher, while acceleration time is reduced.While energy consumption for class-4 e-trucks does not change much, using of a two-speed powertrain makes it possible to improve packaging by reducing the size of the traction motor and inverter, and, consequently, their cost.Though the transmission brings-in its own weight and cost, our estimations show that, in combination with the savings of the motor, the total weight reduction of the complete powertrain may reach up to four times, and up to twice the cost, in comparison with the direct drive option.Further research [12,13] confirmed previous conclusions drawn by the authors.
A novel modular concept of multi-speed transmission for the electric vehicles was proposed by the authors of this paper [14], which allows for simple transmissions with virtually any required number of gears and seamless gearshifting.The transmission consists of two separate gear trains-the underdrive and the overdrive-with common planet carrier and with the number of planetary gear modules in each gear train corresponding to the number of required gears in each mode.
In this paper the concept is developed further by means of a compact version of the multi-speed transmission, with merely half the number of planetary gear sets than reported earlier [14], and two dual clutches.The reduced size of the transmission is especially important for heavy trucks carrying large batteries.Being automatic, the transmission nevertheless does not have a torque converter, since the motor is fully controlled in start, drive or reverse operations.

CONCEPT DESCRIPTION
In the proposed concept modularity is the most important feature.To obtain the required number of gears, the transmission can be designed by simply assembling the appropriate number of modules.Each module is based on a planetary gear set and, in combination with clutches, the stack of modules provides smooth driveability and surgeless swift-shift capability.Contrary to the earlier transmission [14], the new design has only one gear train that produces both the underdrive and the overdrive speed ratios.Each module generates two ratios; for each additional pair of underdrive/overdrive ratios we need only one additional module.This concept makes the transmission lighter and more compact.

Transmission gear train
The gear train of the proposed transmission is shown in Fig. 1.This transmission can be built with the desired number of steps, n, each step providing two speed modes, i.e., the underdrive and the overdrive ratios are paired and their total numbers in this transmission are equal.
The concept is based on the series of n planetary gear sets (modules).All planets are installed on a common planet carrier PC, each axis of the latter carrying a group of n planets P 1 , P 2 , • • • , P n , each planet being coupled with the corresponding sun gear.All sun gears are rigidly fixed to a common shaft.The tooth surface of the planet with the smallest diameter P 1 is in contact with the tooth surface of the biggest sun S 1 , and the tooth surface of the planet with the biggest diameter P n is in contact with the tooth surface of the smallest sun S n .
The gear train also includes n ring gears R 1 , R 2 , • • • , R n of different pitch diameters, matching the dimensions of corresponding planet and sun gears.

Input
Output

Modes of operation 2.2.1 Underdrive mode
The rotation from the traction motor is transmitted from the input transmission shaft to the sun gears.For this, the input clutch C i s of the input dual clutch DC i is engaged and connects the input transmission shaft with the input of the sun shaft.The clutch C i p is released.The input torque and rotation are transmitted from a sun to one of the planets.The planet is selected by engagement of the corresponding friction clutch C k (where k = 1, • • • , n), according to the control algorithm.The engaged friction clutch immobilizes the corresponding ring gear R k .All other friction clutches are released, and the torque/rotation is transmitted via the planet P k to the planet carrier.The output rotation of the transmission is taken from the rotation of the planet carrier with the help of the clutch C o p of the second dual clutch DC o , which engages the planet carrier with the output transmission shaft.
In this mode the output speed of the transmission is lower than that of the input shaft.The ratio of the speed reduction depends on the choice of the ring gear fixed to the housing by the corresponding friction clutch.Totally, the transmission has n different ratios in the underdrive mode.

Overdrive mode
The input rotation is transmitted from the input shaft to the planet carrier.For this, the input clutch C i p of the input dual clutch DC i is engaged and connects the input transmission shaft with the input shaft of the planet carrier.The clutch C i s is released.The input torque and rotation are transmitted from the planet carrier via one of the planets to a corresponding sun gear.The planet is selected by engagement of the corresponding friction clutch C k , according to the control algorithm.The engaged friction clutch immobilizes the corresponding ring gear R k .All other friction clutches are released, and the torque/rotation is transmitted via the planet P k to the sun S k .The output rotation of the transmission is taken from the rotation of the sun shaft with the help of the clutch C o s of the second dual clutch DC o , which engages the sun shaft with the output transmission shaft.
In this mode the output speed of the transmission is higher than that of the input shaft.The ratio of the speed increment depends on the choice of the ring gear fixed to the housing by the corresponding friction clutch.Totally, the transmission has n different ratios in the overdrive mode.
As can be seen, the proposed transmission has the same number of underdrive and overdrive ratios.The value n can be selected by the designer, based on the required specification for the vehicle driveline.

Direct drive, reverse and neutral modes
If both clutches C i s and C i p of the first dual clutch DC i , and both clutches C o p and C o s of the second dual clutch DC o are engaged, and all n friction clutches C 1 , C 2 , • • • , C n are released, the input speed and torque of the transmission are translated directly to its output shaft without any changes.This leads to the direct-drive mode of the transmission.The same arrangement provides transmission of the reversed input rotation to the reversed output rotation, in case of the reverse work mode of the motor.
In the direct drive and reverse modes, all components-the sun gears, the planet carrier, the planets, and the ring gears-rotate together, in a single block, at the same speed.There is no relative motion between the sun gears, the planets and the ring gears.
The total number of speeds in the proposed transmission, including direct drive, is The neutral mode is provided when all clutches of both dual-clutches DC i and DC o are released, and no input rotation is transmitted to the output shaft.As opposed to the multi-speed transmission proposed by the same team in [14], this transmission does not have any intermediate ratios.

TESTBED DESIGN AND PARAMETERS
In order to validate the performance of the proposed multi-speed transmission with double dual clutches for electric vehicles, the testbed, shown in Fig. 2, was developed at McGill University's Centre for Intelligent Machines.
The scaled-down proof-of-concept testbed has a gear train, with two planetary gear sets, which incorporates both underdrive and overdrive modes into the same gearbox using double dual clutches to generate two power transmission routes (Fig. 3).This allows for four gears to be selected for power transmission through to the wheels, where each planetary gear set counts for two speeds-one overdrive and one underdrive.As well, there is a direct-drive mode that serves as Gear 3 among others.Therefore, this testbed has a total of five speeds.Input Output The gear ratios of the transmission modules in the underdrive mode are 4:1 and 2.67:1; in the overdrive mode, 1:2.67 and 1:4.

SIMULATION RESULTS AND MODEL VERIFICATION 4.1 Multi-speed transmission system with constant torque input
Figure 4 illustrates a simplified simulation model of the powertrain of an electric vehicle with the proposed fivespeed transmission, using Matlab/Simdriveline, to evaluate the gear shifting performance.A constant torque of τ i = 100 N m is applied to the input end of the model.The detailed layout for the five-speed transmission with a double dual-clutch subsystem is illustrated in Fig. 5.
As described in Sec. 3, the devised upshifting process was implemented in the simulation, with the gear ratios and clutch states listed in Table 1.
The input and output angular velocities of the five-speed transmission are plotted in Fig. 6, from which a smooth transition from rest to ascending speed can be observed.It is noteworthy that in this preliminary simulation test the input acceleration torque was constant, since our goal was to estimate the transition effect during shifting and not the actual gear shifting schedule.Figures 7(a) and (b) illustrate the normalized clutch pressure signals and transmission ratios during the upshifting process, respectively, which tally with the clutch schedule listed in Table 1.From Fig. 7(b), it is apparent that vibration occurs during the gear shifting periods, especially at the beginning of the simulation and during the transition from the first gear ratio to the second one.The main reason lies in that the constant input torque signal is not capable of simulating the actual gear shifting process for the vehicle precisely.Hence, to better evaluate the gear shifting performance, a simulation test of the five-speed transmission combined with a complete vehicle model was carried out, as discussed below.

Multi-speed transmission system with the complete vehicle model
As shown in Fig. 8, the proposed five-speed transmission was further tested with a complete vehicle model, including the engine, the transmission, as well as the vehicle and tire dynamics.The vehicle parameters are listed in Table 2 4 .The preprogrammed clutch signal schedule is plotted in Fig. 9(a).With reference to Table 1, we can observe that the preprogrammed transmission controller aims to implement an upshifting process, similar to the constant-input-torque example discussed earlier.Specifically, the vehicle will start with the first underdrive mode, i.e., with a gear ratio of 4; then it will shift to the second underdrive, neutral, the first overdrive and the second overdrive modes, consecutively, at 10 s, 35 s, 55 s and 75 s, respectively.
The vehicle velocity obtained is shown in Fig. 9(b).Besides, the plots for the input and the output angular velocity of the transmission system are illustrated in Fig. 10(a).In Fig. 9(b), one can observe "small" peaks on the vehicle ership cost and recycling cost.High manufacturing cost of battery-motor systems are the main reason for the initial high cost of HEVs [1].On average, hybrid vehicles cost 15-20% higher than the identical gasoline models.However, in terms of fuel economy, the mile per gallon (mpg) parameter for HEV can be two-three times bigger than that of the conventional vehicle [2].Besides, battery replacement is the unique additional cost of HEVs, but with the development of technology the influence of this factor obviously will diminish.For delivery trucks the hybrid option is economically efficient only in low mileage and high stop and go driving cycles.Though the maintenance cost per km of a hybrid truck can be close to that in conventional truck, the annual maintenance expenditure remains lower since fuel economy makes sense in these driving cycles only, and the hybrid truck stays in service in such driving cycles.In turn, the gas truck in high stop and go usage costs more both in fuel and maintenance due to higher cost of brake service.Gas trucks do not have regeneration braking and are subject to more intensive brake wear.All these, along with the longer oil change intervals in hybrids (due to the engine running less) make the benefits of hybrid delivery trucks.For example, the research undertaken between 2008 and 2011 for the Purolator delivery fleet showed that the average cost of maintenance per km for both gas and hybrid trucks is very close to each other (both within the range of $0.15-$0.20/km)while the maintenance cost of a hybrid is nearly 30 percent less than of a gas unit (app.$2700 vs. $4000).
Series hybrid-diesel heavy trucks are being developed not only for commercial application.As far as in 2002 Oshkosh Truck Corporation presented the first in the world electric hybrid-drive Heavy Expanded Mobility Tactical Truck HEMTT-LHS featuring Oshkosh's ProPulse electric hybrid-drive propulsion system [3].According to the company expectations, fuel economy could reach 40%.Eventually, few years later OSHKOSH Defence successfully implemented ProPulse diesel electric drive system in the mass production of military Heavy Expanded Mobility Tactical Truck (HEMTT) A3 (first presented at CALSTART's Hybrid Truck Users Forum HTUF in Atlanta in October 2009).However, actual improvement of fuel economy reaches only 20% [4], which is lower than the expected amount but still is quite good.
In a survey of medium and heavy hybrid trucks it is worthy to mention the biggest hybrid truck in the world [5].It was developed for mining applications by Siemens and is powered by an electric drive system consisting of four electric motors, each of 1200 kilowatts, capable of moving the total weight of loaded truck of 800 ton.
After hybridization the next step in application of electric technology to urban, delivery and service fleet is the development of all-electric, or battery-electric, commercial vehicles.The most recent research presented in [6] predicts that battery-electric commercial vehicles in urban fleet will boom, and worldwide sales of electric drive and electric-assisted commercial vehicles will grow ten times between 2014 and 2023, reaching nearly 160,000 per year.The author of [7] analyses the prospects of all-electric medium-duty (Class 3-7) trucks in modern business for the sake of elimination of fossil fuel and achieving zero direct emissions.This will happen due to the main advantages of using all-electric trucks, namely, fuel cost savings, lower maintenance costs and increased productivity, which by 2020 will bring the number of e-trucks in the US market close to 50 percent of the total medium truck fleet.Needless to say, that along with the hybrid versions of the medium trucks the total number of the electrical-based commercial vehicles is expected to become the dominant majority on the market.
In the discussion of the current trends in the market of medium battery electric trucks one can mention the series of prototypes developed by EMOSS Hybrid & Electric drive systems, such as 10-, 12-, 16-and 18-tonne electric trucks 1 .The biggest of them reaches the top speed of 85 km/h, with the range up to 230 km.
For the medium electric trucks the most critical components are the batteries and the traction motors which should have enough power to start and run the vehicle.For the heavy trucks this problem is even more serious.
Regarding the batteries, those ones which have enough power to drive a truck are quite heavy and this fact implies a real challenge for designers while selecting and implementing the appropriate batteries.In order to solve arising problems engineers suggest different creative solutions, e.g., the series of EMOSS trucks with configurable battery

ACKNOWLEDGMENTS
The design and research work reported here was supported by grant under Automotive Partnerships Canada, APCPJ418901-11.The work of the undergraduate students Nicola Houle, Jacob Maynard, Vinh-Hieu Nguyen, Peter Reid, Patrick Arnaud, Justin Antony, and Stefan Ipate is duly acknowledged.
We also gratefully acknowledge the support of our industrial partners: Linamar, TM4 and Infolytica. to the simplicity of the modules, its size and number of speeds can be easily modified and adjusted in the design phase depending on the required parameters of the vehicle.Because of modularity such transmission is cheaper for production, and manufacturing facilities can be easily adjusted to various sizes of transmission.The discussed transmission is more compact than its counterpart described in [12] since the underdrive and the overdrive ratios are combined into pairs in corresponding modules.Therefore, the transmission itself is cheaper for manufacturing, smaller and easier for integration.Manufacturing facilities can be easily adjusted for various sizes

ACKNOWLEDGMENTS
The design and research work reported here was supported by grant under Automotive Partnerships Canada, APCPJ418901-11.The work of the undergraduate students Nicola Houle, Jacob Maynard, Vinh-Hieu Nguyen, Peter Reid, Patrick Arnaud, Justin Antony, and Stefan Ipate is duly acknowledged.
We also gratefully acknowledge the support of our industrial partners: Linamar, TM4 and Infolytica.plot, which occur due to the gear-shifting operations.Further, the corresponding transmission ratios, calculated as the ratio between the input and output angular velocities of the transmission, are shown in Fig. 10(b).We can observe that the transmission ratios obtained tally with the preprogrammed clutch-signal schedule.Moreover, the smoothness over the whole gear-shifting process for the complete vehicle model was satisfactory, in comparison with the vibrations shown in Fig. 7(b).
Furthermore, for the purpose of better imitating the automatic transmission controller in the actual vehicle, the stateflow chart, as shown in Fig. 11, is used to define the control logic, for both upshifting and downshifting processes.The layout of the simulation model, including the automatic controller, is shown in Fig. 12.
For the transmission controller in Fig. 8, the clutch schedule is preprogrammed, i.e., the duration time for each transmission mode is prescribed, as shown earlier in this Subsection.Hence, the current vehicle velocity will not have any effect on the gear-shifting process.On the contrary, the controller in Fig. 12 is capable of realizing the real-time control for gear-shifting, in terms of the feedback from the current vehicle velocity.Hence, a real-time interaction between the transmission controller and the vehicle velocity leads to a more realistic vehicle operation.
The vehicle velocity and calculated gear ratios are plotted in Figs. 13 and 14(a), respectively.It can be seen that the The clutch states 0 and 1 denote disengaged and engaged, respectively.vehicle starts with a transmission ratio of 4. When the vehicle speed increases to 25 km/h at around 1.4 s, it shifts to the ratio 2.67.Then, at 2.6 s, the transmission shifts to a ratio of unity, i.e., direct drive mode, since the vehicle speed exceeds 45 km/h.The vehicle continues to accelerate.At around 5.5 s, the vehicle speed reaches 60 km/h, the transmission thus shifting to the ratio 0.3745 from the direct drive mode.After that, the vehicle speed continues to increase.When the vehicle speed reaches 80 km/h, at round 18.7 s, the vehicle shifts to the last transmission ratio, i.e., 0.25.Apparently, the simulation test shows an upshifting process, with all five speed ratios involved.During this test, the maximum velocity that the vehicle can reach is 94.96 km/h.It is apparent that the shifting process follows faithfully the control logic in Fig. 12.Moreover, this also can be validated by the clutch pressure signals obtained, as illustrated in 14(b).

CONCLUSIONS
The transmission of a modular type was proposed for use in electric vehicles of all sizes.Depending on class, power rating and required number of speed ratios, the transmission can be readily redesigned and modified by adding or removing extra planetary modules.Each module has two possible inputs and two possible outputs.Their serial combination makes up the full transmission, where the speed is smoothly controlled via the ring gears with the help of friction clutches, and by the smooth control of dual clutches installed at the input and the output of the transmission, as demonstrated in the presented simulation.
Due to the modular origins of the transmission and to the simplicity of the modules, its size and number of speeds can be readily modified and adjusted in the design process, depending on the required vehicle parameters.Because of modularity, such transmission is cheaper for production, manufacturing facilities readily adjustable to various transmission sizes.The transmission discussed is more compact than its predecessors [14], since the underdrive and the overdrive ratios are combined into pairs in corresponding modules.Therefore, the transmission itself is cheaper for manufacturing, smaller and easier for integration.Manufacturing facilities can be readily adjusted to various transmission sizes.

ACKNOWLEDGMENTS
The design and research work reported here was supported by grant under Automotive Partnerships Canada, APCPJ418901-11.
We also gratefully acknowledge the support of our industrial partners: Linamar, TM4 and Infolytica.The idea of using electric and hybrid technologies for medium and heavy trucks in recent years became quit ular among automotive manufacturers, and one of the potential sales categories for emerging hybrid and ba powered vehicles is the commercial delivery fleets.

Figure 2 :
Figure 2: Testbed of the five-speed transmission with double dual-clutches

Figure 3 :
Figure 3: Layout of the five-speed testbed of the multi-speed transmission with double dual-clutches

Figure 5 :
Figure 4: SimDriveline model of an electric vehicle powertrain equipped with the proposed 5-speed transmission (τi = 100 N m)

FIG. 10 :Figure 7 :
FIG. 10: Simulated gear ratios based on the actual testbed geometry (b) Figure 7: (a) Normalized clutch pressure signals; and (b) Simulated gear ratios based on the actual testbed geometry (τi = 100 N m)

Figure 8 :FIG. 3 :FIG. 4 :Figure 9 :
Figure 8: Simulation model of a complete vehicle with the proposed 5-speed transmission system

Figure 11 :
Figure 11: Stateflow chart of the clutch schedule for the transmission controller

Figure 12 :
Figure 12: Simulation model of a complete vehicle with the proposed 5-speed transmission system integrated with automatic transmission controller

Figure 13 : 1 INTRODUCTION
Figure 13: Vehicle velocity for the complete vehicle model with automatic transmission controller

Figure 14 :
Figure 14: (a) Speed ratio; and (b) Normalized clutch pressure signals for the complete vehicle model with automatic transmission controller

Table 1 :
Clutch schedule for the 5-speed transmission with double dual-clutch

Table 2 :
Vehicle parameters