Design,analysis,and experimental validation of a novel seamless automatic transmission for electric vehicle

Abstract

The transmission system has an important influence on the dynamic performance, endurance mileage, and energy saving in an all-electric vehicle. This article proposes an innovative two-speed seamless dry-friction automatic transmission system to improve the dynamic performance and endurance mileage of an all-electric vehicle with the existing battery technology. The proposed system consists of two-stage epicyclical gear sets without outer ring gears, a dry-friction clutch, and a brake band, realizes a seamless shifting between any two speeds in an electric vehicle. Based on the working principle and dynamic modeling of the proposed seamless dry-friction automatic transmission system, the ratio optimization was carried out to improve the dynamic performance and the power consumption at the same time, and the combination of the weight ratio method and the multi-island genetic algorithm method was introduced to solve the optimization problem. It is shown both theoretically and experimentally that the proposed seamless dry-friction automatic transmission method demonstrates a better dynamic performance and shifting comfort when compared to the automated manual transmission with same transmission ratio.

Keywords

Seamless auto transmission electric vehicle experiment simulation

Introduction

In the recent years, electric vehicle (EV) technology had been developed rapidly due to the air pollution problems and petroleum shortage. The EVs are usually equipped with a single-speed gearbox to minimize the cost, volumes, losses, and drive train mass.¹ However, EVs with a single-speed gearbox require high-performance traction motor and battery to meet the dynamic performance requirements such as maximum climbing slope, velocity, and acceleration. Compared to the single-speed gearbox transmission system, a two-speed gearbox transmission system with the characteristics of vehicle drivability and high efficiency seems to be a more suitable option for EVs.^2,3 For this reason, several types and structures of the two-speed gearbox transmission system are proposed for the drive train system of EVs. Among these two-speed transmissions, the simulation and experiments on the two-speed automated manual transmission (AMT) are studied,^4,5 and an inverse AMT with the dry clutch located at the rear of the transmissions is introduced to obtain a seamless gear shifting and to avoid the traction interruption of traditional AMT.^6–8 Also, a two-speed continuously variable transmission (CVT) and a two-speed dual-clutch transmission (DCT) were compared with the manual transmission (MT) using simulations on several standard drive cycles and found that both the two-speed DCT and simplified CVT improve the overall power train efficiency. However, each of the configurations has unique cost and energy consumption-related trade-offs.^9–11

Since the key requirements in an EV are least energy consumption and maximum possible endurance mileage, the AMT is of keen interest because of its lower weight and higher efficiency compared to other types of transmissions, such as automatic transmission (AT), CVT, and DCT.¹² However, a fundamental limitation of the AMT is the power interruption during gearshift due to the restriction of mechanism and principle. Hence, a two-speed transmission system with smooth gearshift and high efficiency is necessary and crucial for the EV transmission.¹³

To meet the desired dynamic performance and efficiency for the EV, this article presents a novel seamless dry-friction automatic transmission (SDAT), taking advantages of its mechanical construction and realizing seamless gearshift. The structure and work principle of the proposed SDAT system are introduced. Then, to fit a particular operating driving cycle of the vehicle, the gear ratios are optimized based on the vehicle simulation model using a method combining the weight ratio method and an intelligent optimization method. Finally, the experiments on an EV with SDAT are conducted, and the results show that the EV with SDAT has a seamless upshift.

The structure, working principle, dynamic modeling, and gear ratio optimization for the SDAT system

As mentioned above, the SDAT system has a significant influence on the characteristics of the EV. Hence, a novel SDAT system is proposed considering the basic requirements of EV. The structure, working principle, dynamic modeling, and gear ratio optimization for the SDAT system are presented in this section.

The structure of the proposed SDAT system

As shown in Figure 1, the power train system for EV mainly consists of a battery, motor, SDAT, and final drive. The SDAT comprises a two-stage epicyclical gear set without outer ring gears, as shown in Figures 1 and 2. In Figures 1 and 2, the SDAT system includes dry-friction clutch C, brake band B, input shaft, a front sun gear S1, a rear sun gear S2, carrier, and output shaft. The dry-friction clutch and the brake band are introduced to direct the power flow during the gearshift. The gearbox is divided into two parts. The wet part is used for decorating a planetary gear train, and the dry part is used for decorating the shift control components, such as clutch and brake band. Such design can avoid the quality of gear oil be affected by the wear debris from shift component, improving the operating life time of the gear. The dry-friction clutch is transplanted directly from the clutch of the conventional MT system, and the shift process becomes easier than the MT system since the synchronizer is absent. Therefore, the proposed SDAT has the characteristics of reliable operation and long service. By controlling the speed of the two sun gears, a fast and smooth gearshift is realized. To obtain a smooth gearshift in the brake-to-clutch gearshift of transmission, it is necessary to synchronize the incoming clutch as well as a precise pressure control for the engagement of the off-going brake band. The novel transmission connected to the electric motor and final drive can avoid the need for a torque converter, due to its relatively low efficiency.

Figure 1.

Schematic diagram of the power train system.

Figure 2.

A 3D exploded view diagram of gear set.

The working principle of the SDAT system

As shown in Figure 3, the gearshift for SDAT is easy to realize by controlling the working state of the clutch and the brake band. When the clutch C is disengaged and the brake band B is engaged, the SDAT works in the first gear; when the clutch C is engaged and the brake band B is disengaged, the SDAT works in the second gear; when the clutch C and the brake band B are both disengaged, the SDAT works in the neutral gear.

Figure 3.

Power transmission path: (a) power transmission in the first gear and (b) power transmission in the second gear.

To understand the working principle of SDAT, the kinematic relation among the front sun gear, the rear sun gear, and the carrier need to be examined in detail. The ratio between the front sun gear S1 and the rear sun gear S2 is proposed by the perspective of standing on the carrier (planetary gear train is simplified to fixed axis gear train) and is given as

i_{12}^{C} = \frac{ω_{s 1} - ω_{C}}{ω_{s 2} - ω_{C}} = - \frac{Z_{2}}{Z_{1}}

(1)

where $ω_{s 1}$ denotes the front sun gear speed, $ω_{c}$ is the carrier speed, $ω_{s 2}$ is the rear sun gear speed, $Z_{1}$ is the teeth number of the front sun gear, and $Z_{2}$ is the teeth number of the rear sun gear.

According to equation (1), the gear set of SDAT has 2 degrees of freedom, and two steps of gear ratios are possible by controlling the working state of clutch and brake band. Since the rear sun gear S2 is connected to the input shaft and the carrier to the output shaft, the gear ratio of the transmission (the ratio between the input speed and the output speed) can be expressed as

\frac{ω_{in}}{ω_{out}} = \frac{ω_{s 2}}{ω_{C}}

(2)

where $ω_{in}$ denotes the input speed of transmission and $ω_{out}$ is the output speed of transmission.

By examining equations (1) and (2), three different gear ratios can be achievable:

If the front sun gear is completely grounded by engaging the brake band $(i . e . ω_{s 1} = 0)$ , the first gear ratio can be obtained as

\frac{ω_{in}}{ω_{out}} = 1 + \frac{Z_{1}}{Z_{2}} = i_{1}

(3)

If the front sun gear and the rear sun gear are fixed together by engaging the clutch $(i . e . ω_{s 1} = ω_{s 2} = ω_{C})$ , the second gear ratio is obtained

\frac{ω_{in}}{ω_{out}} = 1 = i_{2}

(4)

If neither the clutch nor the brake band is engaged $(ω_{s 1} \neq 0, ω_{s 1} \neq ω_{s 2})$ , the neutral gear ratio can be obtained and is given as

\frac{ω_{in}}{ω_{out}} = 1 + \frac{Z_{1}}{Z_{2}} - \frac{Z_{1}}{Z_{2}} \frac{ω_{s 1}}{ω_{C}} = i_{g}

(5)

where $i_{1}$ and $i_{2}$ represent the first and the second gear ratios, respectively, and $i_{g}$ is the transient gear ratio during the gear shifting process.

Dynamic modeling of the power train system with SDAT

To carry out the ratio optimization task, it is necessary to build a simulation model which includes a driving cycle, energy storage, a vehicle control, and the power train system (as shown in Figure 4). The power train system consists of an electric motor, input shaft, SDAT, output shaft, final drive, and longitudinal vehicle dynamics, as shown in Figure 5. Due to the page constraints, this section only focuses on the model of the power train system with SDAT.

Figure 4.

Simulation model for the EV with SDAT.

Figure 5.

Block diagram of the power train system simulation model.

Dynamic modeling for motor and flexible input shaft

In this article, the input and output shafts of SDAT are modeled as spring–damp systems, and other components of the power train system are considered as rigid bodies. Thus, the electric motor is considered as a rotating rigid body, and its torque $T_{m}$ can be interpolated from a look-up table as a function of the accelerator pedal position $α_{p}$ and the motor rotational speed $ω_{m}$ ¹⁴

T_{m} = f (α_{p}, ω_{m})

(6)

Then, the equation for the elasticity of input shaft connecting the motor and SDAT can be written as

T_{m} = k_{is} (θ_{m} - θ_{s}) + c_{is} (ω_{m} - ω_{s 2})

(7)

where angle $θ_{m} - θ_{s}$ is the torsion angle of the flexible input shaft, $k_{is}$ is the elastic coefficient of the input shaft, and $c_{is}$ is the damping factor of the input shaft.

Dynamic modeling for SDAT

Equation (1) shows the kinetics of the two-stage epicyclical gear system under steady-state conditions. As shown in Figure 6, the dynamic equations of elements for the transmission system built according to the principle of virtual work are as follows

T_{m} - T_{CL} - R_{s 2} \sum_{j = 1}^{N} F_{s 2 p 2 j} = J_{s 2} {\overset{\cdot}{ω}}_{s 2}

(8)

T_{BR} + T_{CL} - R_{s 1} \sum_{j = 1}^{N} F_{s 1 p 1 j} = J_{s 1} {\overset{\cdot}{ω}}_{s 1}

(9)

R_{s 1} \sum_{j = 1}^{N} F_{s 1 p 1 j} + R_{s 2} \sum_{j = 1}^{N} F_{s 2 p 2 j} - T_{T} = J_{c 0} {\overset{\cdot}{ω}}_{c}

(10)

J_{p 1} {\overset{\cdot}{ω}}_{p 1} - J_{p 1} {\overset{\cdot}{ω}}_{c} = R_{p 1 j} F_{s 1 p 1 j} - R_{p 1 j} F_{p 2 p 1 j} (j = 1, 2, \dots, N)

(11)

J_{p 2} {\overset{\cdot}{ω}}_{p 2} - J_{p 2} {\overset{\cdot}{ω}}_{c} = R_{p 2 j} F_{s 2 p 2 j} - R_{p 2 j} F_{p 1 p 2 j} (j = 1, 2, \dots, N)

(12)

J_{c 0} = J_{c} + N m_{p 1} R_{C 1}^{2} + N m_{p 2} R_{C 2}^{2}

(13)

where $J_{s 1}$ , $J_{s 2}$ , $J_{c}$ , and $J_{c 0}$ denote the inertia of the front sun gear, the rear sun gear, the carrier, and the carrier with pinions, respectively; $J_{p 1}$ and $m_{p 1}$ denote the inertia and mass of the single long planet gear, respectively; $J_{p 2}$ and $m_{p 2}$ denote the inertia and mass of the single short planet gear, respectively; $R_{s 1}$ , $R_{s 2}$ , $R_{p 1}$ , and $R_{p 2}$ denote the front sun gear radius, the rear sun gear radius, the long planet gear radius, and the short planet gear radius, respectively; $R_{c 1}$ is the distance between the centers of the front sun gear and the long planet gear; $R_{c 2}$ is the distance between the centers of the rear sun gear and the short planet gear; $N$ is the number of long planet gears or short planet gears; $F_{s 1 p 1}$ is the meshing force between the front sun gear and the long planet gear; $F_{s 2 p 2}$ is the meshing force between the rear sun gear and the short planet gear; $F_{p 1 p 2}$ is the meshing force between the long planet gear and the short planet gear; and $T_{CL}$ , $T_{BR}$ , and $T_{T}$ denote the torque of clutch, brake band, and the output torque of SDAT, respectively.

Figure 6.

Block diagram of the transmission system.

Moreover, the kinematic relationship between the components of the two-stage planetary gear set is

R_{C 1} ω_{c} = R_{s 1} ω_{s 1} + R_{p 1} ω_{p 1}

(14)

R_{C 2} ω_{c} = R_{s 2} ω_{s 2} + R_{p 2} ω_{p 2}

(15)

According to equations (1) and (8)–(15), the overall dynamic equations of SDAT system can be obtained as

T_{m} + T_{BR} - T_{T} = J_{s 1} {\overset{\cdot}{ω}}_{s 1} + J_{s 2} {\overset{\cdot}{ω}}_{s 2} + J_{c 0} {\overset{\cdot}{ω}}_{c} = J_{1} {\overset{\cdot}{ω}}_{s 2} + J_{2} {\overset{\cdot}{ω}}_{c}

(16)

T_{m} - T_{CL} + \frac{R_{s 2}}{R_{s 1}} (T_{BR} + T_{CL}) = J_{3} {\overset{\cdot}{ω}}_{s 2} + J_{4} {\overset{\cdot}{ω}}_{c}

(17)

where

J_{1} = - J_{s 1} \frac{R_{s 2}}{R_{s 1}} + J_{s 2}

(18)

J_{2} = J_{s 1} (1 + \frac{R_{s 2}}{R_{s 1}}) + J_{c 0}

(19)

J_{3} = - J_{s 1} {(\frac{R_{s 2}}{R_{s 1}})}^{2} + J_{s 2} + {(\frac{R_{s 2}}{R_{p 1}})}^{2} J_{p 1} - {(\frac{R_{s 2}}{R_{p 2}})}^{2} J_{p 2}

(20)

\begin{array}{l} J_{4} = \frac{R_{s 2}}{R_{s 1}} J_{s 1} (1 + \frac{R_{s 2}}{R_{s 1}}) + \frac{R_{s 2}}{R_{p 1}} J_{p 1} (\frac{R_{c 1}}{R_{p 1}} - 1) \\ + \frac{R_{s 2}}{R_{p 2}} J_{p 2} (\frac{R_{c 2}}{R_{p 2}} - 1) \end{array}

(21)

For the SDAT system proposed in this article, the clutch connecting the front sun gear and the rear sun gear is same as the conventional single-plate dry clutch type. Thus, the relation between the normal applied force on the plate $F_{CL}$ and the resulting torque is¹⁴

T_{CL} = - μ_{p} F_{CL} \frac{2}{3} (\frac{R_{o}^{3} - R_{i}^{3}}{R_{o}^{2} - R_{i}^{2}}) sign (ω_{S 2}), F_{CL} \geq 0

(22)

where $μ_{p}$ is the coefficient of friction between the plates and $R_{i}$ and $R_{o}$ denote the inner and outer radii of the friction plate, respectively.

In this article, the brake of the front sun gear is designed to be of dry band brake type. As a result, the relationship between the applied normal force at the end of the band $F_{BR}$ and the resulting torque is

T_{BR} = {\begin{matrix} - F_{BR} R_{D} (e^{μ_{D} θ_{D}} - 1), ω_{s 1} \geq 0, F_{BR} \geq 0 \\ F_{BR} R_{D} (1 - e^{- μ_{D} θ_{D}}), ω_{s 1} < 0, F_{BR} \geq 0 \end{matrix}

(23)

where $R_{D}$ is the radius of the drum brake, $μ_{D}$ is the friction coefficient between band and drum, and $θ_{D}$ is the angle of wrap.

In equation (22), the positive rotational direction of brake band is considered as the energizing mode of the band brake.

According to equations (16) and (17), the gear shifting process can be divided into torque phase and inertia phase for analysis.¹⁵ During the shift process, a coordinated control of the clutch, brake band, and the motor is the key to realize seamless shift and change the SDAT output torque smoothly.

Dynamic modeling for final drive and longitudinal vehicle dynamics

Since the output shaft is modeled as a spring–damp system, the output torque of SDAT is expressed as

T_{T} = k_{os} (θ_{T} - θ_{os}) + c_{os} (ω_{T} - ω_{os})

(24)

where angle $θ_{T} - θ_{os}$ is the torsion angle of the flexible output shaft, $k_{os}$ is the elastic coefficient of output shaft, $c_{os}$ is the damping factor of output shaft, and $ω_{os}$ is the speed at the end of output shaft next to the final drive, and the relationship between $ω_{os}$ and the wheel speed $ω_{w}$ is

ω_{os} = i_{fd} ω_{w}

(25)

Then, using the torque balance equation and lumped mass method,¹⁶ the longitudinal vehicle dynamics can be expressed as follows

{\overset{\cdot}{ω}}_{w} = \frac{i_{fd}}{J_{v}} T_{T} - \frac{1}{J_{v}} T_{v}

(26)

where $J_{v}$ is the combined inertia of the vehicle and wheels, $i_{fd}$ is the final drive ratio, and $T_{v}$ is the resisting torque on the vehicle that can be calculated as follows

T_{v} = T_{wind} + T_{roll} + T_{slope}

(27)

where $T_{wind}$ , $T_{roll}$ , and $T_{slope}$ are the resisting torques from wind, rolling, and slope, respectively, and can be calculated as follows

T_{wind} = R_{w} \frac{C_{D} A_{f}}{21.15} u_{v}^{2}

(28)

T_{roll} = R_{w} m_{v} g \sin (θ_{road})

(29)

T_{slope} = R_{w} f_{roll} m_{v} g \sin (θ_{road})

(30)

where $R_{w}$ is the dynamic radius of the wheel, $C_{D}$ is the frontal area of vehicle, $A_{f}$ is the drag coefficient of vehicle, $m_{v}$ is the mass of vehicle, $g$ is the acceleration due to gravity, $θ_{road}$ is the angle of road slope, and $u_{v}$ is the velocity of vehicle that can be calculated from the following relation

u_{v} = R_{w} ω_{w}

(31)

By combining equations (6), (7), (17), (25), and (26) together, the full-state dynamics of the system are given as follows

{\begin{matrix} T_{m} = k_{is} (θ_{m} - θ_{s}) + c_{is} (ω_{m} - ω_{s 2}) \\ {\overset{\cdot}{ω}}_{s 2} = \frac{J_{4}}{J_{1} J_{4} - J_{2} J_{3}} (T_{m} + T_{BR} - T_{T}) + \frac{J_{2}}{J_{1} J_{4} - J_{2} J_{3}} \\ [T_{m} - T_{CL} + \frac{R_{s 2}}{R_{s 1}} (T_{BR} + T_{CL})] \\ {\overset{\cdot}{ω}}_{c} = \frac{J_{3}}{J_{2} J_{3} - J_{1} J_{4}} (T_{m} + T_{BR} - T_{T}) + \frac{J_{1}}{J_{2} J_{3} - J_{1} J_{4}} \\ [T_{m} - T_{CL} + \frac{R_{s 2}}{R_{s 1}} (T_{BR} + T_{CL})] \\ T_{T} = k_{os} (θ_{T} - θ_{os}) + c_{os} (ω_{T} - ω_{os}) \\ {\overset{\cdot}{ω}}_{w} = \frac{i_{fd}}{J_{v}} T_{T} - \frac{1}{J_{v}} T_{v} \end{matrix}

(32)

The full-state dynamics of the system was applied in the EV simulation in the next section.

The gear ratio optimization for the SDAT system

To improve both the dynamic performance and power consumption for EV, finding the desired values of $i_{1}$ and the final drive gear ratio $i_{0}$ becomes a multi-objective optimization problem. At present, the methods to solve the multi-objective optimization problem mainly include conventional methods and intelligent optimization methods.¹⁷ The conventional methods, such as the weight ratio method, tend to transform the multi-objective optimization problem into a single-objective optimization problem. Obviously, such method is of highly computationally efficient, but it depends on the designer’s experience, and the optimal results are not always guaranteed. To solve the multi-objective optimization problem effectively, this article uses the combination of weight ratio method and the intelligent optimization method. Here, the multi-island genetic algorithm (MIGA) is used for solving the multi-objective optimization problem. For this mission, an EV with the parameters shown in Table 1 is selected as the target vehicle to formulate the optimization problem. The main constraints of optimization are the dynamic performance (Table 2) and high efficiency requirements. The optimization flowchart is shown in Figure 7.

Table 1.

The main parameters of the electric vehicle for ratio optimization.

Components	Parameters	Values
Vehicle body	Curb mass (kg)	9800
	Gross mass (kg)	13,500
	Frontal area (m²)	7.0
	Drag coefficient	0.6
	Rolling radius (m)	0.436
	Final drive gear ratio	$i_{0}$
Battery pack	Rated capacity (AH)	258
	Rated voltage (V)	537
Motor	Rated/peak power (kW)	80/160
	Peak speed (r/min)	4000
	Peak torque (N m)	900

Table 2.

The dynamic performance requirements.

Name	Value
Maximum speed (km/h)	≥100
Maximum slope at 10 km/h vehicle speed (%)	≥20
0–50 km/h acceleration time $t_{50}$ (s)	≤20

Figure 7.

The flowchart of MIGA optimal calculation.

In the optimization process, the weight ratio method was adopted to obtain the dynamic performance objective function from the 0–50 km/h acceleration time, the maximum velocity, and the peak slope. Here, the weight ratio for the acceleration time is 0.7, the weight ratio for the peak slope is 0.2, and the weight ratio for the maximum velocity is 0.1. In addition, the economic objective function was obtained based on the power consumption per kilometer under certain driving cycle. Then, the iterative calculations were carried out using the MIGA method. The optimization objectives and constraints are listed below

Min {\begin{matrix} F_{1} (x) = PC_fator = \frac{E_{100}}{100} \\ F_{2} (x) = D_fator = 20 \frac{G_{\max} - G_{\max}^{*}}{G_{\max}^{*}} + 10 \frac{u_{\max} - u_{\max}^{*}}{u_{\max}^{*}} \\ + 70 \frac{t_{50}^{*} - t_{50}}{t_{50}^{*}} \end{matrix}

(33)

X = [x_{1}, x_{2}] = [i_{0}, i_{1}]

(34)

s . t . G (x) = {\begin{matrix} g_{1} (x) = G_{\max}^{*} - G_{\max} \leq 0 \\ g_{2} (x) = u_{\max}^{*} - u_{\max} \leq 0 \\ g_{3} (x) = t_{50} - t_{50}^{*} \leq 0 \\ g_{4} (x) = F_{t} - F_{φ} \leq 0 \end{matrix}

(35)

where $F_{1} (x)$ and $F_{2} (x)$ are the first and second objective functions, respectively; $PC_fator$ is the electric power consumption per 100 km; $E_{100}$ is the total power consumption during 100-km driving cycle; $D_fator$ is a dynamic performance factor; $G_{\max}^{*}$ is the design value at peak slope on the first gear; $G_{\max}$ is the actual value at peak slope; $u_{\max}^{*}$ is the design value at maximum speed; $u_{\max}$ is the actual value at maximum speed; $t_{50}^{*}$ is the design value at 0–50 km/h acceleration time; $t_{50}$ is the actual value for 0–50 km/h acceleration time; drag coefficient of vehicle; $F_{t}$ is the maximum driving force; and $F_{φ}$ is the maximum adhesion of road surface.

MIGA is an advanced version of the genetic algorithm (GA) of parallel distribution, which has not only a better ability to obtain a global solution but also computationally efficient than the conventional GA. According to the rule of “survival of the fittest” in the process of biological evolution, the GA encodes optimization problem solution space of the individual and takes the encoded individual populations into genetic operations (such as selection, crossover, and mutation). Finally, the optimal solution or the combination of the optimal solution can be found through iterations. MIGA divides a large population into a number of subpopulations, called “island,” and uses conventional GA algorithms on each island to carry out subpopulation evolution. The parameters of MIGA are shown in Table 3.

Table 3.

The parameters of multi-island genetic algorithm.

Name	Value
Value range: $i_{0}$	2.1 < i₀ < 6.2
Value range: $i_{1}$	2.0 < x < 2.2
Default variable bound (absolute value)	1000.0
Migration interval	5
Number of generations	10
Number of islands	10
Random seed value	−1
Rate of crossover	1.0
Rate of migration	0.01
Rate of mutation	0.01
Rel tournament size	0.5
Subpopulation size	10

The calculation results for dynamic and power consumption factors are shown in Figure 7. Then, the optimal ratios for $i_{1}$ and $i_{0}$ are selected from the Pareto solution set. The calculated results of the state point $i_{1} = 2.16$ and $i_{0} = 2.8$ are 0.126 for dynamic factor and 0.522 for power consumption factor. The calculated results of the optimal point $i_{1} = 2.18$ and $i_{0} = 6.19$ are 0.139 for dynamic factor and 0.514 for power consumption factor (Figure 8).

Figure 8.

The iterative results of optimization target: (a) calculated history of dynamic factor and (b) history of power consumption factor.

Using the obtained optimal design point, the characteristics of acceleration and peak slope are shown in Figure 9. As shown in Figure 9(a), the peak slope changes with the speed of EV. For example, the peak slope is 21.8% when the EV is operating at 10 km/h. It can also be observed from this figure that the current velocity changes as the acceleration time increases. For example, the 0–50 km/h acceleration time of the EV is about 17.5 s. The maximum velocity of EV in the simulation is about 103 km/h. Under the NEDC.aut driving cycle, the power consumption is about 0.52 kW h/km at the optimal design point. The velocity tracking feature in Figure 10 shows that the current velocity can follow the desired velocity from driving cycle, which means that the dynamic performance satisfies the driving cycle demand.

Figure 9.

Dynamic characteristic for EV at the optimal design point: (a) characteristics of peak slope and (b) characteristics of acceleration.

Figure 10.

Velocity tracking feature in NEDC.aut.

Experimental verification on the vehicle with novel SDAT

After understanding the design and analysis of the proposed SDAT in the previous sections, the seamless shift process was verified by real EV test. As shown in Figure 11, the results from a real driving cycle were obtained from the experiment on the EV with SDAT. Data collection for the motor speed and velocity from the test carried out on EV is presented in Figure 12. The gear shifting characteristics of a upshift process for the EV with AMT is shown in Figure 13, whereas the proposed SDAT method is shown in Figure 14. Based on the test results shown in Figures 12 –14, it can be concluded that the vehicle with SDAT has a seamless upshift since the velocity increases steadily during the shifting process, but the vehicle with AMT does not have such smooth shift characteristics. It is worth mentioning that the power consumption per kilometer is about 0.53 kW h/km, and the upshift time is about 0.5 s for SDAT, as shown in Figure 15. As stated earlier, the power consumption obtained in simulations is about 0.52 kW h/km, the simulation accuracy is verified by the experiment result.

Figure 11.

The gearshift and power consumption test: (a) the novel SDAT, (b) the vehicle with SDAT for test, (c) data acquisition software for test and (d) additional weight for test.

Figure 12.

Some data from the real velocity test.

Figure 13.

Upshift process of the real velocity test with AMT.

Figure 14.

Upshift process of the real velocity test with SDAT.

Figure 15.

Gear shifting curve in the test.

Conclusion

This article proposed a novel two-speed seamless transmission with two-stage epicyclical gear sets, a dry-friction clutch, and a brake band. By choosing the optimal design point ( $i_{1} = 2.18$ and $i_{0} = 6.19$ ), the maximum velocity, the peak slope, and 0–50 km/h acceleration time of target EV are about 130 km/h, 21.8% at 10 km/h, and 17.5 s, respectively. For the NEDC.aut driving cycle, the power consumption is about 0.52 kW h/km, and the velocity can follow the driving cycle demand. Based on the experimental data analysis, the upshifting time for SDAT is about 0.5 s with the best power consumption of 0.53 kW h. As compared with the vehicle with AMT, the vehicle with SDAT has achieved a seamless shifting characteristic.

Footnotes

Handling Editor: Haiping Du

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or /publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the financial support from the Fujian Science and Technology Agency (2016H6009 & 2015J01179) and the Nature Science Foundation of China (51275092 & 51505085).

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