1. Introduction
With the increase in global energy consumption and the aggravation of natural environment pollution, the adoption of new energy vehicles to replace traditional fuel vehicles has become a global consensus and is being gradually implemented. Pure electric vehicles, as the mainstream products of new energy vehicles, are undergoing continuous technological evolution. Apart from the research on improving battery technology, realizing better energy saving is also a hot issue in the research and development of electric vehicles. Energy saving means a higher mileage range under the same condition. The works on energy saving include an energy-efficient control allocation scheme for dual-actuation electric motors (driving or regenerative braking dual modes) [
1], energy-efficiency optimization allocation based on a motor efficiency map to reduce motor power losses and obtain energy recovery [
2], predictive driving control strategy based on optimal control theory and traffic preview information [
3], energy-efficient optimal control based on dynamic traffic information flow [
4], slide mode control based chassis energy efficiency and driving performance comprehensive control strategy [
5]. Besides the energy-saving aspect, the dynamic performance of electric vehicles, especially small pure electric vehicles, is also another issue that users concern about. Better dynamic performance and energy efficiency have been the desired indicators for small pure electric vehicles. Apart from the above-mentioned energy-efficient control methods, optimizing the powertrain, e.g., power matching and multi-gear transmission, etc., is an additional approach to improve energy saving as well as dynamic performance. The related research is as follows. Ning et al. put forward a comprehensive optimization matching method for the powertrain using traditional longitudinal dynamics to match the electric power system for the drive system and adopting cut-and-try approach for the energy storage system [
6]. Gao et al. proposed a new type of 2-speed inverse automated manual transmission (I-AMT) [
7], and they further studied the shift control after optimizing the gear ratio using dynamic programming methods and realized the smooth shift process without a torque hole. Fang et al. proposed a new two-speed uninterrupted mechanical transmission (UMT), which can realize seamless switching between two gears [
8]. The control system based on a fuzzy logic controller (FLC) detects the driver’s intention according to the speed and gas pedal position signals. Fu proposed a continuous variable transmission (CVT) configuration based on an electric oil pump (EOP) for electric vehicles and constructed a dynamic model of electric vehicles equipped with CVT [
9]. Liu et al. designed a kind of two-speed AMT without a clutch and synchronizer, established the shift dynamics model and the shift-motor model, and controlled the motor and shift time, which reduced the power consumption [
10]. He et al. established a hybrid electric vehicle model and proposed control strategies for the electric motor and engine to achieve clutchless shift control, which effectively improves the shift quality of the vehicle [
11]. Liu et al. proposed a coordinated control strategy for two-speed clutchless AMT based on model predictive control (MPC), which effectively improved shift smoothness [
12]. Because the motor has a good speed-torque characteristic in a large range compared with the engine, as well as the reasons of cost and operating expense, the general pure electric vehicle is only equipped with the transmission with sngle fixed ratio transmission at present. Although it can meet the common requirements of starting, low speed, high speed and other working conditions, there is still much room for improvement. It has become a research direction to improve vehicle performance by adding multi-speed transmission.
Hu et al. proposed a two-speed automatic mechanical transmission for pure electric vehicles, and the test on the two-speed gearbox test bench showed that the ride comfort of the proposed shift-control strategy reached the bus standard [
13]. Qin et al. analyzed the shifting process of a pure electric vehicle equipped with a two-speed automatic mechanical transmission without a clutch and proposed a control strategy that can achieve smooth, reliable and fast shifting for electric vehicles [
14]. In addition, Jaehoon et al. proposed an optimized design method for a lightweight two-speed transmission for electric vehicles [
15], which can improve transmission efficiency through the optimal design of gear train. Angeles et al. designed a new multi-speed transmissions (MSTs) shift control scheme and proposed a two-stage control algorithm to make the electric vehicle shift more smoothly [
16]. Eckert et al. proposed a multi-objective optimization method for design variables such as gear ratio, number of gears, differential ratio, tire size and shift control of an automatic transmission, which improved its economic efficiency and power performance [
17]. Hu et al. proposed dynamic programming(DP)-based optimization method of gear shift schedule for electric buses equipped with 4-AMT to improve the energy economy [
18]. Liang et al. proposed a gear-shifting control strategy for pure electric vehicles with inverse automated manual transmission (I-AMT) to improve the dynamic performance of pure electric vehicles [
19].
To summarize, most of the current research focuses on the design of transmission structure, the shifting smoothness and the mechanical efficiency improvement, whereas the matching design method of an electric vehicle equipped with multiple-gear transmission and its improvement in performance and efficiency of an electric vehicle is less studied and verified. The motivation of this work is to investigate the dynamic performance and energy efficiency when the two-speed gear shifting is optimized to the best status and to assess the application value of two-speed transmission in pure electric vehicles. In this paper, the power-matching design of a small electric car equipped with two-speed gear shifting is carried out based on the application background of a small electric car, and the optimization is done for the purpose of economy and dynamic performance. Particle swarm optimization has been proven to be effective and applied to solve various kinds of optimization problems [
20]. For the above optimization, particle swarm optimization is employed for its higher precision or easier realization compared with GA, DE and other meta-heuristic algorithms [
21]. The model of this electric car is established, and the efficiency and performance improvement effect of the electric car to be equipped with optimal gear shifting is investigated based on the current typical electric vehicle test cycles. The contribution of this work is that it presents a detailed evaluation of the possible maximal dynamic performance and energy efficiency improvement of a pure electric car with multiple shifting gears by optimization, and the resultant data and conclusions are of some references for the multiple-gear electric car design.
2. Power Matching of Pure Electric Car
The pure electric car developed in this paper is a small passenger car that is positioned for short-distance driving within cities, towns, or local areas. Based on this demand, the multiple-gear shifting automatic transmission and other parameters are matched and designed for the whole car. Because the permanent magnet synchronous motor (PMSM) has the characteristics of small space volume, flexible and simple structure, and stable and convenient control, it is also the mainstream driving scheme in the present pure electric car market, so the permanent magnet synchronous motor is selected as the driving motor type in this paper.
If the parameters of the pure electric car powertrain are reasonably matched, the advantages of each component can be fully utilized so that the whole car can overcome the resistances such as wind resistance, rolling resistance, air resistance, and acceleration resistance and simultaneously meet the design indexes of power performance and economy. For the parameter matching of the powertrain of the pure electric car, the parameters of battery, motor, and main reducer should be calculated mainly according to the design indexes such as maximum speed, maximum gradability, acceleration time, and mileage range of the car. The design requirements for the electric car in this paper are shown in
Table 1.
Electrically controlled automatic mechanical transmission has a low cost, simple structure, less failure rate, and cheap maintenance advantages, so the two-speed gear-shifting automatic mechanical transmission scheme is adopted, and the specific powertrain system structure of the electric car is shown in
Figure 1, which consists of three pairs of gears and two shafts, in which gear pair 1 and 2 are for low-speed shift, and gear pair 3 and 4 are for high-speed shift. Gear pairs 5 and 6 form a reverse shift, and the reverse movement is realized by reversing the rotation direction of the motor. Due to the diversity of operating conditions of cars, the motor applied to pure electric cars has the following characteristics: it can adapt to frequent start, stop, acceleration and deceleration, torque dynamic change, and other operating conditions, and it can also provide large torque at a low-speed case and high rotation at high speed case. The main calculation parameters for motor selection include maximum torque, rated power, maximum power, and maximum speed.
Firstly, according to the driving conditions of the car, the driving force demand of the pure electric car is calculated as
where
is the driving force,
is the car gravity,
is the rolling resistance coefficient,
is the climbing angle,
is the air resistance coefficient,
is the windward area,
is the driving speed,
is the rotating mass conversion coefficient,
is the car mass, and
is time.
The motor power is determined based on the maximal designed speed. When the car is running at the maximum speed, the road is level without gradient, so only the resistance generated by air and tires needs to be calculated. The power demand is given by
where
is the transmission efficiency,
is the power required,
is the acceleration of gravity, and the meanings of other parameters are the same as above.
When the electric car is running on the road with a gradient, the acceleration is 0, the acceleration resistance is also 0, and the power demand
is given by
When under acceleration conditions, the car power balance equation is given by
where
is the power required, and
is the post-acceleration speed.
The minimal transmission ratio (corresponding to Gear II) should ensure that the car can reach the expected maximal speed, and the power output of the motor should be able to overcome the driving resistance when running at the maximum speed. The corresponding inequalities are given by
where
is the minimal value of the total transmission ratio of the electric car,
takes the the values of 1 and 2 which denote the transmission and the main reducer respectively, namely
denoting the gear ritio of the tramsmission and
denoting the gear ritio of the reducer,
is the maximum speed of the motor,
is the wheel radius, and
is the peak torque of the motor.
According to Equations (5) and (6), the range of the minimum transmission ratio is .
The maximal transmission ratio (corresponding to Gear I) is determined by considering its gradability and low-speed performance, and its calculation formula is given by
where
is the maximal value of the total transmission ratio of the electric car, and the meaning of subscript
is same as the above.
is the running resistance,
is the peak torque,
is the rolling resistance,
is the slope resistance, and
is the air resistance.
According to the above equations, the initial matching of the transmission ratio is completed in
Table 2.
According to the above calculation results, a certain model of PMSM is selected as the driving motor, the specific parameters is shown in
Table 3, and its efficiency map is presented in
Figure 2. The motor efficiency data revealed by
Figure 2 are stored in a two-dimensional table for further calling in the simulation experiment section.
Compared with other power batteries, lithium batteries have a higher energy density, can be quickly charged, have a long cycle life, and have a high safety factor. In this paper, the lithium battery is selected, and the high-voltage platform is selected. The energy required for the mileage range S of the pure electric car can be calculated by the constant speed method and the working condition method. In the preliminary design, the constant speed method is used for the theoretical calculation of the endurance range, so the resistance power and the energy consumption of the whole car when the pure electric car runs at the constant speed
are given by
where
is the power required for constant speed driving,
is the driving mileage,
is the energy required for the driving mileage
, and
is the travel speed.
Assuming that the effective capacitance coefficient of the power battery pack is 0.9, the energy of the power battery
meets the following conditions:
. Substituting the
value determined by Equation (9) to this inequality obtains
. Because the power battery of pure electric cars in the market all use standard boxes, this paper uses a single battery series to form a standard box and selects several standard boxes in parallel to form the power battery. According to the mileage range and motor voltage requirements, the ternary lithium power battery parameters are selected, as shown in
Table 4.
The system block diagram and the simulation model are further established as shown in
Figure 3 and
Figure 4, respectively. It is noted that in this paper the simulation model part is established in Simulink, and the subsequent algorithm part is realized with Matlab programing language in m file form to ensure the two parts into a seamless joint.