Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission

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1 Automotive Innovation (2018) 1: Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission Xiangyang Xu 1,2 Wenbo Sun 1,2 Tianyuan Cai 1,2 Yanfang Liu 1,2 Xiao Han 1,2 Received: 12 August 2018 / Accepted: 3 November 2018 / Published online: 1 December 2018 China Society of Automotive Engineers(China SAE) 2018 Abstract Two-speed automatic transmission is one solution to increase the economic efficiency and dynamic performance of battery electric vehicles (BEV). Hydraulic control unit (HCU) is a key component in automatic transmissions, which determines the quality of shifting directly. Based on the structural scheme and shift logic of a two-speed dedicated electric vehicles transmission (2DET) with two wet clutches, we designs a 2DET hydraulic control unit composed of three subsystems: pressure regulating and flow control system, shift operated and control system and cooling and lubrication system. The results of the experiments, including the valve body bench test, transmission bench test and vehicle test, show that the design of hydraulic control unit meets the requirements. Keywords Battery electric vehicle Automatic transmission Hydraulic control unit Dynamic simulation Abbreviations BEV HCU 2DET Battery electric vehicle Hydraulic control unit Two-speed dedicated electric vehicle transmission 1 Introduction With energy shortages and environmental pollution becoming ever more serious, battery electric vehicles (BEVs) occupy an increasingly important position in the current market because of their superior energy-saving and environmentally friendly features. Many companies and universities have carried out research on the power characteristics of batteries, charging technology, powertrains and electronic control systems for BEVs. Most BEVs currently on the market, including the BAIC EU260, Tesla Model S and BYD e6, are equipped with a B Yanfang Liu liuyf@buaa.edu.cn 1 School of Transportation Science and Engineering, Beihang University, Beijing , China 2 Beijing Key Laboratory for High-efficient Power Transmission and System Control of New Energy Resource Vehicle, Beihang University, Beijing , China single-gear reducer [1]. Our simulation analysis results show that utilizing a two-speed automatic transmission can both markedly lower the requirements for the motor in the electric vehicle while not significantly increasing the complexity or cost of the powertrain and will keep the motor working in a more efficient operating range. Shifting gear improves the economic efficiency and dynamic performance of the entire vehicle by more than 10% [2]. Oerlikon Graziano of Italy has developed a two-speed transmission designed for a small electric vehicle. AVL, an engineering company based in Austria, has designed a two-speed automatic transmission with fixed-shaft gears and the German branch of GKN, a British global engineering group, has also designed a two-speed automatic transmission based on synchronizer shifting that is currently being used on the BMW i8 hybrid sports vehicle. Prof. Song Jian from Tsinghua University has developed a new type of dual-block uninterrupted mechanical transmission (UMT) with simple planetary rows, centrifugal friction clutches and band brakes that is not yet in mass production. The paper is organized as follows. Section 2 introduces the structure of our two-speed dedicated electric vehicle transmission (2DET) and outlines the design concept proposed firstly in [3]. Section 3 presents the parameter design of the hydraulic control unit (HCU). Section 4 describes the three-dimensional modeling of the hydraulic valve body, and Sect. 5 presents the simulation results from the SimulationX software of Germany. Sections 6 and 7 describe the experi-

2 Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission C1 0 C Fig. 2 Schematic of the design of the 2DET Fig. 1 Transmission schematic of the 2DET Table 1 Shift pattern of the 2DET Speed Clutch C1 C2 R N 1 2 mental results of the bench tests and vehicle tests. Section 8 presents our conclusions. 2 Design Concept for the HCU and 2DET Figure 1 shows the structure of the 2DET. Only two multidisk wet clutches are used as the shift elements. With clutch C1 or clutch C2 engaged, power is transmitted to the intermediate shaft via gear set 3 or gear set 4 to obtain two different speed ratios. All simple shifts can be performed by changing the two shift elements (shown in Table 1). For reverse gear, clutch C1 is engaged and first gear selected, and the motor rotates in reverse. The HCU in the 2DET must meet the following requirements [4 7]. (1) The automatic shift function must be guaranteed. The HCU receives information on the actual working conditions and controls the shift solenoid valve that controls the position of the shift valve s spool and activates separation and engagement of the clutch. (2) Sufficient cooling and lubrication flow for each transmission system must be provided and the flow must be distributed to ensure an appropriate oil pressure in the main line and other systems. (3) Safety must be taken into consideration to prevent the transmission from hanging when two gears are engaged at the same time. When the electronic control system fails, the HCU should be able to avoid invalidation; that is, the car should be able to work even if the electronic control system fails. Figure 2 shows a schematic of the 2DET hydraulic control system we have designed to satisfy the above three design requirements. Table 2 shows the components of each subsystem in the HCU and the functions of each component. DAV_1 and DAV_2inFig.3 are two large flow solenoid valves [8 12] that directly control the oil pressure to the clutches. These valves must be designed to meet the requirements of the clutches. Compared with the two-stage valve structure used in the conventional hydraulic system of an automatic transmission consisting of a proportional valve and a mechanical valve, adopting large flow solenoid valves simplifies the structure of the valve body and improves the rate of response and the accuracy of shift. Valve SV_1 consists of a solenoid valve and a mechanical valve and is not activated when the HCU is operating normally. However, when there is a fault in the HCU, it is designed to cut off the oil circuits for clutch C2 to ensure that two gears are not engaged at the same time. 3 Parameter Design Figure 4 shows a flowchart of the detailed development process of the HCU for an automatic transmission. First, the design objectives of the vehicle should be specified, and the relevant requirements and the design parameters of the 2DET should be determined to match the performance requirements of the powertrain, including the design of the mechanical and electronic systems that will directly determine the design requirements of the HCU as well as the overall space boundaries that will affect the layout of the HCU.

3 302 X. Xu et al. Table 2 Subsystem components of the HCU Subsystem Components Function Pressure regulation and flow Filter Keeps hydraulic oil clean control Electronic oil pump Supplies the oil to HCU Accumulator D_A Reduces fluctuations in the main oil pressure Valve HP_CV Regulates the main line pressure Cooling and lubrication Valve OF_CV Cooperate to regulate the flow of Long throttle hole Cooling and lubrication orifice cooling and lubrication according to the actual needs of the gearbox Shift operation and control DAV_1\DAV_2 Controls the clutches Valve SV_1 Prevents the transmission from hanging when two gears are engaged simultaneously One-way valve Opens when disengaging the clutch Wet clutches C1\C2 Carry out the shift Vehicle design objectives Mechanical system design requirements Electronic system Space limit Mechanical system design HCU design requirements Function definition Fig. 3 Direct shift control Cooling and lubrication flow HCU principle design Clutch design Cooling and lubrication flow Shift flow Shift pressure HCU spatial arrangement The design of the mechanical system of the automatic transmission includes design of the gears and selection of the components. According to the actual design scheme, the requirements for the cooling and lubrication flow of the HCU raised by the internal working friction pairs of the clutches can be obtained. The design of the electronic system includes the shift logic, safety mode and regulatory requirements. The overall design of the HCU is determined by its design requirements, which are based on the design requirements of the mechanical and electronic systems. The clutch is the main control object in the hydraulic system. The total flow and oil pressure requirements for the HCU in the transmission can be obtained by calculating the cooling and lubrication flow demand for clutches, shift flow demand and shift oil pressure demand of the hydraulic system combined with the cooling and lubrication flow demands of the mechanical friction pairs. This allows the component design, HCU structure design, hydraulic valve body layout and oil circuit design to be decided in sequence. After the hydraulic valve body design has been completed, its strength needs to be analyzed. When the strength condi- Total cooling and lubrication Flow verification Total flow Components design of HCU HCU structure Hydraulic valve body layout Oil circuits design Strength analysis Valve body test Transmission test Fig. 4 HCU development process Structure optimization verification tion is met, valve body tests and structural optimization can be carried out simultaneously. Tests are performed to verify the design of the mechanical and hydraulic systems, and if

4 Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission 303 there are problems, design modifications are made until the hydraulic system meets the design requirements. 3.1 Clutch Design The 2DET uses two identical wet clutches, which are the main control objects in the hydraulic control system. The total flow and oil pressure demand for the entire hydraulic control system is obtained by calculating the shift flow demand, the shift oil pressure demand and the cooling and lubricating flow demand for clutches combined with the mechanical system cooling and lubricating flow demand. The detailed design of the HCU can then proceed. Equations (1) (8) are formulas for calculating the clutch-related parameters [13]. F n T max r m μ (1) F clamp F n Z R (2) P k F clamp A k (3) P e F seal + F smax A k (4) P P k + P e (5) { sp s sum + s sin (6) s sum Z R s V oil s p A k (7) Q flow V oil t s min (8) where F n is the total pressing force, Tmax is the maximum torque that needs to be transmitted, r m is the equivalent radius of the friction plate, μ is the friction coefficient, F clamp is the maximum pressing force each friction plate actually receives, Z R is the number of friction plates, A k is the cylinder piston area, P k is the oil pressure at nominal torque, P e is the piston pressure to balance the spring and friction, F seal is the sealed friction, F smax is the maximum spring force, s p is the total piston stroke, s sin is the stroke of the reset spring, s is the separation distance of a single friction plate, V oil is the volume of hydraulic fluid needed for engagement and Q flow is the maximum volume flow required. Calculation and analysis give the required maximum oil filling flow for the 2DET as 4.3 L/min. The clutch requires an oil pressure of 12 bar to transmit a torque of 300 Nm. To prevent the oil pressure generated by the HCU from being too high and damaging the clutches, the hydraulic pressure safety system is designed to activate at 20 bar. 3.2 Flow Distribution for the Cooling and Lubrication System Clutch Cooling and Lubrication Flow The flow required for clutch cooling and lubrication is determined by Eqs. (9) (11) [12]. Q gen M k (ω 10 ω 20 ) (9) ( Q gen (ω 10 ω 20 ) M k 1 t ) dt (10) t s Q oil Q gen A (11) k where Q gen is the heat produced by the clutch sliding friction, M k is the friction torque during clutch engagement, ω 10 and ω 20 are the angular velocities before and after the clutch is engaged, k is the coupling coefficient and A is the clutch friction plate engagement area. Because the two clutches in this project are identical, the total lubrication flow required by the clutches is 3 L/min Bearing Cooling and Lubrication Flow For the bearing, using the calculated rotational speed that can be achieved as the calculation condition, the required flow for cooling and lubrication is determined by Eqs. (12) (14)[12]. Q gen k 4n M (12) M k 1 G 1 (nμ) 0.62 (P ) 0.3 eq (13) Q gen Q oil k b (T 2 T 1 ) (14) where Q gen is the heat produced by the bearing, k 4n is the size factor, M is the operating torque, n is the rotational speed of the bearing, k 1 is the geometric factor, P eq is the equivalent dynamic load, k 1 is the bearing torque constant, k 1 is a coefficient, T 1 is the temperature of the bearing and T 2 is the maximum operating temperature of the bearing. Calculation gives the required flow for cooling and lubrication of all the bearings in the entire machine as 1.09 L/min Gear Cooling and Lubrication Flow The flow required for gear cooling and lubrication can be calculated as follows [12]: Q oil P k c ρ t (15) where P is the power loss, k is a coefficient, ρ is the density of the hydraulic oil, c is the specific heat capacity and t is the temperature drop. The design goal of transmitting a torque

5 304 X. Xu et al. of 300 Nm requires a flow for cooling and lubrication of 1.3 L/min. 3.3 Electronic Pump Because the engine in a BEV does not have an idle state, the design of the electronic oil pump must be matched to the HCU to ensure that the HCU still works normally when the vehicle is stationary. In this project, a gear pump was selected. The main performance parameters are the nominal oil pressure and displacement Nominal Pressure The nominal pressure is the highest oil pressure that the oil pump can reach under normal operation. The actual output pressure of the oil pump depends on the size of the back-end load and the pressure loss of the entire system, regardless of the pump displacement. In this project, the maximum oil pressure of the HCU was the oil pressure required for a clutch transmission torque of 300 Nm when shifting takes place, which is 12 bar. Taking into account oil pressure losses during the flow of hydraulic oil through the oil circuits, the nominal pressure of the oil pump should be slightly higher than the maximum clutch oil pressure. Therefore, the nominal pressure of the oil pump was set at 15 bar Output Volume Disregarding leakages, the displacement of the hydraulic pump is the volume of hydraulic oil that the hydraulic pump outputs in one revolution. The displacement is determined based on the peak flow of the HCU, which in this project was 12 L/min. Thus, the electronic oil pump needs to meet a maximum displacement requirement of 12 L/min. The actual oil pump speed flow measured by experiment is shown in Fig. 5. The flow and speed are basically linear because a quantitative gear pump is used and the performance of the electronic pump meets the requirements. 4 Three-Dimensional Modeling Figure 6 shows the three-dimensional structure of the 2DET hydraulic valve body developed in this project. It is designed with an integral structure that differs from the structure adopted by traditional automatic transmissions (AT). The three-dimensional model of the HCU uses an integrated method that emphasizes the sharing of product characteristics during the design process to reduce modifications and improve the design efficiency. The detailed design flow is shown in Fig. 7. The design of the oil circuits for one hydraulic valve body is based on the layout of the hydraulic Fig. 5 n Q map for the pump Fig. 6 Model of hydraulic valve body valve body. First, a 2D layout of the hydraulic valve body is made, and then, the 3D layout is made to incorporate the limitations of the oil circuits, minimum wall thickness limits and other factors. When the 3D layout meets all requirements, the individual oil circuits can be designed. Because the hydraulic valve body has an integral structure, there are some principles that should be observed in designing the oil circuits, including the method of plugging the circuits and the circuit connections. A draft design of the oil circuits should be produced and then optimized, an operation that is simpler with an integral valve body than with a valve body consisting of three or more components. Finally, all the design processes are completed when the optimized oil circuits meet all the requirements. Following are the four main advantages of the integral valve body compared with the traditional design. (1) Reduced size and volume. The structure is one-third smaller than that of the traditional design. (2) Simple inner structure and low cost. By using oil circuits composed of holes that are perpendicular to the wall of the valve body rather than complex oil sinks, the valve body is easier to manufacture.

6 Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission 305 HCU structure Structural analysis of hydraulic components Hydraulic valve body 2-d layout Oil circuits design Minimum wall thickness limit Boundary dimension Hydraulic valve body 3-d layout Check whether the requirements are met True false Fig. 8 Large flow solenoid valve test bench Oil circuits connection method Oil circuits plugging method Principle of oil circuits design Oil circuits design Oil circuits optimization Check whether the requirements are met True 2DET hydraulic vale body Fig. 7 Design flow for the hydraulic valve body Hydraulic componentsoil ports classification False (3) Reliable sealing and low leakage. Leakage between two valve components is eliminated. (4) Fast response and high accuracy. Reduced leakage and the simple inner structure contribute to improved performance. The above advantages make the integral structure more suitable for a transmission with a low number of gears. 5 Simulation Results The 2DET HCU is modeled with the SimulationX software of Germany. The large flow solenoid valve acts as a direct shift valve in the HCU and is thus of paramount importance. In this project, we considered the multi-physics coupling effect, and simulated and analyzed the dynamics of the large flow solenoid valve. First, the electric field and the magnetic field were combined to simplify the complex physics coupling of the large flow solenoid valve into an electromagnetic mechanical hydraulic triple coupling effect. That is, the key points extracted from the electromagnetic mechanical were air gaps and the key points extracted from the mechanical hydraulic were valve structures. The key points were then coupled to perform complete dynamic modeling and simulation analysis of the valve. The large flow solenoid valve test bench shown in Fig. 8 was set up to verify the simulation model. According to the characteristics of the large flow solenoid valve, the output oil pressure of the valve was approximately linear with the valve current. The response curve of the pressure of the large flow solenoid valve as a function of the current was obtained by varying the input current signal as shown in Fig. 9.Thetemperature of the hydraulic oil was maintained at 90 C, and the input oil pressure was 2.0 MPa. To ensure that the simulation results and the experimental test results were comparable, the same environmental parameters as used in the actual experimental tests were input to the simulation model. Figure 10 shows a comparison between the oil pressure response curve obtained in the experimental test (blue curve) and the simulation results (red curve) for the same parameters. The figure shows clearly that under the same external environmental conditions, the maximum oil pressure values on the pressure response curves obtained by simulation and experiment are close to each other at around 1.26 MPa. In addition, the slopes of the two oil pressure curves are almost identical when increasing and decreasing the current. These curves verified that the model used for the multi-physics coupling and dynamics of the valve was accurate, which indicates that the correct modeling method was selected. The complete HCU model could then be built.

7 306 X. Xu et al. Fig. 9 Current signal Fig. 11 Current signal Fig. 10 Comparison of simulation and experiment The shifting processes of the HCU were simulated with SimulationX. During the simulation, the main oil pressure (17 bar) and total flow (12 L/min) remained unchanged. Figure 11 shows the current signal to the two large flow solenoid valves. To ensure that the control pressure of the large flow solenoid valve corresponds to the main oil pressure, the current curve of the DAV_1 is offset upward. Figure 12 shows the oil pressure curve of the shifting process [14]. In the process of upshifting, clutch C1 is depressurized and the oil pressure to C1 changes smoothly without fluctuation. Clutch C2 is boosted and the oil pressure to C2 fluctuates by a certain amount. At the same time, the main oil pressure drops slightly. However, with the rapid completion of the oil-charging process, the oil pressure to clutch C2 and the main oil pressure are quickly stabilized and the clutch oil pressure begins to rise steadily. The oil pressure fluctuation in clutch C2 during the oil filling process is caused by the change in the load of the clutch control oil passage when the clutch piston cylinder starts to establish the control oil pressure and when the piston starts to move. At the same time, the overall load on the HCU also changes due to changes in the load on the clutch control oil circuits. However, the fluctua- Fig. 12 Oil pressure curve during shifting tion in the main oil pressure is small and transient, so it can be ignored. When downshifting, the change in the clutch oil pressure is the same as when upshifting, and is not described here. 6 Experimental Results After the design had been completed, a series of experiments were carried out on the HCU, including a bench test on the valve body and a bench test on the whole transmission, in which the various functions of the HCU were verified. 6.1 Valve Body Tests The layout of the test rig for the valve body bench tests is shown in Fig. 13. According to the design goals and experimental data, the HCU design mainly needs to satisfy two requirements at the same time: a reasonable oil pressure in the main oil line to ensure full compression of the wet clutch and

8 Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission 307 Fig. 13 Valve body bench test Fig. 15 Oil pressure changes in the clutch Fig. 14 Oil pressure changes at the outlet of the oil pump Fig. 16 Changes in the valve body inlet flow sufficient cooling lubrication flow to prevent critical components such as bearings and gears from burning out. Because the viscosity characteristics of the hydraulic oil are affected by the temperature, the outlet oil pressure of the oil pump and the clutch oil pressure are greatly affected by the temperature. Figure 14 shows how the oil pressure at the outlet of the oil pump changes at different temperatures, and Fig. 15 shows how the oil pressure to the clutch changes. Because the electronic oil pump used is a quantitative gear pump, the flow from the pump depends on the speed of rotation. Therefore, at different temperatures, the flow in the HCU basically remains the same. Figure 16 shows the changes in the valve body inlet flow, and Fig. 17 shows changes in the cooling and lubrication flow. Figures 18 and 19 show further oil pressure tests on the clutches. For the 2DET HCU, because the oil pressure to the clutches is controlled directly by the large flow solenoid valves, we can input a certain input signal to the large flow solenoid valves and verify the response of the output oil pressure to this input signal. Fig. 17 Changes in the cooling and lubrication flow Figure 18 shows the response of clutch C1, which is controlled by DAV_1, a normally high large solenoid valve, to a step signal (black curve) at under 90 C. In the phase where

9 308 X. Xu et al. Fig. 18 Valve experiment with step signal Fig. 19 Valve experiment with slope signal the control oil pressure started to decrease, the oil pressure to the clutch began to respond to the current increase at 0.5A, corresponding to an oil pressure value of 1 MPa. Subsequently, the control oil pressure followed the changes in the current steps, and the output response to each current step was instantaneous and stable, forming oil pressure response steps. Figure 19 shows the response of clutch C1 to a slope signal (black curve) at under 90 C. When the current was increasing, the clutch oil pressure began to respond when the current reached 0.58 A, corresponding to an oil pressure value of 1.25 MPa. The oil pressure continued to decline after the current reached 1 A for 1 s, and after a lag in the current of 0.23 s, it started to rise gradually to a maximum. The valve experiments with a step signal and a slope signal show that the clutch oil pressure followed the changes in the current to the large flow solenoid valve well, although the characteristics of the large flow solenoid valve produced lags in the results. 6.2 Transmission Test The output oil pressure and flow satisfied the requirements of the bench test on the transmission. The hydraulic valve body was installed to carry out functional bench tests, including a static test, no-load test, no-load temperature-increasing test, loading experiment, efficiency test and durability test. Among these, the static test further verified the functions of the HCU. Figure 20 shows the test bench for comprehensive performance testing. The static test results for the hydraulic valve body were obtained from the data in Table 3, where N pump is the speed of the pump, T oil is the temperature of the hydraulic oil, P is the oil pressure in the main circuit and P C1/C2 is the oil pressure to clutches C1 and C2. As the speed of the electronic pump increased, the HCU could provide sufficient oil pressure for the clutches, but the oil pressures to clutches C1 and C2 showed a large drop in comparison with the main circuit oil pressure. The main reason for considering the flow distribution of the HP_CV valve is that part of the hydraulic oil

10 Design of a Hydraulic Control Unit for a Two-Speed Dedicated Electric Vehicle Transmission 309 2DET Fig. 22 Power-on upshift Fig. 20 Comprehensive performance test bench with 2DET Table 3 Static test results N pump /rpm T oil / C P/bar P C1 /bar P C2 /bar Fig. 21 2DET installed on the BAIC EU300 in the main line flows to the cooling lubricating oil circuits, leading to a decrease in the clutch oil pressure. The tests showed that the indicators of the HCU met the basic requirements, and in the loading experiment, the HCU can engage the clutch under an input torque of 300 Nm. Fig. 23 Power-on downshift Figure 22 shows the power-on upshift curve for the whole vehicle, showing that the main oil pressure stabilized at around 14 bar at the beginning. When the shift operation started, the main oil pressure fluctuated when clutch C1 disengaged and clutch C2 engaged, and then stabilized at about 14 bar. The oil pressure of clutch C1 and clutch C2 followed with the target oil pressure well, but the oil pressure of clutch C2 jumped by about 3 bar near KP point. Because the motor speed could not be controlled, motor speed can only be dragged down by increasing the oil pressure of clutch C2. Thus, the lock-up phase of clutch C2 coincided with the inertia phase of clutch C1. The power-on downshift profile is shown in Fig. 23. Similarly, the main oil pressure was stable at more than 12 bar, meeting the requirements. However, when the shift operation started, the main hydraulic pressure fluctuated and was difficult to control. The actual oil pressure to clutches C1 and C2 basically followed the target oil pressure change, but the oil pressure jump at the KP point still existed. Because the motor torque could not be controlled, the torque phase of clutch C2 overlapped the inertia phase of clutch C1. 7 Vehicle Test To further test the performance of the 2DET HCU, the singlestage reducer in the BAIC EU300 was replaced by the 2DET, as shown in Fig Conclusions This project developed an HCU for a 2DET that is suitable for use in other two-speed transmissions for BEVs.

11 310 X. Xu et al. (1) Our design for the 2DET hydraulic control unit adopted the working principles of the mechanical system and shift logic and the valve body was designed with an integral structure that reduced leakages and the size of the unit. (2) The functional tests on the valve body and the transmission bench tests verified the functionality of the hydraulic valve body. The results of the vehicle tests show that the shifting quality was satisfactory. Large flow solenoid valves were used to control the clutches, and these are known to have many advantages, including reducing the number of valves and improving the rate of response and the shifting accuracy. (3) The hydraulic control unit developed in this project is the first prototype version for the 2DET, and there are many factors that remain for future study, such as the efficiency of the HCU and shift quality. Acknowledgements This work is supported by the National Natural Science Foundation of China (No ) and Beijing Key Laboratory for High-efficient Power Transmission and System Control of New Energy Resource Vehicles. References 1. Roberts, S.: Multispeed transmission for electric vehicles. ATZ Worldw. 114(4), 8 11 (2012) 2. Sorniotti, A., Holdstock, T., Pilone, G.L., et al.: Analysis and simulation of the gearshift methodology for a novel two-speed transmission system for electric powertrains with a central motor. Proc. Insti. Mech. Eng. Part D J. Automob. Eng. 226(7), (2012) 3. Xu, X.Y., Chen, Z.F., Liu, Y.J., et al.: Enumerative optimization procedure for the gear train optimization problem of a two-speed dedicated electric transmission. Energies 10, 1362 (2017) 4. Bai, S.S., Joel, M., Peng, H.: Dynamic Analysis and Control System Design of Automatic Transmissions. SAE International, Pennsylvania (2013) 5. Wang, S.H., Xu, X.Y., Liu, Y.F., et al.: Design and dynamic simulation of hydraulic system for a new automatic transmission. J. Central South Univ. Technol. 16(4), (2009) 6. Wang, S.H., Xu, X.Y., Liu, Y.F., et al.: Design and dynamic simulation of hydraulic system for AT. J. Beijing Univ. Aeronaut. Astronaut. 35(7), (2009) 7. Zhang, T., Tao, G., Chen, H.: Simulation and parameter optimization of PCV in shift hydraulic system. In: International Conference on Communication Software and Networks, Xi an, pp (2011) 8. Dongm, P., Liu, Y.F., Jiang, E.Q., et al.: Oil pressure characteristic of automatic transmission s shift control unit and clutch failure analysis. In: ICCASM Conference, Taiyuan, pp (2010) 9. Liu, Z., Han, X., Liu, Y.F., et al.: Dynamic simulation of large flow solenoid valve. In: ASME 2016 International Mechanical Engineering Congress and Exposition, Phoenix (2016) 10. Lee, G.S., Sung, H.J., Kim, H.C., et al.: Flow force analysis of a variable force solenoid valve for automatic transmissions. J. Fluids Eng. 132(3), (2010) 11. Liu, Y.F., Dai, Z.K., Xu, X.Y., et al.: Multi-domain modeling and simulation of proportional solenoid valve. J. Central South Univ. Technol. 18(5), (2011) 12. Xu, X.Y., Han, X., Liu, Y., et al.: Modeling and dynamic analysis on the direct operating solenoid valve for improving the performance of the shifting control system. Appl. Sci. 7(12), 1266 (2017) 13. Han, X.: Research on the Hydraulic Control System of a Two-Speed Dedicated Electric Transmission. Beihang University, Beijing (2018) 14. Chen, Z., Liu, Y., Fu, Y., et al.: Motor-torque-limited power-on upshift control in electric vehicles with automatic transmissions. Proc. Inst. Mech. Eng/ Part D J. Automob. Eng. 230, 1 (2016)