Power-on shifting in dual input clutchless power-shifting transmission for electric vehicles

Mechanism and Machine Theory 121 (2018) 487–501

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Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory

Research paper

Power-on shifting in dual input clutchless power-shifting transmission for electric vehicles Jiejunyi Liang, Haitao Yang, Jinglai Wu, Nong Zhang, Paul D. Walker∗ Faculty of Engineering and IT, University of Technology, 15 Broadway, Ultimo 2007, NSW, Sydney, Australia

a r t i c l e

i n f o

Article history: Received 30 May 2017 Revised 9 October 2017 Accepted 10 November 2017

Keywords: Dual input transmission Clutchless automated manual transmission Electric vehicle Shift control Noise vibration and harshness

a b s t r a c t The purpose of this paper is to study the practical application of a two motor electric vehicle powertrain utilizing a combination of fixed and multiple speed gear ratios. To realize power-on shifting without torque hole and maximize overall efficiency, a high-speed motor is adopted as the primary motor connecting to the multiple speed clutchless automated manual transmission and a low-speed high torque electric motor is employed as the assisting motor connected to the final shaft with fixed gear ratio. Motor torque and speed are controlled using improved model predictive flux control method in conjunction with synchronizer mechanism actuation to best fill the torque hole to improve both drivability and driving comfort. To evaluate the proposed system, a complete mathematical model is built and compared with a conventional single motor transmission system. The detailed transient dynamic results in terms of final shaft torque, acceleration and vehicle jerk demonstrate the effectiveness of the proposed powertrain. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction In order to fulfill the need to reduce exhaust emissions, strengthening the regulation of vehicle emissions has been a trend worldwide. This has been a driver to design more eco-friendly vehicles. As a result, the demand for electric vehicles and hybrid electric vehicles roars, pushing the development of international automotive industry to a new stage. To achieve the goal of making cleaner and more efficient vehicles without losing drivability and comfort, many innovative designs have been brought out and proved to be successful [1]. Prius earned its reputation by greatly reducing its fuel consumption in the meantime maintaining the smoothness in driving, but the eCVT transmission system in Prius is only for hybrid electric vehicle. There are also some successful pure electric vehicles such as Nissan Leaf, Mitsubishi iMIEV and early stage Tesla. They all adopt single fixed ratio transmission system which has the advantages of lower manufacturing cost, relatively smaller powertrain volumes and less drive-train mass [2]. The limitations of this kind of transmission are also obvious. Firstly, the dynamic performance is poor because the speed and torque range are compromised; secondly, overall operating energy efficiencies are lower as the motor has its own efficiency curve that varies with torque and speed. To overcome the problems that single fixed ratio transmissions have encountered, the development of multi-speed transmission attracts considerable attention. It entitles electric vehicles to higher efficiency [3] and better longitudinal behavior [4]. For multi-speed transmission [5], manual transmission (MT) has the highest efficiency which is around 96%, the efficiency of automatic transmission (AT) is about 86% but it can transmit large torque as MT. Continuously variable transmis∗

Corresponding author. E-mail address: [email protected] (P.D. Walker).

https://doi.org/10.1016/j.mechmachtheory.2017.11.004 0094-114X/© 2017 Elsevier Ltd. All rights reserved.

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J. Liang et al. / Mechanism and Machine Theory 121 (2018) 487–501

sion (CVT) is famous for its smoothness but the overall efficiency is 85%. Based on the fundamentals of these transmissions, many novel configurations have been designed. In [6], detailed shifting mechanisms and control strategy for clutchless automated manual transmission (CLAMT) has been carried out, and the experiment results prove it is possible to remove the friction clutch of an AMT in the electric vehicle without compromising the dynamic performance. A planetary transmission is adopted in [7] to construct a seamless two-speed power split system. Walker et al. [8] introduce the dual clutch transmission to a pure electric vehicle and evaluate its detailed transient dynamic performance by both simulation and experiment. Fang et al. [9] bring out a new concept of uninterrupted mechanical transmission by modifying traditional planetary gearbox. In [10], a novel 4-wheel-drive two-speed electric vehicle layout is proposed. Two sets of electric drivetrains are designed for the axles and by controlling the behaviors of both drivetrains, torque hole compensation is achieved which both improves the drivability and the driving comfort. Besides the novelty in transmission configuration, many researchers improve the drivability and the comfort by adding a various numbers of motors [11]. In [12], an on-board configuration is brought and in [13], the motors are mounted on the wheels which will directly provide the required speed and torque. Among the aforesaid configurations, automated manual transmission (AMT) is a promising solution to meet both requirements of dynamic performance and riding comfort, it has the advantages of high efficiency, low manufacture cost, and light in weight as a manual transmission and auto shifting ability as an automatic transmission [14,15]. But AMT also has its own drawbacks, which are the jerks during gear shifting, the excessive wear of the friction components and the torque interruption in the shifting process [6]. To improve the drivability, Galvagno et al. proposed torque assisted AMT in [16], it uses a servo-assisted clutch to replace the fifth gear synchronizer which will provide certain power while the engine is disconnected from the powertrain, but the assisted clutch doesn’ t have its own power source which means it can’ t eliminate the torque hole but alleviate it. In [17], a modified AMT called Inverse-AMT is proposed, it puts the friction clutch after the gears instead before them. Experiment results prove it to some extent solves the torque interruption problem. Extensive study has proved that the two major parasitic loss sources in transmission system are friction clutch elements and electro-hydraulic actuators [18]. The overall efficiency is compromised by 4%–6% because of clutch drag and oil pumping. By comparison in [19,20], it is feasible to greatly minimize the reduction in overall efficiency for the transmission using clutchless variants. For a conventional vehicle which adopts internal combustion engine (ICE), the clutch in the AMT is inevitable because of the speed and torque adjustment delay caused by the poor controllability of the engine, which also entails long speed synchronization duration and exacerbates the wear of the friction plates. But it is not the case for electric vehicles [21], there are three reasons [6]. First, the inertia of a motor is much smaller than that of an ICE which makes it capable of changing speed swiftly. Second, due to the excellent low-speed control capability, by controlling the motor, the vehicles can be launched smoothly. Third, it’ s easy to change the motor from torque mode to speed mode and vice versa. Therefore, after the synchronizer disengages the gears, the motor could change into speed mode which outputs little torque but reaches target speed immediately and then changes back to torque mode. Thus, the friction clutch is removed. Furthermore, because of the wide high-efficiency range, excellent speed regulation capability and fast torque response characteristics, transmission systems for EV need fewer gear ratios [22]. Zeroshift [23] is an example to remove friction clutch by re-designing the dog clutches to engage different gears without the need for speed synchronization. In [24], a series of controllable one-way clutches are employed to realize gear selection. In terms of the control strategy, [25] not only removes the friction clutch but also the synchronizer by refining the control algorithm. And in [26], the speeds and torques of the engine and motor are coordinately controlled to make it not necessary to have a clutch. Aiming at designing a transmission system which could maximize energy efficiency, minimize emissions, and has certain drivability and comfort, this paper brings out a novel clutchless two motor power-shifting transmission where a single fixed ratio motor is utilized in parallel with a multi-speed transmission and second motor to balance the needs for improved motor efficiency in conjunction with power-on shifting capabilities. The structure of the system is presented below in Fig. 1. The first motor drives the wheels through a multispeed transmission, with gear actuation achieved through a combination of motor speed control and synchronizer actuation [27]. This is a cost-effective and efficient method for achieving multispeed functionality without power-on shifting functionality. The second motor drives the transmission output shaft using a fixed reduction ratio and must be designed to achieve torque hole compensation through all of the gear shifts and also act as a driving motor under specified driving conditions. Such configurations have applications for both pure electric and hybrid electric vehicle powertrains. This would include HEV variants with a conventional engine upstream of EM1 would allow for both series and parallel operation of the vehicle. In order to verify the gear shift quality of the proposed transmission system, robust testing criteria are crucial. In [28], a thorough investigation has been done to lay down the benchmark to assess shift quality which links both subjective ratings and objective measurements. And it conducts experiments on six different types of vehicles under six conditions such as launch, creep, hill start, abusive start and so on. Four pairs of words are brought out in [29] by trained drivers to depict the shift quality which are responsive/hesitant, smooth/rough, unperceivable/apparent and strong/weak. And it is proved in [30] these in-direct assessments could adequately reveal the objective criteria. Some researchers recommended [31] that the jerk shouldn’ t exceed 10 m/s3 in order not to be perceived by the driver, and others believe that the root mean square of the jerk also shouldn’ t be larger than 2.83 m/s3 . In [32], vibration dose value is brought out as a standard industry metric which correlates well with human perception. Last but not least, shifting duration is also of great importance [33]. In the proposed transmission system, there are three main stages which are torque down of EM1 and torque up of EM2, speed synchronization and torque restore, as friction clutch is removed from this system, speed synchronization will directly influence the shift performance and it will take about half of the shifting duration.

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Fig. 1. Two motor clutcless AMT configuration.

The remainder of this paper is developed as follows: Section 2 presents the overall system model, including a multibody dynamic model, electric machine model, and simplified synchronizer model. Section 3 details the control algorithm during shifting, and the development of a profile for torque hole compensation. Section 4 presents simulations of shifting for a combination of up and down shifts with different torque demands on the motors. Finally, Section 5 summaries the presented paper and draws conclusions based on the results. 2. System modeling and control methodology In this section the mathematical model is developed to the powertrain under investigation. Components being modeled are: • •

•

Electric motor with improved model-predictive flux control; Simplified synchronizer mechanism, that assumes once speed synchronization is complete the engagement process is successful; Multibody powertrain model using lumped torsional elements.

2.1. Electric motor model and control In order to maximize the drivability and driving comfort, the electric motor should be precisely controlled to follow torque and speed profile to accomplish a seamless gear shifting process. There are many existing high-performance control methods [34] such as field oriented control (FOC), direct torque control (DTC) and model predictive torque control (MPTC). FOC decomposes the stator currents into torque and flux components, which will be regulated by proportional integral controllers separately, in synchronous frame and uses a modulation block to generate the final gating pulses. It would achieve high torque and flux control performance but also requires fine-tuning work. DTC is an effective way to give quick dynamic responses with a simple structure, but it generates high steady-state torque ripples. MPTC takes credits for an intuitive concept, high flexibility and easy incorporation of constraints but the tedious stator flux weighting factor tuning work limits its application. To overcome the aforesaid drawbacks in motor control methods, an improved model predictive flux control (MPFC) method is adopted. Not as conventional MPTC which needs to generate a proper weighting factor between control variables of torque and stator flux, MPFC converts these two components into a stator flux vector in which they have the same unit, eliminating the use of weighting factor. The electric motor can be expressed as:

x˙ = Ax + Bu



where x = is ψ s defined as:



T

(1) are state variables, ψ s stator flux and is is stator current, u = us is the stator voltage. Matrix A and B are

−λ(Rs Lr + Rr Ls ) + jωr A= −Rs

 λ(Rr − jLr ωr ) 0

(2)

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 B=

λLr

 (3)

1

where R and L are stator resistance and inductance and subscripts s, r, and m are stator, rotor and mutual, respectively, and 1 ωr is electrical rotor speed, λ = 2 . (Ls Ll −Lm )

In order to predict x at the next control instant, second-order Euler discretization is adopted instead of the first-order one to improve accuracy:

⎧ ⎨xkp+1 = xk + Tsc (Axk + Buks )

(4)

⎩xk+1 = xkp+1 + Tsc A(xkp+1 − xk ) 2

k+1

where Tsc is the control period and xk+1 = [iks +1 ψ s ] is the predicted state vector. The accuracy of state estimation will directly affect the performance of MPFC, here a full order observer is adopted:

dxˆ = Axˆ + Bu + G (is − ˆis ) dt

(5)

where xˆ is the estimated state and G = −





2b b/(λLr )

is a constant gain matrix used to improve the stability and b is a negative

constant gain. re f Because of the delay compensation, not only reference ψ s at (k + 1 )th instant should be calculated but also reference f ψre at (k + 2 )th instant. The procedure can be summarized as: s

1 k+1 Lr k+1 ψ − i Lm s λLm s

ψkr +1 =

(6)

L R



ψkr +2 = ψkr +1 + Tsc Rr m iks +1 − r − jωr ψkr +1 Lr

k+2

After acquiring ψ r

∠ψ

re f s

re f

, the phase angle of ψ s

k+2 r



+ arcsin

3 2

Tere f k+2 r

pLm |ψ



||ψs |re f

is the torque reference. The final stator flux vector reference can be obtained as:

re f s

= ψ s

re f

(7)

at (k + 2 )th instant could be expressed as:

re f

where Te

ψ

=ψ

Lr

f

 exp( j∠ψ re s )

(8)

(9)

Although eliminating the weighting factor saves much offline time, torque ripples and current harmonics still exist if selected voltage vector is applied during the whole control period. In order to further improve the electric motor performance, it is imperative to optimize the switching instant of the selected vector during [0, Tsc ] which can be expressed as:

topt =

f k+1 k+1 (ψ re − fik+1 Tsc )  ( f old − f i ) s − ψr

| f old − f ki +1 |2

(10)

where fold is the stator flux slope for voltage vector, subscript old means it is applied at the end of the previous control period, f ki +1 is for the selected voltage vector in this control period and  is the dot product. For a given voltage vector uksi+1 , stator flux at (k + 2 )th instant can be obtained after getting the optimal switching time topt as:

ψksi+2 = ψks +1 + (uold − uksi+1 )topt + (uksi+1 − Rr is )Tsc

(11)

In order to force stator flux to track its reference and prevent high deviation of stator flux, a cost function can be built as:

J = ψ s

ψts

re f

k+2

− ψs

ψks +1

re f t

+ ψs − ψs

(12)

where = + uold ti is the stator flux vector at the optimal switching instant. The whole control strategy is summarized in Fig. 2. A comparison has been made in Fig. 3 which shows torque response performance between DTC, FOC and MPFC, to demonstrate the effectiveness of the proposed MPFC. It can be seen in Fig. 3 that DTC and MPFC take only about 0.0 0 03 s to reach 10 Nm while FOC takes about 0.0015 s which means that DTC and MPFC are better in terms of dynamic performance. As to static performance, FOC is better with a ripple amplitude around 1 Nm while DTC has the largest amplitude of 2.5 Nm. MPFC has an acceptable ripple amplitude which is 1.5 Nm. In the current response performance in Fig. 4, FOC and MPTC have similar performance with no obvious harmonic ripple in 0.4 s while DTC has significant distortions, which will cause more losses.

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Fig. 2. Proposed switching instant optimized electric motor control diagram.

2.2. Synchronizer model For the purpose of this study the synchronizer mechanism is simplified to capture the main actuation characteristics. It includes only the speed synchronization stage of engagement, and post-synchronization is considered to be completely locked, with the other states of engagement ignored. This is a consequence of the speed synchronization component being critical to ensure actuation, whilst other stages, such as dog clutch engagement, are not critical to the duration of shifting [27]. Thus the synchronizer model is reduced to a cone clutch. The cone clutch torque is described as follows:

uD RC FS sin α

TSY N =

(13)

where TSYN is the cone torque, uD is the dynamic friction coefficient, RC is the mean cone radius and α is the cone angle. An ideal actuation process is considered for the synchronizer mechanism. The energized and neutral states of the synchronizer mechanism results in two possible engagement states, these are simulated as follows:



FS =

P 0

Energized Neutral

(14)

where FS is the synchronizer load and P is the magnitude of the applied load. Values for P are set based on the duration of actuating the simplified mechanism and are consistent with typical values found in [27]. To compensate the time required to release or engage the synchronizer after an actuation request, a small time delay will be employed to maintain these characteristics. 2.3. Powertrain dynamics model The powertrain of the two motor CLAMT is relatively simple, as shown in Fig. 5, with one motor rotor driving the multispeed transmission via an input shaft, with no need for flywheel, clutch or torsional dampers. The second motor drives the output shaft through a second fixed ratio that is independent of the transmission. As the main changes in the proposed system are concentrated in the transmission system from the motor to the shaft before the open differential, and the simulation system is designed to verify the concept and its effectiveness, not to explore a vehicle’s behavior, the components after the open differential are simplified to fulfill their main functions. The main components are electric motor at elements M1 and M2, input side transmission components at element 1, a rigid body reduction gear and synchronizer mechanism (S), output side transmission components including final drive gear and differential for element 2, wheel hubs and half shafts (3 and 5), and (4 and 6) vehicle equivalent inertia. Input torques include the two motor torques (TM1 and TM2 ), (TSYN ) cone clutch torque, and (TV ) vehicle resistance torque, and equations of motion derived in Eqs. (15)–(23).

¨ = TM1 − CM1 θM1 ˙ − K1 (θM1 − θS ) − C1 (θM1 ˙ − θ˙S ) JM1 θM1

(15)

˙ − θ˙S ) − TSY N JS θ¨S = K1 (θM1 − θS ) + C1 (θM1

(16)

(J1b +

i21 J1a

)θ¨1b = i1 TSY N − K2 (θ1b − i2 θ2b ) − C2 (θ1˙ b − i2 θ2˙ b )

¨ = TM2 − CM2 θM2 ˙ − K7 (θM2 − i3 θ2b ) − C7 (θM2 ˙ − i3 θ2˙ b ) JM2 θM2

(17) (18)

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J. Liang et al. / Mechanism and Machine Theory 121 (2018) 487–501

Fig. 3. Torque response performance of (a) DTC, (b) FOC, (c) MPFC.

    ˙ − i3 θ2˙ b ) i3 (i22 J2a + i23 J2c + J2b )θ¨2b = K2 (θ1b − i2 θ2b ) + C2 (θ1˙ b − i2 θ2˙ b ) i2 + K7 (θM2 − i3 θ2b ) + C7 (θM2 − K3 (θ2b − θ3 ) − C3 (θ2˙ b − θ˙3 ) − K5 (θ2b − θ5 ) − C5 (θ2˙ b − θ˙5 )

(19)

J3 θ¨3 = K3 (θ2b − θ3 ) − C3 (θ2˙ b − θ˙3 ) − K4 (θ3 − θ4 ) − C4 (θ˙3 − θ˙4 )

(20)

J5 θ¨5 = K5 (θ2b − θ5 ) − C5 (θ2˙ b − θ˙5 ) − K6 (θ5 − θ6 ) − C6 (θ˙5 − θ˙6 )

(21)

J4 θ¨4 = K4 (θ3 − θ4 ) + C3 (θ˙3 − θ˙4 ) − TV /2

(22)

J6 θ¨6 = K6 (θ5 − θ6 ) + C6 (θ˙5 − θ˙6 ) − TV /2

(23)

where Jn represents the inertia of any given powertrain element, Cn represents damping coefficients, Kn represents stiffness elements, θ n represents rotational displacement, and its first derivative represents velocity and its second derivative represents acceleration. n represents the nth element of the powertrain model in Fig. 5. i represents the gear ratios, subscript 1 represents any of the given transmission ratios, 2 is the final drive ratio, and 3 is the fixed motor ratio. For the closed transmission condition with any of the gears engaged Eqs. (16) and (17) are reduced as follows





˙ − i1 θ1˙ b ) − K2 (θ1b − i2 θ2b ) − C2 (θ1˙ b − i2 θ2˙ b ) J1b + i21 (J1a + JS ) θ¨1b = i1 K1 (θM1 − i1 θ1b ) + i1C1 (θM1

(24)

The power at the wheel can be determined relatively easily, as follows:



PV = VV Mv (VV )/t + CR Mv g cos β + MV g sin β +

1

2



CD ρ AV VV2 /(ηT ηE M )

(25)

where CR is rolling resistance, g is gravity, β is road incline angle, CD is drag coefficient, ρ is air density, AV is frontal area, VV is linear vehicle speed, MV is the vehicle mass and PV is power to drive the vehicle at the wheel.

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Fig. 4. Current response performance of (a) DTC, (b) FOC, (c) MPFC.

Fig. 5. Clutchless AMT multi-body model.

3. Gear shift process control The methodology for gear shifting is presented in Fig. 6 for dual motor gear shifts, it has 7 primary steps including shift initiation and torque reinstatement. The functional phases of shifting are summarized as follows: 1. Motor torque reduction During this phase the torque of the primary drive motor is reduced to zero, taking the load off the synchronizer mechanism and enabling gear shift. Simultaneously, motor two torque is increased to compensate for the loss of torque in the transmission. 2. Synchronizer release During synchronizer release the mechanism is moved back to the neutral position, here the torque of motor one is held at zero and that of motor two is maintained at a constant torque level.

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Fig. 6. Gear shift methodology.

Fig. 7. Torque reference controlled by bump function.

3. Motor speed synchronization Motor speed synchronization is the process of re-synchronizing the motor and drivetrain to the target speed, completing the speed change process without the use of friction clutches. To achieve this, a speed profile is designed for the motor to track using closed loop control of the system. 4. Synchronizer engagement During the process of synchronizer engagement the motor is controlled to maintain target gear speed in line with the output shaft speed. The actuator will be energized and push the sleeve towards the hub. During the process, the cone clutch will eliminate the slight difference still between target gear speed and the output shaft. 5. Motor torque increase

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Fig. 8. Gear shift schedule and torques, (a) gear shift schedule, (b) torque of EM1, (c) torque of EM2, (d) final shaft torque.

After the target gear is locked with the output shaft, the primary drive motor restore its torque to the demand level and at the meantime, the torque of the second motor drops to offset the increased torque from motor one to its normal driving work load. The primary objective of the delivery of torque impulse is to maintain the desired transmission output torque during the shift process. There are, of course, limitations to such a proposition. Namely, the speed and torque range of the motor. This is partially compensated for through the wise selection of gear ratio, i3 , as well as the overall size of the secondary motor. However complete compensation of the torque hole, particularly for first to second gear up and down shifts (i.e. highest speed and torque changes) may be difficult. For the purpose of this study compensation will be designed to produce a constant output shaft torque, within the limits of the motor capabilities. The output torque TM is determined by the driver by pushing the pedal in the normal driving state. After initiating the shift process, the vehicle control unit takes charge of the torque and speed of the motors and the activation of the actuators. Here, a modified bump function is adopted to realize the closed-loop control. It is defined as: −1

TM = Ae 1−x2

(26)

where A is the coefficient for the bump amplitude to fit the input torque, and x is a variable to control the duration of torque t −t change which is defined as x = 0t . Here, t0 is the time when the torque phase begins and tD is the designed duration for D the phase. For the motor torque reduction phase at time t0 , the torque of motor 1 will be Ae and at the end of this phase which is time tD it will be zero. It is opposite for motor 2 whose torque will be the same as normal driving at time t0 and will rise according to the bump function to compensate the torque drop of motor 1. For the speed synchronization phase, the speed change is also governed by a bump function defined as: −1

˙ = iT i2 θ2˙ b ± iA i2 θ2˙b,0 e 1−x2 θM

(27)

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(a)

Motor 1 torque [Nm]

80

60 40 Torque

reduction

Speed synchronization

20

Torque restoration

0

Synchronizer engagement

Synchronizer disengagement -20 11.8

12

12.2

12.4

12.6

12.8

13

13.2

13.4

Time [s] (b)

Motor 2 torque [Nm]

120

100

Torque increasement

Torque reduction

80

Torque hole compensation

60

40

20 11.8

12

12.2

12.4

12.6

12.8

13

13.2

13.4

Time [s] Fig. 9. Torques during the fifth shifting, (a) torque of EM1, (b) torque of EM2.

where T and A are for target and actual gear, respectively, and subscript 0 is for the initial value at the beginning of this phase. It is worthy pointing out that the speed control is only for the primary motor because it is the one to change gears. Motor 2 should hold to the normal driving speed to make sure there is no sudden change in vehicle speed to guarantee the driving comfort. As to the torque reinstate phase, the bump function is defined as: −1

TM = B − Ae 1−x2

(28)

where B is the target torque for the primary motor, and of course, the torque for motor 2 will drop according to the profile to its original value. Fig. 7 shows how the torque reference changes controlled by the proposed bump function to accomplish torque hole compensation during one gear shifting process. It can be seen that the torque of motor 2 rises to compensate the torque drop of motor 1 to keep the final output torque steady. Under the control of bump function, the torque changes smoothly and gradually that there are no ripples in the final output. 4. Simulation results An integrated simulation model has been built consists of control units such as motor control unit, transmission control unit, vehicle control unit and a complete vehicle body with detailed powertrain system. As suggested in [35], the average driving efficiency is very similar between a large number of gear ratio combinations and gear ratio optimization is not the purpose of this paper, so the gear ratios are set according to Roser et al. [36] 3.46, 2.08 and 1.32 with a counter gear of 2.67. As this paper is focused on the powertrain configuration and its ability in smooth gear shifting, different driving modes and optimal efficiency exceed this scope and will be discussed in further work. Here, the load is divided into two parts, 70% for EM1 and 30% for EM2. In order to demonstrate the effectiveness of the proposed dual motor CLAMT configuration, a comparison simulation model is built with the same structure but only a single motor. Table 1 shows some of the parameters used in the model.

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Fig. 10. Final shaft torque comparison, (a) torque of the single motor configuration, (b) torque of the proposed configuration.

Table 1 Key parameters used in the model. Symbol

Name

Value

Symbol

Name

Value

JM1 JS J1a J1b J2a J2b J2c J3 C1 C2 C3

Motor Synchronizer Driving gear Driven gear Final drive 1 Final drive 2 Final drive 3 Half shaft Damping 1 Damping 2 Damping 3

0.065 kg m2 0.025 kg m2 0.005 kg m2 0.010 kg m2 0.02 kg m2 0.2 kg m2 0.02 kg m2 1 kg m2 50 Nm s/rad 50 Nm s/rad 50 Nm s/rad

C4 K1 K2 K3 K4 MV rt

Tyre damping Motor output Lay shaft Half shaft Tyre stiffness Vehicle mass Tyre radius Air density Road incline Dynamic friction Static friction

100 Nm s/rad 50,0 0 0 Nm/rad 50,0 0 0 Nm/rad 50,0 0 0 Nm/rad 10,0 0 0 Nm/rad 1500 kg 0.3 m 1.127 kg m3 0◦ 0.3 0.35

ρ β μD μS

Fig. 8 shows gear shift schedule, torques for EM1 and EM2 and the final shaft torque. The gear shift schedule includes up shifts from neutral position to the third gear ratio and two down shifts from the second gear ratio to the first and from the third to the second, respectively, in order to cover most gear shifting scenarios and particularly reflect the transient dynamics while conducting down shifts to get greater acceleration. In Fig. 8(b), it can be easily seen that EM1 experiences a sudden torque drop to zero at the beginning of gear shifting which accords to the first step of motor control, and it keeps low till the synchronizer is engaged again. It is worthy pointing out that the torque of EM1 doesn’ t follow torque reference during speed synchronization, which happens because the motor switches to the speed control mode when torque control is not of priority. This is normal and harmless as the motor is disengaged from the driveline and will not influence the dynamic performance. As EM2 serves to compensate the torque hole caused by the

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Fig. 11. Final shaft speed comparison, (a) speed of the single motor configuration, (b) speed of the proposed configuration.

disengaging of EM1, its torque rises at the beginning of gear shifting and holds until EM1 restores its torque. In Fig. 8(c), the torques produced by EM2 during shifting are not the same because at the final shaft, the torques come from EM1 are different due to the difference between gear ratios. Fig. 8(d) shows the final shaft torque, the vibrations during gear shifting are tolerable and the torque hole is eliminated. Fig. 9 shows detailed torque performance during the fifth gear shifting of both motors. The aforesaid gear shift stages can be easily seen in Fig. 9. It takes about 300 ms for EM1 to reduce the torque to zero and at the meantime, EM2 raises its torque to compensate the torque hole caused by EM1. The synchronizer disengagement stage takes about 70 ms while EM1 is still in the torque control mode. After completing disengagement, EM1 switches to speed control mode to reduce the motor speed to match the new gear ratio which accompanied by an abrupt torque impulse and takes about 450 ms. Synchronizer engagement is achieved in a short time which is decided by the synchronizer actuator and then comes torque restoration which takes about 300 ms. It can be seen that the torque of EM1 is 70 Nm which is much lower than the peak of EM2 in Fig. 8 which is around 200 Nm because of the gear ratio. This character gives this powertrain configuration the advantage to maximize the overall efficiency by selecting suitable motors. High-speed motor will achieve high efficiency when working in high-speed condition but only providing low torque, low-speed motor, on the contrary, will provide low speed but high torque. The configuration takes advantages of both types of motors to realize both drivability and efficiency. Fig. 10 shows the final shaft torque comparison between the proposed configuration and the single motor CLAMT system. The torque hole during gear shifting is obvious for the single motor CLAMT system, the drop is abrupt and the amplitude is huge which will inevitably cause significant vehicle jerk. Fig. 10(b) renders a much better result where the torque hole is almost compensated by the second motor and the amplitude of torque drop is reduced by almost half. It also can be seen that in Fig. 10(b) there is still small variation at the beginning and the end of gear shifting, which is due to the engagement of synchronizer. The difference between the peak of final shaft torque is caused by the torque distribution. Peak torque of the single motor configuration is higher than that of the proposed system because the torque produced by EM1 is amplified by the transmission system while the torque produced by EM2 is directly transmitted to the final shaft by a single pair of

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(a) Acceleration of the single motor model Acceleration of dual input model

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Time [s] Fig. 12. Vehicle acceleration and vehicle jerk comparison, (a) acceleration comparison, (b) jerk comparison.

gears without further amplification and in the proposed system, less torque demand is assigned to EM1 while all torque demand is given to the primary motor in the single motor model. Fig. 11 depicts the speed comparison between these two models. In Fig. 11(a), slight speed drop can be discerned in every gear shift process, which is caused by the riding resistance and the torque absence, and the acceleration process is obvious not continuous. In Fig. 11(b), the acceleration interruption doesn’ t occur and the speed curve is much more linear as a result of the successful torque hole compensation. Fig. 12 shows the comparisons of vehicle acceleration and vehicle jerk to further demonstrate how the proposed configuration can improve the drivability and driving comfort. In Fig. 12(a), acceleration drops below zero during gear shifting for the single motor model because of the absence of driving torque and the driving resistance. For the dual input model, the acceleration exactly follows the desired curve with no unexpected interruption. This characteristic gives the proposed configuration great advantage in terms of drivability. Again the peak acceleration of these two models are not the same because EM2 in the proposed model is directly connected to the final shaft with only a pair of gears which does not exist in the single motor model, the output torque can not always stay the same. As to the vehicle jerk in Fig. 12(b), the proposed model renders an even more desired improvement, considering that 1.1 second gear shifting duration is already very short. The differences between the transient peaks of jerks caused by the engagement of synchronizer and the differences between jerk duration caused by motor torque change, which is more perceivable because of the duration, are both significant. It can be seen that in every gear shifting process, there are three main jerks in the single motor model and only two main jerks in the proposed model. The first jerk response in the single motor model is caused by the torque absence from the primary motor so the jerk is very large. The first jerk in the proposed model is not caused by the torque absence, but the final shaft torque change resulting from the gear ratio change. This is because the proposed model can directly reach its target torque, so the jerk is smaller. And it can be seen that sometimes it is opposite phase to the jerk in the single motor model because of the difference between up and down shifts. The second jerk is caused by the engagement of synchronizer in both models, due to the dual input structure, the transient jerk in the proposed model is still smaller. As to the third jerk, in the single motor model, it is caused by torque restoration.

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In the proposed model, there is even no such a jerk because the proposed bump function control method can adequately eliminate the ripples in the torque alternating between the primary motor and the second motor. The improvement in vehicle jerk will largely improve the riding comfort. 5. Conclusion and recommendation The objective of this paper is to propose a high efficient transmission system which has the merits of efficient, robust, low manufacture cost and could achieve torque hole compensation and improve drivability and driving comfort. In order to maximize the overall efficiency and the robustness, a modified clutchless AMT is adopted as the basis of the multi-speed transmission part for the primary motor. To guarantee the quality of gear shifting without traditional friction clutch, an advanced motor control strategy is designed to follow its torque and speed references more accurately and swiftly. As to achieving torque hole compensation to improve the drivability and driving comfort, an assisting motor is designed to provide the required torque during shifting with a control strategy that maintains constant torque. It also provides torque when the torque demand exceeds the capacity of the primary motor. To verify its effectiveness, a detailed mathematical model has been built. The transient shifting dynamics has been studied and the outcomes are compared with those of a traditional single motor CLAMT transmission in terms of torque, acceleration and vehicle jerk. It is demonstrated that the proposed system could adequately achieve the goal to compensate the torque hole during gear changing to realize power-on shifting with cost-effective and low mass CLAMT system. 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