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Research Papers

# Dynamics and Control of Clutchless Automated Manual Transmissions for Electric VehiclesOPEN ACCESS

[+] Author and Article Information
Paul D. Walker

School of Electrical, Mechanical,
and Mechatronic Systems,
Faculty of Engineering and IT,
University of Technology Sydney,
Ultimo NSW 2007, Australia
e-mail: Paul.Walker@uts.edu.au

Yuhong Fang, Nong Zhang

School of Electrical, Mechanical,
and Mechatronic Systems,
Faculty of Engineering and IT,
University of Technology Sydney,
Ultimo NSW 2007, Australia

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 13, 2016; final manuscript received May 11, 2017; published online July 28, 2017. Assoc. Editor: Philippe Velex.

J. Vib. Acoust 139(6), 061005 (Jul 28, 2017) (13 pages) Paper No: VIB-16-1456; doi: 10.1115/1.4036928 History: Received September 13, 2016; Revised May 11, 2017

## Abstract

This paper presents a study of the dynamics and control of clutchless automated manual transmissions (CLAMT) for the purpose of investigating the system behavior during up and down shifts. To achieve this, a multibody dynamic model of the proposed powertrain is implemented to simulate the transient behavior of the system, including a direct current (DC) equivalent model of the electric machine (EM) and a synchronizer mechanism model. Closed-loop control of motor speed and torque is used in conjunction with synchronizer mechanism actuation to functionally achieve gear shifting without the need for a primary friction clutch. This includes nested torque–speed closed-loops to implement alternative motor control functionalities at different stages of gear change. To evaluate the performance of shift control, shift metrics including longitudinal jerk, vibration dose value (VDV), and shifting duration are evaluated from simulation results. These results demonstrate the most significant impact on the transient response of the powertrain results from the reduction and reinstatement of motor torque during shift control. Speed control of the motor during the shift transient directly impacts on the duration of shifting, but not the transient response of the powertrain.

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## Introduction and Background

One of the main considerations in the development of new electric and hybrid electric vehicle (HEV) powertrains is the implementation of cost-effective transmission systems. To an extent, this is achieved by the Toyota Prius through the implementation of planetary gearsets as electrically continuously variable transmissions [1]. However, this is only applied to hybrid vehicles. The implementation of multispeed transmissions for pure electric vehicles (EVs) should come with minimal additional costs and high efficiency to be cost competitive with single reduction gear-based EVs. For example, a two motor variant is developed in Ref. [2] that can be used to simulate a power-on shifting capability with multiple gear ratios for both motors. A conventional electric vehicle, such as the Nissan Leaf or Mitsubishi iMIEV, and early generation Tesla vehicles use a single fixed ratio to deliver load to the road. The hybrid BMW i8 uses a two-speed transmission under certain driving conditions. The use of multispeed transmissions for EV applications has been shown to improve drivability of the vehicle through a more diverse application of motor driving torque [3] and improve driving range.

The modeling and analysis of stepped automatic powertrains, either power shifting or shifting with torque interrupt, covers most conventional and novel transmission configurations. Crowther et al. [4] study the shift transient behavior of compound planetary automatic transmission systems. Dual clutch transmissions (DCT) have been studied using a combination of simulation and experiments by Zhang et al. [5] and Zhu et al. [6], investigating both the transient behavior and control of such systems. More recently, novel transmission architectures have been investigated. For example, an inverse automated manual transmission (AMT) was studied by Gao et al. [7] studying gear ratio optimization and control of the system, demonstrating it to have better performance than a single-speed EV. A torque hole filling AMT was studied in Galvagno et al. [8], where a clutch is used on the highest gear ratio to enable power on up and down shifts using an automated manual transmission. The ultimate objective of such development is to produce cost-effective automatic transmissions that can be applied to hybrid, electric, and conventional vehicle platforms.

Clutchless automated manual transmissions (CLAMT) have come under scrutiny recently as low-cost transmission systems for use in hybrid (HEV) and EVs [9]. Through the integration of multispeed transmissions, higher motor mean operating efficiencies and more diverse driving capabilities are achieved in comparison to single-speed EVs. This additional functionality is achieved through the addition of multiple gear ratios. However, single motor versions of these transmissions also have drawbacks in the lack of clutch-to-clutch power shifting capabilities.

Contrary to the system being studied in this paper, there are a number of torque hole filling and power-on shifting capable transmissions systems available for use in electric vehicles. An experimental and simulation study by Walker et al. [10] demonstrated power-on and power-off shifting for a two-speed dual clutch transmission applied to electric vehicles. Similarly, a two-speed planetary transmission [11] has been developed. Both of these transmissions required complex and precise control to deliver high quality power-on gear shifts. Furthermore, multiple friction elements are also needed. Conversely, a dual motor multispeed EV transmission is developed in Ref. [2]. This requires combined speed control of lay shafts with pulsed torque input from the secondary motor to achieve gearshifts with compensation for the torque hole that would otherwise be present. In Ref. [12], the same functionality is achieved using independent motors combined with two-speed transmissions on front and rear axles of a four-wheel drive. Gear shift in each gearbox is achieved in a power-on manner by compensating for the torque hole with the alternative driving motor. The limitation of these powertrains, where precise clutch control or multiple traction motors are required, is the additional costs associated with the powertrain system. To this, clutchless AMTs present a cost-effective alternative.

A typical clutchless AMT powertrain, shown in Fig. 1, comprises of traction battery and power electronics supplying an EM. This electric machine delivers power to the wheels through a stepped automatic transmission. By varying the selected gear ratio, a more diverse range of applicable torques and speeds can be achieved at high motor efficiency. Furthermore, as seen by the comparison of Zhou et al. [13] and Changenet et al. [14], the use of clutchless variants will reduce the transmission system parasitic losses, thereby minimizing the reduction in overall efficiency for the transmission. Particularly, it must be noted that wet friction elements, such as synchronizer cone clutches or wet clutches, are one of the main contributors to parasitic losses in any transmission, and the minimization of these will provide significant benefit to the overall powertrain efficiency.

Other outcomes resulting from the application of clutchless AMTs to electric vehicles include: (i) significantly reduced transmission costs; (ii) fewer transmission components, reducing size and weight of the system; (iii) simple actuation and control requirements, owing to the improved controllability of the motor; and (iv) lower losses in the system. Limitations to the system are: (i) no high torque friction elements to control speed synchronization, (ii) torque interrupt to the wheels during shifting, and (iii) quality of gear shifting achieved.

Clutchless AMTs have been studied in papers such as Refs. [15] and [16]. These papers have typically used either in benchtop testing or in vehicle experimentation to study part or all of the shifting process. In Ref. [15], only the speed phase control of the entire gearshift process is studied. This paper provides an improved strategy for motor speed control in this phase in particular but does not consider the entire shift process, such as torque release of the motor and dog clutch disengagement. In Ref. [16], synchronizer mechanism control is studied to investigate the application for this type of vehicle. The detriment of these papers is that benchtop tests cannot capture the impact on vehicle response limiting the capacity to evaluate the impact on shift quality of the vehicle. In this paper, the impact of using these automated transmissions on gear shift quality will be studied, as will the entire shift process, including torque control of the motor and release of dog clutches and synchronizers.

The primary limitation of papers such as Refs. [15] and [16] is that the complete engagement process from shift detection through to completion is not studied with consideration of the dynamic behavior of the vehicle. To a limited extent, this is demonstrated in Ref. [17], where an initial strategy for shift control is presented. Through numerical simulation, one of the main aims of this paper is to evaluate the entire gear shift process for clutchless AMTs so as to evaluate the performance of specific engagement stages on the duration and quality of the shift process.

Unlike planetary, dual clutch transmissions or even continuously variable transmissions, clutchless AMTs achieve gear change with torque interruption to the wheels during shifting. With the exception of continuously variable transmissions (CVTs), these transmissions produce power-on gear shifts to minimize the loss of torque to the road [4,8]. This is frequently referred to as the torque hole in the shifting process. This has also been shown to contribute significantly to the quality of the gear shift along with other factors including duration of gearshift and vehicle jerk [6]. Vehicles equipped with automatic transmissions are frequently evaluated in terms of shift quality [18]. Disruption of driving torque to the wheels during gear change can result in noise, vibration, and harshness (NVH), impacting on the perceived shift quality of the vehicle. NVH is a classical term used to define the quality of driving a vehicle under a wide range of operating conditions, including vehicle launch, braking, or gear shift for example. It is strongly linked to driver perception of vehicle quality and hence, highly subjective [18].

Different measures are used for the evaluation of NVH, derived from qualitative assessment of vehicle performance from drivers or quantitative measures of vehicle response, i.e., acoustical noise, longitudinal acceleration, or vehicle jerk. For this paper, the focus will be on vibration and harshness components of this type of study. Both of these can be evaluated using various measures. For example, shifting harshness can be measured using jerk, the rate change of longitudinal acceleration. For power on shifting, i.e., clutch-to-clutch gear shifts, Chen and Gao [19] estimate reasonable peak values for vehicle jerk over 10 m/s3. Alternatively, Huang and Wang [20] provide figures of up to 2.83 m/s3 for root-mean-square (RMS) jerk values. For a CLAMT where there is a significant torque hole created during gear change, this can be expected to be potentially higher. In Ref. [20], rigid body jerk is evaluated using a low pass filter set to 3 Hz to filter out higher transients, which may be considered as vibration rather than rigid body motion; this method will be adopted in this paper. Vibration can be viewed through other methods, such as peak to peak or RMS acceleration [18]. In this paper, the VDV [21] will be used as a measure of vibration as a consequence of gear changes. This is essentially the root mean quad of a band-pass filtered longitudinal acceleration, typical filtering of 1–32 Hz.

The purpose of this paper is to investigate all the different stages of the gear shift process for clutchless AMTs including motor torque control, synchronizer release, and engagement and speed control of the motor through simulation. To achieve this objective, this paper first develops an integral mathematical model of a multispeed EV powertrain that includes an equivalent motor model with a multibody dynamic model of the powertrain that is sufficiently detailed to allow for investigation of both control and vehicle NVH issues. Then the paper presents and applies a comprehensive shift control algorithm that considers: (i) motor torque control, (ii) motor speed control, and (iii) mechanism actuation, enabling investigation of the entire shifting process.

The remainder of this paper is divided into the following components: Section 2 presents the powertrain system modeling. This section includes (a) equivalent DC motor model, (b) the comprehensive powertrain model, and (c) a simplified synchronizer mechanism model. Section 3 contains a detailed development of the control algorithm and the strategy for gear shift control of the CLAMT including two alternative variants. Additionally, (a) description of the nested closed-loop control of the motor, and (b) the actuation strategy for the synchronizer mechanism are presented. Section 4 presents shift quality metrics that will be used to objectively evaluate performance characteristics of simulations. Section 5 presents the simulation results for the study including both step-by-step evaluation of individual shifts and the response through various up and down shifts using variation in shift duration and control strategy. Finally, Sec. 5 summarizes the study and presents the concluding remarks.

## Mathematical Modeling

Mathematical modeling of the powertrain includes: (1) electric machine model, (2) synchronizer model, (3) synchronizer actuator model, and (4) powertrain dynamics model. These models are integrated into a complete system model in the simulink environment of matlab using Stateflow as the primary state machine. Through the application of the proposed control strategy, simulated engagements are performed on the model to demonstrate the impact of control of different phases of engagement on vehicle performance.

To develop this mathematical model, the following assumptions are made and discussed during the model development component of this paper:

• Backlash is ignored in both synchronizers and mated gear pairs, a common assumption in powertrain dynamics and modeling [22].

• DC equivalent model is used to represent the actual motor [15].

• Neither torsional damper nor fly wheel is required as electric machine output torque has significantly less variance than an internal combustion engine.

• Linear damping model for tires, again a common assumption in vehicle dynamics [22].

• Reduced order synchronizer mechanism model is used, similar to references such as Refs. [2] and [10] where indexing and ring alignment are ignored.

###### Electric Machine.

There are several different modeling techniques available for the study of electric machine control. A complete motor model has separate circuits for each motor phase, requiring individual control of phases, typically through modeled inverters/controllers. The simplest form of electric machine modeling is the DC equivalent model. This model groups each phase of the circuit as a single DC equivalent that can be directly controlled via a pseudovoltage input. This is easier to implement than a full model and retains the main dynamic characteristics of the system. Conceptually, this is sufficient for the study in this paper as the dynamic characteristics, i.e., time delay, are maintained in the DC equivalent system with much less detail required in the model. This is consistent with other research in the area, such as Ref. [15]. Additionally, the complexity of simulating power electronics is eliminated and the direct voltage control of the motor is now possible [23]. The equivalent circuit model is shown in Fig. 2.

The differential equation for the electric circuit is defined as Display Formula

(1)$LIEM⋅=Keθ˙1−RIEM+V$

where IEM is the line current, L is the line inductance, Ke is the back emf constant, R is the line resistance, and V is voltage.

The electromagnetic torque produced in the EM is defined as follows: Display Formula

(2)$TEM=KTIEM$

where KT is the torque constant and TEM is the electromagnetic torque. These two equations represent the electrical component of the model equations of motion, and should be considered in conjunction with the equations of motion presented in Sec. 2.2.

Electric machine (motor) and power electronics (inverter or drive unit) modeling and control are extensively studied and well-established fields of research. As with any form of mathematical modeling and control, the structure and detail of any model can impact on the behavior and response of the whole powertrain system, but the response of power electronics systems [23] is much higher than the dynamic response of the powertrain (see free vibration analysis further on in this paper) and the frequencies of interest for NVH considerations (up to 32 Hz). It is possible to ignore the high frequency response of inverter drives and focus on the dynamics of the mechanical powertrain system. This will produce a more compact model, simplify the control problem, and increase computation efficiency for simulations.

###### Powertrain Dynamics Model.

The powertrain multibody model of a clutchless AMT is significantly simplified from an equivalent AMT or similar transmission. It relies on the synchronizer mechanism and precise motor control to realize gearshifts. As such, major components, such as flywheel, primary friction clutches, and torsional dampers, are not present in the transmission, simplifying the overall system. The multibody model is shown in Fig. 3, and equations of motion are derived in Eqs. (3)(9). For the model, J1 represents the motor rotor and is coupled to the DC motor model per Eqs. (1) and (2), J2a is the synchronizer equivalent inertia, Jeq is the equivalent transmission inertia, J4 and J6 represent wheel hubs, and J5 and J7 are the equivalent vehicle inertias. Input torques acting on the system are (TEM) electric machine torque, (TSYN) synchronizer cone clutch torque, and (TV) vehicle resistance torque. Accordingly, each inertia element has a corresponding degree-of-freedom. θn represents rotational displacement corresponding to the nth degree-of-freedom, and its two time derivatives represent velocity and acceleration. Subscript n corresponds to each specific degree-of-freedom (i.e., 1, 2a, eq, 4, 5, 6, or 7) in Fig. 3. i represents the gear ratios, subscript 1 represents any of the given transmission ratios, and 2 is the final drive ratio

Display Formula

(3)$J1θ¨1=TEM−CMθ˙1+K1(θ2a−θ1)+C1(θ˙2a−θ˙1)$
Display Formula
(4)$J2θ¨2a=−K1(θ2a−θ1)−C1(θ˙2a−θ˙1)−TSYN$
Display Formula
(5)$Jeqθ¨eq=i1i2TSYN−CTθ˙eq+K2(θ4−θeq)+C2(θ˙4−θ˙eq)+K4(θ6−θeq)+C4(θ˙6−θ˙eq)$
Display Formula
(6)$J4θ¨4=−K2(θ4−θeq)−C2(θ˙4−θ˙eq)+K3(θ5−θ4)+C3(θ˙5−θ˙4)$
Display Formula
(7)$J5θ¨5=−K3(θ5−θ4)−C3(θ˙5−θ˙4)−TV/2$
Display Formula
(8)$J6θ¨6=−K4(θ6−θeq)−C4(θ˙6−θ˙eq)+K5(θ7−θ6)+C5(θ˙7−θ˙6)$
Display Formula
(9)$J5θ¨5=−K5(θ7−θ6)−C5(θ˙7−θ˙6)−TV/2$

Equations (3)(9) reflect the state with the synchronizer mechanism open. When the mechanism is closed with any of the gears engaged, a degree-of-freedom is lost. Equations (3)(5) are reduced with the transmission inertias lumped to a single-degree-of-freedom. The transmission closed case is as follows: Display Formula

(10)$J1θ¨1=TEM−C1θ˙1−K1(i1i2θ3−θ1)+C1(i1i2θ˙eq−θ˙1)$
Display Formula
(11)$(Jeq+i12i22J2)θ¨eq=−i1i2K1(i1i2θeq−θ1)−i1i2C1(i1i2θ˙eq−θ˙1)−CTθ˙eq+K2(θ4−θeq)+C2(θ˙4−θ˙eq)+K4(θ6−θeq)+C4(θ˙6−θ˙eq)$

The vehicle resistance torque is defined from a combination of road grade, rolling resistance of the vehicle, and aerodynamic drag [3]. It is defined as follows: Display Formula

(12)$TV=(CRMVg cos ∅+MVg sin ∅+12CDρAVVV2)×rt$

where g is gravity, rt is the tire rolling radius, AV is frontal area, CD is drag coefficient, CR is rolling resistance, MV is the vehicle mass, TV is the vehicle torque, VV is linear vehicle speed, ϕ is road incline angle, and ρ is air density.

For reference, natural frequencies resulting from undamped free vibration analysis are presented in Table 1. These results present an interesting comparison for filtering requirements for jerk and VDV analyses. Jerk is filtered at 3 Hz using a low pass filter as detailed in Ref. [20]. Consequently, the rigid body mode and first natural frequency response will be captured. Vibration dose value is filtered using a band gap filter between 1 and 32 Hz according to Ref. [21], so the lowest natural frequencies are retained in the VDV analysis. However, fn5 falls in the cutoff region for the filter. It is therefore pertinent to widen the filtered range to include these additional frequencies in third gear in particular by using a higher bound to the band-gap filter of 34 Hz to ensure any response associated with these frequencies is captured in the analysis.

###### Synchronizer Model.

Synchronizer mechanisms, as shown in Fig. 4, are designed to work through the balance of torque loads during both speed synchronization and later stages such as ring alignment and hub indexing [2427]. Research into closed-loop control of the mechanism in Ref. [24] aims to improve the responsiveness and reduce the duration of engagement. However, such studies demonstrate that the speed synchronization phase is still the longest and therefore most critical phase of engagement. The synchronizer mechanism model is simplified to include only the speed synchronization phase of engagement as a simulated torque. Physical stages of engagement are simulated using a nonlinear spring arrangement to ensure that the displacement and duration of engagement are consistent with published literature [2527]. Consequently, it is ensured that an appropriately simulated duration of synchronizer engagement can be achieved, as such representation of engagement duration is accurately simulated and any delays in engagement are captured.

The model based on the different stages of engagement is described as follows:

• First free fly—here the sleeve moves from the neutral position to contact with the cone clutch. In this model, it is simulated using a spring–damper element to capture delay in actuation.

• Speed synchronization—any residual relative motion between engaging synchronizer elements is eliminated through the loading up of the cone clutch. Friction torque generated in the cone reduced slip speed to zero, enabling completion of the engagement process. The cone clutch torque is described as follows [25]: Display Formula

(13)$TSYN=μDRCFS sin α$
where TSYN is the cone torque, μD is the dynamic friction coefficient, RC is the mean cone radius, FS is the synchronizer load, and α is the cone angle.

• Ring release and hub engagement: for these two stages of engagement, spring damper elements are again used to simulate the engagement process and ensure an appropriate time delay between actuation and completion of engagement. Upon the complete displacement of the synchronizer sleeve, it is assumed that the mechanism is locked and the shifting process can continue to completion.

It is recognized that while this does not strictly simulate the engagement process for a synchronizer mechanism, as studied in Refs. [25] and [26], this process is representative of the actual delays present in synchronizer mechanism engagement.

## Alternative Powertrain Control Strategies

Control of clutchless AMTs requires a combination of speed and torque control strategies. For a conventional AMT, the primary clutch is released prior to gear change. This has the effect of isolating both the transmission and remainder of the driveline from the engine during shifting. The load is significantly reduced on the synchronizer during gear selection. As discussed in Ref. [28], the additional controllability of the electric motor is used to enable precise speed matching prior to engagement of the synchronizer mechanism. Cone torque, per Eq. (13), is used to minimize any residual slip speed and, ideally, would not be required for gear change.

The combined torque–speed control of the gear change process for clutchless AMTs is shown in Fig. 5(a). It includes five phases for changing gear including: (1) motor torque reduction, (2) synchronizer disengagement, (3) motor speed control, (4) synchronizer engagement, and (5) torque re-instatement of the motor. For phases (2) and (4), the synchronizer mechanism is released and engaged according to the method described in Sec. 3.2. Motor torque and speed control phases of gear change use closed-loop control of motor torque for phases (1) and (5) or relative motor speed for phase (3) with predetermined torque or slip speed profiles. Two alternative actuation strategies will also be tested. Figure 5(b) shows parallel synchronizer engagement and motor speed control and (c) no motor speed control. Both methods are simulated giving consideration to the fact that combinations of synchronizer actuation and motor speed control have the most significant impact on the observable duration of gear shift.

The two alternative gear change strategies presented in Figs. 5(b) and 5(c) provide alternative strategies for gear change. The option presented in Fig. 5(b) can be used to minimize the gear shift process by engaging the synchronizer mechanism in parallel with motor torque control, offering the potential to overlap two stages of the gear shift process.

Motor torque control is the predominant control method during driving through throttle control by the driver, and during the gear shift process for the CLAMT powertrain system in this study. During both synchronizer actuation and the inertia phase of shift control, the reference torque is set to zero. During torque release and reinstatement, a modified bump function is used to define the profile for closed-loop motor control Display Formula

(15)$TP1=Ae−11−x2$

where A is the scaling factor to equate the bump amplitude to the input torque at the initiation of shifting, and x = (t0 − t)/tD. Here, t0 is the time at initiation of profiled control and tD is the desired duration of the particular phase. This allows for the control of the duration of torque release and reinstatement. For torque reinstatement, the modified function is used as follows, where B is the target torque at the completion of shifting: Display Formula

(16)$TP2=B−Ae−11−x2$

Slip speed control is utilized for the synchronization of synchronizer mechanism slip speeds. Through this strategy, a speed profile based on the bump function is again used to achieve the desired new speed. This is as follows: Display Formula

(17)$θ˙P=iAi2θ˙3+(iTi2θ˙3±iAi2θ˙3,0)e−11−x2$

where subscripts A and T are for actual and target gear, respectively, and the 0 subscript on the speed is for the speed at the beginning of the inertia phase. Again, the bump function is used to control the duration of shifting so that its impact can be studied in this paper.

###### Electric Machine Control.

There are many forms of motor control including current, torque, speed, or voltage methods [29]. Convention in automotive powertrains requires the use of torque control of the motor [29]; this is realized practically through the design and control of power electronics that regulate the energy flow between batteries and motor. Each of these control methods has their own benefits and limitations in terms of functionality, ease of use, and efficiency of operation [29]. In any case, the electric machine will be controlled through a combination of speed and torque regulation during different phases of engagement, if accurate shift control of the powertrain is to be achieved.

The use of the equivalent DC motor model allows for the direct control of motor functionality through variation of input voltage. Two proportional–integral–derivative (PID) control loops are employed to enable closed-loop speed and torque control of the powertrain. Torque control is used for the primary driving input for the system under normal operation and motor speed control is utilized for the inertia phase of gear shift. In Fig. 6, the desired motor torque reference can be effectively considered the driver input during normal operation or a desired profile reduction in torque during gear change. Furthermore, the motor speed profile would only be considered the desired trajectory change for the motor during the inertia phase of gear shift and would otherwise be set to zero. Through the use of PID controllers in this paper, the torque and speed trajectories and resulting errors are the inputs for closed-loop control, and the PID output is effectively a voltage signal that will drive the equivalent motor model.

###### Synchronizer Actuation.

Synchronizer mechanisms are typically controlled in an on–off manner where the applied load is used to energize the mechanism. Force and torque balancing during actuation rapidly achieve engagement without any requirement for closed-loop control [24]. This removes the need for modeling a complex electromechanical system to engage the synchronizer mechanism, and simplifies its control to constant positive and negative loads on the simplified synchronizer model to simulate engagement. The possible engagement states are represented as follows: Display Formula

(14)$FS={PEngaging0Neutral−PDisengaging$

where P is the magnitude of the applied actuating load. Values for P that are set based on the duration of actuating the simplified mechanism are consistent with typical values found in Ref. [25]. Synchronizer mechanism control is only considered in its most simplistic form for this paper. It is assumed that the synchronizer mechanism will successfully engage when energized; this is the expected case according to papers such as Ref. [27]. On/off control is therefore used to either energize the synchronizer or release it and move it to the neutral position.

## Shift Quality Metrics

Shift quality metrics are generally used to evaluate the performance of power-on gear shifting in automatic transmissions, where power-on shifting is the act of changing gear ratio without losing traction to the road. These techniques have been extended to other forms of gear shift, including AMTs in papers such as Refs. [1821]. For the purpose of this paper, three metrics have been chosen to study the powertrain response:

1. (1)Vehicle jerk: This is a measure of the driver observed rate change of acceleration of the vehicle during gear change. In power shifting, capable transmissions such as DCTs or ATs minimizing this metric will provide the driver with a high quality shift outcome during power-on shifting. However, in transmissions with torque interrupt, such a metric will be significantly higher than in power shifting transmissions. Nevertheless, minimizing jerk will provide demonstration of improving the shift performance, and what factors have the most significant impact on shift quality.
2. (2)VDV: This is a measure of the vibration response of the system during gear shift. According to Ref. [21], it is measured using the filtered longitudinal acceleration with a 2–32 Hz bandpass filter, VDV is the calculated using Eq. (18). A modified VDV is also introduced normalizing against the duration of each gearshift as shift times will vary significantly for different cases studied and for different ratios. It is calculated using Eq. (19). This is to compensate for VDV being a cumulative analysis and a high result can be the outcome of either a long shift time or large response or the combination of the two Display Formula
(18)$VDV=∫totfa4dt4$
Display Formula
(19)$VDV=1tf−to∫totfa4dt4$
where a is the filtered longitudinal acceleration, to is the simulation time at start of shifting, and tf is the simulation time at the completion of the shift.
3. (3)Shift duration: this measures the entire period for which shifting occurs, again it is observable by the driver. In this paper, it is calculated as the entire period for which the driver losses control of the powertrain as shifting occurs.

It should be noted that clutch friction energy for the synchronizer mechanism is not utilized as a metric, as is the case for other papers (i.e., Ref. [30]) as speed change is driven by the motor control rather than clutch friction in this study. It is, therefore, expected to be significant.

## Simulations

Simulation results are presented in Secs. 5.15.7 using alternative configurations in terms of both shift strategy and duration of gear shift. Powertrain model parameters are summarized in the Appendix (Table 2).

###### Typical Up and Down Shift Responses.

The first two simulation results are presented in Figs. 7 and 8. Figure 7 presents a typical upshift from first to second gear, while Fig. 8 presents the equivalent downshift from second to first gear. For both up and down shifts, the duration of speed synchronization and torque control of the motor is constrained according to the equations listed below:

• Stage 1: Motor torque reduction according to Eq. (15)

• Stage 3: Motor speed synchronization according to Eq. (16)

• Stage 5: motor torque reinstatement according to Eq. (17)

The duration of synchronizer engagement and disengagement is constrained by the physical model. These results for synchronizer actuation compare well with published literature [26,27,31]. The DC equivalent motor model results in a system where the voltage is strongly influenced by the speed of the motor and torque by current. Thus, torque reduction and reinstatement stages of engagement (1 and 5) result in small decreases in voltage and large changes in current as motor torque is released at relatively constant speed. However, during the speed control stage (state 3), motor torque requests are used to actively control motor speed. This result produces rapid reduction in input voltage as current (and by inference torque) is varied to synchronize the motor speed with the target gear speed. Note that the ideal speed profile is not shown as it is indistinguishable from the actual motor speed in Figs. 7 and 8.

For the downshift responses shown in Fig. 8, the total shift duration is approximately 700 ms, as opposed to 800 ms for the results in Fig. 7. This shorter shift time results from a faster synchronizer engagement during state 4. This is a consequence of the parameters chosen for that synchronizer, as with previous results, this outcome is still in line with available literature. It is important to recognize that for both instances (Figs. 7 and 8), friction-based synchronization is not required as the motor is able to closely match speeds with the target gear speed. Furthermore, for the dog clutch to engage successfully, the motor must be returned to a neutral torque condition as the chamfered splines in the dog are limited in transmissible torque to about 20 N·m, depending on design [27].

###### Case 1—Typical Powertrain Responses.

To study a series of upshifts and downshifts in the powertrain, the motor torque is initially ramped up to 200 N·m over 5 s followed by a series of upshifts and downshifts taken at 3 s intervals. For the first series of up and down shifts, the stage duration, tD, is constrained to 200 ms, including torque release and reinstatement as well as inertia phase of shifting. The results of these simulations are shown in Fig. 9, (a) includes motor, all three gears and vehicle speeds, (b) is the vehicle acceleration, and (c) presents the vehicle jerk. The results show that the gear shifts, using the constrained speed and torque control profiles, all have durations of approximately 800 ms, corresponding to the results in Figs. 7 and 8. Vehicle jerk is shown to be largest for the 1–2 up and down shifts. This is a result of torque multiplication amplifying the transients resulting from torque release. Results also demonstrate that both speed synchronization and synchronizer release and re-engagement stages of gear shift have no impact on vehicle acceleration or jerk. Therefore, primary consideration should be placed on torque control stages of gear change, as these have a more significant impact on quality of gear change.

###### Case 2—Extended Shift Duration.

The key variable chosen for this part of the study is the duration of each stage of shifting. For the first iteration of shifting the duration is increased to 400 ms for each stage. For each of the up and down shifts shown in Fig. 10, the total shift duration increases to approximately 1400 ms. There is an immediately demonstrated improvement to the simulation results, with peak jerk reduced at a cost of the extended shifting time. These results demonstrate that the reduction in motor torque in preparation for gear shift directly impact on the peak vehicle jerk levels, motor torque reduction, and reinstatement also accounts for 55% of the total shift time, while the speed phase of engagement, where motor speed control is most important, accounts for less than 30% of the total shift time. These results demonstrate that through designing, the torque profiles in particular, it is possible to balance both the observed vehicle jerk and the duration of the gear shift. It is also worthy of noting that the 2–1 down shift that occurs after 15 s has a very large speed change, but again its impact on shift quality is limited. By decreasing the time to complete speed synchronization, it is possible to minimize gear change without reducing shift quality.

###### Case 3—Reduced Shift Duration.

In this case, the reduced duration of gear shift is studied, with the objective of minimizing the duration of the shift. In this case, a period of 20 ms is chosen for each shift stage. The results of both up and down shifting are shown in Fig. 11. The simulation results demonstrate that there is no significant reduction in vehicle speed during gear change, as experienced in the results for Fig. 10. However, the results in Figs. 11(b) and 11(c) demonstrate substantial increases in transient acceleration and vehicle longitudinal jerk, respectively. Thus, while it is possible to minimize the duration of shifting, there are negative impacts on vehicle NVH in terms of both jerk and transient responses. As with previous simulations, there is no impact on vehicle jerk observed through minimizing the duration of speed synchronization stage of engagement. Thus, vehicle jerk is independent of speed synchronization, but highly dependent on torque release and reinstatement.

###### Shift Quality Results From All Simulations.

Summarized results of shift quality metrics are presented in Fig. 12. These results are useful in demonstrating the performance of different shift quality characteristics against both the variation in stage duration and initial motor torque. Figures 12(a) and 12(b) present the results for RMS Jerk in relation to both stage duration and initial torque, demonstrating an inverse proportionality to duration and proportionality to motor torque at the beginning of the gear shift. Conversely, results in Fig. 12(c) show that the unmodified VDV increases with increasing shift time, a result of the time dependency of VDV summation. By normalizing these results against shift time, a more expected result is obtained insofar as VDV* decreases with increasing shift time. The same outcome is achieved in Fig. 12(d), where using the time normalized VDV values produces a more obvious trend in shift performance that is closer to the outcome indicated in Figs. 911. Finally, results in Figs. 12(e) and 12(f) present shift duration results, which are in and of themselves trivial, but when analyzed with other results, such as jerk and VDV, as is achieved in this case, broader conclusions can be established in terms of shift quality. Notably, the tradeoff in quality of gearshift observed by the driver will include a combination of both observed vehicle vibration and harshness against an extended period of gear change, where a loss of road traction is observed.

###### Parallel Speed Synchronization.

The first alternative control strategy to be tested is shown in Fig. 5(b); both closed-loop motor speed control and synchronizer friction are used to complete speed matching during gear change, and simulation results are presented in Fig. 13. In this strategy, the speed reduction profile is still controlled by the nested closed-loop control of the motor speed. For this control method, the synchronizer mechanism is energized so friction aids in the engagement process. However, at the same time, the speed loop of motor control is utilized to aid in synchronizer engagement. If the duration for speed synchronization and synchronizer engagement is matched correctly, it is possible for the peak motor torque requirements to be reduced during this phase of engagement. However, if the synchronizer torque acts to match speeds faster than is desired through motor control, these two control elements will act against each other and constrain the engagement process. This may prove detrimental to the synchronizer friction surfaces by increasing wear, but, at this level, analysis may be unnecessary as the motor is demonstrated to achieve the speed synchronization process effectively.

###### Synchronizer Only Engagements.

For the case where only the synchronizer mechanism drives the speed-matching component of shifting, as summarized in Fig. 5(c), the motor is reduced to zero torque, one synchronizer released and the other engaged. The simulation results of this modified engagement process are presented in Fig. 14: (a) shows the motor voltage and current, (b) presents motor speed and torque, and (c) presents the displacement of the two synchronizer speeds. These results of this modified engagement process demonstrate that the friction-based engagement is the slowest of each presented strategy. The primary reasoning behind this outcome is that the designed peak cone torque used in these simulations is equivalent to a single friction surface cone. The increasing of friction surfaces from 1 to 3, as studied in Ref. [6], will certainly reduce the engagement time, at a cost of higher viscous losses in the transmission. Therefore, it must certainly be observed that the ideal control strategy of using the traction motor for speed synchronization contains the most benefits. Furthermore, this strategy will enable the elimination of friction cones from the synchronizer altogether. The CLAMT design would then rely on dog clutches alone for gear engagement, with motor control taking over the role of speed synchronization. This will further benefit the design by not requiring a synchronizer ring, which contributes a significant portion of the engagement time for the synchronizer [25,27].

## Summary and Conclusions

The principal objective of this paper has been the investigation of gear shifts in clutchless automated manual transmissions and the impact of shift control through the assessment of various shift quality metrics. To do this, a mathematical model of a CLAMT equipped powertrain system was developed that includes DC equivalent electric machine, synchronizer mechanism model, and a multibody dynamic model of the powertrain. Results of various gearshift combinations were evaluated in terms of: (1) vehicle longitudinal jerk, (2) vibration dose value, and (3) total shift duration.

Integrated control of the synchronizer mechanism and the electric machine were then employed to study a series of up and down gear shifts, including three separate variants for shift control. The important stages of gear shift in this study are: (1) motor torque release and re-instatement, (2) inertia phase speed control of the motor, and (3) synchronizer release and re-engagement. Both motor torque and speed control were performed using closed-loop control with the duration of shifting constrained, while synchronizer actuation is an open-loop process.

Results of these simulations include the following:

1. (1)Demonstration that the most significant impact on both vehicle jerk and shift transient vibration is the release and reinstatement of motor torque control in preparation for speed synchronization with the motor.
2. (2)Through the reduction of each stage of shift control the entire shift duration can be minimized at a cost of increased VDV and vehicle jerk. It is also worth noting that using a time normalized VDV value is far more effective as VDV is a cumulatively assessed value as shorter shifting times can mask higher peak transients.
3. (3)Electric machine drive can be used to successfully control the speed change stage of shifting; however, this stage only comprises of about 30% of the entire shift for a typical gear change.
4. (4)With high quality control of electric machine during the shift process, it is possible to achieve gear change without the use of cone friction in the synchronizer mechanism. However, it may still be necessary to include this type of actuator as a redundancy when synchronization fails.

Further research for this study will include the implementation of optimal control strategies that balance the conflicting metrics of shift duration and vehicle jerk. Experimental verification of these results using the UTS Powertrain Test Rig, a purpose built facility for studying the dynamics and control of experimental vehicle powertrains, will also be performed.

## Acknowledgements

The authors would like to gratefully acknowledge the support of the Australian Research Council and AutoCRC for their support on this project.

• The Australian Research Council through DE170100134.

• The AutoCRC through 1-210.

## References

Zhang, X. , Li, C. T. , Kum, D. S. , and Peng, H. , 2012, “ Prius+ and Volt−: Configuration Analysis of Power-Split Hybrid Vehicles With a Single Planetary Gear,” IEEE Trans. Veh. Technol., 61(8), pp. 3544–3552.
Sorniotti, A. , Holdstock, T. , Everitt, M. , Fracchia, M. , Viotto, F. , Cavallino, C. , and Bertolotto, S. , 2013, “ A Novel Clutchless Multiple-Speed Transmission for Electric Axles,” Int. J. Powertrains, 2(2–3), pp. 103–131.
Walker, P. D. , Abdul Rahman, S. , Zhu, B. , and Zhang, N. , 2013, “ Modelling, Simulations, and Optimisation of Electric Vehicles for Analysis of Transmission Ratio Selection,” Adv. Mech. Eng, 5, p. 340435.
Crowther, A. R. , Singh, R. , Zhang, N. , and Chapman, C. , 2007, “ Impulsive Response of an Automated Transmission System With Multiple Clearances: Formulation, Simulation, and Experiment,” J. Sound Vib., 306(3–5), pp. 444–466.
Zhang, Y. , Chen, X. , Zhang, X. , Jiang, H. , and Tobler, W. , 2005, “ Dynamic Modelling and Simulation of a Dual-Clutch Automated Lay-Shaft Transmission,” ASME J. Mech. Des., 127(2), pp. 302–307.
Zhu, B. , Zhang, N. , Walker, P. D. , Zhan, W. , Zhou, X. , and Ruan, J. , 2013, “ Two-Speed DCT Electric Powertrain Shifting Control and Rig Testing,” Adv. Mech. Eng., 5, p. 323917.
Gao, B. , Liang, Q. , Xiang, Y. , Guo, L. , and Chen, H. , 2015, “ Gear Ratio Optimization and Shift Control of 2-Speed I-AMT in Electric Vehicle,” Mech. Syst. Signal Process., 50–51, pp. 615–631.
Galvagno, E. , Velardocchia, M. , and Vigliani, A. , 2011, “ Analysis and Simulation of a Torque Assist Automated Manual Transmission,” Mech. Syst. Signal Process., 25(6), pp. 1877–1886.
Son, H. , Yoon, Y. S. , Kim, K. S. , Kim, S. J. , and Song, C. , 2015, “ Economic Hybrid Transmission System Using Clutchless Geared Manual Transmission,” 28th Electric Vehicle Symposium and Exhibition, Goyang, South Korea, May 3–6, pp. 3–6.
Walker, P. D. , Zhu, B. , and Zhang, N. , 2017, “ Powertrain Dynamics and Control of a Two Speed Dual Clutch Transmission for Electric Vehicles,” Mech. Syst. Signal Process., 85, pp. 1–15.
Rahimi Mousavi, M. S. , and Boulet, B. , 2014, “ Modeling, Simulation and Control of a Seamless Two-Speed Automated Transmission for Electric Vehicles,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 3826–3831.
De Pinto, S. , Camocardi, P. , Sorniotti, A. , Mantriota, G. , Perlo, P. , and Viotto, F. , 2017, “ Torque-Fill Control and Energy Management for a Four-Wheel-Drive Electric Vehicle Layout With Two-Speed Transmissions,” IEEE Trans. Ind. Appl., 53(1), pp. 447–458.
Zhou, X. , Walker, P. , Zhang, N. , Zhu, B. , and Ruan, J. , 2014, “ Numerical and Experimental Investigation of Drag Torque in a Two-Speed Dual Clutch Transmission,” Mech. Mach. Theory, 79, pp. 46–63.
Changenet, C. , Oviedo-Marlot, X. , and Velex, P. , 2006, “ Power Loss Predictions in Geared Transmissions Using Thermal Networks-Application to a Six Speed Manual Gearbox,” ASME J. Mech. Des., 128(3), pp. 618–625.
Zhu, X. , Zhang, H. , Xi, J. , Wang, J. , and Fang, Z. , 2014, “ Robust Speed Synchronization Control for Clutchless Automated Manual Transmission Systems in Electric Vehicles,” Proc. Inst. Mech. Eng., Part D, 229(4), pp. 424–436.
Tseng, C. Y. , and Yu, C. H. , 2015, “ Advanced Shifting Control of Synchronizer Mechanisms for Clutchless Automatic Manual Transmission in an Electric Vehicle,” Mech. Mach. Theory, 84, pp. 37–56.
Liu, H. , Lei, Y. , Li, Z. , Zhang, J. , and Li, Y. , 2012, “ Gear-Shift Strategy for a Clutchless Automated Manual Transmission in Battery Electric Vehicles,” SAE Int. J. Commer. Veh., 5(1), pp. 57–62.
Jeon, B. , and Kim, S. , 2014, “ Measurement and Modeling of Perceived Gear Shift Quality for Automatic Transmission Vehicles,” SAE Int. J. Passeng. Cars Mech. Syst., 7(1), pp. 423–433.
Chen, H. , and Gao, B. Z. , 2014, Nonlinear Estimation and Control of Automotive Drivetrains, 1st ed., Springer, Beijing, China.
Huang, Q. , and Wang, H. , 2004, “ Fundamental Study of Jerk: Evaluation of Shift Quality and Ride Comfort,” SAE Paper No. 2004-01-2065.
Baraszu, R. C. , and Cikanek, S. R. , 2002, “ Torque Fill-In for an Automated Shift Manual Transmission in a Parallel Hybrid Electric Vehicle,” American Control Conference (ACC), Anchorage, AK, May 8–10, pp. 1431–1436.
Walker, P. D. , and Zhang, N. , 2014, “ Transmission of Engine Harmonics to Synchronizer Mechanisms in Dual Clutch Transmissions,” ASME J. Vib. Acoust., 136(5), p. 051009.
Magne, P. , Shi, X. , and Krishnamurthy, M. , 2014, “ Fundamentals of Power Electronics,” Advanced Electric Drive Vehicles, A. Emadi , ed., CRC Press, Boca Raton, FL, pp. 43–106.
Alizadeh, H. V. , and Boulet, B. , 2014, “ Robust Control of Synchromesh Friction in an Electric Vehicle's Clutchless Automated Manual Transmission,” IEEE Conference on Control Applications (CCA), Nice, France, Oct. 8–10, pp. 611–616.
Walker, P. D. , and Zhang, N. , 2011, “ Parameter Study of Synchroniser Mechanisms Applied to Dual Clutch Transmissions,” Int. J. Powertrains, 1(2), pp. 198–220.
Walker, P. D. , and Zhang, N. , 2012, “ Engagement and Control of Synchroniser Mechanisms in Dual Clutch Transmissions,” Mech. Syst. Signal Process., 26, pp. 320–332.
Lovas, L. , Play, D. , Marialigeti, J. , and Rigal, J. , 2006, “ Mechanical Behaviour Simulation for Synchromesh Mechanism Improvements,” Proc. Inst. Mech. Eng., Part D, 220(7), pp. 919–945.
Breen, J. L. , and Bower, G. , 2001, “ Clutchless Shifting of an Automated Manual Transmission in a Hybrid Powertrain,” SAE Paper No. 2011-01-2194.
Nagel, N. J. , 2014, “ Fundamentals of Electric Motor Control,” Advanced Electric Drive Vehicles, A. Emadi, ed., CRC Press, Boca Raton, FL, pp. 187–236.
Pinte, G. , Depraetere, B. , Symens, W. , Swevers, J. , and Sas, P. , 2010, “ Iterative Learning Control for the Filling of Wet Clutches,” Mech. Syst. Signal Process., 24(7), pp. 1924–1937.
Abdel-Halim, N. , Barton, D. , Crolla, D. , and Selim, A. , 2000, “ Performance of Multicone Synchronizers for Manual Transmissions,” Proc. Inst. Mech. Eng., Part D, 214(1), pp. 55–65.
View article in PDF format.

## References

Zhang, X. , Li, C. T. , Kum, D. S. , and Peng, H. , 2012, “ Prius+ and Volt−: Configuration Analysis of Power-Split Hybrid Vehicles With a Single Planetary Gear,” IEEE Trans. Veh. Technol., 61(8), pp. 3544–3552.
Sorniotti, A. , Holdstock, T. , Everitt, M. , Fracchia, M. , Viotto, F. , Cavallino, C. , and Bertolotto, S. , 2013, “ A Novel Clutchless Multiple-Speed Transmission for Electric Axles,” Int. J. Powertrains, 2(2–3), pp. 103–131.
Walker, P. D. , Abdul Rahman, S. , Zhu, B. , and Zhang, N. , 2013, “ Modelling, Simulations, and Optimisation of Electric Vehicles for Analysis of Transmission Ratio Selection,” Adv. Mech. Eng, 5, p. 340435.
Crowther, A. R. , Singh, R. , Zhang, N. , and Chapman, C. , 2007, “ Impulsive Response of an Automated Transmission System With Multiple Clearances: Formulation, Simulation, and Experiment,” J. Sound Vib., 306(3–5), pp. 444–466.
Zhang, Y. , Chen, X. , Zhang, X. , Jiang, H. , and Tobler, W. , 2005, “ Dynamic Modelling and Simulation of a Dual-Clutch Automated Lay-Shaft Transmission,” ASME J. Mech. Des., 127(2), pp. 302–307.
Zhu, B. , Zhang, N. , Walker, P. D. , Zhan, W. , Zhou, X. , and Ruan, J. , 2013, “ Two-Speed DCT Electric Powertrain Shifting Control and Rig Testing,” Adv. Mech. Eng., 5, p. 323917.
Gao, B. , Liang, Q. , Xiang, Y. , Guo, L. , and Chen, H. , 2015, “ Gear Ratio Optimization and Shift Control of 2-Speed I-AMT in Electric Vehicle,” Mech. Syst. Signal Process., 50–51, pp. 615–631.
Galvagno, E. , Velardocchia, M. , and Vigliani, A. , 2011, “ Analysis and Simulation of a Torque Assist Automated Manual Transmission,” Mech. Syst. Signal Process., 25(6), pp. 1877–1886.
Son, H. , Yoon, Y. S. , Kim, K. S. , Kim, S. J. , and Song, C. , 2015, “ Economic Hybrid Transmission System Using Clutchless Geared Manual Transmission,” 28th Electric Vehicle Symposium and Exhibition, Goyang, South Korea, May 3–6, pp. 3–6.
Walker, P. D. , Zhu, B. , and Zhang, N. , 2017, “ Powertrain Dynamics and Control of a Two Speed Dual Clutch Transmission for Electric Vehicles,” Mech. Syst. Signal Process., 85, pp. 1–15.
Rahimi Mousavi, M. S. , and Boulet, B. , 2014, “ Modeling, Simulation and Control of a Seamless Two-Speed Automated Transmission for Electric Vehicles,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 3826–3831.
De Pinto, S. , Camocardi, P. , Sorniotti, A. , Mantriota, G. , Perlo, P. , and Viotto, F. , 2017, “ Torque-Fill Control and Energy Management for a Four-Wheel-Drive Electric Vehicle Layout With Two-Speed Transmissions,” IEEE Trans. Ind. Appl., 53(1), pp. 447–458.
Zhou, X. , Walker, P. , Zhang, N. , Zhu, B. , and Ruan, J. , 2014, “ Numerical and Experimental Investigation of Drag Torque in a Two-Speed Dual Clutch Transmission,” Mech. Mach. Theory, 79, pp. 46–63.
Changenet, C. , Oviedo-Marlot, X. , and Velex, P. , 2006, “ Power Loss Predictions in Geared Transmissions Using Thermal Networks-Application to a Six Speed Manual Gearbox,” ASME J. Mech. Des., 128(3), pp. 618–625.
Zhu, X. , Zhang, H. , Xi, J. , Wang, J. , and Fang, Z. , 2014, “ Robust Speed Synchronization Control for Clutchless Automated Manual Transmission Systems in Electric Vehicles,” Proc. Inst. Mech. Eng., Part D, 229(4), pp. 424–436.
Tseng, C. Y. , and Yu, C. H. , 2015, “ Advanced Shifting Control of Synchronizer Mechanisms for Clutchless Automatic Manual Transmission in an Electric Vehicle,” Mech. Mach. Theory, 84, pp. 37–56.
Liu, H. , Lei, Y. , Li, Z. , Zhang, J. , and Li, Y. , 2012, “ Gear-Shift Strategy for a Clutchless Automated Manual Transmission in Battery Electric Vehicles,” SAE Int. J. Commer. Veh., 5(1), pp. 57–62.
Jeon, B. , and Kim, S. , 2014, “ Measurement and Modeling of Perceived Gear Shift Quality for Automatic Transmission Vehicles,” SAE Int. J. Passeng. Cars Mech. Syst., 7(1), pp. 423–433.
Chen, H. , and Gao, B. Z. , 2014, Nonlinear Estimation and Control of Automotive Drivetrains, 1st ed., Springer, Beijing, China.
Huang, Q. , and Wang, H. , 2004, “ Fundamental Study of Jerk: Evaluation of Shift Quality and Ride Comfort,” SAE Paper No. 2004-01-2065.
Baraszu, R. C. , and Cikanek, S. R. , 2002, “ Torque Fill-In for an Automated Shift Manual Transmission in a Parallel Hybrid Electric Vehicle,” American Control Conference (ACC), Anchorage, AK, May 8–10, pp. 1431–1436.
Walker, P. D. , and Zhang, N. , 2014, “ Transmission of Engine Harmonics to Synchronizer Mechanisms in Dual Clutch Transmissions,” ASME J. Vib. Acoust., 136(5), p. 051009.
Magne, P. , Shi, X. , and Krishnamurthy, M. , 2014, “ Fundamentals of Power Electronics,” Advanced Electric Drive Vehicles, A. Emadi , ed., CRC Press, Boca Raton, FL, pp. 43–106.
Alizadeh, H. V. , and Boulet, B. , 2014, “ Robust Control of Synchromesh Friction in an Electric Vehicle's Clutchless Automated Manual Transmission,” IEEE Conference on Control Applications (CCA), Nice, France, Oct. 8–10, pp. 611–616.
Walker, P. D. , and Zhang, N. , 2011, “ Parameter Study of Synchroniser Mechanisms Applied to Dual Clutch Transmissions,” Int. J. Powertrains, 1(2), pp. 198–220.
Walker, P. D. , and Zhang, N. , 2012, “ Engagement and Control of Synchroniser Mechanisms in Dual Clutch Transmissions,” Mech. Syst. Signal Process., 26, pp. 320–332.
Lovas, L. , Play, D. , Marialigeti, J. , and Rigal, J. , 2006, “ Mechanical Behaviour Simulation for Synchromesh Mechanism Improvements,” Proc. Inst. Mech. Eng., Part D, 220(7), pp. 919–945.
Breen, J. L. , and Bower, G. , 2001, “ Clutchless Shifting of an Automated Manual Transmission in a Hybrid Powertrain,” SAE Paper No. 2011-01-2194.
Nagel, N. J. , 2014, “ Fundamentals of Electric Motor Control,” Advanced Electric Drive Vehicles, A. Emadi, ed., CRC Press, Boca Raton, FL, pp. 187–236.
Pinte, G. , Depraetere, B. , Symens, W. , Swevers, J. , and Sas, P. , 2010, “ Iterative Learning Control for the Filling of Wet Clutches,” Mech. Syst. Signal Process., 24(7), pp. 1924–1937.
Abdel-Halim, N. , Barton, D. , Crolla, D. , and Selim, A. , 2000, “ Performance of Multicone Synchronizers for Manual Transmissions,” Proc. Inst. Mech. Eng., Part D, 214(1), pp. 55–65.

## Figures

Fig. 1

CLAMT powertrain arrangement

Fig. 2

DC equivalent circuit model

Fig. 3

Clutchless AMT multibody model

Fig. 4

Typical synchronizer mechanism

Fig. 5

Alternative shifting strategies

Fig. 6

Combined torque–speed control loops

Fig. 7

First to second gear upshift with a state duration of 200 ms and motor torque of 200 N·m: (a) shift control states, (b) motor voltage (green) and current (red), and (c) motor torque (blue profile, green actual) and speed (cyan)

Fig. 8

Second to first downshift with a state duration of 200 ms and motor torque of 200 N·m: (a) shift control states, (b) motor voltage and current, and (c) motor torque (blue profile, green actual) and speed (cyan)

Fig. 9

Up and down shift transients for clutchless AMT powertrain for a 200 ms stage duration at 200 N·m motor torque: (a) system speeds, (b) vehicle longitudinal acceleration, and (c) vehicle longitudinal jerk

Fig. 10

Up and down shift transients for clutchless AMT powertrain for a 400 ms stage duration at 200 N·m motor torque: (a) system speeds, (b) vehicle longitudinal acceleration, and (c) vehicle longitudinal jerk

Fig. 11

Up and down shift transients for clutchless AMT powertrain for a 20 ms stage duration at 200 N·m motor torque: (a) system speeds, (b) vehicle longitudinal acceleration, and (c) vehicle longitudinal jerk

Fig. 12

Summarized shift quality metrics: (a) RMS vehicle jerk against stage duration, (b) RMS Jerk against peak drive torque, (c) vibration dose value versus stage duration, (d) VDV versus peak drive torque, (e) total shift time versus stage duration, and (f) total shift time versus peak drive torque. Notation: x—simulated values and o—time normalized simulated values for VDV.

Fig. 13

First to second gear upshift with a stage duration of 200 ms and motor torque of 200 N·m for combined motor and synchronizer speed synchronization: (a) motor voltage and current, (b) motor torque (blue profile, green actual) and speed (cyan), and (c) synchronizer position

Fig. 14

First to second gear upshift with a stage duration of 200 ms and motor torque of 200 N·m for synchronizer only control of speed synchronization: (a) motor voltage and current, (b) motor torque (blue profile, green actual) and speed (cyan), and (c) synchronizer position

## Tables

Table 1 Natural frequencies from undamped free vibration analysis in each gear ratio
Table 2 Powertrain system parameters

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