Sage Journals: Discover world-class research

Abstract

A novel motor-driven clutch actuator with force-aided lever has been recently developed. A unique spring is used to assist apply of the clutch that can effectively reduce the motor power requirement, and the actuation system can save power consumption during clutch operations with faster response and higher control precision. In this article, a mathematical model of the conceptual clutch actuation system is developed to study the dynamic behavior of the actuator system via computer simulation. The actuator model is further integrated into a dual-clutch transmission and driveline system to demonstrate the effectiveness of the concept in shifting control. The simulation result demonstrates the smooth and fast clutch-to-clutch gear shift and hence validates the feasibility of this new force-aided lever actuation system.

Keywords

Motor driven force-aided actuation system dry clutch

Introduction

The automotive transmission is currently edging toward improving powertrain system efficiency and driving comfort. Smooth gear shifting control is critical for overall drive quality.^1–3 Clutch actuation is a key component in the clutch control system,⁴ and depending on the transmission type and clutch actuation needs, clutch control can be executed with different actuation mechanisms, particularly for automated manual transmission (AMT),^2,5 dual-clutch transmission (DCT),^3,6 and various hybrid transmission.^7,8 The commonly used systems include electrohydraulic and electromechanical actuation systems,^6,9 where the latter has a greater potential for cost-saving and performance improvement.^5,10,11 Due to its high mechanical efficiency and control precision, electromechanical systems may become the mainstream in the future.^10–12 Compared with electrohydraulic systems, electromechanical systems have faster response, higher energy efficiency, as well as compatibility with intelligent controls.^4,12 However, the drawback of these systems lies in the lower force/torque density, so the force/torque capacity is difficult to meet the design requirement and the actuator needs to grow in size, resulting in packaging infeasibility. To address this issue, various force-aided mechanisms have been designed to increase the actuation force while keeping the package compact.

Wheals et al.^13,14 proposed a force-aided motor-driven actuator by storing and releasing energy using permanent magnet for AMTs and DCTs. Unfortunately, the mechanism also provides the same aiding force even when the clutch is fully open when zero normal force is required. Therefore, the actuation motor has to generate a force to counter the undesired force from magnet at the open position, which will draw additional energy consumption. Yao et al.^4,15–17 designed a wedge-based clutch for automatic transmission, aiming to utilizing the self-reinforcement property from the wedge feature. Kim and Choi^10,18 designed a wedge mechanism for an AMT clutch. The intractable issue of the wedge mechanism lies in the self-weakened effect, which occurs when the clutch slipping speed is reversed. This effect can greatly restrict the application of the wedge mechanism.

Preloaded spring, viewed as an energy storage component, is adopted in several force-aided solutions. One mechanism proposed by Jianwu Zhang releases the preloaded spring during clutch engagement assisting an actuation motor.^19,20 However, such design is not able to reduce the motor size as the aiding force decreases rapidly with the engagement travel, where bigger actuation force is required. Another design involves a preloaded spring acting on a lever with a moving pivot,^21–24 which has been used on a six-speed dry DCT. The experimental results show that the actuation system has a fast response.²⁵ In general, the controllability of the system is essentially rooted in the monotonicity of the clutch diaphragm, and the actuation system becomes uncontrollable when the diaphragm has a “downward force-travel characteristic.”²⁶ Lee et al.²⁷ integrated the spring, lever, wedge, and many other components into an actuation mechanism, and for such complicated system, the reliability, maintainability, and cost limit its practicality.

To date, electromechanical dry-clutch actuation system with large aiding force and good controllability is still of research interest, which includes monotonic or non-monotonic diaphragms. This article is to propose a new force-aided mechanism by adding a rotating preloaded spring to a lever. The spring can rotate along with the lever. With bigger rotational angle, the spring can store and release more energy to assist the clutch apply. In this case, the aiding force becomes larger as the clutch piston travels during the engagement. The aiding force is nonlinear with respect to the rotating angle, and comprehensive modeling and analysis are necessary to study the function and characteristics of the new mechanism.

This article is organized as follows. In section “Design of force-aided lever actuator,” the principle of force-aided lever and the design are presented. In section “System analysis and modeling,” the dynamic model of the actuation system is established. A position-based closed-loop control algorithm is described in section “Controller design.” In section “Results and discussion,” the force-aided feature of new actuation system is studied and the function is validated through simulation. The simulation results demonstrate the performance of the actuator system during clutch engagement. Besides, the force-aided effect, system dynamic characteristics, and controllability are discussed. With the advantages of the fast response, small actuation force, and accurate control, the new actuator system has great potential for practical applications. Finally, the conclusion is drawn in section “Summary.”

Design of force-aided lever actuator

Actuator principle

In a traditional manual or DCT transmission, the clutch is connected to the flywheel and input shaft of transmission. The clutches can be wet or dry.²⁸Figure 1 illustrates a normally open clutch. When no force is applied on the piston, the clutch remains disengaged.²⁸ In the assembly in Figure 1, a clutch pack includes pressure plate, friction plate, diaphragm, piston, and actuation lever. The hydraulic system generates an actuation force $F_{m}$ to push the lever down and causes the lever to rotate clockwise about the pivot. As a consequence, the piston moves down and engages the clutch plate through diaphragm. During the engagement, the lever is pushed by an actuation system, and then, it moves the piston to compress the diaphragm, clutch friction plate, and pressure plate. Control precision and response time are critical for a clutch actuation system, which determines how smooth and how fast a gear shift can achieve.^3,6,29 In addition to the hydraulic-based system shown here, the electromechanical actuation system has become popular and shown promises in meeting the control requirements with a low cost potential.^14,21

Figure 1.

The schematic representation of the dry-clutch assembly with a traditional actuator.

Figure 2 shows an example of the electromechanical actuation system design featured by a moving pivot, which adjusts the force ratio between the two ends of the lever. Besides, one end of the lever is connected to a preload spring, and the lever motion is driven by the preload spring. The spring is compressed and installed along the vertical direction at the end of a lever point B. The other end of the lever point C directly acts against the diaphragm of clutch. In this arrangement, the diaphragm is compressed by the spring force through the lever. A soft leaf spring is attached to the lever on one side and a stiff support D on the other. As soon as the electric motor drives the fulcrum roller O through a power screw, the fulcrum roller in turn pushes the lever along its profile and causes a change in the force arm OB and OC. As a consequence, the piston force $F_{c}$ is controlled by the position of fulcrum roller O.

Figure 2.

The schematic representation of the dry-clutch assembly with an “existing production actuator.”

In this concept, the driving motor is used to move the pivot, and the associated power consumption would be less than the case when the motor is directly acting on the lever. However, at the same time, it has limited the controllability of the lever rotating dynamics, especially under the negative stiffness of the diaphragm. In what follows, a new electromechanical clutch actuation system with a force-aided feature is proposed.

The principle of the force-aided lever for single clutch is described in Figure 3. When the clutch is open, the compressed spring is along the direction of OB. With the force acting on the pivot O in this position, the effective moment generated by the spring force is zero. As soon as the motor force $F_{m}$ pushes the lever downward and causes it to rotate clockwise around the pivot O, point B of the lever will move up. Accordingly, the spring will rotate counterclockwise about the pivot D. When the spring moves away from its original position, the spring starts to generate positive (clockwise) moment on the lever in the same direction as the clutch applies for assistance. The effective moment from the spring depends on the angle of the rotation of the lever. A larger spring stiffness and bigger rotation angle result in a higher aiding force.

Figure 3.

The schematic representation of the dry-clutch assembly with force-aided lever actuation system.

Although both of the electromechanical systems illustrated in Figures 2 and 3 consist of a motor, lever, and spring, their principles differ fundamentally. In the concept illustrated in Figure 2, the force to engage clutch solely comes from the spring, and the motor moves the pivot of lever to change the actual applying force. In force-aided lever actuator in Figure 3, the pivot is fixed, and both motor and spring contribute to the clutch normal force during the clutch apply. The motor provides the torque on the lever directly, so it has a better controllability of the lever rotating dynamics. Consequently, the lever system may have a better stability under the feedback control through the motor.

Table 1 lists the main design properties of the two systems discussed above for comparison. In the existing actuator concept, the pivot of lever is essentially controlled, so that a diaphragm with upward force-travel characteristics can be used, and plus, it needs a high precision in the lever curve manufacturing. However, for the force-aided actuator, the controllability of the system is not sensitive to the lever geometry, but the trade-off here is that it needs a longer lever.

Table 1.

Comparison between “existing production actuator” and “force-aided actuator.”

	“Existing production actuator”	“Force-aided actuator”
Principle	Move pivot rollers	Force-aided lever
Actuator travel (mm)	35	34
Application for “downward force-travel characteristic” diaphragm	×	√
Application for “upward force-travel characteristic” diaphragm	√	√
Motor rated power (W)	170	50
Minimum actuation time (ms)	110	180
Lever length (mm)	80	180

In summary, the force-aided lever mechanism proposed here has the following advantages. First of all, this electromechanical actuation system appears to be more cost-effective compared to a hydraulic system as it eliminates the need for hydraulic circuits, oil pump, solenoid valves, oil pressure sensors, and other hydraulic accessories. In addition, the force-aided spring assists the motor during clutch engagement, so that a smaller motor can be used with less power consumption. Therefore, a 12-V system is sufficient, which is desired from the economic consideration. Besides, the equivalent aiding force increases with the lever rotation, which means that the spring can provide larger aiding force when needed. This characteristic will be studied in the following section. Finally, the electromechanical system improves control robustness under various transmission operation conditions.

Physical structure

Figure 4 and Table 2 illustrate the layout of the novel clutch actuation system and the name of each part for a dry-DCT transmission. For each clutch, the actuation system includes a preload spring (16), lever (4), linear unit with motor (3), and connectors (2, 6, 12, 14, 15, 17, and 18). The lever can rotate about the pivot (13). Driven by motor (3) through a slider (1), the lever rotates and pushes the clutch piston (9) to apply the clutch. A preload spring (16) is installed on the other end of the lever, which can rotate about the pivot (19). Both of the pivots (13 and 19) are fixed on the transmission case. And a sleeve (15) with a roller is installed between the lever (4) and the force-aid spring (16) to transfer the moment generated by the spring to the lever and then to the clutch piston. A motor is used to move the lever for clutch apply and release. It can be a linear motor or a rotary motor with a power screw. We used the latter option in our prototype for cost considerations. The parameters for the actuation system are listed in Table 3.

Figure 4.

3D model of the clutch actuation system.

Table 2.

Description of actuation system.

1	Slider	2	Motor shaft
3	Linear unit with motor	4	Lever I
5	Transmission case	6	Roller of slider
7	Lever II	8	Clutch piston II
9	Clutch piston I	10	Bearing
11	Input shaft	12	Support of pivot O
13	Pivot O	14	Roller of sleeve
15	Sleeve	16	Preload spring
17	Spring piston	18	Support of pivot D
19	Pivot D

Table 3.

Parameter of Actuator.

Symbol	Value	Unit	Description
$P_{mr}$	50	W	Motor rated power
$K_{m}$	0.131	N m/A	Motor moment coefficient
$R$	0.567	$Ω$	Motor electric residence
L	4.13 × 10⁻⁴	H	Motor inductance
$K_{f}$	9.632 × 10⁻⁴	N m s	Motor damping coefficient
$I_{m}$	1.81 × 10⁻⁵	$kg m^{2}$	Motor inertial
$l$	0.18	m	Length of OA
$l_{1}$	0.060	m	Length of OC
$l_{2}$	0.070	m	Length of OD
$l_{0}$	0.030	m	Length of OB
$K_{s}$	7 × 10⁷	N/m	Preload spring stiffness
$F_{p}$	3500	N	Spring preload
$I$	0.002	$kg m^{2}$	Lever inertia about pivot O
$c$	0.1	N m s/rad	Lever rotary damping
$α_{b}$	0.158	rad	Bevel angle of the screw
$r_{m}$	4 × 10⁻³	m	Acting radius on the power screw of the motor
$μ_{Bk}$	0.09	–	Slipping friction coefficient
$μ_{sk}$	0.10	–	Static friction coefficient

System analysis and modeling

A numerical model of the force-aid actuation system in a vehicle is developed to study its dynamic characteristics to further validate the performance of the electromechanical actuator. The model is developed in MATLAB/Simulink. It consists of two layers, as shown in Figure 5. The first layer is the actuator model, including the DC motor, power screw, lever mechanism, and accessories; the second layer is the drivetrain model with a DCT transmission including the engine, dual-mass flywheel (DMF), gearbox with two clutches, and vehicle to simulate a vehicle gear shift.

Figure 5.

Diagram of dynamic model of DCT with new actuation systems.

Each actuation system model is composed of four main components: motor module, power screw, lever mechanism, and diaphragm, as shown in Figure 6. Most components of this system are treated as rigid body, including the lever, motor, and some connectors. The elastic components such as force-aided spring and diaphragm are treated as pure stiffnesses with the possible inertias are neglected. The dotted line illustrates the position of the lever when the clutch is fully open. $F_{m}$ is the actuation force from DC motor, $F_{c}$ is the piston force from diaphragm, $F_{q}$ is the force between slider and lever, $F_{s}$ is the spring force, $θ$ is the rotational angle of the lever, $α$ is the rotational angle of the spring, and $l, l_{1}, l_{2}, and l_{0}$ are the lengths of the force arm OA, OC, OD, and OB, respectively.

Figure 6.

Dynamic analysis of the actuation system.

Motor

The dynamics of the motor consists of electromagnetic and mechanical parts. The resistance of the circuit $R$ and the self-inductance of the armature $L$ are assumed to be constant. The following differential equations describe the behavior of this electromechanical system

V_{app} - K_{b} {\overset{\cdot}{θ}}_{m} = L \frac{d i_{m}}{d t} + R i_{m}

(1)

I_{m} {\overset{\cdot\cdot}{θ}}_{m} = - K_{f} {\overset{\cdot}{θ}}_{m} + K_{m} i_{m} - T_{mo}

(2)

in which $θ_{m}$ is the motor rotating angle and $K_{b}$ is the electromotive force (EMF) constant, which also depends on certain physical properties of the motor. $I_{m}$ is the motor inertia, $K_{f}$ is a linear approximation for viscous friction, $V_{app}$ is the applied voltage, $T_{mo}$ is the load torque or motor output torque, i_m is motor current and $K_{m}$ is the armature constant related to physical properties of the motor, such as magnetic field strength and the number of turns of wire around the conductor coil.

Power screw

The ball screw unit consists of a screw, a screw nut, and bearing balls. For convenience of force analysis, the ball screw unit is supposed to be expanded as shown in Figure 7.

Figure 7.

Force analysis of the ball screw unit.

The force $F_{a}$ is generated by the motor and calculated by

F_{a} = \frac{T_{mo}}{r_{m}}

(3)

in which, $r_{m}$ is the acting radius of the motor torque.

The force balances of the screw yield

F_{a} = F_{bs} \sin α_{b} + F_{fB} \cos α_{b}

(4)

in which, $F_{bs}$ is the normal force acting on the screw by the balls, $F_{fB}$ is the friction force on the screw, and $α_{b}$ is the bevel angle of the screw.

The force balance of the slider yields

F_{m} = F'_{bs} \cos α_{b} - F'_{fB} \sin α_{b}

(5)

in which, $F'_{bs}$ is the normal force acting on the screw nut by the balls and $F'_{fB}$ is the friction force of the screw nut.

The equilibrium of the action and reaction forces yields

F_{bs} = F'_{bs}

(6)

F_{fB} = F'_{fB}

(7)

The friction force $F_{fB}$ is modeled using the coulomb friction model as shown in Figure 8. The mathematical expression is given as follows

F_{fB} = {\begin{matrix} μ_{Bk} F_{bs} sign ({\overset{\cdot}{θ}}_{m}) | {\overset{\cdot}{θ}}_{m} | > ε_{0} \\ [- μ_{sk} F_{bs}, μ_{sk} F_{bs}] | {\overset{\cdot}{θ}}_{m} | < ε_{0} \end{matrix}

(8)

in which, $μ_{Bk}$ and $μ_{sk}$ denote the slipping friction and static friction coefficient, respectively, and $ε_{0}$ is a small positive constant, which is used to differentiate the stick friction from the slip friction.

Figure 8.

Coulomb friction model.

Lever

Figure 6 shows the schematic diagram for the system force analysis. The dynamic equation can be written as

I \overset{\cdot\cdot}{θ} = \frac{F_{q} l}{\cos θ} + F_{s} l_{2} \sin α - F_{c} l_{1} - c \overset{\cdot}{θ}

(9)

in which, $I$ is the inertia of lever rotating with pivot O and $c$ is the rotating damping of lever. $α$ is the spring rotating angle. $l, l_{1}, l_{2}, and l_{0}$ are the geometry lengths of the lever. The force $F_{q}$ is the slider force, which can be calculated as

F_{q} = \frac{F_{m}}{\cos θ}

(10)

The spring force $F_{s}$ can be calculated as

F_{s} = K_{s} (l_{2} - l_{0} + \frac{F_{p}}{K_{s}} - l_{s})

(11)

where $l_{s}$ , $K_{s}$ , and $F_{p}$ denote the spring length DB, stiffness, and preloaded force of spring, respectively. According to the motion constraint of lever, the following equations are obtained

\frac{\sin α}{l_{0}} = \frac{\sin θ}{l_{s}}

(12)

l_{s}^{2} = l_{2}^{2} + l_{0}^{2} - 2 l_{2} l_{0} \cos θ

(13)

The motion constraint of lever and the ball screw yields the calculation of $θ$ as follows

\tan θ = \frac{r_{m} \tan α_{b} θ_{m}}{l}

(14)

Diaphragm

In this article, the DCT clutches are normally open. Figure 3 shows the diaphragm installation in one clutch pack. During the clutch engagement, the spring exhibits the diaphragm characteristics first in clearance phase before the pressure plate comes in contact with the friction plate, and then, it will behave like a lever spring once they touch.¹² The piston force $F_{c}$ and the clutch normal force $F_{n}$ are functions of piston travel $λ$ , which are obtained by experiment using curve fitting with a fifth-degree polynomial and exponential function³⁰

F_{c} = p_{1} λ^{5} + p_{2} λ^{4} + p_{3} λ^{3} + p_{4} λ^{2} + p_{5} λ

(15)

\begin{matrix} F_{n} = a_{1} (x - a_{2} - \frac{1 - e^{- a_{3} (λ - a_{2})}}{a_{3}}) \\ (0.5 \tan h (100 (λ - a_{2})) + 0.5) \end{matrix}

(16)

in which, $p_{1}, p_{2}, p_{3}, p_{4}, and p_{5}$ and $a_{1}, a_{2}, and a_{3}$ are fitting parameters for the piston force and the clutch normal force, respectively. The piston travel $λ$ can be calculated as

λ = l_{1} \tan θ

(17)

Two typical diaphragm characteristics, “upward force-travel characteristic” diaphragm and “downward force-travel characteristic” diaphragm, are used for the validation of the new clutch actuator, as shown in Figure 9. The piston force $F_{c}$ increases with piston travel $λ$ , which is called “upward force-travel characteristic” as shown in Figure 9(a). Figure 9(b) shows the “downward force-travel characteristic” diaphragm. Piston force $F_{c}$ decreases with piston travel $λ$ changing from 1.6 to 5.5 mm, which may cause a stability issue for the actuator design.²⁶

Figure 9.

Two typical characteristics of diaphragm for normally open clutch: (a) “Upward force-travel characteristic” diaphragm and (b) “Downward force-travel characteristic” diaphragm.

The powertrain model

The transmission is based on a dry DCT that has six forward speeds and one reverse, with the odd gears on the hollow shaft connected to clutch 1 and even gears on the solid shaft connected to clutch 2.²⁹ To demonstrate the functionality of the actuator, a typical upshift is investigated without loss of generality. In this case, only a simplified transmission model is used with only necessary components relevant to the shift considered, as shown in Figure 10. Here, the model has been made generic to be able to represent all possible upshift with proper parameters (inertias, ratios, initial conditions, etc.), while the gear selector and its pre-selection procedure are neglected. The drivetrain model further includes engine, DMF, two clutches, gearbox with two-speed gear sets and final drive, half shafts, and a front-wheel-drive (FWD) vehicle body module. The gear shift involves the engagement of the oncoming clutch and the release of the offgoing clutch. Two single-disk dry clutches are housed in a compact assembly which also contains the clutch actuators whose structure has been described.

Figure 10.

Simplified two-speed DCT dynamic model.

A 4-degree-of-freedom (DOF) model is built as shown in Figure 10. The first DOF derives from the motion of the lumped inertia $I_{d 1}$ , which represents the engine and one part of the DMF. The second DOF derives from the motion of the inertia $I_{d 2}$ which represents the other part of the DMF. The third DOF derives from the motion of the transmission, in which, the two clutches and the final drive are represented by the inertias $I_{c 1}$ , $I_{c 2}$ , and $I_{fd}$ , respectively. The fourth DOF derives from the motion of the inertia $I_{v}$ , which represents the vehicle. The angular velocities of the 4-DOF motions are denoted by ${\overset{\cdot}{θ}}_{e}$ , ${\overset{\cdot}{θ}}_{d 2}$ , ${\overset{\cdot}{θ}}_{fd}$ , and ${\overset{\cdot}{θ}}_{v}$ , respectively. The elasticity of the DMF is modeled by the stiffness $k_{d}$ and the damping $c_{d}$ . The elasticity of the drive shafts is modeled by the stiffness $k_{v}$ and the damping $c_{v}$ . The rotational damping from friction and lubrication of the components before the clutches is modeled by $b_{e}$ , and the rotational damping of those after the clutches is modeled by $b_{fd}$ . $i_{1}$ , $i_{2}$ , and $i_{fd}$ are the first gear ratio, second gear ratio, and final drive ratio, respectively.

The governing equations of 4-DOF model for the two-speed DCT system are as follows

I_{d 1} {\overset{\cdot\cdot}{θ}}_{e} = T_{e} - b_{e} {\overset{\cdot}{θ}}_{e} - [k_{d} (θ_{e} - θ_{d 2}) + c_{d} ({\overset{\cdot}{θ}}_{e} - {\overset{\cdot}{θ}}_{d 2})]

(18)

I_{d 2} {\overset{\cdot\cdot}{θ}}_{d 2} = k_{d} (θ_{e} - θ_{d 2}) + c_{d} ({\overset{\cdot}{θ}}_{e} - {\overset{\cdot}{θ}}_{d 2}) - T_{c 1} - T_{c 2}

(19)

\begin{matrix} (i_{1}^{2} i_{fd}^{2} I_{c 1} + i_{2}^{2} i_{fd}^{2} I_{c 2} + I_{fd}) {\overset{\cdot\cdot}{θ}}_{fd} \\ = i_{1} i_{fd} T_{c 1} + i_{2} i_{fd} T_{c 2} - T_{g_out} - b_{fd} {\overset{\cdot}{θ}}_{fd} \end{matrix}

(20)

I_{v} {\overset{\cdot\cdot}{θ}}_{v} = T_{g_out} - T_{load}

(21)

in which, $T_{g_out}$ stands for the transmission output shaft torque

T_{g_out} = k_{v} (θ_{fd} - θ_{v}) + c_{v} ({\overset{\cdot}{θ}}_{fd} - {\overset{\cdot}{θ}}_{v})

(22)

The engine output torque $T_{e}$ is dependent on the throttle position $(TP)$ and the angular velocity ${\overset{\cdot}{θ}}_{e}$ of the engine, which are expressed as

T_{e} = f (TP, {\overset{\cdot}{θ}}_{e})

(23)

Considering the frontal drag and rolling resistance, the vehicle load torque $T_{load}$ is calculated as³¹

T_{load} = (c_{1} + c_{2} \cdot V + c_{3} \cdot V^{2}) R_{tr}

(24)

in which, $R_{tr}$ is the tire radius and $c_{1}$ , $c_{2}$ , and $c_{3}$ are the three coefficients. The vehicle velocity $V$ is calculated as

V = {\overset{\cdot}{θ}}_{v} R_{tr}

(25)

The clutch friction torques $T_{c 1}$ and $T_{c 2}$ are calculated using the same friction model. Let $T_{c}$ denote the general friction torque, and the calculation is given as

T_{c} = μ N R_{cp} F_{n}

(26)

in which, $N$ is the number of friction interfaces of the clutch and $R_{cp}$ is the equivalent radius of the clutch friction interface. $F_{n}$ is the clutch normal force, which is obtained from the actuation system model and treated as an input of the powertrain model. Instead of using the discontinuous Coulomb model,³² the friction coefficient $μ$ is smoothened for computation convenience as follows

μ = μ_{k} [1.0 + (\frac{μ_{s}}{μ_{k}} - 1.0) e^{- ζ | Δ \overset{\cdot}{θ} |}] \tan h (ξ \cdot Δ \overset{\cdot}{θ} \cdot R_{cp})

(27)

in which, $μ_{k}$ and $μ_{s}$ denote the slipping friction and static friction coefficients, respectively; $ς$ and $ζ$ are two tuning parameters; and $Δ \overset{\cdot}{θ}$ is the slipping speed of the clutch.

Controller design

Actuator controller

For a clutch actuator controller, the input is clutch normal force command, and the output is the motor voltage, which will drive the motor to apply the clutch normal force through the lever mechanism. The diagram is shown in Figure 11.

Figure 11.

Actuator controller diagram.

The controller is composed of a force lookup table, a position loop, and a current loop. The force lookup table is based on the diaphragm characteristic (Figure 9), and the motor position command is calculated from the target clutch normal force. Theoretically, if the lookup table is known precisely, clutch normal force can be controlled well if the piston traveling is controlled precisely. Note that the uncertainties of the diaphragm or flat spring usually exist. It needs advance control method to deal with these uncertainties, such as clutch torque estimation or robust control.

Then, the motor position command $θ_{m_cmd}$ is compared with the actual motor position and fed into a proportional–integral–derivative (PID) position loop to output the motor current command, with a saturation of 8 A. Finally, the current loop will output the motor voltage $V_{app}$ with a saturation of 12 V. The PID controller is defined with coefficients ( $K_{pp}$ , $T_{pi}$ , and $τ_{p}$ ) as follows

i_{m_cmd} = K_{pp} (1 + \frac{1}{T_{pi}} \int e_{p} d t + τ_{p} \frac{d e_{p}}{d t})

(28)

V_{app} = K_{ip} (1 + \frac{1}{T_{ii}} \int e_{i} d t)

(29)

in which

e_{p} = θ_{m_cmd} - θ_{m}

(30)

e_{i} = i_{m_cmd} - i_{m}

(31)

Clutch-to-clutch upshift control strategy

Unlike the conventional automatic transmissions, the DCT needs more precise clutch control, since no torque converter is available to dampen possible dynamic impacts during a shift.³¹ The clutch torque needs to be controlled precisely for a good vehicle launch and smooth gear shifting. Both the torque and timing are critical. The objective of the shift control is to maintain the possible torque disturbances minimum with the proper clutch control and coordination to achieve good drive quality.³³

The new force-aided lever actuator system needs to execute the typical clutch-to-clutch control strategy with four phases, that is, fill phase, torque phase, inertia phase, and end phase. The desired $F_{n}$ is controlled by the new actuator motor position. In the fill phase, the oncoming clutch needs to overcome the clearance quickly with minimum impact; during the torque phase, the drivetrain torque needs to be transferred from the offgoing clutch to the oncoming clutch; in the inertia phase, the actuator needs to adjust the clutch normal force in order to synchronize the friction plate and steel plate quickly and smoothly. As the shift enters the inertia phase, the torque carried by the offgoing clutch is zero. The speed ratio starts to change and the torque carried by the oncoming clutch needs to be controlled accurately to facilitate the ratio change. In the end phase, the oncoming clutch increases to the maximum value in order to lock the clutch. The shift strategies are shown in Figure 12.

Figure 12.

Clutch-to-clutch control strategy during upshift.

Results and discussion

The performance validation through simulations for this new system includes three parts. First, the influence of different parameters on force-aided feature will be studied. Second, based on the dynamic model, the actuation performance will be benchmarked with the same actuator without the force-aided spring in terms of clutch engagement and system response. Besides, the stability of the new actuation system will be examined. Finally, the simulation of the actuation system in a complete drivetrain environment including a DCT transmission is used to further demonstrate the actuator capability during a clutch-to-clutch shift. The parameters of actuation system used in simulation are listed in Table 3.

Effect of the influencing factors on aiding force

Suppose the clutch actuator is at equilibrium and the components are static, that is

\overset{\cdot}{θ} = 0, \overset{\cdot\cdot}{θ} = 0

(32)

Substitution of equation (32) into the equations (9) and (10) yields the expression as follows

F_{c} = \frac{F_{m}}{\cos^{2} θ} \frac{l}{l_{1}} + F_{s} \frac{l_{2}}{l_{1}} \sin α

(33)

Equation (33) shows that at equilibrium, the force that compresses the diaphragm is equal to the sum of the actuation force $F_{m}$ and spring force $F_{s}$ . The following equation gives the equivalent aiding force ${F_{s}}_{eq}$ acting on the clutch piston that is generated by the force-aided spring

{F_{s}}_{eq} = F_{s} \frac{l_{2}}{l_{1}} \sin α

(34)

By substituting equations (11)–(13) into the right side of equation (34), the following equation is obtained

\begin{matrix} {F_{s}}_{eq} = [F_{p} - K_{s} l_{2} (\frac{l_{0}}{l_{2}} - 1 + \sqrt{1 + {(\frac{l_{0}}{l_{2}})}^{2} - 2 (\frac{l_{0}}{l_{2}}) \cos θ})] \cdot \\ \frac{(l_{0} / l_{2}) \sin θ}{\sqrt{1 + {(l_{0} / l_{2})}^{2} - 2 (l_{0} / l_{2}) \cos θ}} \cdot \frac{l_{2}}{l_{1}} \end{matrix}

(35)

The equivalent aiding force ${F_{s}}_{eq}$ can show the force-aided feature of this actuation system. Higher ${F_{s}}_{eq}$ means more aiding force from the spring. Equation (35) shows that ${F_{s}}_{eq}$ is related to the rotational angle $θ$ , spring preload $F_{p}$ , stiffness $K_{s}$ , and geometry length $l_{0} / l_{2} and l_{1} / l_{2}$ . Here, the maximum aiding force ${F_{s}}_{eq}$ is taken as the objective. This single-objective problem is generally simpler than those multi-objective problems.^34,35 There are various methods to solve the single or multi-optimization problems.³⁶ In this article, two variable trade-off surfaces³⁷ are used for analyzing the influence of the aiding force.

The lever rotational angle $θ$ , spring preload $F_{p}$ , stiffness $K_{s}$ , and geometry length $l_{1} / l_{2}$ and $l_{0} / l_{2}$ are treated as the five independent influencing factors. Calculated from equation (35), the effect of the spring preload $F_{p}$ and the lever rotational angle $θ$ is shown in Figure 13(a). The aiding force ${F_{s}}_{eq}$ increases when the angle $θ$ is small and then tends to decrease when the angle $θ$ becomes larger. It can be seen that the aiding force ${F_{s}}_{eq}$ can be approximately linear with respect to the angle $θ$ within the range $θ \in [0, 0.26] rad$ or $θ \in [0, 15]$ . In addition, larger spring preload $F_{p}$ generates larger aiding force ${F_{s}}_{eq}$ . Figure 13(b) shows the effect of geometry length $l_{1} / l_{2}$ and $l_{0} / l_{2}$ . Increasing of $l_{1} / l_{2}$ will reduce the aiding force $F_{seq}$ . When the range of $l_{1} / l_{2}$ is relatively small, the effect on aiding force $F_{seq}$ is relatively obvious. Figure 13(c) shows that the aiding force is not sensitive to the spring stiffness.

Figure 13.

Equivalent aiding force analysis under different parameters: (a) aiding force $F_{seq}$ versus rotational angle $θ$ and spring preload $F_{p}$ , (b) aiding force $F_{seq}$ versus length $l_{1} / l_{2}$ and $l_{0} / l_{2}$ , and (c) aiding force $F_{seq}$ versus stiffness $K_{s}$ .

Generally speaking, a large spring preload and long $l_{0} / l_{2}$ should be considered if a high aiding force is desired. However, the geometry dimensions for an actuator are usually constrained in practice. Besides, a large spring preload may possibly result in an unstable system, and it is unfavorable from manufacturing point of view.

System response for step input

This section will study ultimate responsiveness of the actuation system by following the position step input. Using the control scheme designed in section “Controller design,” the actuation system is validated by the dynamic models with two diaphragms of different characteristics discussed in section “System analysis and modeling.”Figure 14 shows the simulation results for a diaphragm with the “upward force-travel characteristics” (Figure 9(a)). The actuation system generates a normal force on the clutch plate by the lever to a certain position controlled by the motor. The motor angular position reference is given as a step function with an amplitude of 36 rad, which corresponds to a 3000 N normal force, as shown in Figure 14(a). The motor current, motor speed, piston force, and clutch normal force are illustrated in Figure 14(b)–(e). The motor speed increases rapidly at first because the motor current starts at a high value to accelerate the motor. After that, the motor current is kept constant at 8 A, which is the maximum current allowed by the motor, while the motor speed decreases as the piston force $F_{c}$ increases. The clutch normal force $F_{n}$ keeps zero until 1.05 s since the clutch is through the clearances (previously defined as the fill phase). In the end, the motor current decreases rapidly in order to avoid any overshoot.

Figure 14.

Step response of the force-aided lever actuation system with “upward force-travel characteristic” diaphragm: (a) motor rotational angle $θ_{m}$ , (b) motor current $i_{m}$ , (c) motor speed ${\overset{\cdot}{θ}}_{m}$ , (d) piston force $F_{c}$ , and (e) clutch normal force $F_{n}$ .

Similar simulation results for a diaphragm with the “downward force-travel characteristics” (Figure 9(b)) are shown in Figure 15. The motor speed is controlled to drop initially followed by an increase from 1.02 to 1.18 s, since the piston force initially increases and then decreases.

Figure 15.

Step response of the force-aided lever actuation system with “downward force-travel characteristic” diaphragm: (a) motor rotation angle $θ_{m}$ , (b) motor current $i_{m}$ , (c) motor speed ${\overset{\cdot}{θ}}_{m}$ , (d) piston force $F_{c}$ , and (e) clutch normal force $F_{n}$ .

Because of the force-aided feature of the actuation system, the clutch engagement can be much faster, as shown in Figure 16. The red line is the command of step input. The response time can be reduced by 24% with the help of the spring (from 205 to 160 ms) for “upward force-travel characteristic” diaphragm and by 19% (from 220 to 180 ms) for “downward force-travel characteristic” diaphragm.

Figure 16.

Fast response comparison between actuators with and without spring: (a) fast response with “upward force-travel characteristic” diaphragm and (b) fast response with “downward force-travel characteristic” diaphragm.

Torque-saving characteristic verification

Due to the spring installed, motor torque is reduced during clutch engagement and disengagement. Figures 17 and 18 show the process of clutch engagement and disengagement. The clutch normal force is changed from 0 to 1000 N and to 3000 N finally. With or without the spring, the motor torque is adjusted, so that the normal force is retained following the same profile. Therefore, the force-aided feature can be compared. The spring can reduce about 30% motor torque in both clutch engagement and disengagement. And the force-aided feature is more obvious with the increase in normal force.

Figure 17.

Force-aided feature during clutch engagement and disengagement for “upward force-travel characteristic” diaphragm: (a) clutch normal force during engagement processing, (b) clutch normal force during disengagement processing, (c) motor torque during engagement processing, and (d) motor torque during disengagement processing.

Figure 18.

Force-aided feature during clutch engagement and disengagement for “downward force-travel characteristic” diaphragm: (a) clutch normal force during engagement processing, (b) clutch normal force during disengagement processing, (c) motor torque during engagement processing, and (d) motor torque during disengagement processing.

The simulation results in Figures 14 –18 show the controllability for both monotonicity and non-monotonicity of the clutch diaphragm since the motor can control the actuation force $F_{m}$ directly by motor torque $T_{mo}$ .

Stability validation

This section validates the stability and shows the advantage of the system by comparing to a production actuation system. Both the force-aided lever actuation system and the production actuation system are controlled by the same PID controller with respect to the motor position. Both the “upward force-travel characteristic” and a “downward force-travel characteristic” diaphragms (Figure 9) are used for the two actuation systems for comparison. In addition, the simulation results of the “existing actuator” actuator are provided for comparison. The dynamic model of the “existing actuator” is derived in Appendix.

Figure 19 shows the simulation results with “upward force-travel characteristics” diaphragm (Figure 9(a)). The motor position is controlled by the PID controller, and the equilibrium state of the actuation system is reached at λ = 1.6 mm. To study the system natural robustness of the two actuation systems, a disturbance force is added on the piston (point C in Figure 3)) at 6 s, as shown in Figure 19(a). Both of the two actuation systems with the PID controller can hold the motor position by adjusting motor current, as shown in Figure 19(b) and (c). The piston position of “existing production actuator” actuation system is shifted from 1.6 to 1.7 mm in the presence of the disturbance, as shown in Figure 19(e). The simulation results show that both the new actuator and the existing production actuator actuation system are stable under a diaphragm with “upward force-travel characteristic.” The new actuation system proposed in this article demonstrates higher robustness disturbance than the existing production system.

Figure 19.

Stability validation with “upward force-travel characteristic” diaphragm (“force-aided + PID” stands for proposed actuation system with a well-tuned PID controller; “existing actuator + PID” stands for “existing production actuator” system with a well-tuned PID controller): (a) disturbance on piston at point C $F_{d}$ , (b) motor current $i_{m}$ , (c) motor rotation angle $θ_{m}$ , (d) motor speed ${\overset{\cdot}{θ}}_{m}$ , (e) piston travel $λ$ , (f) clutch normal force $F_{n}$ , and (g) piston force $F_{c}$ .

Figure 20 shows the simulation results under the same conditions with “downward force-travel characteristics” diaphragm (Figure 9(b)). The equilibrium state of “existing production actuator” seems to be realized and a steady-state normal force at λ = 1.6 mm is obtained (Figure 20(e) and (f)). However, when a small disturbance F_d = 15 N is applied on piston (Figure 20(a)), “existing production actuator” leaves its equilibrium state easily, and the piston travel $λ$ changes from 1.6 to 8.0 mm (Figure 20(e)), which cause the clutch normal force to change from 0 to 3180 N (Figure 20(f)). The operation point passes through the whole “downward” area (1.6 mm < λ < 5.5 mm in Figure 9(b)) and stops at new “upward” area (λ > 5.5 mm in Figure 9(b)). By comparison, the new actuation system is stable and keeps the piston travel λ at 1.6 mm.

Figure 20.

Stability validation with “downward force-travel characteristic” diaphragm (“force-aided + PID” stands for proposed actuation system with a well-tuned PID controller; “existing actuator + PID” stands for existing production actuation system with a well-tuned PID controller): (a) disturbance on piston at point C $F_{d}$ , (b) motor current $i_{m}$ , (c) motor rotation angle $θ_{m}$ , (d) motor speed ${\overset{\cdot}{θ}}_{m}$ , (e) piston travel $λ$ , (f) clutch normal force $F_{n}$ , and (g) piston force $F_{c}$ .

The simulation results in Figures 19 and 20 show that “force-aided + PID” actuation system has strong stability both with an “upward force-travel characteristic” diaphragm and a “downward force-travel characteristic” diaphragm.

Application to clutch-to-clutch shift

The two actuator models are integrated in the vehicle model. The parameters for the powertrain system used in the simulation are listed in Table 4.

Table 4.

Parameters of powertrain.

Symbol	Value	Unit	Description
$I_{d 1}$	0.058	$kg m^{2}$	Lumped inertia
$I_{d 2}$	0.1	$kg m^{2}$	Lumped inertia
$I_{c 1}$	0.02	$kg m^{2}$	First gear shaft inertia
$I_{c 2}$	0.02	$kg m^{2}$	Second gear shaft inertia
$I_{fd}$	0.04	$kg m^{2}$	Final drive inertia
$c_{d}$	3	$N m s$	Dual-mass flywheel damping
$k_{d}$	600	N m/rad	Dual-mass flywheel stiffness
$c_{v}$	100	$N m s$	Output shaft damping
$k_{v}$	33,000	N m/rad	Output shaft stiffness
$i_{1}$	3.917	–	First gear ratio
$i_{2}$	2.249	–	Second gear ratio
$i_{fd}$	3.7	–	Final drive ratio
$μ_{s}$	0.37	–	Static friction coefficient
$μ_{k}$	0.35	–	Slipping friction coefficient
$R_{cp}$	0.1	m	Clutch plate radius
$N$	2	–	Number of friction plate surface
$ς$	4	–	Coefficient for friction calculation
$ξ$	100	–	Coefficient for friction calculation
$R_{tr}$	0.314	m	Wheel radius
$M$	1400	kg	Vehicle mass M
$c_{1}$	189	N	Load torque coefficient
$c_{2}$	1.36	N/(m/s)	Load torque coefficient
$c_{3}$	0.45	N/(m/s)²	Load torque coefficient

The vehicle is simulated with the acceleration under the 25% throttle position. Figure 21 shows the simulation results from the first to second gear. Clutch 1 is the offgoing clutch and clutch 2 is the oncoming clutch. The total shift time here is 0.9 s. The fill phase is finished in 0.1 s. The torque phase lasts 0.2 s, and the inertia phase takes 0.6 s.

Figure 21.

Simulation results for upshift process: (a) motor position, (b) motor current, (c) motor speed ${\overset{\cdot}{θ}}_{m}$ , (d) clutch normal force $F_{n}$ , (e) engine speed ${\overset{\cdot}{θ}}_{e}$ , (f) engine torque $T_{e}$ , and (g) transmission output torque $T_{g_out}$ .

In the fill phase, the motor position command (red dashed line in Figure 21(a)) is set to the position where the clutch plates touch each other, and the motor current and speed are controlled to the maximum value allowed in order for the clutch to go through the clearance with a minimum time. At the end of the fill phase, the motor current is changed to a negative value and its speed is reduced to avoid the impact at clutch kiss point. In the torque phase, the normal force on the oncoming clutch increases gradually to take over the normal force on the offgoing clutch. During this time, the engine torque is transmitted from the offgoing clutch to the oncoming clutch. After that, the oncoming clutch normal force is adjusted in the inertial phase, and the speed ratio is changed to the second gear. The down speeding of the engine and the associated inertias during the ratio change can produce a positive driveline torque. The output torque fluctuation can be clearly observed in the inertia phase. As there is no spike in the output torque profile, it indicates no sudden jerk during the shift, and the gear shift process may be deemed acceptable in terms of running smoothness. The motor position follows the command closely, and the clutch normal force profile also shows that it can be controlled well. The results show that this new force-aided lever actuator system is sufficient for clutch-to-clutch gear shift control.

With the force-aided spring, the motor power requirement can be reduced for gear shifting. Figure 22 shows the motor power for the oncoming clutch during the first to second shift with or without the force-aided spring. In both cases, the normal force is controlled to follow the same profile and the vehicle is controlled with the same acceleration profile. From the simulation results, it can be concluded that the spring can reduce about 30% motor power.

Figure 22.

Motor power comparison between with and without spring.

Summary

The clutch actuation system is a key enabler for fast and smooth gear shift process for a dry DCT. In this article, a force-aided lever actuation system with a spring driven by an electric motor has been proposed. The design concept and physical structure have been presented. The dynamic model of a DCT equipped with two force-aided lever actuators has been developed. The dynamic simulation results demonstrate the feasibility of the force-aided lever actuator to further validate the actuator design. With the aid of the additional spring, it has been demonstrated that a motor of 50 W is sufficient to actuate the clutch for transmission controls. This is about 30% reduction in motor power required. In addition to the fast response, small actuation force, and accurate control, the new actuator cost is less and has shown great potential for practical applications.

Footnotes

Appendix 1

Figure 23 shows the force analysis of the existing production actuation system. When the roller O is being moved by the motor, the lever is displaced simultaneously with a displacement x of barycenter at horizontal direction, and a rotate angle α around the fulcrum roller with respect to power screw center line. The lever displacement y at vertical direction is very small and can be neglected since it is constrained by the leaf spring. Assume the barycenter of lever is in the middle. The dynamic equations of lever are as follows

(36)

F s + F c − F Bl cos α = m y ··

(37)

I α ·· = ( F c − F s ) l 2 + F Bl ( l 2 cos α − l 2 cos α ) − c α

in which

(38)

y = l 0 + ( l 2 − l 2 ) tan α

(39)

F s = k s ( l s 0 − l 0 + l 2 tan α )

where F c is the piston force from the diaphragm; F Bl is the fulcrum roller force; F s is the spring force; l s 0 and k s are the spring initial length and stiffness, respectively; m and I are the mass and inertia of lever, respectively; and l and l 2 are the length of BC and BO at horizontal direction, respectively.

The power screw is used to transfer the moment motion to the linear motion. The dynamic equation of the power screw is given as follows

(40)

I ps θ ·· m = T mo − R p F Bl sin α

(41)

θ m R p = l 2

R p refers to the distance that the power screw travels when the motor rotates a certain angle and I ps is the inertia of power screw.

The dynamics of the motor are same as equations (1) and (2). The piston force F c and clutch normal force F n are obtained from equations (15) and (16). The piston travel λ is calculated as

(42)

λ = y c 0 − ( l − l 2 ) tan α

in which, y co stands for the initial vertical position of piston.

Academic Editor: Aditya Sharma

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was supported by the National Natural Science Foundation of China (grant no. 51475284).

References

Kim

Choi

. Design of self-energizing clutch actuator for dual-clutch transmission. IEEE-ASME T Mech 2016; 21: 795–805.

Gao

Chen

et al . Dynamics and control of gear upshift in automated manual transmissions. Int J Vehicle Des 2013; 63: 61–83.

Van Berkel

Hofman

Serrarens

et al . Fast and smooth clutch engagement control for dual-clutch transmissions. Control Eng Pract 2014; 22: 57–68.

Yao

Chen

Liu

et al . Experimental study on improvement in the shift quality for an automatic transmission using a motor-driven wedge clutch. Proc IMechE, Part D: J Automobile Engineering 2014; 228: 663–673.

Kim

Choi

. Robust feedback tracking controller design for self-energizing clutch actuator of automated manual transmission. SAE technical paper, 2013.

Manyala

. Gearshift actuator dynamics predictions in a dual clutch transmission. SAE technical paper, 2013.

Chen

Sun

. Torque coordination control during mode transition for a series–parallel hybrid electric vehicle. IEEE T Veh Technol 2012; 61: 2936–2949.

Van Berkel

Veldpaus

Hofman

et al . Fast and smooth clutch engagement control for a mechanical hybrid powertrain. IEEE T Contr Syst T 2014; 22: 1241–1254.

Balau

A-E

Caruntu

C-F

Lazar

. Simulation and control of an electro-hydraulic actuated clutch. Mech Syst Signal Pr 2011; 25: 1911–1922.

10.

Kim

Choi

. Design and modeling of a clutch actuator system with self-energizing mechanism. IEEE-ASME T Mech 2011; 16: 953–966.

11.

Glielmo

Iannelli

Vacca

et al . Gearshift control for automated manual transmissions. IEEE-ASME T Mech 2006; 11: 17–26.

12.

Liu

Qin

Jiang

et al . Clutch torque formulation and calibration for dry dual clutch transmissions. Mech Mach Theory 2011; 46: 218–227.

13.

Wheals

McMicking

Shepherd

et al . Proven high efficiency actuation and clutch technologies for eAMT™ and eDCT™. SAE technical paper, 2009.

14.

Wheals

Turner

Ramsay

et al . Double clutch transmission (DCT) using multiplexed linear actuation technology and dry clutches for high efficiency and low cost. SAE technical paper, 2007.

15.

Yao

Chen

Yin

et al . Modeling of a wedge clutch in an automatic transmission. SAE technical paper, 2010.

16.

Yao

Chen

Yin

. Experimental validation of a wedge clutch in automatic transmissions. In: Proceedings of the international conference on advanced vehicle technologies and integration, China, Changchun, 24–28 October 2012.

17.

Yao

Chen

Yin

. Modeling and stability analysis of wedge clutch system. Math Probl Eng 2014; 2014: 712472 (12 pp.).

18.

Kim

Choi

. Self-energizing clutch actuator system: basic concept and design. In: Proceedings of FISITA2010 world automotive congress, Budapest, 30 May–4 June 2010. Budapest, Hungary: Springer.

19.

Taguchi

Soga

Mineno

et al . Development of an automated manual transmission system based on robust design. SAE technical paper, 2003.

20.

Zhang

. Servomechanism for automatic clutch. Google patents, 2004.

21.

Wagner

Berger

Ehrlich

et al . Electromotoric actuators for double clutch transmissions. In: LuK symposium, Schweinfurt, Germany, 3–4 April 2006, pp.137–153. Schaeffler Technologies AG & Co. KG.

22.

Faust

Bünder

DeVincent

. Dual clutch transmission with dry clutch and electro-mechanical actuation. ATZautotechnology 2010; 10: 32–37.

23.

Burkhart

Dreher

. Clutch system. Google patents, 2009.

24.

Deur

Milutinovic

Ivanovic

et al . Modeling of a dry dual clutch utilizing a lever-based electromechanical actuator. J Dyn Syst: T ASME 2016; 138: 091012 (11 pp.).

25.

Ivanović

Hoić

Deur

et al . Design of test rigs for a dry dual clutch and its electromechanical actuator. SAE technical paper, 2012.

26.

Kimmig

Bührle

Henneberger

et al . Dry double clutch-success with efficiency and comfort. In: 9th Schaeffler symposium, Schweinfurt, Germany, 26–28 August 2010, pp.154–163. Schaeffler Technologies AG & Co. KG.

27.

Lee

Jeong

Kam

. Clutch actuator for a vehicle. Google patents, 2013.

28.

Kimmig

Agner

. Double clutch wet or dry, that is the question. In: 8th LuK symposium, Schweinfurt, Germany, 3–4 April 2006, pp.120–135. Schaeffler Technologies AG & Co. KG.

29.

Liu

Qin

Jiang

et al . A systematic model for dynamics and control of dual clutch transmissions. J Mech Design 2009; 131: 061012.

30.

Tarasow

Wachsmuth

Lemieux

et al . Online estimation of time-varying torque characteristics of automotive clutches using a control oriented model. In: IEEE American control conference (ACC), Washington, DC, 16 August 2013, pp.6752–6757. New York: IEEE.

31.

Kulkarni

Shim

Zhang

. Shift dynamics and control of dual-clutch transmissions. Mech Mach Theory 2007; 42: 168–182.

32.

Duan

Singh

. Influence of harmonically varying normal load on steady-state behavior of a 2DOF torsional system with dry friction. J Sound Vib 2006; 294: 503–528.

33.

Gao

Chen

Sanada

. Two-degree-of-freedom controller design for clutch slip control of automatic transmission. SAE technical paper, 2008.

34.

Obayashi

Jeong

Chiba

. Multi-objective design exploration for aerodynamic configurations. In: 35th AIAA fluid dynamics conference and exhibit, Toronto, ON, Canada, 6–9 June 2006. Reston, VA: AIAA.

35.

Huang

Wang

Ingham

et al . Design exploration for a single expansion ramp nozzle (SERN) using data mining. Acta Astronaut 2013; 83: 10–17.

36.

Silvas

Hofman

Steinbuch

. Review of optimal design strategies for hybrid electric vehicles. IFAC P 2012; 45: 57–64.

37.

Skinner

Parks

Palmer

. Comparison of submarine drive topologies using multiobjective genetic algorithms. IEEE T Veh Technol 2009; 58: 57–68.

Modeling and simulation study of a novel electromechanical clutch actuation system

Abstract

Keywords

Introduction

Design of force-aided lever actuator

Actuator principle

Physical structure

System analysis and modeling

Motor

Power screw

Lever

Diaphragm

The powertrain model

Controller design

Actuator controller

Clutch-to-clutch upshift control strategy

Results and discussion

Effect of the influencing factors on aiding force

System response for step input

Torque-saving characteristic verification

Stability validation

Application to clutch-to-clutch shift

Summary

Footnotes

Appendix 1

Declaration of conflicting interests

Funding

References