0. Introduction

The variation range of metal pushing belt continuously variable transmission (CVT) can reach only about 5~6 because of its limit in structures, which makes it unfit for the control requirement of optimal drivability and fuel economy when engine output and the driven condition of vehicle change in a large range^[1-2]. By using hydraulic torque converter at start-up and low speed, a lager range of speed ratio of CVT can be get; and the ability of less impact, big torque at low speed and good fitness to outside load helps vehicle start up steadily and have good drivability at low speed^[3]. However, because of the low efficiency even on the coupling stage, torque converter should lock up when vehicle drives on normal condition for improving transmission efficiency.

Most of vehicles with torque converters determine whether to lock up or unlock by jugging the vehicle speed, which influences the using effect of torque converter on some special conditions, such as cooling machine, braking and so on^[4-5]. So it is necessary to suitably set the unlocking and lock-up conditions for the improving transmission efficiency, the start-up and driving performances at low speed. In order to improve the fuel economy of vehicle under the unlocking condition of torque converter, torque converter should work in the optimal economic region with engine before lock-up according to the control damands of CVT.

1. Lock-up and unlocking

1.1 Lock-up

The conversion of torque converter from unlocking to lock-up should carry out on the condition that the work of torque converter at start-up and low speed has been completed and vehicle speed have reached a limit value, in addition to considering cooling water temperature and the speed difference between turbine and impeller^[6]. Torque converter should lock up at high speed, driver avoids the continual conversion between unlocking and lock-up under complex road condition, but eusure lock-up in time on good road station (vehicle speed reaches 30 km·h^-1). Torque converter should lock up when engine has warmed up and is able to bear every working condition, and the cooling water temperature is higher than the set value, 50 ℃~60 ℃. Torque converter can reduce impact and increase torque under special condition or driving intention if the speed difference between turbine and impeller is larger. It is suitable for lock-up when the speed difference between turbine and impeller lowers a set value (transmission ratio is more than 0.7), or it will cause impact.

1.2 Unlocking

The conversion of torque converter from lock-up to unlocking is because of the decrease of vehicle speed to a limit value (25 km·h^-1). Decreasing vehicle speed is resulted from the driving intention because road state needs the working of torque converter for torque transmission. In addition to considering such special conditions as closing throttle to decrease the speed or the intention to decrease the speed by braking, torque converter should lock up to reduce emission and improve fuel economy.

The conversion of torque converter from lock-up to unlocking is determined by the change of vehicle speed, and the special conditions about the driving intention and working conditions are considered. The convertsion logic is shown in fig. 1.

Figure  1.  Lock-up and unlocking logic

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Torque converter lock up when vehicle runs at high speed (exceed 30 km·h^-1), the engine has warmed up (engine cooling water temperature exceeds 50 ℃~60 ℃) and the speed difference between turbine and impeller is little (transmission ratio exceeds 0.7). Torque converter unlock when vehicle starts up, runs under city complex road conditions at low speed (under 25 km·h^-1), and the driver closes the throttle or brakes. In addition to considering the interval between vehicle speed limit values of unlocking and lock-up for torque converter, the constantly conversion of lock-up and unlocking is avoided when vehicle speed waves in small range. In fig. 1, unlocking state is continued when transiting from unlocking region to buffer area, lock-up state is conti-nued when transiting from lock-up region to buffer area.

2. Speed Ratio control

On the normal working state of torque converter, torque converter has large torque, well automatic adaptability, good shock absorption and buffering performances at start-up and low speed, so that vehicle starts up quickly and steadily and has good accelerating performance. But except the above stages, up to the lock-up region of torque converter, torque converter influences the efficiency of driveline, and the influencing degree has a direct relation with the speed ratio of torque converter^[7]. In order to improve transimission efficiency of torque converter in the region, firstly, torque converter should match well with engine according to its characteristics, then, according to the common features of engine and toruqe converter, the adjustment of speed ratio can improve the fuel economy of vehicle.

2.1 Common working properties

The common work focus of engine and torque converter is the intersectant point of between torque curves and load curves, when engine has small loads (the throttle opening angles of vehicle start-up are α₁~α₄), and torque converter has small transmission ratios, the ratios are 0, 0.1, 0.2, and the torque of the point is maximum. It is a steady point of common work, as the equation (1) shows

${\rm T}{}_{\text{Τ}}=k{}_i{\rm T}{}_{\text{e}}(1)$

Vehicle fuel economy at start-up and low speed is considered and the superposition degree between the workaround of low oil consumption of engine and the high-efficiency area of torque converter is studied, then the best economic common workingarea of engine and torque converter is confirmed (fig. 2), as the equation (2) shows

$b{}_{\text{e}\text{Τ}}=b{}_{\text{e}}/\eta {}_i(2)$

Figure  2.  Input characteristics curves of common work

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2.2 Speed ratio control

At start-up and low speed, the CVT ratio is largest, and the torque is furtherly improved. Because torque converter has well automatic adaptability, good shock absorption and buffering performance, vehicle can start-up quickly and steadily and has good accelerating performance at low speed.After the stages of start-up and low speed, the economy problem of engine and torque converter common work needs to be considered. Adjusting the speed ratio of CVT can make engine work in economic area and torque converter work round the highest efficiency point, thus the best economy of engine and torque converter common working can be carried out^[8-9].

Studied CVT is mental pushing belt CVT, the speed ratio adjustment of CVT is carried out by the change of pulse-width modulation (PWM) driving signal for speed ratio control's proportional electromagnetic valve, and the change of the driving signal will lead to put different forces to the movable part of initiative belt wheel, so that it running radius is changed, thus CVT's speed ratio will be changed.

At different throttle opening angles, the relation between the fuel consumption rate of engine and torque converter common work and the speed radio of torque converter is expressed as

$b{}_{\text{e}\text{Τ}}=f(n{}_{\text{e}})/f(i)(3)$

By experiments, the common economic working line of engine and torque converter can be achieved, the speed ratios of torque converter are taken as abscissa, engine loads are taken as ordinate, the points of the common working lowest fuel consumption rate of engine and torque converter are labelled. According to the economic line, at different throttle opening angles, the object speed ratios of torque converter can be got. Using engine speed signal and CVT's input speed signal that have the same output speed as torque converter, the real speed ratios of torque converter can be calculated.Taking the difference value between the real speed ratio and the object speed ratio of torque converter as input, the PWM driving signal's change value of speed ratio control's proporational electromagnetic valve is calculated by PID controller and exported to carry out the ratio adjustment of CVT. By the ratio adjustment of CVT, the matching relationship between engine and torque converter-transmission-road load will be changed to make the real speed ratio of torque converter reach the object speed ratio, and to improve the fuel economy of vehicle. The ratio control process of torque converter is shown in fig. 3.

Figure  3.  Ratio control process of torque converter

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The proportion coefficient k_p and differential coefficient k_D of PID controller are set to less values, and the integral coefficient k_I is set to bigger value, so that the overshoot can be reduced, the system's steady precision under steady condition can be improved, and the inhibiting ability to disturbance can be increased.

3. Process of lock-up control

The unlocking process of torque converter is converting mechanical transmission into hydraulic transmission. The converting process is smooth depending on the good active suitability to the external load of torque converter. The lock-up process of torque converter is converting hydraulic transmission into mechanical transmission. Although under common situation, the error between pump impeller speed and turbo speed is less, the lock-up without control will reducing the stabilization of vehicle and the useful life of lock-up clutch, especially under uncommon situation. For example, acceleration or the condition variety of road causes the huge error between pump impeller speed and turbo speed, which will bring the vibration or slippage between friction plates of lock-up clutch.

The lock-up process of torque converter is assumed as two sections, the slippage section and the quick engagement section^[10]. There are two points should be considered in the slippage section, the impact degree and the friction work. In the quickly engagement section, there are not the impact degree and the friction work because the speeds of friction plates are equal. It's just making quick engagement and enhancing the transmitted torque. The engagement of lock-up clutch will be controlled according to the principles of stabilizing engine rotation and optimizing the performance of the impact and sliding friction work in the slippage section. The engagement process of lock-up clutch is also the increasing process of the clutch's positive pressure. The positive pressure increase is made by the PWM duty ratio change of high-speed on-off valve.

Engine torque is supposed to a constant in a short time, it is mainly affected by the change rate of pump impeller torque. Therefore, when the ratio is constant, it is surely affected by the change rate of the clutch's positive pressure, as the equation shows

$J{}_{\text{e}}\frac{\text{d}n{}_{\text{e}}}{\text{d}t}=\frac{\text{d}{\rm T}{}_{\text{B}}}{\text{d}t}=\frac{\text{d}i}{\text{d}t}{\rm T}{}_{\text{Τ}}={\rm T}{}_{\text{Τ}}f\left(i,\frac{\text{d}p}{\text{d}t}\right)(4)$

The impact degree of vehicle is defined by the following equation

$j=\frac{\text{d}{}^{2}v}{\text{d}t{}^2}=\frac{ri{}_{0}i{}_{\text{c}\text{v}\text{t}}}{{\rm I}{}_{\text{t}}}\frac{d{}^2\omega {}_{\text{Τ}}}{\text{d}t{}^2}=\frac{ri{}_{0}i{}_{\text{c}\text{v}\text{t}}}{{\rm I}{}_{\text{t}}}f\left(\omega {}_{\text{B}}-\omega {}_{\text{Τ}},\frac{\text{d}p}{\text{d}t}\right)$ (5)

It shows that the impact degree is surely affected by the change ratio of the pressure during lock-up when the error between pump impeller and turbo is constant.

The lock-up signal of torque converter can is measured. When the lock-up demand is satisfied, the lock-up is started, and the engagement control in slippage section begins. Whether the slippage section is over, the quick engagement start is determined through whether the error between pump impeller and turbo is in a small area (considering the measuring error of the actual speed). Firstly, according to the principle of optimizing the performance of impact and sliding friction work, the basic duty ratio is determined, and according to the principle of stabilizing engine rotation, the real-time duty ratio is modified based on the error between real engine speed measured by sensor and object engine speed determined by throttle angle. Finally, the real duty ratio is get. The control process is shown in fig. 4.

Figure  4.  Engagement control strategy of lock-up clutch

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Fig. 5 shows the lock-up fuzzy controller based on the above control strategies^[11]. The impact degree of vehicle and engine speed error are fuzzificated and input the controller. The impact degree of vehicle means the principle of optimizing performance of impact and sliding friction work. PWM signal is adjusted in real-time according to the change of impact degree. If the impact degree is big, the change rate of PWM signal should be reduced, on the contrary, the change rate of the PWM signal should be increased to the target value of optimizing performance of impact and sliding friction work. Engine speed error means the principle of stabilizing engine rotation. According to the error between object speed and real speed, PWM signal in real-time is adjusted. If the real speed is smaller than the object speed, the change rate of PWM signal should be reduced, on contrary, the change rate of PWM signal should be increased to the target value of stabilizing engine rotation, meanwhile, jointing well with the adjusting ratio aimed at the best work point of engine. Finally, the result of the fuzzy inference is converted into control signal (the change rate of PWM signal) of high-speed on-off valve through defuzzification.

Figure  5.  Lock-up fuzzy controller

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The fuzzy controller is planar. The inputs are the error between the object speed and the real speed and the imapct degree obtained from the CVT output speed after handling. The output is the change rate of the duty ratio of high-speed on-off valve. The language values of the speed error and the impact degree are NL (negative big), NS (negative small), ZO (zero), PS (positive small) and PL (positive big). The language values of the change rate of the duty ratio are also PL, PS, ZO, NS and NL. The relations between the language values of the speed error and the change rate of the duty ratio and between the impact degree and the change rate of the duty ratio are established. And then, the fuzzy rules are made up by using product strategy.

The experiments are executed under two different lock-up states. Fig. 6 shows the engagement controls, input speeds and output speeds of lock-up clutch during accelerating slowly and quickly. In fig. 6, line 1 means the input speed (equalling to engine speed), line 2 means the output speed. Torque converter is affected obviously by the states. When the big change rate of throttle angle causes vehicle speed reaching the lock-up value, the error between pump impeller and turbo will increase, and the demanding torque transmitted by lock-up clutch will increase also. Aimed at the change of torque converter, the engagement process is adjusted by the control strategies. In fig. 6 (b), the error is bigger. In order to avoid impact, the engagement time is prolonged.The 1.92 s in fig. 6 (b) is bigger than the 1.38 s in fig. 6 (a). In order to transmit bigger torque effectively, when the slippage ends, the duty ratio is 63.2% in fig. 6 (b), it is bigger than 49.8% in fig. 6 (a). The fig. 6 shows also that when the demanding torque transmitted by lock-up clutch reaches the biggest point, for the purpose of stabilizing engine rotation, the duty ratio changes are not obvious sometime. Under the two situations, the change of object engine speed is only resulted from throttle angle change, however, it is stable, meanwhile, the change trend of the output speed is smooth. Through analyzing the experiment data, the designed controller performs excellent and it satisfies the control demands.

Figure  6.  Experimental results of locking-up control

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4. Conclusion

The rational transition between the unlocking and lock-up states of hydraulic torque converter for vehicle with CVT is beneficial to make the most of its working characteristics and improve the transmission efficiency when vehicle runs at medium or high speed, moreover, it meets the running requirements of vehicle on special conditions.The speed ratio is regulate to change the output load of the converter. The PID control strategy designed for vehicle running at low speed can achieve the optimal economy of engine and converter working together. The designed fuzzy controller with two inputs can optimize performance of impact and slipping friction work and stabilize engine speed.

Nomenclatures

a_i throttle angle

T cooling water temperature

t time

T_T turbo torque (N·m)

k_i torque coeffient

T_e engine torque (N·m)

b_eT common working fuel consumption rate of engine and torque converter[g· (kW·h)^-1]

b_e fuel consumption rate of engine[g· (kW·h)^-1]

η_i transmission efficency of torque converter

n_e engine speed (r·min^-1)

i speed ratio of torque converter

J_e engine moment of inertia (kg·m²)

T_B pump impeller torque (N·m)

p clutch positive pressure (N·m^-2)

j impact degree of vehicle (m·s^-3)

v vehicle speed (km·h^-1)

r rolling radius of driving wheel (m)

i₀ main speed ratio

i_cvt CVT speed ratio

I_t equivalent inertia of output axle conver-ted from vehicle inertia rigid connectedwith CVT output axle (kg·m²)

ω_T turbo speed (r·min^-1)

ω_B pump impeller speed