WU Jing-yan(武景燕)，WEI Wei(魏巍)，QU Jing-yao(曲婧瑤)，YAN Qing-dong(閆清東)

(1.National Key Lab of Vehicular Transmission，Beijing Institute of Technology，Beijing 100081，China;2.School of Mechanical Engineering，Beijing Institute of Technology，Beijing 100081，China)

Introduction

The optimized performance of automatic transmission is based on automatic shift schedule，a kind of important automatic gear-shifting technique which can make advances in mobility，fuel economy，stability and comfortableness of tracked vehicle.Appropriate shift schedule can utilize the engine power thoroughly，increase the average driving speed，and improve the passability.The main methods include single parameter shift control，double-parameter shift control，dynamic three-parameter shift control［1］，construction machinery four-parameter shift control［2］and intelligent shift control.

The single parameter control shift schedule is used rarely because it is unable to intervene the shifting by drivers，and balance the performance of mobility and fuel economy with its simple structure.The double parameter control shift schedule overcomes the disadvantages of single parameter control shift schedule.It uses vehicle speed and throttle opening for optimal mobility and fuel economy.The dynamic three-parameter shift control is complex to practical application［3］.In recent years，the intelligent control theory has been used in shift schedule to build a shifting knowledge database with driver's experience and expert's specialized knowledge，and theconventionaldouble-parameterand three-parameter controls have been corrected and improved.But the intelligent shift control depends on the driver's experience and driving level，and the perception degree of designers［4］.Ref.［5］presents a kind of optimum shift schedule based on traditional mechanical mathematical model.The extraction and optimization proceed of parameters in this method are limited to a simplified clutch model.

A simulation model of dynamic transmission system in a tracked vehicle is established by MATLAB/Simdriveline.The double-parameter shift schedule is derived using speed and throttle opening，and the optimum design is performed by iSight and MATLAB.The sketch of design process is shown in Fig.1.

Fig.1 Sketch of optimum design process

1 Simulation ModelofAutomatic Shifting

A dynamic model for whole vehicle is established by modular modeling according to a top-down method.As shown in Fig.2，the sub models included engine，lock-up hydrodynamic torque convertor，multi-gear shifting，load system and gear-shift controller，and the corresponding non-causal and reusable MATLAB/Simdriveline models are established.

During the simplification of physical system，the following principles should be followed:

1)System gaps are neglected;

2)Lumped mass of each part is concentrated in rotary plane centerline;

Fig.2 Non-causal system simulation model of vehicle gear-shifting

3)The elasticity and damp of parts in the transmission are not considered.

1.1 Engine Model

The 2-D polling list MAP graph is plotted under the experimental data of throttle opening and speed of the variable speed diesel engine.The dynamic equation of engine is as follows:

whereIeis the inertia of engine flywheel;ωeis engine speed，Teis engine torque，which is obtained by MAP graph in simulation;Tacis the resistance moment of auxiliary system;Tloadis the load torque of engine.

1.2 Lock-up Hydrodynamic Torque Converter

Fig.3 Lock-up hydrodynamic torque converter model

The dynamic model of the lock-up hydrodynamic torque convertor is shown in Fig.3，and the mathematic model［6］is as follows:whereandare the dynamic torques of pump and turbine shaft in unsteady work condition，respectively;andare the dynamic torques of pump and turbine shaft in steady state condition，respectively;Ipis the rotational inertia of pump and pump shaft;ITis the rotational inertia of turbine，turbine shaft and chief rotating elements which are rigidly connected to it;ωPand ωTare the rotational speeds of impeller and turbine，respectively;TFis the friction torque of lock-up clutch.

When the clutchis separated，TF=0，while==0 after it locks up.The drive torque could be calculated according to clutch friction torque equation during lock-up process.

1.3 Multi-gear Model

The three-axis speed-shifting mechanism consists of three basic shafts and six hydraulic shift clutches，while the driving parts of planetary mechanism，such as fixed axis gear，clutch and rotation axis，are modular parts.

Fig.4 Simplified dynamic model of speedshifting mechanism

1.4 Other Modules

The load module provides the varied road excitation from data file gained in time sequence from dynamic test，while the gear-shifting controller is built based on finite state machine theory with MATLAB/Simdriveline，which could solve the complex monitor logical problem.

2 Problem Description of Optimum Design of Shift Schedule

2.1 Optimization Model

Design variable:different up-shifting speedviand down-shifting speed difference between different shift gearssiwith different throttle openingα;ais the acceleration.

The object function:

1)Accelerating performanceis 0－32 km/h during throttle full open:

2)Gear-shifting smoothness:

where the impact degree is the change rate of longitudinal acceleration，and the dynamic load coefficient reflects the fluctuation of the torque output in typical working condition(driving or working).

3)Object of transmission system efficiency:t

where

The efficiency of transmission system is increased to reduce the heat generated after long time driving or working by adjusting the throttle opening，controlling actively the working load，and controlling the gearshifting.

Constraints:

1)Up-shifting speed

The engine power is used sufficiently，the upshifting speed is the speed corresponding to rated power(standard power)，andandare upper and lower search boundary of up-shifting speed in optimizing acceleration performance.

2)Down-shifting speed difference

The different types of shift schedule(divergent，convergent or universal type)provide the different constraints for down-shifting speed difference between different shift gears.The given speed difference domain is search boundary during optimization of shift schedule.

2.2 Optimization Scheme Features

The above automatic shifting simulation model acts as a solver system called continuously，which inputs the optimized variables corrected according to the outputs and outputs the running results until the perfect performance is obtained.The features of this optimization scheme are:

1)Different simulation models are established for different power transmission systems.

2)Optimization parameters are defined by the specifications and operation performance.The parameter setting and selection are limited by given optimizing constraints.

3)According to different optimization problems，the dynamic model and optimization model are modified easily，corresponding to single or compound optimizing algorithm.For complex multi-object optimization problem，the genetic algorithm can be used to simulate the organic evolution process in nature and search in solution space parallelly and globally，realizing the optimal convergence.For single object optimization，the secondary sequence planning algorithm converges faster.

3 Example Analysis

The different object functions are chosen in optimum problem according to the different driving conditions which respond to the different gear-shifting modes(dynamic mode for fine road，off-road mode for rough road，and ramp mode for ramp road).The optimizing process and theory are the same for the different modes，but the simulation conditions and the object parameter selection are different.An example of which the vehicle runs at 2－4 gear under good road condition is analyzed to verify the feasibility of optimization design method.In the calculation，αis given to be 55%，77%and 100%，as shown in Fig.5.

Fig.5 Optimization results for given α values

It can be found in dynamic simulation that the fluctuation coefficient of output torque increases when reducing the throttle opening.So the average values of resistance coefficients are given to be 0.015 and 0.04 when correspondingαvalues are 55%and 77%for the object torque fluctuation coefficient;whenαis 100% ，the acceleration time for 0－32 km/h is added to be an object to optimize.

The parameters before and after optimization are listed in Tab.1.One object could be used as a constraint and controlled in a certain domain to achieve the optimization result of multiple object(its parameter change is small for the multiple object).The results in Fig.5(a)and(b)show that the method mentioned above is effectively worked for the fluctuation coeffi-cient，and the efficiency of the transmission system has a reverse change tendency，which verifies the two indexes are paradoxical for the system.In addition，the power utilization ratio and torque fluctuation decrease with the increase in the throttle opening.

The gear-shifting point for reducing acceleration time and decreasing torque fluctuation is calculated in the form of multiple objectives because of the increase in acceleration time，which judges the vehicle dynamic in full acceleration.The result proves that:1)a high gear should be shifted in advance to improve the acceleration performance of vehicle，but the utilization ratio of engine power may be reduced;2)the change tendency of shifting points from the multiple optimizing results shows that the reduction in the maximum gear speed or the speed difference between gear 3－4 or 4－5 has a great impact on the output torque fluctuation of gear-shifting mechanism.

Tab.1 Parameters comparison before and after optimization

4 Conclusions

An integrated optimum design method for automatic gear-shift schedule of general vehicle is presented for a certain tracked vehicle with hydrodynamic mechanism transmission.The optimization calculation of gear-shifting point is performed by taking power utilization ratio，torque fluctuation coefficient and acceleration time as the optimization targets according to different driving conditions.Simulation result indicates that the method is significant to improve the dynamic performance and the gear-shifting smoothness theoretically and practically.

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