Simulation of 8 x 8 Heavy Duty Truck for Evaluating Effects of Torque Converter Characteristics on Vehicle Performance

Heavy duty trucks are frequently used to serve in transportation, military or fire extinction missions. Last few decades have witnessed the increasing attention to technologies of heavy duty vehicle powertrain systems. These technologies are focused on both conventional powertrain [1] and hybridization [2] of conventional vehicles. Powertrain system modeling and simulation of conventional heavy duty trucks have the potential to improve the existing system performance. The main goal of modeling and simulation of powertrain is to improve the traction performance and fuel economy by redefining each system component’s properties and detecting its suitability of vehicle operating conditions. Mathematical model of vehicle powertrain system can have carried out by dynamic [3] or quasi static [4,5] approach based on longitudinal vehicle dynamics [6,7,8] equations. When a part of system is interested for the determination of dimensioning or strength, the powertrain model can be arranged for one or a couple components of all system [9]. But the calculation of efficiency (overall), consumption (energy, fuel) and performance (traction, acceleration) of vehicle are needed to set up full model of powertrain system. For instance, analysis of vehicle and powertrain dynamics with an automatic gearbox was implemented [9] for the determination of vehicle velocity and engine speed versus time. Speed and moment requirements of automatic gearbox components such as sun gear and pinion gear are determined the analysis either. Energy efficiency analyses of a vehicle was simulated [10] by using powertrain model for all system according to vehicle velocity profile named drive cycle. Tao et al. [11] focused on automatic transmission model and applied evaluation models for heavy duty vehicle performance. Meng et al. [12] investigated the control of automatic transmission by using engine to wheel powertrain model for heavy duty vehicle. Input parameters are characteristic map of engine and hydrodynamic torque converter characteristics. 8x8 heavy duty truck has two power module at the rear side of vehicle including diesel engine, hydrodynamic torque converter and automatic transmission. The hydrodynamic torque converter is a major component among of all which affects driving performance [10]. Required power is transferred from engines to transmissions and engine torque is also increased by torque converter. The increasement can arrange according to engine operational area. For better vehicle performance and fuel economy, torque converter parameters are determined correctly. Correct torque converter parameter determination means greater operational area of the converter curves inside the engine torque curve. To show the effects of torque converter, two different designs that have different operational area, are integrated into powertrain model individually. The study compares the results of traction performances according to a drive cycle. Drive cycles can be utilized to predict vehicle performance, fuel consumption and exhaust emissions. New European Drive Cycle (NEDC), Urban Dynamometer Driving Schedule (UDDS) and Federal Test Procedure (FTP-75) are used as standard drive cycle for reaching and testing legislative boundaries about vehicle design [10,5]. Heavy Duty Urban Dynamometer Driving Schedule (HD-UDDS) is developed for heavy duty vehicles. The load on the wheels are calculated to simulate driving resistance on the vehicle such as rolling, aerodynamic and acceleration resistance and powertrain simulations are performed on HD-UDDS cycle. Essentially, this paper is aimed to investigate the effects of torque converter characteristic on the result of vehicle performance and fuel consumption by the drive cycle analysis of the 8x8 heavy commercial vehicle powertrain.


Introduction
Heavy duty trucks are frequently used to serve in transportation, military or fire extinction missions.Last few decades have witnessed the increasing attention to technologies of heavy duty vehicle powertrain systems.These technologies are focused on both conventional powertrain [1] and hybridization [2] of conventional vehicles.Powertrain system modeling and simulation of conventional heavy duty trucks have the potential to improve the existing system performance.The main goal of modeling and simulation of powertrain is to improve the traction performance and fuel economy by redefining each system component's properties and detecting its suitability of vehicle operating conditions.
Mathematical model of vehicle powertrain system can have carried out by dynamic [3] or quasi static [4,5] approach based on longitudinal vehicle dynamics [6,7,8] equations.When a part of system is interested for the determination of dimensioning or strength, the powertrain model can be arranged for one or a couple components of all system [9].But the calculation of efficiency (overall), consumption (energy, fuel) and performance (traction, acceleration) of vehicle are needed to set up full model of powertrain system.For instance, analysis of vehicle and powertrain dynamics with an automatic gearbox was implemented [9] for the determination of vehicle velocity and engine speed versus time.Speed and moment requirements of automatic gearbox components such as sun gear and pinion gear are determined the analysis either.Energy efficiency analyses of a vehicle was simulated [10] by using powertrain model for all system according to vehicle velocity profile named drive cycle.Tao et al. [11] focused on automatic transmission model and applied evaluation models for heavy duty vehicle performance.Meng et al. [12] investigated the control of automatic transmission by using engine to wheel powertrain model for heavy duty vehicle.Input parameters are characteristic map of engine and hydrodynamic torque converter characteristics.
8x8 heavy duty truck has two power module at the rear side of vehicle including diesel engine, hydrodynamic torque converter and automatic transmission.The hydrodynamic torque converter is a major component among of all which affects driving performance [10].Required power is transferred from engines to transmissions and engine torque is also increased by torque converter.The increasement can arrange according to engine operational area.For better vehicle performance and fuel economy, torque converter parameters are determined correctly.Correct torque converter parameter determination means greater operational area of the converter curves inside the engine torque curve.To show the effects of torque converter, two different designs that have different operational area, are integrated into powertrain model individually.The study compares the results of traction performances according to a drive cycle.
Drive cycles can be utilized to predict vehicle performance, fuel consumption and exhaust emissions.New European Drive Cycle (NEDC), Urban Dynamometer Driving Schedule (UDDS) and Federal Test Procedure (FTP-75) are used as standard drive cycle for reaching and testing legislative boundaries about vehicle design [10,5].Heavy Duty Urban Dynamometer Driving Schedule (HD-UDDS) is developed for heavy duty vehicles.The load on the wheels are calculated to simulate driving resistance on the vehicle such as rolling, aerodynamic and acceleration resistance and powertrain simulations are performed on HD-UDDS cycle.Essentially, this paper is aimed to investigate the effects of torque converter characteristic on the result of vehicle performance and fuel consumption by the drive cycle analysis of the 8x8 heavy commercial vehicle powertrain.

Powertrain of 8x8 heavy duty vehicle
The powertrain components have been consisted on two diesel engines, two automatic gearboxes with torque converters, drive shafts, summation box, transfer box, four differential and eight reduction units in axles which are shown in Fig. 1.Each diesel engine has maximum 425 kW power at 1600 rpm and 2800 Nm torque at 1100 rpm.Seven speed automatic gearbox is located after hydrodynamic torque converter.Output drive shafts from the automatic gearboxes are connected with each other into the summation box.Propulsion is transferred after summation box via drive shaft to a transfer case and it transmits the torque to differentials.Differential distributes torque to the wheels and planetary system inside the wheel hub increases it as the last reduction from engine to tire road contact.

Torque converter alternatives for powertrain
Torque converter assembly is composed of three major components [10].Impeller is the input element of converter which is attached directly to the engine and turns at engine speed.A stator changes the direction of flow inside the torque converter and torque is transferred to the turbine as a result of the induced flow from the impeller and stator [13].Characteristic of torque transferring depends on dimensions of each component, shape of blades and volume of torque converter.Capacity factor is also depending on fluid density, torque coefficient and effective diameter of torque converter.Torque ratio, speed ratio and impeller test moment MP,test are achieved by constant test speed np,test.Constant test speed was arranged at 1000 rpm in the test bench.Capacity factor is described by the function of speed ratio as: Impeller moment MP, which is called as the input torque of the torque converter, is changed by impeller speed (np), which is called as input speed of the torque converter.The equation is given as: The steady-state turbine moment-output moment of torque converter MT and turbine speed-output speed of torque converter nT can be presented as follows: Output torque MT is transferred at output speed nT of torque converter from an engine to the automatic gearbox unit smoothly.The torque converter unit is also multiples the input torque especially in low engine speeds according to its characteristics of capacity factor and torque transfer ratio.Therefore, two different type hydrodynamic torque converters are integrated into powertrain model separately for comparison of the performance results of the vehicle.Torque converter alternatives called Design 1 and Design 2, have different torque ratio im and capacity factor k. The characteristics of the two design options are shown in Fig. 2 as function of speed ratio in of torque converter.The main differences of converter alternatives are explained as the Design 2 has lower torque ratio (1.673) than Design 1 (1.829), however, test moment of impeller and capacity factor are higher in Design 2 torque converter.
Experimental impeller speed and numerically calculated impeller speed (Eq.( 3)) are compared for the torque converter of Design 1 in Fig. 3. Speed characteristics of both numerical and experimental results show progressive form at increasing turbine speed at the range of 2200 rpm and 1700 rpm.This comparison for Design 1 torque converter is considered as verification of moment transfer from engine to gearbox.Numerical Experimental the output moment is higher in Design 2 than Design 1 because of the difference of their torque ratio (im).Torque ratio and capacity factor are affected on operational impeller moment inside the engine moment curves also.Engine operational area are restricted with impeller moments at maximum and minimum speed ratio (in=0 and in=1).Engine torque-speed characteristic and operational area of torque converter designs are shown in Fig. 5. Moment requirements that caused from tire road interactions are supplied by restricted area (black for design 1 and red for design 2).

Longitudinal driveline dynamics of vehicle
The modelling of powertrain is especially useful for determination of performance characteristics such as grading and accelerating, but they are strongly depending on the measurements for experimental verification [3].An intermediate model which includes comprehensive theoretical model and simulation on a drive cycle without experiment is preferred in heavy duty vehicle industry because of financial anxiety.The powertrain model is presented in this paper, based on the following assumptions:  The model taking into account the longitudinal motion only.
 Slipping of tire is ignored and adhesive coefficient of the tire-ground contact assume sufficient for traction and barking.
 Each element is regarded as discrete system. System vibration and damping are ignored. Dynamic tire radius assumed constant.
Engines of the vehicle have to produce required power in order to overcome resistance forces and losses of propulsion system for the continuity of motion.Resistance forces consist of rolling resistance force FR and air resistance forces FL in no grade road conditions.Additionally, with vehicle move up grade, grading resistance FSt and under acceleration conditions, acceleration force Fa occurs.Those resistance forces can be expressed by: where m is total mass of vehicle, g is the gravity of acceleration, fR is the rolling resistant coefficient, δ is the slope angle of the road, ρ is the density of air, CW is aerodynamic coefficient of the vehicle, A is projection area of vehicle, V is the velocity of vehicle, λ is the coefficient of the effect of rotating masses and a is acceleration of vehicle.
In two power module (engine-torque convertergearbox) turbine moment (Eq.( 3)) is transferred to gearbox depends on drive ratio τGB at the same time for maximum traction effort.Output moments of gearbox MGB are summed inside the summation box.Summation box principle is shown in Fig. 6.Gearbox output shafts connected the gears with speeds of nGB1 and nGB2 and moments of MGB1 and MGB2 (red in Fig. 6) which is gear teeth numbers represented as z1 and z2.Gear ratio of summation box τSB is represented in Eqn. 9.
where z3 is the output gear teeth (green in Fig. 6).At the output speed of nSB, expression of output moment of summation box MSB: Vehicle performance is determined by traction force diagram which is calculated torque and speed transfer from the engine to wheels.Using with torque converter output moment MT, at various gear stages (represented by subscript i) moments on traction tires FTi are defined as: where τGB is the ratio of transfer case, τA is the ratio in axles (including differential ratio and reduction on wheel hub) and ηT is the overall mechanical efficiency of powertrain model.Mechanical efficiency which is expressed in below includes gearbox ηGB, summation box ηSB, transfer case (ηTB) and reduction in the axles ηA.Parameters and coefficients about vehicle are shown in Table 1.Drive ratios of powertrain components and their mass moment of inertia are presented in Table 2. Speed and torque reduction are implemented in 7 speed transmission τGBi, summation box τSB, transfer box τT and inside of four driven axles τA (differentials and wheel hubs).Torque converter reduction ratio is defined in Fig. 2 before and it is not shown in Table 2. Driven axles have same gear ratio as 5.46.To complete defining the traction force curve, conversion of angular velocity of torque converter output nT to vehicle speed at various gear stages Vi can be expressed by:

Longitudinal driveline dynamics of vehicle
Traction force curve of heavy duty vehicle are calculated by Eqs. ( 11) and ( 13) for seven speed gearbox.Maximum tractive force curve is determined by the assumptions of:  Gear shifting times are depending on theoretically usage of maximum traction force.
 Gear shifting process is applied in pre-determined engine speed that is related to intersection point of traction curves in each gear numbers.
Maximum tractive force area for grading and accelerating is defined as the area between traction curves and ressistive forces on tires in straight motion.Rolling and air ressitance (Eqs.(5, 7)) forces are effected on tire in straight motion of vehicle.Vehicle can use the area as reserve forces for accelerating and climbing which are the most crucial performance characteristics of a vehicle.Fig. 7 shows the maximum traction forces for usage of design 1 torque converter, reserve forces area and ressistive forces.Maximum reachable speed of vehicle is also determined by finding the point of equal maximum force and ressistive force value (black and red line).
Acceleration capacity of vehicle is expressed by the derivation of speed by time.When reserve forces are used for accelerating the dynamic equilibrium of the acceleration is written where λi is the coefficient of the factor of rotating masses as mentioned before which is changed with gear shifting.The definition of λi is given by: , mr    (15) where θred i is the reduction mass moment inertia of all powertrain components to tire rotating axis and rdyn is the dynamic rolling radius of tire.With the consideration of all gear ratios and components, θred i is evaluated

GB SB TB A TC GB SB TB A GB GB SB TB A SB SB TB A TB TB
where θE, θTC, θGB, θSB, θTB and θR are presented the mass moment of inertia of engine, torque converter, gearbox, summation box, transfer box and tires respectively.θR is taken 81,9 kgm 2 for each tire.The values of gear ratios and mass moment inertias are presented in Table 2.
Fig. 7 Reserve forces on traction tires (black; maximum traction force curve, red; ressistive forces-FR and FL) Effect of the integration design 1 and design 2 type hydrodynamic torque converters to powertrain model on accelerations of vehicle are calculated by Eq. ( 14).Acceleration capacities of the vehicle for loaded and unloaded operating conditions in various vehicle speeds are presented in Fig. 8. Results are clearly showed that acceleration capacity of unloaded operation is always higher.Torque converter type design 2 yields better performance on vehicle acceleration.
Acceleration time results of the heavy duty vehicle are calculated by using reserve forces and arranged by Eq. ( 14).Times for acceleration of the vehicle are expressed as: where Vmax is the maximum velocity of vehicle that is determined with solution of maximum traction force and resistance force curves illustrated in Fig. 7, FT is the maximum traction force of vehicle which is shown as example for torque converter of design 1. FR represents rolling resistance force and FL is the air resistance force.Results are shown in Fig. 9 for both torque converter types and operating load conditions.Difference of acceleration times between the usages of torque converter types are clear especially in loaded operation.Depending on the exerting torque from design 1 and 2 types of converters, accelerating time is higher with using of Design 2 than Design 1.

Drive cycle simulation and discussions
HD-UDDS drive cycle is as standardised driving pattern, which has been developed by The United State Environmental Protection Agency (EPA) Urban Dynamometer Driving Schedule (UDDS) for chassis dynamometer testing of heavy duty vehicles [8].It is mostly uses for the calculation of fuel consumption and exhaust emissions.Driving patterns are composed of specific speed trajectories over time which are included constant speed periods, acceleration and deceleration phases [14].HD-UDDS drive cycle are used in the vehicle industry for determination of vehicle performance in real world driving conditions for heavy duty vehicle.In this work the HD-UDDS are chosen for the case study.Speed profile of HD-UDDS drive cycle is shown in Fig. 10, a and required gear ratio on transmissions are illustrated in Fig. 10, b.Characteristics of the cycle are expressed as; duration is 1060 seconds, distance is 8.9 km, average speed is 30.4 km/h, maximum speed is 93.3 km/h and idle time are 353 s for 14 number of stops.Gear ratio is calculated by using Eq. ( 13) and traction force curve on tires which is illustrated in Fig. 7. Gear positions of seven speed gearbox are determined according to differences between the maximum reserve forces and total resistance force on vehicle traction tires.Required torque on summation box is split two equals for transmission unit.Devices before the summation box (gearboxes, torque converters and engines) are worked synchronously during the drive cycle.To compare the effects of torque converter on heavy duty vehicle powertrain model, drive cycle simulations were performed by using HD-UDDS cycle.Required moment on torque converter Mrequired,TC during the test cycle is defined: Speed requirement at the torque converter nrequired,TC is expressed as: where Vcycle is the speed of vehicle that is defined by test cycle.
Acceleration requirement because of HD-UDDS speed profile can be calculated by Eq. ( 14).Output moment of torque converter and maximum acceleration capacity of vehicle were given in Figs. 4 and 9. before.Acceleration and moment requirement points in related speed must be smaller than capacitive curves of them.Achievement of test cycle speeds is ensured by that.Fig. 11 shows the acceleration and moment requirement and their comparisons with torque converter designs (Design 1 and Design 2) for both loaded and unloaded conditions of the vehicle.In loaded operating condition that is showed in Fig. 11, a and b, required acceleration and moment higher than their maximum capacities.It shows that the vehicle cannot reach the speed values of test cycle when vehicle is fully loaded.Difference between torque converter selections are clearly shown in unloaded vehicle operation.Torque converter moment output for design 2 seems enough to achieve test cycle speeds in Fig. 11,  d.However, design 1 of torque converter moment output is under two required operating points.Additionally, fuel consumption of a heavy duty vehicle is crucial as well as vehicle performance.Fuel consumption of the vehicle can be investigated by using specific fuel consumption data of engine which is shown in Fig. 12. Consmption data is given for engine speed and power in g/kWh unit.
Engine operating points during the test cycle speed profile were found by using Eqs.( 2), ( 3) and ( 4) with the torque convertes data which is given in Fig. 2. Engine moment requirements conversation from the required moment of torque converter which was calculated by Eq. ( 18) and shown in Fig. 11, can be considered the same procedure with creating power output curve of the torque converter.
The operating points give moment requirements MEng and speed requirements nEng of the engine.The formulation of power requirements PEng of the engine is expressed as:  Specific fuel consumption result indicates that although some points are higher in design 2 rather than design 1, 204 g/kWh average fuel consumption are occurred in design 1 which is less than 196 g/kWh consumption in design 2.

Conclusion
This paper has introduced a heavy-duty fire truck powertrain, integrating two different types torque converter designs (Design 1 and 2) to provide better performance and less fuel consumption by increasing operational area of engine.Powertrain model of vehicle is presented for the simulation by using HD-UDDS drive cycle.
Performance results consist maximum acceleration and acceleration time from 0 km/h to its maximum speed.Additionally, effects of torque converter designs on fuel consumption of vehicle are investigated.Performance results were given both loaded and unloaded mass of vehicle.However, many points was not achieved to drive cycle requirements for loaded condition that is clearly shown in Fig. 11 (points above the curves in Fig. 11, a and  b).Therefore, fuel consumption results were given just unloaded conditions of vehicle to provide more accurate evaluations.
The results and prospects are summarized through the investigations of the effects of design 1 and 2 types torque converters as follow:  Maximum acceleration capacity can be increased 5% by using Design 2 type torque converter.
 Although, loaded vehicle can reach from 0 to 100 km/h speed in 43.14 s with Design 1 type torque converter, Design 2 type provides 36.97 s.The acceleration time can be reduced 14.5% with the usage of Design 2.
 The acceleration time of unloaded vehicle from 0 to 100 km/h speed is 22.56 s in Design 1. But, 19.64 s accelerated time can be provided with Design 2 which is reduced 12.9% the time for needed.
 4% fuel consumption savings can be obtained with Design 2 for coworking two engines.
 Power reuirements of HD-UDDS drive cycle can be achived by only Design 2 type in unloaded condition which is clearly shown in Fig 11,d.This results leads to the conclusion that the powertrain analysis and simulation can use the investigation of the effects of component characteristics.In this paper, different torque converter characteristics in terms of Design 1 and Design 2 are investigated.The study can be extended to evaluate on cost or comfort of vehicle by using this method in future works.

Fig. 1 8x8
Fig. 1 8x8 Heavy duty vehicle powertrain Different transferring characteristics of torque converter effect the torque ratio im and capacity factor k.Both of them are the function of torque converter speed ratio in.Capacity factor is also depending on fluid density, torque coefficient and effective diameter of torque converter.Torque ratio, speed ratio and impeller test moment MP,test are achieved by constant test speed np,test.Constant test speed was arranged at 1000 rpm in the test bench.Capacity factor is described by the function of speed ratio as:

Fig. 4
Fig. 4 Output moments of torque converter designs

Fig. 8 Fig. 9
Fig. 8 Acceleration performance results of the vehicle

Fig. 11
Fig. 11 Simulation results of acceleration requirements for loaded (a) and unloadaed (c) vehicle and moment requirements for loaded (b) and unloadaed (d) vehicle HD-UDDS cycle simulation for fuel consumption of the vehicle is implemented and the results are shown in Fig.13for the Designs 1 and 2 of torque convertors.

Fig. 12
Fig. 12 Fuel consumption data of the engine

Table 2
Drive ratios and mass moment of inertia of powertrain components