The Evaluation of Cornering Behavior of Low Floor Electric Bus : the Effected to Mass Distribution and Friction Coefficient

The Low Floor electric bus, which had been promoted by the Government of Thailand, boost design technologies and research in the automotive industry. In order to fulfill the safety requirements regulated by the Department of Land Transport of Thailand, it must undergo both static and dynamic analysis. The vehicle dynamic cornering behavior plays an important role to demonstrate handling stability especially for active safety. In this paper, we study effect of the parameters of weight distribution and the road friction coefficient, which were indicated in terms of understeer gradient. The analysis had been conducted by ADAM CARS based on the vehicle’s multi-body model. The analysis was applied under steady state cornering conditions based on three front to rear weight distribution configurations in percent of 50/50, 45/55 and 40/60, and a lateral tire road friction coefficient of 0.5, 0.7 and 0.9. The results show that the greater the friction coefficient between road and tire, the better handling behavior. The trends are in the same fashion when the three weight distributions are varied and the 40/60 configuration has the smallest understeer gradient. But in the real design we should consider other behavior like ride performance and static analysis, so that the configuration of 45/55 is chosen in our real design.


Notation
In this paper, the following notation is used throughout:

Introduction
Concerning mass transportation, a number of countries have researched and developed a bus industry.So do Thailand, domestic electric buses are promoted for design and development tasks in order to achieve the main goals like performance as well as safety issues.
Referring to the statistics from the Department of Transport of Thailand, there are approximately 80,000 busses per year which have registered to serve more than 35 million passengers traveling by bus.Consequently, traffic accidents are occurred by evaluating damage and dead about 600 million baht [1].For this reason, in the bus design process, both static and dynamic behaviors analysis is required to indicate the safety of the bus.The static stability test relates to the vehicle's resistance to rollover, which involves a pose of center of gravity.
The parameters of vehicle weight distribution can be designed and calculated via the position of battery, air condition, axle and other component.In the case of vehicle dynamics, the subject deals with the study of vehicle response related to driver input, ability of the vehicle to stabilize its motion against external disturbances for purpose of handling characteristics, especially cornering dynamic characteristic [2] (e.g., lateral acceleration, side slip angle, Yaw rate and understeer gradient) [3,4].
This study is aimed at evaluating the cornering dynamic characteristics of the Low Floor Electric bus under the effect of mass distribution.The analysis had been applied by ADAM CARS [5] based vehicle multi-body model under thee steady state cornering conditions.Three possible configurations front/rear axle weight distribution (in percent) of 50/50, 45/55 and 40/60 are taken into account as well as the variation of the friction coefficient in the wet to dry road condition of 0.5, 0.7 and 0.9.The handling characteristics are mainly determined from understeer gradient wheel slip angle and yaw rate.[7,8] The understeer gradient could be evaluated by operating the vehicle around a constant radius turn by observing steering angle versus lateral acceleration.

Problem Definition
The evaluation of the cornering dynamic behavior of buses [9] plays an important role to make it capable of operating in the most of road condition safely.So that there are the cooperation between bus manufacturer Cherdchai industrial co.ltd and Suranaree University of Technology for design and development of electric bus in the theme of weight distribution during steady state condition.

Steady State Vehicle Cornering Condition
To explain the cornering characteristic, a simple bicycle model is considered in order to identify the kinematics characteristics among the parameters like lateral, longitudinal as well as yaw dynamics.In figure 1, X-Y reference coordinate frame is defined using compass directions (e.g.east and north) and an x-y rotating frame at the vehicle' s center of gravity in longitudinal and lateral dynamics respectively.In plane kinematics, one of the rotation angle about z-axis, called yaw angle ( ), was taken into account.
To define the relationship between the fixed frame X-Y and the rotating frame x-y, the acceleration analysis was perform.The acceleration of the vehicle in global coordinate frame is defined as The term y is interesting because it shows that the vehicle slip behavior and it cannot be negligible in some case of operation as discuss later.Steady state cornering is implemented to verify the handling characteristic which is aimed at understeer gradient.
As shown in figure 1, the front and rear wheel slip angle, denoted by f  and r  respectively, are defined as the angle between the longitudinal axis of the wheel and the velocity vector.The instantaneous turn centre IC of the vehicle is the point at which the two lines perpendicular to the velocities of the two wheels meet.It is assumed throughout that the road radius is much larger than the wheel base of the vehicle.From this geometry, we approximate a kinematics relationship for the wheel steering angle  as: Fig. 2. Lateral Force acting on the vehicle and the components of friction force at each wheels [12].
Considering the dynamics model of the vehicle mentioned in figure 2, there are lateral forces acted on the tires due to the centripetal action during cornering following equation 4 so that the wheel side slip angle, f  and r  are varied to the lateral tries force.Assuming the small slip condition, the lateral tire force is proportional to its slip angle with the constant called cornering stiffness and they are denoted for the front and rear as f C and r C respectively.The steady state steering angle in equation 3 then can be rewritten as: Or equivalently: Where K is understeer gradient, In case of understeer K should greater than zero due to a larger slip angle at the front tires compared to the rear tires.The relationship between weight transfer and wheel slip angle is interpreted in following equation 7.
The coefficient of friction is concerned the contact surface between tire and ground.The faster the vehicle negotiates a bend, the higher the coefficient of friction used to prevent the undesired understeer behavior.

Multi-Body Dynamic Simulation
A multi body dynamic (MBD) system is a simulation modeling method, consisting of solid bodies, or links, that are connected to each other by joints that restrict their relative motion.Motion analysis is important because product design frequently requires an understanding of how multiple moving parts interact with each other and their environment.From automobiles and aircraft to washing machines and assembly lines moving parts generate loads that were often difficult to predict.Complex mechanical assemblies present design challenges that require a dynamic system level analysis to be met.
To study the cornering dynamic behavior of buses under steady state and transient state conditions, multi-body model of the bus had been built in MSC ADAMS CARS software tool.The multi-body bus model was built based on the specification in Table 1.Fig. 3. Low Floor Electric Bus model.

The Virtual Low Floor Electric Bus
According to the virtual model of the Low Floor Electric bus model, the multi-body dynamic modelling had been carried out in MSC ADAMS/ Truck tool ( MSC software) .The virtual model consisted of the sub-systems in the Low Floor Electric bus specification, with the center of gravity from experiments shown in figure 4.
Where t is the track width of the vehicle (mm), and h is the height of center of gravity (mm).The SSF of pick-up trucks, vans and buses will be in the range of 1 to 1. 3. For the purpose of calculations herein, it is assumed to be 1.The basic information required to understand multibody dynamic simulation is its mathematical formulation.It explains how lateral forces are generated while a vehicle is turning, and their relation with the slip angle and lateral acceleration, as well as understeer gradient.The Low Floor Electric bus model was used to estimate vehicle handling characteristics required for the model.

Simulation condition
The vehicle dynamic test under steady state condition was simulated virtually on a constant radius cornering test.The aim of this test was to assess the lateral acceleration, side slip angle, Yaw rate and understeer gradient of different configurations of virtual model.The characteristics of the test vehicle were investigated in a total of nine conditions: three friction coefficients (0. 5, 0. 7, and 0. 9) [ 11] at each of three different weight distributions (front/ rear axle weight in percent, as 55/45, 50/50 and 45/55).For the test, the vehicle models were maneuvered on the test track at initial longitudinal velocity 10 km/ h for left turn.The data were carried out by 0. 1 interval time up to 45 km/ h under 50 seconds on the flat track.The lateral coefficient of friction relates to the ease with which a vehicle will skid on a road.It is the ratio between the lateral force and the normal force acting on the contact point, given by:

Lateral Friction Coefficient
The maximum lateral friction coefficient is related to the maximum forces that the tires can provide.It corresponds to the value where the lateral force reaches saturation and there is a risk of an exit route.Maximum friction was largely related to road conditions and effects between the tire and the road.It was an indication of road status and possible loss of adhesion.
This parameter cannot be measured by conventional sensors, so it requires an estimation technique for its estimation based on available measurements and tire/ road interaction models.The true values of friction coefficient used by the simulator in the generation of the dynamic parameters, for a dry road the maximum friction coefficient is 0. 9 and wet road the maximum friction coefficient is 0.6 [11].

Results and Discussion
Under steady state cornering investigation, the lateral acceleration consists of two components as described in equation ( 2) it was evidenced that the lateral acceleration yaw rate and vehicle speed can be measured and calculated.
Both were not equal because of the lateral slip acceleration cannot be measured directly, but by comparison.Its value occurs and leads to instability in the real world.Figure 6 demonstrates the components among them.From each test condition, the result show that the more increase of bus speed, the more gap between them or slip accelerations were raised and there were in the same fashion.In relation to the friction coefficient and slip, the lateral force at each wheels determines the cornering behavior as discussed in section 4. It was known that the lateral force was roughly dependent on the square of vehicle speed, but the friction forces at each wheel increased unfortunately not at the same rate as the lateral force.It caused the bigger side slip angle at wheel unequally because of the tire contact geometry.Figure 7 shown the relationship between the lateral forces in term of wheel side slip angle in case mentioned below.The slopes of these graphs Side slip plays an important role in understanding the cornering behavior.We investigate and found out the difference between them in order to calculate the understeer gradient.At lower speeds, during the turn the direction of the wheel side slips are shown in figure 9( a).They were in the opposite direction, and from the kinematics analysis the velocity vector of the vehicle makes it behave like understeer.In contrast, in figure 9( b) at higher speed, the rear wheel slip was in the same direction as rear wheel slip angle, causing the bus to also understeer with higher understeer gradient.Based on the result of steady state vehicle dynamic test, the understeer gradient by varying CG and friction coefficient were evaluated.Understeer gradients were derived from equation ( 5) by evaluating the slope of the graph ( in figure 10. ) between front wheel steering angle versus lateral acceleration.The trend seems to be nonlinear but it was approximated as bilinear curve during low speed and high speed criteria, as stated in table 3 and 4   Fig. 12 The relationship between understeer gradient and friction and the weight ratio at velocity 30-45 km/h.

Conclusion
Considering the multi-body dynamic simulation, we studied the effect of weight distribution and friction coefficient in steady state cornering condition.The vehicle handling characteristic of Low floor electric bus was performed via understeer gradient.The effect of various friction coefficients are significantly in the same pattern when varying the weight transfer configuration.The greater value of the coefficient leads the bus better handling.The weight distribution in format 40/60 seems to be the best understeer gradient in compare to three models.But in the real design we choose the 45/55 because of compromising other condition like ride performance.In this study, the center of gravity at low speed and higher speeds was not over than the value from literature review.So that for propose in bus design process should be realized require to know the weight of bus component and design to get the highest balance of the bus.

f===
Slip angle of the front tire r  = Slip angle of the rear tire  = Side slip angle of vehicle  = Front wheel steering angle y a Lateral acceleration at vehicle C.G. f C Effective cornering stiffness of the Front axle r C = Effective cornering stiffness of the rear axle K = Understeer gradient L = Wheelbase f m = Front axle weight r m = Rear axle weight R = Turning radius V = Vehicle speed m = Total mass  = Friction coefficient y F = The lateral force z F = The normal force g = Gravitational acceleration  = Yaw angle  = Yaw rate y = Lateral slip acceleration DOI: 10.12792/iciae2017.046

Fig. 4 .
Fig. 4. Experimental of Center of Gravity (CG.)From the experiment realting to the center of gravity, the front axle weight was found to be 5,750 kg, and the rear axle weight was 6,780 kg, giving the weight distribution %(F/ R) of 45/55.For the height of center of gravity, it was necessary to use the static stability factor ( SSF) , which is an at rest calculation of the roll-over resistance based on exterior dimension of vehicle.The SSF formula is /2 SSF t h 

Fig. 5 .
Fig. 5. Location of Center of Gravity (CG.) Table2.show the weight distribution of Low Floor Electric bus model and the distance of CG position from front axle in this study.

Fig. 7 . 5 Fig. 8
Fig. 7.The relationship between lateral force and wheel side slip in the case of 45/55 weight distribution and friction coefficient 0.5

Fig. 9 .Fig. 10
Fig. 9. Front and rear side slip during (a) lower speed 10-30 km/h and (b) higher speed 30-45 km/h . Both table3 and 4displayed the comparison of weight distribution and friction coefficient .The decrease in weight distribution F/R ratio as 50/50 45/55 and 40/60 affect minor change in understeer gradient.Unlike the variation of friction coefficient, it was obviously shown the better handling behavior.By the way all values are acceptable based on our experience of handling behavior. ......... ........

Fig. 11
Fig.11The relationship between understeer gradient and friction and the weight ratio at velocity 10-30 km/h.

Table 1 .
Specification of Low Floor Electric Bus.

Table 2 .
The Weight Distribution of Low Floor Electric Bus.

Table 3 .
Understeer gradient of each layout in fiction condition at velocity 10-30 k/h.

Table 4 .
Understeer gradient of each layout in fiction condition at velocity 30-45 k/h.