DEMAC - UNESP

EESC - USP

Mercedes-Benz do Brasil S.A.

Two important parameters for the comparison and the project of vehicles are the time and the distance in the acceleration and in the velocity retaking, that is, the time and the distance traveled for the vehicle to accelerate between the velocities vi and vf, with a larger vf than vi. When vi=0, the time and the distance in the acceleration are denominated. When vi>0, the time and the distance in the retaking of velocity are denominated. KOFFMAN [1] developed a graphic method for the determination of the time and the distance traveled in the acceleration and velocity retaking. CANALE [2] presents a study for the acceleration and velocity retaking a passenger car "Kadett" of General Motors do Brasil.

The time for the vehicle to accelerate between the velocities vi and vf is expressed by the integral

in which the acceleration a(v) is the function of the velocity calculated by the equation (2).

The vehicle available acceleration as function of the installed systems (engine, gearshift, differential, among others) is calculated according to the expression:

In the vehicles with manual gearshift and the same tires in the traction axes, the total engine force Ftot is expressed according to the equation

and the velocity of the vehicle, according to the expression

a=mv+n, where: (6)

with the values of the accelerations aca and acb, calculated by the expressions

Therefore, the integral for time calculation can be approached by the expression

In a similar way, the distance traveled by the vehicle when it accelerates from the velocity vi to the velocity vf is calculated by the expression

and for vb>va the solution of the equation (12) is:

The criteria for the shift gears can be in a certain chosen rotation, in the rotation of maximum potency, in the engine maximum rotation or when the acceleration of the vehicle becomes smaller than the acceleration of the posterior engaged gear. The time of shift gears should be supplied and, with that, two approaches can be considered: the first one, for the vehicle traveling in constant velocity during the shift gears and, the second one, being considered a loss of velocity during the time of shift gears due to the action of the resistance forces. In both cases, the engine is considered as being disengaged. In the same way, the distance should be calculated during the time in which the vehicle is shifting gears. The time and distance values during the shift gears should be computed in the general sum.

In order to obtain each punctual acceleration for each velocity v of the vehicle, according to the expression (2), it should be verified if there is not a total slip of the wheels. If that happens, the acceleration should be limited by the vehicle limit acceleration.

In the calculation of the time and traveled distance during the acceleration or the velocity retaking, there is usually a sequence of gears used by the vehicle. In this calculation, it is necessary to verify if it is possible that the velocity vf of the vehicle can be reached with the chosen gears stagger, as well as if vf is not smaller than the maximum velocity in the last gear of the stagger. The sequence of gears that presents the smallest time for the vehicle to accelerate from the velocity vi to the velocity vf is obtained by the developed computational system.

In the time and traveled distance calculations, when the rotation of the shift gear is the maximum of the engine, the vehicle can use an over-rotation to reach a certain velocity vf without the necessity of shift gear. In this case, the engine potency stays constant in a small over-rotation range, decreasing later until zero (data observed in tests done at Mercedes-Benz do Brasil (MBB) for Diesel engines). According to the experience in the section of engine development of the MBB, when the engine is in over-rotation the potency stays constant in approximately 50 min^-1 being later decreased to zero in a 15% rotation larger than the engine maximum rotation. For the calculation of the time and of the distance in the acceleration and in the velocity retaking only a percentage of the over-rotation range is used (10% is an acceptable value, according to the section of engines of MBB).

In the calculation of the time and of the distance for the vehicle to accelerate starting from idle position, vi=0, the process of clutch engage should be taken into account. Before the vehicle starts move from idle position, the engine is in the maximum rotation, in which its inertia helps to accelerate the vehicle. Immediately before the engage, the vehicle velocity is zero and the engine rotation is relatively high. Sometime after t=0, the engine velocity is directly related to the vehicle velocity and the velocity of the clutch slip is zero. During that interval of time, the vehicle accelerates and the engine decreases its rotation. For the calculation of the acceleration during the engage, a detailed mathematical model was proposed by LUCAS [4]. According to this same author, a simplified model, that considers the maximum torque of the motor as being constant during the engage period. This simplified model was used in the computational system developed.

Another performance parameter is the time and the final velocity of the vehicle as it accelerates and travels a preset distance starting from a velocity vi. So, for each velocity increment a new time and a new traveled distance are calculated. In this process, it can happen that, after an increment of velocity, the distance is larger than preset one. In this case, the velocity increment should be divided by two and the calculations are supposed to be refined until that the preset distance fits a tolerance.

The analyzed vehicle is a Mercedes-Benz tractor semitrailer, with the tractor denominated LS1935 with 4x2 traction system. The main characteristics of the vehicle are presented below, according to information given by the tractor and semitrailer manufacturers:

- model of the tractor: LS1935;

- traction system: 4x2;

- wheelbase of the tractor: 4,600 mm;

- front wheel tread of the tractor: 1,993 mm;

- rear wheel tread of the tractor: 1,800 mm;

- length of the tractor: 7,060 mm;

- width of trailer of the tractor: 2,540 mm;

- height of trailer of the tractor: 2,930 mm;

- number of rearward axles of the tractor: 1;

- distance of the king-pin to the back axle of the tractor: 660 mm;

- height of the king-pin in relation to the pavement: 1,210 mm;

- length of the semitrailer: 12,400 mm;

- width of the semitrailer: 2,600 mm;

- height of the semitrailer: 1,959 mm;

- number of axles of the semitrailer: 3;

- distance between the king-pin and the first back axle of the semitrailer: 5,755 mm;

- distance between the king-pin and the second back axle of the semitrailer: 7,000 mm;

- distance between the king-pin and the third back axle of the semitrailer: 8,245 mm;

- tires: 11R22;

- dynamic rolling radius: 550 mm;

- coefficient of air resistance: 0.80;

- air density: 1.225 kg/m³;

- coefficient of rolling resistance: 0.008 constant;

- measure of grade: 0%;

- projected vehicle area: 6.5 m²;

- maximum adhesion coefficient between the tires and the pavement: 0.75;

- resistance coefficient due to the inertia of the rotate parts: calculated in function of the moments of inertia of the engine and clutch (the moments of inertia of the transmission were not taken into account);

- inertia of the wheels: they contribute in 4% in the mass factor due to the inertia of the rotate parts;

- time of shift gears: 0,7 s (according to average observed in tests of road done at MBB);

- strategy of shift gears: maximum rotation of the engine, using over-rotation of the engine;

- engine: : OM447LA/360 cv. Velocity range: from 665 to 1,898 min^-1. Maximum torque = 1,780 Nm in 1,000 min^-1 (values reduced for conditions in accordance test NBR5484 [5]).

- transmission: ZF 16S130/1650, efficiency: from 0.96 a 1.00 according to numerical ratio;

- ratio of final drive: 3.77;

- efficiency of final drive: 0.92;

- weight of loaded combined vehicle: 40,000 kgf;

- weight of empty tractor: 10,000 kgf.

center of gravity position for the empty tractor: longitudinal center of gravity: 1,930 mm; transversal center of gravity: 997 mm; vertical center of gravity: 950 mm;

- weight of empty semitrailer: 7,275 kgf.

center of gravity position for the empty semitrailer: longitudinal center of gravity: 6,133 mm; transversal center of gravity: 1,000 mm; vertical center of gravity: 1,400 mm;

limit weight in the front axle of the tractor: 6,000 kgf;

- limit weight in the back axle of the tractor: 10,000 kgf;

- limit weight for axle of the semitrailer: 8,500 kgf;

- height of the platform of load of the semitrailer: 1,500 mm.

The center of gravity position for the loaded vehicle (40 ton) is determined by the maximum weight in the axles and by the load center of gravity.

- longitudinal center of gravity (X) - distance to front axle: 1,930 mm;

- transversal center of gravity (Y): 997 mm;

- vertical center of gravity (Z): 950 mm.

- longitudinal center of gravity (X) - (maximum weight in the axles) - distance to king-pin: 5,496 mm;

- transversal center of gravity (Y) - (maximum weight in the axles) -distance by the passengers side: 1,000 mm;

- vertical center of gravity (Z) - (load center of gravity 2.75 m from the road surface) - height: 2,248 mm.

In the table 1, the results of the time and of the distance in the acceleration (0-20 km/h; 0-40 km/h; 0-60 km/h; 0-80 km/h; 0-100 km/h) and in the velocity retaking (20-40 km/h; 20-60 km/h; 20-80 km/h; 40-60 km/h; 40-80 km/h; 60-80 km/h) are presented. The shown results are experimental and calculated in the developed computational system (simulator). The experimental results were accomplished for each test (example: test from 0 to 20 km/h) in several sections. For each test the three best results of the sections of the highway were considered in the direction Rio de Janeiro-Bertioga and the three best results of the sections of the highway in the direction Bertioga-Rio de Janeiro. An arithmetic average was made with the six best results. Table 1 also contains the variations between the experimental results and the theoretical results of the simulator.

The interval of time for the shift gears was 0.7s. During this period, the velocity of the vehicle was constant. The time interval of engage for the vehicle to accelerate from zero to the velocity corresponding to the minimum rotation of the motor was calculated with the maximum torque of the engine[4]. The engine stayed, if necessary, in over-rotation. Those intervals of time, as well as the respective displacements should be computed in the sums for the calculations of the time and of the distance in the acceleration or in the velocity retaking.

Table 1 - Time and distance in acceleration and in the velocity retaking

Table 2 - Vehicle acceleration from zero to 20 km/h.

Table 3 - Vehicle velocity retaking from 40 to 80 km/h.

The results of the time and of the distance in the acceleration and in the retaking of velocity are also expressed by the graphs illustrated in the figures 1, 2, 3 and 4, which show a good convergence of the experimental and theoretical values, validating the proposed model.

Figure 1 - Time in a acceleration

Figure 2 - Distance in a acceleration

Figure 3 - Time in the velocity retaking from 20 km/h

Table 4 - Time and distance in the acceleration and in the velocity retaking for the vehicle in a 3 % road climbing

Table 4 shows the time and the distance in the acceleration and in the velocity retaking for the vehicle in a 3% road climbing.

The computational system also allows the calculation of the time and of the final velocity of the vehicle accelerating in a preset distance starting from a velocity vi . As a calculation example, it is considered the vehicle accelerating from vi=0 km/h in the distance of 1,000 m, using the gears 5, 9, 12, 14 and 15. Table 5 contains the results of the simulator system. The experimental result for this test was 70.5 s for the vehicle travel 1,000 m. The variation between the experimental result and the theoretical result obtained with the simulator is -5.86%.

Table 5 - Time and final velocity in the vehicle acceleration in 1,000 m from zero km/h

D'Elboux e-mail : jedelboux@ig.com.br