Measuring of Traction and Speed Characteristics as Well as of Fuel Economy of a Car in Road Conditions

This article is devoted to the identification of traction and speed characteristics as well as of fuel economy of motor vehicles in road conditions. Among common variants of measuring of the above stated values, the preference was given to the immediate gaining of factors by means of a computer-aided measuring system. There is a theoretical justification given to the suggested approach as well as methods and results allowing to provide a practically sufficient solution accuracy of the problem.


Introduction
Vehicular transport is widely used in various areas of national economy. The utilization efficiency of vehicles affects production costs as well as delivery performance of passengers and cargos. It is also significantly defined by the type and the characteristics of internal combustion engines (ICE). The most widespread type of engines is diesel engine (over 90% in freight transport, and a constantly growing ratio among cars).
In practice, the lack of possibility to constantly control the technical conditions of vehicles results in the fact that they are often used with defects which are invisible to the driver but provoke the growing fuel consumption, raise transportation costs as well as increase the content of harmful substances in exhaust gases. Fuel economy as well as traction and speed characteristics of a motor vehicle are very important performance indicators that designate the exploitation efficiency of vehicles [1]. That is why a well-timed control, including diagnostics, is a vital task.
State-of-the-art. Following measuring methods of motor vehicle parameters have been considered in road conditions: 1. Data acquisition by means of GSP/GLONASS technologies [2] 2. Recording of a data log by using a dealer scanner with subsequent data transfer onto an external medium [3,4] 3. Immediate measuring of parameters by means of a computer-aided measuring system The usage of satellite-assisted technologies and fuel consumption monitoring by fuel level in the tank are not suited for the given task because they deliver quite averaged data, while, in our case, during diagnostics, the process is considered to be very fast flowing. The second variant provides with quite exact data, however, these still need to be processed after being saved in a log. As for the fuel consumption registered by an on-board system, the calculation of fuel economy parameters can bring inaccurate results because of the difference between actual and expected injection rate. Taking into consideration all the above mentioned facts, it was decided to use the third variant with computeraided technologies. The concept of this approach is depicted in the publication [5].
Mathematical model Theoretic preconditions. We shall start to define the vehicle motion parameters by making up an analytical model of forces and moments that affect the motor vehicle ( fig. 1) when accelerating uphill.
We shall define current net torque that is spent for the overcoming of motion resistance moment at every integration step on the basis of a force balance equation of a motor vehicle: M ei =M am +(F w +F f +F i ±m eq ·j a )· r k / (i t ·η t ) (1) where M am is the moment spent for the gearing of auxiliary machinery, N·m F w is air resistance force, N F f is rolling resistance force, N F i is the force that affect the motor vehicle on the road inclination, N m eq is the equivalent mass of the motor vehicle, kg j a is the acceleration rate of the motor vehicle, m/s 2 r k is the radius of rolling circle, m i t is the gear transmission ratio η t is the transmission efficiency factor We shall admit that there is no crutch skidding and the crutch is rigidly closed, while the motor vehicle has elastic tires subject to force and speed deformation. The equivalent mass of the motor vehicle is defined taking into account the rotational inertia coefficient δ, by means of a familiar equation: where G is the weight of the motor vehicle, N g is the gravitational acceleration, m/s 2 . In its turn, we shall define the rotational inertia coefficient the following way: I e is the deduced inertia moment of the engine I k is the inertia moment of a car with a tire Thus, taking into account equations (1-3), we shall write down the equation of motion of a motor vehicle: ρ is the air density c x is the aerodynamic drag factor f is the coefficient of rolling resistance α is the road inclination S x is the maximum mid-section of the motor vehicle The speed of the motor vehicle at the i th step shall be calculated by means of numerical computation methods of differential equations. In our case, we used Euler's method: where V i-1 is the speed of the motor vehicle at the previous counting step, m/s Δt is the counting step, c The rotational rate of the crankshaft shall be defined on the basis of the current speed taking into account all made admittances: Let us esteem the overall loss of capacity in the tires of leading wheels [6]. In a general case, the overall efficiency factor of a tire  k is defined by the following equation: (7) where N k and N m are the delivered and the withdrawn power of the wheel respectively; ω k and V are the angular rate of the =resistance moment of the tire; R x is the direct-axis reaction in the contact patch; r k and r ko are the rolling radius and the rolling radius in the conducted mode; М k is the drive torque delivered to the wheel.
The efficiency factor of leading wheels depicts the loss of capacity and speed in the process of rolling. The efficiency factor of the tires of leading wheels  k is the product of two multipliers: The first multiplier reflects the friction force loss (hysteresis loss) of capacity in the tire while rolling. This component of capacity loss is calculated quite easily and exactly. There are usually no difficulties with its computation.
The second multiplier depicts speed losses of capacity connected with tangential elasticity of a tire, i. e. it takes into account the fact that the number of rotations made by a wheel as well as the covered distance do not always fit together exactly. The most of the hardships arise namely when determining the value of this multiplier. These complications are based on the definition of the kinematic radius r k (the rolling radius of a wheel with an elastic tire): The diagram below shows the dependence of the efficiency factor of tires (and in particular of every component of this) on the moment М k delivered to the wheel. The maximum efficiency factor of tires of light vehicles, when the wheels are rolling in the conducted mode, tops  k max ≈0,92÷0,93. That means that at least 6…7% of engine capacity is lost in the tires of a light vehicle for hysteresis and speed losses. The maximum efficiency factor of tires of freight vehicles equals to  k max ≈ 0,90…0,87. It is obvious that the capacity loss in the tires of freight vehicles amounts to at least V 10…13% of engine capacity. Thus, if we are given the parameters of the motor vehicle, the road type and its inclination, while measuring the speed of the motor vehicle, we find the drive torque that affects the axle tree and the capacity.
The given task can be solved by continuous measuring of the speed of the wheel(s) that work in a conducted mode.

Experimental procedure
The experiments were conducted on the motor vehicle "Sobol" (GAZ 2217) equipped with a diesel engine ISf 2.8 Cummins with Common Rail fuel injection system. The experiment was held on an even, dry road segment in a fine windless weather; the journey was made in two opposite directions. The method included the measuring of factors in the acceleration mode up to 100 km/h with a fullypressed control pedal of fuel injection. The measuring system ( fig. 3) consisted of an analog-digital converter to the input of which there were impulse signals delivered from the ABS wheel sensor of the front wheel, as well as of fuel flow meters mounted in the direct and in the reverse fuel-delivery lines. When calculating the fuel economy, the consumed fuel was determined as the difference between the direct and the reverse (returned into the tank) flow. The data delivered to the input of the analog-digital converter were identically processed for fuel consumption as well as for the determination of the distance and the speed of the motor vehicle, because the signals are represented by rectangular pulses (fig. 4). In order to facilitate data processing, there was a special script written, the essence of which is clarified in fig. 4. With a certain number of impulses given, the time of passing these intervals is registered, while the previous point is considered to be the initial point for the next interval.
Below, there is an example of equation for the calculation of line speed of a motor vehicle: where z ii is the pre-defined number of impulses, imp k is the calibration value, imp/meas. unit (for speed calculation of the motor vehicle GAZ 2217 there was the value assigned of 482 imp/km Δt i is the passing time of z ii , s. In order to measure the direct and the reverse flow, there were volume-flow rate sensors used with oval gears Microstream OF05ZAT by Aichi token (Japan) which are characterized by a high reproducibility of results and a practically sufficient measurement accuracy.
The metrological evaluation of the system allowed to conclude that the relative tolerance of line speed measurement of a motor vehicle and the angular rate of the wheel does not exceed 2.4%; the tolerance of fuel consumption does not exceed 3.8%.  The calculated data available from experiments accord well with passport full-load curve of this diesel. In particular, the true values of an effective drive torque in the range of 2000-3500 rpm differ to 6.5% (in the initial specification, the maximum drive torque amounts to 310 Nm in the range of 2000-3500 rpm). The mentioned circumstance is not based on the calculation tolerance but on the difference in the versions as well as testing and exploitation conditions. a) b) Fig. 6: Estimated data of the full-load curve of the motor vehicle GAZ 2217 with a diesel engine ISf 2.8 Cummins a -effective drive torque; b -effective capacity The conducted research led to the following conclusions: 1. The elaborated computer-aided system for the measuring of traction and speed characteristics as well as of fuel economy of a motor vehicle in road conditions helps to estimate the acceleration, the VII International Scientific Practical Conference "Innovative Technologies in Engineering" IOP Publishing IOP Conf. Series: Materials Science and Engineering 142 (2016) 012101 doi:10.1088/1757-899X/142/1/012101 speed, and the distance covered by a motor vehicle with a practically sufficient accuracy (relative tolerance equals to 2.4%).
2. In order to collect the data of traction and speed characteristics of a motor vehicle, it is most viable to use a regular sensor of angular rate of the antilock braking system for a wheel working in a conducted mode. In the case of usage of a sensor of angular rate of the conducted wheel, it is necessary to take into account speed and force losses in the tire.
3. In common rail fuel injection systems, it is rational to use the engine fuel consumption method as the difference between the direct and the reverse flow, because they grow the number of diagnosis information about the technical state of fuel injection system by themselves.