METHOD FOR SIZING AN ELECTRIC DRIVE OF SMALL CLASS ELECTRIC VEHICLES

ABSTRACT

The implementation of mechatronic control of an electric vehicle depends on the totality of the joint work of many systems and their information communication. Therefore, the use of modern mechatronic systems in electric vehicles is among the factors that improve the mechatronic control of an electric vehicle and allow us to offer the customer a new level of electric vehicle control. The paper presents the calculation of the characteristics of the traction motor as part of the electric transmission of a vehicle using the example of a typical small class car. The parameters necessary for calculating the limiting mechanical characteristics are indicated. The article presents the main types of electric motors currently used as traction drives used in electric transmissions: a collector DC motor, an asynchronous squirrel cage motor, a synchronous motor with excitation from permanent magnets, a self-excited valve motor and a valve motor with independent excitement. Their main advantages and disadvantages from the point of view of application as a traction electric motor are noted. The work indicates the forces acting on the vehicle, on the basis of which the traction balance equation is drawn up. The driving cycles used for electric vehicles are considered. It is necessary to use a modern test-driving cycle when calculating the limiting mechanical characteristic of a traction electric motor as part of an electric transmission of a car to determine some operational parameters and the main mechanical characteristics of a traction electric motor.

АННОТАЦИЯ

Реализация мехатронного управления электромобилем зависит от совокупности совместной работы многих систем и их информационной связи. Таким образом, использование современных мехатронных систем в электромобилях является одним из факторов, которые улучшают мехатронное управление электромобилем и позволяют нам предложить заказчику новый уровень управления электромобилем. В статье представлен расчет характеристик тягового двигателя как части электрической трансмиссии транспортного средства на примере типичного автомобиля малого класса. Указаны параметры, необходимые для расчета предельных механических характеристик. В статье представлены основные типы электродвигателей, используемых в настоящее время в качестве тяговых приводов, используемых в электрических передачах: коллекторный двигатель постоянного тока, асинхронный двигатель с короткозамкнутым ротором, синхронный двигатель с возбуждением от постоянных магнитов, вентильный двигатель с самовозбуждением и вентильный двигатель с независимым возбуждением. Отмечены их основные преимущества и недостатки с точки зрения применения в качестве тягового электродвигателя. В работе указаны силы, действующие на транспортное средство, на основе которых составляется уравнение баланса тяги. Рассмотрены циклы вождения, используемые для электромобилей. Необходимо использовать современный цикл тест-драйва при расчете предельной механической характеристики тягового электродвигателя как части электрической трансмиссии автомобиля для определения некоторых эксплуатационных параметров и основных механических характеристик тягового электродвигателя

Keywords: Electric vehicle, electric drive, electric motors, mechatronics, diagnostics, information systems, electronic system. vehicle, automobile, driving cycle, traction balance, traction electric motor, mechanical characteristic.

Ключевые слова: Электромобиль, электропривод, электродвигатели, мехатроника, диагностика, информационные системы, электронная система. транспортное средство, автомобиль, цикл вождения, баланс тяги, тяговый электродвигатель, механическая характеристика.

1. Introduction

The drive control in an electric vehicle is a complex mechatronic system. This article discusses theoretical calculations of the parameters of electric vehicles. The goal is to develop universal calculations for the selection of electric drive parameters for electric vehicles, taking into account different climatic conditions of electric vehicle operation. Most of the above calculations will be similar for a car, and, at the same time, many electric cars are alterations of production cars, the following procedure will be described, which is also valid for calculating a car.

2. Research methodology

When making calculations for the choice of electric drives for electric vehicles, we resort to basic calculations for determining the forces acting on classic cars and methods for calculating them, but at the same time we take into account the absence of a classic traction drive and an internal combustion engine. Also, when carrying out road tests, it is necessary to take into account the absence of the addition of some changes in the regulation of the driving cycle time [[6, 8, 12]].

Calculations for the choice of an electric drive for electric vehicles and their justification are necessary for the correct and optimal use of energy and units in various operating and climatic conditions.

In order to start the calculations, you need to decide on the main forces acting on the electric car. In further calculations, we will define the following designations: F_d - traction force on the driving wheels; F_f - friction force in the transmission; F_rf - rolling friction force of wheels; F_r - force of resistance to rise; F_ar - air resistance force; F_fi - force of resistance to acceleration (force of inertia)[11].

For the electric car to start moving, the traction force on the driving wheels must exceed the sum of the remaining forces - the forces of resistance to movement[7].

Since the traction force on the drive wheels can be expressed in terms of the torque on the engine, taking into account the gear ratios of the main gear and the gearbox, as well as the power loss in the transmission and the radius of the wheels of the electric vehicle. You can write the following expression:

,                                (1) 

where: F_d - traction force on the driving wheels, N;

Η_f - coefficient of power loss in the transmission of an electric vehicle (in an automobile transmission for a passenger car η_tr = 0,9-0,92);

M_e - effective engine torque, N * m;

u_tr - gear ratio of the gearbox;

u_fd - gear ratio of the final drive;

r is the radius of the driving wheel, m.

To calculate the speed of movement of an electric vehicle, depending on the speed of the engine shaft, the following formula is applied:

,                                   (2)

where: ν is the speed of the electric vehicle, km / h;

3,6 - coefficient of speed conversion from m / s to km / h;

r is the radius of the driving wheel, m;

n is the rotational speed of the electric motor shaft, Hz;

u_tr - gear ratio of the gearbox;

u_fd - gear ratio of the final drive[8].

To calculate the rolling resistance force, it is required to take into account tire deformation, road deformation, tire friction force on the road and friction force in wheel bearings. Since the calculation of the influence of these values is rather complicated, in practice, the empirically obtained rolling friction coefficient is used, which, in the future, is involved in the calculation of the rolling resistance force [3, 9].

Table 1.

Table for determining the rolling friction coefficient [8]

Let us give a formula for calculating the rolling resistance force:

                                                   (3)

where: F_rf - rolling resistance force, N;

ƒ - rolling friction coefficient;

m is the mass of the electric vehicle, kg;

g - acceleration of gravity, m / s²;

α - slope angle of the road, degree.

When the electric vehicle (car) moves downhill, it is affected by the resistance force of the rise:

                                                (4)

where: Fr - force of resistance to rise (gradeability), N;

m is the mass of the electric vehicle, kg;

g - acceleration of gravity, m / s²;

α - slope angle of the road, degree.

When an electric vehicle (car) moves at speeds exceeding the speed of a pedestrian, the force of air resistance has a noticeable effect. To calculate the force of air resistance, use the following empirical formula:

                                         (5)

where: F_air - force of air resistance, N;

C_x – aerodynamic drag coefficient (streamlining coefficient), Н * с² / (m * kg). C_x is determined experimentally for each body;

ρ - air density (1,29 kg / m³ under normal conditions);

S - frontal area of an electric vehicle (car), m².

To calculate the acceleration characteristics of an electric vehicle (car), the force of resistance to acceleration (inertia force) should be taken into account. Moreover, it is necessary to take into account not only the inertia of the electric vehicle itself, but also the influence of the moment of inertia of the rotating masses inside the electric vehicle (rotor, gearbox, cardan, wheels). The following is the formula for calculating the force of resistance to acceleration[4, 14]:

                                                              (6)

where: F_in. - force of resistance to acceleration, N;

m is the mass of the electric vehicle, kg;

a - acceleration of an electric vehicle, m / s²;

σ_cr - coefficient of accounting for rotating masses.

The approximate coefficient of accounting for rotating masses σ_cr can be calculated by the formula[2]:

                                   (7)

It is necessary to describe the adhesion of the wheels to the road. However, this force is of little use in further calculations, so we will postpone it for now.

Now we already have an idea of the main forces acting on an electric vehicle (car). Knowledge of this theoretical issue will soon lead us to study the next issue - the issue of calculating the characteristics of an electric vehicle necessary for an informed choice of engine, battery, and controller[10] .

At the moment, we already have some theoretical basis for calculating the parameters of an electric vehicle (car): Forces acting on an electric vehicle (car). Based on the previous calculations, now we can calculate the parameters of the electric car engine. What has been said below will also apply to the calculations of the car engine. However, for internal combustion engines, the torque parameters change depending on the rotational speed, therefore, the calculation of the required parameters of a car engine is more complicated and will not be presented below, although the meaning of the calculations will remain in this case [2].

For the correct choice of an electric car engine, you need to know characteristics such as nominal and peak power, as well as the value of torque and shaft speed. The rated power is used to maintain a given constant speed. Peak power is required to accelerate an electric vehicle. Knowledge of the power characteristics of the engine will be required to calculate the parameters of the battery and the controller. Knowledge of the torque and speed of the motor shaft is required to determine the parameters of the gearbox and select the motor itself.

To calculate the minimum engine speed required for movement, we will use the formula already known to us:

                                 (8)

where: ν is the speed of the electric vehicle, km / h;

3,6 - coefficient of speed conversion from m / s to km / h;

r is the radius of the driving wheel, m;

n is the frequency of rotation of the motor shaft, Hz;

u_tr - gear ratio of a gearbox or electric motor reducer.

u_gt is the gear ratio of the main gear (when using a gearbox, it is taken to be equal to one).

From it we derive the required formula for calculating the engine speed: 

.                                 (9)

Since many motors mark the shaft speed not in hertz, but in revolutions per minute, to convert the values, the result obtained in Hz must be multiplied by 60 [5].

The formula for the balance of forces required to describe the uniformly accelerated movement of an electric vehicle (car):

                                                                            (10)

where: F_d - traction force on the driving wheels;

F_rf - rolling friction force of wheels;

F_r - force of resistance to rise;

F_ar - air resistance force;

F_fi - force of resistance to acceleration (force of inertia).

Now we substitute the already known formulas into the equation:

                                       (11)

where: η_tr - coefficient of power loss in the transmission of an electric vehicle (in an automobile transmission for a passenger car ηtr. = 0,9-0,92);

M_e - effective engine torque, N * m;

u_tr - gear ratio of the gearbox;

u_gt - gear ratio of the main transfer;

r is the radius of the driving wheel, m;

ƒ - rolling friction coefficient;

m is the mass of the electric vehicle, kg;

g - acceleration of gravity, m / s²;

α - slope angle of the road, °;

C_x - coefficient of air resistance (streamlining coefficient), Н * s² / (m * kg). C_x is determined experimentally for each body.

S - frontal area of an electric vehicle (car), m². S is the projection area of the body on a plane perpendicular to the longitudinal axis.

ρ is the air density;

ν is the estimated speed of the electric vehicle (car), km / h;

a is the required acceleration of the electric vehicle, m / s², calculated by dividing; values of the design speed for the time t required to accelerate to this speed;

σ_vr - coefficient of accounting for rotating masses.

The formula turned out to be great. Next, we add the missing elements of the resulting mosaic, make the formula gigantic and transform it into a form suitable for further coding:

.                   (12)

The above calculations are already enough to calculate the required engine parameters. We select an engine with slightly higher effective torque and shaft speed, which will allow further calculations based on a model with a real engine. As we remember from the days of school, in order to determine the power required to maintain a constant speed, it is necessary to know the value of the force that balances the action of the forces that impede movement and the value of the speed itself. Multiplying these parameters, we get the value of the rated power [3, 13].

Similarly, you can calculate the peak power consumed by the motor during acceleration (you need to take the average acceleration speed), only in this case, for the accuracy of the calculations, you need to calculate the average value of the air resistance force during the acceleration. 

This cycle consists of four EDC15 sections and one for driving outside the city. The required torque of the electric motor, both static and dynamic components are taken into account, is determined[1]:

                                     (13)

where M_tn - engine torque, Nm;

ƒ - rolling friction coefficient; m is the mass of the electric vehicle, kg;

g - acceleration of gravity, m / s²;

C_x - coefficient of air resistance (streamlining coefficient), N · s² / (m · kg), determined experimentally for each body and taken in the calculations equal to 0,36;

ρ - air density (1,29 kg / m³ under normal conditions);

S - frontal area electro mobile, m², S is the projection area of the body on a plane perpendicular to the longitudinal axis;

ν is the speed of the electric vehicle (car), km / h;

u_tr - gear ratio of the gearbox;

η_tr - coefficient of power loss in the transmission of an electric vehicle (in an automobile transmission for a passenger car η_fr = 0,9 ... 0,92).

3. Discussion of the results.

The mathematical model of the vehicle described in the previous chapter will be used to validate the peak parameters of power and torque for small class Electric Vehicle Wuling Macaron.

Table 2.

Technical specification of small class electric vehicle Wuling Macaron EV

The validation of the peak vehicle performance was validated in two experiments. The first experiment implied driving the car at a road with zero inclination. The idea was to establish a relationship between the vehicle speed and the electric drive power deliver and compare the results with the results of the mathematical model (Figure 1). The second experiment involved driving the vehicle at the constant speed of 60 km/h at roads with different inclination to validate the capacity of the vehicle to overcome the gradeability of city roads (Figure 2).

Figure 1. Dependence of Power required from the electric drive on the vehicle speed, with a zero inclination

Figure 2. Dependence of Power required from Electric drive on the road inclination (vehicle speed is taken to be equal to 60km/h)

Besides, the proposed model offers the estimation of how much more power needs to be provided by electric drive (with respect to the power require at a zero road grade) at different road inclinations.

Figure 3. Power to be added (%) due to road inclination (vehicle speed is equal to 60 km/h)

4. Conclusion

According to the proposed model for the sizing of the electric drive, the theoretical results and the experimental show a fairly good similitude, with an acceptable difference of 5-8%. As a matter of further studies, the model could be improved by adding the sub-model of the DC-DC controller, including its losses.

The development and research of electric drives for small class electric vehicles are an urgent task. Existing developments of electric vehicles require careful study, generalization of results, government support to expand research, development, and implementation in the domestic electric vehicle industry.

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