Научная статья на тему 'CONTROL OF PNEUMATIC ACTUATOR FOR AUTOMATED MECHANICAL TRANSMISSION DRY FRICTION CLUTCH BASE ON THE PULSE WIDTH MODULATION SIGNAL'

CONTROL OF PNEUMATIC ACTUATOR FOR AUTOMATED MECHANICAL TRANSMISSION DRY FRICTION CLUTCH BASE ON THE PULSE WIDTH MODULATION SIGNAL Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

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Ключевые слова
АВТОМАТИЗИРОВАННАЯ МЕХАНИЧЕСКАЯ ТРАНСМИССИЯ / АВТОМАТИЗИРОВАННАЯ МЕХАТРОННАЯ СИСТЕМА / СУХОЕ ФРИКЦИОННОЕ СЦЕПЛЕНИЕ / АВТОМАТИЗИРОВАННЫЙ ПРИВОД / ПНЕВМАТИЧЕСКИЙ ИСПОЛНИТЕЛЬНЫЙ МЕХАНИЗМ / ПРОПОРЦИОНАЛЬНЫЙ ЭЛЕКТРОМАГНИТНЫЙ КЛАПАН / ШИРОТНО-ИМПУЛЬСНАЯ МОДУЛЯЦИЯ / AUTOMATED MECHANICAL TRANSMISSION / AUTOMATED MECHATRONIC SYSTEM / DRY FRICTION CLUTCH / AUTOMATED DRIVE / PNEUMATIC ACTUATOR / PROPORTIONAL SOLENOID VALVE / PWM

Аннотация научной статьи по электротехнике, электронной технике, информационным технологиям, автор научной работы — Kharytonchyk S. V., Kusyak V. A., Le Nghia Van

To ensure quality of dry friction clutch engagement in automated mechanical transmission during vehicle starting-up and maneuvering the control range of clutch actuator has to be maximum wide. It depends on the consistency of the clutch actuator geometric parameters with the electrical characteristics of the used solenoid valves, the output stage of the controller and the PWM control signal frequency. In addition to precision electronic control the driver must be able to “manually” operate the dry friction clutch in emergency. That is why friction clutch must have two independent control circuits. The original automated drive with a duplicate pneumohydraulic circuit for the friction clutch is presented in the paper, as well as the research results of the PWM frequency influence on operating range of the clutch pneumatic actuator. The research was based on the analysis of semi-natural experiment for assessing the functional performance of the designed automated mechatronic control system for the truck mechanical transmission. Ecomat R360 controllers were used as a hardware base of the test bench information control system. The developed software for the controller with one-parameter feedback on the clutch release lever movement allows to provide the PWM signal of varying duty ratio to the proportional solenoid valve of the automated drive. A graphical representation of the research results was performed with visualization possibilities of CoDeSys V2.3. During the semi-natural experiment, the polynomial dependence between variation of the clutch actuator control range and the generated PWM signal frequency in the range up to 400 Hz was revealed as well as practical recommendations on the choice of the optimum PWM signal frequency are also given in activity. The research results can be used in an adaptive control algorithm for automated mechanical transmission of trucks and road trains to ensure precise control of the clutch actuator in the starting-up and maneuvering processes.

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Текст научной работы на тему «CONTROL OF PNEUMATIC ACTUATOR FOR AUTOMATED MECHANICAL TRANSMISSION DRY FRICTION CLUTCH BASE ON THE PULSE WIDTH MODULATION SIGNAL»

ТРАНСПОРТ TRANSPORT

https://doi.org/10.21122/2227-1031-2021-20-1-26-32 UDC 629.113.585

Control of Pneumatic Actuator for Automated Mechanical Transmission Dry Friction Clutch Base on the Pulse Width Modulation Signal

S. V. Kharytonchyk1), V. A. Kusyak1), Le Van Nghia2)

1)Belarusian National Technical University (Minsk, Republic of Belarus),

2)Hanoi University of Science and Technology (Hanoi, Socialist Republic of Vietnam)

© Белорусский национальный технический университет, 2021 Belarusian National Technical University, 2021

Abstract. To ensure quality of dry friction clutch engagement in automated mechanical transmission during vehicle starting-up and maneuvering the control range of clutch actuator has to be maximum wide. It depends on the consistency of the clutch actuator geometric parameters with the electrical characteristics of the used solenoid valves, the output stage of the controller and the PWM control signal frequency. In addition to precision electronic control the driver must be able to "manually" operate the dry friction clutch in emergency. That is why friction clutch must have two independent control circuits. The original automated drive with a duplicate pneumohydraulic circuit for the friction clutch is presented in the paper, as well as the research results of the PWM frequency influence on operating range of the clutch pneumatic actuator. The research was based on the analysis of semi-natural experiment for assessing the functional performance of the designed automated mechatronic control system for the truck mechanical transmission. Ecomat R360 controllers were used as a hardware base of the test bench information control system. The developed software for the controller with one-parameter feedback on the clutch release lever movement allows to provide the PWM signal of varying duty ratio to the proportional solenoid valve of the automated drive. A graphical representation of the research results was performed with visualization possibilities of CoDeSys V2.3. During the semi-natural experiment, the polynomial dependence between variation of the clutch actuator control range and the generated PWM signal frequency in the range up to 400 Hz was revealed as well as practical recommendations on the choice of the optimum PWM signal frequency are also given in activity. The research results can be used in an adaptive control algorithm for automated mechanical transmission of trucks and road trains to ensure precise control of the clutch actuator in the starting-up and maneuvering processes.

Keywords: automated mechanical transmission, automated mechatronic system, dry friction clutch, automated drive, pneumatic actuator, proportional solenoid valve, PWM

For citation: Kharytonchyk S. V., Kusyak V. A., Le Van Nghia (2021) Control of Pneumatic Actuator for Automated Mechanical Transmission Dry Friction Clutch Base on the Pulse Width Modulation Signal. Science and Technique. 20 (1), 26-32. https://doi.org/10.21122/2227-1031-2021-20-1-26-32

Управление пневматическим исполнительным механизмом

сухого фрикционного сцепления автоматизированной механической

трансмиссии на основе модулированного широтно-импульсного сигнала

Докт. техн. наук С. В. Харитончик1), канд. техн. наук, доц. В. А. Кусяк1), канд. техн. наук Ле Ван Нгиа2)

^Белорусский национальный технический университет (Минск, Республика Беларусь), 2)Ханойский университет науки и технологий (Ханой, Социалистическая Республика Вьетнам)

Реферат. Для обеспечения качества включения сухого фрикционного сцепления в автоматизированной механической трансмиссии в процессе трогания транспортного средства с места и маневрирования диапазон управления

Адрес для переписки

Кусяк Виктор Анатольевич

Белорусский национальный технический университет ул. Я. Коласа, 12,

220013, г. Минск, Республика Беларусь Тел.: +375 17 296-65-14 [email protected]

Address for correspondence

Kusyak Victor A.

Belаrusian National Technical University 12, Ya. Kolasa str., 220013, Minsk, Republic of Belarus Tel.: +375 17 296-65-14 [email protected]

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итехника. Т. 20, № 1 (2021)

исполнительным механизмом сцепления должен быть максимально широким. Ширина диапазона зависит от согласованности геометрических параметров исполнительного механизма сцепления с электрическими характеристиками используемых электромагнитных клапанов, выходным каскадом контроллера и частотой управляющего ШИМ-сигнала. Помимо прецизионного электронного управления водитель должен иметь возможность «вручную» управлять сухим фрикционным сцеплением в аварийной ситуации, вследствие чего последнее должно иметь два независимых контура управления. В статье представлены оригинальный автоматизированный привод фрикционного сцепления с дублирующим пневмогидравлическим контуром, а также результаты исследования влияния частоты ШИМ-сигнала на рабочий диапазон управления пневматическим исполнительным механизмом сцепления. Исследования базировались на анализе результатов полунатурного эксперимента по оценке функциональной работоспособности спроектированной автоматизированной мехатронной системы управления механической трансмиссией грузового автомобиля. В качестве аппаратной основы информационной системы управления испытательным комплексом использовались контроллеры Есоша! Я360. Разработанное программное обеспечение контроллеров с однопарамет-рической обратной связью по перемещению рычага выключения сцепления позволяет подавать ШИМ-сигнал переменной скважности на пропорциональный электромагнитный клапан автоматизированного привода. Графическое представление результатов исследований производилось с помощью средств визуализации СоБеВу8 У2.3. В ходе полунатурного эксперимента выявлена полиномиальная зависимость между изменением диапазона управления исполнительным механизмом сцепления и частотой генерируемого ШИМ-сигнала в интервале до 400 Гц, а также даны практические рекомендации по выбору оптимальной частоты модулированного широтно-импульсного сигнала. Результаты исследований могут быть использованы в адаптивном алгоритме управления автоматизированной механической трансмиссией грузовых автомобилей и автопоездов для обеспечения прецизионного управления исполнительным механизмом сцепления в процессах трогания с места и маневрирования.

Ключевые слова: автоматизированная механическая трансмиссия, автоматизированная мехатронная система, сухое фрикционное сцепление, автоматизированный привод, пневматический исполнительный механизм, пропорциональный электромагнитный клапан, широтно-импульсная модуляция

Для цитирования: Харитончик, С. В. Управление пневматическим исполнительным механизмом сухого фрикционного сцепления автоматизированной механической трансмиссии на основе модулированного широтно-импуль-сного сигнала / С. В. Харитончик, В. А. Кусяк, Ле Ван Нгиа // Наука и техника. 2021. Т. 20, № 1. С. 26-32. https://doi.org/10.21122/2227-1031-2021-20-1-26-32

Overview of transmission mechatronic systems showed that automated drive of dry friction clutch has, as a rule, an additional duplicate control circuit [1-5]. The electronic components of mechatronic systems, despite their relatively high reliability, characterized by intermittent faults and suddenness of failures occurrence. Additionally, working medium may leak from the actuator circuit that reduces or eliminates the control system operability and vehicle mobility.

Considering the above, as well as using the experience of foreign companies, specialists of the BNTU Automobile Department have developed an original duplex drive [6] of dry friction clutch, which is integrated into powertrain control mecha-tronic system (Fig. 1) and has two independent control loops.

Automated drive, as the primary circuit, includes a pneumatic actuator 14 and the proportional solenoid valve 13 installed on the gearbox (Fig. 1). Duplicate hydraulic drive consists of a pedal 8 with a hydraulic cylinder 7, pipeline and pneumo-hydraulic booster 6 (Fig. 1, 2). Clutch release node is a lever mechanism, which consists of two levers 16 and 17 mounted on the bush of clutch fork shaft. One of the levers is connected

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итехника. Т. 20, № 1 (2021)

with a power actuator of the clutch automated drive. Another one comes into the duplicate hydraulic drive.

Calculation of the actuator active diameter is based on the maximum clutch disengagement force, the drive ratio and system's nominal pressure. When designing automated dry clutch for serial production, the actuator active diameter is tended to choose from a standard series of pneumatic cylinders. As known well about actuator on cylindrical type, the dead zone and friction between the piston and the cylinder surface are changed during operation of the vehicle, that influence on the control quality of the clutch transition process. At the test stand of the BNTU, a brake chamber (type 16) with diaphragm type was used as a clutch actuator to improving the control quality by reducing the dead zone and friction.

At the clutch engagement in the automatic mode, for example during starting or maneuvering, in order to control proportional solenoid valve 13, the strategy of the Direct Semi-Active Control [7] is offered to use. The meaning of the strategy is applied to the solenoid coil PWM signal with a subsequent change of its duty ratio according to a predetermined algorithm.

Fig. 1. Schematic diagram of powertrain control mechatronic system with clutch duplex drive: 1 - brake pedal; 2 - mode selector; 3 - position sensor; 4 - accelerator pedal; 5 - display; 6 - pneumo-hydraulic booster; 7 - hydraulic cylinder; 8 - clutch pedal; 9 - air supply; 10 - gearbox actuator; 11 - contact sensors; 12 - speed sensors; 13, 21 - proportional solenoid valves; 14 - clutch actuator; 15, 22 - displacement sensors; 16, 17 - clutch release levers; 18 - splitter actuator; 19 - auxiliary brake valve; 20 - pressure sensors; 23 - engine actuator; 24 - pneumatic cylinder for engine turn off; 25 - engine brake actuator

-I-E-

-I

From the air receiver

From proportional solenoid valve

To pneumo-hydraulic _

booster From hydraulic

cylinder

Fig. 2. Duplex drive of dry friction clutch: 6 - pneumo-hydraulic booster; 7 - hydraulic cylinder; - clutch pedal with return spring 26; 14 - clutch actuator; 16, 17 - clutch release levers; 27 - expansion tank

At all transient processes electronic system has to provide such a clutch engagement tempo that would to avoid dynamic overloads in the transmission on the one hand and not to exceed the criterial limits for energy loading of friction clutch, evaluated by specific work and power of slipping [8], on the other.

If the mode selector 2 is subsequently set by the driver (Fig. 1) to the "D" position (drive) and

the accelerator pedal is pressed, the transmission ECU sends a signal to the clutch control proportional solenoid valve 13 and in parallel by CAN the information about the current position mode selector and accelerator pedal 4 is transmitted to the engine ECU. As soon as the clutch is disengaged, the transmission ECU generates sequential control signals to the solenoid valve block

Наука

итехника. Т. 20, № 1 (2021)

8

of gearbox and splitter actuators for the first selecting the rod, and then enabling the optimum gear step by actual driving conditions as: actual vehicle speed and mass, the rotation speeds of the engine crankshaft and driving wheels, the number of the previous gear steps. After that, the signal on the solenoid valve 13 is modified and the clutch is engaged on the set rate. Depending on the degree to which the clutch is engaged, the fuel supply gradually increases in proportion to the position of the accelerator pedal set by the driver in the initial phase.

AMT start-up adaptive algorithm [9] in the automatic mode of the power unit is the following sequence of operations: transmission mode selector control - full clutch disengagement - main and additional gearbox control - engine control - full clutch engagement.

After moving the mode selector 2 to the "D" (drive) position (Fig. 1), the driver presses on the accelerator pedal 4 for vehicle starting-up. The proportionality between the pedal rotation angle (by position sensor 3) and the movement of the fuel injection pump regulator lever (by displacement sensor 22) is provided by the engine ECU by pulse-width modulation (PWM) signal to a proportional solenoid valve 21 with using feedback on the movement of the fuel injection pump regulator lever and the engine crankshaft rotation frequency [10]. The required rate of vehicle star-t-up is determined by the "gas" pedal press speed, on the basis of which the transmission ECU calculates the pro-required clutch engagement rate and the enable gear number. In parallel, while receiving signals from the mode selector limit switch, the engine speed sensor, the fuel supply position sensor and the accelerator pedal position sensor, the transmission ECU generates a control signal to open the proportional solenoid valve 13. The valve is activated and the compressed air comes from the receiver of the supply part 9 into the clutch actuator 14 (pneumatic chamber), as the result of which the clutch is disengaged. After working out the signal from the clutch lever sensor 15, the transmission ECU sequentially generates signals to the solenoid valve block of the gearbox actuator, as well as the air-control valve for shifting the splitter. After shifting on the required gear (the respective gearshift limit switches are closed), the transmission ECU sends a PWM-signal to the proportional solenoid valve 13, increasing the duty cycle of the signal by a certain amount depending on the "gas" pedal press speed. The compressed air from the clutch actuator - pneumatic chamber 14

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итехника. Т. 20, № 1 (2021)

through the proportional solenoid valve 13 is gradually discharged into the atmosphere, providing the required clutch engagement rate. To avoid "overloading" of the clutch, feedback is introduced into the control circuit according to the increment by time of difference between angular velocities of the driving and driven clutch parts (dAa/dt). The feedback is also entered into the engine control circuit to avoid ICE stalling by the reduction in the crankshaft angular velocity oh while the clutch is engaging.

Control algorithm adaptation occurs when the mechanical and (or) electrical characteristics of the mechatronic system components vary, as well as the driving behavior or the vehicle weight state change.

The functionality of the developed AMT mecha-tronic system (Fig. 1) and the operational integrity of the vehicle start-up adaptive algorithm are confirmed by the result of a semi-real experiment on test complex BNTU.

Clearly, that the control quality of dry friction clutch will depend on the width of the PWM signal range. The range value is influenced by the consistency of the actuator geometrical parameters, solenoid valve operating characteristics and the controller output stage. At constant parameters of the last dominant influence on control range has generated the PWM signal frequency.

For debugging powertrain automated mecha-tronic system a special test bench was created in the laboratory of the BNTU Automobile Department. The test bench consists of diesel engine, dry friction clutch, mechanical gearbox, inertial mass and a load device. Ecomat R360 controllers of CR2500 series were used as a hardware basis of the designed control system.

To investigate the influence of PWM signal frequency to control range of clutch actuator, a special software has developed. It allows to initialize the signal generator and to provide the PWM signal of varying duty ratio (but a certain frequency) in automatic mode to the proportional solenoid valve VEP 3121-1 that controls the clutch actuator. During the experiments, PWM frequency was varied from 150 to 250 Hz in steps of 10 Hz. The clutch lever position, fixed by the potentiometric sensor MY-615A of angular displacements, was used as a feedback. A graphical representation of the semi-natural experiment results was performed with visualization possibilities of CoDeSys V2.3. Some records of engagement/disengagement of dry friction clutch are shown at Fig. 3.

Jj CoDeSys - clutch_calibr.pr

I Файл Правка Проект Вставить Дополнения Онлайн Окно Справка

__ Ресурсы B-Q Глобальные

1.....ф.SYSTEM

□ библиотека IFM_CF!2500_V040002.LIB 1 Ш-О библиотека Util.lib 6.11.0715:39:24: глоб ^ Бортжурнал (Щ Конфигурация ПЛК Конфигурация задач (Ш Конфигурация тревог |JjJ Менеджер библиотек С^ Менеджер просмотра ^ Настройки целевой платформы fj-j ПЛК-Браузер

Рабочая область (Щ Цифровая трассировка

В FOU]' " Типы...|р|Еизуа..|^1Ресур..р

21000 ins 24000 ms 27000 ms 30000 ms 33000 ms 36000 ms ЗЭ000 ms 42000 ms 45000 ms 48000 ms

Tracing

current configuration T

Pen 0_

|chastota_vracheniya.w

| с h a stota_vra с h e n iya. О UTP UTj Pen 2

|chastota_vrachemya.NOR.Y Pen 3

| Статус: Запись трассировки окончена ОНЛАЙН: Fls232 |ЭМУЛ. |ЗАПУЩЕНО [То" |ФИКС. [ЗАМ" ¡ПРОСМОТР

Fig. 3. Oscillogram of clutch engagement/disengagement process at PWM frequency of 150 Hz: first screen - digitizing the signal from the clutch lever position sensor, bits; second screen - current to the coils of the solenoid valve, mA; third screen - PWM reload value, bit

Pen 1

Pen 4

Pen 5

Pen 6

Pen 7

As shows the results of experiments the PWM signal range was the greatest at a frequency of 150 Hz. Its value was 40.7 %. There is a steady trend towards a narrowing of the control range with frequency increasing. Already at 200 Hz control range decreased by 26.04 % and was 30.1 %. At 250 Hz the range decreased by 34.15 % and was 26.8 %. The above described control range dependence of the PWM frequency is illustrated in Fig. 4.

о

PWM, % 20

40

60

80

100

65535 60000

PWM

40000

20000

/// V/ 1,7% V/y Z/ v?

VY /// y3i v% V/ 7X .8%

/// V/ /// У/ V' V/ // >26

130

150 170 190 210 230 v, Hz 270

Fig. 4. Control range dependence of the PWM signal frequency

During the vehicle operation, the friction plates of the clutch are wore and resulting of which is a change in the control range of actuator. To improve the quality of the clutch transition process when starting-up vehicle, adaptation of the control

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algorithm is required. Adaptation to control range of clutch actuator can be implemented at the software level by the dependence of the control range variation on the PWM signal frequency in an analytical form. The dependence of the control range variation on the frequency of the control PWM signal can be expressed by an approximating polynomial whose coefficients are obtained by processing experimental data using the Polyfit function [11, p. 379] in the МatLab package.

Justification of the polynomial degree choice was carried out on the basis of the smallest modules criterion MAPE (Mean absolute percentage error) [12, p. 1104, (1)], which makes a possible to estimate the approximation error by the formula

1 h £ 1 h У

MAPE =1Y^ .100% =1Y^-

h^

-У1

h j y j

У1

•100%, (1)

where eJ - prediction step error; yJ, yj - actual

and predicted trend point value (PWM control range, %); h - number of points.

The errors calculation results of the approximating by polynomial on various degree are presented in Tab. 1.

Наука

итехника. Т. 20, № 1 (2021)

0

Table 1

The errors of the approximating polynomial

Coefficient Degree of approximating polynomial

I II III IV V

b0 59.91281818 118.1773636 142.5556 177.362515 161.286182

b1 -0.14097090 -0.73855599 -1.1155831 -1.83458 -1.4192847

b2 - -0.00149396 0.003407 0.0089159 0.00466

b3 - - -3.19E-06 -2.17E-05 -1.22E-07

b4 - - - 2.32E-08 -3.13E-08

b5 - - - - 5.45E-11

Criterion MAPE, % 3.630 0.224 0.088 1.328 0.117

For a given approximation error less than 0.1 %, the dependence of the control range variation on the frequency of the control PWM signal is

described by a 3nd order polynomial as in formula

Aw = 142.56 - 1.116V + + 0.0034V2 -3.19E - 06v3,

(2)

where DPWM - control rate of clutch actuator, %; v - frequency of control PWM signal, Hz.

The variation of PWM frequency does not influence on the current range. During the clutch lever movement the magnitude of the current to the solenoid valve coils varies from 0.272 to 0.614 A (Fig. 3), i. e. operating current range is 0.342 A. Taking into account operating characteristic of the used solenoid valve and its zone of stable operation it is 50.3 %, which is a satisfactory result. Clutch actuator hysteresis is shown in Fig. 5.

1400| 780|

0

16001

878| 0

1201

40 9001

0

FALSE!

FALSE; 120

0

true;

Clutch actuator hysteresis should be integrated in AMT adaptive control algorithm of vehicle star-ting-up process. The semi-real experience results of start-up process when debugging of AMT adaptive control algorithm with PWM frequency 150 Hz on test complex BNTU are shown in Fig. 6. 130 t, bit 110 100 90

80 70

0.2 0.3 0.4 0.5 I, A 0.7

30 40 50 PWM, % 80

Fig. 5. Clutch actuator hysteresis: I - current to the solenoid valve, A; x - digitizing the signal from the clutch lever position sensor, bit

Tracing

current configuration *

Trigger

_ Pen 0_

I.Starting.Eng_nSpd Pen 1

I.Freq.Shaft_Out_nSpd_W

Pen 3_

I.PWM_current.ACTUAL_CURRENT 1 Pen 4

I.ID32_BINARY_IN6 Pen 5

J.PWM_Clutch.VALUE

Pen7_

I.ID1 BINARY OUT2

current configuration: current trace configuration

2500 ms 3750 ms 5000 ms 6250 ms 7500 ms 8750 ms 10000 ms 11250 ms 12500 ms

Fig. 6. Oscillograms of start-up process on test stand BNTU: 1, 2 - engine crankshaft speed œ1 and driven cluth part speed w2, rev/min; 3 - movement of the clutch lever, bit; 4 - current on clutch control valve, mA; 5 - movement of the splitter shift lever, bit; 6 - PWM, bit; 7 - sign stage «1» straight line of splitter solenoid control valve

■ HayKa

uTexHMka. T. 20, № 1 (2021)

I.ID32_ANALOG_IN3 Pen 6

CONCLUSION

The research has shown that the PWM frequency has a significant influence on the actuator control range: change in frequency of 50 Hz results in a change of the PWM control range for about 4-10 % (Fig. 4). However, at too high or low frequencies valve coils heating or periodic instability of the whole system is possible. The last one expressed in a substantial increment of clutch lever displacement with a slight change of the PWM signal. Therefore, the choice of the optimum frequency must be done on the basis of the specific features of the designed system.

REFERENCES

1. Brugger F., Moser F., Ruhl T. (1988) Clutch Operating Cylinder for a Pressure-Medium Operated Clutch: Pat. USA No 4745999.

2. Bates J. (1999) Actuator System for Vehicle Automated Clutches with Electric Motor Actuator and Pressurized Fluid Override: Pat. USA No 5934432.

3. Inoue A. (2003) Clutch Operating System and a Hydraulic Mechanism Used in the Same: Pat. USA No 6607060 B2.

4. Leigh-Monstevens K. V., Branum L. P. (1991) Dual Mode Motor Vehicle Clutch Control System: Pat. USA No 5002166.

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Received: 17.11.2020 Accepted: 15.01.2021 Published online: 29.01.2021

Наука

итехника. Т. 20, № 1 (2021)

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