В данной работе построена математическая модель движения автомобиля при трогании с места и выполнена ее реализация в Simulink. Системы обыкновенных дифференциальных уравнений, которые описывают модель, оказываются жесткими. Такие системы требуют использования специальных численных методов. В связи с этим особое внимание уделено выбору метода для решения дифференциальных уравнений движения. В разделе «Модель трогания автомобиля с места» получены системы дифференциальных уравнений, описывающих модель. В разделе «Реализация в Simulink» приведено описание реализации модели в виде программы, созданной средствами Simulink и StateFlow. В разделе «Ошибка! Источник ссылки не найден.. Жесткие системы. Алгоритм Zero-crossing» рассматриваются и сравниваются имеющиеся в Simulink солверы, после чего дается обоснованное предпочтение одному из них. Так как в данной работе решаются системы дифференциальных уравнений с переключениями, то обнаружение правильного момента переключения является очень ответственным. За это отвечает алгоритм Zero-Crossing, реализованный в Simulink. В этом же разделе приведена демонстрация необходимости использования данного алгоритма при решении рассматриваемых систем с переключениями. В последнем разделе приведены результаты моделирования реальных сценариев работы педалями газа и сцепления. Модель трогания автомобиля с места Задача моделирования процесса трогания автомобиля с места является многоструктурной. В различные периоды времени в зависимости от того движется автомобиль или стоит, от состояния сцепления и величины момента двигателя характер нагружения трансмиссии автомобиля описывается [5-7] различными дифференциальными уравнениями движения (см. рис. 1). В начальный момент времени автомобиль стоит на месте. От двигателя на маховик подается крутящий момент M e , который обеспечивает его вращение. Сцепление выключено. Расчетная схема приведена на рисунке 1а. При постепенном отпускании педали сцепления маховик и ведомый диск сцепления приводятся в соприкосновение. Момент от двигателя передается трансмиссии, приводя во вращение ведомый диск сцепления. Элементы трансмиссии закручиваются на некоторый угол. Когда этот угол достигает критического значения, а именно, упругий момент на колесах превышает момент сопротивления покоя M c , автомобиль трогается с места. Система переходит в следующее состояние, когда автомобиль уже имеет ненулевую скорость, но маховик и ведомый диск сцепления вращаются с разными угловыми скоростями, т.е. имеет место проскальзыва-Рис. 1. Расчетная динамическая схема При исследовании процесса трогания автомобиля с места должен задаваться режим работы двигателя. Крутящий момент двигателя зависит от положения органа подачи то
Modern high-torque low-speed internal combustion engines (ICEs) generate torsional vibrations close in disturbance frequency to gearboxes natural oscillation frequencies. Effective absorption of such oscillations requires a new torsional vibration damper between the internal combustion engine and gearbox design, which is implemented in the form of a dual-mass flywheel (DMF). One of the main reasons for DMF failure is its spring components destruction. The article develops mathematical and simulation (in MATLAB Simulink environment) model of a car with DMF in the period of starting, which takes into account the dependence of torque and power of the internal combustion engine on the number of the crankshaft revolutions and uneven rotation, car inertial and stiffness parameters, road resistance. It is established that when the car starts in first gear, the maximum load on spring components of DMF and transmission occurs at the initial moment of clutch engagement and exceeds the maximum effective torque of the internal combustion engine 1.6 times, has a pronounced oscillatory character and stabilizes as the car accelerates. With smooth acceleration of a car, when torque of internal combustion engine reaches, but does not exceed its maximum value of 250 N‧m, elastic moment in transmission components is stabilized at 230 N‧m. During intensive acceleration and transition through the extremum on torque curve of internal combustion engine on number of crankshaft revolution, the maximum DMF spring components and transmission load initially doesn’t change significantly, but reduces the duration of oscillatory processes and elastic moment of 160 N·m after attenuation of oscillations. A similar nature of stress changes is observed in the elastic links of DMF, which eventually leads to their fatigue failure and DMF failure. To increase a DMF service life, it is advisable to accelerate a car when moving intensively, bringing a number of revolutions to a value that is located at the extreme of torque of internal combustion engine on its performance characteristic, followed by switching to the next gear.
Automobile manufacturers, when designing new cars, are increasingly faced with the need to reduce the weight of components in order to achieve the required level of fuel consumption and environmental standards. As a result, internal combustion engines (ICEs) with a small number of cylinders are designed and manufactured, which allows to achieve an increase in output power due to increased pressure in the cylinder and more efficient fuel combustion. As a result of this, torsional vibrations occur on the crankshaft, which are transmitted and negatively affect the transmission, causing it to fail prematurely. The damping properties of dual-mass flywheel (DMF) in a straight line depend on their structure and design parameters. All modern DMF contain a certain amount of thick lubricant, which in one way or another improves its characteristics. But in addition to parts, flywheels that constantly work in an environment with lubricant, there are also elements between which dry friction occurs, which also affects the damping characteristics of the flywheel. Therefore, it can be assumed that its presence affects the elastic-damping properties of the DMF. The purpose of the work is to develop simulation models and study the effect of friction between DMF elements on oscillatory processes in the car transmission and to develop recommendations for reducing the load on DMF elements and transmission links. The effect of dry and viscous friction between the elements of a DMF on the damping of oscillations in the links of its elastic-damping system and the drive links of the car was studied. It is shown that an increase in the coefficient of dry friction between DMF elements from 0 to 0.3 does not provide a noticeable damping of oscillations in the drive links and tension in the DMF springs. The coefficient of viscous friction between the links of the DMF has a significant influence on the amount of tension in the springs of the DMF. To increase the resource of the DMF, it is advisable to install separators made of polymer material between the elastic links with a small coefficient of friction between it and the steel body of the DMF.
Driving systems for hybrid cars and electric vehicles equipped with electric motors have different structures and characteristics. In the vast majority of hybrids, depending on the driving mode, the torque on the wheels of the car can be generated separately by both the internal combustion engine and the electric motor, or by working together. Based on the research results it is established that at the moment of starting the electric motor, the torque in the transmission sections steeply increases to 17 N•m, and for about 1 s decreases to the value of 7 N•m. In the period from 4 to 5.5 s, the torque increases to 14 N•m, which is explained by the overcoming of the inertial load during acceleration of the driven weight, and rapidly decreases to the value of 4 N•m, which corresponds to the consolidated moment of resistance to movement. The electromagnetic moment of electric motor thus also increases steeply in the initial stage of starting the motor up to 66 N•m and after 1 s decreases to the value of 15 N•m. After 5.5 s there is an increase in the moment to the value of 66 N•m and after 5.8 s it stabilizes and ranges from -6 to 22 N•m. In turn, the calculations for an electromechanical transmission equipped with a resilient-elastic coupling showed that the maximum torque in its sections Т2 during the start-up period decreased to 9 N•m, and the acceleration time to a steady turning velocity of the driven weight slightly increased to 6.8 s. The torque that occurs in the transmission sections during acceleration to a steady velocity does not exceed 13 N•m. The torque in the resilient-elastic coupling sections during the start-up period does not exceed 10 N•m, and its value, upon reaching the steady motion of the driven weight, is slightly less than 5 N•m. Peak torque in the resilient-elastic coupling sections Т1 reaches 22 N•m, while in the transmission Т2 it is 13 N•m, which confirms the efficiency of resilient-elastic coupling operation. Thus, the use of resilient-elastic coupling in an electromechanical transmission can reduce the amplitude of the torque in the drive sections during the start-up period by about 1.9 times, as compared to the amplitude of the torque without resilient-elastic coupling, and reduce the peak torque of the transmission sections by 1.7 times. Keywords: asynchronous electric motor, dynamic model, mathematical model, simulation model, torque.
Introduction: The movement smoothness of transport and handling machines (THM) (excavators, cranes, road maintenance equipment, etc.) on a vehicle chassis significantly affects their durability as a result of the large weight of equipment and uneven load distribution along the axes of the base chassis, which causes heavy dynamic loads when moving along roads with imperfect pavement. However, THM often have to move along those very roads. Purpose of the study: We aimed to increase the movement smoothness of THM on a vehicle chassis by using a shock absorber of new design as the main vehicle undercarriage suspension element. Methods: The hydropneumatic shock absorber is considered the most common. The principle of its operation is based on hydraulic resistance that occurs when the piston with the rod move in a space filled with oil, while the gas in the closed part is compacted, compensating for changes in the internal volume. Most often, the main disadvantage related to the operation of hydropneumatic shock absorbers (HPSA) is the probability of bottoming when hitting a barrier (obstacle), which results in dynamic loads reducing the service life of the vehicle and the parts of the shock absorber. Results: The paper describes a new shock absorber design ruling out bottoming, provides a mathematical model of its elastic response, and presents the results of modeling in Mathcad, confirming the operability of the device.
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