In this paper, a mathematical simulation model of an electric vehicle traction battery has been developed, in which the battery was studied during the dynamic modes of its charge and discharge for heavy electric vehicles in various driving conditions—the conditions of the urban cycle and movement outside the city. The state of a lithium-ion battery is modeled based on operational factors, including changes in battery temperature. The simulation results will be useful for the implementation of real-time systems that take into account the processes of changing the characteristics of traction batteries. The developed mathematical model can be used in battery management systems to monitor the state of charge and battery degradation using the assessment of the state of charge (SOC) and the state of health (SOH). This is especially important when designing and operating a smart battery management system (BMS) in virtually any application of lithium-ion batteries, providing information on how long the device will run before it needs to be charged (SOC value) and when the battery should be replaced due to loss of battery capacity (SOH value). Based on the battery equivalent circuit and the system of equations, a simulation model was created to calculate the electrical and thermal characteristics. The equivalent circuit includes active and reactive elements, each of which imitates the physicochemical parameter of the battery under study or the structural element of the electrochemical battery. The input signals of the mathematical model are the current and ambient temperatures obtained during the tests of the electric vehicle, and the output signals are voltage, electrolyte temperature and degree of charge. The resulting equations make it possible to assign values of internal resistance to a certain temperature value and a certain value of the degree of charge. As a result of simulation modeling, the dependence of battery heating at various ambient temperatures was determined.
This article proposes a calculation method for mechanical (electromagnetic) forces arising in an electromechanical energy converter acting on current circuits in a magnetic field, or on capacitor plates in an electric one. Transformations were performed on the basis of the principle of possible displacements involving the apparatus of partial derivatives. It was found that the power converted into mechanical power is partially spent on changing the energy of the electromagnetic field, and the remaining power, determined by the co-energy, is converted into mechanical power. Expressions for the mechanical (electromagnetic) forces were obtained based on the power balance. The reliability of the obtained results was compared with the known results. Of these, one can observe the well-known 50/50 principle, which states that only part of the power associated with the movement of the circuits is converted into mechanical power, while the rest is intended for changing the energy of the magnetic field.
Currently, the estimated range of an electric vehicle is a variable value. The assessment of this power reserve is possible by various methods, and the results of the assessment by these methods will be quite different. Thus, building a model based on these cycles is an extremely important task for manufacturers of electric vehicles. In this paper, a simulation model was developed to determine the range of an electric vehicle by cycles of movement. A mathematical model was created to study the power reserve of an electric vehicle, taking into account four driving cycles, in which the lengths of cycles and the forces acting on the electric vehicle are determined; the calculation of the forces of resistance to movement was carried out taking into account the efficiency of the electric motor; thus, the energy consumption of an electric vehicle is determined. The modeling of the study of motion cycles on the presented model was carried out. The mathematical evaluation of battery life was based on simulation results. Simulation modeling of an electric vehicle in the MATLAB Simulink software environment was performed. An assessment of the power reserve of the developed electric vehicle was completed. The power reserve was estimated using the four most common driving cycles—NEDC, WLTC, JC08, US06. Studies have shown that the highest speed of the presented US06 cycle provides the shortest range of an electric vehicle. The JC08 and NEDC cycles have similar developed speeds in urban conditions, while in NEDC there is a phase of out-of-town traffic; therefore, due to the higher speed, the electric vehicle covers a greater distance in equal time compared to JC08. At the same time, the NEDC cycle is the least dynamic and the acceleration values do not exceed 1 m/s2. Low dynamics allow for a longer range of an electric vehicle; however, the actual urban operation of an electric vehicle requires more dynamics. The cycles of movement presented in the article provide a sufficient variety and variability of the load of an electric vehicle and its battery over a wide range, which made it possible to conduct effective studies of the energy consumed, taking into account the recovery of electricity to the battery in a wide range of loads. It was determined that frequent braking, taking into account operation including in urban traffic, provides a significant return of electricity to the battery.
A mathematical model of a coating which grows during magnetron sputtering has been formulated and investigated. To estimate the average mechanical stresses, both the thermal and the chemical diffusion contribution are taken into account. It has been shown that the kinetics of the reaction on the surface is no less important in the evolution of stresses than the relationship between the mechanical properties of the growing coating and of the substrate.
The mathematical model of pulsed electric contact sintering of carbide powder compositions are suggested and investigated. The distributions of temperature, density and thickness of the rate during sintering are determined
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