### THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE

K. O. Soroka, D. A. Lychov

#### Abstract

Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods of numerical integration. The calculation expenses are reduced. The accuracy is improved; provided possibility to consider different parameters influencing the motion. A certain environmental effect can be achieved by orientation calculation methods for the practical development of the process charts of the movement of electric vehicle funds in different operating conditions at a constant change of filling the interior of the vehicle.

#### Keywords

urban electric transport; electric power costs; equation of motion; conceptual and mathematical models; Euler-Lagrange equation; conservative and dissipative forces

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DOI: https://doi.org/10.15802/stp2015/46056

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1. SYSTEM FOR AUTOMATIC SELECTION OF THE SPEED RATE OF ELECTRIC VEHICLES FOR REDUCING THE POWER CONSUMPTION
K. O. Soroka, T. P. Pavlenko, D. A. Lychov
Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport  Issue: 3(69)  First page: 77  Year: 2017
doi: 10.15802/stp2017/104360