Comparative analysis of methods of approximation of the working characteristics of elastic element of suspension of the vehicle

In the article the nonlinear characteristic of the elastic element of the vehicle suspension is investigated. Suspension is an important part of any car and its performance, in many ways, determines the correct operation of the entire car as a whole. When designing the suspension, special attention is paid to the elastic element that is part of the suspension design, while an important task is to consider the performance of this element. As a rule, performance characteristics are non-linear, difficult to be mathematically described when studying suspension dynamics. This circumstance creates problems for the construction of a mathematical model of suspension, hampers analysis, numerical and analytical integration of a system of differential equations describing the operation of the suspension. Therefore, in practice, an approximation is made of the working characteristic of the elastic element. The article compares various methods for approximating the performance characteristics of elastic elements of vehicles, reveals the positive and negative aspects of these methods. Most often when compiling mathematical models of a car, the working characteristic of an elastic element is assumed to be linear. However, this assumption does not allow us to fully appreciate the dynamic processes taking place in the system. Often the approximation of the working characteristic is carried out using a piecewise linear function having a rather simple structure. This approach requires consideration of the suspension work cycle in sections. It is necessary to study the operation of the suspension as a system with a variable structure, which causes considerable difficulties in constructing periodic solutions and determining their stability. The paper proposes a new method for approximating the working characteristic of an elastic element with the help of an analytic function, which considers an elastic element as a system with a constant structure, describing the work of an elastic element by only one system of differential equations with analytic functions. This makes it possible to obtain solutions of the system as a whole, without considering individual sections of the work of the elastic element. Such an opportunity helps to design a suspension of vehicles with optimal characteristics, to create cars, the parameters of which meet the most advanced modern requirements.