The work objective is to develop a mathematical model of the force characteristics of shock absorbers based on viscous friction, including elastomeric ones. For this purpose, the following tasks are solved in the work: the existing approaches to the mathematical modelling of hydraulic shock absorbers are analysed, a mathematical model based on hydraulic equations (the Darcy–Weisbach equation) is proposed, the developed mathematical model is verified and the results are compared with the results obtained based on the existing approach. Research methods: the equation of fluid flow through holes with hydraulic friction; D'Alembert's principle for composing the equation of car swaying motions; the Euler method for numerical integration of the differential equation. The novelty of the work consists in the fact that a mathematical model of the power characteristics of shock absorbers with viscous friction is proposed, based on the quadratic dependence of the reaction on the deformation rate. The results are the study of car swaying motions based on the traditional and proposed approaches. The proposed mathematical models can be used to develop shock absorbers with improved characteristics when designing passenger cars.

The study objective is to develop and analyze mathematical models of vibrations of a passenger car with elastomeric dampers. The problem to which the paper is devoted is to improve the dynamic characteristics of the undercarriage of passenger cars and increase passenger comfort. The research methods used in this study are typical for solving the problems of rolling stock dynamics. The car is approximated by a system of concentrated masses connected by elastic and dissipative bonds. The external impact is track irregularities of different types. Differential equations of motion are combined using D'Alembert's principle. The set of equations is integrated by numerical method. The novelty of the work is, firstly, in the use of an elastomeric vibration dampener on the bogie of a passenger car, secondly, in the analysis of the dynamic qualities of this car when moving over the irregularities of the main types, and thirdly, in the choice of rational parameters of elastomeric dampers. The results of the study are graphs, nomograms and tables of the dependencies of maximum force values on various parameters, as well as an assessment of the movement smoothness. The conclusions of the work contain an assessment of the dependence of dynamic parameters on speed, recommendations on the characteristics of elastomeric dampers, the validity of using elastomeric dampers.