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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.

In the paper there is considered a car basic bearing element – center sill which because of long operation is subjected to corrosion destruction (on surface and in depth). The elimination of such corrosion spots mechanically is not effective and results in local decrease of a unit thickness and also in some cases in through corrosion. The authors of the paper have carried out investigations in places where intensive corrosion took place. For this there were cut out four fragments of the center sill and carried out etching-out and measuring residual stresses and a deformation value from etching depth of each fragment through Davidenkov’s method and CNIITMach’s procedure. As a result of the investigation carried out there is offered a fulfillment of center sill strengthening in the area of intermediate and end girder welding by means of shot cleaning in these areas, and also by additional corrosion resistant coating application on these surfaces. The investigations are carried out through Davidenkov’s method and on the basis of CNIITMach’s procedure. The work novelty: there are defined conditions for corrosion spot formation and technology is developed to ensure units life increase. According to the results of the investigations carried out there is made a conclusion: for the purpose of decrease and exclusion of corrosion processes and service life increase of both the center sill and a car in the whole it is necessary to carry out strengthening center sill elements in the areas of intermediate and end girders welding by means of the shot cleaning fulfillment in these places, and also an additional corrosion resistant coating application on these areas.