PSI - Issue 81

Dmytro Voloshyn et al. / Procedia Structural Integrity 81 (2026) 264–268

267

1,86

t

1 exp    = − −

  

( )

(1)

F t

15,87

The probability function for the failure-free operation of roller bearings allows us to conclude that the average operating time before failure of the bearings is approximately 3-4 years, which is significantly less than the standard level. 3. Theoretical model for ensuring the reliability of axlebox assemblies in railway wagons Careful analysis of the causes of failures and the development of the most effective measures to eliminate them is facilitated by the construction of a ‘failure tree’ and the development of inoperable states. Such an analysis is carried out for each pe riod of operation, each part or the system as a whole. The failure tree (of accidents, events, consequences, undesirable events, etc.) forms the basis of a logical-probabilistic model of cause-and-effect relationships between system failures and failures of its elements and other events (influences). Failure analysis consists of sequences and combinations of disturbances and malfunctions, and thus represents a multi-level graphological structure of causal relationships obtained by tracing hazardous situations in reverse order in order to find possible causes of their occurrence. The effectiveness of this method lies in its focus on failures and the description of their interrelationships. It should also be noted that this method is best suited for analysing the reliability of systems with a large number of elements. When constructing a failure tree, the primary task is to establish the top event for the system under study or its part, which subsequently refers to the failure of one of the system elements. The established events (failures), as well as the top event, are further logically decomposed into simpler events (Fig. 3). The basis for analysing the cause-and-effect mechanism is the failure of elements, which, according to the failure tree construction scheme accepted in practice, are classified into primary failures and secondary failures.

Fig. 3 . The example of the basic structure of a ‘fa ilure tree’ for a box node.

After constructing the graphical model, a quantitative reliability analysis was performed to determine reliability indicators in accordance with the developed theoretical model. To formalise the functioning of the axlebox assembly, it is necessary to record the structural function of its operating states. To do this, in the first stage, an equivalent ‘tree’ model was constructed, where elementary events were matched with independent variables of a numerical series x 1 , x 2 , x 3 ... x n ordered by elementary failures (Fig. 4). An auxiliary variable parameter in binary form was used to describe the state of the initial event. That is, the final event of the ‘tree’ with the logical sign ‘AND’ exists if and only if all the initial events A 1 , A 2 , A 3 ... A n . In this case, the structural function has the following form: