Analytical formulae for the design of a railway vehicle suspension system

A simple two-degree-of-freedom (2DOF) model is used to derive a number of analytical formulae describing the dynamic response of railway vehicles to random excitations generated by vertical track irregularities. The dynamic response is given in terms of standard deviations of a number of relevant performance indices such as body-bogie suspension stroke and body acceleration. The derived analytical formulae can be used either during preliminary design or for other special purposes, especially when approximated results are acceptable. An estimation of the degree of approximation offered by analytical formulae is attempted and the results seem satisfactory. By inspection of the analytical formulae a parameter sensitivity analysis may be readily performed. In the second part of the paper, an optimization method for the improvement of the dynamic behaviour of railway vehicles is introduced. The method, based on multiobjective programming (MOP), is a general one and can be exploited for many engineering purposes. In the paper the method has been applied with the aim of achieving the desired trade-off among conflicting performances such as standard deviation of the body acceleration versus standard deviation of the secondary suspension stroke. As a result, new analytical formulae defining the settings of some relevant vehicle suspension parameters have been derived.