Development of a Mathematical Model for a Railway Track Using a Gray-Box Modelling Technique
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ORIGINAL CONTRIBUTION
Development of a Mathematical Model for a Railway Track Using a Gray-Box Modelling Technique Durlav Hazarika1 • Jyoti Kumar Barman1
Received: 28 June 2019 / Accepted: 3 September 2020 The Institution of Engineers (India) 2020
Abstract Mathematical model of a system provides the relationship between the input and the output variables. There are different methods of modelling a system, viz. utilising system dynamics, black box modelling and graybox modelling. In literature, there are many works that describe modelling of a railway track using the system dynamics of a track or interaction between track and train wheel. In standard black-box modelling, most of the time standard test signals such as impulse and step are used to model a system. In this paper, a simple method is described that uses ‘‘system subjected to a pulse input’’ to model a system. This approach is very helpful especially in modelling of a railway track as the track may be subjected to an impulse, step or any signal (i.e. pulse of variable length) in between depending on the speed of the train. Keywords Mathematical modelling Gray-box modelling Pulse excitation Vibration
Introduction Mathematical modelling of a system helps in understanding the dynamics of the system better. Modelling of a railway track has been a fascinating area for researchers since a long time. Modelling of a railway track as an electrical transmission lines system was done by few & Durlav Hazarika [email protected] Jyoti Kumar Barman [email protected] 1
Assam Engineering College, Jalukbari, Guwahati, Assam, India
researchers such as Hill et al., Berova etc. [3, 11]. One of the earliest models of a railway track was presented by Timoshenko, where the rail was considered as an infinite uniform Euler beam [21]. Again according to Grassie et.al., railway track can be modelled as a track resting on a simple elastic support, track resting on a continuous, two-layer support and track resting on discrete supports [10]. Another popular approach for rail track modelling is by finite element model [7, 12, 13, 20]. Mathematically modelling a railway track is an age old practice to calculate the stress pattern of different components. It helped in anticipating and estimating the service periods and specific values of life-spans of different components. Aim of mathematical model may be different from situations to situations. Few models aimed at studying particular problem or phenomenon while few may aim at the validity of models at different frequencies. To model train and track interaction utilising dynamic behaviour, Knothe et al. considered five sub-systems as shown in Fig. 1 [14]. In this way, it is needed to model different sub-systems separately. Many researchers model the rail as Bernoulli-beam. In some cases, the rail is modelled as series of interconnected plates. Rail fastening system along with the railpads is modelled. Railpads are generally modelled as spring and viscous dampers. Sleepers are modelled as a Timoshenko beam of variable t
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