An Efficient Numerical Model to Predict the Mechanical Response of a Railway Track in the Low-Frequency Range

Abstract

With railway interoperability, new trains are allowed to move on the French railway network. These trains may present different designs from standard trains. This work aims to complete the current approach for vehicle admission on the railway network, which is defined in technical baselines. Historically, computation rules for traffic conditions are based on simplified analytical works, which are considerably qualitative. They have evolved through feedback and experimental campaigns to comply with the track structure evolution. An efficient methodology based on numerical simulation is needed to evaluate railway vehicle admission to answer this issue. A perspective to update these computation rules is to evaluate the structural fatigue in the rail. That is to say, fatigue is caused by bending and shear stresses. The complexity of the railway system has led to an investigation at first of the vertical response of the railway track and quantifying its contribution to the rail’s stress response. In that sense, this paper investigates the vertical track response to a moving railway vehicle at low frequencies. For this purpose, a lightweight numerical model for the track, a multi-body model for the vehicle, and a random vertical track irregularity are proposed. More explicitly, the track model consists of a two-layer discrete support model in which the rail is considered as a beam and sleepers are point masses. The rail pads and ballast layer are modelled as spring/damper couples. Numerical results show a negligible effect of track inertia forces due to high track stiffness and damping. Nevertheless, this assumption is valid for normal rail stresses but not for ballast loading, especially in the case of sleeper voids or unsupported sleepers. Hence, the prediction of the mechanical stress state in the rail for fatigue issues is achieved through a static track model where the equivalent loading is obtained from a dynamic study of a simplified vehicle model. A statistical analysis shows that the variability of the vertical track irregularity does not influence the output variabilities like the maximum in time and space of the normal and shear stress.

Using Detailing Concept to Assess Railway Functional Safety

“…Such divisions do not exist when solving problems using the theory of elasticity. Hence, when studying the influence of both the impulse itself [89][90][91][92][93] and its repetition [94][95][96][97], as well as in modeling and validation [98][99][100], it is considered as a formed oscillation process. The theory of propagation of elastic waves allows directly forming this process, using the property of all types of waves to transfer momentum without change to all points in space, taking into account both the time the force field reaches each element of the railway structure and the absorption of each element of the force impact during the collision of waves.…”

Optimal Vibration Fields in Problems of Modeling Dynamic States of Technical Objects

“…Динамическое состояние формируется при нарушении скользящего контакта головки пантографа с контактным проводом [10]. В данном контексте следует упомянуть и задачи анализа реакции рельса на вертикальные воздействия со стороны движущегося транспортного средства [11].…”

“…где z -вектор амплитуд колебаний внешних кинематических возмущений; T e0 -матрица, определяющая квадратичную форму энергетического функционала (11). Внешние возмущения , z σ формирующие необходимое вибрационное поле, множители Лагранжа Λ находятся решением системы:…”

“…,005 Сглаженные 0,002 0,0027 0,0035 0,0043 0,005 В качестве энергетического функционала используется выражение (11), которое можно представить с помощью оператора T e :…”

“…Нулевое значение энергетического функционала(11) определяет равномерное вибрационное поле, амплитуды колебаний точек которого равны между собой. Минимизация энергетического функционала с учетом заданных условий на амплитуды колебаний в контрольных точках(10) определяет форму вибрационного поля, экстремально близкую к равномерной.…”