• Rail Vehicles, Semester 3, position 3

1. Acquiring knowledge about the dynamic behavior of rail vehicles. 2. Exploring methods for studying the dynamic behavior of rail vehicles. 3. Training for the application of knowledge in the design, development, repair and maintenance of railway vehicles.

After completion of the course the student should be able to: 1. Explain the characteristic phenomena of dynamic behaviour of rail vehicles. 2. Apply computational methods for determining the main parameters of the dynamic behaviour of the rail vehicles. 3. Participate in the preparation of the test procedures for tests of the dynamic behaviour and proper assesment of the test results. 4. Apply appropriate regulations for design or refurbishment of rolling stock in order to achiеve the prescribed dynamic behaviour.

Modeling of the dynamic behaviour of the rail vehicles. Geometrical deviations of the track and deviations of wheelset geometry as the excitation source. An elementary model of the vertical oscillation of vehicles with single-stage suspension. The appearance of resonances during movement along track with vertical harmonic deformations. The influence of damping. The behavior of vehicles with dry damping elements. Model of the railway vehicle with two-stage suspension in vertical direction. Application of matrix calculus in solving the dynamic problems. Fundamentals of rail vehicle lateral dynamics. A hunting movement of the wheelset-Klingel solution. The contact geometry. Equivalent conicity. The forces in the wheel-rail contact. The movement of bounded wheelset. Stability of motion. Critical speed. Modelling of stationary, quasi-static motion of the bogie in the curve using the center of friction method. Criteria for assessing the behavior of rail vehicles in motion. (Y/Q) criterion. Criterion of the H forces. Sperling Ride Index. Tests according to UIC 518. Criteria ISO/ORE (UIC518).

Examples of excitation: denivelation of the rails, out off roundness and eccentricity of the wheel, track deformations, harmonic deformations. Excitation simulation. Linear and nonlinear characteristics of elastic and damping elements. Linearization of the characteristics. Examples of one degree of freedom models. Typical dry friction elements used on rail vehicles. The model with dry friction. Example of two axle bogie model in the vertical plane. Effect of selection of generalized coordinates to equation coupling. Example of the freight wagon model with bogies. Example of model of passenger coach two-stage suspension in the vertical plane. Solving problems with more degrees of freedom using computer software. Review of tests of passenger coach dynamic behaviour.

Previously passed courses in Mechanics of rigid bodies and at least 18 EPSB, with at least one course of Dynamics.

G. Simic, D. Milkovic, Fundamentals of rail vehicle dynamics, hand-out. User guides for appropriate software.

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 15
Laboratory exercises: 0
Calculation tasks: 15
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 6
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 4
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 40
Laboratory practice: 0
Calculation tasks: 30
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 30

Milutinovic, D., Simic, G., Loads and calculation of railway vehicles' wheels, Faculty of Mechanical Engineering, Belgrade, 2006., ISBN: 978-86-7083-543-6; Milkovic, D., Wayside system for wheel-rail contact forces, Faculty of Mechanical Engineering, Belgrade, 2017., ISBN: 978-86-7083-939-7