Report of Railway Engineering Research at Chalmers University in Gothenburg

Lundén R. Järnvägshjul med krympförband—beräkningar och experiment för verifiering av toleranser (Railway wheels with shrink-fit assembly—calculations and experiments) (in Swedish). A joint project with ABB SURA Traction AB. Report F110, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1988, 39 pp.

Lundén R. Fatigue durability of tread braked railway wheels—on admissible combinations of axle load, train speed and signalling distance. Proc. Instn Mech. Engrs, J. Rail and Rapid Transit, Part F, 1991, 205 (F1), 21–33. A mathematical model for the prediction of relative lifetimes of railway wheels exposed to block braking under stop braking cycles is presented. Analytical and finite element thermoelastic calculations are employed together with a model for low-cycle fatigue. Durability curves are established describing limiting combinations of axle load and train speed for given combinations of signalling distance and required wheel lifetime. Application of the method is demonstrated on an existing freight car wheel that conforms to UIC standards. The numerical results should also be useful for other wheels.

Ahlm A. Fejde P. Grundberg K. Langer R. Axlar, lager och lagerboxar till järnvägsfordon (Axles, bearings and axleboxes for railway vehicles) (in Swedish). A joint project with ABB SURA Traction AB. Student report T112, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1988, 58 pp.

Berghel F. Grundberg E. Jergéus J. Johansson Ö. Optimal utformning av skiva hos järnvägshjul (Optimal design of disc of railway wheel) (in Swedish). A joint project with ABB SURA Traction AB. Student report T120, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1990, 43 pp.

Fermér M. Flexible wheels for railway freight cars considering thermal and mechanical aspects of block braking. Presented at Tenth International Wheelset Congress, Sydney, Australia, 27 September–1 October 1992, 5 pp. A railway wheel with flexible steel elements between the hub and rim is suggested. Twelve S-shaped steel spokes as studied here is one possibility. By use of finite elements, transient temperatures and thermoelastoplastic strains and stresses in the wheel exposed to block braking are calculated and compared to those for a standard solid freight car wheel. The results are verified through experiments on a full-scale inertia dynamometer. Based on the present study, several advantages are foreseen for the suggested wheel. Because of its low unsprung mass, the wheelset can carry a higher axle load with preserved lifetimes of the vehicle and track. No thermally induced residual stresses from block braking will occur in the wheel tread. The wheel was also found to radiate less noise than a standard solid wheel used on passenger and freight trains today.

Bergström J. Granlund L. Brake discs for rail vehicles. A joint project with ABB SURA Traction AB. Student report T113, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1988, 54 pp.

Fermér M. Lundén R. Transient brake temperatures found by use of analytical solutions for finite hollow cylinders. A joint project with ABB SURA Traction AB. Report F134, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1990, 29 pp. Also in Proc. Instn Mech. Engrs, J. Mech. Engng Sci., Part C, 1991, 205(C3), 189–200. A linear analytical model for calculating transient axisymmetric temperature distributions in finite hollow cylinders is established and adapted for practical use. A homogeneous isotropic material with temperature-independent thermal properties is assumed. Among possible applications are brake discs, brake drums and block braked railway wheels. The thermal power from braking is applied as prescribed heat influxes over parts of the lateral and radial surfaces of the cylinder. Bessel series solutions to the heat conduction equation are found where Newton's law for heat transfer is used in the boundary conditions. In addition to convection, prescribed surface temperatures and insulated surfaces are also studied. Arbitrary thermal loading histories are treated by use of Duhamel's principle where step loadings are superposed. Convergence and limitations of the method and required computer times are discussed. Calculated numerical results for some typical braking operations are compared with those of other studies.

Fermér M. Brake discs for passenger trains—a theoretical and experimental comparison of temperatures and stresses in solid and ventilated discs. A joint project with ABB SURA Traction AB. Report F139, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1991, 16 pp. Also in Proc. Instn Mech. Engrs, J. Rail and Rapid Transit, Part F, 1992, 206(F1), 37–46. The ventilated brake discs currently used in passenger trains can be replaced with solid discs when there is no need to design for drag braking of long duration. This is a conclusion arrived at in the present study where transient temperatures and stresses induced in the disc during drag braking and during single and repeated stop braking are calculated by use of a previously established analytical model. The results are verified through full-scale experiments carried out on a recently built inertia dynamometer. A forged solid steel disc is compared with a standard ventilated cast iron disc. Measurement techniques and various observations are discussed.

Andersson K. Johnsson K. Simonsen H. Wang E. Martensite formation in railway wheel treads. A joint project with ABB SURA Traction AB. Student report T126, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1991, 40 pp.

Berglund S. Karlsson R. Olsson P.-A. Stübner C. Formation of wheel flats and martensite in railway wheel treads. A joint project with ABB SURA Traction AB. Student report T131, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1992, 48 pp.

Lundén R. Contact region fatigue of railway wheels under combined mechanical rolling pressure and thermal brake loading. A joint project with ABB SURA Traction AB. Report F135, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1990, 18 pp. Also in Wear, 1991, 144(1–2), 57–70 (this issue of Wear constitutes Proceedings of 3rd International Conference on Contact mechanics and wear of rail/wheel systems, Cambridge, July 1990). The combined effect on railway wheels of a periodically varying contact pressure and an intermittent thermal brake loading is investigated in this paper. The development and redistribution of residual stresses in the wheel rim are clarified. Elastoplastic strain cycles are calculated for some often occurring loading histories. These cycles are used as input to a damage mechanics model where the relative lifetime of the wheel rim can be estimated. Shakedown, cyclic plasticity and ratcheting are central phenomena discussed in the paper. A commercial FEM computer program for thermoelastoplastic analysis is employed. Temperature-dependent material data for a real wheel steel are used. Simulations with varying material data are carried out and measures to increase the lifetime of railway wheels are discussed.

Jergéus J. Wheel/rail contact problems modelled with three-dimensional finite elements in a supercomputer. A joint project with ABB SURA Traction AB. Student report T125, Division of Solid Mechanics, Chalmers University of Technology, Gothenberg, Sweden, 1991, 40 pp.

Lundén R. Cracks in railway wheels under rolling contact load. Presented at Tenth International Wheelset Congress, Sydney, Australia, 27 September–1 October 1992, 5 pp. Crack initiation and crack propagation in the contact region of a railway wheel are studied by use of analytical and numerical methods assuming a Hertzian contact pressure without and with friction. Triaxial contact and residual stresses are considered in a three-dimensional model for crack initiation. Crack propagation is considered in a simplified model mainly involving mode II cracks. Stress intensity factors are computed for plane conditions. The numerical results obtained are compared with experimentally found threshold values for a real wheel material. Observed cracks in wheels exposed to service loads are investigated and the allowable size of such defects is discussed.

Dahlberg T. Dynamic interaction between train and track—a literature survey (with 133 references). Report F120, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1989, 21 pp.

Nielsen J. C. O. Eigenfrequencies and eigenmodes of beam structures on elastic foundation. J. Sound and Vibr., 1991, 145(3), 479–487. A method for determining the eigenfrequencies of continuous structures containing beams in a plane bending-shearing vibration was presented. Each beam member may rest on a general Winkler-type elastic foundation (including the Pasternak foundation as a special case) and may carry a large static axial load calling for use of a second-order theory. The method could preferably be implemented in the Wittrick-Williams bisection algorithm. A numerical verification was given for a repetitive structure where an alternative solution is available through the use of exact difference equations. Practical applications to a rail/pad/sleeper system on its ballast and roadbed were foreseen.

Ågårdh L. Sliprar av förspänd betong. Bestämning av resonansfrekvenser, moddämpningar och modformer med experimentell modanalys (Reinforced concrete sleepers. Determination of resonance frequencies, modal dampings and modal shapes by use of experimental modal analysis) (in Swedish). Report SP-AR 1009–09, The Swedish National Testing Institute, Byggnadsteknik, Borås, Sweden, 1990, 43 pp.

Dahlberg T. Nielsen J. C. O. Dynamic behaviour of free-free and in-situ concrete railway sleepers. Proceedings of International Symposium on Precast concrete railway sleepers, Madrid, Spain, 8–11 April 1991, pp. 393–416 (Colegio de Ingenieros de Caminos, Canales y Puertos, Madrid, Spain). The dynamic behaviour of free-free and in situ concrete railway sleepers was studied. A method developed by Nielsen [reference (15) above] to calculate eigenfrequencies and eigenmodes of general beam structures on a general elastic foundation was used. Measurements on free-free precast concrete railway sleepers have been performed. Calculated and measured eigenfrequencies and eigenmodes in bending vibration in the vertical plane of the sleepers were compared. It was found that, except for the lowest two bending mode eigenfrequencies, the refined Rayleigh-Timoshenko beam theory was required for the eigenfrequency and eigenmode calculations. The natural frequencies of a beam on an elastic foundation (that is the in situ sleeper) will differ from those obtained for the free-free beam (sleeper). The foundation introduces two eigenfrequencies coupled to two almost rigid-body eigenmodes (translation and rotation) of the sleeper. The lower eigenfrequencies in bending are also influenced by the foundation stiffnesses, whereas higher eigenfrequencies are almost unaffected. Dynamic responses (bending moments) of a sleeper as a component in a track structure subjected to transient excitation were investigated. It was found that an irregular rail profile had a significant influence on the dynamic responses.

Dahlberg T. Vehicle-bridge interaction—Part 1. Report F90, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1984, 17 pp.

Dahlberg T. Vehicle-bridge interaction—Part 2. Report F92, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1984, 29 pp.

Dahlberg T. Vehicle-bridge interaction. Veh. System Dynamics, 1984, 13(4), 187–206. With the emergence of high-speed trains, dynamic loads on bridges have changed. A method for estimation of the time-dependent vehicle-bridge interaction forces has been developed. The increase (or decrease) of the bridge response due to dynamic effects was determined. The moving constant-force problem was reviewed in some detail. Results obtained by the present method for the moving-mass problem were compared with existing experimental and theoretical results as reported in the literature. A parametric study of bridge responses was made. The parameters varied were the vehicle speed, the ratio of vehicle mass to bridge mass, the ratio of vehicle eigenfrequency to bridge eigenfrequency, and the relative damping of the vehicle. Finally, the influence of an initial bridge deflection was discussed.

Dahlberg T. Structural responses to moving forces determined by reciprocity relations. Veh. System Dynamics, 1990, 19(3), 113–130. Reciprocity relations are valid also for dynamic problems. In this paper, the reciprocity relation was first used to determine the response of a simply supported beam subjected to an arbitrarily time-varying force moving with constant speed. Then the reciprocity relation was used to determine the response of a beam-like structure (a beam on mass-spring supports, a model of a railway track) subjected to a moving constant force. Numerical solutions, including also a pair of moving forces, were given.

Nielsen J.C.O. Abrahamsson T. J. S. Complex eigensolutions used for beam structures on elastic foundation loaded by moving nonlinear dynamic systems. Proceedings of Ninth International Conference on Modal analysis, Florence, Italy, 15–18 April 1991, Vol. 2, 1991, pp. 1110–1116 (Union College, Schenectady, N.Y.).

Nielsen J. C. O. Abrahamsson T. J. S. Coupling of physical and modal components for analysis of moving nonlinear dynamic systems on general beam structures. Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1990, 22 pp. Also in Int. J. Numer. Meth. Engng, 1992, 33, 1843–1859. A general, well-structured and efficient method is advanced for the solution of a large class of dynamic interaction problems including a non-linear dynamic system running at a prescribed time-dependent speed on a linear track or guideway. The method uses an extended state-space vector approach in conjunction with a complex modal superposition. It allows for the analysis of structures containing both physical and modal components. The physical components studied here are vehicles modelled as linear or non-linear discrete mass-spring-damper systems. The modal component studied is a linear continuous model of a track structure containing beam elements which can be generally damped and which can be embedded in a three-parameter damped Winkler-type foundation. The complex modal parameters of the track structure are solved for. Algebraic equations are established that impose constraints on the transverse forces and accelerations at the interfaces between the moving dynamic systems and the track. An irregularity function modelling a given non-straight profile of the non-loaded track or a non-circular periphery of the wheels is also accounted for. Loss of contact and recovered contact between a vehicle and the track can be treated. The system of coupled first-order differential equations governing the motion of the vehicles and the track and the set of algebraic constraint equations are together compactly expressed in one unified matrix format. A time-variant initial-value problem is thereby formulated such that its solution can be found in a straightforward way by use of standard time-stepping methods implemented in existing sub-routine libraries. Examples for verification and application of the proposed method are given. The present study should be of particular value in railway engineering.

Nielsen J. C. O. Dynamic interaction between wheel and track—a parametric search for best performance of railway tracks. Report F147, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1991, 22 pp. Submitted for international publication. The dynamic vertical interaction between a moving rigid wheel and a flexible railway track was studied. A round and smooth wheel tread and an initially straight and non-corrugated rail surface were assumed. A linear three-dimensional beam structure model of a finite portion of the track was suggested including rails, pads, sleepers and ballast with spatially non-proportional damping. The full interaction problem was numerically solved by use of an extended state-space vector approach in conjunction with complex modal superposition for the track. Transient bending stresses in sleepers and rails were calculated. The influence of seven selected track parameters on the dynamic behaviour of the track was investigated. A two-level fractional factorial design method was used in the search for a combination of numerical levels of these parameters, making the maximum bending stresses a minimum.

Fenander Å. Igeland A. Nonlinear vehicles on randomly profiled tracks—Monte Carlo simulation of excitation and frequency analysis of response. Student report T127, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1991, 21 pp.

Dahlberg T. Dynamic interaction between railway vehicle and track. Final report of a three-year railway engineering research program. Report F140, Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden, 1991, 20 pp.