Contents 1 INTRODUCTION 1 I THEORY AND APPLICATIONS. 4 2 MULTIAXIAL FATIGUE (literature review) CLASSIFICATIONS OF THE METHODS

Transcription

1 Zwischenbericht ZB-119 A MULTIAXIAL FATIGUE METHOD AND ITS APPLICATION TO A RADIAL-ELASTIC RAILWAY WHEEL Nicola Pederzolli Matr Advisors: Prof. Dr. Ing. W. Schiehlen Dipl. Ing. H. Claus University of Stuttgart Institute B of Mechanics Prof. Dr. Ing. W. Schiehlen Advisors: Prof. Dr. Ing. B. Atzori Dr. Ing. N. Petrone University of Padova Department of Mechanics March 2000

2 Contents 1 INTRODUCTION 1 I THEORY AND APPLICATIONS. 4 2 MULTIAXIAL FATIGUE (literature review) CLASSIFICATIONS OF THE METHODS Notations Symbols GOUGH-POLLARD SINES CROSSLAND SOCIE McDIARMID DANG-VAN PAPADOPOULUS MATAKE GARUD Relations between deformation components Relations between stress components Relations between stress and deformation i

3 Description of the method Incremental plasticity : theory and assumptions ZENNER METHOD Description of the method Sinusoidal stress THE USED FATIGUE ANALISYS METHOD MODIFIED ZENNER I Description of the method BIAXIAL METHOD ( FATIGUE I ) Description of the method TRIAXIAL METHOD (FATIGUE II) Description of the method CLASSIFICATION OF THE METHODES LIMITATIONS AND POSSIBLE EVOLUTIONS FLEXIBLE MULTIBODY SYSTEMS THEORY [60] APPLICATIONS Program ANSYS Data converter FEMBS 6.0 [63] Program NEWEUL Program MODIS Program MOSIG II INVESTIGATION TO A RADIAL-ELASTIC WHEEL 77 5 GEOMETRY DEFINITION 79 ii

4 5.1 WHEEL GEOMETRY Wheel rim Rubber ring Wheel disc RAILWAY TRACK COUPLING WHEEL - RAILWAY TRACK STATICAL ANALYSIS PERFORMING A STATICAL ANALYSIS Steps in a statical analysis Creating the model geometry and mesh Applying appropiate displacements and loads RESULTS STRESS and DEFORMATION SUMMARY OF THE RESULTS DETERMINATION OF THE CONTACT AREA PERFORMING A SURFACE-SURFACE CONTACT ANALYSIS Steps in a contact analysis Creating the model geometry and mesh Identifying contact pairs Designating contact and target surface Asymetric contact Defining the deformable target surface Defining the deformable contact surface Real constants and material properties Set the real constant and elements options Applying displacements and forces to the bodies Solving the contact problems iii

5 Reviewing the results RESULTS STRESS TRAJECTORIES TO CRITICAL POINTS PERFORMING A DYNAMIC ANALYSIS Steps in a dynamic analysis Obtaining the necessary files with ANSYS FEMBS Defining the MBS model Defining the timevariing loads Performing an analysis with NEWEUL and NEWSIM RESULTS : Wheel RESULTS : Wheel RESULTS : Wheel DETERMINATION OF THE FATIGUE LIFE VALUE Choice of the markers and the time step T Obtaining the stress trajectory for the point P using the program FATIGUE II RESULTS : Wheel RESULTS : Wheel RESULTS : Wheel Life value determination using program LIFE CONCLUSIONS 178 BIBLIOGRAPHY 181 iv

6 Chapter 10 CONCLUSIONS This work is devoted to the life time estimation of a radial-elastic railway wheel. The wheel is modeled with finite elements and introduced in a multibody system model of a quater of ICE bogie. This type of model is called flexible multibody system model. Due to the time variing load acting on the wheel rim and the resulting three dimensional deformation of the rim this life time estimation requires not only a sophisticated modeling of the wheel as well as of the representative part of the coach but also a suitable life time program. The loads won't be sinusoidial and the directions of the principle stresses won't be constant either. Therefore, this work starts with a literature study of fatigue methods, then the different methods for multiaxial fatigue estimation are discussed and the requirements for a suitable method are worked out. The method of shear stress intensity (SIH) of Zenner, which is proposed to consider time variing principle stress directions, is investigated in detail. During this study it becomes clear that the method of Zenner is restricted to sinusoidal input loads and the stress contitions have to be biaxial. Such biaxial stress status exists on the surface of a mechanical component but only when the principle stress 1 is higher than zero and the principle stress 3 lower. Furthermore, this method is only able to determine whether a mechanical component has a infinite life or not. Therefore, some modifications are derived. Due to the approach of flexible multibody systems the stress distribution of arbitrary material points can be determined at all time steps of simulation. The stress components can be obtained in the reference coordinate system as well as in local coordinate systems, for example in body fixed systems. The method ZENNER I 178

7 is derived here from Zenners method and adopted to input of stress data given in such body fixed systems. Then, the stress is computed in a number of planes perpendicular to surface. From this stresses a stress intensity is evaluated which determines if the life time is infinite or no. Moreover, the real life fatigue value has to be evaluated. Therefore, the method FATIGUE I is derived from method ZENNER I. This method requires biaxial stress conditions as well but the life time of each particular plane is evaluated from its stress history and the lowest life time is considered to be the critical one. This method can be understood as critical plane method but here at first the life time estimation is carried out and then, if required, the critical plane can be determined. The evaluation of stress histories on the surface of a wheel rim shows that the stress distribution is not biaxial. In this case the two principle stresses have the sime sign and the third principle stress is equal to zero. The application of the above mentioned method FATIGUE I would give an underestimation of life time because the critical plane isn't one of the investigated planes perpendicular to the surface. For this reason the method FATIGUE II is developed starting from method FATIGUE I. The method FATIGUE II don't reduce its investigation to planes perpendicular of the surface but considers additionally planes being inclined 45 o to the surface. Since the two principle stress which are not zero have the same sign FATIGUE II finds the smallest life time value in one of the planes of 45 o inclination. Otherwise FATIGUE II will find the smalles value in a plane perpendicular to surface like FATIGUE I. In the second part, the railway wheel is investigated. The applied forces are time variing according to the random excitation and the eigen dynamics of the model. The wheel is composed of three components with different material properties, steel and rubber. Here, solid elements with 8 nodes and 3 translational degrees of freedom are used. Due to the complex geometry the stress analysis requires a huge number of elements. After analysis of static behavior and eigen dynamics of the wheel the contact between the wheel and the railway track is investigated. The static contact analysis shows that the non-linearity due to the surface contact can be neglected in first order. For calculation of the stress trajectories at critical points the flexible multibody method is used. For this purpose some files has to be created in ANSYS. One that contains the structural properties of the finite elements model and another 179

8 that comprises the eigen and the static modes. For computation of the structural properties a substructur has to be created. Unfortunately, in this procedure ANSYS is limited in the number of master degrees of freedom (DOF) that cannot exceed This is equivalent to a limitation of 1500 nodes with 3 DOF each (SOLID 45: x, y and z translations). This is a strong restriction when defining a complex geometry in detail. To overcome this problem, only a half wheel is modelled and the nodal results are mapped to the other half of the wheel. So the element density is doupled without loss in accuracy. Then the flexiblility properties of the wheel are introduced in the MBS model of the coach. During time integration the wheel is excited by random track irregularities. The outcome of the integration that are files containing stress histories at the chosen material points is used as input for FATIGUE II. The results show that for non-polygonalized wheel with radius = 433 mm and travel on straight rails the life time is favour of security (fatigue life value bigger as Km). On the other hand, the influence of polynonalized wheels, travel through curves and eventually some impacts when traveling through switches with high velocity may decrease the life time value drastically. It is possible to said that in the reality the wheel with radius = 433 mm is not sure. On going investigations indicated that the minimal secure radius is 440 mm. Therefore, wheel other radii are investigated to find correlations between the radius of wheel and the fatigue life value. The additionally considered radii are 410 mm and 418 mm. The obtained correlation is in first approssimation assimilable to a parabola where the life value for the wheel with radius = 410 mm is so little that identified the point of sure crack failure. The parabolic shape of the curve implies that a few variation of the radius induce a huge variation in the corresponding fatigue life value. This work shows that even in case of time variing loads and on complex geometries such as on a rim of a radial-elastic wheel the life time value can be determined. The investigation of fatigue life time of a radial-elastic wheel gives hints how strong even small variations of geometrie changes the savety and service time. Although a lot was done in this work, in future travel through curves, poligonalized wheel circumferences as well as impacts when traveling over switches should be considered to obtain even more accurate results. 180