Institute of Fundamental Technological Research

The main objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with viscoplastic and plastic material models. In this paper, the problem of convergence and uniqueness of the problem of non-linear simulation of sheet metal forming processes modeled using rigid-viscoplastic material model is considered. In the numerical simulation of the deformation process MFP2D and MFP3D Finite Element programs were used. The simplicity of the algorithm is the main advantage of these codes, the Direct Differentiation method and optimization modules can be implemented in the source code. The numerical instability caused by high values of the condition number of the main system of equations is the main disadvantage of the codes. The penalty approach contact model used in the program makes the stiffness matrix condition number worse.

finite element method, sheet metal forming, computational stability, flow approach

The objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with rigid-viscoplastic and plastic material models. Two numerical codes, MFP2D and MFP3D, were used previously for practical industrial solutions (Sosnowski, 2001; Sosnowski, 1995; Sosnowski et al., 1992). Relative simplicity of both the codes allowed to include “exact” sensitivity calculations by direct differentiation method. This made it possible to perform very effective optimization of the whole sheet metal forming process simulation. One of significant drawbacks of rigid-viscoplastic shell approach is poor stability and convergence due to relatively high values of the condition number of the resulting system of equations. The reasons include the absence of elasticity terms in the constitutive material law and asymptotic character of the relationship between viscosity and effective plastic strain rate. Approximate character of the contact modeling (penalty approach) also affects conditioning of the system. This drawback can be overcome by some measures proposed in this paper.

sheet drawing, flow approach, matrix condition number

In this paper the numerical method for prediction of fatigue life of structure is presented. The fmite element model-ling and damage parameter calculation are based on the algorithm de-scribed originally by Chaboche (1987), Luccioni et al. (1996) and 011er et al. (2005). This al-gorithm is simplified, i.e. the Goodman relationships between the mean and stress amplitude are included. It is extended and applied for simulation of crack propagation in the rotor shaft. The mate-rial constitutive model includes plastic effects and damage. The S—N fatigue func-tions taken from experiment are modi-fied so as to be dependent on the real ratio between minimum and maximum stress in the critical zones. So the coupling between damage, plastic-ity and fatigue is taken into account.

metal fatigue, damage mechanics

The objective of this research is to include mixed friction effects into existing models of hydrodynamic journal bearings described e.g. in [1]. The problem of partial hydrodynamic lubrication caused by roughness of sliding surfaces has been investigated for many years by numerous researchers. But majority of theoretical studies in this field were focused on very fundamental aspects taking into consideration general principles of bearing operation from the viewpoint of flow determination between sliding surfaces of various roughness description. The considerations in this paper are devoted to partial hydrodynamic lubrication effects in typical cylindrical transverse journal bearings applied for supporting of heavy rotor-shafts of the rotating machines. For this purpose there is used the average flow theory for an oil film interaction with rough journals and bushings. In order to carry out a qualitative analysis of the problem a simple mechanical model of the partially lubricated “super-bearing” is assumed. This model consists of the rigid mass rotating with constant speed and performing translational in-plane motion within the non-rotating rigid ring which is elastically suspended in this plane. The rigid mass represents the entire inertia of the rotating parts of the rotor machine and the rigid ring corresponds to the housing of such “super bearing”. Translational in-plane motion of the rigid mass is coupled with translational motion of the rigid ring by means of mass-less springs and dampers representing respectively visco-elastic properties of the oil film in the “super-bearing” with rough sliding surfaces. These visco-elastic properties of the oil film in such bearing are determined by numerical solving of the average Reynolds equation describing partial oil flow between the rough journal and bushing. Here, according to, the pressure flow factors and the shear flow factors standing in the average Reynolds equations are determined analytically using proper empirical formulae obtained by numerical simulations of the model flows between partially lubricated surfaces for various roughness geometry and average oil film thicknesses. Solving in this way the average Reynolds equation for the entire oil gap by means of the finite difference method enables us to determine resultant viscous friction retarding force as well as transverse hydrodynamic load of the bearing. For various roughness geometry the former enables us to determine the frictional power yielded by the bearing and the latter makes possible calculation of stiffness and damping coefficients of the mass-less springs representing visco-elastic properties of the oil film in the assumed model of the “super-bearing”. In the numerical examples numerous roughness amplitudes of the journal and the bushing surface as well as various directional orientations of roughness asperities, which follow from final machining of the journal and the bushing, are taken into consideration in order to investigate their influence on kineto-static and dynamic behaviour of the transverse oil-film bearing. In the next steps of research in this field, beyond the partial lubrication, also the metal-to-metal friction effects are going to be investigated, i.e. for so high loadings of the journal bearing, when the hydrodynamic lubrication theory for the oil film stops to be in force

partial hydrodynamic lubrication, journal bearings, mixed friction effects

W niniejszej pracy rozważamy problem zbieżności i jednoznaczności rozwiązania nieliniowego problemu symulacji procesów tłoczenia blach modelowanych z wykorzystaniem sztywno-lepkoplastycznego modelu materiału. Do symulacji wykorzystujemy programy MFP2D i MFP3D sprawdzone w kilku zastosowaniach przemysłowych. Zaletą obydwóch kodów numerycznych jest względna prostota algorytmu, a co za tym idzie możliwość dokładnej analizy wrażliwości i optymalizacji procesu tłoczenia blach. Niestety oba programy mają poważną wadę związaną z przyjętym modelem materiału. W trakcie obliczeń obserwujemy niestabilność wywołaną stosunkowo wysokim wskaźnikiem uwarunkowania macierzy układu równań. Dodatkowo przyjęty model kontaktu zawierający funkcję kary pogarsza wskaźnik uwarunkowania macierzy sztywności. Celem badań jest między innymi poprawienie tego wskaźnika.

tłoczenie blach, teoria plastycznego płynięcia, wskaźnik uwarunkowania macierzy

In the paper the structural one-dimensional hybrid dynamical model of the entire vibrating rotor-shaft system and the three-dimensional fmite element model of its cracked shaft zone were applied for a fatigue life prediction of the machine faulty segment under coupled bending-torsional-axial vibrations. The steady-state dynamic response amplitudes, obtained by means of the one-dimensional model of the system, have been used for the three-dimensional model as an input data for determination of maximal stresses and stress intensity factors at the crack tip. These quantities together with the Wohler curves enable us an approximate determination of load limits responsible for a probable further crack propagation. By means of the proposed approach one can predict a damage probability of the faulty rotor-shaft system of arbitrary structure operating under various dynamic and quasi-static loads affecting a crack of various sizes and shaft locations. From the investigations performed for various crack axial locations on the shaft with respect to bearing supports of the single- and double-span rotor-shaft systems, it follows that a strength of the cracked zone is much more sensitive to normal stresses due to bending and axial oscillations than to tangential stresses caused by torsional vibrations.

hybrid dynamical mode, vibrating rotor-shaft system, fatigue analysis