英文原文 Case StudyTheoretical and practical aspects of the wear of vane pumpsPart A. Adaptation of a model for predictive wear calculationAbstract The aim of this investigation is the development of a mathematical tool for predicting the wear behaviour of vane pumps uscd in the standard method for indicating the wcar charactcristics of hydraulic fluids according to ASTM D 2882/DIN 51389. The derivation of the corresponding mathematical algorithm is based on the description of the combined abrasive andadhesive wear phenomena occurring on the ring and vanes of the pump by the shear energy hypothesis, in connection withstochastic modelling of the contacting rough surfaces as two-dimensional isotropic random fields. Starting from a comprehensive analysis of the decisive ring-vane tribo contact, which supplies essential input data for the wear calculation, the computational method is adapted to the concrete geometrical, motional and loading conditions of thetribo system vane pump and extended by inclusion of partial elastohydrodynamic lubrication in the mathematical modej. For comparison of the calculated wear behaviour with expenmental results, a test series on a rig described in Part B was carried out. A mineral oil-based lubricant without any additives was used to exclude the influence of additives which cannot be described in the mathematical model. A good qualitative correspondence between calculation and experiment regarding the temporal wear progress and the amount of calculated wear mass was achieved.Keywords: Mathematical modelling; Simulation of wear mechanisms; Wear testing devices; Hydraulic vane pumps; Elastohydrodynamic lubrication;Surface roughness1. Introduction In this study, the preliminary results of a newmethodological approach to the development of tribo- meters for complicated tribo sysLems are presented. The basic concept involves the derivation of a mathematical algofithm for wear calculation in an interactive process with experiments, which can be used model of the tribo system to be simulated. In this way, an additional design tool to achieve the correlation of the wear rates of the model and original system is created. The investigations are performed for the Vickers vane pump V104 C usedin the standard method forindicating the wear characteristics of hydraulic fluids according to ASTM D 2882/DIN 51 389. In a first step, a mathematical theory based on the description of abrasive and adhesive wear phenomena by the shear energy hypothesis, and including stochastic modelling of the contacting rough surfaces, is adapted to the tribological reality of the vane pump, extended by aspects of partial elastohydrodynamic lubrication and verified by corresponding experiments. Part A of this study is devoted to the mathematical modelling of the wear behaviour of the vane pump and to the verification of the resulting algorithm; experimental wear investigations represent the focal point of Part B, and these are compared with the results of the computational method derived in Part A.2. Analysis of the tribo contact The Vickers vane pump V 104 C is constructed as a pump for constant volume flow per revolution. The system pressure is led to the bottom side of the 12 vanes in the rotor slots to seal the cells formed by each pair of vanes, the ring, the rotor and the bushings in the tribologically interesting line contact of the vane and inner curvature of the ring (Fig. 1). Simultaneously, all other vane sides are stressed with different and periodically alternating pressures of the fiuid. A comprehensive structure and stress analysis based on quasistatic modelling of all inertial forces acting on the pump, and considering the inner curvature of the ring, the swivel motion of the vanes in relation to the tangent of curvature and the loading assumptions, is described in Refs. 1-3. Thereby, a characteristic graph for the contact force Fe as a function of the turn angle can be obtained, which depends on the geometry of the vanes used in each run and the system pressure. From this, the inner curvature of the ring can be divided into four zones of different loading conditions in vane-ring tribo contact (Fig. 2), which is in good agreement with the wear measurements on the rings: in the area of maximum contact force (zone n), the highest linear wear could be found 2,3 (see also PartB).3. Mathematical modelling3.1. Basic relations for wear calculation The vane and ring show combined abrasive and adhesive wear phenomena (Fig. 3). The basic concepts of the theory for the predictive calculation of such wear phenomena are described in Refs. 4-6. Starting from the assumption that wear is caused by shear effects in the surface regions of contacting bodies in relative motion, the fundamental equation (1)for the linear wear intensity Ih in the stationary wear state can be derived, which contains the specific shear ener