Contact problem on the wear of the elastic half-plane by canonical form stamps
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 78, Issue 2
Abstract
The problems of contact interaction of the canonical form stamps (cylindrical, elliptical, hyperbolic) with the elastic half-plane taking into account the wastage of material, are solved. The integral equation, based on the model of abrasive wastage, is made to determine the contact pressure. Numeric methods of solving integral equations of this type are analyzed. The method of solving the integral equation is developed, that reduces the problem to a generalized problem of eigenvalues. Analytical and numerical methods of solving the generalized eigenvalue problem are analyzed and comparative analysis of them is conducted. To find the eigenvalues and vectors the method of Holetskyi and QZ-factorization is applied. The theoretical similarity of this methods and numerical change of eigenvalues with increasing the dimension of input matrix are analyzed. Software for the writing software modules with the possibility of automation process of solving a generalized eigenvalue problem and making contact pressure graphs with variable number of eigenvalue (with different number of range members for the contact pressure), are chosen. To check correctness of obtained eigenvalues, procedure of solving generalized eigenvalue problem was performed in different softwares. On the base of obtained eigenvalues, numerical calculation of contact pressure is hold. An algorithm of finding the contact area at any given moment of time for a given power of pressing the stamp is developed. For fixed moments of time contact area at a given initial force was found. The number of line members for the contact pressure is experimentally found, so that the error can be ignored. An algorithm of bringing to the one scale graphs of contact pressure in different areas of contact was developed and realized. The analysis of the features of its distribution to the various forms of stamps was hold. Graphics of the size of wastage in dimensionless quantities for a given contact area, for a given contact force, are constructed. The size of wastage for different contact areas for different stamps, are analyzed. On the base of the size of wastage the analysis of the wastage process, is hold.
Authors and Affiliations
Yuriy Sachuk, Oleksandr Maksymuk
Keywords
Related Articles
- EP ID EP571394
- DOI -
- Views 55
- Downloads 0
Cyber-physical model of the immunosensor system in a rectangular lattice with the use of lattice difference equations of population dynamics
The article developed a cyber-physical model for immunosensory systems. The main attention is paid to the mathematical description of the discrete dynamics of populations in combination with dynamic logic, which is used...
Structure-forming and destructive role of cracks in life cycle of construction-system [in Ukrainian].
Practically in all build constructions there are active elements in the form of cracks and inner surfaces of partition which predetermine structural changes of material of construction-systems. A driving force of spontan...
The procedure of the specimen loading parameters in fixing video frame of crack profile
Digital videography, which makes it possible to accomplish direct measurements of geometric parameters of the crack profile in real time, finds wide use in experimental fracture mechanics. Practical implementation of vid...
Modeling of the fatigue crack growth after overload-underload in aluminum alloy D16T
Experimental investigations have been carried out and the main regularities of the fatigue crack growth (FCG) have been determined under single overload and complex overload – underload in the alloy D16T. It was found th...
The issue of improve the manufacturability of devices for manipulating by miniature objects
The article discusses the creation of element base micromanipulators that meet certain requirements, such as manufacturability, handheld control, resistance to the adverse effects of the environment and the possibility o...