Abstract
This paper considers the modelling of extreme-capability working platforms that are operated in periodic cycles, each cycle having a predefined number of operations that affect the working surfaces. A novel hypothesis is introduced about the platform-degrading effects that cause an equivalent decrease in the successful operations after repeated cycles. Deterministic modelling, based on the basic equations of Lanchester and Dinner, is generalized here to include coupling between parameters. The newly developed mathematical model of performance degradation is in good agreement with both experimental measurements and numerical simulations. It is assumed that the new variables and their correlations link the Gaussian distribution and the observed performances of the testing platforms. Relative probability dispersions of affected surfaces are derived, as a new indirect referencing figure of merit, to describe simulations and compare them to experimental test data. The model proves a hypothesis that the degrading effects are a function of the platform capacity, frequency of operations and the number of available cycles. Degradation effects are taken into account through an equivalent decrease of effective operation capacities, reflected on the properties of the affected operating surfaces. The obtained estimations of degradation could be used in the planning of platform capacity as well as in the selection of real affected surfaces in various machining systems and for a wide range of different materials.
Highlights
Machines operating in cycles and their properties have not been studied in depth in literature and, as such, are not well described by integral mathematical models
If the effects of their operation are actions on the given working surfaces under given constraints, the quality of the affected surfaces can be described by reliability functions
Platform capacities and cycles performances presented in Table 1 are used for simulation testing, as well as in experimental modelling
Summary
Machines operating in cycles and their properties have not been studied in depth in literature and, as such, are not well described by integral mathematical models. If the effects of their operation are actions on the given working surfaces under given constraints, the quality of the affected surfaces can be described by reliability functions In this manner, the operating capabilities of the platform can be determined. A majority of the published papers use a standard approach to the measured performances that depend on the machine’s designed purposes. Such processes are described in [1] to [3] for the abrasive flow machines (AFM) with which material is hardened by randomly treating the working surface with abrasive particles with polymeric fillers, and dispersed within the flow media. There is no mathematical modelling of the process
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