Abstract
The paper deals with a mathematical model that simulates the random occurrence of events during cutting processes by milling. The evolution of certain parameters that typify the cutting processes depends on predictable and non-predictable variables. In this context, either the material hardness that varies in different sides of billet, or cutting depth, can act as non-predictable variables. In order to design a response in terms of cutting parameters to non-predictable variations of inputs, a simulation of such phenomena is very useful. A mathematical model that generates random events, both in terms of non-uniform frequency and intensity is here described. A virtual instrument built in LabVIEW generates (pseudo) random events based on a combination of random numbers, as the evolution of the simulated process to be much like a real one. Furthermore the user of virtual instrument can generate himself events at certain moments and of certain intensity. This can be a useful tool to study the algorithms of designing the response which should re-balance the process within adaptive control systems.
Highlights
The cutting processes are supposed to be deterministic ones, that is the input is predictable, and the output depends on input according to a certain function
Many options are available for the user of this software tool, so he can describe in different ways the evolution of a process affected by random events
Calibrating an adaptive control systems is a difficult task, because a mathematical model has to be developed in order design correctly the reaction that has to be provided to an unbalanced process that was affected by an unpredictable event, in order to re-balance it, to bring it under control again
Summary
The cutting processes are supposed to be deterministic ones, that is the input is predictable, and the output depends on input according to a certain function (e.g. the cutting torque is a function of feed-rate). Occurrence of random events, as variation of input parameters that are supposed to be constant, have a bad influence on cutting output, and they have to be balanced by acting on controllable inputs. To design the correct reaction to a random event occurred during cutting process, a simulated evolution of input is needed to save resources. In [2] are described by means of simulation the possible effects of small probabilities (10-6) Random signals and their influence in opposition with deterministic signals in the electrical domain, in terms of collecting, transmitting and processing information are described in [3]. That encouraged the work to build a simulation model of the random events occurred during the cutting processes
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