Transient processes occurring in electrochemical machining that lead to stationary, self-similar or other modes, are considered. These modes can apply to a part of the surface during a process for a limited time. The problem is formulated as a Hele-Shaw problem. Special high-precision numerical-analytical methods are developed for its solution The singularities of the solution are removed by representing it by the sum of a known function that includes the singularities and an unknown function without singularities. The unknown functions are determined by splines and a Schwarz integral.
The modication of statement of electrochemical formation problem is oered for mathematical modelling of the precision technologies. As an example the process of cutting with a plate electrode-tool is considered. For the description of the technologies with high localization of the processes a stepwise function of current eciency is used. It realizes for simulation of the anode dissolution process in passivating electrolytes under short impulse current. This function determines the movement rate of the anode boundary in the areas of an active electrochemical dissolution and also it denes the boundaries of the areas where dissolution is absent. The stationary and limiting-stationary machining problems are formulated and solved on the base of the oered model. The limiting model describes the maximum localization process. The stationary problem is characterized by the presence of anode surface part, on which the current density is equal to a critical value. Investigations in the whole range of ratio of the maximal and critical values of electrical eld strength on the anode surface are carried out.
In order to increase data reliability, between two and four methods may be used to solve the same problem, with the results being compared. An estimation of the error in every method must be found. The paper offers a mathematical model for the unobservable component of the error, which may be caused by various factors (for example, software implementation). This gives a numerical characteristic of certainty. The main assumption is that the errors from the different methods may be considered as independent random quantities. Moreover, the probability density of the error has a single maximum at zero. In connection with the indeterminacy of the probability densities, the worst case distribution functions (leading to maximum error probability) must be found. An estimate is obtained of the probability of the existence of an error greater than some given value, under the condition that the results coincide up to the accuracy of the computations.
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