Automated Planning And Optimization of Machining Processes a Systems Approach
Automated Planning And Optimization of Machining Processes a Systems Approach
Krishna Challa
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Hence, it is converted to a * chance constraint' of the form PrfT > tj^} 2 a. where a is chosen depending on the degree of assurance with which the tool life constraint is desired to be satisfied. It is obviously in- convenient to handle the tool life constraint in its probabilistic form directly. If the probability distribution of the tool life is known, the constraint can be transformed into a more convenient form by using the properties of the distribution. The foregoing inequality can be re...written as Pr {- ^^^^ > — } > a 27 vhere E(T) and a_ are the mean and standard deviation of the tool life respectively. Let K be K }- a a where e is the standardized variate of the distribution. Using this notation, Pr{i^-Effl->K . >■» life constraint can thus be expressed as t, - E(T) o^ -^« T Substituting for t- and transforming, ^dep '^wid L C' TV ^j y
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