Disjointed sum of products by a novel technique of orthogonalizing ORing

This work presents a novel combining method called ‘orthogonalizing ORing $\bigcirc\!\!\!\!\!\!\vee $’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, axioms and rules for this linking technique are also defined which have to be considered getting correct results. Additionally, a novel equation, based on orthogonalizing ORing, is set up for orthogonalization of every Boolean function of disjunctive form. Thus, disjointed Sum of Products can be easily calculated in a mathematical way by this equation.

Application of a Transfer Function, Obtained by Variation Principles for a Steam Turbine Journal Failure Analysis Based on “DOE” and Optimization Techniques

There are many engineering situations where is not necessary to analyze whole domain of a physical model. According with these situations we demonstrate that is possible, with a transfer matrix and variation principles, to obtain an equivalent bilinear form using Lax-Milgram theorem with an orthogonal form applied to turbomachinery. This transfer matrix solves a problem in shorter time than the Traditional DOE-FEA (design of Experiments) (Finite Element Analysis) Method. In this method we consider a solution sub-space that contents generalized forces in a given location and maximum displacements in other location of the same domain, which may cause a failure, Kij = a(vhj*,uhi) is the transfer matrix, with a small range. The coefficients in matrix are obtained by n runs, (where n is the number of variables to be consider), with FEA, applying unitary forces in n directions. With the Traditional DOE-FEA method, FEA runs require great computational efforts because this method shall need 2n runs, on the basis of this fact, this proposal can be 75 and up to 99% (n/2n) shorter in time to obtain the transfer function and apply it into the FEA than the Traditional DOE-FEA method. Analysis in short time helps to confront many fields’ problems. In this paper we will analyze the case of a steam turbine journal, where was possible to find the amount of the limit loads that cause its failure, under prescribed displacements.