Simulation of a finishing operation : milling of a turbine blade and influence of damping

Milling is used to create very complex geometries and thin parts, such as turbine blades. Irreversible geometric defects may appear during finishing operations when a high surface quality is expected. Relative vibrations between the tool and the workpiece must be as small as possible, while tool/workpiece interactions can be highly non-linear. A general virtual machining approach is presented and illustrated. It takes into account the relative motion and vibrations of the tool and the workpiece. Both deformations of the tool and the workpiece are taken into account. This allows predictive simulations in the time domain. As an example the effect of damping on the behavior during machining of one of the 56 blades of a turbine disk is analysed in order to illustrate the approach potential

Simulation of a finishing operation : milling of a turbine blade and influence of damping

Milling is used to create very complex geometries and thin parts, such as turbine blades. Irreversible geometric defects may appear during finishing operations when a high surface quality is expected. Relative vibrations between the tool and the workpiece must be as small as possible, while tool/workpiece interactions can be highly non-linear. A general virtual machining approach is presented and illustrated. It takes into account the relative motion and vibrations of the tool and the workpiece. Both deformations of the tool and the workpiece are taken into account. This allows predictive simulations in the time domain. As an example the effect of damping on the behavior during machining of one of the 56 blades of a turbine disk is analysed in order to illustrate the approach potential

Quantum Mechanics: Harbinger of a Non-Commutative Probability Theory?

In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to see the structure of quantum processes in terms of non-commutative probability theory, a non-Boolean structure of the implicate order which contains Boolean sub-structures which accommodates the explicate classical world. We move away from mechanical `waves' and `particles' and take as basic what Bohm called a {\em structure process}. This enables us to learn new lessons that can have a wider application in the way we think of structures in language and thought itself.Comment: 20 pages, one figure. Invited pape

Automatic Deduction in Dynamic Geometry using Sage

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagrams constructed with the open source dynamic geometry system GeoGebra are accepted. In this worksheet, Groebner bases are used to either compute the equation of a geometric locus in the case of a locus construction or to determine the truth of a general geometric statement included in the GeoGebra construction as a boolean variable. In the second worksheet, locus constructions coded using the common file format for dynamic geometry developed by the Intergeo project are accepted for computation. The prototype and several examples are provided for testing. Moreover, a third Sage worksheet is presented in which a novel algorithm to eliminate extraneous parts in symbolically computed loci has been implemented. The algorithm, based on a recent work on the Groebner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Detailed examples are discussed.Comment: In Proceedings THedu'11, arXiv:1202.453