A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Feature recognition & tool path generation for 5 axis step-nc machining of free form / irregular contoured surfaces

This research paper presents a five step algorithm to generate tool paths for machining Free form / Irregular Contoured Surface(s) (FICS) by adopting STEP-NC (AP-238) format. In the first step, a parametrized CAD model with FICS is created or imported in UG-NX6.0 CAD package. The second step recognizes the features and calculates a Closeness Index (CI) by comparing them with the B-Splines / Bezier surfaces. The third step utilizes the CI and extracts the necessary data to formulate the blending functions for identified features. In the fourth step Z-level 5 axis tool paths are generated by adopting flat and ball end mill cutters. Finally, in the fifth step, tool paths are integrated with STEP-NC format and validated. All these steps are discussed and explained through a validated industrial component.

Integration of cad/ tool path data for 5-axis step-nc machining of free form / irrregular contoured surfaces

This research paper presents the work on feature recognition, tool path data generation and integration with STEP-NC (AP-238 format) for features having Free form / Irregular Contoured Surface(s) (FICS). Initially, the FICS features are modelled / imported in UG CAD package and a closeness index is generated. This is done by comparing the FICS features with basic B-Splines / Bezier curves / surfaces. Then blending functions are caculated by adopting convolution theorem. Based on the blending functions, contour offsett tool paths are generated and simulated for 5 axis milling environment. Finally, the tool path (CL) data is integrated with STEP-NC (AP-238) format. The tool path algorithm and STEP- NC data is tested with various industrial parts through an automated UFUNC plugin.