Dressing monitoring with a digital signal processor

Grinding is a finishing process in machining operations, and the topology of the grinding tool is responsible for producing the desired result on the surface of the machined material The tool topology is modeled in the dressing process and precision is therefore extremely important This study presents a solution in the monitoring of the dressing process, using a digital signal processor (DSP) operating in real time to detect the optimal dressing moment To confirm the monitoring efficiency by DSP, the results were compared with those of a data acquisition system (DAQ) and offline processing The method employed here consisted of analyzing the acoustic emission and electrical power signal by applying the DPO and DPKS parameters The analysis of the results allowed us to conclude that the application of the DPO and DPKS parameters can be substituted by processing of the mean acoustic emission signal, thus reducing the computational effort

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Evaluating residues and integrals through negative dimensional integration method (NDIM)

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.

Tool condition monitoring of aluminum oxide grinding wheel in dressing operation using acoustic emission and neural networks

The grinding operation gives workpieces their final finish, minimizing surface roughness through the interaction between the abrasive grains of a tool (grinding wheel) and the workpiece. However, excessive grinding wheel wear due to friction renders the tool unsuitable for further use, thus requiring the dressing operation to remove and/or sharpen the cutting edges of the worn grains to render them reusable. The purpose of this study was to monitor the dressing operation using the acoustic emission (AE) signal and statistics derived from this signal, classifying the grinding wheel as sharp or dull by means of artificial neural networks. An aluminum oxide wheel installed on a surface grinding machine, a signal acquisition system, and a single-point dresser were used in the experiments. Tests were performed varying overlap ratios and dressing depths. The root mean square values and two additional statistics were calculated based on the raw AE data. A multilayer perceptron neural network was used with the Levenberg-Marquardt learning algorithm, whose inputs were the aforementioned statistics. The results indicate that this method was successful in classifying the conditions of the grinding wheel in the dressing process, identifying the tool as "sharp''(with cutting capacity) or "dull''(with loss of cutting capacity), thus reducing the time and cost of the operation and minimizing excessive removal of abrasive material from the grinding wheel.