In-process grinding monitoring by acoustic emission

This work aims to investigate the efficiency of digital signal processing tools of acoustic emission signals in order to detect thermal damages in grinding process. To accomplish such a goal, an experimental work was carried out for 15 runs in a surface grinding machine operating with an aluminum oxide grinding wheel and ABNT 1045. The acoustic emission signals were acquired from a fixed sensor placed on the workpiece holder. A high sampling rate data acquisition system at 2.5 MHz was used to collect the raw acoustic emission instead of root mean square value usually employed. Many statistics have shown effective to detect burn, such as the root mean square (RMS), correlation of the AE, constant false alarm (CFAR), ratio of power (ROP) and mean-value deviance (MVD). However, the CFAR, ROP, Kurtosis and correlation of the AE have been presented more sensitive than the RMS.

Neural network detection of grinding burn from acoustic emission

An artificial neural network (ANN) approach is proposed for the detection of workpiece `burn', the undesirable change in metallurgical properties of the material produced by overly aggressive or otherwise inappropriate grinding. The grinding acoustic emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors that appear to be suitable for ANN processing. Two feature vectors are represented: one concerning band power, kurtosis and skew; and the other autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified on the basis of hardness and profile tests after grinding. The trained neural network works remarkably well for burn detection. Other signal-processing approaches are also discussed, and among them the constant false-alarm rate (CFAR) power law and the mean-value deviance (MVD) prove useful.

In-process grinding monitoring through acoustic emission

This work aims to investigate the efficiency of digital signal processing tools of acoustic emission signals in order to detect thermal damages in grinding processes. To accomplish such a goal, an experimental work was carried out for 15 runs in a surface grinding machine operating with an aluminum oxide grinding wheel and ABNT 1045 Steel as work material. The acoustic emission signals were acquired from a fixed sensor placed on the workpiece holder. A high sampling rate data acquisition system working at 2.5 MHz was used to collect the raw acoustic emission instead of the root mean square value usually employed. Many statistical analyses have shown to be effective to detect burn, such as the root mean square (RMS), correlation of the AE, constant false alarm rate (CFAR), ratio of power (ROP) and mean-value deviance (MVD). However, the CFAR, ROP, Kurtosis and correlation of the AE have been presented more sensitive than the RMS. Copyright © 2006 by ABCM.

Fuzzy logic to predict thermal damages of ground parts

One of the critical problems in implementing an intelligent grinding process is the automatic detection of workpiece surface burn. This work uses fuzzy logic as a tool to classify and predict burn levels in the grinding process. Based on acoustic emission signals, cutting power, and the mean-value deviance (MVD), linguistic rules were established for the various burn situations (slight, intermediate, severe) by applying fuzzy logic using the Matlab Toolbox. Three practical fuzzy system models were developed. The first model with two inputs resulted only in a simple analysis process. The second and third models have an additional MVD statistic input, associating information and precision. These two models differ from each other in terms of the rule base developed. The three developed models presented valid responses, proving effective, accurate, reliable and easy to use for the determination of ground workpiece burn. In this analysis, fuzzy logic translates the operator's human experience associated with powerful computational methods.

The mean value concept in mono-linear regression of multi-variables and its application to trace studies in geosciences

IEECAS SKLLQG

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

A mean value for pairs of integrals

Se prueba que para dos funciones continuas reales, una determinada ecuación posee solució única. Se presenta también una generalización a integrales con peso.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.