Analytical prediction of chatter stability for variable pitch and variable helix milling tools

Regenerative chatter is a self-excited vibration that can occur during milling and other machining processes. It leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Variable pitch and variable helix milling tools have been previously proposed to avoid the onset of regenerative chatter. Although variable pitch tools have been considered in some detail in previous research, this has generally focussed on behaviour at high radial immersions. In contrast there has been very little work focussed on predicting the stability of variable helix tools. In the present study, three solution processes are proposed for predicting the stability of variable pitch or helix milling tools. The first is a semi-discretisation formulation that performs spatial and temporal discretisation of the tool. Unlike previously published methods this can predict the stability of variable pitch or variable helix tools, at low or high radial immersions. The second is a time-averaged semi-discretisation formulation that assumes time-averaged cutting force coefficients. Unlike previous work, this can predict stability of variable helix tools at high radial immersion. The third is a temporal-finite element formulation that can predict the stability of variable pitch tools with a constant uniform helix angle, at low radial immersion. The model predictions are compared to previously published work on variable pitch tools, along with time-domain model simulations. Good agreement is found with both previously published results and the time-domain model. Furthermore, cyclic-fold bifurcations were found to exist for both variable pitch and variable helix tools at lower radial immersions

Regenerative block empirical likelihood for Markov chains

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method cannot be directly applied on the data but rather on blocks of consecutive data catching the dependence structure. Generalization of empirical likelihood based on the construction of blocks of increasing nonrandom length have been proposed for time series satisfying mixing conditions. Following some recent developments in the bootstrap literature, we propose a generalization for a large class of Markov chains, based on small blocks of various lengths. Our approach makes use of the regenerative structure of Markov chains, which allows us to construct blocks which are almost independent (independent in the atomic case). We obtain the asymptotic validity of the method for positive recurrent Markov chains and present some simulation results

Index to NASA Tech Briefs, 1975

This index contains abstracts and four indexes--subject, personal author, originating Center, and Tech Brief number--for 1975 Tech Briefs

Diffusional Electrochemical Catalytic (EC’) Mechanism Featuring Chemical Reversibility of Regenerative Reaction-Theoretical Analysis in Cyclic Voltammetry

We consider theoretically a specific electrochemical-catalytic mechanism associated with reversible regenerative chemical reaction, under conditions of cyclic staircase voltammetry (CSV). We suppose scenario in which two electrochemically inactive substrates “S” and “Y”, together with initial electrochemically active reactant Ox are present in voltammetric cell from the beginning of the experiment. Substrate “S” selectively reacts with initial electroactive reactant Ox and creates electroactive “product” Red (+ Y) in a reversible chemical fashion. The initial chemical equilibrium determines the amounts of Ox and Red available for electrode transformation at the beginning of the electrochemical experiment. Under conditions of applied potential, the electrode reaction Ox(aq) + ne– ⇋ Red(aq) occurs, producing flow of electric current. Under such circumstances, the chemical reaction coupled to the electrochemical step causes a regeneration of initial electroactive species during the time-frame of current-measuring segment in CSV. The features of cyclic voltammograms get significantly affected by the kinetics and thermodynamics of reversible regenerative reaction. We elaborate several aspects of this specific electrode mechanism, and we focus on the role of parameters related to chemical step to the features of calculated voltammograms. While we provide a specific set of results of this particular mechanism, we propose methods to get access to relevant kinetic and thermodynamic parameters relevant to regenerative chemical reaction. The results elaborated in this work can be valuable in evaluating kinetics of many drug-drug interactions, but they can be relevant to study interactions of many enzyme-substrate systems, as well. This work is licensed under a Creative Commons Attribution 4.0 International License

A method for analyzing the performance aspects of the fault-tolerance mechanisms in FDDI

The ability of error recovery mechanisms to make the Fiber Distributed Data Interface (FDDI) satisfy real-time performance constraints in the presence of errors is analyzed. A complicating factor in these analyses is the rarity of the error occurrences, which makes direct simulation unattractive. Therefore, a fast simulation technique, called injection simulation, which makes it possible to analyze the performance of FDDI, including its fault tolerance behavior, was developed. The implementation of injection simulation for polling models of FDDI is discussed, along with simulation result