Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Third order nonlinear optical studies in europium naphthalocyanine using degenerate four wave mixing and Z-scan

Third order nonlinear susceptibility χ(3) and second hyperpolarizability (γ) of a bis-naphthalocyanine viz. europium naphthalocyanines, Eu(Nc)2, were measured in dimethyl formamide solution using degenerate four wave mixing at 532 nm under nanosecond pulse excitation. Effective nonlinear absorption coefficient, βeff and imaginary part of nonlinear susceptibility, Im(χ(3)) were obtained using open aperture /Z-scan technique at the same wavelength. Optical limiting property of the sample was also investigated. The role of excited state absorption in deciding the nonlinear properties of this material is discussed.

Simultaneous determination of nonlinear optical and thermo-optic parameters of liquid samples

The authors apply the theory of photothermal lens formation and also that of pure optical nonlinearity to account for the phase modulation in a beam as it traverses a nonlinear medium. It is used to simultaneously determine the nonlinear optical refraction and the thermo-optic coefficient. They demonstrate this technique using some metal phthalocyanines dissolved in dimethyl sulfoxide, irradiated by a Q-switched Nd:YAG laser with 10 Hz repetition rate and a pulse width of 8 ns. The mechanism for reverse saturable absorption in these materials is also discussed.

Nonlinear Optical Properties of Organic and Polymer Systems

Present thesis has discussed the design and synthesis of polymers suitable for nonlinear optics. Most of the molecules that were studied have shown good nonlinear optical activity. The second order nonlinear optical activity of the polymers was measured experimentally by Kurtz and Perry powder technique. The thesis comprises of eight chapters.The theory of NLO phenomenon and a review about the various nonlinear optical polymers has been discussed in chapter 1. The review has provided a survey of NLO active polymeric materials with a general introduction, which included the principles and the origin of nonlinear optics, and has given emphasis to polymeric materials for nonlinear optics, including guest-host systems, side chain polymers, main chain polymers, crosslinked polymers, chiral polymers etc.Chapter 2 has discussed the stability of the metal incorporated tetrapyrrole molecules, porphyrin, chlorin and bacteriochlorin.Chapter 3 has provided the NLO properties of certain organic molecules by computational tools. The chapter is divided into four parts. The first part has described the nonlinear optical properties of chromophore (D-n-A) and bichromophore (D-n-A-A-n-D) systems, which were separated by methylene spacer, by making use of DPT and semiempirical calculations.Chapter 4: A series of polyurethanes was prepared from cardanol, a renewable resource and a waste of the cashew industry by previously designed bifunctional and multifunctional polymers using quantum theoretical approach.Chapter 5: A series of chiral polyurethanes with main chain bis azo diol groups in the polymer backbone was designed and NLO activity was predicted by ZlNDO/ CV methods.In Chapter 7, polyurethanes were first designed by computational methods and the NLO properties were predicted by correction vector method. The designed bifunctional and multifunctional polyurethanes were synthesized by varying the chiral-achiral diol compositions

Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Nonlinear Analysis of Shear Dominant Prestressed Concrete Beams using ANSYS

This study reports the details of the finite element analysis of eleven shear critical partially prestressed concrete T-beams having steel fibers over partial or full depth. Prestressed T-beams having a shear span to depth ratio of 2.65 and 1.59 that failed in shear have been analyzed using the ‘ANSYS’ program. The ‘ANSYS’ model accounts for the nonlinearity, such as, bond-slip of longitudinal reinforcement, postcracking tensile stiffness of the concrete, stress transfer across the cracked blocks of the concrete and load sustenance through the bridging action of steel fibers at crack interface. The concrete is modeled using ‘SOLID65’- eight-node brick element, which is capable of simulating the cracking and crushing behavior of brittle materials. The reinforcement such as deformed bars, prestressing wires and steel fibers have been modeled discretely using ‘LINK8’ – 3D spar element. The slip between the reinforcement (rebars, fibers) and the concrete has been modeled using a ‘COMBIN39’- nonlinear spring element connecting the nodes of the ‘LINK8’ element representing the reinforcement and nodes of the ‘SOLID65’ elements representing the concrete. The ‘ANSYS’ model correctly predicted the diagonal tension failure and shear compression failure of prestressed concrete beams observed in the experiment. The capability of the model to capture the critical crack regions, loads and deflections for various types of shear failures in prestressed concrete beam has been illustrated.