C. Steve Suh

Interpretation of crack-induced rotor non-linear response using instantaneous frequency

Instantaneous frequency was introduced to describe the dependency of frequency components on time for non-stationary signals. A powerful alternative to the Fourier-based spectral analysis that provides insufficient resolution for the temporal progression of all frequency components, the concept of instantaneous frequency has rarely been applied to machine monitoring and diagnosis. The confusing fact that instantaneous frequencies determined could occasionally be negative and the associated amplitudes could be infinite for certain types of vibration signals inevitably limits the adaptability of the concept to fault detection as a result. Significant insight into the applicability of instantaneous frequency is gained through re-examining the fundamentals upon which the concept was first defined. It is found that the Hilbert-transform-based definition of instantaneous frequency is applicable only to signals of monocomponent, thus implying the need for separating a multicomponent signal into its monocomponent subsets. Misuse of the definition to multicomponent signals would result in the individual instantaneous frequency associated with each inherent monocomponent being averaged and thus obscure the underlying characteristics of the signal. A mathematically complete decomposition scheme effective in resolving a multicomponent signal into an orthogonal space spanned by its intrinsic monocomponents is explored. Several examples are considered to show that the scheme not just enables the removal of the difficulties commonly encountered in applying instantaneous frequency but also imparts valid renditions to the interpretation of fault-induced bifurcation and dynamic instability.

Ultrafast Laser-Induced Elastodynamics in Single Crystalline Silicon Part I: Model Formulation

The various responses of a silicon wafer excited by a femtosecond pulsed laser are investigated. A multi-time scale axisymmetric model that governs the transport dynamics in silicon is presented based on the relaxation-time approximation of the Boltzmann equation. Temperature-dependent multi-phonons, free-carrier absorptions, and the recombination and impact ionization processes are considered using a set of balance equations. The mechanical response of the lattice is described by momentum equations. To solve the model of 17 coupled time-dependent partial differential equations without having to be concerned with non-physical oscillations in the solution, an implicit finite difference scheme on a staggered grid is developed. The staggered finite difference scheme allows velocities and first-order spatial derivative terms to be calculated at locations midway between two consecutive grid points, and shear stresses to be evaluated at the center of each element. A multi-time-scale approach involving the use of varying time steps ranging from 5 fs to 5 ps is implemented to successfully obtain time integration results up to 10 ns.

On the nonlinear features of time-delayed feedback oscillators

Abstract An alternative approach to using phase plots, bifurcation diagrams, or Fourier analysis for characterizing the various responses displayed by time-delayed feedback oscillators of both autonomous and non-autonomous types is presented. The alternative employs the fundamental notion of instantaneous frequency to describe characteristics innate to periodic, quasi-periodic and chaotic motions in response to varying positive feedback and forcing parameters. Simultaneous periodicity-modal aberrations are seen to precede the birth of new modes, which explicitly signifies the inception of bifurcation. Modes thus defined in the context of instantaneous frequency are obtained using a separation scheme referred to as the empirical mode decomposition and thus, by definition, they are also an orthogonal set of intrinsic monocomponents each retaining the physical features inherent to the motions being studied.

Ultrafast Laser-Induced Elastodynamics in Single Crystalline Silicon Part II: Near-Field Response

The multi-time scale ultrafast laser model of axisymmetric geometry presented in Part I is validated with computed carrier densities and melting thresholds that agree well with published physical data. Transport phenomena initiated by femtoseconds heating including the spatial and temporal evolutions of electron and lattice temperatures and electron-hole carrier density are highly localized in both time and space. The temporal and spatial scales associated with the generation of thermal stress waves are significantly larger at tenths of nanoseconds and microns, respectively. Ultrashort laser pulse induced transverse stress waves are highly dispersive and characteristically of broadband, low amplitude, and extremely high frequency and power density contents. Near-field responses that precede the development of a full-blown plate wave are also localized in space with a power density magnitude on the order of 1013 Watts per cubic meters in volume.

Multi-dimensional time-frequency control of micro-milling instability

Micro-milling is inherently unstable and chattering with aberrational tool vibrations. While the time response is bounded, however, micro-milling can become unstably broadband and chaotic in the frequency domain, inadvertently rendering poor tolerance and frequent tool damage. A novel simultaneous time-frequency control theory is applied to negate the various nonlinear dynamic instabilities including tool chatter and tool resonance displayed by a multi-dimensional, time-delayed micro-milling model. The time and frequency responses of the force and vibration of the model agree well with the experimental results published by Jun et al. A multi-variable control scheme is realized by implementing two independent controllers in parallel to follow a target signal representing the desired micro-milling state of stability. The control of unstable cutting at high spindle speeds ranging from 63,000 to 180,000 rpm and different axial depth-of-cuts are investigated using phase portrait, Poincaré section, and instantaneous frequency (IF). The time-frequency control scheme effectively restores dynamic instabilities, including repelling manifold and chaotic response, back to an attracting limit cycle or periodic motion of reduced vibration amplitude and frequency response. The force magnitude of the dynamically unstable cutting process is also reduced to the range of stable cutting.

Machining Dynamics Involving Whirling Part II: Machining Motions Described by Nonlinear and Linearized Models

The nonlinear model presented in Part I is linearized and numerically evaluated to investigate the impact of linearization on interpreting turning dynamics. As described in Part I, the equations of motion are so derived that the motion of the workpiece machining surface is in the plane orthogonal to the spindle axis and the motion of the tool is along the axis and coupled with the machining surface. The nonlinear 3D model is linearized about an operating point at (0, 0, Z 0), where zt = Z 0 is the equilibrium location of the tool associated with the (x 2 = 0, y 2 = 0) position of the workpiece. The (0, 0, Z 0 ) operating point is selected to satisfy the ultimate machining goal for always achieving precise workpiece geometry without surface error and waviness. Taylor series expansion about the operating point is applied to linearize the nonlinear equations of motion. Modifications are also made to the nonlinear tool stiffness term and the cutting force to minimize linearization errors. The mass and stiffness of the workpiece remain functions of time after the modifications are performed. Numerical results show that the linearized model underestimates tool vibrations in the time domain and overestimates system behavior in the frequency domain; whereas the nonlinear model agrees with the physical results reported in the literature in describing machining stability and chatter.

On Controlling Milling Instability and Chatter at High Speed

Risk assessment is one of the main pillars of the framework directive and other directives in respect of health and safety. It is also the basis of an effective management of safety and health as it is essential to reduce work-related accidents and occupational diseases. To survey the hazards eventually present in the workplaces the usual procedures are i) gathering information about tasks/activities, employees, equipment, legislation and standards; ii) observation of the tasks and; iii) quantification of respective risks through the most adequate risk assessment among the methodologies available. From this preliminary evaluation of a welding plant and, from the different measurable parameters, noise was considered the most critical. This paper focus not only the usual way of risk assessment for noise but also another approach that may allow us to identify the technique with which a weld is being performed.In this paper, we present two Partial Least Squares Regression (PLSR) models for compressive and flexural strength responses of a concrete composite material reinforced with pultrusion wastes. The main objective is to characterize this cost-effective waste management solution for glass fiber reinforced polymer (GFRP) pultrusion wastes and end-of-life products that will lead, thereby, to a more sustainable composite materials industry. The experiments took into account formulations with the incorporation of three different weight contents of GFRP waste materials into polyester based mortars, as sand aggregate and filler replacements, two waste particle size grades and the incorporation of silane adhesion promoter into the polyester resin matrix in order to improve binder aggregates interfaces. The regression models were achieved for these data and two latent variables were identified as suitable, with a 95% confidence level. This technological option, for improving the quality of GFRP filled polymer mortars, is viable thus opening a door to selective recycling of GFRP waste and its use in the production of concrete-polymer based products. However, further and complementary studies will be necessary to confirm the technical and economic viability of the process.

Elasto-Viscoplastic Response of Silicon to Femtosecond Laser Heating at Elevated Temperature

The elasto-viscoplastodynamics of single-crystalline silicon in response to femtosecond laser pulsing at elevated temperature is studied. Hyperbolic energy transport dynamics is considered in conjunction with the Haasen–Sumino constitutive law to explore the thermo-elasto-visco-plastic response of the silicon material subjected to ultrafast optical heating. A computational scheme with staggered-grids is developed to time-integrate the coupled thermal-mechanical responses of silicon wafer at annealing temperatures up to 1,100 K. Non-thermal melting fluence threshold is examined favorably against published physical data. The elasto-viscoplastic response at high annealing temperature is characterized by thermal stress waves that propagate with increased oscillation amplitude and modified frequency spectrum. It is shown that the induced transverse and longitudinal displacements along with the normal stress components all establish well-defined relations with temperatures, suggesting that they may be utilized for the thermometric profiling of silicon wafers undergoing Rapid Thermal Processing (RTP) with desired thermal resolution.

ELASTO-VISCOPLASTIC WAVE THERMOMETRY FOR SINGLE CRYSTALLINE SILICON PROCESSING

Laser-induced stress wave thermometry (LISWT) is a non-contact thermal diagnostic technique for the rapid thermal processing (RTP) of silicon wafers using laser-generated, ultrasonic, dispersive stress waves. The required knowledge base for establishing LISWT as a viable alternative to current pyrometric technology for temperature measurement up to 1000°C with ±1°C resolution is presented. A 3D elasto-viscoplastic wave model is developed for describing wave behaviors from being elastic to viscoplastic subject to the RTP annealing temperature ranging from room temperature to exceeding 1000°C. The model is a system of nine coupled first-order hyperbolic equations formulated based on the kinematics of elasto-plastic deformation, conversion of linear momentum and a temperature-dependent viscoplastic constitutive law for single crystalline silicon derived from the material models developed by Hassen–Sumino and Tsai. The group velocity of the wave propagating in silicon wafer is a nonlinear function of temperature. As nonlinearity becomes prominent at high temperature for high frequency components, low frequency components are preferably exploited to achieve the desired thermal resolution at high temperature.

Machining Dynamics Involving Whirling Part I: Model Development and Validation:

A complex machining model describing the coupled tool—workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut and workpiece whirling due to material imbalance is presented. The workpiece is modeled as a system of three rotors, namely, unmachined, being machined and machined, connected by a flexible shaft, thus enabling the motion of the workpiece relative to the tool and tool motion relative to the machining surface to be three-dimensionally established as functions of spindle speed, depth-of-cut, rate of material removal and whirling. A rich set of nonlinear behaviors of both the tool and workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various depth-of-cuts is observed. Results presented herein agree favorably with physical experiments reported in the literature. It is found that, at and up to certain ranges of depth-of-cuts, whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. Additionally, contrary to ones intuition, whirling is found to have insignificant impact on tool motions.