Sudhakar M. Pandit

Application of data dependent systems approach for evaluation of fracture modes during a single-grit scratching

Brittle fracture and the associated material removal mechanisms in model brittle materials were investigated using single-grit scratch experiments. The objective was to develop a fundamental understanding of the mechanisms of brittle material removal during machining (e.g., grinding) processes and mathematically describe the induced topological features. Initial experiments were conducted on metals and the ductile material removal response was captured in the form of smooth lenticular shaped scratch trace and a smooth semi-sinusoidal force profile. Scratch experiments on model brittle materials, namely, Homalite-100 and Pyrex glass, revealed intermittent material removal patterns and oscillatory force profiles. In Homalite, material removal occurred in periodic bursts with the size of the burst proportional to the instantaneous depth of cut, and accordingly the force profiles reflected periodic oscillations. In Pyrex glass, the material removal occurred in random bursts at irregular intervals and accordingly the force profiles reflected irregular/random force oscillations. To further characterize the nature of material removal process, the experimentally obtained force data were analyzed using data dependent systems (DDS) approach. The analysis revealed that the physical features of the induced damage in the scratch groove are effectively captured in the respective Greens functions. Based on the energy contributions arising from the characteristic roots of the DDS models, a brittleness measure, that characterizes the propensity for brittle fracture in ceramics, has been proposed. This measure can be used in more complex machining situations for on-line monitoring of the nature of material removal process.

Data-dependent systems methodology for noise-insensitive phase unwrapping in laser interferometric surface characterization

Phase unwrapping recovers the actual surface topography from a calculated phase map, which is often degraded by a combination of surface defects and measurement noise. Prevalent unwrapping techniques are unable to differentiate between the surface and noise-created discontinuities, resulting in an improper surface recovery. In our approach the stochastic nature of the phase map is used by the data-dependent systems (DDS) methodology to separate the surface from noisy measurements. The DDS methodology identifies an adequate autoregressive moving-average model representing the measured phase values. An adaptive thresholding scheme carries out the phase discontinuity removal from the model residuals, employing statistical outlier detection. We then recover the surface by using the model and clean residuals. The proposed technique is found useful for unwrapping especially noisy and degraded phase maps.

Variation in friction coefficient with tool wear

Abstract The acceleration component resulting from flank wear alone is isolated from vertical tool vibration signals collected by an accelerometer mounted safely away from the cutting process. The friction force and friction coefficient are computed from this component to show that they decrease at the initial stages of wear, reach a minimum near the critical wear, and increase again. Empirical models are proposed and estimated with the computed values. The importance of these models in predicting the coefficient in the hazardous region of large wear, from data collected in the safe region below critical wear, is delineated. Possible mechanisms for this behavior based on the current theories of friction and wear are discussed.

Data-dependent-systems and Fourier-transform methods for single-interferogram analysis

Results of wave-front phase detection obtained from a spatial method based on data-dependent-systems (DDS) methodology are compared with those obtained from the Fourier-transform method. DDS is a novel approach that extends and improves the way the stochastic autoregressive moving-average models are obtained and interpreted. The methodology is robust to noise influence and insensitive to the errors commonly associated with the Fourier transform. Both the Fourier-transform and the DDS methods use one interference pattern, and both offer means for filtering out disturbances such as noise and background variations. We present a brief review of the two methods to compare them theoretically, and then we describe their experimental implementation. The methods were applied to the same interferometric data sets, and the results are presented and compared to discuss relative advantages and disadvantages. In particular, it is shown that the DDS method preserves the detailed surface texture because a convolution of the component that represents the surface dynamic aspect with the component that corresponds to the independent and dynamic-free aspect is able to recover the original details. In contrast the Fourier-transform method smooths such details to an extent that depends on the subjective choice of filters.

Comparison of Fourier-transform and data-dependent system profilometry by use of interferometric regeneration

Fourier-transform profilometry (FTP) and data-dependent system profilometry (DDSP) are the two major phase-extraction methods that use a single interferogram. The difficulty in verifying surface profiles obtained by these methods is that the exact spot on an actual surface cannot be measured with two different instruments. An interferogram regeneration procedure is developed to solve this problem. The surface profile is then extracted from the regenerated interferogram by both FTP and DDSP. Comparisons of the actual surface profile with the extracted surface profiles show that both methods perform equally well in measuring the root mean square and the center line average, but only DDSP is able to reproduce the detailed surface profile of the reference surface.

Fault detection and prognosis of assembly locating systems using piezoelectric transducers

Fixture faults have been identified as a principal root cause of defective products in assembly lines; however, there exists a lack of fast and accurate monitoring tools to detect fixture fault damage. Locating fixture damage causes a decrease in product quality and production throughput due to the extensive work required to detect and diagnosis a faulty fixture. In this paper, a unique algorithm is proposed for fixture fault monitoring based on the use of autoregressive models and previously developed piezoelectric impedance fixture sensors. The monitoring method allows for the detection of changes within a system without the need for healthy references. The new method also has the capability to quantify deterioration with respect to a calibrated value. Deterioration prognosis can then be facilitated for structural integrity predictions and maintenance purposes based on the quantified deterioration and forecasting algorithms. The proposed robust methodology is proven to be effective on an experimental setup for monitoring damage in locating fixtures. Fixture wear and failure are successfully detected by the methodology, and fixture structural integrity prognosis is initiated.

Interferogram analysis based on the data-dependent systems method for nanometrology applications.

A spatial method of wave-front phase detection from an interferogram is presented. The method uses data-dependent systems methodology, an approach that extends and improves the way the stochastic autoregressive moving average models are obtained and interpreted. Its application to interference data addresses the fundamental problem of recovering the self-coherence function commonly used to retrieve the wave-front phase. The self-coherence function is efficiently computed by means of a complex autoregressive model and is used for surface reconstruction. The method is shown to be robust and suitable for surface testing. The correspondence of the data-dependent systems methodology and its physical meaning as related to the classical interferometry are presented. The theoretical development is illustrated by experimental implementation, with the results obtained from one- and two-dimensional interferometric fringe analysis of a computer hard disk.

Deterministic and Stochastic Separation of Digital Images

Abstract The digital image of a scene is composed of patterned and textured regions, which are separated by boundaries or edges. This paper presents a three stage approach to separating the regions which constitute the structural or deterministic component of the image and the textures which constitute the stochastic part of the image. The data dependent system methodology is extended to the boundary value problem, to achieve time (space) and frequency localization on the image data. The peculiarity of this approach is that it identifies each texture as one entity, as opposed to conventional approaches which give rise to a number of edgelets for each texture in the image. The first stage generates a mathematical characterization of the image using the intrinsic spatial dependencies of the image intensities. The dynamics of the image intensities is characterized by the Greens function of the adequate model. The components of intensities unexplained by the Greens function are captured in the model residuals. These residuals contain both boundary values and noise. Boundary values occur at the outlier residual locations and are nonzero only at the region boundaries. In the second stage a linear regression that minimizes the stochastic part of the model is used to estimate the boundary values, which are measures of edge strength. The third stage involves the deterministic and stochastic reconstruction of the image, which demonstrates the structural and textural separation of the image. Convolution of boundary values with Greens function gives the structural component, whereas convolution of white noise with Greens function produces the textural component of the image. The results show excellent structural textural separation in addition to large data reduction capability.

Data-dependent systems profilometry of two-dimensional surfaces

Fourier-transform profilometry (FTP) and data-dependent systems profilometry (DDSP) are two methods that are available for recovering one-dimensional fine surface profiles from the phase of a single interferogram. FTP has already been extended to two-dimensional surfaces; a similar extension of DDSP is introduced here. Inasmuch as this extension involves autoregressive modeling of the rows or columns of an interferogram, the feasibility of using a common model order is explored. The common order reduces not only the amount of computation but also the errors caused by the heterodyned phase-removal procedure. As autoregression requires masking the first few data values, the length of the mask is determined by means of a Greens function. A comparison shows that DDSP outperforms FTP in roughness measurements in terms of rms and center-line average. The comparison also shows that DDSP is able to recover a detailed surface, whereas FTP outlines only the global features. An interferogram regeneration procedure provides a reference surface for the verification of results.

Prediction of surface roughness and wavelength with progress of cut in grinding

Abstract The topography of a grinding wheel was modeled as a convolution of random waves of large wavelength for the grain and of small wavelength for the cutting edges. The superimposition of these two waveforms gives the “characteristic grain”. On the basis of these concepts, expressions for the roughness and wavelengths, taking into account elastic deflection, were derived for the ground surface along the longitudinal and transverse directions. The fracture and attritious wear mechanisms were used to introduce separate wear rates for the grains and the cutting edges with the progress of cut. These wear rates were used in developing expressions for the roughness and wavelength of the surface generated with the subsequent cuts. Given the wheel type and dressing conditions, predictions obtained from these expressions were validated with the experimental results.