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 Green's 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.

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.

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.

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.

Analysis of peridural scar formation and its prevention after lumbar laminotomy and discectomy in dogs

STUDY DESIGN

Peridural fibrosis after lumbar laminectomy and discectomy has been implicated (not proven) as one of the factors that contribute to continuing or recurrent radicular and/or low back pain. This animal experimental study was designed to unequivocally show the stages in the development of scar tissue and to what extent, if any, scar tissue development is influenced by interposing fat grafts and Na hyaluronate of different molecular weights.

METHODS

A four-level unilateral lumbar laminotomy, anular fenestration, and nucleotomy was performed in 11 dogs. In each dog, levels were selected at random: one to serve as an empty control and three to insert the following: a fat graft, a viscous (1.9%) solution of Na hyaluronate, and a 1% high molecular weight solution of Na hyaluronate solution. The animals were killed at 1 day, 2 days, and 1, 2, 4, and 12 weeks postoperatively. Immediately after the dogs were killed, the lumbar spines were frozen in situ with dry ice, the lumbar spines were harvested and sectioned with a cryomicrotome. Close-up photographs taken at submillimeter intervals at each level were digitized and postprocessed with a computer.

RESULTS

In the early postoperative period a hematoma was found in the pathway of the surgical dissection. During a 2-4 week period, this hematoma was replaced by a thick, white fibrotic tissue mass. Fibrosis was markedly less pronounced at the hyaluronate levels, especially the high molecular weight subset. Two-way statistical analysis of variance without replications revealed significantly less scar formation at the 0.05 level in the hyaluronate vs. the control segments. Dunnett's test, comparing each group individually with the control, revealed no difference between the fat groups and the control subjects. There was a significant difference between 1.9% Na hyaluronate and control.

CONCLUSIONS

Viscous hyaluronate solution with its semifluid properties coats the nerve roots and dura anteriorly and posteriorly and reduces peridural fibrosis in the critical anterior region where adhesions form between the nerve root and anulus fibrosus.

Image Enhancement: A Data Dependent Systems Approach

A new image enhancement scheme based on a mathematical model obtained by data dependent systems (DDS) approach is described in this paper. A separable 2-D AR model is fitted to the image. Analysis of this model leads to the identification of modes corresponding to dominant physical features. Other intrinsic modes, inherent to the image, are highly damped and constitute difficult-to-interpret local image behavior. Although exerting a minor influence on the image intensities, they hinder a clear perception of the image. In order to enhance the image, these modes must be filtered out. ARMA image enhancement filters are formed using the major inherent modes. Residuals, the part of the image not modeled by this ARMA filter, comprise the enhanced image. This approach can also be used to selectively enhance the desired image features. Examples illustrating clear enhancement of a real image, with natural degradations created by shadows and other artifacts as well as artificially added noise, are given.

Signature of Machine Tool Errors on Surface Texture by DDS

The dynamic effect of machine tool errors leaves its signature on machined surfaces. This paper proposes an application of data dependent systems (DDS) methodology to recover this signature from the surfaces in a comprehensive manner and provides a realistic basis for machine-tool acceptance. The approach is illustrated by experimental results from three different lathes. It is shown that relative contributions due to the feed wavelength reveal the dynamic performance of the machine tools. The deviation from the nominal and the spread of the estimated feed wavelength quantify the accuracy and rigidity, the feed wavelength being precisely maintained with minimal spread in a machine tool with high accuracy and high rigidity. Presence of other wavelengths and their relative contribution to the RMS surface roughness serve as quantitative indicators of other machine tool errors.

Verification of On-Line Computer Control of EDM by Data Dependent Systems

A new method of computer control of electro-discharge machining based on Data Dependent Systems (DDS) methodology has been recently proposed. The control is based on a parameter which effectively represents the resistance of arc and is isolated by the DDS model from the random current and voltage signals in spite of the large noise. This paper presents an experimental verification to show that this parameter indeed represents the arc resistance which cannot be measured by any other means and that the parameter is quite sensitive to the change from beneficial sparking condition to the harmful arcing condition. Off-line analysis of the EDM process under different conditions is presented with this parameter as the response variable. Development of the control strategy using the results of this analysis is illustrated. Implementation of the strategy by means of a Motorola microcomputer is described. A comparison of metal removal rate (MRR), surface roughness, and tool wear for the computer control and the optimal manual adjustment recommended by the EDM machine manufacturer is presented. It shows that the computer control yields an increase in the MRR of 47 percent and 19 percent, while the ratio of tool wear to MRR reduces by 26 percent and 16 percent, respectively, in finishing and roughing conditions.

Formation and Ejection of EDM Debris

This paper presents a theoretical and experimental investigation into the debris formation and ejection mechanism. An expression for the size of a debris particle is derived using the drop formation energy and the kinetic energy of the ejected debris particle. The velocity of the ejected particle is obtained from expressions derived on the basis of the analysis of hydrodynamic propagation of shock waves generated due to electrical breakdown in dielectric. The debris particles were collected by machining AISI 1020 steel under various operating conditions. The projected areas were measured by a microscope following the standard procedure of particle size measurement. The particle size has been found to be log normally distributed. The experimental values of debris size compare well with the theoretical estimation indicating the validity of the proposed analysis.

Data-Dependent Systems Approach to Surface Generation in Grinding

This paper initiates a new approach to the analysis of surface generation, by fitting mathematical models to wheel and work surface profiles under actual grinding conditions. Data Dependent Systems (DDS) methodology has been used to model work surface profiles in the longitudinal (across the width of cut) and transverse (along the direction of feed) directions, and the wheel profile along the longitudinal direction. A model for the “characteristic grain” consisting of the superimposition of a large and small wavelength is used to provide an indication about the grain-wear and surface roughness. The large wavelength representing the grain has been used in establishing the deflection of the grain. Due to the elastic deflection, the small wavelength representing the cutting edges cuts a smaller groove, which provides a prediction of the rms value of the ground surface in the transverse direction. From the wavelength decomposition of longitudinal profiles, the superimposition of components due to topography of the wheel and kinematic conditions have been identified. The mechanism that leads to such a superimposition is analyzed. Experimental verification of the theory and predictions is given.

Quantitative Expressions for Some Aspects of Surface Integrity of Electro Discharge Machined Components

An on-line adaptive control of the Electrical Discharge Machining (EDM) process needs proper quantitative relationships between output parameters and input variables of the process. This paper presents an attempt to develop mathematically simple expressions for the depth of cracks, the depth of damaged layer, and the depth of martensitic layer in terms of pulse duration and current. The transient temperature distribution developed by Data Dependent Systems analysis of the EDM process is used in obtaining thermal stress expressions. The hypothesis that the cracks are the consequence of thermal stresses exceeding the fracture level leads to the expression for the depth of occurrence of cracks. The estimation of the thickness of martensitic layer is based on the phase transformation temperature isothermal obtained from the temperature distribution. A simple expression for the depth of the damaged layer is also obtained using the experimental conclusions reported in the literature. Regression equations suitable for the on-line adaptive control of the EDM process are developed. The theoretical estimates are compared with the experimental measurements.

Echocardiogram processing and classification using data-dependent systems analysis

This paper presents results of a study on M-mode echocardiogram analysis and classification using the recently developed data-dependent system (DDS) methodology along with clustering techniques. Results of thirty clinically obtained waveforms yielded a correct classification rate of between 83% and 90%, depending on the features used for clustering. The choice of features was facilitated, in part, by a study of six hypothetical waveforms representing an echocardiogram in transition from normal to stenosed. The DDS approach offers potential in the identification and recognition of various cardiac abnormalities, based on echocardiographic data. A comparison with Fourier analysis confirmed the results and points to the advantages of DDS in (a) minimizing false negatives and (b) providing additional features for improved discrimination.

A Data Dependent Systems Strategy of On-Line Tool Wear Sensing

An indirect method of tool wear sensing and critical wear detection is suggested. It is based on the Data Dependent Systems (DDS) modeling of vibrations from an accelerometer mounted on the tool holder at a safe distance away from the cutting process. The DDS provides an estimate of the tool acceleration component, sensitive to wear alone, at the natural frequency of the tool confirmed by impulse response testing. This acceleration decreases at the beginning, approaches a minimum at the critical wear, and increases again, much the same way as a rate of wear curve. The trend remains unchanged under different cutting conditions, although the actual values change. Based on this finding, an on-line tool wear sensing strategy is proposed, verified by a confirmation experiment and supplemented by a block diagram of microprocessor implementation.

A Data Dependent Systems Approach to Dynamics of Surface Generation in Turning

A new investigative approach to metal cutting dynamics is proposed based on wavelength decomposition of surface roughness by data dependent systems (DDS). This approach distinguishes from the commonly used Fourier transform analysis. It is shown to be capable of throwing light on both macroscopic and microscopic aspects of cutting mechanics. Workpiece surfaces from turning experiments, changing only speed and only feed, are used to illustrate that the macro-effects of cutting conditions and vibrations can be related to RMS components due to large wavelengths of a few tenths of mm magnitude. In particular, the so-called Spanzipfel effect is accounted for and its RMS is derived. It is also shown that wavelengths of a few micrometer magnitude, estimated from the workpiece surface roughness, seem to provide an independent estimate of chip surface lamellar widths in micro-morphology, well in agreement with earlier investigations.

Crater Geometry and Volume From Electro-Discharge Machined Surface Profiles by Data Dependent Systems

This paper applies a recently developed methodology called Data Dependent Systems to model and analyse the process of Electro-Discharge Machined (EDM) surface generation. A first order stochastic differential equation is developed and physically interpreted from the EDM surface profile measurements under varying pulse duration and machining time. The impulse response function of this model is used to define a characteristic crater geometry. The depth and diameter to depth ratio of such a crater is determined and employed in deriving the radius of curvature and the volume. Experimental measurements are utilized to illustrate the development of regression equations and nomograms, useful in practice to obtain surfaces with desired geometry. It is shown that the depth diameter to depth ratio, and volume of the characteristic craters obtained from actual multiple discharge situation under operating conditions agree fairly well with the past single discharge physics investigations.

Data Dependent Systems Approach to Stochastic Tool Life and Reliability

A Data Dependent Systems approach is outlined for obtaining tool life distribution and reliability models directly from shop floor and/or laboratory failure data. The approach does not require any a-priori knowledge of the distribution and can be used with a limited amount of data. Estimation of the first order model is illustrated by application to HSS tools in turning. The tool life signatures at three different speeds are exhibited in the form of plots of hazard rate, reliability and failure time probability density functions. Formulation of simple tool replacement strategies from these plots by the shop personnel is illustrated; the mathematical expressions given for these functions can be used to develop more elaborate optimal strategies in computerized adaptive control. It is shown that most of the commonly used tool life distributions are well approximated by special cases of the first order model and hence are included in the approach.

A New Approach to the Analysis of Machine-Tool System Stability Under Working Conditions

A new stochastic approach is developed in this paper for analyzing the machine-tool system stability under working conditions. Mathematical models are fitted to the relative longitudinal cutter-workpiece displacement data recorded under different cutting conditions during the face-milling operation on a milling machine. The stability of the system is judged from the characteristic roots of these models. The variation in stability is examined versus both the cutting speed and the feed, and good results are obtained. It is shown that not only the dynamic but also the static stability can be ascertained. Furthermore, the stability of subsystems can also be determined. The significance of these results is discussed with special reference to on-line chatter control. The analysis of vibration signals produced by similar but evenly and unevenly spaced face milling cutters is presented as a vindication of the new approach.

Stochastic Geometry of Anisotropic Random Surfaces With Application to Coated Abrasives

This paper analyses the stochastic geometry of anisotropic random surfaces. Explicit expressions are derived for computing three-dimensional surface spectral moments from two-dimensional profile spectral moments. A new approach for obtaining good estimates of profile spectral moments from digitized measurements is presented. Application to actual data on five profiles of coated abrasive papers illustrates that the procedure is simple, efficient, and statistically optimal and is applicable to any type of homogeneous surface. Some typical characteristics of coated abrasive surface geometry such as the density of summits, the maximum slope, and the principal direction are calculated and their physical interpretations are explained.

A Stochastic Approach to Characterization of Machine Tool System Dynamics Under Actual Working Conditions

The machine tool dynamics is evaluated under actual working conditions by using a time series technique. This technique develops mathematical models from only one signal, viz., the relative displacement between the cutter and the workpiece. Analysis of the experimental data collected on a vertical milling machine indicates that the new methodology is capable of characterizing the machine tool structure and the cutting process dynamics separately. Furthermore, it can also detect and quantify the interaction between these two subsystems.

Stability of Random Vibrations With Special Reference to Machine Tool Chatter

Static and dynamic stabilities of self-excited random vibrations are investigated in terms of the differential equation and time series model for the vibrational signal. Various instabilities are demarcated in the parameter space of the time series model, so that the stability of random vibrations can be ascertained by locating the parameters obtained from the vibration data. These results are applied to machine tool chatter by analyzing tool point vibrations in a turning operation under different degrees of chatter. This analysis substantiates the theoretical investigation, which is further confirmed by resonance curves obtained for the workpiece and cutting tool.

Modeling Machine Tool Chatter by Time Series

Machine tool chatter is formulated as self-excited random vibration with white noise forcing function. The formulation takes into account the unknown factors and random disturbances present in the cutting process when chatter occurs. Based on this formulation, a procedure for modeling chatter using the time series of sampled observations on vibration signals is developed. Feasibility of this procedure is established by modeling data obtained from a turning operation under conditions of severe chatter.

Characterization of Abrasive Tools by Continuous Time Series

A succinct characterization of abrasive tools using continuous time series is developed. It is based on three parameters: natural frequency ωn, damping factor ζ, and variance γ0. These parameters can be readily interpreted in terms of the visual records. The interpretation, along with the effects of the physical constituents on the parameters, is discussed and illustrated for profiles of 8 grinding wheels, with different grit size, hardness, and structure.