Condition Monitoring Methodology for Manufacturing and Design

Part production requires constant monitoring to assure the effective manufacturing of high-quality components. The choice of monitoring methods can become a crucial factor in the decisions made during and prior to manufacturing. In an ideal world, designers and manufacturers will work together to interpret manufacturing and part data to assure the elimination of faults in manufacturing. However, manufacturing still lacks mathematically robust means of interpreting the manufacturing data so that a channel of communication can be established between design and manufacturing. To address part production concerns, we present a systematic methodology to interpret manufacturing data based on signals from manufacturing (e.g., tool vibrations, part surface deviations). These signals are assumed to contain a fingerprint of the manufacturing condition. The method presented in this paper is based on a mathematical transform to decompose the signals into their significant modes and monitor their changes over time. The methodology is meant to help designers and manufacturers make informed decisions about a machine and/or part condition. An example from a milling process is used to illustrate the method's details. BACKGROUND AND MOTIVATION In this paper, we present a method to detect faults and monitor changes during manufacturing. The method extends a mathematical transform, namely, the Karhunen-Lo eve transfor m, to provide a mathematical decomposition of manufacturing signals into their fundamental components. These components are monitored to detect significant stationary and nonstationary changes in the manufacturing fingerprint. The methodology is presented for use by both designers and manufacturers with the purpose of providing an accurate and clear picture of the manufacturing condition. In the following, we begin with an example in manufacturing, then present the steps of a fault detection and monitoring methodology, including a set of guidelines to interpret the results. We then apply the methodology steps and guidelines to an example in manufacturing, namely, the surface condition of parts from a milling process. Engineering Surfaces and Their Analysis The motivation for this work stems from a crucial need in part production to assess the condition of a part and control deviations from the specified design. An important question when manufacturing a component is how to enable the workpiece to work according to the designer' s specifications and goals. The designer has a specific function in mind and the manufacturer has to make sure that the part is produced to satisfy this functionality (Whitehouse, 1994). By gaining an understanding of process variation, the design and manufacturing engineers can work as a team to assess the process capability and determine whether a part will function properly (Zemel and Otto, 1996). To assess the functionality of a workpiece, it is crucial to identify possible deviations and control them. As a first step, it 1 Copyright 1998 by ASME is crucial that we measure and characterize these deviations. Dimensional measurement satisfies part of this need: by measuring the length, area, position, radius, etc., we assure that the workpiece conforms to the designer' s specifications. This step, in turn, ensures that the component will assemble into an engine, gearbox, etc. However, the measurement of the dimensional characteristics of the component is not sufficient to ensure that the workpiece will satisfy its function. To complement the dimensional measurement, surface measurement is used to assure that all aspects of the surface geometry are known and controlled. In other words, if the shape and texture of the component are correct, then it will be able to move at the speeds, loads, and temperatures specified by the designer. As a result, the measurement of the surface characteristics of the component hence becomes a crucial factor in assuring its quality (Whitehouse, 1994). These surface characteristics are typically lumped together in the form of surface texture measurement, which includes the roughness, waviness, and form errors on the component. Roughness refers to irregularities on component surfaces, such as tool marks left on the surface as a result of a milling process, or the marks left on the surface by a grinding process. Waviness refers to irregularities of longer wavelength typically caused by an improper manufacturing condition, such as vibration between the workpiece and the cutting tool. Very long waves are the form errors caused by errors in workpiece table motion, errors in rotating members of the machine, or thermal distortion. The surface texture of a manufactured component provides a “fingerprint” of the machine, process, and part condition (Whitehouse, 1994). The factors which result in one of these three types of errors are often different. As a result, it becomes crucial to accurately decompose the different components of the surface and attempt to understand their nature and potential for damage to the part' s quality (Sottile and Holloway, 1994). In particular, it is important to enable the monitoring of the factors which result in these deviations and determine their severity and originating source so that they can be controlled or eliminated. Traditionally, Statistical Process Control (SPC) is used to measure the process during production, and correlated to a model to understand the sources of variation (Zemel and Otto, 1996). SPC often uses average measures, such as surface roughness and waviness measures, which often fail to provide accurate information about the nature of the surface errors (Whitehouse, 1994; Rohrbaugh, 1993). To overcome this shortcoming, random process analysis tools from the signal processing field are often adapted to the field of surface characterization (Bendat and Piersol, 1986; Whitehouse, 1994; Braun, 1986; Serridge, 1991; Spiewak, 1991). More advanced methods in the research community involve mathematical transforms, such as the wavelet transforms and higher-order spectral transforms (Berry, 1991; Jones, 1994; Rohrbaugh, 1993; Geng and Qu, 1994; Fackrell et al., 1994). The shortcomings of these techniques are provided in (Tumer et al., 1995; Tumer et al., 1997a). Current Focus In our work, we have proposed the use of an alternative transform, namely, the Karhunen-Lo eve transform, for the purpose of condition monitoring in manufacturing (Tumer et al., 1997a; Tumer et al., 1997c; Tumer et al., 1997b). Specifically, we have demonstrated that a fault detection and monitoring method in manufacturing, based on the Karhunen-Lo eve tran sform, provides an accurate decomposition of the fault patterns in manufacturing signals, and a means to monitor any significant changes over time. In this paper, we present the details of this method in the form of steps of a methodology and a set of guidelines for interpretation. The guidelines are based on extensions to the aforementioned method, assuring that the results are clear and easily interpretable for manufacturers and designers. The details of the extensions are not presented in this paper. Instead, the set of guidelines provided contain these extensions in a summarized form. Specifically, the KL-transform-based method is extended for use in manufacturing and design, by assuring that the outputs provide an accurate and physically-meaningful interpretation of manufacturing signals. Our goal is to provide designers and manufacturers with a common means of exchanging accurate information about the manufacturing condition and making informed decisions about the status of the manufacturing process, machine, and part (Eppinger et al., 1995; Zemel and Otto, 1996). A thorough systematic approach in detecting and monitoring faults on manufactured component surfaces, with the purpose of integrating design and manufacturing tasks, does not exist. We believe that the set of specific steps and guidelines based on our method provides an accurate representation of the part surface condition. We also believe that the physical understanding of the fault condition for manufactured parts will help bridge the gap between designers and manufacturers, as well as reduce scrap during manufacturing and reduce the time and money spent to produce a part. KL-Based Detection and Monitoring To analyze and monitor manufacturing signals, the Karhunen-Lo eve (KL) transform decomposes the signals int o completely decorrelated components in the form of empirical basis functions that contain the variations in the original data. An estimate of the original signal is computed using a linear combination of these empirical basis functions and their respective coefficients in the new transform domain. To obtain a KL decomposition of a collection of signals, zero-mean input data are assembled in a covariance matrix, from which the eigenvectors and eigenvalues corresponding to the principal axes of highest variability are computed. These axes correspond to the fundamental modes in the input data, and their corresponding coefficient vectors are used to monitor stationary and nonstationary changes in the fundamental modes. The mathematical details 2 Copyright 1998 by ASME of the method are presented in previous publications by the authors (Tumer et al., 1997a; Tumer et al., 1997b; Tumer et al., 1997c), and are hence not repeated here. The KL transform has been used in many signal processing applications in literature, ranging from the characterization of pictures of human faces (Sirovich and Keefe, 1987), to the analysis of turbulent flow mechanics (Ball et al., 1991). The literature background is described in further detail in (Tumer et al., 1997c; Tumer et al., 1997b; Tumer et al., 1997a). In this work, the transform is applied to signals measured from manufacturing processes, to analyze and quantify the fingerprint indicative of potential errors on part surfaces. The application of the KL transform to manufacturing is rare, limited to multivariate statistical process control (Martin et al., 1996; Zhang et al., 1995), mainly due to the difficulty in obtaining physically-significant outputs. Improvements proposed as a set of guidelines in this paper assure that we will obtain physically-meaningful outputs. Signals and Modes from Manufacturing Signals contain many characteristics which can be categorized either as deterministic or stochastic. An example of a deterministic signal is a periodic waveform (Bendat and Piersol, 1986; Braun, 1986). As opposed to deterministic signals, which can be predicted by known models, stochastic signals require probabilistic statements to describe their structure. Most signals contain a combination of stochastic and deterministic signals, and exhibit either stationary or nonstationary characteristics. Nonstationary characteristics are indicative of a time-varying structure in the data, where the statistical properties vary with time. Nonstationary signals, which can be regarded as deterministic factors operating on otherwise stationary random processes (Bendat and Piersol, 1986; Box et al., 1994), are difficult to predict, and often cause difficulties in the detection of otherwise predictable modes. In this work, we focus on signal types that are encountered typically in manufacturing processes. Most manufacturing processes generate periodic waveforms that are indicative of many potential error sources. Examples are the tool marks from a turning process, feed marks from a milling process, or roller chatter marks from a Selective Laser Sintering process (Tumer et al., 1998; Tumer et al., 1997b). Stationary or nonstationary changes in these periodic waveforms can be indicative of potential or already existing faults in the machine or material. Furthermore, the appearance of additional periodic components (e.g., harmonics) can be indicative of inherent errors in the manufacturing machine. In addition, component surfaces may contain linear trends such as slopes and offset changes due to impulsive forces during machining (e.g., surface hardness variations, chip breakage, and tool wear). As a result, in this work, we focus on periodic and linear trends, and their stationary and nonstationary changes in the presence of high-variability stochastic noise. Depth of Cut Spindle Workpiece Feed Tool Holder