A Multivariate Control Chart for Autocorrelated Tool Wear Processes

Abstract

Full automation of metal cutting processes has been a long held goal of the manufacturing industry. One key obstacle to achieving this ambition has been the inability to monitor completely the condition of the cutting tool in real time, as premature tool breakage and heavy tool wear can result in substantial costs through damage to the machinery and increasing the risk of non-conforming items that have to be scrapped or reworked. Instead, the condition of the tool has to be indirectly monitored using modern sensor technology that measures the acoustic emission, sound, spindle power and vibration of the tool during a cut. An online monitoring procedure for such data is proposed. Firstly, the standard deviation is extracted from each sensor signal to summarise the state of the tool after each cut. Secondly, a multivariate autoregressive state space model is specified for estimating the joint effects and cross-correlation of the sensor variables in Phase I. Then we apply a distributionfree monitoring scheme to the model residuals in Phase II, based on binomial type statistics. The proposed methodology is illustrated using a case study of titanium alloy milling (a machining process used in the manufacture of aircraft landing gears) from the Advanced Manufacturing Research Centre in Sheffield, UK, and is demonstrated to outperform alternative residual control charts in this application.

A multivariate triple exponentially weighted moving average control chart

“…The smaller the $$ERC$$, the better the performance of the control chart for a range of shifts between $${\delta _{{\rm{min}}}}$$ and $${\delta _{{\rm{max}}}}$$. Note though that the size of the mean shift in standard deviation is determined by the distance from the IC mean vector $${{\bm{\mu }}_0}$$ to the OOC mean vector $${{\bm{\mu }}_1}$$, and can be measured by the non‐centrality parameter $$\delta \ = {( {{{( {{{\bm{\mu }}_1} - {{\bm{\mu }}_0}} )}^{\prime}}{{\bm \Sigma }}_0^{ - 1}( {{{\bm{\mu }}_1} - {{\bm{\mu }}_0}} )} )^{1/2}}\ $$ (see Harris et al 24 …”

“…For more details on multivariate statistical process control, readers are referred to the review paper by Psarakis and Panaretos 18 . Readers are also referred to the papers by Champ and Jones‐Famer, 19 Mahmoud and Maravelakis, 20 Adegoke et al., 21 Haq and Khoo, 22 Sabahno et al., 23 Harris et al 24 . and Katebi and Moghadam 25 for recent developments on multivariate control charts.…”

Tool Wear Condition Monitoring in Milling Process Based on Current Sensors

“…The limitations associated with the single-sensor TCM applications discussed above have generated an increasing interest in multi-sensor TCM [45], [46]. For example, Torabi et al applied the signals obtained from dynamometer, accelerometer, and AE sensors to conduct TCM for a ball nose milling process [47].…”

A novel approach to machining process fault detection using unsupervised learning

“…Several review papers from recent years, including those by Teti et al, 13 Liang et al, 3 O'Donnell et al 16 and Bryne et al, 17 do not explore texts on unsupervised learning; however, they do highlight the issue that training data are expensive and presents a challenge to the production application. Some statistical methods have been applied in a few cases such as multivariate control charts as shown by Harris et al 18 Furthermore, an unsupervised approach was presented by Dou et al 19 that reconstructed monitoring signals from a sparse auto-encoder (SAE), then used the reconstruction error to indicate a change in state of the system due to tool wear.…”