Control charts based on models derived from differential equations



The development of technical processes over time can often be adequately modelled by means of differential equations. In order to monitor such processes, control charts may be derived from stochastic models based on such differential equations. In this work, this is demonstrated for a deep-hole drilling process used for producing holes with a high length-to-diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances classified as either chatter vibration or spiraling. For chatter, a differential equation for the drilling torque and a model known to well approximate processes with similar characteristics are used to set up monitoring procedures. For spiraling a control chart can be based on a statistical model for the spectrum of the structure-born vibrations derived from a differential equation for the deflection of the boring bar. Copyright © 2010 John Wiley & Sons, Ltd.