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Threaded fastenings are a common assembly method, accounting for over a quarter of all assembly operations. Threaded fastenings are popular because they permit easy disassembly for maintenance, repair, relocation and recycling. Screw insertions are typically carried out manually and are a difficult problem to automate. As a result there is very little published research on automating threaded fastenings, and most research on automated assembly focus on the peg-in-hole assembly problem. This paper investigates the problem of automated monitoring of the screw insertion process. The monitoring problem deals with predicting the integrity of a threaded insertion, based on the torque vs. insertion depth curve generated during the insertion. The authors have developed an analytical model to predict the torque signature signals during self-tapping screw insertions. However, the model requires parameters on the screw dimensions and plate material properties, and some of these parameters are difficult to obtain. This paper presents a study on on-line parameter estimation during screw fastenings. A methodology for estimating the friction properties and screw-diameter during a general self-tapping screw insertion process is presented. It is shown that friction and screw-diameter required by the model can be reliably estimated on-line. Computer simulation results, with and without simulation noise are presented to validate the estimation procedure.