Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 21 (2007) 514–534 Identification of pre-sliding and sliding friction dynamics: Grey box and black-box models K. Worden a,Ã , C.X. Wong a , U. Parlitz b , A. Hornstein b , D. Engster b , T. Tjahjowidodo c , F. Al-Bender c , D.D. Rizos d , S.D. Fassois d a Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK b Drittes Physikalisches Institut, Universita ¨t Go¨ttingen, Bu ¨ rgerstraX e 42-44, D-37073 Go¨ttingen, Germany c Department of Mechanical Engineering Division, K.U. Leuven, P.M.A., Celestijnenlaan 300B, 3001 Heverlee (Leuven), Belgium d Department of Mechanical & Aeronautical Engineering, University of Patras, GR 265 00 Patras, Greece Received 18 April 2005; received in revised form 25 August 2005; accepted 6 September 2005 Available online 8 November 2005 Abstract The non-linear dependence of pre-sliding and sliding friction forces on displacement and velocity is modelled using different physics-based and black-box approaches including various Maxwell-Slip models, neural networks, non- parametric (local) models and recurrent networks. The efficiency and accuracy of these identification methods is compared for an experimental time series where the observed friction force is predicted from the measured displacement and estimated velocity. All models, although varying in their degree of accuracy, show good prediction capability of friction. Finally, it is shown that better results can be achieved by using an ensemble of the best models for prediction. r 2005 Elsevier Ltd. All rights reserved. 1. Introduction Friction is a complex non-linear phenomenon that exists in mechanical systems. It is the result of interactions between two neighbouring surfaces and is dependent on many parameters, such as: surface topography and materials, presence and type of lubrication and relative motion. The friction phenomenon can usually be divided into two operating regimes, pre-sliding friction and gross sliding friction. Pre-sliding friction is largely dependent on the elastic and plastic deformations of asperities. Gross sliding friction is due to the shearing resistance of the asperities. In reality, the transition between these two regimes in the friction process is a continuous one and a good model should reflect this. A more detailed explanation about friction and its many modelling techniques can be found in various works in the literature [1–3]. The problems caused by friction such as limit cycles, tracking error and stick-slip motion have been studied extensively in engineering. This non-linearity (and other usually less severe—or possibly, easier to model— non-linearities, i.e. backlash, motor saturation, etc.) poses a problem in the control of mechanisms that require ARTICLE IN PRESS www.elsevier.com/locate/jnlabr/ymssp 0888-3270/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2005.09.004 Ã Corresponding author. Tel.:/fax: +44 114 222 7758. E-mail addresses: k.worden@sheffield.ac.uk (K. Worden), parlitz@dpi.physik.uni-goettingen.de (U. Parlitz), farid.al-bender@mech.kuleuven.ac.be (F. Al-Bender), fassois@mech.upatras.gr (S.D. Fassois).