Wear 269 (2010) 339–343 Contents lists available at ScienceDirect Wear journal homepage: www.elsevier.com/locate/wear Determining the coefficient of friction between solids without sliding S. Reina a , R.J.H. Paynter b , D.A. Hills b , D. Dini a,∗ a Department of Mechanical Engineering, Imperial College London, South Kensington Campus, Exhibition Road, SW7 2AZ London, United Kingdom b Department of Engineering Science, University of Oxford, Parks Road, OX1 3PJ Oxford, United Kingdom article info Article history: Received 22 May 2009 Received in revised form 23 March 2010 Accepted 15 April 2010 Available online 2 May 2010 Keywords: Friction Partial Slip Sliding Quadratic Programming Fretting Test abstract A novel method for measuring the interfacial coefficient of friction between two solids which avoids sliding is described, and sample results are given. The technique makes use of the fact that a carefully controlled sequence of partial slip states between contacting bodies may be used to produce relative motion whose extent is a strong function of the coefficient of friction. It is argued that this approach induces much less surface damage in the components, and therefore yields a value for the coefficient of friction which is much more representative of their unmodified condition. © 2010 Elsevier B.V. All rights reserved. 1. Introduction It is truism in physics that quantities cannot be measured with- out changing them; a voltmeter draws current; the insertion of a load cell in a load path introduces compliance, and so forth. Sim- ilarly, the coefficient of friction is normally measured by sliding solids pressed together, and the process of sliding normally causes significant surface modification, and hence a change in the coef- ficient of friction. It could be argued that conducting tests under an even lower normal force, and extrapolating back to zero would circumvent the problem, but this presumes that the coefficient of friction is truly load independent, and it may be desirable to mea- sure its value at representative contact pressures. One situation where a really detailed knowledge of the value of the coefficient of friction is important, and sliding in the prototype is absent, is the stationary contact suffering partial slip, or fretting. It may seem a contradiction in terms to measure the coefficient of friction with- out sliding the bodies, but this is not so, and a careful exploitation of the phenomenon of partial slip may reveal the value of the coef- ficient of friction. One attempt at this has already been made by Pasanen et al. [1], who used visible evidence of surface damage caused by slip to measure the extent of the slip annulus in a Cat- taneo [5] type experiment. Previous attempts to infer the friction from the hysteretic response of contact pairs subjected to partial slip include the work by Fouvry and co-workers (see e.g. [2]). Other ∗ Corresponding Author. Tel.: +44 0 2075947242; fax: +44 0 2075947023. E-mail address: d.dini@imperial.ac.uk (D. Dini). authors have developed techniques for estimating the slip zone fric- tion coefficient from a measured mean value for different contact configurations [3,4]. In this paper completely different quantitative evidence is used to deduce the coefficient of friction. The experiment utilises the same apparatus employed at Oxford and elsewhere to investigate fretting fatigue, but it might, potentially, be executed with a sim- pler single actuator machine, as will become clear. Fig. 1 shows an idealisation of the apparatus, and its key features. The basic idea is to induce a cyclic set of loads which alternately inject a slip region into one end of the contact and abstract it at the other, so that, after each cycle of loading, there is, potentially, a net rigid body move- ment of the indenter. In many respects the idea was foreshadowed by Dundurs and Comninou [6] in a paper where they describe drag- ging a rug over the floor by injecting a ‘ruche’ or dislocation at one end which may emerge at the other. Although, in principle, a wide range of different loading histories might be exploited, to reduce the number of possibilities which might be investigated the fol- lowing was chosen: first, the indenter is pressed into contact by a normal force, P, so as to produce contact over a strip of half-width a, and where the contact pressure distribution, p(x), taken as positive when compressive, is given explicitly by the usual Hertz formula: p(x) =-p o  1 - (x/a) 2 where p o = 2P a . (1) A shear force, Q, insufficient to cause sliding, is then applied and held constant. A bulk tension, , is now developed, and it is assumed that this varies cyclically between limits  max and  min where, for reasons of ensuring stability of the specimen, we would prefer the latter to be positive. The question we now ask is whether there is 0043-1648/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2010.04.017