1=f Noise in Sliding Friction under Wear Conditions: The Role of Debris M. Duarte, 1 I. Vragovic, 1 J. M. Molina, 1,2 R. Prieto, 1 J. Narciso, 2 and E. Louis 3 1 Departamento de Fı ´sica Aplicada and Instituto Universitario de Materiales, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain 2 Departamento de Quı ´mica Inorga ´nica and Instituto Universitario de Materiales, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain 3 Departamento de Fı ´sica Aplicada, Unidad Asociada del CSIC and Instituto Universitario de Materiales, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain (Received 13 September 2008; published 28 January 2009) It has been shown that the friction force time series in sliding friction under wear conditions is self- similar and has a 1=f power spectrum. Albeit a variety of models, mostly inspired in the field of earthquakes, has been explored, an important factor was overlooked: the role of debris. This Letter describes sliding friction experiments on steel with alumina pins, carried out with and without debris blowing, that prove the role of loose debris in determining the 1=f character of the friction force. A damped-forced harmonic oscillator with two friction terms, one purely random and another inversely proportional to the amount of loose debris, calculated by means of a modified sandpile model, is proposed to describe the dynamics of friction under wear conditions. DOI: 10.1103/PhysRevLett.102.045501 PACS numbers: 62.20.Qp, 05.40.a, 46.55.+d, 89.20.Kk Depending upon the sliding speed and the elastic prop- erties of the experimental device, three regimes have been identified in sliding dynamics [1]: (i) the steady regime characterized by a constant friction force, (ii) a stick-slip regime in which the friction force varies periodically with time, and (iii) stick-slip with a friction force showing irregular fluctuations. Experimental studies indicate that whereas regime (ii) shows up whenever wear effects are weak [2], regime (iii) has been observed in several systems having in common the presence of strong wear effects [3– 6]. In the latter case experiments suggest that the power spectrum of the friction force time series has a 1=f char- acter [3–6]. Earlier theoretical or numerical analyses of this issue triggered a vivid debate [7,8], despite the various features that friction and wear share with earthquakes, phenomena in which self-organized criticality and 1=f noise had been identified [9]. More recently, it was pro- posed to combine a Tomlinson-like and a modified Robin Hood model [4,10] to describe both high and low- frequency regions of the friction force power spectrum. None of these models, however, take into account a key ingredient in sliding friction under wear conditions, namely, debris that are generated at the contact area. The role of debris in sliding friction is well documented [12– 17]. Depending on the system at hand, debris may favor plowing of the worn surface, thus increasing the friction coefficient [13], or form a protective tribolayer [13–17] that decreases friction and subsequently wear. Moreover, if debris are loose [15], they may act as a fluidized bed that also reduces friction. These effects are usually concomi- tant, and which of them predominates depends on the type, morphology, and size of debris. In this Letter we investigate the effects of debris on the power spectrum of the friction force. To this end dry sliding friction experiments were carried out on a pin-on-disc equipment with or without blowing debris. Because of the characteristics of the experimental setup, the sample material (steel) and the pin material (alumina spheres) wear effects are expected to be strong and debris (oxidized iron particles) to be mostly loose. The results show that loose debris are determinant in what concerns the 1=f character of the friction force. Dry friction experiments were carried out in a CSEM instruments pin-on-disk tribometer. Static and dynamic measurements allowed determining the spring constant of the apparatus k ¼ 59 k N=m, and its characteristic fre- quency ! 0 ¼ 92 rad=s, and estimating the average value of the damping constant b ¼ 65 N s=m. Experiments were carried out on samples of SAE 52100 steel, 20 mm in diameter and 5 mm thick, cut from commercial rods and polished. Care was taken to ensure good surface finishing and that the two disc faces were parallel (see Ref. [18] for a discussion of the surface roughness of untested samples and of wear tracks). A container with silica gel was placed close to the sample. Alumina pins (spheres) 6 mm in diameter were used. The sample, in contact with the alu- mina pin, rotates at a fixed speed producing a wear track of average radius 0.5 cm. The friction force versus time FðtÞ was recorded using a data acquisition card controlled by LABVIEW. It was checked that internal machine fluctuations had much smaller amplitude than those of the friction force. Experiments were carried out at applied loads of Q ¼ 5–10 N and sliding speeds of 1–10 cm=s, without or with debris blowing by means of a synthetic air jet (20% O 2 , 80% N 2 , water  3 ppm, and hydrocarbons 0:1 ppm). Debris produced during the experiments were examined visually and by means of scanning electron microscopy (SEM). Almost all debris appeared to be oxi- PRL 102, 045501 (2009) PHYSICAL REVIEW LETTERS week ending 30 JANUARY 2009 0031-9007= 09=102(4)=045501(4) 045501-1 Ó 2009 The American Physical Society