Friction Noise of Rough Surfaces

When two solids with rough surfaces are rubbed against each other, a distinctive friction sound known as roughness noise is produced. If we examine the contact at the microspic level, we observe the asperities Examining the contact at the microscopic scale reveals that the peaks of surface asperities can strike the asperities of the opposing surface. These impacts trigger vibrations within the solids, which in turn can radiate sound into the surrounding air. Roughness noise is a typical example of phenomenon which involves the dynamics of multicontact interfaces.

The following experiment is designed to measure the empirical laws of roughness noise versus: roughness of surfaces, material of solids, sliding speed and contact area.

The friction sound is found to have an increasing level with both, roughness of surfaces and sliding speed. The following figures show an example of empirical laws obtained with our experiment.

The sound pressure level is observed to follow a logarithmic relationship with roughness and sliding speed. If we denote by \( Lp\) the sound pressure level, \(Ra\) the roughness, and \(V\) the sliding speed, they are related by

The most intriguing question is not whether the sound follow a power law but rather if it is possible to predict the value of the exponents \(n\) and \(m\) by a statistical approach. This question is more difficult than it appears at first sight. For instance, we should say that the induced sound power \(P\) depends on both the number \(n\) of impacts per second and the energy \(\epsilon\) transmitted during each impact with \( P = N\epsilon \). But the rate of impact is proportional to the sliding speed \(V\) while the energy of impact is proportional to the square of the sliding speed \(\epsilon \propto V^2\). Substituting gives \(P \propto V^3\) and therefore \(Lp = 10 \log_{10} (P) + \text{cste} = 20 \log_{10} V^{3/2} + \text{cste} \) that is \(n=3/2\), far, very far from our best experimental value \(n \approx 3/4\).

1. H. Ben Abdelounis, A. Le Bot, J. Perret-Liaudet, H. Zahouani. An experimental study on roughness noise of dry rough flat surfaces, Wear, vol. 268, pages 335-345, 2010.

2. B. Stoimenov, S. Maruyama, K. Adachi, K. Kato, The roughness effect on the frequency of frictional sound, Tribology International, vol. 40, p. 659-664, 2007.

Take some sugar lumps and rub them on a large surface like a wood table for instance. Do you think that the friction sound will be stronger with a larger number of sugar lumps? Definitely yes (try it!). If the number of lumps is multiplied by ten, then the sound is ten times much stronger (10 dB/decade).

But if you do again the experiment on a drum, you will observe that the sound is almost constant and does not depend on the number of lumps (do it!). This is an illustration of the fact that the sound power is not proportional to contact area.

Friction sound does not depend on the number of sugar lumps on a drum membrane.

4. A. Le Bot, E. Bou Chakra and G. Michon. Dissipation of vibration in rough contact, Tribology Letters, vol. 41, pages 47-53, 2011.

Curiously, the dependence of friction sound with the contact area (in fact the number of sliders with same nominal area) is not proportional. Two regimes are found. For small contact area, the proportionality applies (slope ~10 dB/decade). In this regime, the sound produced by sliders is added explaining the linear law. But for large area, the sound is constant and does not depend on the number of sliders (slope ~0 dB/decade). This is a strange result since there is apparently no reason for which the additivity of sound would no longer apply.

3. A. Le Bot and E. Bou Chakra. Measurement of friction noise versus contact area of rough surfaces weakly loaded, Tribology Letters, vol. 37, pages 273-281, 2010.

The direct numerical simulation of the sliding of deformable rough surfaces is possible in principle but very difficult in practice. The size of surface asperities being of order of micrometer, the number of contacts per second is very large and a very large computer is required to perform these computations. We did it and we observed that micro-impacts occurring in the interface generate vibration of surfaces which, in turn, is responsible for the sound.

In this first video, we see a schematic contact between two flexible beams with one asperity on the top surface and six on the bottom one. The top beam is maintained at an imposed distance above the bottom beam and slides at a constant horizontal speed. When a shock occurs, repulsive contact forces impose a transverse vibration of the beams that persists beyond the duration of the impacts.

In this second video, we see a small rigid cube with a rough bottom face sliding on a rough track. The sliding speed is relatively low. We can observe the vertical and rotational motions of the cube induced the the multiple contacts. In the bottom view, we see in red the contact points. We observe that the population of contact spots renews rapidly and that there is never loss of contact.

In this third video, we see the same simulation but with a higher sliding speed. Now, we can observe loss of contact. During contact, the spots are rather localized on the border of the cube.

5. V.H. Dang, J. Perret-Liaudet, J. Scheibert, A. Le Bot. Direct numerical simulation of the dynamics of sliding rough surfaces, Computational Mechanics, vol. 52, pages 1169-1183, 2013.