Tribology Letters

, 67:31 | Cite as

A Fractal Model of Acoustic Emission Signals in Sliding Friction

  • Qiushi Hao
  • Yi ShenEmail author
  • Yan Wang
  • Xin Zhang
Original Paper


Acoustic emission (AE) technology has been applied in condition monitoring of mechanical systems. In this paper, in order to deepen theoretical understanding of the relation between AE signals and contact mechanisms, the principle of deformation is unified by a deformation ratio, then a scale-independent AE model of sliding friction is proposed based on the fractal theory. The new model considers a complete process of elastic-plastic deformation. Influences of the sliding velocity and the normal load on the AE signal in different fractal circumstances are specified. By theoretical and experimental comparisons, the effectiveness and feasibility of the proposed model are demonstrated. The work offers a theoretical basis for future studies and applications of AE technology on tribological problems.


Acoustic emission Fractal model Rough surface Sliding friction 

List of Symbols


Distance (m)


The Weierstrass–Mandelbrot function of position x (m)


The height of the surface profile at distance x (m)


Fractal dimension of a surface profile


Fractal roughness parameter (m)

\(\gamma \)

Scaling parameter for the Weierstrass–Mandelbrot function


The frequency level of the asperities

\(\phi _n\)

The random phase of level n (rad)

\(S(\omega )\)

The power spectrum


Length scale of an asperity or a contact spot (m)

\(\delta \)

Interference or deformation of an asperity (m)


Area of a contact spot (m\(^2\))


Young’s modulus (N/m\(^{2}\))

\(\nu \)

Poisson’s ratio


Radius of asperity curvature (m)


Hardness (N/m\(^{2}\))

\(\eta \)

Deformation ratio

\(P(\delta )\)

Load of contact spot of interference \(\delta \) (N)


Number of the contact spots


Area (m\(^2\))

\(\varDelta \)

Interference or deformation (m)


Size-distribution density of contact spots of area a

\(n(\delta )\)

Size-distribution density of contact spots of interference \(\delta \)


Energy of the deformed asperities (J)


Energy release rate of the deformed asperities (W)


Period (s)


Radius of the contact surface in the mechanical seal (m)


Sliding velocity (m/s)


The normal load on a surface (N)


Energy converting rate through transmission


The gain of AE measurement system


Voltage (V)







Material 1


Material 2








Root mean square


Acoustic emission





This research was supported by the National Natural Science Foundation of China (Nos. 61771161 and 61601139), China Postdoctoral Science Foundation funded Project (No. 2017M610209), and Shenzhen Science & Technology Program (No. JCYJ20160429115309834).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Control Science and EngineeringHarbin Institute of TechnologyHarbinChina
  2. 2.Shenzhen Engineering Lab for Medical Intelligent Wireless Ultrasonic Imaging TechnologyHarbin Institute of TechnologyShenzhenChina

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