Qiang Li, Fabian Forsbach, Justus Benad

DOI Number
First page
Last page


Two numerical methods are proposed to improve accuracy of the numerical calculation of fretting wear in the framework of the Method of Dimensionality Reduction (MDR). Due to the singularity of the transformation equations, instabilities appear at the border between the stick and slip regions after many transformations from the one-dimensional to the three-dimensional contact and back. In these two methods, the transformation equations are reformulated to weaken the singularity of the integrals and a stable simulation of fretting wear is realized even with the wear models which go beyond the classical Archard law. With an example of dual-oscillation, we show the change in the worn profile of a parabolic indenter as well as the stress distribution on the contacting surface during the oscillating cycles under the Archard’s law of wear and Coulomb’s law of friction.


Fretting Wear, Method of the Dimensionality Reduction, Singularity, Numerical Simulation

Full Text:



Popov, V.L., Heß, M., 2015, Method of dimensionality reduction in contact mechanics and friction, Springer, Berlin.

Kevin Truyaert, K., Aleshin, V., Koen Van Den Abeele, Delrue, S., 2019, Theoretical calculation of the instantaneous friction-induced energy losses in arbitrarily excited axisymmetric mechanical contact systems, Int. J. Solids Struct., 158, pp. 268-276.

Popov, V.L., Heß, M., 2014, Method of dimensionality reduction in contact mechanics and friction: a user’s handbook. I. Axially-symmetric contacts, Facta Universitatis-Series Mechanical Engineering, 12, pp. 1–14.

Popov, M., Popov, V.L., Pohrt, R., 2015, Relaxation damping in oscillating contacts, Sci. R., 5, 16189.

Dimaki, A.V., Dmitriev, A.I., Chai, Y.S., Popov, V.L., 2014, Rapid Simulation Procedure for Fretting Wear on the basis of the method of dimensionality reduction, Int. J. Solids Struct., 51, pp. 4215-4220.

Dimaki, A.V., Dmitriev, A.I., Menga, N., Papangelo, A., Ciavarella, M., Popov, V.L., 2016, Fast High-Resolution Simulation of the Gross Slip Wear of Axially Symmetric Contacts, Tribol. Trans., 59, pp. 189-194.

Dasch, C.J., 1992, One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods, Appl. Opt., 31, pp. 1146-1152.

Kolhe, P.S., Agrawal, A.K., 2009, Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques, Appl. Opt., 48, pp. 3894-3902.

Benad, J., 2018, Fast numerical implementation of the MDR transformations, Facta Universitatis-Series Mechanical Engineering, 16, pp. 127–138.

Krylov, V.I., 1962, Approximate calculation of integrals, The Macmillan Company, Now York.



  • There are currently no refbacks.

ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4