Frictional Damping in Mechanical Systems


Friction is ubiquitous in mechanical systems: often it is rather an undesired side effect, sometimes it is used on purpose (e.g. in friction brakes).

The term "friction" itself is usually used to describe resistance to tangential relative motion in contact points, with a distinction being made between static friction (sticking) and dynamic friction (sliding).

Just as diverse as the physical causes of friction are its concrete characteristics and behavior. Important limiting cases are, on the one hand, classical dry friction (Coulomb friction) and, on the other hand, viscous friction of lubricated contact points. In general, the magnitude and shape of friction depends on many factors such as surface properties, material pairing of the contact partners or their relative velocity.


The current activities of the department are primarily concerned with the dynamic behavior of mechanical systems that show friction-excited oscillations. Here, the influence of joint damping as well as the occurrence of stick-slip vibrations (caused by the velocity dependence of the friction characteristic) are investigated.

Of particular interest is, on the one hand, the modelling and phenomenology, and on the other hand, the development of efficient methods for the analysis of self-excited oscillations in systems with many degrees of freedom. In that context, a semi-analytical approximation method [1] was developed and implemented, consisting of a combination of two established approximation methods for nonlinear differential equations. This is available as computational code in MATLAB at the department and is subject to continuous further development.

Another focus is on the of multiphysical influences (e.g. influence of contact tribology on the squealing of disc brakes).

[1] J. Kappauf, S. Bäuerle & H. Hetzler: A Combined FD-HB Approximation Method for Steady-State Vibrations in Large Dynamical Systems with Localised Nonlinearities. Computational Mechanics, accepted - tbp

[2]: J. Kappauf & H. Hetzler: On A Hybrid Concept for Approximating Self-Excited Periodic Oscillations of Large-Scaled Dynamical Systems, PAMM, 2021

[3]: J. Kappauf & H. Hetzler: Initialization of the continuation of stick-slip vibrations for a two dof friction oscillator, Proceedings of 8th GACM Colloquium on Computational Mechanics: For Young Scientists From Academia and Industry August 28th–30th, 2019 University of Kassel, Germany, p. 87-89. kassel university press GmbH, 2019

[4]: J. Kappauf & H. Hetzler: Bifurcations and limit cycles due to self-excitation in nonlinear systems with joint friction: Initialization of isolated solution branches via homotopy methods, PAMM, 2019

[5]: J. Kappauf & H. Hetzler: Bifurcations and limit cycles due to self-excitation in nonlinear systems with joint friction: Phenomena and approximation schemes. Proceedings of ISMA 2018, p. 3343-3352, 2018

[6]: J. Kappauf & H. Hetzler: A comparison of methods for approximating periodic limit cycles in nonlinear systems with joint friction, PAMM, 2018

[7]: H. Hetzler: Bifurcations in Autonomous Mechanical Systems under the Influence of Joint Damping , Journal of Sound & Vibration, 2014

[8]: H. Hetzler: Stability and Bifurcation of Equilibria in the Presence of Non-Smooth Damping due to Coulomb Friction, Proc. of 11th Intl. Conf. on Vibration Problems (ICOVP), Lisbon, 2013

[9]: H. Hetzler: Friction induced vibrations under the influence of Joint-damping,
Proc. of EUROBRAKE 2013, 2013, Dresden

[10]: H. Hetzler: On the Effect of Non-Smooth Coulomb Damping on Flutter-type Self-Excitation in a Non-Gyroscopic Circulatory 2-DoF-System, Nonlinear Dynamics, 2013

[11]: H. Hetzler: On the effect of nonsmooth Coulomb friction on Hopf bifurcations in a 1-DoF oscillator with self-excitation due to negative damping,
Nonlinear Dynamics, 2012

[12]: H. Hetzler, K. Willner: On the influence of contact tribology on brake squeal, Tribology International, 2011

[13]: H. Hetzler: On the Approximtion of Limit-Cycles in N-DoF Systems near Hopf-Bifurcations, Proc. of EUROMECH Nonlinear Oscillations Conference (ENOC) 2011, Rome

[14]: H. Hetzler: Bifurcation Analysis for Brake Squeal, Proceedings of ASME ESDA 2010, Istanbul

[15]: H. Hetzler: On Moving Continua with Contacts and Sliding Friction: Modeling, General Properties and Examples, International Journal of Solids and Structures, 2009

[16]: H. Hetzler, W. Seemann: Friction Induced Vibrations: Oscillatory Instability with Dissipative and Gyroscopic Influences, VDI-Berichte 2022, 2007

[17]: H. Hetzler, W. Seemann: Friction Induced Brake Vibrations at Low Speeds: Experiments, State-Space Reconstruction and Implications on Modelling, Proceedings of ASME IMECE 2006, Chicago, USA (IMECE2006-14034) 

[18]: H. Hetzler, D. Schwarzer, W. Seemann: Steady-state stability and bifurcations of friction oscillators due to velocity dependent friction, Proceedings of the Institution of Mechanical Engineering - Part K: Journal of Multi-body Dynamics, 2007

[19]: H. Hetzler, D. Schwarzer, W. Seemann: Analytical investigation of steady-state stability and Hopf-bifurcations occuring in sliding friction oscillators with application to low-frequency disc brake noise, Communications in Nonlinear Sciences and Numerical Simulation (CNSNS), 2007

[20]: H. Hetzler, W. Seemann, D. Schwarzer: Analytical investigation of Hopf Bifurcations occuring in a 1DOF sliding-friction oscillator with application to disc-brake vibrations, Proceedings of ASME IDETC 2005, Long Beach, USA (DETC2005-84312)