Investigation of frictional dynamic systems: modelling, energy flow analysis and identification

Abstract

Vibrations induced by dry friction considerably degrade component lifespan, control precision, and operational stability of mechanical systems. This research systematically investigates the regulatory mechanisms of friction on vibration transmission and energy dissipation, tackling challenges in modelling and parameter identification due to its nonlinear and non-smooth nature. By combining theoretical modelling, power flow analysis (PFA), parameter identification, and experimental validation across single-degree-of-freedom (SDOF) and multi-degrees-of-freedom (MDOF), as well as inerter-based isolators, this study identifies key energy dissipation sources and develops novel strategies for friction parameter identification and control.
Focusing initially on an SDOF mass-on-belt system with dry friction, an analytical power flow model for the friction interface was established using the Harmonic Balance (HB) method. The study found that friction is the main dissipation mechanism, surpassing viscous damping, and can suppress resonant force transmissibility under excitation, though it may enhance it at higher frequencies. Increased excitation force raised the damper's dissipation ratio from 36.5% to 74.5% at peak frequency.
This study was further extended to MDOF friction systems. The HB method with alternating frequency-time (AFT) scheme was employed. A quantitative analysis of internal power flow and energy dissipation between two masses identified non-uniform friction distributions as a primary factor governing dissipation patterns. Friction also actively alters the system’s effective isolation bandwidth and resonance frequency, with strong dissipation during sliding that drops markedly upon stiction.
Furthermore, the study explored the influence of inherent friction in inerters on system isolation performance, revealing that a nonlinear frictional inerter vibration isolation system (NFI-VIS) can reduce force and vibration energy transmission across a broad frequency band. Power flow analysis showed that friction can contribute over 20% of the total inertial force when excitation frequency is far from the peak.
To enhance the control precision of friction systems, this study proposed an improved sparse identification method, a parallel implicit sparse identification of nonlinear dynamics (SINDy-PI) integrated with sliding window resampling (SWR) and hybrid regularisation, significantly improving the noise robustness of friction parameter identification. The root mean square error (RMSE) of parameter identification was reduced by over 90% for Coulomb friction models under high noise level (0.3). It successfully solved the failure problem of identifying complex models like Stribeck in high-noise scenarios. Experimental validation further confirmed the method's effectiveness and revealed a frequency-dependent behaviour in friction dynamics that guided model selection.
To precisely characterise friction behaviour at low relative velocity, an experimental system featuring a rubber-aluminium friction pair was designed. Experimental results found that the stick-slip vibration initiation requires deceleration processes and low speeds. The critical triggering condition (≤ 0.76 mm/s) for stick-slip vibration and the sustained velocity range (< 3.86 mm/s) were determined. Effects of relative velocity, normal load, and tangential tension on stick-slip motion were systematically studied.
Overall, this study systematically disclosed the regulatory mechanisms of dry friction in power flow transmission in mechanical systems using theoretical modelling, multi-scale analysis, and experimental validation. It establishes a complete framework for nonlinear vibration isolation, encompassing analysis, identification, and verification, and outlines future directions for friction multi-physics coupling and coordinated energy control in complex scenarios.

Date of Award	15 Jul 2026
Original language	English
Awarding Institution	University of Nottingham
Supervisor	Jian Yang (Supervisor) & David T. Branson (Supervisor)