title: Stochastic Friction-Induced Vibration with rough contact surfaces: from non-deterministic field modelling to Isogeometric analysis-based solution method
Creators: name: Hu, Han
Publisher: name: University of Liverpool Repository
Year: 2024

description: Friction-induced vibration is a traditional yet fundamental topic flourishing in widespread engineering applications. The friction force is usually deemed as a deterministic quan- tity. In recent years, theoretical and experimental studies have emerged showing that the friction force is inherently random due to various factors such as surface roughness, temperature, external loads, etc. In this work, the randomness in friction is accounted for through considering rough- ness of contact surfaces. This work is divided into two parts. In the first part, rigid contact problems are investigated. The contact of rough surfaces leads to friction force fluctuations, which are simulated by modelling the coefficient of friction as a random field even under a constant normal force. Theoretical analyses of statistical properties of friction forces and the generated frictional torques are conducted for planar sliding. Closed-form solutions are obtained under simple settings, e.g. pure translation, and nu- merical solutions are sought for other settings. The correlation length of the random field to the characterised geometry length ratio is found to be paramount to the fluctuations in frictional responses. The stochastic planar stick-slip motions are further investigated using a slider-on-belt model. To effectively capture the dynamical behaviours and accu- rately, new three-variable stick-slip transition criteria are proposed. Dynamic analyses demonstrate that the correlation length of the coefficient of friction random field is dominantly responsible for the stochastic behaviours of the system. Besides, the time duration of the sticking state is found to be influenced significantly by factors like belt velocity. The second part of this thesis addresses elastic contact problems with random friction using the Isogeometric analysis-based approach. The randomness in friction is accounted for by enforcing random roughness to the contact surface. This enforcement is accom- plished by the newly proposed Isogeometric random geometry modelling framework, which combines the random field generation based on Karhunen-Lo`eve expansion the- ory with the Non-Uniform Rational B-Spline interpolation method. To fulfil the contact analysis, a mortar-based frictional contact algorithm in a two-dimensional large defor- mation regime is developed, incorporating a modified closest point projection method for contact detection. Quantities of interest, such as the ratio of the global coefficient of friction to the prescribed local one, are characterised under different settings distin- guished by various contact surface properties, e.g. correlation length and root mean square. Moreover, a new explicit dynamical algorithm incorporating the LuGre friction model is proposed to demonstrate the stick-slip effect in elastic contact problems. The effectiveness and accuracy of the proposed algorithm are validated through several sim- plified two-dimensional cases. The sticking time ratio and the progress of the global coefficient of friction of a three-dimensional plate in contact with a rigid body with a randomly rough contact interface are investigated as an application. For non-deterministic modelling of friction in the rigid contact regime, sometimes the only available information on the coefficient of friction is its interval. In such a case, the last part of this work proposes a new interval field modelling method, named B-spline based interval field decomposition method. The proposed method entails B-spline basis functions to represent the dependencies of interval variables in the field. Inhomogeneous interval fields can be effectively modelled by incorporating truncated hierarchical B- spline basis functions and the multi-patch stitching method. Several numerical cases are provided to demonstrate the applicability of the proposed method in predicting the output response’s bounds. Finally, the proposed interval field modelling method is applied to model non-deterministic friction force of the contact interface of a two-rigid- plate system to investigate the differences in system performance compared with the deterministic model and the bounds of such differences.