Nonlinear time series analysis using Bayesian recurrence plot quantification to analyse the dynamics of friction-induced vibrations, in particular wear and damping in artificial synovial joints.

点击翻译按钮获取中文摘要

Unwanted vibrations particularly owing to friction are encountered in various industries. While vibrations usually decay with time owing to damping, friction-induced instabilities cause positive and energy providing positive system damping. Positive damping lets vibration amplitudes grow, leading to excessive wear and premature product failure. These positive feedback loops, once established, also lead to audible noises, which are also problematic in artificial synovial joints, as found in total knee or hip replacements. In the past most research concentrated on reducing wear particles or improving their biocompatibility using experimental testing. However, damping and lubrication considering the cartilage or synovial fluid and their effect on artificial synovial joints friction has never been studied numerically or from the dynamics point of view. Here, nonlinear dynamics as output quantity is employed to develop highly innovative Bayesian recurrence plot quantification analysis measures based on recurrence plots and Bayesian updating in combination with the Maximum Entropy Theory. Dynamic variants with credibility bounds, embedding parameters, and unstable periodic orbits are estimated. Attractor-based templates are used to generate inversely reduced-order models to explore the nonlinear dynamics. The basin of attraction and its linear stability boundary is estimated using the templates and analytical models. The influence of noise on invariant estimations in practical measurements is considered. This novel methodology is applied to nonlinear benchmark systems and then to a large database of experimental biomechanical tests of hip and knee implants, considering different driving parameters, various lubricants and running times. By using sophisticated vibration testing over laser vibrometry and kinematics determined over Roentgen stereo photogrammetric analysis, in a bottom up process, a high-fidelity finite element model coupled to computational fluid dynamics simulations is setup to study artificial synovial hip joint with focus on lubrication and squeeze film damping considering the synovial fluid. Modern methods of uncertain parameter identification are employed taking into account the component, the subassembly and the assembly level with and without fluid. Numerical time traces are then analysed by applying the novel Bayesian recurrence plot quantification measures and invariant estimations which allow the numerical model being further updated, both evidence- and response-based and in a top-down approach. Different stages according to the gate cycle are analysed rendering the model updating as a multi-stage process and allow finally to study the effect of the synovial fluids thin film on damping and dissipation. Findings will lead to significant insights of underlying the physics in friction and wear in artificial synovial joints which can be used to design quieter hip inserts by making use of optimised thin film or squeeze film damping.