Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction

Summary The dynamics of sliding friction is mainly governed by the frictional force. Previous studies have shown that the laboratory-scale friction is well described by an empirical law stated in terms of the slip velocity and the state variable. The state variable represents the detailed physicochemical state of the sliding interface. Despite some theoretical attempts to derive this friction law, there has been no unique equation for time evolution of the state variable. Major equations known to date have their own merits and drawbacks. To shed light on this problem from a new aspect, here we investigate the feasibility of periodic motion without the help of radiation damping. Assuming a patch on which the slip velocity is perturbed from the rest of the sliding interface, we prove analytically that three major evolution laws fail to reproduce stable periodic motion without radiation damping. Furthermore, we propose two new evolution equations that can produce stable periodic motion without radiation damping. These two equations are scrutinized from the viewpoint of experimental validity and the relevance to slow earthquakes.

Study on the influence of radial stiffness on the nonlinear vibration of brake system

Purpose A dynamic model of the brake system considering the tangential and radial motion of the pad, and the torsion and wobbling motion of the disk is established in this paper. The influence of radial stiffness on the brake system is investigated under different tribological conditions. This paper aims to prove that sufficient radial stiffness is indispensable in the design of the brake system with good tribological performance. Design/methodology/approach By using the lumped mass method, a dynamic model of the brake system is established. A Stribeck-type friction model is applied to this model to correlate the frictional velocity, pressure and friction force. The stability of pad vibration is analysed by analysis methods. A new stability evaluation parameter is proposed to study the influence of radial stiffness on stability of pad vibration in a certain friction coefficient brake pressure range. Findings The findings show that the tangential vibration of the pad transits from periodic motion to quasi-periodic motion under a low tangential stiffness. The influence of radial stiffness on motion stability is stronger under a low nominal brake radius. The stability of the brake system can be ensured when the brake radius and radial stiffness are sufficient. Originality/value The influence of tangential stiffness of pad on stability of the brake system has been researched for decades. The insufficiency of stiffness in radial direction may also generate certain levels of instabilities but has not been fully investigated by modelling approach. This paper reveals that this parameter is also strongly correlated to nonlinear vibration of the brake pad.

Dynamics analysis of a gyrostat system with intermittent forcing

The dynamical characteristics of a gyrostat system with intermittent forcing are investigated, the main work and contributions are given as follows: (1) The gyrostat system with an intermittent forcing is studied, and its dynamical characteristics are investigated by the corresponding Lyapunov exponent spectrums and bifurcation diagrams with respect to the amplitude of intermittent forcing. The modified gyrostat system exists chaotic motion when the amplitude of intermittent forcing belongs to a certain interval, and it can be at a state of stable point or periodic motion by the design of amplitude. (2) The gyrostat system with multiple intermittent forcings is also investigated through the combination of Lyapunov exponent spectrums and bifurcation diagrams, and it behaves periodic motion or chaotic motion when the amplitude or forcing width is different. (3) By the selection of parameters in intermittent forcings, the modified gyrostat system is at a state of stable point, periodic motion or chaotic motion. Numerical simulations verify the feasibility and effectiveness of the modified gyrostat system.

Study on Dynamics of a Two-Stage Gear Transmission System with and without Tooth Breakage

This paper studies the dynamics of a two-stage gear transmission system in both the normal state and the fault state with tooth breakage. The torsional vibration model of the two-stage parallel shaft gear was developed by using the lumped parameter method. The time-varying meshing stiffness of the gear transmission system is described by Fourier series which is determined by the periodical meshing characteristics of the gears with both the single-tooth and the double-tooth contacts. By introducing the pulse into the regular time-varying meshing stiffness, the tooth breakage existing in the gear transmission system is mimicked. Based on the numerical simulation of the developed dynamic model, both the time domain analysis and the frequency domain analysis of the gear transmission system under both the normal condition and the tooth breakage are compared accordingly. The influence of the tooth breakage on the dynamic characteristics of the gear transmission system is analyzed comprehensively. Furthermore, based on the developed test bench of a two-stage gear transmission system, the experimental research was carried out, and the experimental results show great agreements with the results of numerical simulation, and thus the validity of the developed mathematical model is demonstrated. By comparing the periodic motion with the chaotic motion, the fault identification for the gear transmission system is verified to be tightly related to its vibration condition, and the control of the vibration condition of the gear transmission system as periodic motion is of great significance to the fault diagnosis.

Feature Engineering for Motion Classification in Machine Vision

With the most advanced classification algorithms in the technological platform, the computational power requirement is on the surge. The paper hereby presents computationally trivial algorithms to simplify the process of computational intensive classifications techniques, especially in the Motion Classification arena. The proposed methods prove crucial in acting as a lightweight and computationally fast stepping stone to a fundamentally more significant application of Motion indexing and classification, Action recognition, and predictive analysis of motion energy. The algorithms classify the motions into linear, circular, or periodic motion types by following an appropriate execution order. They consider the tracked motion path of the object of interest as a sequence and use it as a starting point to perform all operations, resulting in a feature that can be classified into separate classes. Using a single parameter for classifying the motion engenders a faster and relatively more straightforward route to motion identification and elicits the algorithm’s uniqueness. Two algorithms are proposed, namely, Angle Derivative Technique and Determinant Method for classifying the motion into two classes (linear & circular). On the other hand, a different algorithm identifies periodic motion using the principle of correlation on the motion sequences. All the algorithms show an average accuracy of over 95%. It also elicited an average processing time of 15.6 ms and 19.86 ms for Angle Derivative Method and Determinant Method, respectively, and 31.2 ms for periodic motion on Intel(R) Core(TM) i3-5005U CPU @ 2.00 GHz and 8GB RAM. A dataset of camera-captured videos consisting of three motion types is used for testing while the proposed methods are trained on a dataset of motion described by mathematical equations with added 3σ noise levels.