Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

Computational Model for Radial Plain Bearing with Non-Circular Bearing Surface Profile and Fusible Coating on Shaft Surface

The paper presents a study based upon: a Newtonian fluid flow equation (“thin layer”), a continuity equation, and an equation of the molten-profile radius for a shaft coated with a fusible metal alloy; considering a mechanical energy dissipation rate formula, the authors produced an asymptotic and accurate automodel solution for the zero approximation (melting ignored) and first approximation (adjusted for melting) of a radial plain bearing featuring a fusible metal coating and a bearing profile adapted to the specific friction parameters. The paper further presents analytical dependencies describing the molten surface radius, velocity and pressure fields for zero and first approximation. Besides, it determines the key operating parameters of the frictional couple, the bearing capacity, and the friction. It also shows how the parameters arising from the melting of the surface affect the bearing capacity and friction where the bearing surface profile is adapted to the specific conditions of friction.

Repeating caldera collapse events constrain fault friction at the kilometer scale

Fault friction is central to understanding earthquakes, yet laboratory rock mechanics experiments are restricted to, at most, meter scale. Questions thus remain as to the applicability of measured frictional properties to faulting in situ. In particular, the slip-weakening distance dc strongly influences precursory slip during earthquake nucleation, but scales with fault roughness and is challenging to extrapolate to nature. The 2018 eruption of K̄ılauea volcano, Hawaii, caused 62 repeatable collapse events in which the summit caldera dropped several meters, accompanied by MW 4.7 to 5.4 very long period (VLP) earthquakes. Collapses were exceptionally well recorded by global positioning system (GPS) and tilt instruments and represent unique natural kilometer-scale friction experiments. We model a piston collapsing into a magma reservoir. Pressure at the piston base and shear stress on its margin, governed by rate and state friction, balance its weight. Downward motion of the piston compresses the underlying magma, driving flow to the eruption. Monte Carlo estimation of unknowns validates laboratory friction parameters at the kilometer scale, including the magnitude of steady-state velocity weakening. The absence of accelerating precollapse deformation constrains dc to be ≤10 mm, potentially much less. These results support the use of laboratory friction laws and parameters for modeling earthquakes. We identify initial conditions and material and magma-system parameters that lead to episodic caldera collapse, revealing that small differences in eruptive vent elevation can lead to major differences in eruption volume and duration. Most historical basaltic caldera collapses were, at least partly, episodic, implying that the conditions for stick–slip derived here are commonly met in nature.

Inferring Critical Slip-Weakening Distance from Near-Fault Accelerogram of the 2014 Mw 6.2 Ludian Earthquake

To better assess potential earthquake hazards requires a better understanding of fault friction and rupture dynamics. Critical slip-weakening distance (Dc) as one of the key friction parameters, however, is hard to determine on natural faults. For strike-slip earthquakes, we may directly estimate the Dc from Dc″—the double near-fault ground displacement at the time of the peak velocity (Fukuyama and Mikumo, 2007). Yet near-fault observations are very few, and, thus, there were only limited earthquakes with such Dc″ estimation. In 2014, an Mw 6.2 strike-slip event—the Ludian earthquake—occurred in southwest China. The strong-motion station (LLT) that is ∼0.45 km from the fault recorded the earthquake and enabled us to estimate Dc″ from the accelerograms. We inspect the polarity of the accelerometers and compare the integrated velocities with waveforms of nearby broadband stations. We also analyze the particle motion at the LLT station and retrieve the earthquake initiation at the intersection of the conjugated faults. We then apply the baseline correction to the seismograms, recover the ground velocities and displacements, and obtain the value of Dc″=0.1 m at the station. The recovered final displacements are compared with the predicted ground displacements of a finite-fault model. The discrepancy of fault-parallel displacements might imply limited underestimation of Dc″, and the estimated upper limit is 0.3 m. Comparison between the Dc″ and final slip on the fault patch follows the scaling of previous larger earthquakes. Analysis of the near-fault accelerometer data enhances our understanding on the earthquake source of the Ludian earthquake. This case extends the lower magnitude boundary of the Dc″ values obtained from natural faults and opens a window into the friction property in the seismically active region.

Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

The responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Mechatronic system parameter idenfitcation [i.e. identification] via genetic algorithms

This thesis develops a novel way to identify both the joint friction parameters and a built in torque sensor gain and offset. The identification method is based on a genetic algorithm (GA). A model based friction compensation method and a real coded GA are selected from a variety of methods available. A model of a single degree of freedom mechatronic joint with a link is presented. Numerical simulations are run to determine the optimum configuration of the GA with respect to the population size and maximum number of generations necessary to identify the parameters to within 5% of their actual value. The GA identification technique is then used on an experimental mechatronic joint with a harmonic drive and built-in torque sensor. The friction parameters as well as the sensor gain and offset are identified in the experimental system and the position tracking error is reduced. Based on the experimental results, the method is found to be an effective way of identifying system parameters in a mechatronic joint.

Mechatronic system parameter idenfitcation [i.e. identification] via genetic algorithms

This thesis develops a novel way to identify both the joint friction parameters and a built in torque sensor gain and offset. The identification method is based on a genetic algorithm (GA). A model based friction compensation method and a real coded GA are selected from a variety of methods available. A model of a single degree of freedom mechatronic joint with a link is presented. Numerical simulations are run to determine the optimum configuration of the GA with respect to the population size and maximum number of generations necessary to identify the parameters to within 5% of their actual value. The GA identification technique is then used on an experimental mechatronic joint with a harmonic drive and built-in torque sensor. The friction parameters as well as the sensor gain and offset are identified in the experimental system and the position tracking error is reduced. Based on the experimental results, the method is found to be an effective way of identifying system parameters in a mechatronic joint.