Analysis of Dry Friction Dynamics in a Vibro-impact Energy Harvester

Automobile windshields are typically curved, creating an oblique angle of attack between the wiper blade and the windshield. This attack angle means that the wiper may jump off the windshield while wiping, causing a chattering noise and preventing the rainwater from being fully wiped off the windshield. Thus, it is important to examine the dynamics of the wiper blade under friction. In this study, the relationship between the attack angle and the jumping phenomenon is clarified through dynamic analysis. We introduce an analytical two-link model corresponding to an actual wiper blade that considers the exchange of dynamic and static friction between the windshield and the blade. The dynamic friction is assumed to be negatively correlated with the relative velocity, and the static friction is described by a set-valued function. As the motion transitions from the stick state to the slip state, the equation to be solved changes. Hence, the initial condition after a transition must agree with the final condition before the transition. Because the governing equations are nonlinear and the solution is highly dependent on the initial condition, the transition time and corresponding state variables are vital. The slack variable method is used to obtain the exact transition time and initial conditions. The sign of the normal force acting on the blade from the windshield determines the occurrence of the jump phenomenon. A larger attack angle makes the jump phenomenon more likely. However, the jump phenomenon does not occur when the motion of the blade reverses. Experimental observations support the theoretical description of the wiper blade.

Summary A new model technique is described for comprehensive dynamic stress and displacement analysis of wellbore-completion tubulars, including friction loads with history. A dynamic model of tubing forces is necessary to predict local pipe velocity, which in turn determines the magnitude and direction of localized frictional contact. By tracking dynamic changes in axial force starting from the initial running state, a complete load history can be simulated for the installed casing and tubing through the service life of the well. The dynamic friction model subdivides the casing or tubing string joint by joint and uses an elastic pipe-momentum balance. Pipe velocity is related to axial force by the elasticity equation. Dynamically determined velocity is necessary to predict the magnitude and orientation of local node-friction vectors. Damping for the dynamic analysis is provided by annular fluid viscosity. The elastic equations are solved as a set of algebraic equations in terms of past and future values of pipe axial force and velocity. Key model inputs such as pressure, temperature, fluid, and wellbore-friction coefficients can be changed at each successive load step. Running loads and packer setting with slackoff or pickup loads determine the initial tubing-stress configuration. Given the initial configuration, each subsequent load case is calculated starting from the prior load and resultant friction state, allowing for full history dependence. The surface velocity profile of running individual stands is a key input. Unexpected magnitudes of downhole transfer of surface load are demonstrated. A change in the operation-load sequence is shown to produce significant differences in tubular axial loads, indicating that special attention to load history should be considered when performing a tubular-stress analysis. For slackoff, overpull, or packer-setting events, the model can track dynamic load response at downhole points, such as a packer or cement top. An example well with a deviated profile and a planned sequence of life-cycle operations including stimulation, production, and shut-in was simulated for a variety of load sequences. The model has been validated against field data using the actual hookload plot during installation of a single-trip, multizone intelligent completion in an offshore highly deviated extended-reach-drilling (ERD) well. Example calculations are given for a high-pressure/high-temperature (HP/HT) subsea well and a horizontal unconventional well. The dynamic friction model allows for the seamless integration of running loads with friction into a fully sequential stress analysis of subsequent well life-cycle loads for landed completion strings. Although dynamic analysis has been extensively applied to complex drilling phenomena such as drillstring vibration or bottomhole-assembly design, current industry models for completion tubulars such as casing and tubing separate the installation state from the in-service life envelope or attempt to solve the problem with a static analysis. This represents a critical deficiency in the current industry state of the art for completion tubulars, which the present work proposed herein strives to address. From a comparison with appropriate static analytic solutions and industry-standard drag-and stress-models, dynamics were found to affect friction-force directions and magnitudes, suggesting that tubular dynamics cannot be neglected.

The dynamic analysis of Three-Link planar robot arm and control system with (PID) are presented and investigated. The dynamic analysis is very important in the design and control of the robot. The difference between the actual dynamic analysis and ideal dynamic analysis is the presence of friction in the robot joints. In this work, the frictional effect in the joints of three-link planar robot is inserting in the dynamic equations and that makes the dynamic analysis is more reality and difficult. The mathematical model that represent the friction consist of two types of friction (Coulomb and viscous friction). A Lagrange method is used and applied to evaluate the generalized forces in the two cases (without and with the effect of friction). Control system with (PID) controller is presented with Simulink block set to evaluate and show the dynamic response of each link in two cases (without and with friction). MATLAB software is used for programing and simulation the equations. In addition, with that, error signals are presented and analyzed for each link. It is concluded from the results that the values of generalized forces in case of presence of friction are more about (12%) than the values of the forces in case of without friction and the behaviors of the dynamic response is linear in case of without friction while the behavior become (non-linear) by inserting the frictional effect in the robot joints. The results indicate that the effect of friction is very important and must be not neglected.

The magnetically induced multi-stable piezoelectric vibration energy harvesters have garnered significant attention due to their strong nonlinear characteristics, wide operating bandwidths, and high electromechanical energy conversion efficiency. However, a traditional penta-stable design typically requires four rectangular external magnets. The excessive number of structural parameters amplify complexities in system optimization, dynamic analysis, and prototype installation, impeding harvester manufacturing and application. This study presents a novel penta-stable harvester design that utilizes interaction forces among a rectangular magnet and two annular magnets, resulting in a simplified system requiring only two external magnets. This design approach streamlines system design, dynamic analysis, and prototype installation, providing a fresh perspective on magnetic penta-stable vibration energy harvester design. The magnetizing current method is employed to accurately determine the system’s magnetic field and magnetic force. Stability analysis indicates that the multi-stability of the harvester is influenced by both the vertical magnetic force and equivalent linear elastic force, which can be effectively controlled by adjusting the system’s components. Dynamic simulations conducted under Gaussian white noise excitation confirm the penta-stable behavior of the system, and the dynamic responses verify that a shallower potential well depth contributes to the system’s ability to attain a higher output voltage. Experimental validations closely align with simulation results, providing strong evidence for the accuracy of the study’s findings. Furthermore, a practical application experiment demonstrates the harvester’s capability to power a hygrothermograph, highlighting its potential for real-world energy harvesting applications.

We present the analytical and experimental studies of a piezoelectric energy harvesting device that can be used as a standalone energy source for powering microsensors and electronics. Single crystal piezoelectric Pb(Mg1/3 Nb2/3)O3-xPbTiO3 (PMN-PT) with large electromechanical coupling coefficient was employed for device design and fabrication in this study. An analytical model for estimating the power-harvesting performance was derived for a cantilever-mounted aluminum alloy plate with a PMN-PT device bonded near the clamped end and a proof mass at the other end. Considering the plate was subjected to both a steady-state sinusoidal vibration and a pulse impact excitation, static, and dynamic analyses were performed for device structure to achieve efficient energy harvesting. In the static analysis, the effect of geometrical dimension of piezoelectric device on the energy harvesting performance has been discussed. In the dynamic analysis, transient response of the device subjected to a pulse impact excitation was studied using a single degree of freedom system model. The resonance characteristics and the power generation capability of the device were discussed. Based on the analytical results, a cantilever device was fabricated and evaluated with sinusoidal excitation and impact excitation. The results are applicable for the structural design of piezoelectric energy harvesting devices.

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

A general methodology for the dynamic modelling and analysis of planar multi-body systems with a continuous friction model in joint clearance is presented. Joint clearance is the critical factor that influences the dynamic response and the performance of mechanisms for high-speed application. In light of recent developments in the joint clearance studies, the number of contact force models has been introduced with ignoring friction continuity. The selection of an appropriate continuous friction model is still challenging and essential, which requires further development. Therefore, a perfect continuous friction model, including the Stribeck effect, static, dynamic and viscous friction terms, is proposed and validated. Investigating the dynamic modelling and analysis of double rocker four-bar linkage mechanisms with frictional revolute clearance joints is presented to investigate friction models' effect when surfaces collide with a non-zero tangential velocity. Unlike the smooth crank input mechanism, a double rocker four-bar linkage mechanism is analysed as a challenging problem in the impact mode. Resolving this concern, the novel friction model avoids discontinuity at zero velocity considering the accurate static friction zone. The results reveal that the novel friction model, compared with the piecewise friction model, is more effective in reflecting the mechanical systems' dynamic behaviour. In order to grasp the nonlinear characteristics of the high-speed four-bar linkage mechanism with our model in joint clearance, the Poincaré portrait, and Fast Fourier transformation plot are employed. It is proved that chaos exists in the dynamic response with the influence of the restitution coefficients and kinetic coefficient of friction.

This study primarily investigates the internal friction (IF) behaviour of Ti 50 Ni 48 Cu 2 (TNC2) shape memory alloy (SMA) through temperature, frequency, isothermal, and strain sweep analysis using a Dynamic mechanical analyser (DMA). The total internal friction (IF Total ) value of TNC2 alloy is 0.0686 at 323.4 K. The frequency sweep analysis reveals that increasing the frequency reduces the IF Total by 15.97% due to restricted martensitic interface movement. Isothermal analysis shows a significant drop in IF Total during the B2-B19′ transformation peak, with reductions of 79.02%, stabilising as intrinsic damping dominates. Strain sweep tests demonstrate that higher strain at isothermal temperature (323.4K) increases inherent internal friction (IF PT + IF Int ) B2–B19′ , with a frequency-dependent trend. The secondary focus is decomposing the IF Total into its intrinsic (IF Int ) and inherent internal friction (IF PT + IF Int ) B2–B19′ , components using an iterative method. The iterative method effectively separates IF Total , allowing precise calculation of the transformed volume fraction n(T). After eight iterations, convergence is achieved with a minimal error rate. The predicted IF spectrum closely matches experimental data, highlighting the method’s reliability for decomposing IF Total into its contributions.

Deformation in dielectric elastomers (DEs) induces electrostriction, significantly impacting their electromechanical properties and actuation performance. Three distinct materials – VHB 4910, Ecoflex 0030, and Oppoband 8001 for DEAs are analyzed under pre-strain conditions ranging from λi = 1–4 and λj = 2–5, where λi ≠ λj , to capture a broad range of electromechanical responses associated with varying stiffness and permittivity. Static analysis reveals an anisotropic stress distribution throughout the regimes of pre-strain, highlighting material-dependent responses. VHB 4910 shows the highest stress values, compared to Ecoflex 0030 and Oppoband 8001. Whereas, dynamic analysis under constant electrical and mechanical loading reveals an inverse relationship between deformation and frequency – amplitude and stretch rate increase with deformation, while frequency decreases, indicating reduced stiffness. Lower deformation enhances stability and energy dissipation through higher frequencies and reduced amplitudes. root mean square error (RMSE) analysis from both static and dynamic analysis indicates that models using polarization-based and linear relationships between permittivity and stretch predict stress more accurately than those using a logarithmic relationship. These findings highlight the interplay between electrostriction and deformation, offering insights into optimizing DE actuators (DEAs) for applications requiring precise dynamic responses, such as soft robotics and energy harvesting.

We perform extended numerical simulation of the dynamics of dry friction, based on a model derived from the phenomenological description proposed by T. Baumberger et al.. In the case of small deviation from the steady sliding motion, the model is shown to be equivalent to the state- and rate-dependent friction law which was first introduced by Rice and Ruina on the basis of experiments on rocks. We obtain the dynamical phase diagram that agrees well with the experimental results on the paper-on-paper systems. In particular, the bifurcation between stick-slip and steady sliding are shown to change from a direct (supercritical) Hopf type to an inverted (subcritical) one as the driving velocity increases, in agreement with the experiments.

Fundamental Investigations and Applications of Liquid Marbles

Blanket fabrics are treated with softeners with an aim to reduce the friction values and to improve the tactile feel of the fabrics. A study was conducted to examine the effects of type of softener and its concentration levels on the physical properties of woollen blanket. Three types of blanket fabrics prepared from 100% Bharat Merino (BM) wool, 100% Chokla wool and 100% Avikalin wool were treated with three types of softener namely cationic, amino silicone or silicone softener using exhaust method. Softener treatment was given at 3 levels i.e. 0.5, 1.0 and 1.5% on weight of material (owm) and blanket fabrics were tested for coefficient of static and dynamic friction. Higher dynamic friction coefficient (1.03) was observed for BM and Chokla wool as compared to Avikalin (0.98) wool fabrics. Bending length found to decrease with increasing levels of concentration and no trend was observed for ends and picks per dm and areal density. Regardless of the type of softener, dynamic friction coefficient gets reduced due to application of softeners. The coefficient of dynamic friction initially dropped when the concentration was increased from 0.5 to 1.0%; however, it increased when the concentration was increased to 1.5%. The effect of softener on static coefficient was similar to the effect of softener in dynamic friction. It was observed that silicone softener gave the least coefficients of dynamic and static friction and recommended to use softener at concentration level of 1.0% to get optimum friction values.

Dynamic friction coefficient between tire and compacted asphalt mixtures using tire-pavement dynamic friction analyzer

This paper introduces dynamic impact analysis as an effective technique for studying the response of horizontal vibrated conveyor with time-varying impact excitation by the falling of the scrap. A two degree-of-freedoms impact dynamic model is formulated considering the static and dynamic coulomb friction between the scrap and chute. Then the time integration algorithm was applied in the program to solve the dynamic equations. Using the proposed method, the impact effects of ideal single scrap and multiple scraps on the dynamic response of the conveyor were analyzed. Computational results reveal numerous interesting dynamic characteristics which can be used to forecast and control the vibration of the scrap and conveyor system.

Isogeometric optimization of piezoelectric functionally graded material for energy harvester