Energy Harvesting System Whose Potential Is Mapped with the Modified Fibonacci Function.

In this paper, we compare three energy harvesting systems in which we introduce additional bumpers whose mathematical model is mapped with a non-linear characteristic based on the hyperbolic sine Fibonacci function. For the analysis, we construct non-linear two-well, three-well and four-well systems with a cantilever beam and permanent magnets. In order to compare the effectiveness of the systems, we assume comparable distances between local minima of external wells and the maximum heights of potential barriers. Based on the derived dimensionless models of the systems, we perform simulations of non-linear dynamics in a wide spectrum of frequencies to search for chaotic and periodic motion zones of the systems. We present the issue of the occurrence of transient chaos in the analyzed systems. In the second part of this work, we determine and compare the effectiveness of the tested structures depending on the characteristics of the bumpers and an external excitation whose dynamics are described by the harmonic function, and find the best solutions from the point view of energy harvesting. The most effective impact of the use of bumpers can be observed when dealing with systems described by potential with deep external wells. In addition, the use of the Fibonacci hyperbolic sine is a simple and effective numerical tool for mapping non-linear properties of such motion limiters in energy harvesting systems.

Intelligent Diagnostics of Radial Internal Clearance in Ball Bearings with Machine Learning Methods.

This article classifies the dynamic response of rolling bearings in terms of radial internal clearance values. The value of the radial internal clearance in rolling-element bearings cannot be described in a deterministic manner, which shows the challenge of its detection through the analysis of the bearing's dynamics. In this article, we show the original approach to its intelligent detection through the analysis of short-time intervals and the calculation of chosen indicators, which can be assigned to the specific clearance class. The tests were carried out on a set of 10 brand new bearings of the same type (double row self-aligning ball bearing NTN 2309SK) with different radial internal clearances corresponding to individual classes of the ISO-1132 standard. The classification was carried out based on the time series of vibrations recorded by the accelerometer and then digitally processed. Window statistical indicators widely used in the diagnosis of rolling bearings, which served as features for the machine learning models, were calculated. The accuracy of the classification turned out to be unsatisfactory; therefore, it was decided to use a more advanced method of time series processing, which allows for the extraction of subsequent dominant frequencies into experimental modes (Variational Mode Decomposition (VMD)). Applying the same statistical indicators to the modes allowed for an increase in classification accuracy to over 90%.

Double-Versus Triple-Potential Well Energy Harvesters: Dynamics and Power Output.

The basic types of multi-stable energy harvesters are bistable energy harvesting systems (BEH) and tristable energy harvesting systems (TEH). The present investigations focus on the analysis of BEH and TEH systems, where the corresponding depth of the potential well and the width of their characteristics are the same. The efficiency of energy harvesting for TEH and BEH systems assuming similar potential parameters is provided. Providing such parameters allows for reliable formulation of conclusions about the efficiency in both types of systems. These energy harvesting systems are based on permanent magnets and a cantilever beam designed to obtain energy from vibrations. Starting from the bond graphs, we derived the nonlinear equations of motion. Then, we followed the bifurcations along the increasing frequency for both configurations. To identify the character of particular solutions, we estimated their corresponding phase portraits, Poincare sections, and Lyapunov exponents. The selected solutions are associated with their voltage output. The results in this numerical study clearly show that the bistable potential is more efficient for energy harvesting provided the corresponding excitation amplitude is large enough. However, the tristable potential could work better in the limits of low-level and low-frequency excitations.

Energy Harvesting in a System with a Two-Stage Flexible Cantilever Beam.

The subject of the research contained in this paper is a new design solution for an energy harvesting system resulting from the combination of a quasi-zero-stiffness energy harvester and a two-stage flexible cantilever beam. Numerical tests were divided into two main parts-analysis of the dynamics of the system due to periodic, quasiperiodic, and chaotic solutions and the efficiency of energy generation. The results of numerical simulations were limited to zero initial conditions as they are the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, three cases of piezoelectric mounting were analyzed-only on the first stage of the beam, on the second and both stages. The analysis has been carried out with the use of diagrams showing difference of the effective values of the voltage induced on the piezoelectric electrodes. The results indicate that for effective energy harvesting, it is advisable to attach piezoelectric energy transducers to each step of the beam despite possible asynchronous vibrations.

Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum.

We use friction to simultaneously damp and excite a pendulum system. A Froude pendulum attached to a suspension shaft is subjected to a frictional load. We investigate two types of response of the system: regular and chaotic responses, depending on the excitation frequency. A transient chaotic solution was also obtained. We identify the motions using phase portraits, Poincaré maps, and Fourier spectra. Finally, the composite multiscaled entropy was estimated for the specified cases to confirm the preliminary classification.

Hydroxyapatite Use in Spine Surgery-Molecular and Clinical Aspect.

Hydroxyapatite possesses desirable properties as a scaffold in tissue engineering: it is biocompatible at a site of implantation, and it is degradable to non-toxic products. Moreover, its porosity enables infiltration of cells, nutrients and waste products. The outcome of hydroxyapatite implantation highly depends on the extent of the host immune response. Authors emphasise major roles of the chemical, morphological and physical properties of the surface of biomaterial used. A number of techniques have been applied to transform the theoretical osteoconductive features of HAp into spinal fusion systems-from integration of HAp with autograft to synthetic intervertebral implants. The most popular uses of HAp in spine surgery include implants (ACDF), bone grafts in posterolateral lumbar fusion and transpedicular screws coating. In the past, autologous bone graft has been used as an intervertebral cage in ACDF. Due to the morbidity related to autograft harvesting from the iliac bone, a synthetic cage with osteoconductive material such as hydroxyapatite seems to be a good alternative. Regarding posterolateral lumbar fusion, it requires the graft to induce new bone growth and reinforce fusion between the vertebrae. Hydroxyapatite formulations have shown good results in that field. Moreover, the HAp coating has proven to be an efficient method of increasing screw fixation strength. It can decrease the risk of complications such as screw loosening after pedicle screw fixation in osteoporotic patients. The purpose of this literature review is to describe in vivo reaction to HAp implants and to summarise its current application in spine surgery.

Nonlinear Dynamics of a Star-Shaped Structure and Variable Configuration of Elastic Elements for Energy Harvesting Applications.

The subject of the model research contained in this paper is a new design solution of the energy harvesting system with a star-shaped structure of elastic elements and variable configuration. Numerical experiments focused mainly on the assessment of the configuration of elastic elements in the context of energy harvesting efficiency. The results of computer simulations were limited to zero initial conditions as it is the natural position of the static equilibrium. The article compares the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, four cases of elastic element configurations were compared. The results are visualized based on the diagram of RMS voltage induced on piezoelectric electrodes, bifurcation diagrams, Lyapunov exponents, and Poincaré maps, showing the impact of individual solutions on the efficiency of energy harvesting. The results of the simulations show that the harvester's efficiency ranges from 4 V to 20 V depending on the configuration and the frequency range of the excitation, but the design allows for a smooth adjustment to the given conditions.

New Horizons for Hydroxyapatite Supported by DXA Assessment-A Preliminary Study.

Dual Energy X-ray Absorptiometry (DXA) is a tool that allows the assessment of bone density. It was first presented by Cameron and Sorenson in 1963 and was approved by the Food and Drug Administration. Misplacing the femoral neck box, placing a trochanteric line below the midland and improper placement of boundary lines are the most common errors made during a DXA diagnostic test made by auto analysis. Hydroxyapatite is the most important inorganic component of teeth and bone tissue. It is estimated to constitute up to 70% of human bone weight and up to 50% of its volume. Calcium phosphate comes in many forms; however, studies have shown that only tricalcium phosphate and hydroxyapatite have the characteristics that allow their use as bone-substituted materials. The purpose of this study is aimed at analyzing the results of hip densitometry and hydorxyapatite distribution in order to better assess the structure and mineral density of the femoral neck. However, a detailed analysis of the individual density curves shows some qualitative differences that may be important in assessing bone strength in the area under study. To draw more specific conclusions on the therapy applied for individual patients, we need to determine the correct orientation of the bone from the resulting density and document the trends in the density distribution change. The average results presented with the DXA method are insufficient.

On Theoretical and Numerical Aspects of Bifurcations and Hysteresis Effects in Kinetic Energy Harvesters.

The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the restoring force is studied. The proposed system consists of a bistable oscillator based on a cantilever beam structure. The elastic force potential is modified by magnets. The hysteresis is an additional effect of the composite beam considered in this system, and it effects the modal solution with specific mass distribution. Consequently, the modal response is a compromise between two overlapping, competing shapes. The simulation results show evolution in the single potential well solution, and bifurcations into double-well solutions with the hysteretic effect. The maximal Lyapunov exponent indicated the appearance of chaotic solutions. Inclusion of the shape branch overlap parameter reduces the distance between the external potential barriers and leads to a large-amplitude solution and simultaneously higher voltage output with smaller excitation force. The overlap parameter works in the other direction: the larger the overlap value, the smaller the voltage output. Presumably, the successful jump though the potential barrier is accompanied by an additional switch between the corresponding shapes.

Ceramic-Based Piezoelectric Material for Energy Harvesting Using Hybrid Excitation.

This paper analyzes the energy efficiency of a Micro Fiber Composite (MFC) piezoelectric system. It is based on a smart Lead Zirconate Titanate material that consists of a monolithic PZT (piezoelectric ceramic) wafer, which is a ceramic-based piezoelectric material. An experimental test rig consisting of a wind tunnel and a developed measurement system was used to conduct the experiment. The developed test rig allowed changing the air velocity around the tested bluff body and the frequency of forced vibrations as well as recording the output voltage signal and linear acceleration of the tested object. The mechanical vibrations and the air flow were used to find the optimal performance of the piezoelectric energy harvesting system. The performance of the proposed piezoelectric wind energy harvester was tested for the same design, but of different masses. The geometry of the hybrid bluff body is a combination of cuboid and cylindrical shapes. The results of testing five bluff bodies for a range of wind tunnel air flow velocities from 4 to 15 m/s with additional vibration excitation frequencies from 0 to 10 Hz are presented. The conducted tests revealed the areas of the highest voltage output under specific excitation conditions that enable supplying low-power sensors with harvested energy.

Adaptive stochastic resonance in bistable system driven by noisy NLFM signal: phenomenon and application.

The stochastic resonance (SR) in a bistable system driven by nonlinear frequency modulation (NLFM) signal and strong noise is studied. Combined with empirical mode decomposition (EMD) and piecewise idea, an adaptive piecewise re-scaled SR method based on the optimal intrinsic mode function (IMF), is proposed to enhance the weak NLFM signal. At first, considering the advantages of EMD for dealing with non-stationary signals, the segmented NLFM signal is processed by EMD. Meanwhile, the cross-correlation coefficient is used as the measure to select the optimal IMF that contains the NLFM signal feature. Then, the spectral amplification gain indicator is proposed to realize the adaptive SR of the optimal IMF of each sub-segment signal and reconstruct the enhanced NLFM signal. Finally, the effectiveness of the proposed method is highlighted with the analysis of the short-time Fourier transform spectrum of the simulation results. As an application example, the proposed method is verified adaptability in bearing fault diagnosis under the speed-varying condition that represents a typical and complicated NLFM signal in mechanical engineering. The research provides a new way for the enhancement of weak non-stationary signals. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Tribological Properties of Chromium Nitride on the Cylinder Liner under the Influence of High Temperature.

The chromium nitride coating is a hard coating used to improve the sliding friction and wear behavior and is applied to engine components in various operating conditions even at an elevated temperature. In this study, chromium nitride was deposited by a physical vapor deposition process onto the cast iron substrate. All tribological tests were performed on linear reciprocating tribometer with a stroke length of 5 mm in a dry condition at variable temperature levels of 28 °C, 100 °C, 200 °C, and of 300 °C corresponding to loads of 10 N, 20 N, 30 N, and 40 N against the cylinder liner material. The worn surfaces of chromium nitride(CrN) coatings after friction tests were analyzed by scanning electron microscope (SEM) and energy-dispersive spectroscopy (EDS). The results showed that friction coefficients (COF) ranged from 0.93 to 0.34 from room temperature to 300 °C against the cylinder liner material as a counter-body of 6 mm in diameter; higher temperature results in the positive tribological performance of CrN, with at least 0.34 COF at 300 °C. The wear mechanisms of CrN and counter-body surfaces are abrasive wear accompanied by the slight oxidation. This study guides the wear behavior of cylinder liner coatings in an environment similar to the engine.

Identification and quantification analysis of nonlinear dynamics properties of combustion instability in a diesel engine.

The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.

Chaotic vibrations of the duffing system with fractional damping.

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.

Multifractal and statistical analyses of heat release fluctuations in a spark ignition engine.

Using multifractal and statistical analyses, we have investigated the complex dynamics of cycle-to-cycle heat release variations in a spark ignition engine. Three different values of the spark advance angle (Delta beta) are examined. The multifractal complexity is characterized by the singularity spectrum of the heat release time series in terms of the Holder exponent. The broadness of the singularity spectrum gives a measure of the degree of mutifractality or complexity of the time series. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, the complexity in heat release variations is compared for the three spark advance angles (SAAs). Our results reveal that the heat release data are most complex for Delta beta=30 degrees followed in order by Delta beta=15 degrees and 5 degrees. In other words, the complexity increases with increasing SAA. In addition, we found that for all the SAAs considered, the heat release fluctuations behave like an antipersistent or a negatively correlated process, becoming more antipersistent with decreasing SAA. We have also performed a statistical analysis of the heat release variations by calculating the kurtosis of their probability density functions (pdfs). It is found that for the smallest SAA considered, Delta beta=5 degrees, the pdf is nearly Gaussian with a kurtosis of 3.42. As the value of the SAA increases, the pdf deviates from a Gaussian distribution and tends to be more peaked with larger values of kurtosis. In particular, the kurtosis has values of 3.94 and 6.69, for Delta beta=15 degrees and 30 degrees, respectively. A non-Gaussian density function with kurtosis in excess of 3 is indicative of intermittency. A larger value of kurtosis implies a higher degree of intermittency.

Cutting process dynamics by nonlinear time series and wavelet analysis.

We have modeled the dynamics of a cutting process by a two-degree-of-freedom mass-spring system with dry friction. Using nonlinear time series and wavelet analysis, we have investigated the vibrational instabilities of the system for different values of the cutting force. By constructing the phase portraits and calculating the Lyapunov exponents we have delineated the conditions for which a periodic or chaotic motion can occur. The results are verified by means of a time-scale representation of the wavelet power spectrum.