Hertz Contact Theory Research Articles

Development and optimization of ultimate performance self-levelling epoxy asphalt concrete (USEA) for prefabricated deck pavement

Developing prefabricated bridge deck pavement systems can fundamentally avoid the drawbacks caused by traditional on-site construction such as poor continuity of the construction process and significant differences in pavement layer performance. Prefabricated bridge deck pavement requires that the bridge pavement is completed with the steel deck together in the factory indoors thus it needs the concrete has better self-leveling characteristics which is rare for existing pavement materials. This article develops the ultimate performance self-levelling epoxy asphalt concrete (USEA) which both have excellent self-leveling properties and comprehensive performance. The study initially established the self-leveling asphalt concrete rolling model based on asphalt film thickness theory and Hertz contact theory and the critical rolling mechanical calculation results states that the aggregate particles and the skeleton amounts are the key elements for fluidity of concrete. Comprehensive the analysis of rolling model and research on the curing reaction process of epoxy resin, the study raises the material configuration of USEA and determine the gradation by the Bailey’s method. To guarantee the better pavement performance of USEA, the study designs the orthogonal test and establish the Entropy-TOPSIS model to optimize the details mortar schemes of concrete. Through the model calculation, the epoxy resin content and the SBS modified asphalt oil-stone ratio are determined as 20 % and 8.0 % respectively. In this scheme, the high temperature stability is 2805 times·mm-1, the low temperature bending strain is 3662με and the fatigue life can reach 1.200 million times. The study provides a material selection for the development of prefabricated bridge pavement system and the technical reference for the development of other self-leveling materials which has constructive practical significance.

Fundamental Study of Phased Array Ultrasonic Cavitation Abrasive Flow Polishing Titanium Alloy Tubes

A new method of machining ultrasonic cavitation abrasive flow based on phase control technology was proposed for improving the machining efficiency of the inner wall of TC4 (Ti-6Al-4V) titanium alloy tubes. According to ultrasonic phase control theory and Hertzian contact theory, a model of ultrasonic abrasive material removal rate under phase control technology was established. Using COMSOL Multiphysics 6.1 software, the phase control deflection effect, acoustic field distribution, and the size of the phase control cavitation domain on the inner wall surface were examined at different transducer frequencies and transducer spacings. The results show that the inner wall polishing has the most excellent effect at a transducer frequency of 21 kHz and spacing of 100 mm. In addition, the phased deflection limit was explored under the optimal parameters, and predictive analyses were performed for voltage control under uniform inner wall polishing. Finally, the effect of processing time on polishing was experimented with, and the results showed that the polishing efficiency was highest from 0 to 30 min and stabilized after 60 min. In addition, the change in surface roughness and material removal of the workpiece were analyzed under the control of the voltage applied, and the experimental results corresponded to the voltage prediction analysis results of the simulation, which proved the viability of phase control abrasive flow polishing for the uniformity of material removal of the inner wall of the tube.

Time-varying displacement excitation and dynamic modeling of angular contact ball bearing with local defects

Angular contact ball bearings will produce fault damage when working for a long time, thus affecting the normal operation of the system. This paper takes angular contact ball bearings with local defects on the outer ring as the research object, proposes a method to distinguish different local defect profiles, establishes a generalized characterization model of time-varying displacement excitation of local defects in angular contact ball bearings, and studies the evolution process of local defects and their displacement excitation mechanism. On this basis, considering the influence of time-varying displacement caused by bearing defects on dynamic characteristics, based on Hertz contact theory, a fault dynamics model of angular contact ball bearings is established, and the correctness of the established model is verified by experiments. In addition, the analysis results show that rectangular local defects will eventually evolve into trapezoidal shapes; the displacement excitation change trends induced by different defect morphologies are different; compared with the length of local defects, the width has a greater impact on displacement excitation. The research results provide a theoretical basis for bearing optimization design and fault diagnosis.

Dynamic Modeling of Angular Contact Ball Bearing with Local Defects under EHL Considering Impact Force

In order to analyze the operating status of angular contact ball bearings(ACBBs) with local defects in more detail, a dynamic model of ACBB with local defects considering impact force under elastohydrodynamic lubrication conditions is proposed. Firstly, an elastohydrodynamic lubrication model for defective bearings considering spin is established, the film thickness and film stiffness of the defective bearings are calculated, and then time-varying displacement excitation model and time-varying stiffness model for local defects in angular contact ball bearings is presented. Based on this, an instantaneous impact force function related to defect size and bearing speed is established. Secondly, based on Hertz contact theory and impact force function, a dynamic calculation method for ACBBs with local defects on the outer ring is proposed. Finally, the vibration characteristics of ball bearings with faults are investigated, and the influence of different parameters on the dynamic response of the bearings is analyzed. The calculation results show that under lubrication conditions, the impact force on the vibration of the bearing is significantly weakened. With the increase of defect size and load, the frequency of bearing fault characteristics remain unchanged, but its amplitude increases. As the bearing speed increases, the characteristic frequency and amplitude of bearing faults increase.

Acoustics response of granular porous material: experiment and modeling

Granular porous materials such as activated carbon have drawn increasing attention due to their good sound absorption performance at low frequency. However, some unique acoustical behaviors have been observed during sound absorption measurements of granular porous materials in impedance tubes: e.g., circumferential edge-constraint effects, level-dependent absorption behavior, and time-dependent absorption behavior. In order to explain these observations, a 1-dimensional poro-elastic model was first applied to describe the sound propagation in granules stacked in a cylindrical sample holder, as in a standing wave tube. Then this model was extended to a 2-dimensional finite difference (2DFD) model with depth-dependent stiffness of the granule stack considered by combining Janssen's model and Hertzian contact theory. The 2DFD model was validated with the measurements of the granular porous materials, and it was found that the 2DFD model is a powerful tool to analyze the acoustic response of granular porous material, thus providing a means of characterizing the granular materials. In the present work, the above-mentioned experimental observations and the 2DFD model are introduced, and the experiment results are analyzed with the 2DFD model. Finally some future work on granular porous materials is introduced.

Wheel-rail wear characteristics of a modern tram passing curves with small radius

The wheel-rail wear was predicted for modern trams with independently rotating wheelset running on a groove-shaped rail. The tram vehicle-track coupled dynamics model, considering the wheel-rail multi-point contact, was developed using software UM to evaluate the dynamic responses of the vehicle and track. Hertz contact theory, the FastSim algorithm, and Archard material wear model were used to solve the normal contact stress, tangential contact stress, and wheel-ail wear, respectively. The wheel and rail profiles were updated when the wear depth reached to 0.1 mm. In calculation, the wheel and rail wear was calculated and analyzed separately. The results of groove rail and independently rotating wheelset wear predicted by this model coincided with relevant literature, which proved the effectiveness of this model. The wheel and rail wear characteristics of modern trams passing through curved tracks with small radii and the influence of wheel-rail friction coefficient on wheel and rail wear were calculated and analyzed using this model. The results show that the wheel and rail wear on the circular curve and the rear transition curve is more intense. The wheel wear is the most intense on circular curve while the rail wear is on the rear transition curve. The wear of inner and outer rails and wheels of wheelset one increases with the increase of wheel-rail friction coefficient while the wear of inner and outer wheels of wheelset three have no obvious change. The wear of the inner and outer rails is the most intense at the gauge corner position while is the lightest at the guard rail. The wear of wheelset one is more intense than that of wheelset three and the inner wheel wear is more intense than that of the outer wheel. The present analysis contributes to improve the life of tram wheel and rail and reduce the frequency of wheel-rail maintenance during operation.

Study on the Damage Characteristics of Wheat Kernels under Continuous Compression Conditions.

Peeling wheat yields higher-quality flour. During processing in a flaking machine, wheat kernels undergo continuous compression within the machine's chamber. As this compression persists, damage to the kernels intensifies and accumulates, eventually leading to kernel breakage. To study the damage characteristics of wheat kernels during peeling, this study established a continuous damage model based on Hertzian contact theory and continuous damage theory. The model's accuracy was validated through experiments, culminating in the calculation of critical parameters for wheat peeling. This study focused on different wheat varieties (Ningmai 22 and Jichun 1) and kernel sizes (the thicknesses of the small, medium, and large kernels were standardized as follows: Ningmai 22-2.67 ± 0.07 mm, 2.81 ± 0.07 mm, and 2.95 ± 0.07 mm; Jichun 1-2.98 ± 0.11 mm, 3.20 ± 0.11 mm, and 3.42 ± 0.11 mm). Continuous compression tests were conducted using a mass spectrometer, and critical damage parameters were analyzed and calculated by integrating the theoretical model with experimental data. The test results showed that the average maximum crushing force (Fc) for small, medium, and large-sized kernels of Ningmai 22 was 96.71 ± 2.27 N, 110.17 ± 2.68 N, and 128.41 ± 2.85 N, respectively. The average maximum crushing deformation (αc) was 0.65 ± 0.08 mm, 0.68 ± 0.13 mm, and 0.77 ± 0.17 mm, respectively. The average elastic-plastic critical pressure (Fs) was 50.21 N, 60.13 N, and 59.08 N, respectively, and the average critical values of elastic-plastic deformation (αs) were 0.37 mm, 0.38 mm, and 0.39 mm, respectively. For Jichun 1, the average maximum crushing force (Fc) for small-, medium-, and large-sized kernels was 113.34 ± 3.15 N, 125.28 ± 3.64 N, and 136.15 ± 3.29 N, respectively. The average maximum crushing deformation (αc) was 0.75 ± 0.11 mm, 0.83 ± 0.15 mm, and 0.88 ± 0.18 mm, respectively. The average elastic-plastic critical pressure (Fs) was 58.11 N, 64.17 N, and 85.05 N, respectively, and the average critical values of elastic-plastic deformation (αs) were 0.45 mm, 0.47 mm, and 0.52 mm, respectively. The test results indicated that during mechanical compression, if the deformation is less than αs, the continued application of the compression load will not result in kernel crushing. However, if the deformation exceeds αs, continued compression will lead to kernel crushing, with the required number of compressions decreasing as the deformation increases. If the deformation surpasses αc, a single compression load is sufficient to cause kernel crushing. Since smaller wheat kernels are more susceptible to breakage during processing, the peeling pressure (F) within the chamber should be controlled to remain below the average elastic-plastic critical pressure (Fs) of small-sized wheat kernels. Additionally, the kernel deformation (α) induced by the flow rate and loading in the chamber should be kept below the average elastic-plastic critical deformation (αs) of small-sized wheat kernels. This paper provides a theoretical foundation for the structural design and optimization of processing parameters for wheat peeling machines.

Experimental investigation of edge preparation for cemented carbide profile cutting tools using flexible abrasive jet polishing

This paper investigates the impact of a novel Flexible Abrasive Jet Polishing (FAJP) method on the edge preparation of profile cutting tools based on Hertz contact theory. FAJP employs flexible rubber particles encapsulating diamond micro-powders as abrasives for air jet polishing. The results indicate a significant improvement in material removal rate with FAJP compared to traditional drag finishing methods, along with superior surface quality near the tool edge. The duration of abrasive usage has the greatest impact on FAJP, depending on the specific requirements of the tool edge, with options ranging from 400 to 200 h. There exists a correlation between jet pressure and jet time, with a recommended jet pressure of 225 kPa, and different coating effects achievable by adjusting the jet time. A tool speed of 280 rpm is recommended.

Study on Temperature Field Distribution of a High-Speed Double-Helical Gear Pair with Oil Injection Lubrication

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise.

Experimental Analysis of Stress Shielding Effects in Screw Spacers Placed in Porcine Spinal Tissue.

Bone cortical tissues reorganize and remodel in response to tensile forces acting on them, while compressive forces cause atrophy. However, implants support most of the payload. Bones do not regenerate, and stress shielding occurs. The aim is to analyze the biomechanical behavior of a lumbar cage to study the implant's stress shielding. The ASTM E-9 standard was used with the necessary adjustments to perform compression tests on lumbar and thoracic porcine spinal vertebrae. Twelve cases were analyzed: six with the metal prosthesis and six with the PEEK implant. A mathematical model based on the Hertz contact theory is proposed to assess the stress shielding for endoprosthesis used in spine pathologies. The lumbar spacer (screw) helps to reduce the stress shielding effect due to the ACME thread. The best interspinous spacer is the PEEK screw. It does not embed in bone. The deformation capability increases by 11.5% and supports 78.6 kg more than a system without any interspinous spacer.

Dynamic contact and stiffness characteristic analysis of angular contact ball bearings under combined external loads

A nonlinear dynamic model of angular contact ball bearing under combined external loads is established based on the nonlinear elastic Hertz contact theory and raceless control theory. The established dynamic model is solved by employing variable step size Newton Raphson iteration method and the validation of model is verified by comparing the proposed results with the corresponding results come from the existing literatures. The solution of the presented model has high accuracy compared with the existing experimental results. In addition, the computational efficiency of the proposed model is improved significantly by introducing iteration step size adjustment factor. According to the proposed model, the dynamic contact and stiffness characteristics of angular contact ball are studied systematically by investigating the effects of combined external load working conditions on the contact parameters including contact angle and contact force and the stiffness parameters including diagonal stiffness and off-diagonal stiffness. This research can provide the theoretical basis and technique guidance for the designation and manufacture of angular contact ball bearing under combined external loads.

A novel model for detecting prestress by external anchor head section of prestressed anchor cables

Prestressed anchor cables are widely used in ocean engineering, the accurate and efficient prestress measurement is crucial for ensuring their safety and stability. In this study, a new theoretical model based on the Hertz contact theory and fractal theory was proposed to establish the relationship between tangential contact stiffness (TCS) at the interface of the anchorage and the anchor bedding plate in the external anchor head section. This model was validated through indoor static load tests, and its feasibility for practical application was explored by indoor dynamic load tests. The results demonstrate that both tangential load and tensile load are the primary factors determining the value of TCS. TCS decreases with increasing tangential load, but increases with growth in tensile force. The calculated theoretical values based on the proposed model align closely with test data from indoor static load tests, indicating the efficiency of the proposed model in prestress evaluation. The correlation trends between TCS and tensile force observed in dynamic load tests exhibit good consistency with those found in static load tests, which also align with calculated values based on the proposed model, demonstrating its feasibility in dynamic load tests. The proposed model is modified by considering the interactions between the micro-convex bodies, and other parameter such as fractal dimension D need to be considered when applying the proposed model. These findings can provide valuable insights for the application of prestressed anchor cables in ocean engineering.

Wear characteristics evolution of helical gear with initial defects of bearing inner ring

This study investigated the wear characteristics and operational condition of gears with initial defects of the bearing inner ring. The working states of gears were evaluated through a combination of vibration signal analysis, wear debris concentration analysis, qualitative analysis of the wear debris, and tooth surface analysis. Based on the Hertz contact theory, a dynamic model for the gear drive system was constructed, enabling the simulation and comparison of vibration acceleration signals under normal and fault conditions. The research results revealed that bearing defects induced irregularities in vibration frequency and amplitude, adversely affecting the performance and stability of the gear system. Furthermore, these defects trigger the creation of substantial wear debris, which exacerbates gear wear and reduces the gear lifespan by about 15%. Additionally, bearing defects induced intermittent load spikes and uneven stress distribution across tooth contacts, resulting in localized high shear stresses, material flaking, and surface spalling. Consequently, initial defects of the bearing will accelerate gear wear progression and lead to abnormal wear patterns, potentially resulting in the premature failure of the gear train system. The study investigates the underlying mechanisms of gear wear evolution influenced by these defects and offers practical guidelines for the engineering, manufacturing, and maintenance of gear systems.

Contact electrification characteristics of solid oxygen particle-laden flows in liquid hydrogen transportation

The issue of electrostatic safety in liquid hydrogen systems has garnered increasing attention, especially concerning the potential threat of electrostatic explosions due to the collision-electrification phenomenon of solid oxygen particles formed after air leakage in liquid hydrogen pipelines. To delve into the contact electrification characteristics of solid oxygen particle-laden flows in liquid hydrogen transportation, a mathematical model based on the computational fluid dynamics-discrete element method (CFD-DEM) two-phase flow dynamics has been developed. This model integrates the Hertz contact theory for describing particle collision processes and the condenser model for describing particle collision-electrification. The reliability of this model has been validated in existing literature through its ability to capture the flow characteristics of two-phase flow and the electrification characteristics of particle groups. Using density functional theory to compute the solid oxygen work function and considering the low-temperature properties of liquid hydrogen, a series of numerical studies on the flow sedimentation and electrification characteristics of solid oxygen particle-laden flows in liquid hydrogen pipelines have been conducted. The results indicate that particles carry negative charges after colliding with stainless steel pipe walls, with single charge exchange magnitudes of approximately 10−12C for particle-wall continuous collision processes and 10−14C for particle-particle collision processes, resulting in particle charge-to-mass ratios on the order of tens of μC/kg at the outlet interface. The impact of electrostatic forces on particle motion is significant and cannot be overlooked. Furthermore, the effects of velocity, particle diameter, and pipe diameter on particle charge characteristics have been thoroughly analyzed. At low flow velocities, severe particle settlement occurs, leading to increased collision frequency between particles and walls and significant charge accumulation. Increasing flow velocity can mitigate particle settlement and reduce charge levels. Changes in particle and pipe diameters have a minor impact on particle settlement but can increase single charge amounts with larger particle diameters and intensify particle charging with reduced pipe diameters due to shortened radial travel distances, leading to increased collision frequency. Our study meticulously illustrates the charge characteristics of individual particles and particle groups, providing a theoretical basis for assessing the electrostatic safety of liquid hydrogen transportation systems under extreme conditions.

Research on thermal characteristics of double-nut ball screw

Abstract Preload, external load, and feed speed have significant effects on thermal characteristics of ball screws. In this paper, ground on friction heat generation theory and Hertz contact theory, a thermodynamic modeling of the double-nut ball screw is established, heat generation under different preload forces and feed speeds is analyzed, and temperature field is estimated based on finite difference method. The results show that preload and feed speed have a obvious impact on screw nuts temperature. The finite difference method makes numerical calculation of temperature field more convenient.

Contact analysis of output mechanism of cycloidal pinwheel reducer

In order to study the effect of design parameters on the contact performance of cycloid reducer, a new contact collision force model applicable to various restitution coefficients is proposed. Firstly, based on the L-N nonlinear contact theory and improved Winkler model, a contact force model with contact depth index and damping was proposed. Secondly, Hertzian contact theory was used to clarify the contact area, precise position and relative contact speed between the output pin and the cycloidal wheel in the presence of a clearance. By using the improved contact force model and simulation analysis, the effects of structural design parameters and working condition parameters on contact force were discussed. Finally, with the goal of reducing the contact force and volume of the reducer, the NSGA-II multi-objective genetic algorithm was used to construct an optimization model for the structural parameters of the reducer. The results show that the optimized structural parameters can effectively reduce the contact force of the output mechanism.

A modified Hertzian-based wheel-rail contact model for vehicle system dynamics simulation

This paper develops a modified Hertzian-based wheel-rail contact model (MHM) to improve the robustness and accuracy of the traditional Hertzian contact model in vehicle-track coupling dynamics simulation. First, the wheel-rail non-Hertzian contact area is estimated based on the virtual penetration (VP) area, and an equivalent ellipse of the non-Hertzian contact area is calculated. Then, taking the equivalent elliptical contact patch as the input, the wheel-rail normal problem is solved by using Hertzian contact theory. Finally, considering the effect of the non-elliptical contact patch on Kalker’s linear coefficient, a modified Shen–Hedrick–Elkins model is proposed. The computation accuracy, robustness, and efficiency of the developed MHM are assessed by comparing it with a robust Kalker variational method (RKVM), a VP-based non-Hertzian contact model RNHM, and two traditional Hertzian-based models. The comparison results show that the MHM improves the computational robustness and accuracy of the traditional Hertzian-based contact models. MHM achieves almost the same computational accuracy as the RNHM, but its computational efficiency is 2.4 times faster than RNHM. The developed MHM is an ideal model for vehicle-track coupling dynamics simulation.

Analysis and optimization of repetitive positioning precision for kinematic couplings of opto-mechanical components considering uncertainty

Kinematic coupling, as an efficient form of connection, is frequently employed for the repeated assembly and accurate positioning of replaceable opto-mechanical assemblies within high-power solid-state laser systems. During the kinematic coupling process, uncertainties in the mechanical behavior within the contact region often hinder the attainment of consistent positioning precision, potentially leading to an inability to meet operational requirements. This study aims to enhance the repetitive positioning precision of kinematic couplings. A predictive model for repetitive positioning precision is established, accounting for uncertainties in contact region forces. Based on this model, an optimization design of kinematic couplings is conducted to mitigate these challenges. Initially, accounting for uncertainties in mechanical parameters within the contact region, we formulate a static analysis computational model to elucidate the probabilistic distribution of these parameters. Subsequently, employing Hertz contact theory and Holm-Archard wear theory, we quantify the elastic deformation and equivalent wear for each contact region through the calculation of normal pressures. Building upon this foundation, we establish a predictive model for repetitive positioning precision. Finally, optimization design is carried out on the friction coefficient of contact surfaces and the structural dimensions of positioning elements. The proposed optimization design is validated through experimental verification. The findings demonstrate that optimization of structural dimensions and contact surface friction coefficients resulted in enhanced repetitive positioning precision of 35.9 %, effectively ameliorating the assembly quality. This study contributes a quantifiable analytical approach to the prediction and optimization design of repetitive positioning precision in kinematic couplings.

Numerical and experimental investigation into tool-workpiece interaction in flexible abrasive tool finishing

The present work examines the finishing performance of oxygen-free high conductivity (OFHC) copper using a fabricated flexible abrasive tool. It is challenging to finish soft materials like copper and aluminium using traditional finishing techniques due to frequent scratching. Flexible finishing tool can protect the surface integrity of the workpiece samples during finishing action. Flexible abrasive tools are fabricated using solvent casting method. This method fabricates the flexible tools with homogeneous abrasive dispersion and an open-cell porous structure. The developed tool is self-sharpening and self-lubricating and can finish soft materials efficiently. The flexible abrasive tools can be fabricated in different shapes and sizes to finish internal features and complex shapes. The interaction between the tool and workpiece is examined by the forces exerted by the flexible tool on the workpiece. The areal surface roughness of the finished surface is reduced to 33 nm from its initial roughness of 937 nm after 20 min of finishing a pre-defined region. Theoretical analysis is carried out to estimate contact pressure using Hertz contact theory. The results obtained from numerical and theoretical analysis have a close correlation with the experimental results. The maximum deviation of peak contact pressure obtained in theoretical estimation and numerical analysis from experimental results is found to be 20.73 % and 12.83 %, respectively. As the model includes the basic physics of the tool-workpiece interaction, the results can be improved with the inclusion of micro-level analysis of fluid-filled flexible abrasive tools with embedded abrasives.

Design criteria for conformal integration of flexible electronics on advanced aircraft surfaces

This paper introduces a set of design criteria that aim to integrate flexible electronics onto three-dimensional surfaces in a mechanically adaptive manner. Previous studies have been limited to conformal integration on specific shapes (Such as spherical surfaces and corrugated surfaces) of rigid surfaces or soft substrates, there is a lack of a universal design strategy that takes into account the complexity of substrate shapes and varying hardness. To address this gap, the paper outlines a mechanical model that utilizes Hertzian contact theory to describe the interaction between the thin film and the substrate, and the conformal surface morphology and stress state were derived from minimizing the total energy of the island-substrate structure. The proposed formulations are verified through finite element methods and experiments, analyzing the effects of Young's modulus, in-plane size, and thickness of the “island” on its conformability. Therefore, this paper proposes a generic on-demand conformal design strategy that takes into account the complexity and hardness of the substrate. This study's findings will contribute to the development of conformal electronics that can be used in various fields, such as epidermal electronics, flexible robots, robot electronic skin, and aircraft smart skin.