Trapezoidal Beam Research Articles

A Novel Design Strategy for Cantilever Based MEMS Piezoelectric Vibration Energy Harvesters: FEM Parametric Analysis and Modeling

Vibration-based energy-harvesting (VEH) technology is a viable alternative power source that addresses the issue of battery capacity constraints in portable electronic devices. A novel design strategy for developing a piezoelectric vibrational energy harvester (PVEH) based on a microelectromechanical system (MEMS) is proposed in this paper. Through FEM simulation and analysis, a correlation between the proof mass coverage (PMC) and piezoelectric coverage (PEC) for energy harvesters with different beam geometries is developed. The results show that the output power and resonant frequencies of the energy harvester are strongly dependent on the amount of PMC, PEC, and beam geometry. The optimum piezoelectric layer length for a PVEH depends on the amount of PMC and geometry of the beam. Moreover, as the PMC increases, the output power is found to be increasing. The structure with 80% PMC provides maximum output power. Also, a trapezoidal beam will give a lower resonant frequency than a rectangular beam. Thus the optimum design methodology for a cantilever-based MEMS PVEH in a given layout is to select the trapezoidal-shaped beam with a PMC of 60% to 80% and piezoelectric layer length equal to the beam length. This method would provide optimised resonant frequency and output power performance. Additionally, an analytical model is developed for the optimised cantilever PVEH based on trapezoidal geometry, and the simulation findings are validated with the analytical results.

The Force-Frequency Characteristics of Quartz Wafers under a Cantilever Beam Structure.

This study investigated the force-frequency characteristics of quartz wafers inside a cantilever beam frame. Firstly, the force-frequency coefficient formula of quartz wafers with fixed ends under axial force was analyzed. Firstly, the formula for the force-frequency coefficient of quartz wafers with fixed ends under axial force was analyzed. A force-frequency coefficient formula suitable for cantilever beam structures was derived by considering the changes in surface stress and stiffness of quartz wafers with fixed ends and one end under force on the other. Subsequently, the formula's accuracy was verified by experiments, and the accuracy was more than 92%. In addition, strain simulation analysis was performed on three different shapes of quartz wafers, and experimental verification was carried out on two of them. The results revealed that trapezoidal quartz wafers and cantilever beam structures exhibited superior stress distribution to rectangular chips. Furthermore, by positioning electrodes at various locations on the surface of the quartz chip, it was observed that, as the electrodes moved closer to the fixed end, the force-frequency coefficient of the rectangular quartz chip increased, along with an increase in chip strain under the cantilever structure. In summary, this study provides a new approach for designing cantilever quartz resonator sensors in the future.

Design and experimental investigation of a positive feedback magnetic-coupled piezoelectric energy harvester

A positive feedback magnetic-coupled piezoelectric energy harvester (PFM) is proposed to address the limitations of current piezoelectric energy collectors, including restricted acquisition direction, limited acquisition bandwidth, and low energy output. Firstly, the dynamic theoretical model of the energy harvester was established, and the optimization factors were explored, providing a solid theoretical foundation for subsequent research endeavors. The energy capture characteristics of rectangular beam and compound trapezoidal beam were compared through finite element simulation analysis. Subsequently, an experimental platform was constructed and an optimized experimental methodology was devised to analyze the energy capture characteristics and enhance the performance of the energy harvester. The results demonstrate that the positive feedback magnetic-coupled PFM with a trapezoidal beam exhibits superior energy capture efficiency. Furthermore, it is observed that the optimized energy harvester possesses wide frequency coverage, multi-directional capabilities, low-frequency adaptability, and facilitates easy vibration. When the 45 kΩ resistor is connected in series and subjected to a longitudinal external excitation amplitude of 0.5 g, it is capable of generating an average voltage and power output of 4.20 V and 0.39 mW respectively at a vibration frequency of 9 Hz. Similarly, when exposed to a transverse external excitation amplitude of 1 g, it can produce an average voltage output of 6.2 V and power output of 0.85 mW at a vibration frequency of 19 Hz. When the inclination angle of the energy harvester is set to 35 degrees, the maximum voltage output occurs at a frequency of 18 Hz and the Z-axis to X-axis force ratio of the energy harvester is 1.428. These research findings can serve as valuable references for piezoelectric energy harvesting applications in self-powered microelectronic systems.

The geometry uniformity parameters effect on the dynamic behaviour of trapezoidal beam

Understanding the delicate interplay between geometric design principles and dynamic responses is vital for numerous engineering applications because it allows optimization of structural integrity and performance for manufacturing and special use of this structures. In this study, a complete numerical analysis is undertaken to investigate how differences in geometric parameters impact the structural behaviour of a cantilever smart trapezoidal beam, giving useful insights for engineering applications. The beam consists of a host structure made of aluminum couple with two piezoelectric layers on its top and bottom surface. For such purpose, the study a 3D finite element model has been implemented in ANSY APDL and applied by Matlab we used the interfaces between the two software, considering that the beam changes its form in the axial direction following polynomial based function. The function takes two geometric parameters as an input which are the tapering ratios and the degree of non-uniformity. The beam is then subjected to a harmonic based excitation and the effect of changing tapering ratios and the degree of non-uniformity is analyzed., allowing analysis of the effects of altering tapering ratios and the degree of non-uniformity The results led to a conclusion that just by manipulating the mentioned parameters a considerable changing in the fundamental frequency and the amplitude has been noticed. Addition our numerical analysis shows that small changes to the tapering ratios and degree of non-uniformity have a considerable influence on the behavior of cantilever smart trapezoidal beams. These discoveries add to continuing research in smart materials, paving the road for creative engineering solutions.

Experimental study on the piezo-based energy harvester utilizing the ambient vibrations for smart applications

The proposed energy harvester has novel construction, its performance evaluated through frequency response, force response and power harvested under an optimum load, is presented. This harvester is more suitable for low power applications like IoT devices, Wireless sensor nodes and biomedical implants. The suggested harvester has two sections namely truncated cone and rectangular beam section (TCRB). The analytical model is formulated and natural frequencies are obtained using FEA tool. Simulations for natural frequencies and associated comprehensive parameters are done along with distribution of stress across the piezo patch. The tapered radius ratio of the truncated cone is analysed to obtain the optimal value. The simulated model is fabricated and verified experimentally. The result is compared with uniform cantilever beam harvester. The voltage produced by a TCRB harvester is 56.76 % higher than the harvester with a homogeneous rectangular cantilever beam. The rectangular harvester has a resonant frequency of 52.8 Hz, while the TCRB harvester has 39.4 Hz. Also, the TCRB type piezoelectric vibration energy harvester with optimum taper radius ratio provides greater power, than uniform and trapezoidal cantilever beams. The obtained experimental results match the simulation results, ascertains the validity of the proposed harvester.

Trapezoidal dual-function splitter under second Bragg incidence

In this paper, a reflective trapezoidal dual-functional beam splitter grating is proposed, which performs two independent functions at 1550 nm. For TE polarization, the grating can achieve a uniform three-port output with efficiencies of 32.85%, 32.89%, and 32.75% for 0th, -1st, and -2nd orders respectively. For TM polarization, the grating can achieve a highly-efficient single-channel output of order -2nd with an efficiency of 93.27%. HfO2 is chosen as the material of grating ridge layer, the structural parameters of the grating are studied by using rigorous coupled-wave analysis (RCWA) and simulated annealing algorithm (SAA), and the results are verified by using finite element method (FEM). In addition, the influence of structure and incident error on grating efficiency was also analyzed, the results indicate that the grating has good incident bandwidth and manufacturing tolerance with excellent performance.

Distributions of tension and torsion in a threaded connection

Threaded connection is a common structure in engineering applications, and its load distribution plays a critical role on the static and dynamic performances of the system. Although Sopwith (1948) studied the tension distribution along a thread helix, a model that includes the tension and torsion distributions in threaded connections is still missing. In this paper, we establish a comprehensive model which takes tension–torsion coupling into consideration for thread connection for the first time. In the proposed model, the bolt and nut are considered as two linearly elastic bodies with a tension–torsion coupling deformation, and deformation of the thread is calculated by the modified theory of the trapezoidal cantilever beam model. Based on the compatibility condition of these deformations, tension–torsion coupling equilibrium equations for the threaded connection can be built up. Our theoretical analysis shows that the proposed model agrees with the Sopwith’s theory when the lead angle of the threaded connections is sufficiently small. However, the torque neglected by the Sopwith’s theory must be taken into account in the cases of threaded connections with large lead angles. In addition, we perform a three-dimensional finite element analysis to demonstrate the validity of the proposed model. Finally, influence of geometrical and material parameters on load distribution is investigated. The finding of this work may provide a new insight into the fastening and anti-loosening design for threaded connections.

Linear analysis of the gravitational beam–plasma instability

We investigate the well-known phenomenon of the beam–plasma instability in the gravitational sector when a fast population of particles interacts with the massive scalar mode of a Horndeski theory of gravity, resulting in linear growth of the latter amplitude. Following the approach used in the standard electromagnetic case, we start from the dielectric representation of the gravitational plasma, as introduced in a previous analysis of the Landau damping for the scalar Horndeski mode. We then set up the modified Vlasov–Einstein equation, using a Dirac delta function to describe the fast beam distribution. We thus provide an analytical expression for the dispersion relation, and we demonstrate the existence of a nonzero growth rate for the linear evolution of the Horndeski scalar mode. A numerical investigation is then performed with a trapezoidal beam distribution function, which confirms the analytical results and allows us to demonstrate how the growth rate decreases as the beam spread increases.

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. The current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

Development of Three-Dimensional (3D) Biodegradable Polyglycolic Acid Fiber (PGA) Preforms for Scaffold Applications: Experimental Patterning and Fiber Volume Fraction-Porosity Modeling Study.

Three-dimensional (3D) biodegradable polyglycolic acid fiber (PGA) preforms were developed as temporary scaffolds for three-dimensional tissue regeneration applications. Three-dimensional biodegradable polyglycolic acid fiber (PGA) preforms including various degrees of interlaced structures called 3D plain, semi-interlaced, and orthogonal woven preforms were designed. Analytical relations and finite element model-based software (TexGen) on fiber volume fraction and porosity fraction were proposed to predict scaffolds' stiffness and strength properties considering micromechanics relations. It was revealed that yarn-to-yarn space, density, and angles of all 3D PGA fiber preforms were heterogeneous and demonstrated direction-dependent features (anisotropy). Total fiber volume fractions (Vfp) and porosity fraction (Vtpr) predicted by analytic and numerical modelling of all 3D scaffolds showed some deviations compared to the measured values. This was because yarn cross-sections in the scaffolds were changed from ideal circular yarn (fiber TOW) geometry to high-order ellipse (lenticular) due to inter-fiber pressure generated under a tensile-based macrostress environment during preform formation. Z-yarn modulus (Ez-yarn) and strength (σz-yarn) were probably critical values due to strong stiffness and strength in the through-the-thickness direction where hydrogel modulus and strengths were negligibly small. Morphology of the scaffold showed that PGA fiber sets in the preform were locally distorted, and they appeared as inconsistent and inhomogeneous continuous fiber forms. Additionally, various porosity shapes in the preform based on the virtual model featured complex shapes from nearly trapezoidal beams to partial or concave rectangular beams and ellipsoid rectangular cylinders. It was concluded that 3D polyglycolic acid fiber preforms could be a temporary supportive substrate for 3D tissue regeneration because cells in the scaffold's thickness can grow via through-the-thickness fiber (z-yarn), including various possible mechanobiology mechanisms.

Quasi-Zero Stiffness Isolator Suitable for Low-Frequency Vibration

This paper proposes a quasi-zero stiffness (QZS) isolator based on an inclined trapezoidal beam to explore its advantages in low-frequency passive vibration isolation. The nonlinear stiffness of the inclined trapezoidal beam due to the buckling effect is investigated through finite element simulation, and a linear positive stiffness spring is connected in parallel to form a QZS isolator with high-static and low-dynamic stiffness performance. The natural frequency of the isolator in the QZS region is simulated and analyzed, and the dynamic response of the QZS isolator under different damping ratios, excitation and load conditions is explored. The prototype of the QZS isolator was manufactured, and a static compression experiment was conducted to obtain its nonlinear stiffness. The dynamic experiment results verify the correctness of the simulation conclusions. The simulation and experimental data demonstrate that the QZS isolator has the characteristics of lower initial isolation frequency compared with the equivalent linear isolator. The proposed QZS isolator has an initial isolation frequency of 2.91 Hz and achieves a 90% isolation efficiency at 7.02 Hz. The proposed QZS isolator has great application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

Simulation and Experiment of Trapezoidal Beam‐Based Piezoelectric Energy Harvesters

Piezoelectric energy harvesters (PEHs) are thought to be one of the best ways to power wireless sensors. However, how to improve the electrical properties of PEHs is still a key matter. Herein, a trapezoidal beam (TB) is adopted to improve the electrical outputs of PEHs, where the elastic substrate and thinned piezoelectric ceramic element are combined to obtain a piezoelectric beam with 100 μm total thickness. The simulation results indicate that the TB‐based piezoelectric energy harvester (TB‐PEH) possesses a better electrical output performance than the traditional rectangular beam‐based piezoelectric energy harvester (RB‐PEH). The presented TB‐PEH can generate a 5.4 V voltage output, and an average power of 0.2 mW with the 55 kΩ optimal resistance. The 100, 220, and 470 μF capacitors are used to demonstrate charging from the TB‐PEH, and these capacitors are saturated at 5.1, 5.0, and 4.9 V during 40, 85, and 175 s charging time, respectively. The energy harvester can generate enough power to directly light up four light emitting diodes in real time, indicating its potential to be used as microenergy source for wireless sensor networks in mechanical vibration circumstance under harmonic vibration excitation. The proposed TB‐PEH is conclusively proved potential for charging low‐power electronic devices.

Performance Analysis of Learning-Based Disturbance Observer for Pulsed Superconducting Cavity Field Control

The use of Disturbance Observer-based (DOB) control is widespread in stabilizing the electromagnetic field in superconducting radio frequency cavities to facilitate beam acceleration in particle accelerators. Repetitive disturbances such as beam loading and Lorentz force cavity detuning are compensated by DOB control, and their suppression is enhanced through the incorporation of a learning scheme into the conventional disturbance observer. This paper evaluated the performance of a learning-based disturbance observer for compensating beam loading and cavity detuning in pulsed superconducting radio frequency cavities and proposes modifications for better field stability. A superconducting cavity baseband model for π-mode was simulated in Matlab/Simulink with a trapezoidal beam pulse as the input disturbance and different cavity detuning values to analyze the controllers’ performance. The simulations were conducted for multiple observer filter bandwidths to evaluate the performance of the learning-based disturbance observer under plant model uncertainties and different detuning values. The results demonstrate that the learning-based disturbance observer yields faster convergence to the reference input and lower tracking errors during the flat top of pulse voltage in comparison to conventional disturbance observer control.

Modelling and Characterization Piezoelectric Transducer for Sound Wave Energy Harvesting

Energy harvesting system is using ambient energy conversion in the environment. The environmental energy will be converted into usable electrical energy that can be used in controlling wireless electronic devices. The available mechanical vibration from the sound energy will then be converted to electrical energy by using a piezoelectric transducer. The size of the piezoelectric represents the surface area of the electrode on the piezoelectric model. A smaller size piezoelectric transducer is unable to produce a good vibration due to the smaller surface area. The bigger dimension of the piezoelectric model would be able to harvest more electrical energy output because the vibration from the bigger piezoelectric model which would able to produce more sound wave energy. The piezoelectric material Lead Zirconate Titanate (PZT-5H) vibration is focused on the resonance frequency at below 1 kHz with sound level decibel is between the range of 35-100 dB. This research is to concentrate on rectangular and trapezium-shaped cantilever. The trapezium shaped cantilever produces higher energy output due to its shape which has better in terms of stress and strain distribution. In addition, researchers have modelled and validated energy harvesters with different proof masses shapes. The improved piezoelectric vibrational energy harvester has a trapezoidal beam and an added triangular proof mass. The arrangement of the piezoelectric tested in parallel, series, combination series and parallel configuration to investigate the performance of the output power generated from the sound wave. The rectangular and trapezium shaped cantilever are resulted in a resonant frequency of 269.4 Hz and 269.88 Hz, respectively. The rectangular and trapezium shaped cantilever produced a maximum output voltage of 3.105 V and 3.635 V respectively. The piezoelectric output during the parallel array configuration, which is 5.636 V, 0.497 mA and 2.803 mW. The output power produced by parallel is 81 % higher than compare in series array configuration and 35.8 % higher than combination of series and parallel. Thus, the produced energy output 5 V would be able to apply at several low power supply applications such as mobile phones, power bank or wireless sensor networks (WSN).

A Miniaturized Piezoelectric MEMS Accelerometer with Polygon Topological Cantilever Structure.

This work proposes a miniaturized piezoelectric MEMS accelerometer based on polygonal topology with an area of only 868 × 833 μm2. The device consists of six trapezoidal cantilever beams with shorter fixed sides. Meanwhile, a device with larger fixed sides is also designed for comparison. The theoretical and finite element models are established to analyze the effect of the beam′s effective stiffness on the output voltage and natural frequency. As the stiffness of the device decreases, the natural frequency of the device decreases while the output signal increases. The proposed polygonal topology with shorter fixed sides has higher voltage sensitivity than the larger fixed one based on finite element simulations. The piezoelectric accelerometers are fabricated using Cavity-SOI substrates with a core piezoelectric film of aluminum nitride (AlN) of about 928 nm. The fabricated piezoelectric MEMS accelerometers have good linearity (0.99996) at accelerations less than 2 g. The measured natural frequency of the accelerometer with shorter fixed sides is 98 kHz, and the sensitivity, resolution, and minimum detectable signal at 400 Hz are 1.553 mV/g, 1 mg, and 2 mg, respectively. Compared with the traditional trapezoidal cantilever with the same diaphragm area, its output voltage sensitivity is increased by 22.48%.

Thermal buckling analysis of thin-walled closed section FG beam-type structures

In this paper, thermal buckling analysis of thin-walled, functionally graded (FG) beam-type structures with closed cross-sections and various boundary conditions is investigated. One dimensional finite element model, based on Euler–Bernoulli–Vlasov​ theory, is employed under the assumptions of large rotations and small strains. Two cases of temperature rise across the thickness of the cross-section walls are considered, which are uniform and linear. Stability analysis has been performed in eigenvalue manner and in load–deflection manner using Newton–Raphson method. Numerical results for thin-walled box beams and trapezoidal beams for two different FG materials configurations are presented to investigate the effects of temperature distribution, boundary conditions, and material properties on the critical buckling temperature and global buckling behaviour. The accuracy and reliability of the beam model is verified by comparing it with several benchmark examples. Good agreement was observed, showing possibility of further application of the proposed model which requires reduced computational time and provides greater modelling flexibility compared to commercial codes.

Tapered substrate thickness to enhance the performance of a piezoelectric energy harvester

In this paper, the improvement of the performance of a piezoelectric (PZ) cantilever beam using a non-uniform substrate thickness is presented. This reduces the resonant frequency, improves the stress distribution and generates more output voltage and power. Both analytical and finite-element method analyses were performed to investigate the effect of a tapered substrate thickness on a PZ cantilever beam. A tapered substrate thickness was used in rectangular and trapezoidal cantilever structures. All of the designed cantilever structures had the same fabrication area, and their performance was evaluated and compared using an excitation acceleration of 1g (9.8 m/s2). The tapered-down trapezoidal cantilever achieved a minimum resonant frequency of 62.41 Hz, which was 48.83% less than the resonant frequency of the uniform rectangular cantilever beam. The output peak voltage and average power of the proposed tapered-down trapezoidal cantilever beam were 12.36 V and 21 μW, respectively, which were improved by 44 and 74.48%, respectively, compared with those of the uniform rectangular cantilever structure.

Design and Optimization of Piezoelectric Cantilever Beam Vibration Energy Harvester.

Piezoelectric cantilever beams are commonly utilized to harvest energy from environmental vibrations due to their simple structures. This paper optimizes a single crystal trapezoidal hollow structure piezoelectric cantilever beam vibration energy harvester with a copper substrate to achieve high energy density at a low frequency. Finite element analysis (FEA) is adopted to optimize the size of the copper substrate at first, and the piezoelectric energy harvester (PEH) is further optimized with a trapezoidal hollow structure under the optimal size of the copper substrate. The developed PEH with a trapezoidal hollow structure (La = 20 mm, Lb = 15 mm, and Lh = 40 mm), with a copper substrate of 80 mm × 33 mm × 0.2 mm, can obtain the best output performance. Under the condition of 1 g acceleration, the resonance frequency and peak voltage output were 23.29 Hz and 40.4 V, respectively. Compared with the unhollowed PEH, the developed trapezoidal hollow structure PEH can reduce its resonant frequency by 12.18% and increase output voltage by 34.67%, while also supplying a power density of 7.24 mW/cm3. This study verified the feasibility of the optimized design through simulation and experimental comparison.

ШИРИНА РАСКРЫТИЯ НОРМАЛЬНЫХ ТРЕЩИН В ЖЕЛЕЗОБЕТОННЫХ БАЛКАХ ТРАПЕЦИЕВИДНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

The article discusses experimental studies of the values of the crack opening width at various stages of loading the investigated trapezoidal beams. For comparison, reference samples of rectangular and tee cross-sections with the same overall dimensions are also considered. The use of trapezoidal beams in construction practice can significantly reduce the consumption of concrete in comparison with rectangular beams. It should be noted that when constructing trapezoidal beams, complete disassembly of the formwork is not required in comparison with beams of T-shaped and rectangular profiles. The paper compares the values of the loads of the appearance of the first cracks in beams with different transverse outlines. The values of the loads corresponding to the achievement of the normative limiting value of the crack opening width have been determined. In the course of the study, it was found that cracks in trapezoidal beams reach the maximum opening width at a higher loading level than cracks in rectangular and tee beams due to a greater number of cracks along the length of the element. An analysis of both absolute and relative characteristics was carried out, taking into account the consumption of concrete over the section of the elements. The main advantages and disadvantages of bending reinforced concrete elements of trapezoidal cross-section in comparison with reference samples are highlighted

High-Stiffness Torque Sensor With a Strain Amplification Mechanism for Cooperative Industrial Manipulators

This study presents a high-stiffness torque sensor with a strain amplification mechanism for cooperative industrial manipulators. A novel strain amplification mechanism for a torque sensor has been designed to increase the stiffness of the sensor. The mechanism has a single structure composed of trapezoidal beams, flexure structures, and inner and outer frames. In this configuration, the displacement that occurs in the beam is amplified by the flexure structure. The amplified displacement is measured using capacitance sensing technology. As a result, the developed torque sensor has a high stiffness (198.7 kN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cdot$</tex-math></inline-formula> m/rad) and compactness (diameter of 110 mm and a thickness of 9.8 mm) that integrates with all the electronics. Additionally, it has a low cost and it is easy to manufacture. Through several experimental setups, we evaluated the sensing performances of the sensor with regard to accuracy, high stiffness, and repeatability.