Friction Force Measurements Research Articles

Quasi-static cyclic tests of FRP-confined steel-reinforced HPFRCC circular columns

This study presents a novel composite component comprising of steel-reinforced high-performance fiber reinforced cementitious composites (HPFRCC) circular columns confined by fiber-reinforced polymer (FRP), with the goal of improving the mechanical behavior of conventional reinforced concrete (RC) columns. Quasi-static cyclic loading tests were conducted to investigate various aspects of the column specimens, including failure phenomena, load-displacement response, sectional compression-bending performance, plastic hinge length, and lateral strain distributions in the FRP jacket, etc. A self-designed frictional force measurement device was employed to accurately measure the actual force borne by the specimen. The experiment results revealed that FRP confinement effectively improved the load-bearing capacity and deformation capacity of the specimens and delayed the deterioration of the sectional compression-bending performance. The superior tensile ductility of HPFRCC led to increased yielding displacement and peak load compared to FRP-confined concrete specimen, although this enhancement was limited. Furthermore, the peak load of the FRP-confined HPFRCC specimen increased with axial load, while the sectional compression-bending performance after the peak load remained relatively stable until approaching the collapse prevention (CP) limit state.

Parasitoid attachment ability and the host surface wettability

Climbing animals such as geckos and arthropods developed astonishing adhesive mechanisms which are fundamental for their survival and represent valuable models for biomimetic purposes. A firm adhesion to the host surface, in order to successfully lay eggs is necessary for the reproduction of most parasitoid insects. In the present study, we performed a comparative investigation on the attachment ability of four parasitoid species (the egg parasitoid Anastatus bifasciatus (Eupelmidae), the aphid parasitoid Aphidius ervi (Braconidae), the fly pupal ectoparasitoid Muscidifurax raptorellus (Pteromalidae) and the pupal parasitoid of Drosophila Trichopria drosophilae (Diapriidae)) with hosts characterized by a surface having different wettability properties. The friction force measurements were performed on smooth artificial (glass) surfaces showing different contact angles of water. We found that attachment systems of parasitoid insects are tuned to match the wettability of the host surface. Sexual dimorphism in the attachment ability of some tested species has been also observed. The obtained results are probably related to different microstructure and chemical composition of the host surfaces and to different chemical composition of the parasitoid adhesive fluid. The data here presented can be interpreted as an adaptation, especially in the female, to the physicochemical properties of the host surface and contribute to shed light on the coevolutionary processes of parasitoid insects and their hosts.

Electrical measurement method of static friction force on rough surface

Friction plays a key role in the assessment of the safety and stability of mechanical systems (such as superconducting magnet quench explosion, aerospace vehicle bearing wear, etc.). Due to the closeness of the interfaces in engineering structures and the randomness of the contact surfaces, existing methods for measuring static friction force are unable to measure it at the contact interfaces of engineering structures under service conditions. In this paper, a new method for measuring the static friction force at the interface based on electrical signals is proposed. This method enables the measurement of the static friction force at interfaces of complex engineering structures under service conditions solely through electrical signals. The results indicate that the contact resistance gradually decreases with the increase in tangential load during the static friction stage until a monotonic behavior of macroscopic sliding occurs. The evolution of contact resistance is linked to the evolution of the real contact area, and this monotonic behavior can be explained as the deformation form of contact points. The accuracy of the proposed electrical measurement method is verified by comparison with experimental results (with an error of less than 9%). The indirect measurement method of friction force proposed in this paper can effectively measure the static friction force at the interfaces of engineering structures under service conditions, and it is expected to be applied to the detection of friction performance at engineering structure interfaces in extreme service environments.

Evaluation of Temperature-Dependent Boundary Lubrication Behavior of Stearic Acid Using a Force-Controlled Tribometer.

A quick evaluation of the effectiveness of additives is important in lubricant formulation. In this study, we employed a friction-force measurement approach using a newly designed lateral force-controlled tribometer. This tribometer evaluates the lubricant properties under boundary lubrication. In this lateral force-controlled tribometer, the absence of a stiffness-altering sensor enables the modeling of the actual contact conditions without altering the contact stiffness. Indirect friction force measurement ensures precise measurements of friction properties while avoiding common measurement errors encountered in conventional tribometers, such as sensor misalignment and changes in the stiffness of the machine due to the sensor. The tribometer designed and built consists of a pendulum that measures the rate of dissipation of the oscillation amplitude as a function of time. The unique characteristics of the machine are the possibility of changing the energy input into the tribosystem without altering the tribo-contact conditions and the capability to do experiments at higher temperatures. To evaluate the capabilities of this tribometer, the impact of temperature on the frictional properties of a base oil and a blend of base oil and stearic acid (SA) (a prominent Organic Friction Modifier) is investigated. The test result shows that frictional energy dissipation decreases when stearic acid is present in the lubricant. And, as the temperature of the oil increases, the energy dissipation increases for pure base oil but reduces for the blend. The observed frictional trends are attributed to the decrease in the viscosity of the base oil with an increase in the temperature. The decrease in friction for the SA blend is attributed to tribofilm formation. Fourier transform infrared (FTIR) and X-ray Photoelectron Spectroscopy (XPS) analyses confirm the presence of the SA tribofilm on the surface. XPS indicates an increase in tribofilm quantity with rising temperatures. The kinetics of film formation and thickness increase with temperature, consequently reducing the friction in the SA blend.

Nature‐Inspired Directional Microneedle Structures for Reversible Gripping on Skin and Fibrous Materials

Plants such as Galium aparine show directional gripping to various surfaces because of their microscale hook structures. A bio‐inspired artificial version of microhooks holds potential as a bidirectional, reversible, and reusable dry adhesive for soft, wet, or fibrous substrates such as skin or textiles. However, current methods for fabricating 3D structures are often costly, time‐consuming, or require precise alignment steps. Herein, a facile, cost‐effective, scalable, and unconventional microfabrication technique is proposed using tilted photolithography on a rotary stage and shear molding to fabricate a soft polydimethylsiloxane polymer mold containing the inverse replica of directional microneedle structures. To demonstrate the proof‐of‐concept, polyurethane is then added to the mold to obtain directional microneedles, referred to as microhooks. Friction force measurements using a nanotribometer show anisotropic performance (strong attachment in one direction and easy detachment in the opposite direction over multiple cycles) similar to the natural microhooks. Tribological characterization of the microhooks shows a gripping force 2.25 times greater than the sliding force. The fabricated microhook structures also provide an adhesion force of ≈0.62 N cm−2 to artificial skin. This biomimetic approach promises precise adhesion control and material versatility for attaching wearable devices and patches to the skin in biomedical applications.

ALTERNATE SLIDING FRICTION FORMULATIONS OF ELASTO - HYDRODYNAMIC OF SPUR GEARS

In this paper, several sliding friction formulations used in spur gear dynamics are examined and compared in terms of the predictions of interfacial friction forces and off-line-of-action. Computing friction formulations include Coulomb models with time-varying friction coefficients and empirical expressions based on elasto - hydrodynamic and/or boundary lubrication regime principles. Predicted results compare well with friction force measurements and appeared completely conformed with specific objectives of this paper are established as follows: (1) propose an improved MDOF spur gear pair model with time-varying coefficient of' friction, µ(t), given realistic mesh stiffness profiles.(2) comparatively evaluate alternate sliding friction models and predict the interfacial friction forces and motions in the off-line-of-action (OLOA) direction: and (3) validate one particular model (III) by comparing predictions to the benchmark gear friction force measurements

Pathways of Water-Induced Lead-Halide Perovskite Surface Degradation: Insights from In Situ Atomic-Scale Analysis.

While organic-inorganic hybrid perovskites are emerging as promising materials for next-generation photovoltaic applications, the origins and pathways of perovskite instability remain speculative. In particular, the degradation of perovskite surfaces by ambient water is a crucial subject for determining the long-term viability of perovskite-based solar cells. Here, we conducted surface characterization and atomic-scale analysis of the reaction mechanisms for methylammonium lead bromide (MA(CH3NH3)PbBr3) single crystals using ambient-pressure atomic force microscopy (AP-AFM) and near-ambient-pressure X-ray photoelectron spectroscopy (NAP-XPS) in environments ranging from ultrahigh vacuum to 0.01 mbar of water vapor. MAPbBr3 single crystals, grown by a solution process, were mechanically cleaved under UHV conditions to obtain an atomically clean surface. Consecutive topography and friction force measurements in low-pressure water (pwater ≈ 10-5 mbar) revealed the formation of degraded patches, one atomic layer deep, gradually increasing their coverage until the surface was entirely covered at a water exposure of 4.7 × 104 langmuir (L). At the perimeters of these degraded patches, a higher friction coefficient was observed, along with an interstitial step height, which we attribute to a structure equivalent to that of the MA-Br terminated surface. Combined with NAP-XPS analysis, our results demonstrate that water vapor induces the dissociation of surface methylammonium ligands, eventually resulting in the depletion of the surface MA and the full coverage of hydrocarbon species after exposure to 0.01 mbar of water vapor.

Tribological devices in cycling: A review

This review, focussed on transmission efficiency and wear in cycling, presents existing friction measuring devices. It discusses their pros and cons and compares the lubrication regime they are in to the ones determined for elite cycling. Finally, it addresses technical guidelines for measuring friction forces from the transmission ( Ft). Ft depend on normal load and coefficient of friction (µ). Indeed, these factors are influenced by chain tension, alignment and velocity, sprocket size, lubricants and contamination. Such parameters also have an impact on lubrication regime which influences µ. To characterise Ft, measuring devices were developed. Forty devices were classified in five categories, ranging from those closest to ecological conditions to the most specific ones. Full transmission (FTR) and single speed rigs (SSR) results can be extrapolated into real cycling, although they are less accurate as they involve more elements. Dedicated rigs engender high precision measurements on precise phenomena. All lubrication regimes are encountered in elite cycling, which is in good accordance with most of the testing conditions presented in this review, especially FTR and SSR. If Boundary and Mixed regimes are unavoidable due to the reciprocating movements of the chain elements, they should be limited. The Elasto-Hydrodynamic regime is on target as it provides low µ and wear. In conclusion, the closer the measure is to real cycling, the higher the variability. Inversely, dedicated rigs are accurate but less representative of complete transmissions. Technology improvements now make FTR and SSR reliable enough to measure small differences, along with a strong protocol.

Designing and Modelling of Pivotal Friction Compensator of Actuator of Hard Disk Drives

Nowadays, hard disk drives are one of the most common devices for storing data. The growing demand for storing the bulk amount of data and retrieving the data as fast as possible from hard disk drives (HDDs) has posed manufacturers with various challenges. To overcome these hurdles different methods, techniques, and control systems are developed to improve the transient response of the HDDs. The transient response of a system is characterized by numerous specifications such as overshooting, peak time, settling time, delay, and rise time. This can also be achieved by using several stages of actuators servomechanism that can also help us to store a large amount of data, it also helps to increase the accuracy of head-positioning of the actuator that eventually leads to enhancement of the transient response of hard disk drives (HDDs). By increasing the accuracy of read/write head actuator there is a challenge to cater the friction at pivot of actuator. This friction can significantly reduce the speed of the actuator and that ultimately leads to the reduced transient responses of the system. This paper aims to design a new modelled-base friction compensator for the servo control of hard disk drives that can improve the transient response of HDDs. Thus, improving the transient responses of HDDs can make the computer more efficient than ever and can save a lot of time while making complex calculations. To achieve this aim measured and replicated responses will be used as guidance and the friction design of HDD will iteratively improve. This can be done by feeding the measured friction forces back to the voice coil motor (VCM) so that the frequencies of the actuator’s head and current be linearized. This proposed design will help in the cancelation scheme and the model-based compensator will be implemented. By improving the tracking seek of HDDs we can also write the data much faster on the HDD and by using numerous techniques we can store a large amount of data on HDDs. Our aim is also to integrate a PID controller into our control system so that we can improve the transient response as much as possible. Our work can be considered important as there are very few frictions compensator control designs that have integrated the PID controller. We are aiming to achieve a significantly improved pivotal friction compensator that can help us to achieve improved transient response of the hard disk drive (HDD).

Investigation of a strain-gauge dynamometer for measuring boundary layer friction force on the wind tunnel wall

A one-component strain-gauge dynamometer with a measuring range of 0-0.33 N was developed and manufactured at the Central Aerohydrodynamic Institute to measure directly the unsteady friction force of the boundary layer on the wall of a wind tunnel at very high Reynolds numbers. The subject of this study is to investigate the static and dynamic characteristics of the dynamometer and its systematic errors. The effects of the temperature, longitudinal, normal, and side forces and position of the longitudinal force application were investigated during the calibration. A block was designed and manufactured to calibrate the dynamometer using the dead weights in a wind tunnel. The calibration was carried out in laboratory conditions to determine friction force in the block. The developed dynamometer is a dynamic system with its own natural frequency of oscillations. The correction for the dynamometer's own dynamics is suggested on the basis of the method developed earlier. To calculate the correction to dynamometer dynamics the mass of the metric part of the dynamometer, its natural frequency in the absence of damping and the damping coeffi cient were determined. The correction is verifi ed by experiment with application of a step force. Effect of static and dynamic temperature components on dynamometer readings is investigated. Corrections are proposed to eliminate the systematic errors due to the effect of temperature on the basis of the previously developed method. It is shown that the side force does not affect the dynamometer readings, while the effect of the normal force is 1.1 % of the main sensitivity coeffi cient. The effect of the static temperature component on the sensitivity coeffi cient of the dynamometer is 0.017 %/°C. The total measurement uncertainty of the friction force dynamometer is estimated – the standard deviation of the measurement results does not exceed 0.076 % of the measurement range and the relative standard deviation of the main sensitivity coeffi cient is 0.03 %. The standard deviation of measurement of the nonstationary friction force will not exceed 0.86 % of the range of the dynamometer in the presence of oscillations of the sensitive element at its natural frequency.

Methodological problems of friction force measurement of plant granular materials

The methodology for measuring the frictional force of granular materials of plant origin is complex, since it requires taking into account both variable material factors and the use of available measurement methods in an appropriate way. This article deals with one of the important aspects of the application of a measurement methodology using bottomless containers. The effect of grain pressure on the side walls of the measuring container on the value of grain pressure on the measuring surface was studied. Five different granular materials (wheat, oat, beans, maize, peas) were used as the research material. To analyse the problem, the Janssen model was used as a basis, which describes the normal pressure of the granular material at the bottom of the container depending on certain factors. The tests were carried out for different heights of the material layer and different load values. After analysing the measurement values with calculated values, modifications of the base model were proposed. This modification allowed a high (close to 1) model fit to the measured values. The proposed approach can be useful in carrying out measurements of the friction force of granular materials, since it allows one to estimate the value of the actual pressure of the material on the contact surface. This provides an opportunity to make better use of the horizontal tribometer with a measuring container with support.

On the effect of temperature in friction force measurements for a simplified piston cylinder set-up: Squeeze film combined with minimum oil film thickness measurements and viscosity index effect

The lubricated interface at the piston-ring and liner and its interaction with different lubricants and testing conditions is examined in terms of experimental measurements that show the minimum oil film thickness developed at the lubricated or depending on conditions partly lubricated conjunction and the surface interaction intensity, as measured from the friction sensor. An analysis is carried out with the use of different parameters for the experiments as well as different lubricants in a simplified piston-ring simulation test rig. This analysis is further enhanced with the squeeze film effect investigations close to the stroke reversals and together with cavitation initiation and load-carrying effect results from previous experimental data, light is shed on the interacting surface’s behaviour at the different lubrication regimes. Another parameter, the viscosity index of the lubricant is used as an indication of the effects of squeeze film shift and friction force measurements and how the load and temperature effect are influencing the squeeze film.

Friction force-based measurements for simultaneous determination of the wetting properties and stability of superhydrophobic surfaces

HypothesisContact angle and sliding angle measurements are widely used to characterize superhydrophobic surfaces because of the simplicity and accessibility of the technique. We hypothesize that dynamic friction measurements, with increasing pre-loads, between a water drop and a superhydrophobic surface is more accurate because this technique is less influenced by local surface inhomogeneities and temporal surface changes. ExperimentsA water drop, held by a ring probe which is connected to a dual-axis force sensor, is sheared against a superhydrophobic surface while maintaining a constant preload. From this force-based technique, static and kinetic friction forces measurements are used to characterize the wetting properties of the superhydrophobic surfaces. Furthermore, by applying increased pre-loads to the water drop while shearing, the critical load at which the drop transitions from the Cassie-Baxter to Wenzel state is also measured. FindingsThe force-based technique predicts sliding angles with reduced standard deviations (between 56 and 64%) compared to conventional optical-based measurements. Kinetic friction force measurements show a higher accuracy (between 35 and 80%) compared to static friction force measurements in characterizing the wetting properties of superhydrophobic surfaces. The critical loads for the Cassie-Baxter to Wenzel state transition allows for stability characterization between seemingly similar superhydrophobic surfaces.

Force-Based Characterization of the Wetting Properties of LDPE Surfaces Treated with CF4 and H2 Plasmas.

Low-density polyethylene (LDPE) films are widely used in packaging, insulation and many other commodity applications due to their excellent mechanical and chemical properties. However, the water-wetting and water-repellant properties of these films are insufficient for certain applications. In this study, bare LDPE and textured LDPE (T-LDPE) films were subjected to low-pressure plasmas, such as carbon tetrafluoride (CF4) and hydrogen (H2), to see the effect of plasma treatment on the wetting properties of LDPE films. In addition, the surface of the LDPE film was textured to improve the hydrophobicity through the lotus effect. The LDPE and T-LDPE films had contact angle (θ) values of 98.6° ± 0.6 and 143.6° ± 1.0, respectively. After CF4 plasma treatments, the θ values of the surfaces increased for both surfaces, albeit within the standard deviation for the T-LDPE film. On the other hand, the contact angle values after H2 plasma treatment decreased for both surfaces. The surface energy measurements supported the changes in the contact angle values: exposure to H2 plasma decreased the contact angle, while exposure to CF4 plasma increased the contact angle. Kinetic friction force measurements of water drops on LDPE and T-LDPE films showed a decrease in friction after the CF4 plasma treatment, consistent with the contact angle and surface energy measurements. Notably, the kinetic friction force measurements proved to be more sensitive compared to the contact angle measurements in differentiating the wetting properties of the T-LDPE versus 3× CF4-plasma-treated LDPE films. Based on Atomic Force Microscopy (AFM) images of the flat LDPE samples, the 3× CF4 plasma treatment did not significantly change the surface morphology or roughness. However, in the case of the T-LDPE samples, Scanning Electron Microscopy (SEM) images showed noticeable morphological changes, which were more significant at sharp edges of the surface structures.

The Influence of Temperature on Anisotropic Wettability Revealed by Friction Force Measurement.

Anisotropic surfaces with special wettability under various temperatures are of both fundamental interest and practical importance in many fields. However, little attention has been paid to the surfaces at temperatures between room temperature and the boiling point of water, which is partially due to the lack of a suitable characterization technique. Here, using the MPCP (monitoring of the position of the capillary's projection) technique, the influence of the temperature on the friction of a water droplet on the graphene-PDMS (GP) micropillar array (GP-MA) is investigated. The friction forces in the orthogonal directions and the anisotropy in the friction decrease when the GP-MA surface is heated up, based on the photothermal effect of graphene. The friction forces also decrease along the pre-stretching direction but increase in the orthogonal direction when the stretching is increased. The change in the contact area, the Marangoni flow inside a droplet, and the mass reduction are responsible for the temperature dependence. The findings strengthen our fundamental understanding of the dynamics of drop friction at high temperatures and could pave the way for the design of new functional surfaces with special wettabilities.

Fluorine-Free Super-Liquid-Repellent Surfaces: Pushing the Limits of PDMS

Methods for fabricating super-liquid-repellent surfaces have typically relied on perfluoroalkyl substances. However, growing concerns about the environmental and health effects of perfluorinated compounds have caused increased interest in fluorine-free alternatives. Polydimethylsiloxane (PDMS) is most promising. In contrast to fluorinated surfaces, PDMS-coated surfaces showed only superhydrophobicity. This raises the question whether the poor liquid repellency is caused by PDMS interacting with the probe liquid or whether it results from inappropriate surface morphology. Here, we demonstrate that a well-designed two-tier structure consisting of silicon dioxide nanoparticles combined with surface-tethered PDMS chains allows super-liquid-repellency toward a range of low surface tension liquids. Drops of water-ethanol solutions with surface tensions as low as 31.0 mN m-1 easily roll and bounce off optimized surface structures. Friction force measurements demonstrate excellent surface homogeneity and easy mobility of drops. Our work shows that fluorine-free super-liquid-repellent surfaces can be achieved using scalable fabrication methods and environmentally friendly surface functionalization.

A study of the role of surface parameters on the relationship between biotribology and cognitive perception involved in the design of tactile graphics

Tactual encoding of information is an essential aspect of communication in many aspects of life, but especially so for persons with visual impairments. The most common encoding is the use of topological features on a static medium such as paper. While Braille is widely used and effective for text transcription, the effective use of tactile graphics to communicate spatial or graphical information is less standardized. Tactile graphical techniques typically employ collections of individual topological features or texture patterns to communicate spatial information (maps, plots, diagrams), with the goal of minimizing reader confusion among the elements. In this study, the authors investigated the tribology and perception aspects of this complex issue in order to identify fundamental surface parameters which play a dominant role. Using texture specification guidelines published by the Braille Authority of North America (BANA), the investigators produced raised parallel-ridge textures on thermally activated tactile paper. The texture parameters modified included the width of ridges, spacing between ridges, and the inclination of the ridges to the pattern boundaries. Subjects reported their perception of tactile similarity or difference between members of texture pairs that were presented under a blind. Measurements of friction force were also collected for these textures to determine if friction mechanisms were most responsible for perceptive ability, or if other surface attributes played a dominant role. The study found that modifying pattern pitch improved perceptive ability to differentiate between adjacent mismatched texture patterns, but that ridge width had a deleterious effect. The results suggested that perceptive ability was not strongly related to various friction mechanisms proposed, but was closely correlated with changes in the number of pattern ridges in contact with the fingertip during tactile graphic exploration.

Empirical research on the friction behavior of O-rings in hydraulic cylinders.

Mechanical products are becoming more diversified with the continuous development of precision processing and materials technologies. The friction force generated by the O-ring seal in a hydraulic cylinder was once considered redundant. However, its utilization has recently been proposed. The hardness of the O-ring and the inner diameter of its groove directly affect the normal pressure between the O-ring and the inner wall of the cylinder, thereby affecting the friction behavior. In order to explore this friction behavior, a strain-based friction force measurement system is developed in this study, and the steady-state and dynamic friction values under different working conditions are studied and discussed in depth. This research on the friction behavior in the cylinder provides a theoretical basis for more convenient design and utilization of the friction force generated between the O-ring and the inner wall of the cylinder.

Viscometer for investigating the viscosity of magnetic fluid media

The rational application of magnetic fluids in various technical systems requires their stability analysis, hydrodynamic particle size, dissipative processes in the colloid control. The existing viscometers do not fully meet all requirements, in particular, they do not allow research in a magnetic field of given magnitude and certain topography. It is proposed to determine rheological properties of magnetic fluids using rotary viscometer, in which two measuring gaps are structurally designed and filled with studied fluid, which is important for calculating characteristics of low viscosity magnetic media. The device design implements practically homogeneous magnetic field, varying within wide range and directed perpendicular to liquid shear stress. The device allows to steadily maintain shear rate in medium under study, and to determine viscosity with a sufficiently large change. A small magnetic fluid volume is required to estimate rheological characteristics. The accuracy of measurements of the internal friction force, device heating temperature, coaxial cylinders rotation speed and magnetic field inside investigated medium meet the requirements of international standards. Laminar fluid flow process in the device gap is described mathematically. This made it possible to justify the construction geometrical dimensions in order to increase the measurements and determine rheological properties of low-viscosity magnetic materials. The formulas for calculation of Newtonian fluid viscosity coefficient, shear stress and shear rate based on experimental data were obtained.

Numerical and Experimental Study of Reciprocating Seals in Seawater Hydraulic Variable Ballast Components for 11000m Operation

Seawater hydraulic variable ballast system (SHVBS) is critical equipment for underwater operations. Reciprocating seals play a vital role in the efficiency and safety of seawater hydraulic components working in SHVBS. However, the sealing performance and friction behavior of reciprocating seals remain unknown under high isostatic and water lubricating conditions. In this work, an innovative mixed lubrication model for reciprocating water hydraulic rod seals is developed based on the elastohydrodynamic lubrication (EHL) theory. An elastic deformation method is introduced to update the film thickness rapidly. The characteristics of the reciprocating seal are studied in a full-ocean-depth pressure range. With the rod speed of 500 mm/s, for sealed pressure of 0.1 MPa and 120 MPa, the maximum friction force increases tenfold from about 30 N to 300 N. A test rig is designed to measure friction force under high pressure. The numerical and experimental results have the same variation pattern, and the relative error is less than 15%.