Finite Element Analysis Software Research Articles

Effect of Cu–Al Ratio on Microstructure and Mechanical Properties of Cu–Al Alloys Prepared by Powder Metallurgy

Cu–Al alloys are widely used in electronics, new energy, and other fields due to the combination of th excellent corrosion resistance and electrical conductivity of Cu and the light weight of Al. In this paper, the powder metallurgy and equal-channel angular pressing compound technology was used to fabricate a Cu–Al alloy joint, which can be used to replace armor. Devices such as an optical microscope, electron scanning microscope, and microhardness scale were used to characterize the microstructure and mechanical properties of the Cu–Al alloys. The finite element analysis software Abaqus was used to analyze stress distribution during equal-channel angular pressing. The results indicated that the microstructure and properties of Cu–Al alloys were closely related to the volume ratio of Cu–Al. The microhardness and tensile strength were significantly increased by increasing the volume ratio of Cu–Al. As the volume ratio of Cu–Al varied from 1:2 to 2:1, the ultimate tensile strength of the Cu–Al alloys increased from 79.9 MPa to 164.9 MPa at room temperature and the microhardness increased from 60 HV to 101 HV. However, the elongation of the Cu–Al alloys hardly changed; this was about 4.4%. Crack initiation occurred at the Cu–Al interface and spread along the bonding surface of the Cu–Al alloys during the tensile process.

A NOVEL MAGNETIC SYSTEM TO TREAT TOTAL HIP ARTHROPLASTY INSTABILITY

Dislocation after total hip replacement (THR) is a devastating complication. Risk factors include patient and surgical factors. Mitigation of this complication has proven partially effective. This study investigated a new innovating technique to decrease this problem using rare earth magnets.Computer simulations with design and magnetic finite element analysis software were used to analyze and quantitate the forces around hip implants with embedded magnets into the components during hip range of motion. N52 Neodymium-Iron-Boron rare earth magnets were sized to fit within the existing acetabular shells and the taper of a hip system. Additionally, magnets placed within the existing screw holes were studied. A 50mm titanium acetabular shell and a 36mm ceramic liner utilizing a taper sleeve adapter were modeled which allowed for the use of a 12mm × 5mm magnet placed in the center hole, an 18mm × 15mm magnet within the femoral head, and 10mm × 5mm magnets in the screw holes.Biomechanical testing was also performed using in-vitro bone and implant models to determine retention forces through a range of hip motion.The novel system incorporating magnets generated retentive forces between the acetabular cup and femoral head of between 10 to 20 N through a range of hip motion. Retentive forces were stronger at the extreme position hip range of motion when additional magnets were placed in the acetabular screw holes. Greater retentive forces can be obtained with specially designed femoral head bores and acetabular shells specifically designed to incorporate larger magnets. Mechanical testing validated the loads obtained and demonstrated the feasibility of the magnet system to provide joint stability and prevent dislocations.Rare earth magnets provide exceptional attractive strength and can be used to impart stability and prevent dislocation in THR without the complications and limitations of conventional methods.

Performance of Composite Steel-Concrete Beam with Stiffener next to Web Opening

Abstract Openings are provided in Composite steel-concrete beams (CB) for the allowance of ducts and pipes, which generally reduces the beam's flexural performance. So, to retain the strength of these beams, stiffeners are introduced adjacent to the web openings. Hence, a numerical study is performed to evaluate the influence of the stiffeners next to web openings through finite element analysis (FEA) software ABAQUS v6.14. Three different shapes of openings with three different placements of stiffeners are considered for the study, namely circular, rectangular, and triangular openings with stiffeners along longitudinal, transverse, and diagonal directions. As revealed from the findings of FEA, comparisons are made based on the ultimate load, stiffness, and stress distribution. From comparisons, it is found that double-sided longitudinal and transverse stiffeners next to the circle opening are comparable to conventional CB. Similarly, Diagonal stiffeners increase strength in rectangular and triangle openings. Transverse stiffeners failed to increase load capacity and decrease stress concentration compared to other longitudinal and diagonal stiffeners. Further validation for the finite element results is done using the Levenberg-Marquardt (LM) algorithm, using the backpropagation variant technique of Artificial Neural Network (ANN). The results of ANN, i.e., Mean Square Error (MSE) and Multiple Determination Coefficient (R2), are above 0.9 and below 1, respectively. Thus, the results of ANN indicate that the provided results are perfectly fit for predicting with the ANN technique.

The influence of length under blast load on the propagation mechanism of interconnected cracks

In order to study the influence of interconnected defects on the rock breaking effect under blast load, the relevant explosion experiment was carried out by prefabricating interconnected cracks on plexiglass plates (PMMA), and the propagation mechanism of interconnected cracks under blast load was studied from the length level. The dynamic caustic line system and finite element analysis software were combined to analyze the stress intensity factor, propagation velocity of the interconnected crack tip, and full-field stress of the specimen; the results show that with the radial stress wave propagation direction as the axis of symmetry, the two interconnected cracks with symmetrical angles but different lengths are under the action of blast load; there is a certain competition between the two cracks; the longer cracks are more likely to initiate and propagate, and the shorter cracks almost do not propagate. In addition, in terms of energy accumulation at the tips of the two cracks, the longer crack has a certain inhibitory effect on the shorter crack, and when the length of the longer crack remains unchanged, the inhibition effect weakens with the increase of the length of the shorter crack, and when the length of the shorter crack remains unchanged, the inhibitory effect increases with the increase of the length of the longer crack. After the crack initiation of the longer crack, the relationship curve between the stress intensity factor and the crack propagation velocity and time of the longer crack tip decreases first, and then the relationship curve rises to the peak as the energy of the tip of the shorter crack is transferred to the longer crack, and then the oscillation decreases, while the stress intensity factor and crack propagation rate of the shorter side crack tip show an overall downward trend. The numerical simulation is used to supplement the analysis of the stress propagation in the full-field of the specimen, which corroborates with the experiment results. The experimental study provides a theoretical basis for the analysis of the propagation mechanism of interpenetrating cracks under blast load in practical engineering.

Numerical investigation of the behavior of reinforced concrete beams produced with self-compacting concrete

In this study, 1/2 scaled 16 reinforced concrete beams were compared in terms of concrete type, concrete strength, and stirrup spacing. The variables of this study consist of self-compacting concrete and normal concrete as concrete type, C30 and C60 as concrete strength, and without stirrup, 20 cm, 10 cm and 5 cm spacing as stirrup spacing. All elements were tested with 4-point bending mechanism. The stiffness, ductility, load bearing capacity and energy consumption capacity values of the beams were obtained from the load-displacement curves acquired from the experimental study and the elements were compared over them, and the damages of the beams during the experiments were interpreted. In addition to the experimental study, the numerical analyzes of the beams were conducted with the finite element analysis software. Experimental study results were validated by finite element analysis. When all the results were examined, it was concluded that although the initial stiffness of SCC (self-compacting concrete) was less than NC (normal concrete), the ductility of SCC was higher than that of NC, especially in high strength concretes.

Design of Radial Flux PM Synchronous Motor for EV Applications

Abstract: High-performance electric propulsion systems are becoming increasingly important as the automotive industry rapidly shifts to electric cars (EVs). The electric motor is an essential part of these systems as it determines the power, efficiency, and overall performance of the vehicle.This project uses Altair Flux, a full-featured finite element analysis (FEA) software suite, to build and optimize a radial flux motor (RFM) with permanent magnet synchronous motor (pmsm) . The main goal is to increase the power density and efficiency of the electric propulsion system for electric cars by utilizing Altair Flux's simulation and analytical capabilities.

Multiphysics Coupling Simulation of Off-Axis Integrated Cavity Optical Sensing System

The optical properties of an off-axis integrated cavity system are influenced by both structural deformation and thermal deformation. In this paper, the finite element simulation and analysis software COMSOL multiphysics was used to numerically simulate the optical system. By coupling geometric optics, solid mechanics, and solid heat transfer and conducting parametric temperature scanning, a multiphysics simulation of the off-axis integrated cavity optical sensing system was achieved. The effects of different temperature conditions on the stress field, displacement field, and optical mirrors were analyzed, and changes in optical properties were assessed using ray trajectories and point diagrams. Additionally, optical simulation software was used to simulate and optimize the experimental optical path, obtaining the distribution of light spots on the detector surface. This provides a theoretical basis for the subsequent optimization of the off-axis integrated cavity optical system.

Study on the Influence of Step-by-step Excavation of Foundation Pit on Supporting Structure

Aiming at the influence of step-by-step excavation of foundation pit on the internal force and deformation of supporting structure, this paper summarizes the research status of domestic and foreign scholars on this issue, introduces the calculation method of internal force of supporting structure, and uses GEO5 software and ABAQUS finite element analysis software to solve the internal force and deformation of supporting structure in the process of step-by-step excavation, and compares it with the measured results.

Research Progress on Numerical Simulation of the Deposition and Deformation Behavior of Cold Spray Particles

It is of significant theoretical and practical value to study the deposition process and deformation behavior of cold-sprayed particles to find the deposition mechanism of cold-sprayed coatings, further improve the coating performance, and expand its application scope. However, observing the deposition process and particle behavior through experiments is difficult due to the brief deposition duration of cold spray particles. Numerical simulation offers a means to slow the deposition process and predict the critical velocity, deformation behavior, bonding mechanism, and residual stress of cold-sprayed particles. This paper uses finite element analysis software, including ANSYS LS Dynamic-2022 R1 and ABAQUS-6.14, alongside various prevalent finite element methods for numerically simulating cold spray particle deposition. These methods involve the Lagrange, Euler, arbitrary Lagrange-Euler (ALE), and Smoothed Particle Hydrodynamics (SPH) to investigate the cold spray particle deposition process. The recent literature primarily summarizes the simulation outcomes achieved by applying these methodologies for simulating the deposition process and deformation characteristics of different particles under varying cold spraying conditions. In addition, the reliability of these simulation results is analyzed by comparing the consistency between the simulation results of single-particle and multi-particle and the actual experimental results. On this basis, these methods’ advantages, disadvantages, and applicability are comprehensively analyzed, and the future simulation research work of particle deposition process and deformation behavior of cold spraying prospects is discussed. Future research is expected to provide a more in-depth study of the micro-mechanisms, such as the evolution of the inter-particle and internal organization of the particles, near the actual situation.

Topology Analysis and Structural Optimization of Air Suspension Mechanical-Vibration-Reduction Wheels

This paper designs a kind of air suspension mechanical-vibration-reduction wheel for mining engineering vehicles; the research work on topology analysis and the structural optimization of the inner and outer rims are carried out with this wheel as the research object. Using Workbench finite-element analysis software, taking the results of static analysis and modal analysis of the two as constraints, a variety of structural improvement styles are obtained through a topology analysis method and compared and verified, and a more reasonable improvement result is selected and assembled into a whole wheel for final analysis and verification. The results show that the optimization results of the wheel still meet the design’s load-bearing requirements, and the weight is lighter; the topology analysis results are ideal.

Robust Fast Fracture Plane Orientation Angle Search Algorithm for Puck 3D Inter-Fibre Failure Criterion

In the present work, a novel fast fracture plane orientation angle (FPOA) search algorithm for the 3D Puck failure criterion is proposed. In the 3D Puck failure criterion, a linear search algorithm is employed to calculate the maximum inter-fibre failure (IFF) value by iterating and comparing the IFF value for each FPOA. This process itself requires a substantial amount of computational resources. The proposed fast FPOA search algorithm is implemented to substitute the linear search algorithm in order to reduce the computational time. A total of 1×105 randomised stress cases are used to analyse the accuracy of the algorithm. The result was then compared with the Puck Stepwise Seach Method (SSM) and other fast FPOA search algorithms. The results show that the proposed fast FPOA search algorithm has better accuracy compared to the other fast FPOA search algorithms and is almost 5 times faster compared to the SSM algorithm by Puck. In addition, a subroutine contains the Puck failure criterion and the proposed fast FPOA search algorithm is embedded into a Finite Element Analysis (FEA) software to simulate the open-hole test (OHT) experiment on the composite material.

Model-Based Thermal Stress and Lifetime Estimation of DFIG Wind Power Converter

Turbine systems equipped with doubly fed induction generation (DFIG) are becoming increasingly vital in wind power generation, with the reliability of the devices serving as a pillar in the industrial sector. Thermal stress and lifetime assessment are fundamental indicators in this regard. This paper primarily addresses the thermal stress and lifespan of power semiconductor devices utilized in a DFIG grid-side converter (GSC) and rotor-side converter (RSC). PLECS (Piecewise Linear Electrical Circuit Simulation) is employed to validate the electrical and thermal stress of the power devices. Additionally, Ansys Icepak, a finite element analysis (FEA) software, is utilized to confirm temperature fluctuations under various operations. The power consumption and junction temperature of the power devices in the GSC and RSC of a 2 MW DFIG are compared. It is evident that the most stressed power semiconductor is the IGBT for the GSC with a temperature swing of 3.4 °C, while the diode in the RSC is the most stressed with a temperature swing of 10.1 °C. This paper also presents a lifetime model to estimate the lifespan of the power device based on the annual wind profile. By considering the annual mission profile, we observe that the lifetime of the back-to-back power converter is limited by the diode of the RSC, whose B10 lifetime is calculated at 15 years.

Comparative assessment of a continuum damage mechanics-based creep damage models for India-specific RAFM steel

ABSTRACT In the present investigation, a comparative assessment of Kachanov-Rabotnov (KR) and Liu-Murakami (LM) Creep Damage Models is presented for India-Specific Reduced Activation Ferritic Martensitic (IN-RAFM) steel, in the framework of Continuum Damage Mechanics (CDM) approach using ABAQUS finite element analysis software. The assessment is made based on the prediction of entire creep curve and creep rupture life of IN-RAFM steel at 823 K under uniaxial tensile loading at the stress levels of 200–260 MPa. Results disclosed that LM model accurately predicts the rupture life and creep deformation in comparison to KR model and the corresponding R-square values are 0.999 (LM model) and 0.993 (KR model), respectively. The material constant q of LM model controlled the damage evolution in tertiary creep stage. In contrast, the high value of constant ∅ in damage rate equation of KR model, led to over prediction of creep strain owing to high damage rate evolution.

A Finite Element Analysis Study of Influence of Femoral Stem Material in Stress Shielding in a Model of Uncemented Total Hip Arthroplasty: Ti-6Al-4V versus Carbon Fibre-Reinforced PEEK Composite

Total hip arthroplasty is one of the most common and successful orthopaedic operations. Occasionally, periprosthetic osteolysis associated with stress shielding occurs, resulting in a reduction of bone density where the femur is not properly loaded and the formation of denser bone where stresses are confined. To enhance proximal load transfer and reduce stress shielding, approaches, including decreasing the stiffness of femoral stems, such as carbon fibre-reinforced polymer composites (CFRPCs), have been explored through novel modular prostheses. The purpose of the present study was to analyse, by the finite element analysis (FEA) method, the effect that the variation of material for the distal part of the femoral stem has on stress transmission between a modulable prosthesis and the adjacent bone. Methods: Through three-dimensional modelling and the use of commercially available FEA software Ansys R2023, the mechanical behaviour of the distal part of the femoral stem made of CFRPC or Ti-6Al-4V was obtained. A load was applied to the head of the femoral stem that simulates a complete walking cycle. Results: The results showed that the use of a material with mechanical characteristics close to the bone, like CFRPC, allowed for optimisation of the transmitted loads, promoting a better distribution of stress from the proximal to the distal part of the femur. This observation was also found in some clinical studies in literature, which reported not only an improved load transfer with the use of CFRPC but also a higher cell attachment than Ti-6Al-4V. Conclusions: The use of a material that has mechanical properties that are close to bone promotes load transfer from the proximal to the distal area. In particular, the use of CFRPC allows the material to be designed based on the patient’s actual bone characteristics. This provides a customised design with a lower risk of prosthesis loss due to stress shielding.

Analysis of structural dynamic response of vertical sound barriers under natural wind and vehicle induced pulsating wind effects

Abstract Aiming at the influence of natural wind and vehicle-induced pulsating wind on vertical sound barriers, a finite element plug-in panel sound barrier is established based on the finite element method for dynamic response analysis. This paper establishes a sound barrier finite element analysis model based on finite element analysis software. It takes the 8-span vertical sound barrier as the basic working condition to analyze the dynamic response analysis of the sound barrier structure under the action of natural wind of different grades, i.e., the influence of pressure and displacement; the dynamic response of the sound barrier structure with a natural wind speed of 7 grades or more. In addition, it analyzes the dynamic properties of the sound barrier structure caused by train-induced pulsating wind pressure at speeds of more than 200 km/h, i.e., the influence of pressure and displacement, and investigates the dynamic characteristics of different vehicles with different wind speeds, pressure, and displacement. Furthermore, the response of the vertical sound barrier at different vehicle speeds is also explored, and the results are compared to examine its dynamic response. The research findings show that the sound barrier structure does not resonate during the self-resonance analysis, but the vibration of adjacent sound barrier panels affects each other. As natural wind speeds increase, the displacement of the steel column endpoints of the vertical sound barrier gradually increases; along the length of the sound barrier, the change of the peak pressure at the top of the steel columns and the top of the unit plate shows a symmetrical trend, and the displacements of the steel columns and the top of the unit plate show a trend of gradual increase in the travelling direction, and they both increase at the end of the column. The displacement of the top of the steel column and the top of the unit plate both show a trend of gradual increase along the direction of the vehicle, and both reach the maximum value at the end of the steel column and the unit plate. With the increase in vehicle speed, the overall peak displacement value also increases synchronously.

Friction and Wear Mathematical Modeling and Optimization Design of Surface Microstructure Parameters of Unfolding Wheel based on Experiment and Numerical Simulation

Objective: In order to improve the friction-increasing and wear-reducing performance of the unfolding wheel surface, the surface microstructure of the unfolding wheel used in the detection of 8 kinds of steel balls was optimized by parameter matching. Method: Firstly, based on Hertz's theory, the contact area between steel balls of different sizes and the unfolding wheel are analyzed. The wear depth model is established based on Archard adhesive wear model. Secondly, the appropriate microstructure parameters for friction and wear experiments were selected. The finite element analysis software is used to simulate the stress on the surface of the microstructure unfolding wheel and calculate the wear depth. According to the experimental results, the relationship between friction coefficient, wear depth and microstructure parameters is obtained by data fitting, and the objective function of optimization design is established. Finally, based on the genetic algorithm DNSGA-II and Python, the parameters are optimized, and the optimal solution is obtained by using the TOPSIS method. Results: The feasibility of the simulation method is verified by friction and wear experiments, and the correctness of the optimization method is verified. Some existing patents on friction and wear of microstructure surfaces are introduced, and the future development of this field is prospected Conclusion: The research shows that the optimal parameters matching of microstructure for steel ball diameters of Ф16.6688 mm~Ф22.2250 mm: the shape is rhombus; the area of a single pit is close to the contact area, which is 0.0319 mm2 ~ 0.0554 mm2; the pit depth is 145 μm~150 μm, and the surface density of microstructure is (5.4~5.6) /mm2.

A two-way coupled fluid–structure interaction method for predicting the slamming loads and structural responses on a stiffened wedge

Ships navigating through rough seas are subjected to slamming loads from waves, which can lead to structural damage and maritime accidents. The wedge model is commonly employed to investigate slamming loads and structural responses. While a stiffened wedge closely resembles a real ship hull plate, incorporating it into fluid–structure interaction simulations presents challenges. This paper proposes a two-way coupled fluid–structure interaction method to examine slamming loads and structural responses of a free fall non-prismatic stiffened steel wedge. Hydrodynamic loads are determined through Reynolds-averaged Navier–Stokes computations using OpenFOAM, while structural responses are predicted using the finite element analysis (FEA) software Calculix. To achieve two-way coupling between computational fluid dynamics and FEA simulations, a coupling library for partitioned multi-physics simulations, preCICE, is introduced. The computed impact pressure and stress align well with available experimental data. Various free fall heights are investigated in the numerical simulations. The results indicate that elastic deformation mitigates impact pressure, while the presence of transverse ribs enhances the rigidity of the flexible plate. The duration of pressure and the peak slamming pressure exhibit an inverse correlation. Greater free fall heights result in shorter pressure duration times, and smaller free fall heights may reduce rise time. Three-dimensional effects cause pressure to decrease along the midpoint of the plate toward both sides. Additionally, structural stress in the central area exceeds that in the areas on both sides at the same height. In conclusion, the proposed two-way coupled model proves suitable for accurately and efficiently computing hydroelastic slamming on flexible wedges.

A comprehensive study of carbon nanoparticle shape and orientation effects on composite elastic properties using FEA

In this study, three critical parameters that influence the effective composite properties of Carbon nanoparticles were tested and modeled using finite elements through Digimat Finite Element Analysis (FEA) software, employing representative volume elements (RVE). The primary parameters under consideration are the fiber shape, fiber orientation, and fiber volume fraction. Four of the many different shapes of Carbon nanoparticles, namely Tubes, Disk, Sphere, and Cylinder, were investigated, coupled with four distinct orientations for tubes: horizontal, aligned at 45°, random, and vertical each varying in the carbon fiber volume fraction. The material of choice was pure epoxy resin because of the nature of the bonding between its two phases and its wide range of usage. Forces were applied along the X-axis, coupled with shear in the XY plane. This study revealed that the orientation of CNTs primarily influences the Elastic Young’s modulus, whereas the size of the CNTs has the main effect on the shear modulus, followed by orientation. The horizontal CNTs demonstrated superior Young’s modulus, but the random orientation had a more pronounced impact on the shear modulus variation. Regarding the analysis of the nanoparticles shapes, the disk shape with fixed orientation revealed the highest elastic modulus, after which the cylinder shape and the sphere recorded the minimum elastic modulus among the three studied shapes.

Failure analysis and comparative study on tunnels under strike-slip fault and oblique-slip fault movements

To deeply study and compare the failure characteristics of tunnels under strike-slip and oblique-slip active faults, with the engineering background of a railway tunnel in western China crossing both strike-slip and oblique-slip active faults, two sets of large-scale indoor model tests with a geometric similarity ratio of 1:35 were conducted. The fissure development patterns and strain trends of the tunnel under the movement of both types of faults were monitored and analyzed. Meanwhile, a three-dimensional model of tunnel-rock-fault interaction was established using ABAQUS finite element analysis software to determine the variation patterns of bending moments and shear forces of the tunnel under the movement of both types of faults. The results showed that under the movement of strike-slip and oblique-slip active faults, circumferential bending fissures appear at the right waist of the hanging wall and the left waist of the footwall of the tunnel, and shear oblique fissures appear at the vault of the fault fracture zone. Among them, the number of cracks, the range of tunnel cracking and the degree of crack damage under the condition of the oblique-slip fault are obviously more serious than those under the condition of the strike-slip fault. Under the dislocation of the oblique-slip fault, a large area of broken zone appears in the vault of the fault fracture zone, the lining falls off, the steel bar is exposed, and there is an obvious uplift phenomenon. The right waist of the tunnel’s hanging wall mainly experiences tension while the left waist experiences compression, whereas on the hanging wall, the right waist experiences compression while the left waist experiences tension. Under the fault movement, the maximum bending moment value mainly occurs at a distance of 10 m from the fault fracture zone on both the hanging wall and the footwall, with the bending moment values at the fault fracture zone nearly approaching zero. The maximum shear force value occurs at the fault fracture zone. Under the movement of both types of faults, the failure mode of the tunnel is mainly characterized by bending failure of the hanging wall and the footwall and shear failure at the fault fracture zone. Compared to strike-slip active faults, the development of fissures in tunnels under oblique-slip active faults is more severe, with larger bending moment and shear force values, and a wider range of tunnel failure. These results can provide theoretical and technical experience for future similar projects.

Design and Testing of Vehicle-Mounted Crop Growth Monitoring System

The aim of this study was to overcome the impact of vibration generated by agricultural machinery on the monitoring accuracy and performance of vehicle-mounted crop growth monitoring systems during field operation. This paper developed a vehicle-mounted crop growth monitoring system with vibration damping capability to achieve this goal. The system consists of a multispectral crop growth sensor, signal conditioning module, and truss-type sensor bracket with self-vibration damping capability. The commercial finite element analysis software ABAQUS 6.10 was used to conduct modal and dynamic simulation analyses of the sensor bracket, which indicate that the truss-type sensor bracket can damp vibrations effectively. The p-values (least significant differences) of crop canopy DNRE (red edge normalized difference vegetation index) under different operating speeds (1.5, 3, and 4.5 km/h) are 0.454, 0.703, 0.81, and 0.838, respectively, for four different crop growth stages. In a comparative experiment between the proposed monitoring system and two similar vehicle-mounted sensors (CropSpec and GreenSeeker RT 200) for measuring agronomic parameters at different stages of crop growth, the proposed monitoring system yielded R2 values of 0.8757, 0.7194, and 0.795, respectively, and RMSE values of 0.7157, 2.2341, and 2.0952, respectively, in the tillering stage, jointing stage, and tillering and jointing stage, outperforming the other two sensors.