Stress Measurement Error Research Articles

Optimizing guided wave propagation for sensitive axial stress measurement in steel pipes

Steel pipe structures are commonly used in the industrial field. Stress-induced structural failures can have a significant impact on equipment safety. Therefore, effective stress monitoring is a crucial area of research. Constrained by the multi-frequency and multi-modal characteristics of ultrasonic guided waves, the limitations of traditional stress measurement methods based on these waves lie in the lack of a systematic analysis of the impact of multi-modal fused signals on stress measurement. To explore the optimal guided wave stress measurement strategy, a mathematical model for the propagation of longitudinal guided waves in prestressed steel pipes, based on the principles of acoustoelasticity, is proposed. Using this model, the sensitivity of stress to each sub-mode of the longitudinal guided waves is analyzed, leading to the identification of the optimal guided wave mode (L(0,2) mode) and frequency range. In order to avoid the excitation of other low-sensitivity modes, further analysis of the optimal parameters for the piezoelectric array is conducted. Simulation results indicate that the designed transducer can effectively excite the target mode with high purity. The stress sensitivity of the target mode was experimentally determined to be −2.5×10−5MPa−1, which closely aligns with the theoretical results. Comparative analysis of the experiments emphasizes the influence of modal control on measurement outcomes. By selecting and controlling the appropriate mode, the maximum relative error in stress measurement is observed to be 5%.

Research on the Method of Absolute Stress Measurement for Steel Structures via Laser Ultrasonic

Accurate measurement of the stress in steel structures is crucial for structural health monitoring. To achieve this goal, a novel technique, the laser ultrasonic technique, was used in absolute stress measurement in this study. The feasibility of this technique has been verified through theoretical analysis and finite element (FE) analysis. A stress measurement experiment in steel specimens was conducted and the relationship between ultrasonic relative wave velocity and stress was explored. The results revealed that there is a similar linear correlation between the ultrasonic relative wave velocity and absolute stress. The stress can be obtained based on ultrasonic relative wave velocity. According to the stress measurement results, it was found that the absolute error between the measured stress and theoretical stress was largest when the stress level was low, and that the measured error of stress gradually decreased with increases in the applied stress. The relative error between the measured stress and the theoretical stress was within 10% when the stress was higher than 100 MPa. This further verifies the reliability of the laser ultrasonic technique under high-stress conditions. Additionally, the impact of temperature and surface roughness on stress measurement was analyzed. The stress error in stress measurement increased similarly linearly with the increase in temperature and increased non-linearly with the increase in roughness. The corresponding compensation methods were proposed to effectively improve the accuracy of measurement.

Pretightening stress measurement method of aero-engine fastening components based on acoustic time difference separation of the coupling layers

Accurate measurement of the pretightening stress of the fastening components in the rotor system is crucial for ensuring assembly accuracy and operational safety in aero-engines. The acoustic time difference (ATD, ultrasonic propagation time difference) of the coupling layer reduces the pretightening stress measurement accuracy of the fastening components. This paper proposes a method for measuring the pretightening stress of the fastening components of the aero-engine based on the separation of the ATD of the coupling layer. Firstly, the echo signal characteristics of the bottom surface of the fastening components are analyzed by simulation, and the influence of the coupling layer ATD on the stress measurement error isstudied. Then, based on the ultrasonic multi-layer medium propagation model, a scheme of adding a transition layer to construct the first echo is proposed. The ATD of the coupling layer is fed back by the first echo propagation time difference, and the ATD caused by the coupling layer and the stress is solved by the second echo. On this basis, the ATD separation method of the coupling layer is proposed and the pretightening stress measurement model of the fastening components based on the ATD separation of the coupling layer is established. The experimental results show that after the ATD of the coupling layer is separated, the maximum measurement error of the pretightening stress of the fastening component is reduced from 13.016 MPa to 4.738 MPa, which effectively improves the measurement accuracy.

Estimating Earth Pressure during Tunneling in Gravel-cobble Stratum by Considering Sensor-particle Size Effect

When tunneling in gravel-cobble stratum with earth balanced shield, the ratio between the diameters of the pressure sensor embodied in muck chamber and cut gravels is generally small. The small sensor-particle size ratio leads to considerable difference between the measured and actual earth pressure. This makes the configuration of earth pressure a difficult task and furtherly affects tunneling efficiency and safety. This work characterizes the variation of stress measurement error in a granular packing with consideration of the sensor-particle size ratio, the particle size distribution as well as the contact force distribution. The probability density function of stress measurement error is built according to a general probability distribution of inter-particle contact force. After then, a probability-based regressive procedure is proposed to estimate the applied stress with the measured stress. For stress samples with a same target stress but different biases, the stress estimated by the probability-based procedure has a minor variation and thus is more reliable than the arithmetic mean stress. Finally, the probability-based procedure is adopted to estimate the actual earth pressure of a well-tunneled section in Chengdu gravel-cobble stratum, according to which the lateral pressure coefficient of Chengdu gravel-cobble stratum is suggested as 0.20 – 0.28.

Modeling and Simulation of Torsional Resistance of Hollow Shaft with Small Diameter Based on ABAQUS

Torsional resistance is an important mechanical property of the shaft. The traditional torsional resistance measurement is based on the deformation of the strain gauge, which needs to be attached to the shaft under test. When the inner diameter of the hollow shaft is small, the stress measurement error of the inner wall of the shaft will be very large because the strain gauge has a certain size. To solve this problem and obtain more accurate data, this study adopts the finite element model simulation method to calculate the torsional resistance of a hollow shaft with a small diameter. The 3D finite element model is built and computed on the server. Rich data and colorful nephograms are acquired. The results show that the stress value of the same position increases with the increase of torque. When the torque is 6 kNm, the shaft is plastically deformed, and the maximum Mises stress reaches 432.2 MPa. The maximum Mises stress occurred on the outer surface of the shaft. When plastic deformation occurs on the outer surface, the stress on each part of the shaft increases. Finite element modeling and simulation can obtain rich data and visual nephograms, which is very helpful to the research of torsional resistance of shaft.

Correction of coupling error in contact-type ultrasonic evaluation of bolt axial stress

The stress monitoring of bolted connections is crucial in the evaluation of mechanical systems’ structural health, and the ultrasonic method using TOF (Time of Flight) is considered promising in this application. However, the discrete nature of couplant layer characteristics can deteriorate the robustness of the ultrasonic method significantly. Here, for the purpose of deducting the coupling error, a compensating method of TOF is proposed. In this method, the components of the waves backscattering from bolt bearing surface within the temporal signal are filtered and utilized. The analytical coupling error correction model is established and the influences of the installation eccentricity upon the model are analyzed. Meanwhile, the proposed method is further verified by a finite element simulation and the results are consistent with the analytical derivations. Ultimately, the proposed method is experimentally validated and the scattering components are extracted from the pulse echo signal by using the synchrosqueezed wavelet transform. The results imply that, after being compensated by the proposed method, the stress measurement error decreased from 5% to 1%. This research provides a novel perspective in reducing the coupling error in a concise manner and is potential in improving the practicality of the ultrasonic bolt axial stress measurement methods.

Accuracy Improvement of Residual Stress Measurement by Chirp Compensation of FBG

A chirp compensation method of fiber Bragg grating (FBG) is proposed to improve the residual stress measurement accuracy in the hole-drilling method. The effects of the radii of the hole, the distance between the FBG and the hole, the Young’s modulus of the material, and the residual stress on the FBG chirped spectra are analyzed. The relationship between radii of the hole, the distance between the FBG and the hole, the full-width at half maximum (FWHM), and the peak wavelength are established. The feasibility of the method is verified through experiments, which shows that the residual stress measurement error can be reduced by the compensation method.

Improvement of indentation technique for measuring general biaxial residual stresses in austenitic steels

Investigations on engineering structures show that residual stresses in combination with external loads can cause failure in loads that are less than the design threshold. Due to the applicability of austenitic steel in important industries (such as oil pipelines), accurate measurement of residual stress in this material is very important. Indentation is a new method for estimating residual stress. In this paper, by performing a large number of finite element simulations, the accuracy of residual stress measurements in austenitic stainless steels using indentation was studied by performing a large number of finite element simulations. Three different models (Suresh's, Wang's and Lee and Kwon's model) were investigated and it was found that the Lee and Kwon's model has a more accurate prediction of residual stress values in austenitic steels.Based on these numerical simulations and by studying how the residual stress measurement error of Lee and Kwon's model changes according the stress ratio, a method is suggested to correct this error and calculate the real amount of non-equibiaxial residual stresses in austenitic steels. The procedure is significantly reducing the error of residual stress measurement (from about 50% to less than 10%) and has been verified by conducting experimental test on a sample made from austenitic steel.

An improved non-contact dynamic stress measurement method for turbomachinery rotating blades based on fundamental mistuning model

It is crucially important to monitor the dynamic stress of turbomachinery rotating blades for residual fatigue life prediction and health management, especially for the aircraft engine mistuned blisk. This paper presents an improved non-contact dynamic stress measurement method based on fundamental mistuning model (FMM). The precision of the dynamic stress measurement can be improved at least 4% by the novel method compared with the direct calculation method, and the total stress measurement error is less than 12%. In this paper, only the tuned finite element model, mistuned natural frequency and vibration displacements at each blade tip are needed. The mistuned dynamic stress is expressed in the mistuned modal coordinate system with the stress coordinate base and coordinate values. The numerical and experimental investigations were carried out. This study provides a roadmap to measure the dynamic stress of rotating mistuned blisk, with a strong application potential in the stress online monitoring for the industrial turbomachinery with a blade tip timing (BTT) monitoring system.

Investigation on the improvement of Brillouin optical time-domain reflectometer with Golay pulse codes in radiation environment

The application of Golay pulse coding technique on Brillouin optical time-domain reflectometer (BOTDR) in a radiation environment is experimentally analyzed. By applying Golay pulse codes on the BOTDR system in the radiation experiment, the enhancement of detection range, accuracy of Brillouin frequency shift (BFS), and reduction of stress measurement error are characterized. By using 64-bit Golay coding, signal-to-noise ratio can be improved significantly and the variation of BFS is more accurate. These results are beneficial for the application of the Golay pulse code technique on BOTDR in the space station.

Numerical study of the effect of yield strain and stress ratio on the measurement accuracy of biaxial residual stress in steels using indentation

Investigations into engineering structures show that residual stresses in combination with external loads can cause failure in loads which are below the design threshold. As a result, the exact study of the magnitude and distribution of these stresses is an important topic in mechanical engineering. Indentation is a new method for estimating residual stress. To measure non-equibiaxial residual stresses, there is only one reliable method presented by Lee et al. In this paper, the effect of yield stress and different values of residual stress on the accuracy of residual stress measurements in steels with similar work hardening behavior was studied by performing a large number of finite element simulations.Based on these numerical simulations and by studying how the residual stress measurement error of Lee and Kwon’s model changes according the stress ratio and the yield strain, a method is suggested to correct this error and calculate the real amount of non-equibiaxial residual stresses. The procedure is significantly reduces the error of residual stress measurement (from more than 100% to less than 10%) and has been verified by conducting experimental indentation.

Numerical Verification of Simplified Identification Method of Yield Function Using Circumscribing Polygon of Yield Locus

A method for identifying the yield function using simple material tests is proposed. The identification accuracy of this method is verified by finite element analysis. In the proposed method, a polygon circumscribing the equal plastic work contour is defined through uniaxial tensile tests, hydraulic bulge test, and plane strain tensile tests. The parameters of the anisotropic yield function are identified as a smooth curve inscribed in the polygon. The virtual material tests of three material models, namely, mild steel, aluminium alloy, and pure titanium, are conducted by the finite element method. On the basis of the results, stress measurement error and yield surface identification error are discussed. When the material exhibits strong in-plane anisotropy, the measurement error of equi-biaxial stress in the hydraulic bulge test becomes large. When the initial gradient of work hardening is large, the stress value of the circumscribed line of the small plastic strain stage in the plane strain tensile test is estimated to be lower than that on the true yield surface. These errors affect the identification accuracy of the material parameters of the yield function quantitatively, but the difference between the identified locus and true yield locus is small. The proposed method is feasible as a simple identification method of the yield function.

Plane residual stress measurement using ultrasonic considering weak anisotropy of metallic material

Ultrasonic velocity variation (UVV) along different directions induced by material weak anisotropy will lead to residual stress measurement error using ultrasonic inevitably. In this research, the influence of weak anisotropy on residual stress measurement is analyzed theoretically and experimentally. Firstly, the in-plane acoustoelastic wave equation is modified by considering material anisotropy, which can be characterized by two in-plane anisotropic parameters. Further, an analysis model is also established to express the linear superposition of weak anisotropy and acoustoelastic effect on UVV. Based on this, a plane residual stress measurement method has been developed, which was verified using the rolling aluminum alloy plate after friction stir welding. From the comparison with hole-drilling method, it was adequate and capable to measure the plane residual stress by the relative UVV along three particular directions.

A Smart High Accuracy Calibration Algorithm for 3-D Piezoresistive Stress Sensor

Numerical and experimental sensitivity analyses in this paper indicate that the accuracy of a silicon multi-element piezoresistive (PR) stress sensor can be dramatically influenced by the microfabrication non-uniformity and the uncertainties in the values of the PR coefficients and the thermal coefficient of resistance (TCR). The results showed that errors as large as 70% FS or more, in the extracted stress values, may be obtained due to uncertainty of about 2.5% in the values of PR coefficients. This paper aims to evaluate the capabilities of the artificial neural network (ANN) to eliminate the error in stress measurement, due to the fabrication non-uniformity within wafer, wafer-to-wafer, and batch-to-batch, for multi-element PR sensing rosettes. In this paper, sensing chips from two different batches were integrated in building the ANN and testing its performance. The proposed calibration technique employs the neural network fitting Toolbox in MATLAB to generate a two-layer feed-forward network, with sigmoid hidden neurons and linear output neurons. Three different configurations of calibration were designed to test the generalization abilities of the ANN in capturing the in-plane stress components exerted on the silicon chip. The results showed that ANN is capable of accurately predicting the stresses applied to the sensing chip with maximum stress error of 1.5% FS with no need for individual, expensive, and time-consuming calibration process for each sensor.

The investigation of expanded polystyrene creep behaviour

The results obtained in long-term testing under constant compressive stress of the cut from the Slabs EPS 50/100 and EPS 150 with the density ranging from 15 to 24 kg/m 3 , which were manufactured by the same manufacturer by foaming EPS solid granules (beads) in closed volume. The creep strain of the above described specimens was used as a criterion for estimating the deformability of the EPS slabs under long-term compressive stress. It was measured using special stands EN 1606, maintaining constant stress during the fixed time interval t n =122 days. Creep strains were determined by the methods described in EN 1606 for constant stress σ c =0.35σ 10% (compressive stress σ 10% was determined in accordance with EN 826:2013. The long-term compressive stress measurement error did not exceed 1 %, while the creep strain measurement error was not larger than 0,005 mm. The tests were conducted at the ambient temperature of (23±2)°С and relative humidity of (50±5) %.The long-term constant compressive load σ c =0.35σ 10% . The method of mathematical and statistical experimental design optimization models taking into account the thickness of specimens is proposed to determine the creep compliance I c ( t n ) the creep strain e c ( t n ) and predictive point estimate of creep strain e c ( T ). Graphical interpretation of the abstained models is also presented. It should be noted that the abstained equations may be used in practice for estimating the creep strains at time t n =122 days and predictive estimates of e c ( T ) for the load time of 10 years.

Correction of error induced by nonlinear movement of feedback mirror in laser feedback stress measurment system

Stress distribution of optical materials can be measured by using the laser feedback effect. Owing to the non-linear movement of the feedback mirror, the result accuracy of the system will decrease. In this work, we measure the displacement of the feedback mirror by using a high precision quasi-common-path laser feedback interferometry. The displacement-time function is obtained by a high-end fitting method. The stress measurement error induced by the non-linear movement of the feedback mirror is calculated according to the displacement-time function and a three-mirror cavity equivalent model, and the correction for the system accuracy is achieved. The results show that the different movement direction of the feedback mirror gives rise to an opposite variation trend of error. Measurement error can be reduced by averaging the results in different directions. In the study we analyze the influence of the non-linear movement of the feedback mirror on the measurement accuracy, and a method of improving the error is proposed. This method is significant for correcting the measurement results and improving the accuracy.

Numerical verification of a biaxial tensile test method using a cruciform specimen

A method of evaluating stress measurement errors in biaxial tensile tests using a cruciform specimen is proposed. The cruciform specimen is assumed to be fabricated from a section of uniformly thick flat sheet metal via laser or water-jet cutting and to have a number of parallel slits cut into each of the four arms. Using finite element analyses with the von Mises yield criterion, the optimum geometry of the cruciform specimen and the optimum strain measurement position necessary to minimize the stress measurement error are determined. Additionally, an experimental validation of the FEA is performed using a sheet material that was experimentally confirmed to be nearly isotropic. The following conclusions are drawn: (i) the thickness of the test material should be less than 0.08B (B: side length of the gauge area of the cruciform specimen); (ii) the geometric parameters for the cruciform specimen should be N≥7, L≥B, ws≤0.01B, and 0.0034≤R/B≤0.1 (N: number of slits, L: length of slits cut into the arms, ws: slit width, and R: corner radius at the junction of the arms to the gauge area); and (iii) the strain components in the gauge area should be measured on the centerline of the specimen parallel to the maximum force direction at a distance of approximately 0.35B from the center of the specimen. The stress measurement error is estimated to be less than 2% when the optimum conditions above are satisfied.

面内圧縮試験における試験片形状の数値解析的検討と実験検証

The optimum geometry of a specimen used for an in-plane compression test on sheet metal was investigated by FEM. Geometrical parameters were determined to minimize the stress measurement error, i.e., the difference between the mean stress, which is calculated from the measured load and compressive strain data assuming a constant volume, and the Cauchy stress at the center of the specimen, where a strain gauge is mounted. The stress measurement error decreases with increasing aspect ratio of the gauge area, where L and W are the length and width of the gauge area, respectively. A maximum error of 1% was achieved by taking an aspect ratio 2.2. Furthermore, the effects of the radius of the fillet, R, connecting the chucking area and gauge area, and the width of the chucking area, B, on the accuracy of stress measurement were investigated. It was found that 1.6 and 1.4 minimize the stress measurement error. Moreover, the optimum geometrical parameters for successfully applying a compressive strain of over to the specimen without in-plane buckling were clarified. The chucking area should be fully covered by chucking jigs to prevent the in-plane buckling of the gauge area.

Effect of stress gradients in the surface layer of beryllium on X-ray stress measurement

The effects of stress gradients in beryllium surface layers on traditional X-ray stress measurements are investigated by relationship analysis of d vs. (sin ψ)2 plots with stress gradient in the surface layers of beryllium. The results show that over the range of (sin ψ)2≤0.5, there are significant effects of stress gradient on the measurement results. The stress measurement error resulting from the stress gradient is decreased using a vanadium target and high ψ range.

ＰＳＰＣを用いた並傾法Ｘ線応力測定における試料セッティング誤差の影響

Recently, the position sensitive proportional counter (PSPC) has been becoming popular as a detector for X-ray stress measurement. However, little information is available in the literature regarding the effects of specimen mis-setting on the stress measurement using the PSPC.In this paper, a modeling of the Ω assembly X-ray stress measurement using a PSPC as the detector is presented enabling us to simulate the stress measurement under the various conditions including specimen mis-setting. As the results of simulation, it was found that the use of collimator yields an apparent stress (intrinsic stress), and that the absolute value of the stress increases with the increase in the width of the collimator and decreases with the increase in its effective length. It was also found that the error in stress measurement due to specimen mis-setting is expressed as a linear relation of the ratio L/R0 (L: offset of mis-setting, R0: goniometer radius), and that the coefficient in the relation is given as a function of secondary order of the ratio 2bψ/Cl (2bψ: width of collimator, Cl: effective length of collimator).