Detection of Multiple Cracks in Triangular Cantilevers Based on Frequency Measurements

2006 ◽  
Vol 324-325 ◽  
pp. 259-262
Author(s):  
Fei Wang ◽  
Xue Zeng Zhao ◽  
Jia Ying Chen
Keyword(s):  
Damage Index ◽  
Maximum Error ◽  
Crack Size ◽  
Force Sensors ◽  
Multiple Cracks ◽  
Cantilever Deflection ◽  
Local Flexibility ◽  
Small Force ◽  
The Relationship ◽  
Number Of Segments

Triangular cantilevers are used as small force sensors. Prediction of location and size of multiple cracks from experimental results will be of value to users and designers of cantilever deflection force sensors. We extend a method for prediction of location and size of multiple cracks in rectangular cantilevers to deal with triangular cantilevers in this paper. The cracks are assumed to introduce local flexibility change and are modeled as rotational springs. The beam is divided into a number of segments, and each segment is associated with a damage index, which can be calculated through the relationship between the damage index and strain energy of each segment and the changes in the frequencies caused by the cracks. The location of cracks can be obtained with high accuracy with sufficient segment numbers. The size of a crack can be calculated through the relationship between the crack size and its stiffness, which can be obtained from the damage index related to the crack. The maximum error in prediction of the crack position in the case of double cracks is less than 15%, and it is less than 25% in prediction of the crack size.

Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement

2007 ◽  
Vol 353-358 ◽  
pp. 2285-2288
Author(s):  
Fei Wang ◽  
Xue Zeng Zhao
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Frequency Measurement ◽  
Crack Size ◽  
Force Sensors ◽  
Rotational Spring ◽  
Cantilever Deflection ◽  
Crack Location ◽  
Small Force ◽  
Point Of Intersection

Triangular cantilevers are usually used as small force sensors in the transverse direction. Analyzing the effect of a crack on transverse vibration of a triangular cantilever will be of value to users and designers of cantilever deflection force sensors. We present a method for prediction of location and size of a crack in a triangular cantilever beam based on measurement of the natural frequencies in this paper. The crack is modeled as a rotational spring. The beam is treated as two triangular beams connected by a rotational spring at the crack location. Formulae for representing the relation between natural frequencies and the crack details are presented. To detect crack details from experiment results, the plots of the crack stiffness versus its location for any three natural modes can be obtained through the relation equation, and the point of intersection of the three curves gives the crack location. The crack size is then calculated using the relation between its stiffness and size. An example to demonstrate the validity and accuracy of the method is presented.

A Flaw Proximity Rule for Interacting Surface Cracks Based on Elastic-Plastic Fracture Analysis

2009 ◽  
Author(s):  
Masayuki Kamaya
Keyword(s):  
Structural Reliability ◽  
Crack Depth ◽  
Crack Size ◽  
Multiple Cracks ◽  
J Integral ◽  
Surface Cracks ◽  
Elastic Plastic ◽  
Offset Distance ◽  
Bending Load ◽  
The Relationship

When multiple cracks approach one another, the stress intensity factor and J-integral value of cracks are likely to change due to the interaction of the stress field. Since the changes in these parameters are not always conservative in structural reliability evaluations, the interaction between multiple cracks should be taken into account. Section XI of the ASME Boiler and Pressure Vessel Code provides a flaw characterization rule for interacting multiple cracks. In Section XI, adjacent cracks are replaced with a coalesced single crack when the distance between the cracks is less than half of the crack depth. However, the criterion for the offset distance is given as an absolute value, although the magnitude of the interaction depends on the crack size. In the current study, an alternative criterion for the offset distance was examined. Elastic-plastic analyses were performed for interacting semicircular and semi-elliptical surface cracks by the finite element method under a tensile and bending load. The change in the J-integral values due to the relative spacing of cracks was investigated. Based on the relationship between the magnitude of the interaction and the relative position of the cracks, the allowable condition for the offset distance was discussed.

scholarly journals Baseline-Free Adaptive Crack Localization for Operating Stepped Rotors Based on Multiscale Data Fusion

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5693
Author(s):  
Zhiwen Lu ◽  
Shancheng Cao ◽  
Rui Yuan ◽  
Yong Lv
Keyword(s):  
Data Fusion ◽  
Reference Model ◽  
Damage Index ◽  
Energy Operator ◽  
Noise Robustness ◽  
Experimental Investigations ◽  
Multiple Cracks ◽  
Practical Applications ◽  
Critical Issues ◽  
Baseline Information

Crack localization in running rotors is very important and full of challenges for machinery operation and maintenance. Characteristic deflection shapes or their derivatives based methods seem to be promising for crack localization in rotors. Despite the substantial advantages, several critical issues still need to be addressed to enhance the efficiency of this kind of method for practical applications. Two problems are considered in this work: 1. How to localize single or multiple cracks accurately avoiding the interference of commonly existing steps without baseline information on pristine rotors; 2. How to improve the crack localization performance under a noisy environment. To circumvent the issues, a novel baseline-free adaptive crack localization method is proposed based on data fusion of multiscale super-harmonic characteristic deflection shapes (SCDSs). In this method, crack induced asymmetry and nonlinearity of crack breathing are utilized to simultaneously eliminate the interference from the steps without a reference model. To enhance the noise robustness, the multiscale representations of SCDSs are made in Gaussian multiscale space, and Teager energy operator is applied to the multiscale SCDSs to amplify the crack induced singularities and construct the multiscale Teager super-harmonic characteristic deflection shapes (TSCDSs). Moreover, fractal dimension is designed as an evaluator to select the proper multiscale TSCDSs for data fusion adaptively. Then, a new damage index is derived for crack localization by Dempster-Shafer’s (D-S) evidence fusion of the adaptively selected multiscale TSCDSs. Finally, the feasibility and the effectiveness are verified by both numerical and experimental investigations.

Calculation of the temperature of crystallization of silicates from basaltic melts

1981 ◽  
Vol 44 (333) ◽  
pp. 19-26 ◽  
Author(s):  
W. J. French ◽  
E. P. Cameron
Keyword(s):  
Crystallization Temperature ◽  
Maximum Error ◽  
Average Error ◽  
Multivariate Statistical Techniques ◽  
Multivariate Statistical ◽  
Marquesas Islands ◽  
Melt Composition ◽  
The Relationship ◽  
Basaltic Melts

AbstractThis paper discusses the relationship between the chemical composition of basic melts and the temperatures at which olivine, clinopyroxene, and plagioclase begin to crystallize at one atmosphere. Diagrams are given which show the correlation between crystallization temperature and melt composition and which allow some of the temperatures to be estimated. Because the relationship between melt composition and crystallization temperature is virtually linear over short compositional ranges, the data available can be subdivided and examined by linear multivariate statistical techniques. The result is a set of equations which permit the crystallization temperatures to be calculated with an average error of less than 6 °C and a maximum error of 27 °C. These equations have been tested by experimental determination of crystallization temperatures for a range of rocks from the Marquesas Islands.

Improved Elastic Compliance Equation and its Inverse Solution for Compact Tension Specimens

2017 ◽  
Author(s):  
Xian-Kui Zhu
Keyword(s):  
Crack Length ◽  
Maximum Error ◽  
Compact Tension ◽  
Crack Size ◽  
Accurate Solution ◽  
Elastic Compliance ◽  
Load Line Displacement ◽  
Standard Specimens ◽  
Specimen Test ◽  
Toughness Testing

ASTM E1820 is a well-developed fracture test standard and has been used worldwide for fracture toughness testing on ductile materials in terms of the J-integral or J-R curve. This standard recommends the elastic unloading compliance technique for measuring crack length in a single specimen test, and an accurate elastic compliance equation is needed to estimate physical crack length. Compact tension (CT) specimen is one of the most often used standard specimens with crack length ratios of 0.45≤a/W≤0.70 prescribed in E1820 for J-R curve testing. The stress intensity factor K of CT specimens used in E1820 was developed by Srawley (IJF, 1976) and has been commonly accepted as the most accurate solution. The compliance equation of CT specimens was developed by Saxena and Hudak (IJF, 1978) and has been used in ASTM E1820 for decades. However, recent results showed that the load-line displacement (LLD) compliance equation is not consistent with that determined from its K solution, and the maximum error of LLD compliance can be larger than 7% at a/W = 0.32 and ∼ 5% at a/W = 0.45 (E1820 standard crack size). The FEA results confirmed that the K solution in E1820 is indeed very accurate, but its compliance equation is less accurate. Thus, an improved compliance equation with high accuracy is developed from the accurate K solution using the numerical integration technique and shooting method.

Investigation of the Cracking Behaviors by Indentation Based on an In Situ Observation

2014 ◽  
Vol 627 ◽  
pp. 361-364 ◽  
Author(s):  
Yasuhiro Yamazaki
Keyword(s):  
Indentation Test ◽  
Crack Size ◽  
Indentation Load ◽  
In Situ Measurement ◽  
Observation System ◽  
In Situ Observation ◽  
Test Machine ◽  
Transparent Ceramics ◽  
The Relationship

In this paper, an in-situ measurement of crack size as a function of applied indentation load during indentation test was conducted. To perform the in-situ measurement, an instrumented indentation test machine with the in-situ observation system was developed and used. The joints of transparent ceramics by diffusion bonding were prepared as the specimen used in this study. The indentations were performed at the interface of the joints, and in the monolithic transparent ceramics by means of the instrumented indenter with the in-situ observation system. The relationship between crack shape and indentation load, as well as, the effect of the indenter shape on it were discussed.

Robotic Peg-Hole Insertion Operations using a Six-Component Force Sensor

1993 ◽  
Vol 207 (5) ◽  
pp. 289-306 ◽  
Author(s):  
H Qiao ◽  
B S Dalay ◽  
R M Parkin
Keyword(s):  
Initial Conditions ◽  
Industrial Robot ◽  
Force Sensor ◽  
Force Sensors ◽  
Geometric Uncertainties ◽  
Two Measures ◽  
Contact Surfaces ◽  
Novel Strategy ◽  
The Relationship ◽  
Component Force

Peg-hole insertion is a widely used industrial robot process. For precise insertion it is common to use force sensors to obtain the deviation between the peg and the hole. In this paper, several examples of six-component force sensors, which are designed to measure the forces and torques in all directions, are reviewed. The problem of how to obtain the deviation between the peg and the hole from the measurement of the forces and the torques exerted on the sensors is then discussed. It is shown that the angle between the peg and the hole and the roughness of the contact surfaces (the end surface of the peg and the surface surrounding the hole) would significantly influence the identification of deviation, no matter how small they are. Two measures to address these phenomena are introduced. A novel strategy of the high-precision chamferless peg-hole insertion with a wrist force sensor is presented and verified experimentally. This strategy is constructed: to obtain the relationship between the peg and hole from the force sensor signal when angular misalignment and the defects of the contact surfaces are present to reduce the angular and lateral errors and to achieve precise chamferless robotic peg-hole insertion. In this paper, it is shown that the insertion can be effected with a reasonably large range of initial conditions. The principle is to move and rotate the peg from an area having many geometric uncertainties to a new area, where the deviation of the peg and hole can be obtained.

A Criterion for Combination Rule in Flaw Assessment of Parallel Surface Cracks

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Masayuki Kamaya
Keyword(s):  
Stress Intensity ◽  
Structural Reliability ◽  
Crack Depth ◽  
Crack Size ◽  
Multiple Cracks ◽  
J Integral ◽  
Surface Cracks ◽  
Linear Elastic ◽  
Offset Distance ◽  
Bending Load

When multiple cracks approach one another, the stress intensity factor and J-integral value change due to the interaction of the stress field. Since the changes in these parameters are not always conservative in structural reliability evaluations, the interaction between multiple cracks should be taken into account. Section XI of the ASME Boiler and Pressure Vessel Code provides a flaw characterization rule for interacting multiple cracks. In Section XI, adjacent cracks are replaced with a coalesced single crack when the distance between the cracks is less than half of the crack depth. However, the criterion for the offset distance is given as an absolute value, although the magnitude of the interaction depends on the crack size. In the current study, an alternative criterion for the offset distance was examined. Linear-elastic and elastic–plastic analyses were performed for interacting semicircular and semi-elliptical surface cracks by the finite element method under a tensile or bending load. The change in the stress intensity factors and J-integral values due to the relative spacing of cracks was investigated. Based on the relationship between the magnitude of the interaction and the relative position of the cracks, the allowable ctriterion for the offset distance was discussed.

scholarly journals Modeling and Experimental Research of One Kind of New Planar Vortex Actuator Based on Shape Memory Alloy

Actuators ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 8
Author(s):  
Xiangsen Kong ◽  
Yilei Gu ◽  
Jiajun Wu ◽  
Yang Yang ◽  
Xing Shen
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Mechanical Model ◽  
Angular Displacement ◽  
Complex Structure ◽  
Maximum Error ◽  
Coefficient Of Determination ◽  
Minimum Error ◽  
Output Torque ◽  
The Relationship

In order to alleviate the problems of complex structure and low reliability of traditional Shape Memory Alloy (SMA) rotary actuator, a planar vortex actuator (PVA) based on SMA material was proposed to directly output torque and angular displacement. Based on the calculation method of PVA and the constitutive model of the phase transition equation of SMA, the mechanical model is established, and the pre-tightening torque, temperature, output torque, and rotation angle are obtained. The relationship expression between the tests has verified the mechanical model. The results show that the relationship between the excitation temperature and the output torque, the coefficient of determination between the calculated value and the tested value, is 0.938, the minimum error is 0.46%, and the maximum error is 49.8%. In the relationship between angular displacement and torque, the coefficient of determination between the calculated value and the test value is 0.939, the maximum error is 58.5%, and the minimum error is 28.0%. The test results show that the calculated values of mechanical model and experimental data have similar representation form.

scholarly journals On the Brittleness of Handwritten Digit Recognition Models

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander K. Seewald
Keyword(s):  
Error Rate ◽  
Maximum Error ◽  
Error Rates ◽  
Classification Systems ◽  
Feature Representation ◽  
Training Data ◽  
Handwritten Digit Recognition ◽  
Digit Recognition ◽  
Handwritten Digit ◽  
The Relationship

Handwritten digit recognition is an important benchmark task in computer vision. Learning algorithms and feature representations which offer excellent performance for this task have been known for some time. Here, we focus on two major practical considerations: the relationship between the the amount of training data and error rate (corresponding to the effort to collect training data to build a model with a given maximum error rate) and the transferability of models' expertise between different datasets (corresponding to the usefulness for general handwritten digit recognition). While the relationship between amount of training data and error rate is very stable and to some extent independent of the specific dataset used—only the classifier and feature representation have significant effect—it has proven to be impossible to transfer low error rates on one or two pooled datasets to similarly low error rates on another dataset. We have called this weakness brittleness, inspired by an old Artificial Intelligence term that means the same thing. This weakness may be a general weakness of trained image classification systems.

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