Using the eigenvalue expansion to solve for crack diffraction in an elastic waveguide with a numerical example of a surface crack on a railroad wheel rim

1984 ◽  
Vol 76 (S1) ◽  
pp. S21-S21
Author(s):  
M. N. Fahmy ◽  
R. D. Finch ◽  
W. E. VanArsdale
Keyword(s):  
Surface Crack ◽  
Railroad Wheel ◽  
Numerical Example ◽  
Elastic Waveguide ◽  
Wheel Rim ◽  
Eigenvalue Expansion

scholarly journals Nondestructive evaluation of residual stress in railroad wheel rim with EMATs.

1990 ◽  
Vol 110 (8) ◽  
pp. 866-872
Author(s):  
Riichi Murayama ◽  
Kazuo Fujisawa ◽  
Sadao Yonehara
Keyword(s):  
Residual Stress ◽  
Nondestructive Evaluation ◽  
Railroad Wheel ◽  
Wheel Rim

Nondestructive Assessments of Residual Stresses in Railroad Wheel Rim by Acoustoelasticity

1985 ◽  
Vol 107 (3) ◽  
pp. 281-287 ◽  
Author(s):  
H. Fukuoka ◽  
H. Toda ◽  
K. Hirakawa ◽  
H. Sakamoto ◽  
Y. Toya
Keyword(s):  
Residual Stress ◽  
Fem Analysis ◽  
Railroad Wheel ◽  
Velocity Difference ◽  
Average Value ◽  
Acoustic Anisotropy ◽  
Wheel Rim ◽  
Principal Directions ◽  
Acoustoelasticity Method ◽  
Destructive Methods

Residual stress in the rim of railroad solid wheel was measured nondestructively by an acoustoelasticity method which makes use of the birefringent effect. The acoustic anisotropy is a fractional velocity difference of two shear waves polarized perpendicularly in principal directions and is proportional to the principle stress difference. However, in order to get the residual stress nondestructively, the contribution of texture anisotropy has to be separated from the total acoustic anisotropy. The scatter of the texture anisotropy was investigated using seven wrought wheels, four of which were used for drag brake tests that were to change the residual stress level. The initial and after braked residual stress was analyzed by acoustoelasticity, and the results were compared with the conventional methods and FEM analysis. Conclusively, it is expected through this study that the residual stress averaged through thickness in the rim can be assessed nondestructively by using the average value of the texture anisotropy in the rim within 40 MPa of difference compared with the estimation by conventional destructive methods.

Development of Railroad Wheel Rim Axial Residual Stress in Heavy Axle Load Service

2013 ◽  
Author(s):  
Cameron Lonsdale ◽  
John Oliver ◽  
Rama Krishna Maram ◽  
Scott Cummings
Keyword(s):  
Residual Stress ◽  
Tensile Stress ◽  
Railroad Wheel ◽  
Stress Profile ◽  
X Ray Diffraction ◽  
X Ray ◽  
Wheel Rim ◽  
Axial Tensile ◽  
Axial Residual Stress ◽  
Class C

Vertical split rim (VSR) failures remain a failure mode for wheels in North America, and are of concern to wheel manufacturers and railroads alike. Both forged and cast wheels have suffered VSRs in service. Extensive testing during the last several years, using x-ray diffraction techniques, has shown the axial residual stress pattern within the railroad wheel rim is significantly different for new AAR Class C wheels vs. AAR Class C wheels that have failed due to a VSR, and non-failed AAR Class C wheels that have been operating in service. VSRs almost always begin at areas of tread damage, resulting from shelling or spalling, and cracking propagates into the rim section under load. At the rim locations tested, the as-manufactured wheels have a relatively “flat” axial residual stress profile, compressive but near neutral, caused by the rim quenching operation, while wheels that have been in service have a layer of high axial compressive stress at the tread surface, and a balancing zone of axial tensile stress underneath. The magnitude and direction of this axial tensile stress is consistent with the crack propagation of a VSR failure. When cracks from tread surface damage propagate into this subsurface axial tensile zone, a VSR can occur under sufficient additional service loading, such as loads caused by in-service wheel/rail impacts from tread damage. Further, softer Class U (untreated) wheels, removed from service and tested, were found to have a balancing axial tensile stress layer deeper below the tread surface than that found in used Class C wheels. This paper describes recent x-ray diffraction testing to measure the axial residual stress profile in wheel rims operated in the Facility for Accelerated Service Testing (FAST) train at the Transportation Technology Center (TTC), in Pueblo, CO. The goal of the testing was to determine the development rate and magnitude of wheel rim axial residual stress, as a function of known load and service mileage. Four new Class C wheelsets and four new Class U wheelsets were placed in service under the FAST train, and these wheelsets were subsequently removed at various mileage levels for evaluation. Two radial rim slices were cut from each wheel at each mileage level, and x-ray diffraction was used to measure the axial residual stress within the wheel rim section. The last two Class C wheelsets and last two Class U wheelsets were also exposed to an extended drag braking event at FAST, where wheel treads were heated by tread braking. The authors describe the testing and discuss the axial residual stress results in detail, with emphasis on implications for service.

SIMPLIFIED MATHEMATICS FOR MULTIPLE BIOASSAYS

1960 ◽  
Vol XXXV (III) ◽  
pp. 454-468 ◽  
Author(s):  
R. Borth
Keyword(s):  
Parallel Line ◽  
Numerical Example ◽  
Dose Levels

ABSTRACT Gaddum's simplified system of computation for the analysis of biological parallel-line assays is extended to the assay of several unknown preparations simultaneously against the same standard, using up to four dose levels of each preparation. Complete working directions and formulae are provided and illustrated by a numerical example. Limiting conditions are briefly discussed.

Fore-Aft Forces in Tire-Wheel Assemblies Generated by Unbalances and the Influence of Balancing

1991 ◽  
Vol 19 (3) ◽  
pp. 142-162 ◽  
Author(s):  
D. S. Stutts ◽  
W. Soedel ◽  
S. K. Jha
Keyword(s):  
Mathematical Model ◽  
Elastic Foundation ◽  
Torsional Oscillation ◽  
Vertical Direction ◽  
Torsional Stiffness ◽  
Rolling Motion ◽  
Vertical Force ◽  
Horizontal Force ◽  
Wheel Rim ◽  
Open Question

Abstract When measuring bearing forces of the tire-wheel assembly during drum tests, it was found that beyond certain speeds, the horizontal force variations or so-called fore-aft forces were larger than the force variations in the vertical direction. The explanation of this phenomenon is still somewhat an open question. One of the hypothetical models argues in favor of torsional oscillations caused by a changing rolling radius. But it appears that there is a simpler answer. In this paper, a mathematical model of a tire consisting of a rigid tread ring connected to a freely rotating wheel or hub through an elastic foundation which has radial and torsional stiffness was developed. This model shows that an unbalanced mass on the tread ring will cause an oscillatory rolling motion of the tread ring on the drum which is superimposed on the nominal rolling. This will indeed result in larger fore-aft than vertical force variations beyond certain speeds, which are a function of run-out. The rolling motion is in a certain sense a torsional oscillation, but postulation of a changing rolling radius is not necessary for its creation. The model also shows the limitation on balancing the tire-wheel assembly at the wheel rim if the unbalance occurs at the tread band.

Seismic stability of the underground main pipeline

2011 ◽  
Vol 8 (1) ◽  
pp. 275-286
Author(s):  
R.G. Yakupov ◽  
D.M. Zaripov
Keyword(s):  
Laplace Transformation ◽  
Seismic Waves ◽  
Generalized Functions ◽  
Seismic Stability ◽  
Main Pipeline ◽  
Motion Equations ◽  
Numerical Example ◽  
Earthquake Force ◽  
Deformed State

The stress-deformed state of the underground main pipeline under the action of seismic waves of an earthquake is considered. The generalized functions of seismic impulses are constructed. The pipeline motion equations are solved with used Laplace transformation by the time. Tensions and deformations of the pipeline have been determined. A numerical example is reviewed. Diagrams of change of the tension depending on earthquake force are provided in earthquake-points.

Box-Cox Transformations

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Maximum Likelihood ◽  
Normal Form ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimate ◽  
Grouped Data ◽  
Numerical Example ◽  
Alternative Method ◽  
Modified Likelihood

This chapter examines the well-known Box-Cox method, which transforms a sample of non-normal observations into approximately normal form. Two non-standard aspects are highlighted. First, the likelihood of the transformed sample has an unbounded maximum, so that the maximum likelihood estimate is not consistent. The usually suggested remedy is to assume grouped data so that the sample becomes multinomial. An alternative method is described that uses a modified likelihood similar to the spacings function. This eliminates the infinite likelihood problem. The second problem is that the power transform used in the Box-Cox method is left-bounded so that the transformed observations cannot be exactly normal. This biases estimates of observational probabilities in an uncertain way. Moreover, the distributions fitted to the observations are not necessarily unimodal. A simple remedy is to assume the transformed observations have a left-bounded distribution, like the exponential; this is discussed in detail, and a numerical example given.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

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