scholarly journals Folding the Carpenter’s Tape: Boundary Layer Effects

2019 ◽  
Vol 87 (1) ◽  
Author(s):  
C. R. Calladine ◽  
K. A. Seffen
Keyword(s):  
Boundary Layer ◽  
Isotropic Material ◽  
Strain Energy ◽  
Energy Analysis ◽  
Steel Strip ◽  
Spring Steel ◽  
Bending Moments ◽  
Physical Conditions ◽  
Measuring Tape ◽  
A Minor

Abstract The “carpenter’s measuring tape” is a thin spring-steel strip, preformed to a curved cross section of radius R, which is straight when being used for measuring. Under bending moments, it forms a localized hinge, in which the transverse curvature is suppressed, and the longitudinal radius r is approximately equal to R. Rimrott made a simple strain energy analysis of the hinge region for isotropic material, which predicted that r = R. Both experimental observations and finite element computations show that ξ = r/R > 1, where the value of ξ exceeds unity by up to 15%, depending on whether the tape is bent in “equal-sense” or “opposite-sense” curvature; ξ varies linearly with Poisson’s ratio in both cases. We make a minor change to Rimrott’s analysis by introducing a boundary layer, in order better to satisfy the physical conditions at the free edges; this successfully accounts for the observed behavior of the tape.

Prediction of Springback in Metal Forming of Diaphragm of Automotive Horn Based on BPANN

2010 ◽  
Vol 139-141 ◽  
pp. 594-599
Author(s):  
Yan Qiu Zhang ◽  
Shu Yong Jiang ◽  
Yu Feng Zheng
Keyword(s):  
Young’S Modulus ◽  
Metal Forming ◽  
Young's Modulus ◽  
Steel Strip ◽  
Back Propagation ◽  
Spring Steel ◽  
Yield Ratio ◽  
Punch Radius ◽  
Cold Rolled ◽  
The Relationship

The spring steel strip 50CrVA which is cold rolled was applied to manufacture the diaphragm of the automotive horn by means of sheet metal forming. The combination of the experiments with back-propagation artificial neural network (BPANN) is used to solve the springback problem of the diaphragm. Experiments have shown that a 4-8-1 BPANN is able to predict the springback of the diaphragm successfully, and the network is able to model the relationship between the springback of the diaphragm and the process parameters rationally. BPANN simulation results and experimental ones have shown that the springback of the diaphragm is particularly influenced by such parameters as blank thickness, Young’s modulus, punch radius and yield ratio. Furthermore, the springback of the diaphragm decreases with the increase of blank thickness and Young’s modulus, but increases with the increase of punch radius and yield ratio.

Optimized Design of Aluminum Cross Car Beam (CCB) Based in Modal Strain Energy Analysis

2016 ◽  
Vol 877 ◽  
pp. 668-673
Author(s):  
Bo Liu ◽  
Zhong Cai Qiu ◽  
Qin Yang ◽  
Ke Wang ◽  
Xian He Wu
Keyword(s):  
Modal Analysis ◽  
Strain Energy ◽  
Energy Analysis ◽  
Simulation Software ◽  
Optimized Design ◽  
Modal Strain Energy ◽  
Car Body ◽  
New Energy ◽  
Nature Frequency ◽  
Energy Contour

An aluminium cross car beam (CCB) for new energy is designed with CATIA. And then,modal analysis is taken by using simulation software-NASTRAN. As nature frequencies can't meet the design target, optimization is performed according to the modal strain energy contour. After structure is strengthen, the first vertical nature frequency of the aluminum CCB(mounted on trimmed car body,with closures and interiors) reaches 35.4Hz.While the first lateral nature frequency reaches 36.5 Hz. Besides,comparing to steel CCB,the weight of the aluminum CCB reduces by4.4 kilogram.

Topology optimization based on the first optimization steps strain energy analysis.

PAMM ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 569-570
Author(s):  
Ryszard Kutylowski ◽  
Marek Szwechlowicz
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Energy Analysis

Design Charts for Symmetrical Ring Girders

1957 ◽  
Vol 24 (1) ◽  
pp. 144-147
Author(s):  
G. P. Fisher
Keyword(s):  
Energy Analysis ◽  
Bending Moment ◽  
Bending Moments ◽  
Bending Energy ◽  
Normal Loading ◽  
Critical Design ◽  
Design Charts ◽  
Ring Location

Abstract Charts, based on classical bending-energy analysis, are presented for the determination of critical design moments in symmetrical ring girders varying in shape from circular through round to sharp-cornered rings. The girders are subjected to uniform normal loading in the plane of the ring. Location and magnitude of all critical bending moments are given, from which the maximum bending moment is easily selected.

Strain Energy Release Rate in Treated Circumferentially Cracked Spring Steel

2012 ◽  
Vol 2 (2) ◽  
pp. 77-87
Author(s):  
Arun K. V. ◽  
Swetha K. V.
Keyword(s):  
Fatigue Strength ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Spring Steel ◽  
Suspension System ◽  
Specimen Preparation

The suspension system is a prominent piece of material that plays a vital role in the stability of a vehicle. During the service, the suspension system is subjected to different environmental conditions, at the same time it has to sustain a variety of loads. The damage of the springs is mainly attributed by its load carrying capacity under fatigue loading. Fatigue strength is the most important property for the spring steel. The energy release rate is an important parameter used to predict the life of the springs. In this experimental analysis, the authors investigate the performance of spring steel under the action of fatigue loads. The specimen preparation and the experimentations have been carried out according to the American Society for Testing of Materials (ASTM) standards. From the experiments, the strain energy release rate of the spring steels has been determined. The effects of tempering and cryogenic treatments on the performance of the spring steel have also been determined. The results have revealed that the fatigue strength and the crack growth resistance have increased with quenching and cryogenic treatments.

The three-dimensional stability of boundary-layer flow over compliant walls

1992 ◽  
Vol 238 ◽  
pp. 537-577 ◽  
Author(s):  
K. S. Yeo
Keyword(s):  
Boundary Layer ◽  
Eigenvalue Problem ◽  
Growth Rates ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Material Anisotropy ◽  
Compliant Walls ◽  
Tollmien Schlichting ◽  
Disturbance Growth

This paper examines the linear stability of the Blasius boundary layer over compliant walls to three-dimensional (oblique) disturbance wave modes. The formulation of the eigenvalue problem is applicable to compliant walls possessing general material anisotropy. Isotropic-material walls and selected classes of anisotropic-material walls are studied. When the properties of the wall are identical with respect to all oblique wave directions, the stability eigenvalue problem for unstable three-dimensional wave modes may be reduced to an equivalent problem for two-dimensional modes. The results for isotropic-material walls show that three-dimensional Tollmien–Schlichting instability modes are more dominant than their two-dimensional counterparts when the walls are sufficiently compliant. The critical Reynolds number for Tollmien-Schlichting instability may be given by three-dimensional modes. Furthermore, for highly compliant walls, calculations based solely on two-dimensional modes are likely to underestimate the maximum disturbance growth factor needed for transition prediction and correlation. However, because the disturbance growth rates on highly compliant walls are much lower than those on a rigid wall, significant delay of transition may still be possible provided compliance-induced instabilities are properly suppressed. Walls featuring material anisotropy which have reduced stiffness to shear deformation in the transverse and oblique planes are also investigated. Such anisotropy is found to be effective in reducing the growth rates of the three-dimensional modes relative to those of the two-dimensional modes.

On Lagrangian drift in shallow-water waves on moderate shear

2010 ◽  
Vol 660 ◽  
pp. 221-239 ◽  
Author(s):  
W. R. C. PHILLIPS ◽  
A. DAI ◽  
K. K. TJAN
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Shallow Water ◽  
Water Waves ◽  
Stokes Drift ◽  
Shallow Water Waves ◽  
Sea Floor ◽  
Langmuir Circulations ◽  
A Minor ◽  
The Waves

The Lagrangian drift in anO(ϵ) monochromatic wave field on a shear flow, whose characteristic velocity isO(ϵ) smaller than the phase velocity of the waves, is considered. It is found that although shear has only a minor influence on drift in deep-water waves, its influence becomes increasingly important as the depth decreases, to the point that it plays a significant role in shallow-water waves. Details of the shear flow likewise affect the drift. Because of this, two temporal cases common in coastal waters are studied, viz. stress-induced shear, as would arise were the boundary layer wind-driven, and a current-driven shear, as would arise from coastal currents. In the former, the magnitude of the drift (maximum minus minimum) in shallow-water waves is increased significantly above its counterpart, viz. the Stokes drift, in like waves in otherwise quiescent surroundings. In the latter, on the other hand, the magnitude decreases. However, while the drift at the free surface is always oriented in the direction of wave propagation in stress-driven shear, this is not always the case in current-driven shear, especially in long waves as the boundary layer grows to fill the layer. This latter finding is of particular interest vis-à-vis Langmuir circulations, which arise through an instability that requires differential drift and shear of the same sign. This means that while Langmuir circulations form near the surface and grow downwards (top down), perhaps to fill the layer, in stress-driven shear, their counterparts in current-driven flows grow from the sea floor upwards (bottom up) but can never fill the layer.

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