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1990 | Buch

Theory of Wire Rope

verfasst von: George A. Costello

Verlag: Springer US

Buchreihe : Mechanical Engineering Series

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Über dieses Buch

Mechanical engineering, an engineering discipline borne of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a new series, featuring graduate texts and research monographs, intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the first page of the volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Professor Leckie, the consulting editor for applied mechanics, and I are pleased to present the third volume of the series: Theory of Wire Rope by Professor Costello. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our readers with topical monographs as well as graduate texts.

Inhaltsverzeichnis

Frontmatter
1. Introduction
Abstract
A property common to structural elements such as rope, yarn, cord, cable, and strand is their ability to resist relatively large axial loads in comparison to bending and torsional loads. Rope [1, 2],* because of this property, is one of the oldest tools that humans have used in their efforts to produce a better life for themselves. A copper cable found in the ruins of Nemeveh near Babylon indicates that wire rope was used as a structural element in about 700 b.c. Sayenga has written an excellent history of the American wire rope industry [3].
George A. Costello
2. Equilibrium of a Thin Wire
Abstract
Consider a curved thin wire that is initially unstressed and that has a uniform cross section. A thin wire can be defined as a wire in which the maximum characteristic length of the cross section, that is, its diameter or diagonal, etc., is small compared to the length of the wire and the radius of curvature of the centerline of the wire.
George A. Costello
3. Static Response of a Strand
Abstract
Figure 3.1 shows the configuration and cross section of a loaded simple straight strand. The strand consists initially of a straight center wire of radius, R1, surrounded by m2 helical wires (six wires are actually shown) of wire radius, R2. It will be assumed, for the present, that the center wire is of sufficient size to prevent the outer wires from touching each other. This is generally the case, since it tends to minimize the effect of friction in the bending of a strand. Hence, the initial radius of the helix of an outside wire is given by the expression
$$ {r_2}\,\, = \,\,{R_1}\,\, + \,\,{R_2}. $$
(3.1)
An expression will now be derived to determine the minimum value of R1 so that the outside wires will not be touching each other.
George A. Costello
4. Static Response of a Wire Rope
Abstract
The equations developed in the previous sections will now be used to generate the solution for ropes with complex cross sections. Consideration will be given, at first, to a cross section consisting of one simple, straight, seven-wire strand surrounded by six seven-wire strands, which are preformed. Figure 4.1 shows such a cross section in which the outside strands are deformed into the helical shape they assume in the unloaded rope and are this shape under no external loads (preformed strands). Such a cross section is often used as a rope core in a more complex rope and as such is sometimes called an independent wire rope core (IWRC). The center strand will be called strand 1, an outside strand will be denoted strand 2.
George A. Costello
5. Friction in Wire Rope
Abstract
Chapter 3 considered the static response of a simple straight strand with the cross section shown in Figure 3.1. It was assumed in that chapter that the wires were frictionless. It will now be shown that friction plays a very small role in the axial loading of a simple strand.
George A. Costello
6. Testing of a Wire Rope
Abstract
Initially, a load deformation curve was obtained experimentally for a 1.306-in. diameter, 6 × 19 Seale IWRC rope on a 600,000-lb testing machine. A plot of the load as a function of the deformation is shown in Figure 6.1. In this test, a 45-in. gage length was used and the total cross-sectional area ΣπR2 i = 0.727 in.2. The experimental effective modulus of the rope is about 18,400,000 psi, although the preceding theory predicts an effective modulus, based on E = 29,000,000 psi, of about 0.7 × E = 20,300,000 psi. The theoretically determined modulus is higher than the experimentally determined one, since contact deformation between the wires is neglected; also, the outer strands tend to settle inside the radius of the IWRC, since the line load on the outer strand acts only at the contact points. This last condition is especially apparent in the initial loading of a rope. In the above theory it was assumed that the modulus of elasticity of the wire material was 29,000,000 psi.
George A. Costello
7. Birdcaging in Wire Rope
Abstract
In many cases, wire rope is subjected to impact loads which send axial and torsional responses up and down the rope. If the loads are severe enough, the outer strands can separate from the core in a permanent manner and thus render the rope useless. Such a phenomenon is generally known as birdcaging. A bird cage is a term often used to describe the permanent appearance of a wire rope forced into compression. Figure 7.1, taken from the Wire Rope Users Manual [4], depicts such an event.
George A. Costello
8. Rope Rotation
Abstract
As was shown previously, the total axial force F and the total axial twisting moment M t acting on a rope can be expressed as
$$ \frac{F}{{AE}}\,\, = \,\,{C_1}\varepsilon \,\, + \,\,{C_2}\beta $$
(8.1)
and
$$ \frac{{{M_t}}}{{E{R^3}}}\,\, = \,\,{C_3}\varepsilon \,\, + \,\,{C_4}\beta , $$
(8.2)
where A = ΣπR2 i , R is the radius of the rope and ε and β are the axial and rotational strains. The rotational strain is defined by the equation
$$ \beta \,\, = \,\,R\tau , $$
(8.3)
where τ is the angle of twist per unit length.
George A. Costello
Backmatter
Metadaten
Titel
Theory of Wire Rope
verfasst von
George A. Costello
Copyright-Jahr
1990
Verlag
Springer US
Electronic ISBN
978-1-4684-0350-3
Print ISBN
978-1-4684-0352-7
DOI
https://doi.org/10.1007/978-1-4684-0350-3