CA1078595A - Thermally stable helically plied cable - Google Patents

Abstract

THERMALLY STABLE HELICALLY PLIED CABLE
Abstract of the Disclosure The cable includes continuous glass filaments which are helically plied in rovings at a constant helical angle from cable center to outer surface and bonded together in elastomeric material. When heated, thermal elongation of the filaments is opposed by simultaneous radially directed thermal volumetric expansion of the elastomeric material.
Thus, with respect to overall cable length, thermal elonga-tion of the cable is opposed by a simultaneous increase in cable cross sectional area such that thermal elongation effects are controllable, dependent upon the thermal expan-sion properties of the filament and elastomeric materials used, by controlling the helical angle at which the filaments are plied to obtain either expanding, contracting or constant length cables, as desired. Thermal contraction effects produced by cooling the cable also are controllable by controlling the helical angle. In some high tensile load cable applications, the helical angle additionally may be related to tensile load, depending upon the modulus of elasticity of the filaments used. The invention is par-ticularly adapted to helically plied glass fiber cables which are thermally stable over a wide range of temperatures.

Description

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Background oE the lnventlon This appliaation is a continuation-ln-part o~ applica~
tion Serial Wo. 466,174, filed May 2, 1974, which is a division o~ application 5erial No. 311,361, iled December 1, 1972, now United States Patent No. 3,821,879.
This invention relates to cables in which thermal elongation effect~ are controllable to obtain cables Which either expand, contract~ or remain essentially constant in length at ~arious temperatures. The in~en-tion is illustrated and described herein with reference to a composite glass ~iber cable comprising helically plied glass filaments which are embedded and bonded to-gether in elas~omeric bonding material; however, it will be apparent that other compatible strength and bonding materials may be used. As used herein, the term "strength material" refers to the ten~ile load bearing elements which serve to bear tensile loads applied ~o the cable and the term "bonding material" refers to the material in which the load bearing element~ are embedded.
Metallic and non-metallic cables, such as glass fiber cables, commonly elongate with increasing temperature. The amount of thermally induced elongation is a function of the linear coeficient of thermal expansion of the cable material and the change in temperature to which the cable is subjected.
In many cable applications, excessive or uncontrolled thermal elongation is highly undesirable. For example, thermal elongation of a cable used as the strength member in suspended electrical transmission lines can produce damaging sag in the line. ;
Summar of the Invention This invention provides a cable in whlch thermal elongation effects can be controlled to provide, depending _ 1 _ 713~3~
upon the thermal expansion properties of the strenyth and bonding materials us~d, cable~ WhiCh either expand, co~tract or remain essentially constant in length under widely varying temperature conditions.
According to a preferred embodiment of the invention, the strength material is comprised of continuous filaments and the bonding material in which the filaments are embedded is comprised of elastomeric material. Preferably, the linear coef~icient of thermal expansion of the elastomeric material is substantially graater than that of the filament3. The filaments are arranged in overlapping concentric la~ers in which they are plied helically at a constant helical angle from cable center to outer surface. The elastomeric material surrounds and bonds individual filaments to the filaments of the same and adjacent layers.
When heated, thermal elonga~ion of the indi~ldual filaments i9 opposed by simultaneous radially directed thermal volumetric expan~ion of the elastomeric material.
The tendency for the individual filaments to elongate with increasing temperature is opposed by a aontractive tendency produced by radial expansion of the elastomeric material.
Thus, with respect to overall cable length, thermal elonga~
tion of the cable with increasing temperature can be nulled by simultaneous increase in cable cross sectional area produced by the radial component of volumetric expansion of the elastomeric material. When cooled, of course, thermal contraction of the individual filaments is opposed by ~imul-taneous radially directed volumetric contraction of the elastomeric material . Thi~ volume-tric contraction of the elasto~eric material produces a dearease in cable cros~
sectional area which serve~ to null therma~ contraation of the cable. In either ca~e, the greater the heliaal angle at which the filament.s are plied, the greater the nulling .

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action obtairled, and vice ver~a. ~rhus, by controllirlg the helical anyle ak which the filament~ are plied and maintain-ing it constant Erom the cable center to outer surface, it i5 possible, depending upon ~he thermal expan~ion properties of the filament and elastomeric materials u~ed, to obtain either expanding, contracting or cGnstant length cables.
In most practical applications, control of cable length is obtained, by controlling the helicai angle, regardless of tensile loading on the cable; however, in some high stress applications, the helical angle may further be related to the elasticity of the filament material u~ed.
The helical angle at which the tensile load bearing eIements may be plied ko obtain a thermally stable cable is determined from the following formula:
sin(x~

where sin(x) = sine helical angle x.
k = linear coeficient of thermal expansion ; B of the bonding material.
k = linear coefficient of thermal expansion ~ o~ the strength material.
~B = volumetric percentage of bonding material~
The principles of thi~ invention are particularly suitable for use in glass fiber cables which compri~e multiple concentric overlapping layer3 of helically plied glass fiber rovings, each of which include~ a plurality of sub~tantially untwisted, generally parallel glass fila-ment~. Each filament is ~urrounded by a cured ela~tomeric sheath which is bonded to the sheath surrounding adjacent filaments in the same and adjacent layers. To ~abricate ' the cable, the rovings are wound together helically to `" 30 form an initial lay-up, and then addi.tional layers of roving are wound helically about the initial lay-up, while maintaining the helical angle con~tant, until a cable of :
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de~ired diameter i~ o~tai~ed. The composite gla~s fiber cable is fabricated u~ing apparatu~ generally similar ~o the apparatus disclosed in Uni~ed States Paten~ No. 3,663,533, assigned to the assignee of this invention.
Brief Description of the Drawinys Fig. 1 is a per3pective of a section of the composike glass iber cable of this invention, depicting a glass fiber roving being applied thereto during lay up;
Fig. 2 is a cross-section of the cable of Fig. l depicting thermal volumetric expansion of the cable of Fig. l;
Fig. 3 is a graph of temperature vO elongation and contraction of conventional cables and the glass fiber cable of Fig. 1 plied at various helical angles;
Fig. 4 is a graph of helical angle v. total contraction o~ the glass fiber cables of Fig. 3;
Fig. 5 is a graph generally similar to Fig. 3 depictiny thermal elongation and contraction of the cable of Fig. 1 formed of different filament materials plied at various helical anglesi Figs. 6-9 are ~chematic~ depicting the effect of temperature upon a unit length of the cable of Fig. l;
Fig. 10 is a graph of calculated helical angle of thermal stability v. the product of linear coefficient of thermal expansion of and percentaye bonding material of the cable of Fig. 1 formed of strength materials of various linear coefficients of therm~l expansion;
Fig. 11 is a graph of temperature v. contraction of the cable of Fig. 1 under varying tensile loadsi Fig. 12 is a schematic depicting the effect of tensile loading upon a unit length of the cable oE Fig. l.
Detailed De~cription of the Drawings The gla~s fiber cable o Fiys. 1 and 2 compri~es multl-ple overlapping concentric layer~ o~ helically pLied gla~

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fiber rovings 2. Each roving is made up o~ a plurality of substantially untwisted, generally parallel gla~s filaments 4. The ~ilament~ 4 are plied helically, as depicted in Fig.
1, at a helical angle (x) which is maintained con~tant from the cable center to outer surface. Each filament i5 sur rounded by a cured elastomeric sheath which is bonded to the elastomeric sheath~ surrounding adjacent filamente in both the same and adjacent layers to form an ela~tomeric cable matrix 6.
The glass fiber cable of Figs. 1 and 2 is fabricated by winding a plurality of glass fiber rovings 2 togethex helically to form an initial lay-up, and thereafter winding additional gla~s fiber rovings 2 about the initial lay-up in helical fashion, as depicted in Fig. 1, to form multiple overlapping concentric layer~ un~il a cable of desired diameter is obtained. Consequently, the finished cable is coreles~
and substantially homogenous in cro~s-section.
The cured elastomeric sheath surrounding eaah filament is formed during the cable fabrication pxocess using a two component elastomeric material. In one known proces~ of manufacture, certain of the rovings are impregnated during lay-up of the initial and subsequent layers with one ~heath - component which is the uncured elastomeric material. The remaining rovings are impregnated with the other sheath component which is a curing agent or hardener. When the rovings are applied to the cable during lay-up, these two components react to form an elastomeric cable matrix in which each filament is surrounded by a cured elastomeric sheath which i~ bonded ko the sheath~ surrounding adjacent .. . .
filament~ in both the same and adjaaent layers. Urethane elastomers are pre~erred ~or -use in the gla~s ~lber aables o~ thi~ inventioni however, the ahoiae of the partiaular bonding material used will depend upon the type o~ filament .

''' : . - . ~, 1~71~5~5 material u~ed ~nd the desired khermal expansion propertie~
of the elastomer. For example, other polymeric bonding rnaterials may be used in this invention. The composite glass fiber cable oE Figs. 1 and 2, and the method and apparatus for making that cable are illustra~ed and described in detail in United States Pa~ent No. 3,662,533, the disclosure of which is hereby incorporated by reference.
It was an unexpected di~covery that the composite glass fiber cable of the -type described herein either expands, contracts or remains e~sentially constant in length under widely varying temperature conditions, depending upon the helical angle at which the glas~ roving is applied. Further, and contrary to conventional cable behavior, the teachings of this invention enable precise control of the thermal behavior of the cable by controlling the helical angle at which the glass ilaments are plied in relation to the thermal expansion properties of the ~il~nent and elastomeric materials used.
- When heated, thermal elongation of the individual fila-ment3 i5 OppO ed by simultaneous thermal volumetric expansion of the elastomeric material. As depicted~by arrows in Fig.

2, the thermal volumetric expansion of the elastomer is primarily in the radial direction. This radially directed component of volumetric expansion o~ the elastomeric mater-i; ial produces a contractive tendency which opposes the tendency for the individual filaments to elongate with ~ .
increasing temperature. Thus, with respect to overall cable length, thermal elongation of the cable with in-creasing ternperature aan be nulled by an increase in cable cros~ ~ectional area produced by the radial component of volumetria expansion of the elastomeric material to obtain a thermally stable cable.

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The amounl: of ela~tomeric mat~rial pr~en~ per unit length of cable, and hence the nulling ackion obtained i~
controlled by the helical angle at which the roving~ are applied. Inasmuch as the filaments are surrounded by the elastomeric material which comprises the cable matrix 6, the amount of elastomeric material contained in a length of cable can be increased by increasing the number of turns of filamen~s 4 per unit length of cable. The greater the number of turn~ or rovingS 2, containing filament3 4, applied per length of cable, the greater the nulling action obtained, and vice versa. The helical angle (x) at which the rovings are applied, of course, determines ~he number of turns of roving, and hence the amount of elastomeric material per length of cable. Thus, the helical angle at which the glass roving is applied can he utilized a~ the controlling factor in determining whether a given length of cable will be thermally stable, contract or elongate when heated to a specific temperature. Consequently, it is possible, by selecting the helical angle at which the glas~ roving~ are 2Q applied in relation to the thermal expansion proper~ias of the filament and elastomeric materials used and by maintaining the helical angle constant from the ca~le center to outer surface during lay-up, to obtain either expanding, contracting or constant length cables. It will be recogrlized, of course, tnat the amount o~ elastomeric or other bonding matexial present per unit length of cable may be controlled by other means.
When cooled, of course, thermal contraction of the ~; individual filament~ i~ oppo~ed hy ~imultaneous thermal 3Q volumetric contraction o~ the ela~tomeric material in the radial direation. This radially directed aomponen~ oE
volumetric aontrac~ion of the ela~tomeric material produces a decrea~e in cable cros ~ectional area which oppo~ thernal ..~
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~3 contraation of the overall cable. Thus, the princi~les of this invention further apply to controlliny thermal contract-ion effects of cables whic~are cooled; however, ~or purposes of clarity and understanding, the invention is illustrated and dèscribed hereina~ter with respect to cables in which thermal elongation effects produced by cable heating are controlled.
The unit length of cable, with respect to a par~icular cable layer, is termed herein the l'leadll distance which is expressed as the product of the cotangent of helical angle and cable circumference:
b = a cot(x) (1.) where: b = lead distance cot(x) = cotangent helical angle (x) a = cable outer circumference ~ The lead distance in Equation (1~ i9 the length traveled, ; measured along the longitudinal axis of the cable, by one complete 360 helical twist o~ roving 2 about the cable. The rovi~g follows the path of a helix, as indicated in Fig. 1.
`~ 20 It will be understood, of cour3e, that the lead distance ~or each cable layer becomes progressively longex, and hence the number of turns of roving in each layer progressively decrea~es, from cable c~nter to outer surface, when the helical angle is maintained constant during lay-up of all ` layers of cable. In most practical cases, however, accurate experimental results and calculations are obtained by `~ referring only to the lead di~tance of the cable outer sur-face or fini~hed diameter. This is due to the physical s characteriatics of the elaatomeric cable ma-trix 6, and the ~act that thermal elongation e~ects with rc~pect to a unit ~ length o~ cable comprialng multiple overlapping la~rs, are -- uni~orm throughout the cable aro~ sectional area. It will be understood, there~ore, that all re~erence hereinaeter to .

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a particular "leadl' refers -to the Illeadll distance of the outer layer of cableO
The unique thermal behavior of the glas~ fiber cable of this invention may best be understood by ~irst referring to the test results depicted in Fig. 3 in which conventional and helically plied glass cables of diffexing helical angles were tested under similar conditions of temperature and tensile loading. The cables tested were subjected to temp-eratures ranging from 70 to 170 F. and a tensile load of about 2,000 lbs.
Of the conventional cables tested, tes~ cable l con~i~ted of a cylindrical grouping of parallel glass fibers which elongated about 0.015 inches for a 100-inch cable section.
Cable 2, a wire rope 5/16 inch in diameter, elongated about 0.045 inches for a 100~inch cable section. Cable 3 consisted of steel banding 0.025 x 0.500 inche3 and elongated about 0.078 inches for a 100-inch cable ection.
O~ the helically plied glas~ fiber cables tested, all were three-eighths inch in diameter and abricated in a manner described in U. S. Patent No. 3,662,533 except that the uncured urethane re~in applied to the glass fiber rovings prior to twisting was incorporated in the curing agent. The filament material used was a commercially available glass, manufactured by Owens Corning Corporation, known a~
"S" glass. ~5 illustrated by Fig. 3, cable (a), made up of filaments plied at a helical angle of about 25 15 minutes, contracted about 0.070 inche~ for a 100-inch cable section.
Cable (b), made up of filaments plied at a helical angle of about 21 50 minute~, contracted about 0.04 inche~ for a 100-inch cable section. Cable (c), made up o~ ~ilaments plied at a helical angle of about 17 25 mlnute~, contracted about 0.025 inches from a 100-inch cable ~ection. Cable (d), made up of filaments plied at a h~lical angle o~ abolt 11 _9_ . ~ , .

7~5~15 45 minute~, contracted about 0.007 inches ~or a 100-inch cable section. Cable (e), mad~ up of ~ilamen~s plied at a helical angle of about 7 6 minutes, contrac~ed about 0~002 inches per 100-inch cable ~ection.
Fig. 4 graphically illustrates the e~fects of helical angle upon thermal stability of the glass fiber cable of Fig. 1. Fig. 4 depicts helical angle v. total contraction of cables (a)-(e) of Fig. 3 Cables (d) and (e), which were plied at helical angles below about 11 45 minutes, maintained essentially constant overall length at temperatures ranging from 70F. to 170F. That i6, these cables were thermally stable when heated 100F. The remaining cables tes~ed, which were plied at helical angles above that helical angle however, tended to contract exceRsively when heated 100F.
such that they were not thermally stable.
As depicted in Fig. 5, the thermal expanision properties -` of the filament material used influences the thermal elonga-tion behavior of the cable of Fig. 1. Cables de~ignated ~d) and ~c) correspond to cable~ (d) and ~c) in Fig. 3 and were fabricated of "S" glass filaments plied at helical angles ~: of about 11 45 minutes and 17 15 minutes, re~pectively.
Two additional generally similar cables (f~ and (g) were fabricated of a commercially available glass, manu~actured by Owens Corning Corporation, known as "E" glas~. The "E'l glass ~; filamentR of cables (f) and (g) were plied at helical angles of about 18 and 11, respectively. The linear coefficients of thermal expansion of "E" and "S" glass are 2.8 x 10~ in/inF.
and 1.6 x 10 6 in/inF., respectively. When these four cables were subjected to the same tensile loading under the temperature conditions indicated, both "S" gla~s cables (d) and ~c) exhibited `~ greater contraction~ The "E" gla3~ cable~ (~) and (g), due to the higher linear coeficient of thermal expansion of the "E"
: glass filament used, contracted less than the "S" gla~s cables ...
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under the sarne temperclture conditions. ~pparently, th~ ~on-tractive influence produc~d by volumetric e~pans.ion of the elastomer which comprised the cable matrix failed to null increased thermal eloncJation produced by the "~" glass fi].aments.
It will be recoynized that the thermal expansion characteristics of the elastomer used also will afect the thermal behavior of cables according to this invention. For example, it is possible, as will presently be described, by using an elastomer, polymer or other bonding material of suficien.t xadial component of thermal expansion, to null the thermal elongation tendency of the "E" g].ass filaments depicted in Fig. 5 ko obtain a thermally stable cable.
It is now possible to calculate, for a selected helical angle, the thermal elongation behavior of a helically plied cable of the type described, given the thermal expansion properties of the filament and elastomeric materials used, or of other mutually compatible strength and bonding materials.
Referring now to E'ic~. 6, the relationship of the cable outer circumference (a), cable unit length or lead distance (b), and :~
t;le lenyth o one full 360 twist of glass fiber roving !c), shown in hroken lines, are represented by a right triangle bounded by sides "a", "b" and "c". The relative leng-ths of sides "a", "b" and "c" is expressed in the equation:
c2 - a2 + ~2 (2.) .~ For each layer of glass roving applied at constant helical ~ angle, the circumference, lead, and roving length will be : represented, with respect to a unit length of cable corres-pondiny to one lead distance, by a generally similar right triang].e in ~hich the xelative lengths of ~ides "a", "b"
j~ 30 and "c" will vary wlth diameter. IIowever, as already des-:~ aribed above, accurate re~;ults are obtained, in most practical : ca.ses, by re~errirlg ~o tlle outside or finlshed cable layer.
Thus, the following calculatiorl refers to t~i.s layer.
. . .
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r ~ ~ ~785~ ~
As the ternperature of the c~ble changes, t'ne glass roving will expand or eontraet in length. ~eferring to Fig. 7, with an inerease in cable temperature the roviny length "c" twisted about a given lead distanee "b" will inerease in length by an increment "~e". Assuminy no inerease in eable eireumferenee "a", this increase in lenyth of roving will produee a simultaneous inerease in the lead diskanee "b" by an inerement "~be". As depieted in Fig. 7, a new triangle results. This new triangle will have increased roving and eable lengths, as indieated in broken lines by the sides "c ~c" and "b +~bell~ The relationship o~ eable cir-cumference, cable length and roving length from Equa~ion (2.) will now be:
(c + ~C)2 = (b ~ ~be)2 -~ a2 By simplifying this equation, the incremental increase in cable length, abe, is determined by substituting ~e2 - a2" for ~ the term "b2" of Equation (1.) and omitting, as negligible, ; seeond order dif~erential terms "~b2" and"4e2":
be = e~e (3.) b As the -temperature of the eable changes, the bonding material will expand and contraet radially. As depieted in Fig. 8, upon increase in eable temperature, the eable will increase in cross sectional area and henee its eircumf~renee "~ "a" will increase by inerement "~a". Assuming no change in `~ length of roving "c", this increase in cable circumference will produce a simultaneous decrease in the lead distanee -~ "b" by an increment ''~bc''. ~s depieted in Fig. 8, a new ` triangle results. This new triangle wi].l have inereased roviny length and deereased eable length indieated in broken '~ lines by the sides "a -~a" and "b - ~bc". The relationship , of eable eircumference, eable length and roving leng-th Erom .~, , Equation (2.) will now be-. .
~.~ ,, .

1~7~o~3Si c~ bC)2 ~ (a -~ aa)2 By sim~lifying this equa-tion, khe decreas~ in ca~le lenyth~ hc is determined by substituting ~c2 _ a2~ for the term "b2" and omitting, as negligible, second order differential terms "~b2" and "~a2".

bc ~ a~a (4.) Summing Equations (3.) and (4.) ~ b +Q b = c~c - ~Ba Therefore, -for no change in cable length:
cac = a~a (5.) It is also possible to arrive at Equation (5.) by another analysis, depicted in Fig. 9. When heated, increase in cross-sectional area and elongation of the cable occur simultaneously, as describe previously, so that when cable elongation ll~bell is equal to cable contraction ''~bc'', the cable is thermally stable.
That is, each cable unit length, or lead distance "b", remains at constant length with changing temperature. This condition is represented by the triangle of Fig. 9 from which:
(c ~ ac)2 - (a ~ ~a)2 = b2 From Equation (2.) c a b Combining these two expressions:
(c ~ c) (a aa) c s 2cac ~ ac2 = 2a~a - ~a2 ..:
The second order differential terms "~c2" and ~laa2ll are negliyible and can be omitted to again arrive at Equation (5.) above.

The term "~c" :in Equation (5.) can be expressed ;lS

Eollows:

~- ~ c -- ckS~T (6.) ,~ . , where:

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k - linear coefflcient o~ thermal expans:ion of -the strerly-th }naterial (i.e., the ylass filaments in the example o~ Fly. 1.
~ T - temperature chanye.
The term "~a" in Equation (5.) can be expressed as ~ollows:
~a = akB ~T%B
where:
k = linear coefficient of thermal expansion ~ of the bonding material (i.e., the elasto-mer in the example of Fig. 1).
= temperature change %B = cross sectional volumetric percentage of bonding material.
Substituting the expressions for "~c" and "~a" of Equations (6.) and (7.) into Equation (5.) C2kS~T = a2kBaT9~B
c2 = a2kB%B (8.) ks From Equation (2.) C2 = a2 .~ b2 Equating the expressions for the term "c2" of Equations (8.) and (2.) and substituting for the term "b" ~rom Equation (l.), it is possible to arrive at an expression for helical angle (x):
a2k~s = a2 ~ a2 [cot(x)]2 ~' :' kS , , cot(x~ l (9a.) Alternativelyj by substituting the expression for sin(x) in Fig. 6 (sin(x) -- a/c) into Equation (8.), i-t is possible to arrive at an equivalent preferred expressi.on Eor helical angle ,'~ 30 (x):
" sin(~) -Iks (9b.) : U~13~
Thus, it is possible, usln~ Equations (9a.) or (9~.), to provide a helical,ly plied cable, cornposed of filament and '~. ,' , bonding ma-terials having certain :Linear coefficients of thermal expansion, which will b~ thermally s~a~l~ or rerna:in essentially constant in lèngth under widely varylng temperature conditions, including both heating and cooling.
Fig. lO represents, in graphical form, helical angles of thermal stability, calculated rom Equations (9a.) and (9b.), for strength and bonding materials of various linear coe~ficients of thermal expansion. Curves (h~, (i) and (j) depict calculated helical anyles of thermal stability for strength and bonding materials having linear coefficients of thermal expansion of: 1.8; 2.8; and 3.8 x 10-6 in/inF., respectively. Cur~es (h) and (i) generally represent "S" and "E" glass cables, res-pectively. As will be appreciated from Fig. 10, the greater the linear coefficient of thermal expansion of and/or the greater the percentage bonding material used, the smaller the helical angle must be to provide a thermally stable cable.
` Likewise, the greater the linear coefficient of thermal expan- -sion of the strength material used, the greater the helical angle must be to provide a thermally stable cable. Preferably, the linear coefficient of thermal expansion of the bonding material is substantially greater than that of the strength material.
It will be recognized that, due to the large difference ; between thermal coefficients of linear expansion of -the pre-ferred strength and bonding materials, volumetric or radial expansion of the strength material, such as glass filaments, is negligible relative to that of most elastomeric bonding materials. Consequently, in Equations (7.), (8.) and (9a.) and ~9b.~ the radial expansion of the strength material and its influence upon radial expansion of ~he bod~ oE bonding material is assumbe to be neglible. ~'he term "%B" u~ed in --~ these equations, in e~fect, relates thermal radial expansion of the cable to the volumetric percentage of bonding materill . ~

usecl. I~ will be under~tood, of course, tha-t, for cables ma~e up of other streng-th and bondiny materials, thermal racliaJ
e~pansion of hoth the strength and bonding materials, or their effects upon each other, may ~e considered in determining the helical angle of thermal stability oE the cable. Furthermore, the e~fects of temperature upon the linear coefficients of thermal expansion of the strength and bonding materials used also may be considered in determininy the helical angle of thermal stability.
Inasmuch as increasing the helical angle produces a greater number of turns of roviny per length o-f cable, the tension modulus of the helically plied cable of this inven-tion can be controlled by controlliny the helical anyle.
The greater tne number of turns of roving per length of cable, the greater the tendency for the cable to stretch as the turns of roving are straightened relatively along the length of cable in response to applied load. Thus, by applying the rovings at a large helical angle, a lower cable tensile modulus is obtained. (i.e., The cable has a greater tendency to stretch in response to applied tensile load.) Conversely, at small helical angels, the rovings are more nearly parallel to the longitudinal axis of the cable, with fewer turns of roving per length of cable, and a higher cable tensile modulus is obtained. (i.e., The cable has a lesser tendency to stretch in response to applied tensile load.) Thus, by referring to Equations (9a.) or (9b.) and Fig. 10, it will be appreciated that it is possible, by selecting the strength and bonding materials used, and the percentage bonding material, to produce a thermally stable cable having a desired tensile modulus. For example, by increasiny the percentage oE bonding material used in Fig. 10, for a certain set of ~trength and bonding mat~rials, the helical anyle oE thermal stability may be reduced sufficiently to obtain a thermally stable cable of increased cable tensile modulus.

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Fig. ll depict~ the e~fec-ts of tensile Joadin~ upon the cable of Fig. 1. Tlle cable tested was ~enerally similar to the three-eighths inch diameter, 100-inch length cables described with reference to Fiy. 3 and was plied at a helical angle of about 17 25 minutes. At tensile loadinys of 500 lbs., 1050 lbs. and 2050 lbs., and under the temperature conditions indicated, overall cable contraction did not change siynifi-cantly. Thus, in most practical cable applications involving tensile loadings similar to those tested, it appears that tensile loading will not affect therrnal elongation of the cable; however, as stated previously, in some cable appli-cations involving very high tensile loads, dependent upon the helical angle at which the filaments are plied, tensile loads may stretch the overall cable to the point that the filaments straiyhten or shift longitudinally. Consequently, with sufficient relative straightening of the filaments, the helical angle is decreased as depicted in Fig. 11. The end result is that the number of turns of roving per unit length of cable is reduced, and less contractive or nulling action is obtained for a given temperature range.
It is now possible to calculate the theoretical tensile loads required to produce sufficient relative straightening of the rovings or filaments to significantly affect the helical angle and hence the nulling action obtained. Referring now in particular to Fig. ll, when tensile load (T) is applied to the cable of Fig. 1, elongation of the cable will occur, dependent upon the modulus of elasticity (E) of the filament material used. The resultant cable elonga-tion, ''~bs'', with respect to a unit length of cahle or lead distance "h", can be expressed as follows:
~ bs -- hS (10.) - where:
b = lead distance (see Equation (l.)) . . .

149~ 35 S ~ tensile stress E = Modulus of elas-ticity o~ the strength ma-terial (i.e., the filament~ in khe example of Fig. 1)~
An expression for the resultant cable length (b +~ bs) is obtained by substituting the previously noted expression for the term lead distance "b" from Equation (1.) into Equation (10. ) S
b + ~bs = a cot(x) (l + E ) (11.) As described previously, the helical angle may decrease, due to longitudinal straightening of the rovinys and filaments, in response to some applied tensile loads. This condition is depicted in Fig. 11 by smaller helical angle "y". Refer-ring to the longitudinally enlarged trianyle which includes angle "y", assuming cable circumference "a" remains constant: -cot(y) = b + ~bs a b + ~bs = a cot(y) (12.) Equating the expressions for "b -~b5" of Equations (11.) and (12.), it is possible to arrive at an expression for the ~` decreased helical angle "y" which is produced in response to tensile loadings:
i cot(y) = cot(x) (1 + S) E (13.) Thus, it is possible, given the plied helical angle "x" of thermal stability, to calculate, using Equation (13.), the helical angle "y" which is or may be produced in res-ponse to tensile load "T". It will now be appreciated from ~ Equation (13.) that, for most practical cable applications, `~` 30 tensile load is insufficient to produce a significant change in helical angle of thermal stability, depending upon the modulus of elasticity of the filarnents used. In fact, the .~
.~ tensile load "T" generally exceeds the tensile stresses which ,, . ~
~- are normally encountered in most practical cable applications, .
`~` including electrical transm:ission line.s, or exceeds the ul-tiMate , .~
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tensile strength of the filaments used. ~or example, a tensile stress of 10,000 psi applied to a cable fabricated of "E" ylass filaments will produce an insignificant change in helical anyle; however, in other applications, it is possible to predict what tensile stress or loading is neces-sary to produce the helical angle "y", using Equation (13.).
In the latter applications, it then is possible to increase the plied helical angle "x" during fabrication an amount sufficient to compensate for the effects of tensile stress ~-or loading. The end result, in the latter applications, is a cable which, in response to applied tensile loads, is thermally stable, or expands and contracts to the same ex-tent as the cables of Figs. 1-10.
It will be recognized by one of ordinary skill that, in addition to glass filaments and elastomeric mater-ials, other mutually compatible strength and bonding materials may be used in this invention. The particular - choice of strength and bonding material will depend upon their chemical and thermal expansion properties, the environ-~- 20 ment in which the cable is to be used, and other factors.
Accordingly, the invention is not to be limited to the specific embodiment illustrated and described herein and the true scope and spirit of the invention are to be determined by reference to the appended claims.

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Claims (8)

The claims are:

1. A cable, comprising:
tensile load bearing elements which can change in length in response to variations in temperature, and, bonding material for bonding the load bearing elements together which has a thermal radial expansion component operatively associated with the tensile load bearing elements in sufficient quantity that the overall cable length is con-trolled under varying temperature conditions by a change in the cross-sectional area of the cable in opposition to and substantially simultaneously with a change in the length of the load bearing elements.

2. The cable of claim 1, wherein the tensile load bearing elements comprise continuous filaments helically plied at a substantially constant helical angle, and wherein the bonding material comprises a plurality of cured elastomeric sheaths, each surrounding a filament and bonded to the sheaths surround-ing adjacent filaments to form a cable matrix which expands and contracts radially in response to increasing and decreasing temperature, respectively, to produce an increase and decrease in cable cross-sectional area.

3. The cable of claim 2 wherein the filaments are glass.

4. The cable of claim 2 wherein the elastomer is a urethane elastomer.

5. The cable of claim 2 wherein the tensile load bearing elements are helically plied at a substantially constant helical angle which is determined by the formula:

sin (x) =
where sin (x) is the sine of helical angle x; kB and ks are the linear coefficients of thermal expansion of the bonding and tensile load bearing elements, respectively; and %B is the volumetric percentage bonding material.

6. The cable of claim 2 wherein the helical angle pro-duced in response to an applied tensile load is determined by the formula:
cot (y) = cot (x) (1 + ?) where cot (y) is the cotangent of helical angle y produced in response to an applied tensile load; cot (x) is the cotangent of helical angle x at which the load bearing elements are plied during lay-up; S is tensile stress produced by an applied tensile load; and E is the modulus of elasticity of the tensile load bearing elements.

7. A method of controlling thermal elongation of a com-posite member including tensile load bearing elements comprising:
controlling the cross-sectional area of the composite member in accordance with transverse thermal expansion and contraction characteristics thereof such that variation in cross-sectional area of the composite member contracts the effects of thermal elongation and contraction characteristics of the tensile load bearing elements on the length of the composite member so that the length of the composite member is controllable under varying temperature conditions.

8. The method of claim 7 including helically plying the tensile load bearing elements at a substantially constant helical angle which is determined by the formula; as in claim 5.
sin (x) = where sin (x) is the sine of helical angle x; kB and ks are the linear coefficients of thermal expansion of the bonding and tensile load bearing elements, respectively, and %B is the volu-metric percentage bonding material, and wherein the helical angle produced in response to an applied tensile load is determined by the formula of claim 6 and explanation.

cot (y) = cot (x) (1 + ?) where cot (y) is the cotangent of helical angle y produced in response to an applied tensile load; cot (x) is the cotangent of helical angle x at which the load bearing elements are plied during lay-up; S is tensile stress produced by an applied tensile load; and E is the modulus of elasticity of the tensile load bearing elements.