length) helical core componentsand contrahelically-laid exter-nal armor wires can be locat-ed by drag and drop opera-tions that are intuitive andeasily performed. The cross-section plot is drawn to scaleand all components have thecorrect shape to verify com-ponent fit. An explodedthree-dimensional plot canbe produced for better visual-ization of the design and fordocumentation purposes.

A finite element mesh ofall components is generat-ed automatically by thecode, and element nodesare created at all compo-nent contact points. Uponsolving, plots of cablestrain, torque or rotation,deformations and stresscontours are generated toassess cable performance.

This cable design softwareis able to model both sym-metrical and asymmetrical,axial and compound heli-cal geometries. Nonlinearmaterial behavior, layerlocking (circumferentialwire contact) and wireindentation into adjacentsoft layers also can be mod-eled.

Construction variablessuch as lay length and num-

Computer-aided Design of CablesFor Optimal PerformanceGeometric Modeling and Finite Element Software for StructuralDesign of Cables

By Dr. R. H. KnappUniversity of Hawaii at ManoaDepartment of Mechanical

EngineeringHonolulu, HawaiiS. DasandT. A. ShimabukuroStructural SolutionsAiea, Hawaii

Today, numerous cable applications requiresophisticated designs that satisfy various

strength, communication and power transmissionfunctions. These cables often have highly com-plex constructions that require structural analysisbeyond simple, idealized mathematical models.Other manufacturing industries have realizedtremendous productivity and product qualitygains through the successful implementation ofgeneral purpose, computer-aided design (CAD)tools into their development process over the past30 years. The cable industry has not benefittedfrom these tools to the same extent, however,because it is difficult to model the helical wiregeometries found in cables.

What is needed is a CAD tool developed specif-ically to model cable geometries. Such a toolshould simplify model creation to facilitate rapidparametric design studies, and it should takeadvantage of known geometrical properties of thecable so that creation of finite element models istransparent to the cable designer.

In this paper, the CableCAD®

software code forgeometric and finite element modeling of cablesis described. The program makes it easy to gener-ate cable models such as for the ROV tether cablemodel depicted. For instance, meshed (same lay

ROV tether cable model.

Reprinted from Sea Technology

gram and this is confirmed visually in the cross-section plot. This operation is valid for any heli-cal lay angle, where large lay angles produce non-circular bean shapes.

The geometric modeler allows rapid creation ofcomplex cable geometries with the followingcapabilities:

• create, modify or delete any cable componentor layer;

• drag and drop placement of helical wires andstrands;

• dynamic layer data table;• solid and jacketed circular, tubular, keystone

and rectangular wire shapes;• single, double and triple helical structures in

cables and wire rope;• user-defined strand library;• user-defined material library (linear, nonlin-

ear and color properties);• color-coding of jacketed conductors;• optimized compaction of cable cores;• automatic generation of finite element mesh

and nodes;• created element boundary and symmetry con-

straints;• pan and zoom of cable cross-section;• printed and graphical documentation.

Finite Element ModelerCable structures consist of components with

complex helical geometries. General purposefinite element programs, though versatile, are not

ber and diameter of tubes or wirescan be modified easily, therebypermitting multiple design itera-tions to be completed in minutes.

Loads that can be applied simul-taneously to the model includetension, twist, bending (includinginternal friction), cable externalpressure or partial pressure (cablepinching), helical hose internal orexternal pressures, clamping andthermal loads (internal flux andexternal convection). Metallic,polymer and synthetic fiber com-ponents can be handled by thecode.

Straight and bent cable analysisoptions provide cable deforma-tions and internal componentstresses. Axial, torsional and flex-ural rigidities can be found interms of elongation, twist andbending curvature.

Comparisons with actual cable test data andother general purpose finite element softwareshow that the CableCAD code provides reason-able estimates of cable behavior. Also, modelingand run times are significantly less than thatrequired for general purpose finite element pro-grams.

CableCAD allows the cable designer to quicklyevaluate many design concepts prior to expensiveprototyping and testing.

The geometric and finite element modelers, andseveral verification examples, are described in thefollowing.

Geometric ModelerAn accurate geometric description of a cable is

needed to define the exact locations where com-ponents make contact. Since the shape of a circu-lar component in the cable cross-section is notcircular, and varies with radial location from thecable axis and the wire lay length, an automatedgeometric modeler is employed.

For contra-helical adjacent layers, contactoccurs on a circle between the layers. For meshedlayers (same lay length), the program automati-cally finds the radial and circumferential loca-tions to fit wires or strands into the interstices ofsubjacent components using a drag and dropoperation. A new component is dragged to theapproximate location where the wire is desiredand then dropped into the space between compo-nents. Its final location is computed by the pro-

Drag and drop helical component.

(top left) Ring element mesh.

(bottom left) ROV cable strainand torque plots.

(right) Pinched cable and CableCAD® stress contours.

tions in the radial direction.1

Element generation and other model parametersare controlled internally so that the details of thefinite element method are transparent to the cabledesigner. This renders the program usable by agreater audience.

ExamplesMany cable examples have been investigated to

validate the CableCAD code, including simpleseven-wire strands and complex electro-optical-mechanical cables. Validations are based on as-built cable test data or parallel modeling effortsusing general purpose finite element codes.

ROV Tether Cable. The depicted ROV tethercable has a core consisting of three electrical con-ductors meshed with three optical fibers and sixhigh density polyethylene (HDPE) filler rods. AnHDPE core sheath and two contra-helically laid

well-suited to analyzing such structures. A con-siderable amount of time must be invested in join-ing components, meshing and applying boundaryconditions. Also, a thorough understanding of thefinite element method is required to generate avalid solution.

The finite element method discretizes structuresinto multiple elements whose shapes are selectedto best match the structural boundaries. In thecase of circular components used in cables, ringelements are employed.

The large, center component is meshed with anumber of ring elements shown by concentricdashed circular rings. Contact points (A-F) withinner and outer adjacent components maintainconnectivity in the radial (u) and circumferential(v) directions.

Each ring element is an axisymmetric solid ele-ment with internal degrees-of-freedom that arecondensed to yield amacro-element stiffnessmatrix with radial and cir-cumferential deforma-tions acting only at thecontact points. Due to theasymmetrical deforma-tions expected for a typi-cal ring element in a cablecomponent, radial and cir-cumferential displace-ment functions, u(r,θ) andv(r,θ), respectively, areexpressed in terms ofFourier series shape func-tions with quadratic varia-

steel armor layers protect the core componentsand provide tensile strength. In creating themodel, color-coding of jacketed conductors havebeen specified. This cable was analyzed withCableCAD using nonlinear material propertiesfor the HDPE core-sheath and for armor wireindentation into this sheath.

2The slightly nonlin-

ear curves of cable axial strain and reactiontorque are in good agreement with test data.

Pinched Cable. In another example, a fiberoptic tube cable is pinched with diametricallyopposed pressure bands.

1Both CableCAD and the

general purpose ANSYS®

software were used tomodel this cable.

3The center component is a steel

wire, the middle layer consists of six helicalpolypropylene tubes and the outer layer is anHDPE jacket.

A cable length corresponding to one lay lengthof the tubular layer is modeled with ANSYS solidelements. Whereas the time for a skilled analystto create the ANSYS model was approximately

one work day, CableCAD modeling was accom-plished in minutes.

Pressure bands with an included angle of 60oare

centered about the top and bottom of the cross-section to simulate a pinching load. Analysisresults from both programs show that the effec-tive stress contour plots differ by only one percentand deformation plots differ by about nine per-cent. The solution time for CableCAD wasapproximately five percent of that required forANSYS.

Strand Bending with Wire Slip. A variablediameter sheave was used to test a simple groundcable for overhead electrical transmission lines.The cable consists of six steel wires laid helicallyaround a single steel core wire. Outer layer wireswere instrumented with electric resistance straingages and the cable was loaded with a tension andthen bent by forcing the sheave fully onto thecable. The bend radius was varied to detect wireslip.

Test results are shown in a plot of wire strainversus bend radius. As the bend radius isdecreased (increased bending curvature), thestrain increases. At about a 36-meter bend radius,the gages recorded a sudden relaxation of wirestrain as wires slipped.

The 33-meter bend radius to initiate slip pre-dicted by the CableCAD frictional bending modelis within eight percent of the measured result.Wire slip is used in determining wire stresses andthe flexural rigidity of bent cables.

DiscussionCableCAD analysis results have compared

favorably with those of general purpose finite ele-ment codes and with actual cable test results.Both cable modeling and cable testing are impor-tant steps in developing a new cable design andshould be regarded as complementary. For exam-ple, a computer model could be used in planningmore focused cable tests, and certain cable behav-ior recorded in cable testing might better beunderstood by means of finite element analysis.

A finite element model can reveal stress distrib-utions that are difficult, if not impossible, to mea-sure directly, and physical testing could revealcable behavior like "constructional stretch" thatmight not be apparent in a computer model.

Finite element analysis is the ubiquitous designtool of choice in most manufacturing industriestoday and is expected to become more common-place in the cable manufacturing sector as well.CableCAD is a design tool that can be used toquickly evaluate many construction concepts for

Wire slip in bent cable.

cables, wire rope and some types of flexible pipe.The program gives the designer the confidence toconsider alternatives outside of historical designrules so that nontraditional cable constructionscan be explored. This will help lead to innovativenew cable constructions that meet the challengingoperational requirements of today. As this type ofdesign tool gains acceptance, improved and morepowerful software ultimately will evolve as it hasin other industries.

AcknowledgmentsThis work was funded in part by the National

Defense Center of Excellence for Research inOcean Sciences (CEROS). CEROS is part of theNatural Energy Laboratory of Hawaii Authority(NELHA), an agency of the Department of Busi-ness, Economic Development and Tourism, stateof Hawaii. CEROS is funded by the AdvancedResearch Projects Agency (ARPA) through grantsto NELHA. This report does not necessarilyreflect the position or policy of the government,and no official endorsement should be inferred.

The authors are grateful to Prof. Peter Hage-dorn, Institute for Mechanics, Technical Uni-versity of Darmstadt, Germany, for support-ing the frictional bending experiments. /st/

References1. Das, S., Knapp, R. H. and Shimabukuro, T.A., "Finite

Element Analysis - A New Tool for Cable Design," Proc.50th Intl. Wire and Cable Symposium, Paper 11-4, LakeBuena Vista, FL, Nov. 12-15, 2001.

2. CableCAD®

v2.0 User Manual, Structural Solutions, 98-030 Hekaha St. Suite 20, Aiea, HI 96701 (2002).

3. ANSYS®

- (Analysis Systems) v5.7 User Manual, AnsysInc., 275 Technology Drive, Canonsburg, PA 15317(2001).

Ronald H. Knapp is a professorof mechanical engineering at theUniversity of Hawaii and is thefounder and president of Struc-tural Solutions. He has beendeveloping numerical models forcables and ropes for nearly 25 years. He obtainedhis M.S.M.E. degree from the California Instituteof Technology in 1969 and his Ph.D. in oceanengineering from the University of Hawaii in1975.

Suvabrata Das joined StructuralSolutions after graduating fromthe University of Hawaii atManoa in 1999 with an M.S. inocean engineering. Since then, hehas been involved in the develop-

ment of finite element models for the structuralanalysis of cables. He obtained his undergradu-ate degree in 1996 from the Indian Institute ofTechnology at Kharagpur, India.

Terry A. Shimabukuro joinedStructural Solutions in 1998 andhas been responsible for the com-mercial implementation of thecomputer code for cable design.He has 20 years of mechanicalengineering design experience in the defense,medical device and computer industries. Heobtained his B.S.M.E. degree from the Universityof Hawaii in 1980 and his M.S.M.E. degree fromStanford University in 1981.