This study includes both an analytical development and laboratory 

 tests to determine the rotational behavior and kinking mechanism of 

 several typical electromechanical (EM) cables. A kinking criterion 

 applicable to most EM cables is established. 



CABLE MODELING 



A cable generally consists of one or more layers of helical strands 

 wound around a core strand.* The mechanics of a single helix are first 

 studied before formulating models for the more complex cable structure. 



Single Helix 



A single helix is defined by the arc length S, the length of the 

 helical wire, and the pitch angle a, the angle that the wire makes with 

 a horizontal line. The helix wire can be rolled out on a plane. With a 

 vertical line drawn parallel to the strand axis from the top of the helix 

 and a horizontal line at the lower end of the wire, a triangle is formed 

 (Figure 1). The length of the helix is L. The pitch of the helix wire 

 is P and the number of turns is n = L/P. A negative pitch length represents 

 a left -lay helix. The length of the horizontal base is X = 2irnR, where 

 R is the helix radius. As long as the wire remains helical, the developed 

 triangle is a right triangle [1], When the wire is tensioned, the helix ra- 

 dius tends to decrease due to the radial force generated by the wire tension. 

 The combination of wire elongation and change in helix radius results in 

 a change in n, which is a measure of end rotation of the helix. If the 

 end is restrained, then a torque will be generated in the wire. Now 

 consider what happens when a torque is applied at the ends of a helix 

 wire. The torque causes an end rotation and wire elongation which, in 

 turn, changes the internal stresses and geometry. The combination of 

 tensile and torsional loadings causes a complex change in cable configuration. 



The main assumptions in the following derivation are that the wire 

 geometry remains helical and symmetrical after deformation and that friction 

 forces are neglected. Other assumptions are as follows: 



1. Wire material follows Hooke's law. 



2. Wire lateral deformation due to contact stress is negligible. 



3. Wire radius reduction due to Poisson's effect is negligible. 



4. Strengths of conductors, dielectrics, fillers, jackets, and 

 other nonstrength members are negligible. 



. Consider now a simple helix under axial tension F and torque T; Prime 

 indicates the state after loading. The pitch angle a changes to a ' , and 

 the wire length S changes to S'. The helix has been stretched and twisted, 

 and the curvature of the helix changes from k = cos^ a/R to k' = cos2 to a'/R' 

 The torsion or twist of the helix changes from x = cos a sin a/R to x ' 

 = cos a 1 sin a'/R 1 . These deformations signify changes in wire tension 

 and torque. The wire tension p due to change in wire length S is 



* A strand generally consists of one or more layers of helical 

 wires wound around a core wire. 



