Bending Characteristics of 2-Layer Spiral Strand Under Typical Contact Conditions

doi:10.12141/j.issn.1000-565X.240061

Abstract

Abstract:

To study the mechanical behavior of 2-layer spiral strand under tension-bending coupling effect and the cooperative working mechanism of internal wires, inter-wire friction and slip were taken into consideration. Static equilibrium relationships for micro-segments of layer-wire were established and analytically derived under two typical contact conditions: inter-layer contact and coupled contact. At the same time, an improved semi-refined finite element model was proposed for numerical simulation and result comparison. Relative slip direction between wires on two contact conditions were obtained from the distribution of shear force on layer-wire, based on which the axial force limit of layer-wire after sliding was derived according to the equilibrium equation. The bending moment-local curvature relation of spiral strand was obtained by summing the bending moments contributed by each wire under tension-bending coupling effect, and a simplified bending moment-mean curvature relation was proposed to describe bending behavior of the spiral strand. The result shows that there are slip stagnation points on contact surface of adjacent wires because layer-wire rotates along the axis of spiral strand periodically, and relative slip direction on both sides of the stagnation point is opposite. The slip stagnation point and initial slip position on contact surface of layer-wire to layer-wire and layer-wire to core-wire are different. When neglecting the progression of internal slip, 2-layer spiral strand exhibits the same bending moment-mean curvature relationship under both contact conditions, and the function graph presents a bilinear form. The relative error of the bending deformation results before and after slipping between semi-refined FE model and analytical values is less than 4%, and the extracted relative slip results are in agreement with the analysis conclusions.

Key words: spiral strand, tension-bending coupling effect, slippage between wires, bending characteristics, contact conditions, semi-refined finite element model

CLC Number:

U443.38

WANG Ronghui, LIU Xiyue, ZHAO Yonglin, ZHEN Xiaoxia, ZHANG Zhuojie. Bending Characteristics of 2-Layer Spiral Strand Under Typical Contact Conditions[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(6): 12-24.

Figures/Tables 24

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Table 1

Comparison of mean curvature under bending moment"

$M x / (N · m)$	解析值	ANSYS层间接触		ANSYS同步接触
$M x / (N · m)$	$κ ¯ M / 10 - 3 m - 1$	$κ ¯ M / 10 - 3 m - 1$	相对误差/%	$κ ¯ M / 10 - 3 m - 1$	相对误差/%
0.0	0.000 0	0.000 0	0.00	0.000 0	0.00
1.4	1.087 1	1.081 1	-0.55	1.091 0	0.36
2.1	1.630 6	1.653 5	1.40	1.636 5	0.36
2.8	2.174 2	2.194 0	0.91	2.182 0	0.36
3.5	2.717 7	2.734 6	0.62	2.727 5	0.36
4.2	3.261 2	3.275 1	0.43	3.273 0	0.36
4.9	3.804 8	3.847 5	1.12	3.818 5	0.36
5.6	4.348 3	4.388 1	0.91	4.364 0	0.36
6.3	4.891 9	4.928 6	0.75	4.909 5	0.36
7.0	5.435 4	5.501 0	1.21	5.455 0	0.36
7.7	5.978 9	6.136 9	2.64	6.000 6	0.36
8.4	6.522 5	7.281 6	11.64	7.080 5	8.56
9.1	10.103 4	10.079 8	-0.23	10.016 0	-0.86
9.8	14.354 6	13.927 3	-2.98	13.900 9	-3.16
10.5	18.605 9	17.997 4	-3.27	17.971 6	-3.41
11.2	22.857 1	22.067 5	-3.45	22.062 9	-3.47
11.9	27.108 3	26.169 4	-3.46	26.170 7	-3.46
12.6	31.359 6	30.303 0	-3.37	30.291 0	-3.41
13.3	35.610 8	34.436 7	-3.30	34.422 8	-3.34
14.0	39.862 1	38.570 4	-3.24	38.565 9	-3.25
14.7	44.113 3	42.735 9	-3.12	42.718 0	-3.16

Table 1

Fig.19

Table 2

Applied bending moment and relative slip direction while COMBIN40 was slipping under inter-layer contact condition"

侧丝	151# （-90°）	161# （-60°）	171# （-30°）	181# （0°）	191# （30°）	201# （60°）	211# （90°）
$w 1$	×	8 260	7 280	6 860	7 280	8 260	×
$w 2$	7 280	6 860	7 280	8 260	×	8 260	7 280
$w 3$	7 280	8 260	×	8 260	7 280	6 860	7 280
$w 4$	×	8 260	7 280	6 860	7 280	8 260	×
$w 5$	7 280	6 860	7 280	8 260	×	8 260	7 280
$w 6$	7 280	8 260	×	8 260	7 280	6 860	7 280

Table 2

Table 3

Applied bending moment and relative slip direction while COMBIN40 was slipping under synchronous contact condition"

接触点	151# （-90°）	161# （-60°）	171# （-30°）	181# （0°）	191# （30°）	201# （60°）	211# （90°）
$P w 1 -$	7 840	6 720	7 840	8 260	×	8 260	7 840
$P w 1 *$	×	8 120	7 840	6 720	7 840	8 120	×
$P w 1 +$	7 840	8 260	×	8 260	7 840	6 720	7 840
$P w 2 -$	7 840	8 260	×	8 260	7 840	6 720	7 840
$P w 2 *$	7 840	6 720	7 840	8 120	×	8 120	7 840
$P w 2 +$	×	8 260	7 840	6 720	7 840	8 260	×
$P w 3 -$	×	8 260	7 840	6 720	7 840	8 260	×
$P w 3 *$	7 840	8 120	×	8 120	7 840	6 720	7 840
$P w 3 +$	7 840	6 720	7 840	8 260	×	8 260	7 840
$P w 4 -$	7 840	6 720	7 840	8 260	×	8 260	7 840
$P w 4 *$	×	8 120	7 840	6 720	7 840	8 120	×
$P w 4 +$	7 840	8 260	×	8 260	7 840	6 720	7 840
$P w 5 -$	7 840	8 260	×	8 260	7 840	6 720	7 840
$P w 5 *$	7 840	6 720	7 840	8 120	×	8 120	7 840
$P w 5 +$	×	8 260	7 840	6 720	7 840	8 260	×
$P w 6 -$	×	8 260	7 840	6 720	7 840	8 260	×
$P w 6 *$	7 840	8 120	×	8 120	7 840	6 720	7 840
$P w 6 +$	7 840	6 720	7 840	8 260	×	8 260	7 840

Table 3

Fig.20

Table 4

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β/（°）	140 kN	210 kN	280 kN	350 kN	420 kN
2	0.003 3	0.005 0	0.006 6	0.008 3	0.009 9
3	0.005 0	0.007 4	0.009 9	0.012 4	0.014 9
4	0.006 6	0.010 0	0.013 3	0.016 6	0.019 9

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