典型接触条件下双层螺旋曲杆束的弯曲特性

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

华南理工大学学报(自然科学版) ›› 2025, Vol. 53 ›› Issue (6): 12-24.doi: 10.12141/j.issn.1000-565X.240061

典型接触条件下双层螺旋曲杆束的弯曲特性

王荣辉¹(), 刘锡月¹, 赵勇霖¹, 甄晓霞¹(), 张卓杰²^,³

^1.华南理工大学土木与交通学院，广东广州 510640
^2.道路与铁道工程安全保障教育部重点实验室石家庄铁道大学，河北石家庄 050043
^3.河北省风工程和风能利用工程技术创新中心，河北石家庄 050043

收稿日期:2024-02-05 出版日期:2025-06-10 发布日期:2024-07-22
通信作者: 甄晓霞 E-mail:rhwang@scut.edu.cn;xxzhen@scut.edu.cn
作者简介:王荣辉（1959—），男，博士，教授，主要从事桥梁结构理论与应用研究。E-mail： rhwang@scut.edu.cn
基金资助:
国家自然科学基金项目(52178138);广东省自然科学基金项目(2024A1515012262)

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

WANG Ronghui¹(), LIU Xiyue¹, ZHAO Yonglin¹, ZHEN Xiaoxia¹(), ZHANG Zhuojie²^,³

^1.School of Civil Engineering and Transportation，South China University of Technology，Guangzhou 510640，Guangdong，China
^2.Ministry of Education Key Laboratory of Roads and Railway Engineering Safety Control，Shijiazhuang Tiedao University，Shijiazhuang 050043，Hebei，China
^3.Innovation Center for Wind Engineering and Wind Energy Technology of Hebei Province，Shijiazhuang 050043，Hebei，China

Received:2024-02-05 Online:2025-06-10 Published:2024-07-22
Contact: ZHEN Xiaoxia E-mail:rhwang@scut.edu.cn;xxzhen@scut.edu.cn
Supported by:
the National Natural Science Foundation of China(52178138);the Natural Science Foundation of Guangdong Province(2024A1515012262)

摘要/Abstract

摘要：

为研究双层螺旋曲杆束在拉-弯耦合作用下的力学行为及其内部钢丝协同工作机理，考虑丝间摩擦滑移，建立了层间接触、同步接触两类典型条件下的侧丝微段静力平衡关系并进行了解析推导，同步提出一种改进的半精细化有限元模型进行数值模拟和结果对比。由弯曲变形时侧丝所受剪切力的分布规律获得了两类接触条件下的丝间相对滑移方向，并在此基础上根据平衡方程推导得到侧丝滑移后的轴力限值；通过对各丝贡献的弯矩求和得到在拉-弯耦合作用下曲杆束各截面的弯矩-局部曲率关系式，并提出一种简化的弯矩-曲率均值关系式描述其整体弯曲行为。结果表明：由于侧丝沿曲杆束整体轴向周期旋转，相邻丝之间接触面有滑移驻点，且驻点两侧相对滑移方向相反；侧丝-侧丝、侧丝-芯丝接触面的滑移驻点、初始滑移位置不同；忽略内部滑移扩展过程，两类接触条件下双层螺旋曲杆束具有相同的弯矩-曲率均值关系式，函数图像呈双折线；半精细化有限元模型滑移前后的弯曲变形结果与解析值的相对误差小于4%，且提取的丝间相对滑移结果规律与分析结论相符。

关键词: 螺旋曲杆束, 拉-弯耦合, 丝间滑移, 弯曲特性, 接触条件, 半精细化有限元模型

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

中图分类号:

U443.38

王荣辉, 刘锡月, 赵勇霖, 甄晓霞, 张卓杰. 典型接触条件下双层螺旋曲杆束的弯曲特性[J]. 华南理工大学学报(自然科学版), 2025, 53(6): 12-24.

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.

图/表 24

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

图15

图16

图17

图18

表1

弯矩荷载下曲率均值结果对比"

$M x / (N · m)$	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

表1

图19

表2

层间接触情况下COMBIN40滑移时所施弯矩以及相对滑移方向 (N·mm)"

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

表2

表3

同步接触情况下COMBIN40滑移时所施弯矩以及相对滑移方向 (N·mm)"

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

表3

图20

表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

典型接触条件下双层螺旋曲杆束的弯曲特性

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

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