﻿ 山地轨道运载机牵引钢丝绳空间结构分析与几何建模
 哈尔滨工业大学学报  2021, Vol. 53 Issue (1): 184-192  DOI: 10.11918/202004136 0

### 引用本文

OUYANG Yuping, WANG Tianyu, SUN Han, SUN Xudong, HONG Tiansheng, HUANG Zhiping, JIANG Xiaogang. Spatial structure analysis and geometric modeling of traction wire rope of mountain track carrier[J]. Journal of Harbin Institute of Technology, 2021, 53(1): 184-192. DOI: 10.11918/202004136.

### 文章历史

1. 华东交通大学 机电与车辆工程学院，南昌 330013;
2. 载运工具与装备教育部重点实验室(华东交通大学)，南昌 330013;
3. 华南农业大学 工程学院，广州 510642;
4. 广东振声科技股份有限公司，广东 梅州 514700

Spatial structure analysis and geometric modeling of traction wire rope of mountain track carrier
OUYANG Yuping1,2,3,4, WANG Tianyu1, SUN Han1, SUN Xudong1,2, HONG Tiansheng3, HUANG Zhiping4, JIANG Xiaogang1,2
1. School of Mechanical and Electrical and Vehicle Engineering, University of East China Jiaotong University, Nanchang 330013, China;
2. Key Laboratory of Transportation Tools and Equipment, Ministry of Education(University of East China Jiaotong University), Nanchang 330013, China;
3. College of Engineering, University of South China Agricultural University, Guangzhou 510642, China;
4. Guangdong Zhensheng Technology Co. Ltd., Meizhou 514700, Guangdong, China
Abstract: Traction system of mountainous track carrier mainly includes driving drum, wire rope, and cargo trolley, but the wire rope is the core component. At present, there is no clear spatial mathematical model for the wire rope of mountainous track carrier. To further study the mechanical model and failure behavior of the wire rope, it is necessary to derive the spatial geometric mathematical model and three-dimensional model, so as to avoid large-scale tests to explore the service life and damage rules of the wire rope. The spatial spiral equation of the traction wire rope in the upright and curved state are derived by using differential geometry and the principle of spatial coordinate transformation, and the software of MATLAB and Solidworks are utilized to parameterize design and establish entity array. The results show that the curvature and deflection of the straight section and the bending section of the wire rope are periodically changing. The space spiral equation provides a basis for the establishment of mechanical model of mountainous track carrier wire rope and the study of damage mechanism.
Keywords: agricultural transportation machinery    wire rope    space spiral equation    curvature    torsion    trailed double rail transport

1 运输机钢丝绳选型及捻制特征 1.1 运输机钢丝绳选型

 1—卷筒; 2—载物滑车; 3—托辊; 4—横梁; 5—轨道; 6—载物滑车; 7—钢丝绳; 8—滑轮 图 1 运输机牵引系统示意图 Fig. 1 Structure of transport traction system

 ${L = {L_1} + {L_2} + {L_3}, }$ (1)
 ${{F_{\max }} = \frac{{{F_{\min }}}}{{{K_a}}}, }$ (2)
 ${F_{\max }} - Mg(\sin \alpha + {f_1}\cos \alpha ) + mgL(\sin \alpha + {f_2}\cos \alpha ),$ (3)
 $m = {K_g}{D^2},$ (4)
 ${F_{\max }} = Mg(\sin \alpha + {f_1}\cos \alpha ) + {K_g}{D^2}gL(\sin \alpha + {f_2}\cos \alpha ).$ (5)

 ${{F_n} = {K_{\min }}{D^2}{E_t}, }$ (6)
 ${{F_{\min }} = {K_h}{F_n}, }$ (7)

 ${F_{\min }} = {K_h}{K_{\min }}{D^2}{E_t},$ (8)

 $\begin{array}{l} Mg(\sin \alpha + {f_1}\cos \alpha ) + {K_g}{D^2}gL(\sin \alpha + {f_2}\cos \alpha ) \le \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \frac{{{K_h}{K_{\min }}{D^2}{E_t}}}{{{K_a}}}, \end{array}$ (9)
 $d \ge \sqrt {\frac{{M(\sin \alpha + {f_1}\cos \alpha )}}{{\frac{{{K_h}{K_{\min }}{E_t}}}{{{K_a}g}} - {K_g}L(\sin \alpha + {f_2}\cos \alpha )}}} .$ (10)

 $\begin{array}{*{20}{l}} {d \ge \sqrt {\frac{{500(\sin {{40}^\circ } + 0.05\cos {{40}^\circ })}}{{\frac{{1.214 \times 0.338 \times 1670}}{{9.8 \times 7.1}} - 0.36 \times 2(\sin {{40}^\circ } + 0.1\cos {{40}^\circ })}}} \approx }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 6.03{\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{mm}}{\rm{.}}} \end{array}$

1.2 钢丝绳捻制特征

6×19+FC类圆股右交互捻钢丝绳由侧丝绕中心丝左旋捻制成单股，再由6侧股绕绳芯右旋捻制而成，侧股侧丝由内层丝及外层丝组成.所采用绳芯材质为纤维，因此该类钢丝绳只有螺旋股，无直股.钢丝绳捻制示意图如图 2所示，每股由1条中心丝，6条内层丝与12条外层丝捻制而成.为便于阐述钢丝间空间位置关系，对股及丝进行编号，以初始截面最左端为第1股，逆时针依次编为第1、2、3、4、5、6股；侧股中心丝逆时针依次编为1、2、3、4、5、6丝；侧股内层丝以每股中心线与绳芯中心线连线逆时针的第一钢丝中心为第01丝，逆时针依次编为第02、03、04、05、06丝；外层丝以每股中心线与绳芯中心线连线逆时针的第一钢丝中心为第07丝，逆时针依次编为第08、09、10、11、12、13、14、15、16、17、18丝.

 1—侧股; 2—侧股单丝; 3—整绳; 4—纤维绳芯; r0—绳芯至股芯中心距; r1—内层丝芯至股芯中心距; r2—外层丝芯至股芯中心距 图 2 钢丝绳捻制示意图 Fig. 2 Wire rope twisting diagram

 图 3 钢丝绳展开示意图 Fig. 3 Wire rope expansion diagram

 $AB = {r_0}{\alpha _a}, BC = {r_1}{\alpha _b}, BD = {r_2}{\alpha _c},$ (11)

 ${r_1} = 0.50{\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{mm}}, {r_2} = 0.97{\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{mm}}, {r_0} = 2.63{\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{mm}},$
 ${\beta _0} = {18.30^\circ }, {\beta _1} = {7.16^\circ }, {\beta _2} = {13.10^\circ }.$

2 钢丝绳螺旋方程 2.1 直线段钢丝绳空间螺旋方程

 图 4 钢丝绳第1股中心丝及其第18丝空间曲线模型 Fig. 4 Space curve model of first share center wire and its eighteenth wire

 $\mathit{\boldsymbol{O}}{\mathit{\boldsymbol{A}}^x} = \left\{ {\begin{array}{*{20}{l}} x\\ y\\ z \end{array}} \right\} = \left\{ {\begin{array}{*{20}{l}} {{r_0}\cos ({\theta _1} + {\alpha _a})}\\ {{r_0}\sin ({\theta _1} + {\alpha _a})}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \frac{{{r_0}{\alpha _a}}}{{\tan {\beta _0}}}} \end{array}} \right\},$ (12)
 $\mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^n} = \left\{ {\begin{array}{*{20}{l}} n\\ b\\ t \end{array}} \right\} = \left\{ {\begin{array}{*{20}{c}} {{r_2}\cos ({\theta _{18}} - {\alpha _c})}\\ {{r_2}\sin ({\theta _{18}} - {\alpha _c})}\\ 0 \end{array}} \right\}.$ (13)

 $[n, b, t] = \left[ {\begin{array}{*{20}{c}} { - \cos ({\theta _1} + {\alpha _a})}&{\cos {\beta _0}\sin ({\theta _1} + {\alpha _a})}&{ - \sin {\beta _0}\sin ({\theta _1} + {\alpha _a})}\\ { - \sin ({\theta _1} + {\alpha _a})}&{ - \cos {\beta _0}\cos ({\theta _1} + {\alpha _a})}&{\sin {\beta _0}\cos ({\theta _1} + {\alpha _a})}\\ 0&{\sin {\beta _0}}&{\cos {\beta _0}} \end{array}} \right].$ (14)

 $\mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^x} = [n, b, t] \times \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^n}.$ (15)

 $\mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^x} = [n, b, t] \times \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^n} = \left\{ {\begin{array}{*{20}{l}} {{\kern 1pt} {\kern 1pt} {\kern 1pt} {r_2}[\cos {\beta _0}\sin ({\theta _1} + {\alpha _a})\sin ({\theta _{18}} - {\alpha _c}) - \cos ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c})]}\\ {{r_2}[ - \cos {\beta _0}\cos ({\theta _1} + {\alpha _a})\sin ({\theta _{18}} - {\alpha _c}) - \sin ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c})]}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {r_2}\sin {\beta _0}\sin ({\theta _{18}} - {\alpha _c})} \end{array}} \right\}.$ (16)

 $\mathit{\boldsymbol{O}}{\mathit{\boldsymbol{B}}^x} = \mathit{\boldsymbol{O}}{\mathit{\boldsymbol{A}}^x} + \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^x} = \left\{ {\begin{array}{*{20}{c}} {{r_0}\cos ({\theta _1} + {\alpha _a}) + {r_2}[\cos {\beta _0}\sin ({\theta _1} + {\alpha _a})\sin ({\theta _{18}} - {\alpha _c}) - \cos ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c})]}\\ {{r_0}\sin ({\theta _1} + {\alpha _a}) + {r_2}[ - \cos {\beta _0}\cos ({\theta _1} + {\alpha _a})\sin ({\theta _{18}} - {\alpha _c}) - \sin ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c})]}\\ {\frac{{{r_0}{\alpha _a}}}{{\tan {\beta _0}}} + {r_2}\sin {\beta _0}\sin ({\theta _{18}} - {\alpha _c})} \end{array}} \right\}.$ (17)

 $\left\{ {\begin{array}{*{20}{l}} {{e_1} = \frac{{{r_0}\tan {\beta _1}}}{{{r_1}\sin {\beta _0}}}, }\\ {{e_2} = \frac{{{r_0}\tan {\beta _2}}}{{{r_2}\sin {\beta _0}}}, } \end{array}} \right.$ (18)

 $\mathit{\boldsymbol{OA}}_i^x = \left\{ {\begin{array}{*{20}{l}} x\\ y\\ z \end{array}} \right\} = \left\{ {\begin{array}{*{20}{l}} {{r_0}\cos ({\theta _i} + {\alpha _a})}\\ {{r_0}\sin ({\theta _i} + {\alpha _a})}\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \frac{{{r_0}{\alpha _a}}}{{\tan {\beta _0}}}} \end{array}} \right\}.$ (19)

 $\mathit{\boldsymbol{OB}}_{ij}^x = \left[ {\begin{array}{*{20}{c}} {{r_0}\cos ({\theta _i} + {\alpha _a}) + {r_1}[\cos {\beta _0}\sin ({\theta _i} + {\alpha _a})\sin ({\theta _j} - {e_1}{\alpha _a}) - \cos ({\theta _i} + {\alpha _a})\cos ({\theta _j} - {e_1}{\alpha _a})]}\\ {{r_0}\sin ({\theta _i} + {\alpha _a}) + {r_1}[ - \cos {\beta _0}\cos ({\theta _i} + {\alpha _a})\sin ({\theta _j} - {e_1}{\alpha _a}) - \sin ({\theta _i} + {\alpha _a})\cos ({\theta _j} - {e_1}{\alpha _a})]}\\ {\frac{{{r_0}{\alpha _a}}}{{\tan {\beta _0}}} + {r_1}\sin {\beta _0}\sin ({\theta _j} - {e_1}{\alpha _a})} \end{array}} \right],$ (20)
 $\mathit{\boldsymbol{OB}}_{ik}^x = \left[ {\begin{array}{*{20}{c}} {{r_0}\cos ({\theta _i} + {\alpha _a}) + {r_2}[\cos {\beta _0}\sin ({\theta _i} + {\alpha _a})\sin ({\theta _k} - {e_2}{\alpha _a}) - \cos ({\theta _i} + {\alpha _a})\cos ({\theta _k} - {e_2}{\alpha _a})]}\\ {{r_0}\sin ({\theta _i} + {\alpha _a}) + {r_2}[ - \cos {\beta _0}\cos ({\theta _i} + {\alpha _a})\sin ({\theta _k} - {e_2}{\alpha _a}) - \sin ({\theta _i} + {\alpha _a})\cos ({\theta _k} - {e_2}{\alpha _a})]}\\ {\frac{{{r_0}{\alpha _a}}}{{\tan {\beta _0}}} + {r_2}\sin {\beta _0}\sin ({\theta _k} - {e_2}{\alpha _a})} \end{array}} \right].$ (21)
2.2 弯曲段钢丝绳空间螺旋线方程

 图 5 弯曲段钢丝绳接触示意图 Fig. 5 Contact sketch of bending section of wire rope
 1—钢丝绳中心路径; 2—钢丝绳单股中心路径; 3—钢丝绳单股侧丝中心路径 图 6 过滑轮时钢丝绳钢丝缠绕示意图 Fig. 6 Contact diagram of wire rope when winding pulley

 ${\mathit{\boldsymbol{O}}^\prime }\mathit{\boldsymbol{B}} = {\mathit{\boldsymbol{O}}^\prime }\mathit{\boldsymbol{C}} + \mathit{\boldsymbol{CA}} + \mathit{\boldsymbol{AB}}.$ (22)
 1—侧股螺旋半径(整绳螺旋半径)对应圆; 2—侧股侧丝中心线；3—侧股侧丝螺旋半径画出的圆; 4—侧股股芯中心线 图 7 过滑轮时钢丝绳空间曲线模型 Fig. 7 Wire rope space curve model when winding pulley

 ${\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{C}}^l} = \left\{ {\begin{array}{*{20}{l}} l\\ m\\ n \end{array}} \right\} = \left\{ {\begin{array}{*{20}{c}} 0\\ {{r_3}\cos {\alpha _d}}\\ {{r_3}\sin {\alpha _d}} \end{array}} \right\}.$ (23)

 $[X, Y, Z] = \left[ {\begin{array}{*{20}{c}} 0&1&0\\ { - \cos {\alpha _d}}&0&{ - \sin {\alpha _d}}\\ { - \sin {\alpha _d}}&0&{\cos {\alpha _d}} \end{array}} \right],$ (24)

 $\begin{array}{l} [N, B, T] = [X, Y, Z] \times [n, b, t] = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \left[ {\begin{array}{*{20}{c}} { - \sin ({\theta _1} + {\alpha _a})}&{ - \cos {\beta _0}\cos ({\theta _1} + {\alpha _a})}&{\sin {\beta _0}\cos ({\theta _1} + {\alpha _a})}\\ {\cos {\alpha _d}\cos ({\theta _1} + {\alpha _a})}&{ - \sin {\beta _0}\sin {\alpha _d} - \cos {\beta _0}\cos {\alpha _d}\sin ({\theta _1} + {\alpha _a})}&{ - \cos {\beta _0}\sin {\alpha _d} + \sin {\beta _0}\cos {\alpha _d}\sin ({\theta _1} + {\alpha _a})}\\ {\sin {\alpha _d}\cos ({\theta _1} + {\alpha _a})}&{\sin {\beta _0}\cos {\alpha _d} - \cos {\beta _0}\sin {\alpha _d}\sin ({\theta _1} + {\alpha _a})}&{\cos {\beta _0}\cos {\alpha _d} + \sin {\beta _0}\sin {\alpha _d}\sin ({\theta _1} + {\alpha _a})} \end{array}} \right]. \end{array}$ (25)

ABn转换为坐标系LMN上的表达式ABl

 $\begin{array}{l} \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^l} = [N, B, T] \times \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^n} = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \left\{ {\begin{array}{*{20}{c}} { - {r_2}\sin ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c}) - {r_2}\cos {\beta _0}\cos ({\theta _1} + {\alpha _a})\sin ({\theta _{18}} - {\alpha _c})}\\ {{r_2}\cos {\alpha _d}\cos ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c}) - {r_2}\sin ({\theta _{18}} - {\alpha _c})[\cos {\beta _0}\cos {\alpha _d}\sin ({\theta _1} + {\alpha _a}) - \sin {\beta _0}\sin {\alpha _d}]}\\ {{r_2}\sin {\alpha _d}\cos ({\theta _1} + {\alpha _a})\cos ({\theta _{18}} - {\alpha _c}) - {r_2}\sin ({\theta _{18}} - {\alpha _c})[\cos {\beta _0}\sin {\alpha _d}\sin ({\theta _1} + {\alpha _a}) + \sin {\beta _0}\cos {\alpha _d}]} \end{array}} \right\}. \end{array}$ (26)

 ${\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{A}}^l} = {\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{C}}^l} + \mathit{\boldsymbol{C}}{\mathit{\boldsymbol{A}}^l},$ (27)
 $\mathit{\boldsymbol{C}}{\mathit{\boldsymbol{A}}^x} = \left\{ {\begin{array}{*{20}{c}} {{r_0}\cos ({\theta _1} + {\alpha _a})}\\ {{r_0}\sin ({\theta _1} + {\alpha _a})}\\ 0 \end{array}} \right\},$ (28)

CAx转换为坐标系LMN上的表达式CAl

 $\begin{array}{l} \mathit{\boldsymbol{C}}{\mathit{\boldsymbol{A}}^l} = \left[ {X,Y,Z} \right] \times \mathit{\boldsymbol{C}}{\mathit{\boldsymbol{A}}^x} = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \left\{ {\begin{array}{*{20}{c}} {{r_0}\sin ({\theta _1} + {\alpha _a})}\\ { - {r_0}\cos {\alpha _d}\cos ({\theta _1} + {\alpha _a})}\\ { - {r_0}\sin {\alpha _d}\cos ({\theta _1} + {\alpha _a})} \end{array}} \right\}, \end{array}$ (29)
 $\begin{array}{l} {\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{A}}^l} = {\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{C}}^l} + \mathit{\boldsymbol{C}}{\mathit{\boldsymbol{A}}^l} = \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \left\{ {\begin{array}{*{20}{c}} {{r_0}\sin ({\theta _1} + {\alpha _a})}\\ {{r_3}\cos {\alpha _L} - {r_0}\cos {\alpha _d}\cos ({\theta _1} + {\alpha _a})}\\ {{r_3}\sin {\alpha _L} - {r_0}\sin {\alpha _d}\cos ({\theta _1} + {\alpha _a})} \end{array}} \right\}, \end{array}$ (30)
 $\begin{array}{l} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{B}}^l} = {\mathit{\boldsymbol{O}}^\prime }{\mathit{\boldsymbol{C}}^l} + \mathit{\boldsymbol{C}}{\mathit{\boldsymbol{A}}^l} + \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{B}}^l} = \\ \left\{ {\begin{array}{*{20}{l}} {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sin ({\theta _1} + {\alpha _a})[{r_0} - {r_2}\cos ({\theta _{18}} - {\alpha _c})] - {r_2}\cos {\beta _0}\cos ({\theta _1} + {\alpha _a})\sin ({\theta _{18}} - {\alpha _c})}\\ {{r_3}\cos {\alpha _d} - \cos {\alpha _d}\cos ({\theta _1} + {\alpha _a})[{r_0} + {r_2}\cos ({\theta _{18}} - {\alpha _c})] - {r_2}\sin ({\theta _{18}} - {\alpha _c})[\cos {\beta _0}\cos {\alpha _d}\sin ({\theta _1} + {\alpha _a}) - \sin {\beta _0}\sin {\alpha _d}]}\\ {{r_3}\sin {\alpha _d} - \sin {\alpha _d}\cos ({\theta _1} + {\alpha _a})[{r_0} + {r_2}\cos ({\theta _{18}} - {\alpha _c})] - {r_2}\sin ({\theta _{18}} - {\alpha _c})[\cos {\beta _0}\sin {\alpha _d}\sin ({\theta _1} + {\alpha _a}) + \sin {\beta _0}\cos {\alpha _d}]} \end{array}} \right\}. \end{array}$ (31)

 图 8 钢丝绳侧股芯丝与滑轮接触示意图 Fig. 8 Contact diagram between side wire of wire rope and pulley

 ${{\alpha _d} = \frac{{{r_0}}}{{{r_3}\tan {\beta _0}}}{\alpha _a}, }$ (32)

 ${{e_3} = \frac{{{r_0}}}{{{r_3}\tan {\beta _0}}}, }$ (33)

 ${\mathit{\boldsymbol{O}}^\prime }\mathit{\boldsymbol{A}}_i^l = \left\{ {\begin{array}{*{20}{c}} {{r_0}\sin ({\theta _i} + {\alpha _a})}\\ {{r_3}\cos {e_3}{\alpha _a} - {r_0}\cos {e_3}{\alpha _a}\cos ({\theta _i} + {\alpha _a})}\\ {{r_3}\sin {e_3}{\alpha _a} - {r_0}\sin {e_3}{\alpha _a}\cos ({\theta _i} + {\alpha _a})} \end{array}} \right\}.$ (34)

 $\begin{array}{*{20}{l}} {{\mathit{\boldsymbol{O}}^\prime }\mathit{\boldsymbol{B}}_{ij}^l = }\\ {\quad \left\{ {\begin{array}{*{20}{l}} {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sin ({\theta _i} + {\alpha _a})[{r_0} - {r_1}\cos ({\theta _j} - {e_1}{\alpha _a})] - {r_1}\cos {\beta _0}\cos ({\theta _i} + {\alpha _a})\sin ({\theta _j} - {e_1}{\alpha _a})}\\ {{r_3}\cos {e_3}{\alpha _a} - \cos {e_3}{\alpha _a}\cos ({\theta _i} + {\alpha _a})[{r_0} + {r_1}\cos ({\theta _j} - {e_1}{\alpha _a})] - {r_1}\sin ({\theta _j} - {e_1}{\alpha _a})[\cos {\beta _0}\cos {e_3}{\alpha _a}\sin ({\theta _i} + {\alpha _a}) - \sin {\beta _0}\sin {e_3}{\alpha _a}]}\\ {{r_3}\sin {e_3}{\alpha _a} - \sin {e_3}{\alpha _a}\cos ({\theta _i} + {\alpha _a})[{r_0} + {r_1}\cos ({\theta _j} - {e_1}{\alpha _a})] - {r_1}\sin ({\theta _j} - {e_1}{\alpha _a})[\cos {\beta _0}\sin {e_3}{\alpha _a}\sin ({\theta _i} + {\alpha _a}) + \sin {\beta _0}\cos {e_3}{\alpha _a}]} \end{array}} \right\}.} \end{array}$ (35)

 $\begin{array}{l} {\mathit{\boldsymbol{O}}^\prime }\mathit{\boldsymbol{B}}_{ik}^l = \\ \left\{ {\begin{array}{*{20}{l}} {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sin ({\theta _i} + {\alpha _a})[{r_0} - {r_1}\cos ({\theta _k} - {e_2}{\alpha _a})] - {r_1}\cos {\beta _0}\cos ({\theta _i} + {\alpha _a})\sin ({\theta _k} - {e_2}{\alpha _a})}\\ {{r_3}\cos {e_3}{\alpha _a} - \cos {e_3}{\alpha _a}\cos ({\theta _i} + {\alpha _a})[{r_0} + {r_1}\cos ({\theta _k} - {e_2}{\alpha _a})] - {r_1}\sin ({\theta _k} - {e_2}{\alpha _a})[\cos {\beta _0}\cos {e_3}{\alpha _a}\sin ({\theta _i} + {\alpha _a}) - \sin {\beta _0}\sin {e_3}{\alpha _a}]}\\ {{r_3}\sin {e_3}{\alpha _a} - \sin {e_3}{\alpha _a}\cos ({\theta _i} + {\alpha _a})[{r_0} + {r_1}\cos ({\theta _k} - {e_2}{\alpha _a})] - {r_1}\sin ({\theta _k} - {e_2}{\alpha _a})[\cos {\beta _0}\sin {e_3}{\alpha _a}\sin ({\theta _i} + {\alpha _a}) + \sin {\beta _0}\cos {e_3}{\alpha _a}]} \end{array}} \right\}. \end{array}$ (36)
3 钢丝绳曲率和挠率求解

 $\begin{array}{l} k = \frac{{\left\| {f{{({\alpha _a})}^\prime } \times f{{({\alpha _a})}^{\prime \prime }}} \right\|}}{{{{\left\| {f{{({\alpha _a})}^\prime }} \right\|}^3}}} = \\ \frac{{\sqrt {{{({y^\prime }{z^{\prime \prime }} - {z^\prime }{y^{\prime \prime }})}^2} + {{({z^\prime }{x^{\prime \prime }} - {x^\prime }{z^{\prime \prime }})}^2} + {{({x^\prime }{y^{\prime \prime }} - {y^\prime }{x^{\prime \prime }})}^2}} }}{{{{({{({x^\prime })}^2} + {{({y^\prime })}^2} + {{({z^\prime })}^2})}^{3/2}}}}, \end{array}$ (37)
 $\begin{array}{l} \tau = \frac{{(f{{({\alpha _a})}^\prime }, f{{({\alpha _a})}^{\prime \prime }}, f{{({\alpha _a})}^{\prime \prime \prime }})}}{{{{\left\| {f{{({\alpha _a})}^\prime } \times f{{({\alpha _a})}^{\prime \prime }}} \right\|}^2}}} = \\ \frac{{{x^\prime }{y^{\prime \prime }}{z^{\prime \prime \prime }} + {x^{\prime \prime \prime }}{y^{\prime \prime }}{z^\prime } + {x^{\prime \prime }}{y^{\prime \prime \prime }}{z^\prime } - {x^{\prime \prime \prime }}{y^{\prime \prime }}{z^\prime } - {x^\prime }{y^{\prime \prime \prime }}{z^{\prime \prime }} - {x^{\prime \prime }}{y^\prime }{z^{\prime \prime \prime }}}}{{{{({y^\prime }{z^{\prime \prime }} - {z^\prime }{y^{\prime \prime }})}^2} + {{({z^\prime }{x^{\prime \prime }} - {x^\prime }{z^{\prime \prime }})}^2} + {{({x^\prime }{y^{\prime \prime }} - {y^\prime }{x^{\prime \prime }})}^2}}}. \end{array}$ (38)

 图 9 钢丝绳曲率及挠率在MATLAB中计算流程 Fig. 9 Wire rope curvature and torsion calculation flow in MATLAB

 图 10 直线段钢丝绳外层丝曲率与挠率变化规律 Fig. 10 Curvature and torsion variation of straight section of wire rope outer wires
 图 11 弯曲段钢丝绳外层丝曲率与挠率变化规律 Fig. 11 Curvature and torsion variation of bending section of wire rope outer wires
4 钢丝绳三维建模

 图 12 单丝与单丝缠绕几何实体模型 Fig. 12 Winding geometry entity model between single wire and single wire
 图 13 直立状态钢丝绳整绳三维实体模型 Fig. 13 Three-dimensional entity model of upright wire rope
 图 14 弯曲段钢丝绳三维实体模型 Fig. 14 Three-dimensional entity model of bending section of wire rope

5 结论

1) 在确定运输机钢丝绳型号及直径基础上，对钢丝绳股、丝进行编号，运用微分几何学及空间坐标变换原理，推导了6×19+FC类钢丝绳在直立及弯曲状态的空间螺旋方程，并推导了该类钢丝绳侧股外层钢丝曲率及挠率的连续变化规律，为钢丝绳在各种载荷下的工作状态的数值分析和实验分析提供理论依据.

2) 图 10结果表明：直线段钢丝绳的曲率与挠率呈明显的周期性变化规律，变化周期均为180°；挠率峰值均出现于曲率的波谷处，曲率处于波峰时，挠率变化较为平缓；曲率与挠率的极值较明显. 图 11结果表明：弯曲段钢丝绳曲率与挠率同样具有明显的周期性变化规律，变化周期均为360°；曲率处于波峰时，挠率发生突变；曲率处于波谷时，挠率变化率最大；曲率和挠率的极值大小明显.

3) 根据所推导的钢丝绳空间螺旋方程、曲率及挠率表达式，运用MATLAB参数化及SolidWorks曲线、扫描及装配等功能，绘制了运输机钢丝绳直立及弯曲状态的三维几何模型，并得到运输机钢丝绳股、丝参考点系列坐标，为后续建立钢丝绳力学模型及分析结构参数对钢丝绳损伤的影响奠定基础.

 [1] 粘雅玲, 沈嵘枫, 张小珍, 等. 果园运输机械研究进展[J]. 农业技术与装备, 2014(22): 24. NIAN Yaling, SHENG Rongfeng, ZHANG Xiaozhen, et al. Research progress of orchard transportation machinery[J]. Agricultural Technology & Equipment, 2014(22): 24. DOI:10.3969/j.issn.1673-887X.2014.22.011 [2] 洪添胜.农机农艺融合就是"未来强壮的果农"[N].农民日报, 2015-11-19(008) HONG Tiansheng. The integration of agricultural machinery and agronomy is "the strong fruit farmers in the future"[N]. Farmers' Daily, 2015-11-19(008 [3] 欧阳玉平, 洪添胜, 苏建, 等. 山地果园牵引式双轨运输机断绳制动装置设计与试验[J]. 农业工程学报, 2014, 30(18): 22. OUYANG Yuping, HONG Tiansheng, SU Jian, et al. Design and test of rope breaking braking device of traction type double track transporter in mountain orchard[J]. Transactions of the Chinese Society of Agricultural Engineering, 2014, 30(18): 22. DOI:10.3969/j.issn.1002-6819.2014.18.003 [4] 欧阳玉平, 洪添胜, 马煜东. 山地果园双轨运输机牵引系统动力学仿真与试验[J]. 系统仿真学报, 2015, 27(7): 1502. OUYANG yuping, HONG Tiansheng, MA Yudong. Dynamic simulation and test of mountain orchard double-track transport traction system[J]. Journal of System Simulation, 2015, 27(7): 1502. DOI:10.16182/j.cnki.joss.2015.07.013 [5] 欧阳玉平, 洪添胜, 苏建, 等. 山地果园牵引式双轨运输机排绳装置的设计[J]. 华中农业大学学报, 2014, 33(5): 123. OUYANG Yuping, HONG Tiansheng, SU Jian, et al. Design of rope arrangement device of traction type double track conveyor in mountain orchard[J]. Journal of Huazhong Agricultural University, 2014, 33(5): 123. DOI:10.13300/j.cnki.hnlkxb.2014.05.046 [6] 洪添胜, 苏建, 朱余清. 山地橘园链式循环货运索道设计[J]. 农业机械学报, 2011, 42(6): 108. HONG Tiansheng, SU Jian, ZHU Yuqing. Design of chain cycle freight ropeway in mountain orangery[J]. Transactions of the Chinese Society for Agricultural Machinery, 2011, 42(6): 108. [7] PÉRIERA V, DIENG L, GAILLET L, et al. Influence of an aqueous environment on the fretting behaviour of steel wire sused in civil engineering cables[J]. Wear, 2011, 271(9-10): 1585. DOI:10.1016/j.wear.2011.01.095 [8] WAHID A, MOUHIB N, OUARDI A, et al. Experimental prediction of wire rope damage by energy method[J]. Engineering Structures, 2019, 201: 1. DOI:10.1016/j.engstruct.2019.109794 [9] BELTRÁN J F, DE VICO E. Assessment of static rope behavior with asymmetric damage distribution[J]. Eng Struct, 2015, 86: 84. DOI:10.1016/j.engstruct.2014.12.026 [10] 赵敏, 张东来, 周智慧. 钢丝绳缺陷漏磁信号的通道均衡化方法[J]. 哈尔滨工业大学学报, 2013, 45(9): 47. ZHAO Min, ZHANG Donglai, ZHOU Zhihui. Channel equalization method for MFL signals of wire rope defects[J]. Journal of Harbin Institute of Technology, 2013, 45(9): 47. [11] FONTANARI V, BENEDETTI M, MONELLI B D. Elasto-plastic behavior of a warrington-seale rope: experimental analysis and finite element modeling[J]. Eng Struct, 2015, 82: 113. DOI:10.1016/j.engstruct.2014.10.032 [12] PETERKA P, KREŠÁK J, KROPUCH S, et al. Failure analysis of hoisting steel wire rope[J]. Eng Fail Anal, 2014, 45: 96. DOI:10.1016/j.engfailanal.2014.06.005 [13] ZHANG Peng, DUAN Menglan, MA Jianmin, et al. A precise mathematical model for geometric modeling of wire rope strands structure[J]. Applied Mathematical Modelling, 2019, 76. DOI:10.1016/j.apm.2019.06.005 [14] WANG Xiaoyu, MENG Xiangbao, WANG Jixin, et al. Mathematical modeling and geometric analysis for wire rope strands[J]. Applied Mathematical Modelling, 2015, 39(3-4): 1019. DOI:10.1016/j.apm.2014.07.015 [15] ARGATOV I I, GÓMEZ X, TATO W, et al. Wear evolution in a stranded rope under cyclic bending: implications to fatigue life estimation[J]. Wear, 2011, 271(11): 2857. DOI:10.1016/j.wear.2011.05.045 [16] MA W, ZHU Z C, PENG Y X, et al. Computer-aided modeling of wire ropes bent over a sheave[J]. Advances in Engineering Software, 2015, 90: 11. DOI:10.1016/j.advengsoft.2015.06.006 [17] WU Weiguo, CAO Xin. Mechanics model and its equation of wire rope based on elastic thin rod theory[J]. International Journal of Solids and Structures, 2016, 102-103: 21. DOI:10.1016/j.ijsolstr.2016.10.021 [18] ARGATOV I. Response of a wire rope strand to axial and torsional loads: asymptotic modeling of the effect of interwire contact deformations[J]. International Journal of Solids and Structures, 2011, 48(10): 1413. DOI:10.1016/j.ijsolstr.2016.10.021 [19] 闻邦椿, 张义民, 鄂中凯, 等. 机械设计手册[M]. 第五版. 北京: 机械工业出版社, 2010. WEN Bangchun, ZHANG Yimin, E Zhongkai. Mechanical design manual[M]. Fifth Edition. Beijing: China Machine Press, 2010. [20] 张德英, 李广宇, 向卫国. 斜井提升用钢丝绳的选择方法[J]. 煤矿机电, 2005(2): 69. ZHANG Deying, LI Guangyu, XIANG Weiguo. Selection method of steel wire rope for inclined shaft lifting[J]. Coal Mine Electrical, 2005(2): 69. DOI:10.16545/j.cnki.cmet.2005.02.027 [21] 苏世晨, 苏永春. 矿井提升钢丝绳直径计算新公式[J]. 煤矿安全, 2003, 34(6): 32. SU Shichen, SU Yongchun. New formula for calculating the diameter of mine hoisting wire rope[J]. Coal Mine Safety, 2003, 34(6): 32. DOI:10.13347/j.cnki.mkaq.2003.06.013 [22] 张惠波.提升钢丝绳几何特性及有限元分析研究[D].阜新: 辽宁工程技术大学, 2011 ZHANG Huibo. Research on geometric characteristics and finite element analysis of hoisting steel wire rope[D]. Fuxin: Liaoning University of Engineering and Technology, 2011