深井提升动力学研究

何满潮

doi:10.6052/1000-0992-21-032

深井提升动力学研究

doi: 10.6052/1000-0992-21-032

何满潮^,

中国矿业大学(北京)深部岩土力学与地下工程国家重点实验室, 北京 100083

基金项目: 国家重点研发计划专项（2016YFC0600900）资助.

详细信息

作者简介:
何满潮, 矿山工程岩体力学专家、中国科学院院士、全国政协第十三届委员、俄罗斯矿业科学院院士、阿根廷国家工程院院士、中国矿业大学(北京)教授, 兼任国际岩爆专委会主席、中国岩石力学与工程学会理事长、中国矿业科学协同创新联盟理事长、中国矿业知识产权联盟理事长, 曾任国际岩石力学学会副主席、教育基金会主席. 全国杰出科技人才奖(2016年)、全国创新争先奖状(2017年)和何梁何利科技进步奖(2014年)获得者.　　主要从事矿山岩体大变形灾害控制理论和技术研究. 提出了“缓变型”和“突变型”大变形灾害的理论体系, 研发了多套大变形灾害机理实验系统, 创建了深部岩体力学实验室. 形成了无煤柱自成巷110/N00工法技术体系，引领了矿业科学技术第三次革命. 提出了“双体灾变力学”理论, 研发了基于NPR锚索传感技术的地质灾害牛顿力远程监测预警系统, 成功预测滑坡灾害17次, 均提前3.5 ~ 20小时发出临滑预警, 挽救了百余人生命和数以亿计的财产损失. 获国家技术发明二等奖1项, 国家科技进步二等奖3项, 中国专利金奖1项, ISRM技术发明奖1项

通讯作者:
hemanchao@263.net

中图分类号: O343,O424
计量
- 文章访问数: 2260
- HTML全文浏览量: 942
- PDF下载量: 170
- 被引次数: 0
出版历程
- 收稿日期: 2021-06-03
- 录用日期: 2021-09-22
- 网络出版日期: 2021-09-27
- 刊出日期: 2021-09-25

Research on deep shaft hoisting dynamics

HE Manchao^,

State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology(Beijing), Beijing 100083, China

More Information

Corresponding author: hemanchao@263.net

摘要

摘要: 随着浅部煤炭资源的日益枯竭, 我国煤炭开采朝着深部化和大型化方向发展, 新建和改扩建的大型立井年生产能力已达1000万吨, 开采最大深度已达1500 m. 千米深井在提升过程中, 造成提升钢丝绳、容器振荡, 特别是自由悬挂平衡尾绳大幅度摆动, 严重影响多绳摩擦提升系统向高速度、深度化发展. 在国家重点研发计划“深地资源勘查开采”重点专项“煤矿深井建设与提升基础理论及关键技术”支持下, 建立了单元数量自动调整的自由悬挂平衡尾绳提升系统动力学模型, 揭示了传统提升系统诱发平衡尾绳大摆动的机理; 提出了深井SAP提升新模式, 构建了多元耦合下的SAP提升系统动力学模型与非光滑动力学模型, 揭示了多参数影响下系统的非光滑动力学特性及非线性振动演化规律; 研发了适用于深部提升的SAP提升技术与装备, 开展了SAP提升技术与装备的现场研究, 解决了大强煤矿立井提升系统运行过程中尾绳大摆动、提升容器大振动等关键问题, 提高了提升系统高速运行的安全性, 消除了尾绳大摆动难控制的问题.
- 深部开采 /
- 矿井提升 /
- 动力学 /
- 平衡尾绳 /
- 预应力自适应
Abstract: With the increasing depletion of shallow coal resources, China’s coal mining is developing in the direction of deepening and large-scale development. The annual production capacity of newly built and expanded large vertical shafts has reached 10 million tons, and the maximum mining depth has reached 1 500 m. During the hoisting process of kilometer deep well, the vibration of hoisting wire rope and container is caused, especially the large swing of free-hanging balance rope, which seriously affects the development of multi rope friction hoisting system to high speed and depth. Supported by the key special project “the basic theory and key technology of deep coal mine construction and upgrading” within the national key research and development plan “Deep Ground Resources Exploration and Mining,” the dynamic model of free-hanging balance rope hoisting system with adaptive grid number is established. The mechanism of large swing of balance rope induced by traditional hoisting system is revealed. A new deep shaft SAP hoisting mode is proposed. The SAP hoisting system dynamic model and non-smooth dynamics model are constructed, and the non-smooth dynamic characteristics and nonlinear vibration evolution law of the system under the influence of multiple parameters are revealed. Developed SAP hoisting technology and equipment suitable for deep hoisting and carried out on-site research on SAP hoisting technology and equipment. It solves the key problems of large swing of balance rope and large vibration of hoisting container during the operation of the vertical shaft hoisting system of Daqiang Coal Mine. The safety of the high-speed operation of the hoisting system is improved, and the problem that the large swing of the balance rope is difficult to control is eliminated.
- deep mining /
- mine hoisting /
- dynamics /
- balance rope /
- self-adaptive prestressed

HTML全文

图 1 传统提升系统. (a)单滚筒缠绕, (b)双滚筒缠绕, (c)塔式摩擦, (d)落地式摩擦

下载: 全尺寸图片幻灯片

图 2 立井摩擦提升系统简化模型及平衡尾绳简化模型. (a)立井摩擦提升系统简化模型, (b)平衡尾绳模型, (c) 平衡尾绳简化模型

下载: 全尺寸图片幻灯片

图 3 平衡尾绳节点单元转换示意图

下载: 全尺寸图片幻灯片

图 4 平衡尾绳单元转换流程图

下载: 全尺寸图片幻灯片

图 5 单元转换后动能相对误差率

下载: 全尺寸图片幻灯片

图 6 左右两侧平衡尾绳距离容器中心线最大摆动位移. (a) 左侧平衡尾绳距离左侧容器中心线最大摆动位移图, (b) 右侧平衡尾绳距离右侧容器中心线最大摆动位移图

下载: 全尺寸图片幻灯片

图 7 SAP提升系统动力学模型

下载: 全尺寸图片幻灯片

图 8 张紧牵引系统(蓝线)与传统(红线)牵引系统纵向固有频率比较

下载: 全尺寸图片幻灯片

图 9 不同张紧轮质量作用下张紧轮处的纵向响应. (a) Terminal tension = 7.0 × 10⁴, (b) Terminal tension = 1.0 × 10⁵, (c) Terminal tension = 1.5 × 10⁵, (d) Terminal tension = 2.0 × 10⁵

下载: 全尺寸图片幻灯片

图 10 不同导向阻尼作用下的张紧导向轮纵向响应时频特性. (a) Damping = 0, (b) Damping = 5.0 × 10⁴ N/s, (c) Damping = 2.0 × 10⁵ N/s

下载: 全尺寸图片幻灯片

图 11 系统上升侧(a)和下降侧(b)纵向振动的最大振幅随时间的变化. (a)系统上升侧, (b)系统下降侧

下载: 全尺寸图片幻灯片

图 12 调节轮跳动情况分析示意图

下载: 全尺寸图片幻灯片

图 13 不同频率的顶部激励作用下调节轮的非光滑动力学特性. (a)基频激励作用, (b) 三倍频激励作用

下载: 全尺寸图片幻灯片

图 14 SAP提升系统关键装备现场安装图

下载: 全尺寸图片幻灯片

图 15 SAP提升系统满载常速运行监控图

下载: 全尺寸图片幻灯片

图 16 SAP系统与原系统不同工况下尾绳摆动对比

下载: 全尺寸图片幻灯片

图 17 SAP提升系统与原提升系统尾绳振动对比曲线

下载: 全尺寸图片幻灯片

图 18 空载时不同加速度尾绳位移曲线. (a)加速过程, (b) 减速过程

下载: 全尺寸图片幻灯片

参考文献(68)

[1]	蔡翔, 曹国华, 韦磊, 王磊, 王海鑫. 2018. 基于线扫描图像技术的立井多绳摩擦提升钢丝绳承载特性研究. 振动与冲击, 37: 36-41 (Cai X, Cao G H, Wei L, Wang L, Wang H X. 2018. Load-bearing characteristics of hoisting wire rope of a vertical shaft with multi-rope friction based on line scanning image technique. Journal of Vibration and Shock, 37: 36-41).
[2]	曹国华. 2009. 矿井提升钢丝绳装载冲击动力学行为研究. [博士论文]. 徐州: 中国矿业大学 Cao G H. 2009. Impact dynamic behaviors of mine hoisting rope during loading process. [PhD Thesis]. Xuzhou: China University of Mining and Technology
[3]	曹国华, 朱真才, 彭维红, 陈国安. 2009a. 绳式防坠器制动过程制动绳冲击行为研究. 中国矿业大学学报, 38: 244-250 (Cao G H, Zhu Z C, Peng W H, Chen G A. 2009a. Impact characteristic of wire rope during gage braking by rope parachute gear. China University of Mining & Technology, 38: 244-250). doi: 10.3321/j.issn:1000-1964.2009.02.019
[4]	曹国华, 朱真才, 彭维红, 彭玉兴. 2007. 箕斗在装载过程中的震动特性研究. 煤炭学报, 32: 105-108 (Cao G H, Zhu Z C, Peng W H, Peng Y X. 2007. Study on vibrant characteristic in skip's loading. Journal of China Coal Society, 32: 105-108).
[5]	曹国华, 朱真才, 彭维红, 邵杏国. 2009b. 缠绕提升矿车进出罐笼过程钢丝绳耦合振动行为. 煤炭学报, 34: 702-706 (Cao G H, Zhu Z C, Peng W H, Shao X G. 2009b. Coupled vibration of hoisting rope during tramcar pushing into or out cage in winding hoist system. Journal of China Coal Society, 34: 702-706). doi: 10.3321/j.issn:0253-9993.2009.05.025
[6]	曹国华, 朱真才, 彭维红, 邵杏国. 2010. 变质量提升系统钢丝绳轴向一扭转耦合振动特性. 振动与冲击, 29: 64-68 (Cao G H, Zhu Z C, Peng W H, Shao X G. 2010. Extension-torsionally coupled vibration of wire rope in a variable mass hoisting system. Journal of Vibration and Shock, 29: 64-68).
[7]	何满潮. 2021. 深部建井力学研究进展. 煤炭学报, 46: 726-746 (He M C. 2021. Research progress of deep shaft construction mechanics. Journal of China Coal Society, 46: 726-746).
[8]	霍磊, 李玉瑾. 2015. 立井提升系统在井口解除二级制动时的动力学特性分析. 起重运输机械, 23-27 (Huo L, Li Y J. 2015. Dynamic characteristics analysis of shaft hoisting system when the wellhead releases the secondary braking. Lifting the Transport Machinery, 23-27). doi: 10.3969/j.issn.1001-0785.2015.07.010
[9]	李楠, 李玉瑾. 2015. 深井提升钢丝绳的扭转研究与计算. 煤炭工程, 47: 21-23 (Li N, Li Y J. 2015. Study and calculation of torsion of deep well hoisting wire rope. Coal Engineering, 47: 21-23).
[10]	李玉瑾. 2003. 多绳摩擦轮提升系统的动力学研究与设计. 煤炭工程, 6-9 (Li Y J. 2003. Dynamic research and design of multi rope friction wheel hoisting system. Coal Engineering, 6-9). doi: 10.3969/j.issn.1671-0959.2003.09.002
[11]	李玉瑾, 霍磊. 2015a. 立井提升系统的松绳动力学特性及事故分析. 煤炭工程, 47: 12-13,17 (Li Y J, Huo L. 2015a. Dynamic characteristics of rope loosening and accident analysis of vertical shaft hoisting system. Coal Engineering, 47: 12-13,17). doi: 10.11799/ce201505005
[12]	李玉瑾, 寇子明. 2015b. 立井提升系统钢丝绳安全系数研究. 煤炭科学技术, 43: 96-99, 103 (Li Y J, Kou Z M. 2015b. Study on safety coefficient of steel wire rope in mine shaft hoisting system. Coal Science and Technology, 43: 96-99, 103).
[13]	李玉瑾, 张安林. 2014a. 立井提升系统的卡罐动力学分析与研究. 煤炭工程, 46: 23-25 (Li Y J, Zhang A L. 2014a. Analysis and study on cage jammed mechanics of mine shaft hoisting system. Coal Engineering, 46: 23-25).
[14]	李玉瑾, 张保连. 2012. 矿井提升系统安全事故分析与防治. 煤炭工程, 100-102 (Li Y J, Zhang B L. 2012. Analysis and prevention of safety accidents in mine hoisting system. Coal Engineering, 100-102).
[15]	李玉瑾, 张保连. 2014b. 斜井提升系统动力学计算及跑车防护问题探讨. 起重运输机械, 79-82 (Li Y J, Zhang B L. 2014b. Dynamic calculation of inclined shaft hoisting system and discussion on sports car protection. Lifting the Transport Machinery, 79-82). doi: 10.3969/j.issn.1001-0785.2014.12.032
[16]	李玉瑾, 张保连. 2016. 立井提升装置过卷动力学研究. 煤炭科学技术, 44: 157-160 (Li Y J, Zhang B L. 2016. Study on overwinding dynamics of mine shaft hoisting device. Coal Science and Technology, 44: 157-160).
[17]	梁敏, 寇子明. 2015. 立井提升系统卡罐时钢丝绳的横向振动分析. 煤炭技术, 34: 289-291 (Liang M, Kou Z M. 2015. Analysis of rope transverse vibration for block cage of mine hoisting system. Coal Technology, 34: 289-291).
[18]	王进杰. 2016. 施工立井提升系统动态特性研究.[博士论文]. 徐州: 中国矿业大学. Wang J J. 2016. Study on dynamic characteristics of construction shaft hoisting system. [PhD Thesis]. Xuzhou: China University of Mining and Technology.
[19]	王磊. 2021. 摩擦提升系统动力学特性与振动控制研究.[博士论文]. 徐州: 中国矿业大学 Wang L. 2021. Study on dynamic characteristics and vibration control of friction hoisting system. [PhD Thesis]. Xuzhou: China University of Mining and Technology
[20]	王乃格. 2019. 施工立井柔性导向提升系统动力学建模与控制.[博士论文]. 徐州: 中国矿业大学 Wang N G. 2016. Dynamic modeling and control of flexible guide hoisting system in construction shaft. [PhD Thesis]. Xuzhou: China University of Mining and Technology
[21]	王彦栋. 2018. 深立井施工并联悬吊系统动力学行为研究.[博士论文]. 徐州: 中国矿业大学 Wang Y D. 2018. Study on dynamic behavior of parallel suspension system in deep shaft construction. [PhD Thesis]. Xuzhou: China University of Mining and Technology
[22]	吴娟, 寇子明, 梁敏. 2016. 摩擦提升系统钢丝绳横向动力学分析. 振动与冲击, 35: 184-188 (Wu J, Kou Z M, Liang M. 2016. Transverse dynamics analysis of rope in multi-rope friction hoisting system. Journal of Vibration and Shock, 35: 184-188).
[23]	吴娟, 寇子明, 梁敏, 吴国雄. 2015. 摩擦提升系统钢丝绳纵向-横向耦合振动分析. 中国矿业大学学报, 44: 885-892 (Wu J, Kou Z M, Liang M, Wu G X. 2015. Theoretical model and experimental verification of the coupling longitudinal- transverse vibration of rope for friction hoisting system. Journal of China University of Mining& Technology, 44: 885-892).
[24]	杨盼盼. 2020. 面向深井大惯量提升容器过卷保护的直线永磁涡流缓速方法研究. [博士论文]. 徐州: 中国矿业大学 Yang P P. 2000. Study on linear permanent magnet eddy current braking method for overwinding protection of the hoisting containers with large kinetic energy used in the ultra-deep shaft. [PhD Thesis]. Xuzhou: China University of Mining and Technology
[25]	朱真才. 2000. 矿井提升过卷冲击动力学研究. [博士论文]. 徐州: 中国矿业大学 Zhu Z C. 2000. Study on over coiling impact dynamics of mine hoisting. [PhD Thesis]. Xuzhou: China University of Mining and Technology
[26]	朱真才. 2003. 多绳摩擦提升安全保障关键技术及装备研究. [博士后论文]. 长沙: 中南大学 Zhu Z C. 2003. Research on key technology and equipment of safety guarantee for multi rope friction hoisting. [PostDoc Thesis]. Changsha: Central South University
[27]	朱真才, 曹国华, 彭维红, 彭玉兴. 2007. 钢丝绳在箕斗装载过程中的纵向振动行为研究. 中国矿业大学学报, 325-329 (Zhu Z C, Cao G H, Peng W H, Peng Y X. 2007. Analysis of longitudinal vibration of wire rope in loading of skip. Journal of China University of Mining & Technology, 325-329). doi: 10.3321/j.issn:1000-1964.2007.03.010
[28]	朱真才, 李翔, 沈刚, 汤裕. 2020. 双绳缠绕式煤矿深井提升系统钢丝绳张力主动控制方法. 煤炭学报, 45: 464-473 (Zhu Z C, Li X, Shen G, Tang Y. 2020. Wire rope tension active control of double-rope winding deep well hoisting systems. Journal of China Coal Society, 45: 464-473).
[29]	Arnold M, Brüls O. 2007. Convergence of the generalized-α scheme for constrained mechanical systems. Multibody System Dynamics, 18: 185-202. doi: 10.1007/s11044-007-9084-0
[30]	Arrasate X, Kaczmarczyk S, Almandoz G. 2014. The modelling, simulation and experimental testing of the dynamic responses of an elevator system. Mechanical Systems and Signal Processing, 42: 258-282.
[31]	Berzeri M, Shabana A A. 2000. Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. Journal of Sound and Vibration, 235: 539-565. doi: 10.1006/jsvi.1999.2935
[32]	Brüls O, Acary V, Cardona A. 2014. Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-α scheme. Computer Methods in Applied Mechanics and Engineering, 281: 131-161. doi: 10.1016/j.cma.2014.07.025
[33]	Cao G H, C X, Wang N G, Peng W H, Li J S. 2017. Dynamic response of parallel hoisting system under drive deviation between ropes with time-varying length. Shock and Vibration, 1-10.
[34]	Cao G H, Wang J J, Zhu Z C. 2018. Coupled vibrations of rope-guided hoisting system with tension difference between two guiding ropes. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232: 231-244. doi: 10.1177/0954406216677103
[35]	Cao G H, Wang J J, Zhu Z C, Wang Y D, Peng W H. 2015. Lateral response and energetics of cable-guided hoisting system with time-varying length. Journal of Vibroengineering, 17: 4575-4588.
[36]	Chen Q Z, Acary V, Virlez G. 2013. A nonsmooth generalized-α scheme for flexible multibody systems with unilateral constraints. International Journal for Numerical Methods in Engineering, 96: 487-511. doi: 10.1002/nme.4563
[37]	Crespo R S, Kaczmarczyk S, Picton P. 2018. Modelling and simulation of a stationary high-rise elevator system to predict the dynamic interactions between its components. International Journal of Mechanical Sciences, 137: 24-45. doi: 10.1016/j.ijmecsci.2018.01.011
[38]	Dvorak R, Freistetter F, Kurths J. 2005. Chaos and Stability in Planetary Systems. Secaucus: Springer.
[39]	Escalona J L, Hussien H A, Shabana A A. 1998. Application of the absolute nodal co-ordinate formulation to multibody system dynamics. Journal of Sound and Vibration, 214: 833-851. doi: 10.1006/jsvi.1998.1563
[40]	Guo Y B, Zhang D K, Chen K, Feng G N, Ge S R. 2018. Longitudinal dynamic characteristics of steel wire rope in a friction hoisting system and its coupling effect with friction transmission. Tribology International, 119: 731-743. doi: 10.1016/j.triboint.2017.12.014
[41]	Huang J H, Luo C X, Yu P, Hao H M. 2020. A methodology for calculating limit deceleration of flexible hoisting system: A case study of mine hoist. Proceedings of the Institution of Mechanical Engineers. Part E, Journal of process mechanical engineering, 234: 342-352. doi: 10.1177/0954408920925017
[42]	Jiang Y Q, Ma X P, Xiao X M. 2014. Research on transverse parametric vibration and fault diagnosis of multi-rope hoisting catenaries. Journal of Vibroengineering, 16: 3419-3431.
[43]	Kaczmarczyk S. 1997. The passage through resonance in a catenary-vertical cable hoisting system with slowly varying length. Journal of Sound and Vibration, 208: 243-269. doi: 10.1006/jsvi.1997.1220
[44]	Kaczmarczyk S, Ostachowicz W. 2003a. Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model. Journal of Sound and Vibration, 262: 219-244. doi: 10.1016/S0022-460X(02)01137-9
[45]	Kaczmarczyk S, Ostachowicz W. 2003b. Transient vibration phenomena in deep mine hoisting cables. Part 2: Numerical simulation of the dynamic response. Journal of Sound and Vibration, 262: 245-289. doi: 10.1016/S0022-460X(02)01148-3
[46]	Ma Y S, Xiao X M. 2016. Dynamic analyses of hoisting ropes in a multi-rope friction mine hoist and determination of proper hoisting parameters. Journal of Vibroengineering, 18: 2801-2817. doi: 10.21595/jve.2016.16890
[47]	Ren H, Zhu W D. 2013. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems-Part II: Application. Journal of Vibration and Acoustics-transactions of the ASME, 135: 051037.
[48]	Shabana A A, Yakoub R Y. 2001. Three dimensional absolute nodal coordinate formulation for beam elements: Theory. Journal of Mechanical Design, 123: 606-613. doi: 10.1115/1.1410100
[49]	Terumichi Y, Ohtsuka M, Yoshizawa M, Fukawa Y, Tsujioka Y. 1997. Nonstationary vibrations of a string with time-varying length and a mass-spring system attached at the lower end. Nonlinear Dynamics, 12: 39-55. doi: 10.1023/A:1008224224462
[50]	Wang D G, Wang D A. 2016. Dynamic contact characteristics between hoisting rope and friction lining in the deep coal mine. Engineering Failure Analysis, 64: 44-57. doi: 10.1016/j.engfailanal.2016.03.006
[51]	Wang D G, Zhang D K, Mao X B, Peng Y X, Ge S R. 2015. Dynamic friction transmission and creep characteristics between hoisting rope and friction lining. Engineering Failure Analysis, 57: 499-510. doi: 10.1016/j.engfailanal.2015.08.010
[52]	Wang G Y, Xiao X M, Liu Y L. 2019. Dynamic modeling and analysis of a mine hoisting system with constant length and variable length. Mathematical Problems in Engineering, 1-12.
[53]	Wang L, Cao G H. 2018. Dynamic behavior of traction system with tension at the pulley of compensating rope// 8th Symposium on Lift and Escalator Technologies, Hong Kong, China.
[54]	Wang L, Cao G H, Wang N G, Tang C, He Z, Wang P. 2019. Modeling and dynamic behavior analysis of rope-guided traction system with terminal tension acting on compensating rope. Shock and Vibration, 1-24.
[55]	Wang L, Cao G H, Wang N G, Zhang Y C. 2020. Dynamic behavior analysis of a high-rise traction system with tensioned pulley acting on compensating rope. Symmetry, 12: 129. doi: 10.3390/sym12010129
[56]	Wang N G, Cao G H. 2021. Adaptive fuzzy backstepping control of underactuated multi-cable parallel suspension system with tension constraint. Transactions of the Institute of Measurement and Control, 43: 1971-1984. doi: 10.1177/0142331220985947
[57]	Wang N G, Cao G H, Lu Y. 2020a. Modelling and passive control of flexible guiding hoisting system with time-varying length. Mathematical and Computer Modelling of Dynamical Systems, 26: 31-54. doi: 10.1080/13873954.2019.1699121
[58]	Wang N G, Cao G H, Wang L, Lu Y, Zhu Z C. 2020b. Modelling and control of flexible guided lifting system with output constraints and unknown input hysteresis. Journal of Vibration and Control, 26: 112-128. doi: 10.1177/1077546319877704
[59]	Wang N G, Cao G H, Yan L, Wang L. 2018. Modeling and control for a multi-rope parallel suspension lifting system under spatial distributed tensions and multiple constraints. Symmetry, 10: 412. doi: 10.3390/sym10090412
[60]	Wang Y D, Cao G H, van Horssen Wim T. 2018. Dynamic simulation of a multi-cable driven parallel suspension platform with slack cables. Mechanism and Machine Theory, 126: 329-343. doi: 10.1016/j.mechmachtheory.2018.04.014
[61]	Wang Y D, Cao G H, Zhu Z C, Wang J J, Wang N G. 2014. Longitudinal response of parallel hoisting system with time-varying rope length. Journal of Vibroengineering, 16: 4088-4101.
[62]	Yakoub R Y, Shabana A A. 2001. Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications. Journal of Mechanical Design, 123: 614-621. doi: 10.1115/1.1410099
[63]	Yang P P, Zhou G B, Zhu Z C, et al. 2019. Linear permanent magnet eddy current brake for overwinding protection. IEEE Access, 7: 33922-33931. doi: 10.1109/ACCESS.2019.2902892
[64]	Yao J N, Deng Y, Xiao X M. 2017. Optimization of hoisting parameters in a multi-rope friction mine hoist based on the multi-source coupled vibration characteristics of hoisting catenaries. Advances in Mechanical Engineering, 9: 2071938409.
[65]	Zemljaric B, Azbe V. 2019. Analytically derived matrix end-form elastic-forces equations for a low-order cable element using the absolute nodal coordinate formulation. Journal of Sound and Vibration, 446: 263-272. doi: 10.1016/j.jsv.2019.01.039
[66]	Zhang J, Wang D G, Zhang D K, Ge S R, Wang D A. 2017. Dynamic torsional characteristics of mine hoisting rope and its internal spiral components. Tribology International, 109: 182-191. doi: 10.1016/j.triboint.2016.12.037
[67]	Zhang N, Cao G H, Yang F. 2021. Dynamic analysis of balance rope under multiple constraints with friction// Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, DOI: 10.1177/0954406216677103.
[68]	Zhu W D, Ren H. 2013. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems-Part I: Methodology. Journal of Vibration and Acoustics-transactions of the ASME, 135: 051036.