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 引用本文: 赵天骄, 齐朝晖, 王天堉, 徐金帅. 基于K-T条件的核环吊空间滑轮绳索接触段计算方法研究. 力学学报, 2024, 56(4): 1123-1137.
Zhao Tianjiao, Qi Zhaohui, Wang Tianyu, Xu Jinshuai. Research on the calculation method of the space pulley rope contact section of nuclear ring crane based on K-T condition. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1123-1137.
 Citation: Zhao Tianjiao, Qi Zhaohui, Wang Tianyu, Xu Jinshuai. Research on the calculation method of the space pulley rope contact section of nuclear ring crane based on K-T condition. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1123-1137.

## RESEARCH ON THE CALCULATION METHOD OF THE SPACE PULLEY ROPE CONTACT SECTION OF NUCLEAR RING CRANE BASED ON K-T CONDITION

• 摘要: 滑轮绳索系统是一类可以利用内嵌于其中的绳索控制的多体系统, 一般存在大量绳索接触段, 随着机械系统的复杂化和智能化, 对这类系统的精确性和可靠性提出了高要求. 针对核环吊起升机构中空间滑轮绳索接触段, 推导了接触段绳索微元体平衡方程, 得到了接触力密度的解析表达式. 将绳索应变求解转化为优化问题, 利用库恩塔克(K-T)条件, 建立了绳索轴向应变以及应变对弧长导数满足的非线性方程, 并求出了内部应变对滑轮两端参数的导数, 计算了滑轮与绳索接触段的应变分布, 推导了绳索方位角与弧长应满足的协调方程. 同时结合接触段滑轮槽截面的几何特点, 推导了切向和法向接触力密度与绳索轴向应变之间的关系, 提出了滑轮两侧绳索应满足的边界条件, 利用边界点处绳索与滑轮物质速度相等的条件, 建立了约束方程. 数值算例表明, 计算结果符合绳索受力变形规律和接触力变化趋势. 提供的方法为包含空间滑轮绳索机构的核环吊机构以及其他大型机械系统分析提供了新的思路.

Abstract: The pulley rope system is a type of multi body system that can be controlled by ropes embedded within it , generally, there are a large number of contact segments,with the complexity and intelligence of mechanical systems, high demands have been placed on the accuracy and reliability of such systems . This paper mainly focuses on the space pull rope contact section of the nuclear ring lifting mechanism. Firstly,the equilibrium equation of the element body of the rope in the contact section is derived, and the analytical expression of the contact force density is obtained. Secondly,the solution of rope strain is transformed into an optimization problem.The nonlinear equation of strain and arc length derivative of strain is established by using Kuhntak condition. The derivative of internal strain to parameters at both ends of pulley is obtained. The strain distribution in contact section and the coordination equation between azimuth Angle and arc length are calculated. At the same time, the relationship between tangential and normal contact force density is derived based on the geometric characteristics of the pulley groove section, and the boundary conditions that the rope on both sides of the pulley should meet are proposed. Based on the condition that the material velocity of rope and pulley at the boundary point is equal, the constraint equation is established. In this paper, the contact forces of pulleys with different radius and different types of pulleys are analyzed, and the strain distribution rules of the contact section are summarized.The numerical examples show that the calculated results are consistent with the law of stress deformation and the trend of contact force change of the rope. The method presented in this paper provides a new idea for the analysis of large-scale mechanical systems including pulley and rope mechanisms. Moreover, it also provides theoretical preparation for the analysis of pulley-rope systems.

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