钢丝绳捻制成形数值模拟与制品力学强度分析
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摘要
钢丝绳是一种重要的空间螺旋结构制品,具有高强度、柔软性和稳定可靠的特点,因而被广泛地应用于机械、建筑、交通、通讯和航空航天等领域。到目前为止,大量文献研究了钢丝绳承受拉伸、弯曲和扭转载荷时的变形情况,但很少有对钢丝绳成形过程进行数值模拟的研究,特别是没有考虑自扭转系数和接触摩擦对捻制成形影响。捻制成形过程中变形复杂,必须同时考虑材料非线性和接触非线性。钢丝绳的加工应力不仅影响成形性,而且由其引起的残余应力对钢丝绳结构强度有很大影响。因此,本文进行了钢丝绳成形过程数值模拟和制品力学强度分析的研究工作。
本文首先建立了考虑自扭转系数时的钢丝绳空间几何模型,该模型是捻制成形过程有限元计算模型的重要组成部分;根据钢丝绳捻制成形原理,考虑捻制成形中的材料非线性,以虚功原理为基础,建立了捻制成形数值模拟中弹塑性增量分析的有限元方程。
接触摩擦模型是捻制成形过程有限元计算模型的另外一个重要组成部分。接触摩擦与钢丝绳变形之间是复杂的非线性关系,直接影响着钢丝绳的成形性。接触摩擦问题的处理包括接触单元的搜索和接触力的计算两个方面。本文采用捻制成形中三维Splitting-pinball接触搜索计算模型,该算法大大提高了搜索接触单元的精确性。
采用罚函数法,讨论了接触界面本构关系的增量形式和接触单元技术,用径向回映算法处理接触摩擦中的粘着/滑动状态;在罚函数法的基础上,进一步给出了采用Augmented Lagrangian法处理法向接触力和切向接触力的计算模型。该方法的优点是可以得到问题的精确解,且节约CPU消耗时间和减少控制方程出现病态。
为了考虑捻制成形工艺对钢丝绳结构强度的影响,本文建立了钢丝绳制品力学强度分析计算模型,对载荷作用下简单直股和IWRC 7×7独立绳芯中钢丝的受力情况进行分析,并对钢丝截面危险点采用第三强度理论进行强度校核计算。
考虑钢丝绳的捻制过程的双重非线性,根据所建立的捻制成形过程有限元计算模型,在分析钢丝绳捻制成形数值模拟和制品力学强度校核程序系统的设计原则和功能需求的基础上,建立了系统的各个功能模块;运用图形用户界面(GUI),利用通用有限元软件ANSYS的开放性结构,用VC++ 二次开发了钢丝绳捻制成形过程数值模拟
和力学强度分析程序系统(LayingWireRope)。该系统生成ANSYS参数设计语言(APDL)格式的数据文件,数据文件可以被ANSYS直接调用,进行捻制成形的材料非线性和接触非线性分析,且可以进行制品的力学强度分析;讨论了系统开发中涉及到的ANSYS封装、注册表编程、多进程编程和进程的终止等关键技术,以保证在接口程序中正常启动、运行和关闭ANSYS应用程序。
利用所开发的系统研究了自扭转系数、摩擦系数和捻向组合等捻制工艺参数对钢丝绳捻制成形的影响。研究结果表明:① 非零自扭转系数进行一次捻制成形时,加工形状冻结性好,且整绳在使用过程中扭转应力小,故使用安全性好;② 钢丝绳捻制成形过程中摩擦系数对剪应力的影响比对Von-Mises 应力和等效塑性应变的影响大。综合考虑钢丝绳的结构强度和摩擦系数的影响,合理的自扭转系数取略大于1.0;③ 二次捻制时侧股的侧线钢丝的应力应变呈现不均匀分布,且交互捻制钢丝绳不易松散,即形状冻结性好,但柔软性较差;而同向捻制钢丝绳的柔软性较好,但易松散;④ 通过对Augmented Lagrangian 法中计算结果和收敛性比较,合理的法向接触刚度因子的取值为0.01。
另外,对IWRC 7×7独立绳芯制品进行了力学强度分析,具体讨论了绳股的受载分配和捻向组合对制品强度的影响。分析结果表明,侧股承受了整绳的主要载荷,但整绳的最危险点在芯股侧线钢丝与芯股中心钢丝的接触点处;交互捻制钢丝绳的相当应力要明显大于同向捻制钢丝绳的相当应力。
最后,对钢丝捻制成形终了钢丝内轴向残余应力采用X射线法进行了测定。结果表明,在考虑摩擦的情况下,钢丝内的轴向残余应力计算结果与实验结果更接近,且说明本文提出的捻制成形有限元计算模型是有效的。
Metal wire rope is an important kind of space spiral product. Since it has the characteristic of high strength, flexibleness and stability, it is widely applied in many fields, such as mechanism, architecture, transport, communication, aviation and aerospace, etc. Up to now, although the behaviors of stranded rope under loads, including tension, shear, bending and torsion, have been studied in many literatures, little information is available to predict the simulation for the laying process of wire rope, especially without regard to the self-rotating ratio and friction contact condition. Material non-linearity and contact non-linearity must be considered for the complicated deformation of laying wire rope. The formation stress affects the formability of wire rope, and the resultant residual stress greatly affects the structural strength. So the research of numerical simulation on the laying process and strength analysis of wire rope has been carried out in this paper.
The space geometric model of wire rope with self-rotating ratio has been described and the model is an important component of finite element computation model for laying wire rope. Taking the laying process theory of wire rope and material non-linearity into consideration, and based on the principle of virtual work, elasto-plastic incremental FE equations have been established for the numerical simulation for laying wire rope.
Friction contact model is another important component of finite element computation model for laying wire rope. It is a complicated nonlinear relationship between friction contact and deformation of wire rope. And friction contact has direct effect on the formability of wire rope. Friction contact routines carry out two tasks: to search the contact elements being in contact and to compute the contact forces. 3D Splitting-pinball contact searching model for laying wire rope has been adopted, and the accuracy has been improved by the Splitting-pinball algorithm.
Using penalty method, the incremental constitutive relationship and contact element technology of contact interface have been discussed. And Radial-Return Mapping algorithm has been employed to handle stick/slip phases of friction. Based on penalty method and using Augmented Lagrangian method, computation model has been presented to calculate both the normal contact force and friction contact force. The advantage of Augmented Lagrangian method is that the exact solution can be obtained and that considerable savings in the CPU-time can be realized and ill-condition of governing equations can be decreased.
In order to consider the effect of laying formation on the structural strength, Strength analysis model of metal wire rope has been presented in this paper. The behaviors of wires in simple strand and IWRC 7×7 Independent Wire Rope Core under loads are analyzed. With the third strength theory, the strength on the dangerous point in the wire cross is checked.
With dual non-linearity of the laying process, based on the finite element computation model for laying wire rope, and considering the design principle and function requirement of the program system for numerical simulation and strength analysis of metal wire rope, function modules of the system has been established. And with graphical user interface (GUI) and opening structure of the commercial finite element ANSYS software, the program system for numerical simulation on laying process and strength analysis of metal wire rope (LayingWireRope) has been redeveloped with VC ++. The system can create data files, which are in the format of ANSYS parametric design language (APDL). And the data files can be directly accessed by ANSYS for the analysis of material non-linearity and contact non-linearity. Also, the system can analyze strength of wire rope. The key technologies, such as encapsulating ANSYS, programming registry and multi-process, terminating thread, etc., have been discussed so that the interface program can activate, run and close ANSYS.
Using the developed program system, the effects of self-rotating
本文首先建立了考虑自扭转系数时的钢丝绳空间几何模型,该模型是捻制成形过程有限元计算模型的重要组成部分;根据钢丝绳捻制成形原理,考虑捻制成形中的材料非线性,以虚功原理为基础,建立了捻制成形数值模拟中弹塑性增量分析的有限元方程。
接触摩擦模型是捻制成形过程有限元计算模型的另外一个重要组成部分。接触摩擦与钢丝绳变形之间是复杂的非线性关系,直接影响着钢丝绳的成形性。接触摩擦问题的处理包括接触单元的搜索和接触力的计算两个方面。本文采用捻制成形中三维Splitting-pinball接触搜索计算模型,该算法大大提高了搜索接触单元的精确性。
采用罚函数法,讨论了接触界面本构关系的增量形式和接触单元技术,用径向回映算法处理接触摩擦中的粘着/滑动状态;在罚函数法的基础上,进一步给出了采用Augmented Lagrangian法处理法向接触力和切向接触力的计算模型。该方法的优点是可以得到问题的精确解,且节约CPU消耗时间和减少控制方程出现病态。
为了考虑捻制成形工艺对钢丝绳结构强度的影响,本文建立了钢丝绳制品力学强度分析计算模型,对载荷作用下简单直股和IWRC 7×7独立绳芯中钢丝的受力情况进行分析,并对钢丝截面危险点采用第三强度理论进行强度校核计算。
考虑钢丝绳的捻制过程的双重非线性,根据所建立的捻制成形过程有限元计算模型,在分析钢丝绳捻制成形数值模拟和制品力学强度校核程序系统的设计原则和功能需求的基础上,建立了系统的各个功能模块;运用图形用户界面(GUI),利用通用有限元软件ANSYS的开放性结构,用VC++ 二次开发了钢丝绳捻制成形过程数值模拟
和力学强度分析程序系统(LayingWireRope)。该系统生成ANSYS参数设计语言(APDL)格式的数据文件,数据文件可以被ANSYS直接调用,进行捻制成形的材料非线性和接触非线性分析,且可以进行制品的力学强度分析;讨论了系统开发中涉及到的ANSYS封装、注册表编程、多进程编程和进程的终止等关键技术,以保证在接口程序中正常启动、运行和关闭ANSYS应用程序。
利用所开发的系统研究了自扭转系数、摩擦系数和捻向组合等捻制工艺参数对钢丝绳捻制成形的影响。研究结果表明:① 非零自扭转系数进行一次捻制成形时,加工形状冻结性好,且整绳在使用过程中扭转应力小,故使用安全性好;② 钢丝绳捻制成形过程中摩擦系数对剪应力的影响比对Von-Mises 应力和等效塑性应变的影响大。综合考虑钢丝绳的结构强度和摩擦系数的影响,合理的自扭转系数取略大于1.0;③ 二次捻制时侧股的侧线钢丝的应力应变呈现不均匀分布,且交互捻制钢丝绳不易松散,即形状冻结性好,但柔软性较差;而同向捻制钢丝绳的柔软性较好,但易松散;④ 通过对Augmented Lagrangian 法中计算结果和收敛性比较,合理的法向接触刚度因子的取值为0.01。
另外,对IWRC 7×7独立绳芯制品进行了力学强度分析,具体讨论了绳股的受载分配和捻向组合对制品强度的影响。分析结果表明,侧股承受了整绳的主要载荷,但整绳的最危险点在芯股侧线钢丝与芯股中心钢丝的接触点处;交互捻制钢丝绳的相当应力要明显大于同向捻制钢丝绳的相当应力。
最后,对钢丝捻制成形终了钢丝内轴向残余应力采用X射线法进行了测定。结果表明,在考虑摩擦的情况下,钢丝内的轴向残余应力计算结果与实验结果更接近,且说明本文提出的捻制成形有限元计算模型是有效的。
Metal wire rope is an important kind of space spiral product. Since it has the characteristic of high strength, flexibleness and stability, it is widely applied in many fields, such as mechanism, architecture, transport, communication, aviation and aerospace, etc. Up to now, although the behaviors of stranded rope under loads, including tension, shear, bending and torsion, have been studied in many literatures, little information is available to predict the simulation for the laying process of wire rope, especially without regard to the self-rotating ratio and friction contact condition. Material non-linearity and contact non-linearity must be considered for the complicated deformation of laying wire rope. The formation stress affects the formability of wire rope, and the resultant residual stress greatly affects the structural strength. So the research of numerical simulation on the laying process and strength analysis of wire rope has been carried out in this paper.
The space geometric model of wire rope with self-rotating ratio has been described and the model is an important component of finite element computation model for laying wire rope. Taking the laying process theory of wire rope and material non-linearity into consideration, and based on the principle of virtual work, elasto-plastic incremental FE equations have been established for the numerical simulation for laying wire rope.
Friction contact model is another important component of finite element computation model for laying wire rope. It is a complicated nonlinear relationship between friction contact and deformation of wire rope. And friction contact has direct effect on the formability of wire rope. Friction contact routines carry out two tasks: to search the contact elements being in contact and to compute the contact forces. 3D Splitting-pinball contact searching model for laying wire rope has been adopted, and the accuracy has been improved by the Splitting-pinball algorithm.
Using penalty method, the incremental constitutive relationship and contact element technology of contact interface have been discussed. And Radial-Return Mapping algorithm has been employed to handle stick/slip phases of friction. Based on penalty method and using Augmented Lagrangian method, computation model has been presented to calculate both the normal contact force and friction contact force. The advantage of Augmented Lagrangian method is that the exact solution can be obtained and that considerable savings in the CPU-time can be realized and ill-condition of governing equations can be decreased.
In order to consider the effect of laying formation on the structural strength, Strength analysis model of metal wire rope has been presented in this paper. The behaviors of wires in simple strand and IWRC 7×7 Independent Wire Rope Core under loads are analyzed. With the third strength theory, the strength on the dangerous point in the wire cross is checked.
With dual non-linearity of the laying process, based on the finite element computation model for laying wire rope, and considering the design principle and function requirement of the program system for numerical simulation and strength analysis of metal wire rope, function modules of the system has been established. And with graphical user interface (GUI) and opening structure of the commercial finite element ANSYS software, the program system for numerical simulation on laying process and strength analysis of metal wire rope (LayingWireRope) has been redeveloped with VC ++. The system can create data files, which are in the format of ANSYS parametric design language (APDL). And the data files can be directly accessed by ANSYS for the analysis of material non-linearity and contact non-linearity. Also, the system can analyze strength of wire rope. The key technologies, such as encapsulating ANSYS, programming registry and multi-process, terminating thread, etc., have been discussed so that the interface program can activate, run and close ANSYS.
Using the developed program system, the effects of self-rotating
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