水电工程重型缆机架空索道系统动力学及可靠性研究
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摘要
缆索起重机(以下简称缆机)是以悬挂于两支点之间的钢索作为承载结构,利用载重小车在其上往返移动进行物料吊运,兼有垂直运输(通过起升机构的起重绳实现)和水平运输功能的特种起重运输机械。缆机主要由塔架、架空承载部分、工作驱动机构、机电控制设备及安全保护装置等组成,其中架空部分主要由承载索、起重绳、牵引绳、承马及载重小车等部件组成。缆机在水利电力建设工程、桥梁建筑、码头施工、森林工业、采矿工业、堆料场装卸以及港口装卸等方面都有广泛的用途。
我国在三峡大坝施工中,首次引进德国克虏伯所设计制造的缆机,并开始对国外先进缆机设计与制造技术进行引进、消化和吸收。目前我国在缆机设计、制造和使用过程中,塔架、驱动及控制系统等方面的设计和制造技术都较为成熟,使用过程也很少出现故障。但是,在对缆机中关键部件——架空系统的研究方面与国外类似产品相比仍有差距,反映在对于架空部件的优化设计、产品精细化程度不够,可靠性不高,缺乏基础性研究的支持。
通过查阅文献获知,大量缆机方面的文献仅仅涉及缆机的维护、保养、运行等方面的内容。在研究中有两个明显的不足：其一是对于重型缆机索道系统的动力学特性研究不够；其二是没有运用现代设计分析方法与手段对缆机架空索道系统设计中的关键问题进行研究。由于缆机架空部分的承载索、起重绳、牵引绳及承马等部件之间存在强耦合关系,保证缆机架空部分的平稳运行成为缆机设计的关键。随着我国对缆机速度及载荷量要求的不断提高,迫切需要应用动力学和现代设计分析方法与手段,对缆机架空部分部件的运动机理进行深入的研究,以提高缆机运行的平稳性和使用可靠性。
论文以现代设计理论为指导,对重型缆机中的架空系统的动力学特性以及设计中的关键问题进行了系统的研究,主要研究内容和研究成果归纳如下：
1.系统地研究了重型缆机承载索的动力学建模方法。针对缆机架空部分中起升系统与承载索之间存在的强耦合作用及缆机的结构特点,把缆机架空系统合理的抽象成悬挂于两等高固定端的均质弹性连续体和具有一定质量—刚度—阻尼的移动振子的物理模型。然后应用汉密尔顿(Hamilton)原理列写了该系统的运动方程,通过力和位移协调推导出了一组控制索—振子运动的偏微分方程组,在方程中考虑了科氏(Coriolis)惯性力以及缆索的非线性弹性恢复力。由于该微分方程组不存在封闭的解析解,因而运用伽辽金法(Galerkin)方法,把偏微分方程组转化成了常微分方程组以便利于数值积分求解。
2.针对控制索-振子运动的微分方程,对数值积分和动力学仿真的方法分别进行了研究。首先研究了形函数的阶数对收敛性的影响,根据重型缆机架空部分的结构形式,并考虑跨度、垂度以及载重量等因素,选择正弦函数作为形函数并编制了MATLAB程序。应用该程序,在缆机的匀速、紧急加(减)速、加载以及减载等典型工况下,对悬索的动力学特性进行了研究。为了对动力学分析结果进行验证,在动力学仿真软件ADAMS平台上建立了缆机承载索的动力学模型并进行了仿真,仿真结果与数值积分的求解结果基本一致。研究结果表明：小车的运动速度、吊重等对悬索的动力学特性有比较明显的影响,而其中对缆机运行平稳性影响最大的是载重小车的运行速度。对于目前使用最多的30t级缆机及其相应的架空结构,小车的最大匀速不宜超过7.5m/s,否则会导致缆索的急剧跳动,对缆机的平稳运行十分不利。结论解释了为何缆机载重小车的工作速度存在速度限制闽值。
3.运用三维建模软件和机械系统动力学分析软件,对架空系统中的重要部件——承马的结构进行了优化设计研究。论文结合承马的结构特征和设计流程,具体研究了承马的三维设计方法,并用实例进行了验证；在ADAMS平台上对承马进行了动力学仿真,通过参数优化设计,确定了保证承马托轮臂得到合理张开角度时托轮臂铰点的最优位置,在此基础上通过对承马关闭弹簧的刚度和阻尼参数的优化,可整体提高承马启闭过程的平稳性和可靠性,并提高承马启闭响应的灵敏度。
4.通过对缆机不同工况和载荷下的运行状况分析,求解状态方程确定了缆机工作时各个承马中从空中脱落风险最大的承马。以该承马的载荷和受力特性为基础,选择空载、轻载以及满载等典型工况对缆机运行过程中承马的受力状况进行有限元结构分析,确定了承马结构中最为薄弱的部分。研究方法和结果可直接应用于承马的设计工作,对承马结构轻型化、提高承马工作的可靠性具有一定参考价值。
5.对于缆机承载索的疲劳问题进行了理论研究。通过单根钢丝及整条缆索的受力分析,证明缆机承载索的疲劳与悬索桥等其他悬索结构中索的疲劳有所不同,悬索桥等其他悬索结构中索的疲劳属于轴向疲劳问题,而缆机承载索的疲劳属于弯曲疲劳问题,并从理论上论证了缆机承载索的疲劳发生在承载索的表面而非靠近索中性面的原因。通过对承载索进行有限元分析,计算出载重小车运行过程中承载索交变应力的幅值,并结合经典的应力-寿命S—N曲线,对缆机承载索的疲劳寿命的主要影响因素进行了研究,证明了承载索的疲劳寿命与缆机载重小车的循环次数、吊运重量及承载索直径等参数的关联度。通过工程实例的验算,计算出某30t级缆机在吊运300kN载荷时承载索的寿命仅仅略高于30万个工作循环,从理论上论证了承载索的国外供货方不愿对承载索的寿命做出高于30万个工作循环承诺的原因,对目前承载索安全系数的选择是一个很好的补充,并可提高缆机的使用安全性。
论文对工程对象进行分析与综合,原始参数来源于工程案例,研究成果均有相应的工程实例验证,对缆机设计具有指导意义。
Cable-crane is a special hoisting and conveying machine which uses the flexible steel cable as its supporting structure, on which a trolley runs from one end to the other end to perform horizontal and vertical transportation (realized by hoisting rope of hoisting mechanism). Cable-crane is principally composed of tower, aerial and bearing parts, working and driving mechanism, electromechanical and control equipment and safety protection device. Its aerial and bearing parts possess track rope, hoisting rope, traversing rope (to traverse trolley), carrier and trolley. In the case of span over200m, carrier is necessary to be installed to support lifting rope and traversing rope and to avoid winding of working ropes. According to the difference of span, it can be installed two or even more carrier. Actually, cable-crane has been found wildly used in hydraulic and electric engineering construction, bridge construction, wharf construction, forest industry, mining industry, loading and unloading process of stock yard, port handling and other fields.
In the constructioin of Three Gorges dam, China for the first time introduced the cable-cranes made by Germany Krupp, and then commenced the introduction, digestion and absorption of the advanced design and manufacture technology of foreign countries. Actually, China in its process of design, manufacture and operation of cable-crane, the design and manufacture techniques of tower, electrical and control equipments are well-developped and there appear few faults in the operation. However, compared to the products introduced from developed countries, much progress rest to be made on the research of aerial ropeway system which is the key parts of cable-crane. This shortage can be reflected from the design of our products. For example, in the research and development of the aerial ropeway system, we still lack of optimization design and it causes the problem of refinement and reliability. It can be trusted that this problem stems from the lack of fundamental research.
According to the literature referenced in our research, much literature concerns only maintenance and operation of cable-crane. Generally, there are two obvious disadvantages in research:the first is that profound research has not been made on the dynamic characteristics of ropeway system of cable-crane; the second one is that the modern design methods and techniques are not applied in the research on the key problem-the design of ropeway system. Because of strong coupled effect among track rope, lifting rope and traversing rope, how to ensure the stable operation of cable-crane is the key of the design of cable-crane. Actually, with the demand to the load and working speed of cable-crane becomes higher and higher, it is urgent need to apply modern design methods and techniques to perform profound research on the aerial parts of cable-crane. In this way the stability and reliability of cable-crane can be ensured.
With the guidance of new advancements of modern mechanics and modern design theory, this paper has performed systematic research on the dynamic characteristics and the key problems of the design of aerial ropeway system. The main research results can be concluded as followed:
1. Dynamic modelization on the track rope of a heavy cable-crane is systematic studied. Considering the structural features of cable-crane and the strong coupled effects between of lifting system and the track rope, the ropeway system of cable-crane is reasonably abstracted to a physical model—a homogeneous elastic continuum suspended to two fixed ends with equal height coupled to a mass-spring-damper system with a moving oscillator. Then, by applying Hamilton principle the motion equation of the system is written. On investigating the compatibility of force and displacement, a set of nonlinear differential equations governing cable-oscillator are derived. In the equations Coriolis inertial force and nonlinear restoring force of cable are integrated. Because there exists no closed-form analytical solution, to obtain the numerical integral solution, Galerkin method is applied and the partial differential equations are transformed to the ordinary differential equations.
2. In chapter2, for the differential equations governing cable-oscillator, numerical integration method and dynamic simulation method are investigated. Firstly, the order of shape function to the influence of the convergence is discussed. Then, considering the structural features and span, sag, load and other parameters. Sine function is determined as shape functions and MATLAB code are developed. Under the various typical working case of cable-crane such as constant velocity, urgent acceleration (deceleration), loading and unloading, the dynamic characteristics of track rope are analyzed respectively. For further validation the dynamic model of track rope is created on the ADAMS platform and the relative simulations are performed. The simulation results obtained are essentially consistent with the numerical integral results. It can be demonstrated from results that both of velocity of trolley and hoisting weight has significant influence to the dynamic characteristics of track rope. Compared to the hoisting weight, velocity of trolley plays the greatest impact to the stability of cable-crane. It can be also concluded that, for the30t level cable-crane (which are the most commonly used in engineering fields) with the relative aerial structure, the highest uniform speed can not exceed over7.5m/s. Otherwise, it would result the sharp vibration of cable and it is extremely unfavorable to the stable operation of cable-crane. The puzzle that there exists a limit value to the working speed of trolley, which obsesses the designers and users for many years, is explained reasonably.
3. Professional three-dimensional modeling software and dynamic analysis of mechanical systems are applied to perform optimization research on the optimization design of the key parts—carrier of ropeway system. Firstly, combined the structural characteristics with its design process, three-dimensional design method of carrier is investigated and an engineering example is realized and valided later. Moreover, by applying dynamic simulation and parameter optimization design, the optimal pivot-points which ensure the appropriate opening angle of two arms of carrier are determined. On this base, through the optimization of stiffness and damping parameter, the stability and reliability of carrier in its open-close process are ensured. The response rate of carrier during its open-close process is sensibly improved.
4. In chapter4, working conditions and loads of a cable-crane are seriously analyzed. Through the solution of state equation, the most dangerous carrier which possesses the greatest dropping risk during the operation is determined. On the base of analysis of the loads and stress characteristics, carrier is performed the finite element structural analysis under the several of typical working conditions such as no-load, light-load and full-load. The weakest parts of carrier are analyzed and determined. The research method and results can be applied directly to the design of carrier, and it possesses certain reference value to the light-duty design of structure and to the improvement of reliability during its operation.
5. In chapter5, fatigue failure of track rope of cable-crane is theoretically investigated. Through the analysis of single steel-wire and whole cable, it can be concluded that fatigue failure of track rope is different from that of other cable-suspended structures for example suspension bridge. In the suspension bridge or other cable-suspended structures fatigue failure belong to the axial fatigue. However, the fatigue failure of track rope of cable-crane belongs to the bending fatigue. The reason why fatigue failure of track rope stems from the surface of the cable not near the neutral plane is reasonably explained. Through the FEM analysis on the track rope, the alternating stress of track rope can be exactly calculated. Combining with the classical stress—life S—N curve, the main effects to the fatigue life of track rope are investigated seriously. It can be demonstrated that the cycle numbers, load and the diameter of track rope have significant effect to the fatigue life of track rope. Through a validation of a real engineering example, for a30t level of cable-crane the cycle numbers is just a little higher than300000. The reason why the foreign suppliers don't want to make the promise higher than300000working cycles can be explained and it is a good supplement to the determination of the safety factor of track rope.
The thesis performs analysis and synthesis on the real engineering objects. All original parameters stem from the engineering examples and research results are valided by engineering examples. It can be expected that the system research has the guiding significanceon to the design of cable-crane.
我国在三峡大坝施工中,首次引进德国克虏伯所设计制造的缆机,并开始对国外先进缆机设计与制造技术进行引进、消化和吸收。目前我国在缆机设计、制造和使用过程中,塔架、驱动及控制系统等方面的设计和制造技术都较为成熟,使用过程也很少出现故障。但是,在对缆机中关键部件——架空系统的研究方面与国外类似产品相比仍有差距,反映在对于架空部件的优化设计、产品精细化程度不够,可靠性不高,缺乏基础性研究的支持。
通过查阅文献获知,大量缆机方面的文献仅仅涉及缆机的维护、保养、运行等方面的内容。在研究中有两个明显的不足：其一是对于重型缆机索道系统的动力学特性研究不够；其二是没有运用现代设计分析方法与手段对缆机架空索道系统设计中的关键问题进行研究。由于缆机架空部分的承载索、起重绳、牵引绳及承马等部件之间存在强耦合关系,保证缆机架空部分的平稳运行成为缆机设计的关键。随着我国对缆机速度及载荷量要求的不断提高,迫切需要应用动力学和现代设计分析方法与手段,对缆机架空部分部件的运动机理进行深入的研究,以提高缆机运行的平稳性和使用可靠性。
论文以现代设计理论为指导,对重型缆机中的架空系统的动力学特性以及设计中的关键问题进行了系统的研究,主要研究内容和研究成果归纳如下：
1.系统地研究了重型缆机承载索的动力学建模方法。针对缆机架空部分中起升系统与承载索之间存在的强耦合作用及缆机的结构特点,把缆机架空系统合理的抽象成悬挂于两等高固定端的均质弹性连续体和具有一定质量—刚度—阻尼的移动振子的物理模型。然后应用汉密尔顿(Hamilton)原理列写了该系统的运动方程,通过力和位移协调推导出了一组控制索—振子运动的偏微分方程组,在方程中考虑了科氏(Coriolis)惯性力以及缆索的非线性弹性恢复力。由于该微分方程组不存在封闭的解析解,因而运用伽辽金法(Galerkin)方法,把偏微分方程组转化成了常微分方程组以便利于数值积分求解。
2.针对控制索-振子运动的微分方程,对数值积分和动力学仿真的方法分别进行了研究。首先研究了形函数的阶数对收敛性的影响,根据重型缆机架空部分的结构形式,并考虑跨度、垂度以及载重量等因素,选择正弦函数作为形函数并编制了MATLAB程序。应用该程序,在缆机的匀速、紧急加(减)速、加载以及减载等典型工况下,对悬索的动力学特性进行了研究。为了对动力学分析结果进行验证,在动力学仿真软件ADAMS平台上建立了缆机承载索的动力学模型并进行了仿真,仿真结果与数值积分的求解结果基本一致。研究结果表明：小车的运动速度、吊重等对悬索的动力学特性有比较明显的影响,而其中对缆机运行平稳性影响最大的是载重小车的运行速度。对于目前使用最多的30t级缆机及其相应的架空结构,小车的最大匀速不宜超过7.5m/s,否则会导致缆索的急剧跳动,对缆机的平稳运行十分不利。结论解释了为何缆机载重小车的工作速度存在速度限制闽值。
3.运用三维建模软件和机械系统动力学分析软件,对架空系统中的重要部件——承马的结构进行了优化设计研究。论文结合承马的结构特征和设计流程,具体研究了承马的三维设计方法,并用实例进行了验证；在ADAMS平台上对承马进行了动力学仿真,通过参数优化设计,确定了保证承马托轮臂得到合理张开角度时托轮臂铰点的最优位置,在此基础上通过对承马关闭弹簧的刚度和阻尼参数的优化,可整体提高承马启闭过程的平稳性和可靠性,并提高承马启闭响应的灵敏度。
4.通过对缆机不同工况和载荷下的运行状况分析,求解状态方程确定了缆机工作时各个承马中从空中脱落风险最大的承马。以该承马的载荷和受力特性为基础,选择空载、轻载以及满载等典型工况对缆机运行过程中承马的受力状况进行有限元结构分析,确定了承马结构中最为薄弱的部分。研究方法和结果可直接应用于承马的设计工作,对承马结构轻型化、提高承马工作的可靠性具有一定参考价值。
5.对于缆机承载索的疲劳问题进行了理论研究。通过单根钢丝及整条缆索的受力分析,证明缆机承载索的疲劳与悬索桥等其他悬索结构中索的疲劳有所不同,悬索桥等其他悬索结构中索的疲劳属于轴向疲劳问题,而缆机承载索的疲劳属于弯曲疲劳问题,并从理论上论证了缆机承载索的疲劳发生在承载索的表面而非靠近索中性面的原因。通过对承载索进行有限元分析,计算出载重小车运行过程中承载索交变应力的幅值,并结合经典的应力-寿命S—N曲线,对缆机承载索的疲劳寿命的主要影响因素进行了研究,证明了承载索的疲劳寿命与缆机载重小车的循环次数、吊运重量及承载索直径等参数的关联度。通过工程实例的验算,计算出某30t级缆机在吊运300kN载荷时承载索的寿命仅仅略高于30万个工作循环,从理论上论证了承载索的国外供货方不愿对承载索的寿命做出高于30万个工作循环承诺的原因,对目前承载索安全系数的选择是一个很好的补充,并可提高缆机的使用安全性。
论文对工程对象进行分析与综合,原始参数来源于工程案例,研究成果均有相应的工程实例验证,对缆机设计具有指导意义。
Cable-crane is a special hoisting and conveying machine which uses the flexible steel cable as its supporting structure, on which a trolley runs from one end to the other end to perform horizontal and vertical transportation (realized by hoisting rope of hoisting mechanism). Cable-crane is principally composed of tower, aerial and bearing parts, working and driving mechanism, electromechanical and control equipment and safety protection device. Its aerial and bearing parts possess track rope, hoisting rope, traversing rope (to traverse trolley), carrier and trolley. In the case of span over200m, carrier is necessary to be installed to support lifting rope and traversing rope and to avoid winding of working ropes. According to the difference of span, it can be installed two or even more carrier. Actually, cable-crane has been found wildly used in hydraulic and electric engineering construction, bridge construction, wharf construction, forest industry, mining industry, loading and unloading process of stock yard, port handling and other fields.
In the constructioin of Three Gorges dam, China for the first time introduced the cable-cranes made by Germany Krupp, and then commenced the introduction, digestion and absorption of the advanced design and manufacture technology of foreign countries. Actually, China in its process of design, manufacture and operation of cable-crane, the design and manufacture techniques of tower, electrical and control equipments are well-developped and there appear few faults in the operation. However, compared to the products introduced from developed countries, much progress rest to be made on the research of aerial ropeway system which is the key parts of cable-crane. This shortage can be reflected from the design of our products. For example, in the research and development of the aerial ropeway system, we still lack of optimization design and it causes the problem of refinement and reliability. It can be trusted that this problem stems from the lack of fundamental research.
According to the literature referenced in our research, much literature concerns only maintenance and operation of cable-crane. Generally, there are two obvious disadvantages in research:the first is that profound research has not been made on the dynamic characteristics of ropeway system of cable-crane; the second one is that the modern design methods and techniques are not applied in the research on the key problem-the design of ropeway system. Because of strong coupled effect among track rope, lifting rope and traversing rope, how to ensure the stable operation of cable-crane is the key of the design of cable-crane. Actually, with the demand to the load and working speed of cable-crane becomes higher and higher, it is urgent need to apply modern design methods and techniques to perform profound research on the aerial parts of cable-crane. In this way the stability and reliability of cable-crane can be ensured.
With the guidance of new advancements of modern mechanics and modern design theory, this paper has performed systematic research on the dynamic characteristics and the key problems of the design of aerial ropeway system. The main research results can be concluded as followed:
1. Dynamic modelization on the track rope of a heavy cable-crane is systematic studied. Considering the structural features of cable-crane and the strong coupled effects between of lifting system and the track rope, the ropeway system of cable-crane is reasonably abstracted to a physical model—a homogeneous elastic continuum suspended to two fixed ends with equal height coupled to a mass-spring-damper system with a moving oscillator. Then, by applying Hamilton principle the motion equation of the system is written. On investigating the compatibility of force and displacement, a set of nonlinear differential equations governing cable-oscillator are derived. In the equations Coriolis inertial force and nonlinear restoring force of cable are integrated. Because there exists no closed-form analytical solution, to obtain the numerical integral solution, Galerkin method is applied and the partial differential equations are transformed to the ordinary differential equations.
2. In chapter2, for the differential equations governing cable-oscillator, numerical integration method and dynamic simulation method are investigated. Firstly, the order of shape function to the influence of the convergence is discussed. Then, considering the structural features and span, sag, load and other parameters. Sine function is determined as shape functions and MATLAB code are developed. Under the various typical working case of cable-crane such as constant velocity, urgent acceleration (deceleration), loading and unloading, the dynamic characteristics of track rope are analyzed respectively. For further validation the dynamic model of track rope is created on the ADAMS platform and the relative simulations are performed. The simulation results obtained are essentially consistent with the numerical integral results. It can be demonstrated from results that both of velocity of trolley and hoisting weight has significant influence to the dynamic characteristics of track rope. Compared to the hoisting weight, velocity of trolley plays the greatest impact to the stability of cable-crane. It can be also concluded that, for the30t level cable-crane (which are the most commonly used in engineering fields) with the relative aerial structure, the highest uniform speed can not exceed over7.5m/s. Otherwise, it would result the sharp vibration of cable and it is extremely unfavorable to the stable operation of cable-crane. The puzzle that there exists a limit value to the working speed of trolley, which obsesses the designers and users for many years, is explained reasonably.
3. Professional three-dimensional modeling software and dynamic analysis of mechanical systems are applied to perform optimization research on the optimization design of the key parts—carrier of ropeway system. Firstly, combined the structural characteristics with its design process, three-dimensional design method of carrier is investigated and an engineering example is realized and valided later. Moreover, by applying dynamic simulation and parameter optimization design, the optimal pivot-points which ensure the appropriate opening angle of two arms of carrier are determined. On this base, through the optimization of stiffness and damping parameter, the stability and reliability of carrier in its open-close process are ensured. The response rate of carrier during its open-close process is sensibly improved.
4. In chapter4, working conditions and loads of a cable-crane are seriously analyzed. Through the solution of state equation, the most dangerous carrier which possesses the greatest dropping risk during the operation is determined. On the base of analysis of the loads and stress characteristics, carrier is performed the finite element structural analysis under the several of typical working conditions such as no-load, light-load and full-load. The weakest parts of carrier are analyzed and determined. The research method and results can be applied directly to the design of carrier, and it possesses certain reference value to the light-duty design of structure and to the improvement of reliability during its operation.
5. In chapter5, fatigue failure of track rope of cable-crane is theoretically investigated. Through the analysis of single steel-wire and whole cable, it can be concluded that fatigue failure of track rope is different from that of other cable-suspended structures for example suspension bridge. In the suspension bridge or other cable-suspended structures fatigue failure belong to the axial fatigue. However, the fatigue failure of track rope of cable-crane belongs to the bending fatigue. The reason why fatigue failure of track rope stems from the surface of the cable not near the neutral plane is reasonably explained. Through the FEM analysis on the track rope, the alternating stress of track rope can be exactly calculated. Combining with the classical stress—life S—N curve, the main effects to the fatigue life of track rope are investigated seriously. It can be demonstrated that the cycle numbers, load and the diameter of track rope have significant effect to the fatigue life of track rope. Through a validation of a real engineering example, for a30t level of cable-crane the cycle numbers is just a little higher than300000. The reason why the foreign suppliers don't want to make the promise higher than300000working cycles can be explained and it is a good supplement to the determination of the safety factor of track rope.
The thesis performs analysis and synthesis on the real engineering objects. All original parameters stem from the engineering examples and research results are valided by engineering examples. It can be expected that the system research has the guiding significanceon to the design of cable-crane.
引文
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