船舶复杂推进轴系耦合振动理论及试验研究
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摘要
船舶推进系统作为船舶的心脏,是船舶动力装置最重要组成部分之一,其对船舶营运的经济性、机动性、安全可靠性等起着至关重要的作用。随着造船行业对造船技术、造船工艺与质量要求的提高以及全球“低碳经济”的提出,船舶推进系统的性能需满足更高的要求,使得其在结构、功能以及性能上变得更加复杂,由此造成原有的轴系振动计算方法在某些场合中因误差过大而不再适用。同时,由于国际规范的加强,船舶轴系振动计算中还存在大量未解决或值得考虑的问题,因此需要对船舶复杂轴系的振动进行更深入的研究。本文围绕自行设计的多机并车联合动力装置综合试验台,针对目前船舶推进装置的研究热点,综合采用数学推导、数值计算、动力学仿真和试验等手段,进行了从梁单元的耦合振动到关键零部件的计算分析直至系统的整体研究分析。论文的主要工作如下：
1)分析了目前耦合振动研究中存在的不足,从材料力学和弹性力学的基本原理入手,分析了耦合振动产生的原因；总结了圆截面梁的轴向-横向以及扭转-横向耦合振动方程,并推导了圆截面梁的扭转-轴向耦合振动方程,分析了其振动耦合固有频率的变化规律；并根据三种振动形式下的两两耦合振动方程,导出了圆截面梁的轴向-横向-扭转耦合振动方程。
2)由于船用齿轮箱是造成轴系结构和功能复杂化的根本条件,因此以齿轮系统为研究对象,总结了目前求解齿轮啮合刚度和啮合阻尼的常用方法,建立了船用齿轮箱考虑齿轮啮合传动计算方法下的扭振方程。通过理论计算和建模仿真分析了系统的固有频率以及齿轮啮合误差对扭振的影响；通过斜齿轮的受力分析,解释了斜齿轮副产生耦合振动的原因,推导得出了斜齿轮副啮合耦合振动模型；通过实船测试数据与各种理论计算结果的对比,认为在忽略齿轮啮合误差的情况下,考虑齿轮啮合刚度的推进轴系扭振计算比传统的计算方法更精确,与实测结果更一致。
3)联轴器的使用使得轴系的性能更加复杂,因此以目前船舶推进轴系中应用较多的十字轴万向联轴器为研究对象,通过坐标变换的方法,推导了主动轴、从动轴和夹角之间的运动规律,得到了十字轴的运动方程；利用第一类拉格朗日方程推导出最基本的万向联轴器的扭转振动的基本的非线性方程,通过仿真分析了夹角对万向联轴器系统的固有频率的影响,得到夹角在小范围内变化时,可忽略因为夹角变化引起的扭矩波动的结论；在其运动学的的基础上,利用拉格朗日方程推导出了考虑十字轴的万向联轴器的扭转振动方程,发现分析得出无论主动轴、中间轴和从动轴之间的夹角如何变化,该系统均是稳定的。同时,随着中间轴和从动轴之间的夹角依次逐渐增大,系统达到稳定的时间依次相应延长,但振幅依次不断降低,同时与最大峰值处对应的频率依次减小。
4)以所建立的试验台为原型,利用所开发的复杂轴系的扭振计算软件,计算分析了三缸柴油机带测功机工作、四缸柴油机带测功机工作以及双机并车带测功机工作时系统扭转振动的固有频率。同时,考虑了双机并车时柴油机相位差对振动响应的影响,建立了系统的三维模型,并利用动力学仿真软件,综合考虑了齿轮系统以及耦合振动的影响,分析了不同转速下中间轴的角速度变化情况。
5)设计并建立了多机并车联合动力装置综合试验台,对其硬件组成和监控系统进行了简要说明；概述了三种不同工况下的测试方案,通过测试数据验证了前述相关理论的正确性。
Serving as the heart of ship, marine propulsion system is one of the most important components of marine power plant. It plays a vital role on aspects of marine's economy, mobility, safety and reliability. Due to the higher requirements on the process and technology in shipbuilding industry and the put-forward of global low-carbon economy concept, marine propulsion system is required to meet higher requirements like more complex structure, function and performance. As a result, the former method for shaft vibration calculation, which sometimes leads to unacceptable error, is out of requirements. At the same time, due to the strengthening of international norms, there are many points which are unresolved or worthy to consider in-depth in the field of vibration calculation of ship shafting, more efforts need to be put in analysis of complex ship shafting vibration. This paper, based on the self-designed comprehensive experiment platform with multi-engine parallel operation power plant, focusing on the research hotspot in current marine propulsion system and in combination of mathematical derivation, numerical calculation, dynamics simulation, experimental testing, etc., performed the calculation of the coupling vibration of beam element and computational analysis of key parts and the whole system. The main research work is as follows:
1) Analyzed the current shortcomings in the coupled vibration research; analyzed the causes of coupled vibration based on basic principles of mechanics of materials and elasticity; summarized the axial-transverse and torsional-lateral coupling vibration equation for beam with round section and performed derivation of torsion-axial coupling vibration equation, analyzed the rules of coupled natural frequency, derived-transverse-torsion coupling vibration equation for beam with round section axial from twin-coupled vibration equation.
2) Since marine gearbox is the root course of the complex structure and function, the common methods of solving the gear mesh stiffness and mesh damping have been summarized, the torsional vibration equation taking gear meshing in marine gearbox into account has been established. The influence of system natural frequency and the gear meshing error on torsional vibration has been analyzed by means of theoretical calculation, modeling and simulation. Through the stress analysis of helical gear, a complete explanation of helical gear meshing coupled vibration is given and the gear pair coupling vibration model is derived. Comparing the results between the test data of measurement and calculation from various theories, it can be found that the torsional vibration equation considering gear meshing in marine gearbox is more accurate and consistent with the measurement.
3) As the joints'application has made the shafting performance more complicated and the cross-joint-type universal coupling is wildly used in marine propulsion system, it is set as the research object in chapter4. The motion law between driving and driven shaft is derived and the equations of motion for cross joint shaft is given. The basic nonlinear equations of the torsional vibration for the universal coupling have been derived from the first class of the Lagrange equation. The simulation analysis of the impact of the angle on the natural frequency of the universal coupling system has been performed. From this, it can be found that the torque fluctuations coming from angle changing can be ignored when angle changing is within a small range. Based on the kinematics of universal coupling, the torsional vibration equation in consideration of the cross shaft universal coupling has been derived from the Lagrange equation. Analysis reveals that no matter how the angle changes within the driving shaft, intermediate shaft and the driven shaft the system is stable. Meanwhile, while gradually increasing the angle between the intermediate shaft and the driven shaft, the time that the system takes to reach a stable state extends accordingly, but the amplitude is lower and the frequencies corresponding to the maximum peak value decreases.
4) Based on the experiment platform and developed software for calculation of complex shafting torsional vibration, the natural frequency of vibration of three-cylinder diesel engine with a dynamometer, four-cylinder diesel engine with a dynamometer and two-engine parallel operation with a dynamometer is calculated and analyzed. Meanwhile, with consideration of the influence of phase difference between the parallel engines, the three-dimensional model has been built. Assisted by the dynamic simulation software and considering the influent of the gear system and coupling vibration, the intermediate shaft angular velocity in different speed of revolution is given.
5) Designed and built the multi-engine parallel operation power plant platform, a brief description of its hardware components and the monitoring system is given. An overview of three test program in different conditions is given and test data proved the correction and convenience of the theory above.
1)分析了目前耦合振动研究中存在的不足,从材料力学和弹性力学的基本原理入手,分析了耦合振动产生的原因；总结了圆截面梁的轴向-横向以及扭转-横向耦合振动方程,并推导了圆截面梁的扭转-轴向耦合振动方程,分析了其振动耦合固有频率的变化规律；并根据三种振动形式下的两两耦合振动方程,导出了圆截面梁的轴向-横向-扭转耦合振动方程。
2)由于船用齿轮箱是造成轴系结构和功能复杂化的根本条件,因此以齿轮系统为研究对象,总结了目前求解齿轮啮合刚度和啮合阻尼的常用方法,建立了船用齿轮箱考虑齿轮啮合传动计算方法下的扭振方程。通过理论计算和建模仿真分析了系统的固有频率以及齿轮啮合误差对扭振的影响；通过斜齿轮的受力分析,解释了斜齿轮副产生耦合振动的原因,推导得出了斜齿轮副啮合耦合振动模型；通过实船测试数据与各种理论计算结果的对比,认为在忽略齿轮啮合误差的情况下,考虑齿轮啮合刚度的推进轴系扭振计算比传统的计算方法更精确,与实测结果更一致。
3)联轴器的使用使得轴系的性能更加复杂,因此以目前船舶推进轴系中应用较多的十字轴万向联轴器为研究对象,通过坐标变换的方法,推导了主动轴、从动轴和夹角之间的运动规律,得到了十字轴的运动方程；利用第一类拉格朗日方程推导出最基本的万向联轴器的扭转振动的基本的非线性方程,通过仿真分析了夹角对万向联轴器系统的固有频率的影响,得到夹角在小范围内变化时,可忽略因为夹角变化引起的扭矩波动的结论；在其运动学的的基础上,利用拉格朗日方程推导出了考虑十字轴的万向联轴器的扭转振动方程,发现分析得出无论主动轴、中间轴和从动轴之间的夹角如何变化,该系统均是稳定的。同时,随着中间轴和从动轴之间的夹角依次逐渐增大,系统达到稳定的时间依次相应延长,但振幅依次不断降低,同时与最大峰值处对应的频率依次减小。
4)以所建立的试验台为原型,利用所开发的复杂轴系的扭振计算软件,计算分析了三缸柴油机带测功机工作、四缸柴油机带测功机工作以及双机并车带测功机工作时系统扭转振动的固有频率。同时,考虑了双机并车时柴油机相位差对振动响应的影响,建立了系统的三维模型,并利用动力学仿真软件,综合考虑了齿轮系统以及耦合振动的影响,分析了不同转速下中间轴的角速度变化情况。
5)设计并建立了多机并车联合动力装置综合试验台,对其硬件组成和监控系统进行了简要说明；概述了三种不同工况下的测试方案,通过测试数据验证了前述相关理论的正确性。
Serving as the heart of ship, marine propulsion system is one of the most important components of marine power plant. It plays a vital role on aspects of marine's economy, mobility, safety and reliability. Due to the higher requirements on the process and technology in shipbuilding industry and the put-forward of global low-carbon economy concept, marine propulsion system is required to meet higher requirements like more complex structure, function and performance. As a result, the former method for shaft vibration calculation, which sometimes leads to unacceptable error, is out of requirements. At the same time, due to the strengthening of international norms, there are many points which are unresolved or worthy to consider in-depth in the field of vibration calculation of ship shafting, more efforts need to be put in analysis of complex ship shafting vibration. This paper, based on the self-designed comprehensive experiment platform with multi-engine parallel operation power plant, focusing on the research hotspot in current marine propulsion system and in combination of mathematical derivation, numerical calculation, dynamics simulation, experimental testing, etc., performed the calculation of the coupling vibration of beam element and computational analysis of key parts and the whole system. The main research work is as follows:
1) Analyzed the current shortcomings in the coupled vibration research; analyzed the causes of coupled vibration based on basic principles of mechanics of materials and elasticity; summarized the axial-transverse and torsional-lateral coupling vibration equation for beam with round section and performed derivation of torsion-axial coupling vibration equation, analyzed the rules of coupled natural frequency, derived-transverse-torsion coupling vibration equation for beam with round section axial from twin-coupled vibration equation.
2) Since marine gearbox is the root course of the complex structure and function, the common methods of solving the gear mesh stiffness and mesh damping have been summarized, the torsional vibration equation taking gear meshing in marine gearbox into account has been established. The influence of system natural frequency and the gear meshing error on torsional vibration has been analyzed by means of theoretical calculation, modeling and simulation. Through the stress analysis of helical gear, a complete explanation of helical gear meshing coupled vibration is given and the gear pair coupling vibration model is derived. Comparing the results between the test data of measurement and calculation from various theories, it can be found that the torsional vibration equation considering gear meshing in marine gearbox is more accurate and consistent with the measurement.
3) As the joints'application has made the shafting performance more complicated and the cross-joint-type universal coupling is wildly used in marine propulsion system, it is set as the research object in chapter4. The motion law between driving and driven shaft is derived and the equations of motion for cross joint shaft is given. The basic nonlinear equations of the torsional vibration for the universal coupling have been derived from the first class of the Lagrange equation. The simulation analysis of the impact of the angle on the natural frequency of the universal coupling system has been performed. From this, it can be found that the torque fluctuations coming from angle changing can be ignored when angle changing is within a small range. Based on the kinematics of universal coupling, the torsional vibration equation in consideration of the cross shaft universal coupling has been derived from the Lagrange equation. Analysis reveals that no matter how the angle changes within the driving shaft, intermediate shaft and the driven shaft the system is stable. Meanwhile, while gradually increasing the angle between the intermediate shaft and the driven shaft, the time that the system takes to reach a stable state extends accordingly, but the amplitude is lower and the frequencies corresponding to the maximum peak value decreases.
4) Based on the experiment platform and developed software for calculation of complex shafting torsional vibration, the natural frequency of vibration of three-cylinder diesel engine with a dynamometer, four-cylinder diesel engine with a dynamometer and two-engine parallel operation with a dynamometer is calculated and analyzed. Meanwhile, with consideration of the influence of phase difference between the parallel engines, the three-dimensional model has been built. Assisted by the dynamic simulation software and considering the influent of the gear system and coupling vibration, the intermediate shaft angular velocity in different speed of revolution is given.
5) Designed and built the multi-engine parallel operation power plant platform, a brief description of its hardware components and the monitoring system is given. An overview of three test program in different conditions is given and test data proved the correction and convenience of the theory above.
引文
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