大型船用齿轮箱系统动态性能分析方法研究
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摘要
本文的研究依托于浙江省重大科技专项重点工业项目：《大功率船用齿轮箱关键技术的研究与应用》(2009C11062)。研究对象为与船用中速柴油发动机匹配的某款大型减速齿轮箱系统。项目是针对目前我国在大型船用减速齿轮箱系统的动态设计手段欠缺、更新换代缓慢、自主设计和研发能力薄弱而确立的,其目的是研发和完善能与10000-50000吨大型运输船舶和舰只相配套的大功率减速齿轮箱系统,为开发更大功率的船用减速齿轮箱系统作技术储备,并形成基于动态性能分析方法的箱体优化、减振降噪和抗冲击性能的设计技术。
作为运输船舶和舰船主动力系统关键设备的大型减速齿轮箱正朝着高效率、高可靠性、高稳定性、高速重载、轻量化、低振动、低噪声和短设计制造周期的方向发展,对基于动态分析方法的设计能力提出了更高的要求。另外,本文所研究的大型减速齿轮箱系统是作为军民两用设计的,依照相关军用规范,须保障其结构在水下爆炸冲击作用下的强度安全性能。本文主要着眼于某款大型船用减速齿轮箱系统,查阅大量国内外技术资料和学术文献,通过理论研究、数值模拟与实验研究相结合的手段,系统的将转子动力学、齿轮系统动力学、有限元方法、机械振动理论和测试原理等理论和技术集成,对齿轮箱系统的动态性能进行了系统的考察和评估,为形成大型船用齿轮箱系统关键动态性能的计算方法提供了理论依据和技术解决方案。论文的主要研究内容可归纳如下：
1)建立了耦合的啮合齿轮传动多平行轴转子的动力学模型,并将其用于分析大型船用齿轮箱传动系统中执行顺车工况的传动轴系,计算了该多轴系统耦合和未耦合情况下的临界转速,以及耦合系统的弯曲、扭转振动的振型,分析了在啮合齿轮多轴传动系统中考虑扭转振动的必要性；计算了不同啮合刚度时,耦合系统转子的各阶涡动转速,得到工作转速下各阶弯曲、扭转振动的自然频率随啮合刚度变化的规律,从转子稳定性的角度为齿轮箱传动系统的啮合齿轮副提供了最小设计刚度参考值；
2)建立了齿轮箱系统零部件的三维有限元模型,采用装配有限元技术将各零部件按原空间位置集成,并通过节点间自由度耦合、1D刚／柔性单元、1D弹簧阻尼单元和接触控制等方法,在轴承与轴承座、轴承座与转轴、啮合齿轮对的啮合面之间建立了耦合关系,使箱体、轴承座、转轴、联轴器和齿轮形成了一个可以用于计算分析的总装模型。
3)计算得到了齿轮箱系统及其传动系统的0-5000Hz内的模态频率和模态振型,在采用锤击法对该大型船用齿轮箱系统进行了模态试验的基础上,将试验模态分析得到的数据与理论计算值进行对比,对理论模型进行了验证。
4)基于转子动力学、齿轮啮合原理和有限元方法,研究了齿轮箱系统所受到的外部激励和内部激励,基于振型叠加法计算了系统的动态响应,得到了各输出节点的位移、速度、速度响应的时频域信号,并通过与振动试验数据对比,验证了理论模型的合理性。在此基础上,分析了该齿轮箱系统在频域上的振动特性,并对系统的振动烈度和结构噪声进行了量化评估。
5)基于军用规范中设计冲击谱的计算方法,结合齿轮箱系统的固有振动参数,制作了该系统在其各阶固有频率上的DDAM设计冲击谱,并将该设计谱拟合为二折线的冲击响应谱,以冲击响应谱为激励,计算了在左右舷向、垂向和艏艉向三个冲击加载方向上,齿轮箱系统的加速度、位移和应力响应峰值情况。
6)推导了静态应力与响应谱分析得到的动态应力的合成方法,得到了齿轮箱系统在正常工作状况下,突然受到冲击载荷作用时的有效应力,对齿轮箱系统在水下非接触性爆炸冲击作用下的安全性能进行评估。同时,采用衰减正弦基波组合法对冲击响应谱进行了拟合,得到了既具有时域爆炸冲击信号特点,又能在能量上匹配军用规范设计冲击响应谱的模拟时域冲击信号,并分析了箱顶在瞬态爆炸信号作用下的响应情况。
7)在箱体设计和改进中引入了拓扑优化技术,结合箱体的实际运行工况和动态性能分析方法,推导了动响应目标函数。采用优化准则算法,按照变密度法求解了多约束、多目标的箱体拓扑优化SIMP模型,根据优化分析得到的材料密度分布图,对箱体进行了优化改进。
This study originates from one of the Key Industrial Projects founded by Zhejiang Province Science and Technology Department:"Investigation and Application of the Key Technologies for Large Marine gearboxes"(2009C11062). The research object is a type of large marine reduction gearboxes matching the medium-speed diesel engines. This project is aimed at developing and improving the dynamic performances of large marine gearboxes which can match the10000～50000-tons large transport ships and warships, for technical reserves of the development for more powerful reduction-gearbox systems, and the formation of dynamic performances for box structural-design and optimization, vibration and noise reduction, shock resistance performance assessment.
As one of the most important equipments for the transport ship and warship main power system, the large marine reduction gearbox is developing towards high rotating speed, high efficiency, high stability, light-weight design, low vibration and noise, heavy-duty, short cycle of design and manufacturing, which put towards higher requirements on the dynamic transmission characteristics of gear transmission system and the manufacturing capabilities. In addition, the large marine gear system is designed for both military and civilian use, because of that, the design, construction and improvement should be subjected with relevant military specifications, in which the particular important ones are about the shock resistance performance assessment under the under-water explosion. This paper focuses on a certain models of large marine reduction gearbox systems, by accessing to a large number of domestic and foreign technical materials and academic literatures. By the means of combining theoretical investigations, numerical simulations and experimental studies, and systematically utilizing geared rotor dynamics, gear system dynamics, finite element method, modal analysis theories and techniques, dynamic response analysis methods, vibration test theories and methods, response spectrum analysis methods and etc., this study conducts a comprehensive survey and assessment of the dynamic performances for the large marine gearbox system, and provides theoretical basis and technical solutions for the dynamic performance design methods formation of large-scale marine gearbox systems. The main investigation contents can be summarized as follows:
1). Based on finite element theories, coupling geared multi-transmission parallel shafts rotor dynamics model is established. Then the model is utilized to analyze the geared dual parallel shafts in cis-turner working conditions for driving shafts of the large marine gearbox transmission system. The critical speed of coupled and uncoupled system is calculated, and then by analyzing the modal shapes of bending and torsional vibration for the coupled system, the necessity to consider the torsional vibration in the geared rotors is investigated. The critical rotating speeds of the coupled system with different gear meshing stiffness are computed to gain the bending and torsional vibration frequencies changing trends versus meshing stiffness changing. The investigation provides the minimum meshing stiffness for the design of the gearbox transmission system from the perspective of rotor dynamics. After that, the unbalance response is calculated for the drive system, and the sensitivities of different parts for the dual-rotor are studied.
2). The refined3D finite element models for components of the large marine gearbox system are built, then the assembled finite element technology is used to integrate the various components in accordance with the original spatial location for the entire gearbox system. Coupling functions, such as inter-node freedom coupling,1D connecting elements,1D spring-damper elements, contacting control coupling and etc are used to build the relationships between bearings, bearing houses, shafts, mating surfaces of gears. Then the computational model of the entire gearbox system is established, including box, bearing houses, shafts, and gears.
3). Modal frequencies and modal shapes between0-5000Hz of the large marine gearbox system are analyzed utilizing modal analysis theories. By means of simulated tests before real modal experiments, frequency responses of different parts on the box to force-hammer pulse excitation are extracted to provide a reference of location choices for the real tests. Then hammering method of modal experiments is adopted for modal tests of the large marine gearbox system. The theoretical modal analysis data are compared with experimental modal analysis data, to verify the effectiveness of the theoretical model.
4). Based on rotor dynamics, gear system dynamics and finite element method, the inner and outside excitations are studied for the large marine gearbox system. Then, based on modal superposition method of vibration theories, the dynamic response simulation is carried out. By means of comparing the theoretically analyzed response data and experimental vibration data, the rationality of the theoretical model is proved. On this basis, the main vibration frequencies are analyzed, and then the vibration intensity and structural noise are assessed for the gearbox system.
5). Based on calculation method of military specification, combined with the vibration parameters of the large marine gearbox system, DDAM design shock spectrum of natural frequencies is produced. Then the DDAM design shock spectrum was fitting into dual-polyline shock response spectrum, which is exerted as excitation of under-water explosion to the foundation of the gearbox system. After that, the response peak values of acceleration, velocity, displacement and stress for the marine gearbox of vertical, athwartship and fore-aft loading directions are computed.
6). Mapping relationship between nodes and elements of each sub-system and entire assembly finite element system is established. Synthetic method is derived to combine the static stress under normal working condition and dynamic stress obtained from response spectrum analysis. Then, this method is used to assess the safety performance for the gearbox system under under-water explosion. At last, damping sinusoid method is used to fitting the time domain explosion shock signal from the shock response spectrum, and the time domain signal is utilized to analyze the transient response characteristics of the gearbox system.
7). Topology optimization technology was introduced to improve the structural design and optimization for the gearbox. The objective function of dynamic response was derived according to the actual operation condition and dynamic performance analysis method. Multi-constraint and multi-objective optimized model was established according to the SIMP algorithm optimization criteria. After optimization analysis, optimized improvement was done to the gearbox structure.
作为运输船舶和舰船主动力系统关键设备的大型减速齿轮箱正朝着高效率、高可靠性、高稳定性、高速重载、轻量化、低振动、低噪声和短设计制造周期的方向发展,对基于动态分析方法的设计能力提出了更高的要求。另外,本文所研究的大型减速齿轮箱系统是作为军民两用设计的,依照相关军用规范,须保障其结构在水下爆炸冲击作用下的强度安全性能。本文主要着眼于某款大型船用减速齿轮箱系统,查阅大量国内外技术资料和学术文献,通过理论研究、数值模拟与实验研究相结合的手段,系统的将转子动力学、齿轮系统动力学、有限元方法、机械振动理论和测试原理等理论和技术集成,对齿轮箱系统的动态性能进行了系统的考察和评估,为形成大型船用齿轮箱系统关键动态性能的计算方法提供了理论依据和技术解决方案。论文的主要研究内容可归纳如下：
1)建立了耦合的啮合齿轮传动多平行轴转子的动力学模型,并将其用于分析大型船用齿轮箱传动系统中执行顺车工况的传动轴系,计算了该多轴系统耦合和未耦合情况下的临界转速,以及耦合系统的弯曲、扭转振动的振型,分析了在啮合齿轮多轴传动系统中考虑扭转振动的必要性；计算了不同啮合刚度时,耦合系统转子的各阶涡动转速,得到工作转速下各阶弯曲、扭转振动的自然频率随啮合刚度变化的规律,从转子稳定性的角度为齿轮箱传动系统的啮合齿轮副提供了最小设计刚度参考值；
2)建立了齿轮箱系统零部件的三维有限元模型,采用装配有限元技术将各零部件按原空间位置集成,并通过节点间自由度耦合、1D刚／柔性单元、1D弹簧阻尼单元和接触控制等方法,在轴承与轴承座、轴承座与转轴、啮合齿轮对的啮合面之间建立了耦合关系,使箱体、轴承座、转轴、联轴器和齿轮形成了一个可以用于计算分析的总装模型。
3)计算得到了齿轮箱系统及其传动系统的0-5000Hz内的模态频率和模态振型,在采用锤击法对该大型船用齿轮箱系统进行了模态试验的基础上,将试验模态分析得到的数据与理论计算值进行对比,对理论模型进行了验证。
4)基于转子动力学、齿轮啮合原理和有限元方法,研究了齿轮箱系统所受到的外部激励和内部激励,基于振型叠加法计算了系统的动态响应,得到了各输出节点的位移、速度、速度响应的时频域信号,并通过与振动试验数据对比,验证了理论模型的合理性。在此基础上,分析了该齿轮箱系统在频域上的振动特性,并对系统的振动烈度和结构噪声进行了量化评估。
5)基于军用规范中设计冲击谱的计算方法,结合齿轮箱系统的固有振动参数,制作了该系统在其各阶固有频率上的DDAM设计冲击谱,并将该设计谱拟合为二折线的冲击响应谱,以冲击响应谱为激励,计算了在左右舷向、垂向和艏艉向三个冲击加载方向上,齿轮箱系统的加速度、位移和应力响应峰值情况。
6)推导了静态应力与响应谱分析得到的动态应力的合成方法,得到了齿轮箱系统在正常工作状况下,突然受到冲击载荷作用时的有效应力,对齿轮箱系统在水下非接触性爆炸冲击作用下的安全性能进行评估。同时,采用衰减正弦基波组合法对冲击响应谱进行了拟合,得到了既具有时域爆炸冲击信号特点,又能在能量上匹配军用规范设计冲击响应谱的模拟时域冲击信号,并分析了箱顶在瞬态爆炸信号作用下的响应情况。
7)在箱体设计和改进中引入了拓扑优化技术,结合箱体的实际运行工况和动态性能分析方法,推导了动响应目标函数。采用优化准则算法,按照变密度法求解了多约束、多目标的箱体拓扑优化SIMP模型,根据优化分析得到的材料密度分布图,对箱体进行了优化改进。
This study originates from one of the Key Industrial Projects founded by Zhejiang Province Science and Technology Department:"Investigation and Application of the Key Technologies for Large Marine gearboxes"(2009C11062). The research object is a type of large marine reduction gearboxes matching the medium-speed diesel engines. This project is aimed at developing and improving the dynamic performances of large marine gearboxes which can match the10000～50000-tons large transport ships and warships, for technical reserves of the development for more powerful reduction-gearbox systems, and the formation of dynamic performances for box structural-design and optimization, vibration and noise reduction, shock resistance performance assessment.
As one of the most important equipments for the transport ship and warship main power system, the large marine reduction gearbox is developing towards high rotating speed, high efficiency, high stability, light-weight design, low vibration and noise, heavy-duty, short cycle of design and manufacturing, which put towards higher requirements on the dynamic transmission characteristics of gear transmission system and the manufacturing capabilities. In addition, the large marine gear system is designed for both military and civilian use, because of that, the design, construction and improvement should be subjected with relevant military specifications, in which the particular important ones are about the shock resistance performance assessment under the under-water explosion. This paper focuses on a certain models of large marine reduction gearbox systems, by accessing to a large number of domestic and foreign technical materials and academic literatures. By the means of combining theoretical investigations, numerical simulations and experimental studies, and systematically utilizing geared rotor dynamics, gear system dynamics, finite element method, modal analysis theories and techniques, dynamic response analysis methods, vibration test theories and methods, response spectrum analysis methods and etc., this study conducts a comprehensive survey and assessment of the dynamic performances for the large marine gearbox system, and provides theoretical basis and technical solutions for the dynamic performance design methods formation of large-scale marine gearbox systems. The main investigation contents can be summarized as follows:
1). Based on finite element theories, coupling geared multi-transmission parallel shafts rotor dynamics model is established. Then the model is utilized to analyze the geared dual parallel shafts in cis-turner working conditions for driving shafts of the large marine gearbox transmission system. The critical speed of coupled and uncoupled system is calculated, and then by analyzing the modal shapes of bending and torsional vibration for the coupled system, the necessity to consider the torsional vibration in the geared rotors is investigated. The critical rotating speeds of the coupled system with different gear meshing stiffness are computed to gain the bending and torsional vibration frequencies changing trends versus meshing stiffness changing. The investigation provides the minimum meshing stiffness for the design of the gearbox transmission system from the perspective of rotor dynamics. After that, the unbalance response is calculated for the drive system, and the sensitivities of different parts for the dual-rotor are studied.
2). The refined3D finite element models for components of the large marine gearbox system are built, then the assembled finite element technology is used to integrate the various components in accordance with the original spatial location for the entire gearbox system. Coupling functions, such as inter-node freedom coupling,1D connecting elements,1D spring-damper elements, contacting control coupling and etc are used to build the relationships between bearings, bearing houses, shafts, mating surfaces of gears. Then the computational model of the entire gearbox system is established, including box, bearing houses, shafts, and gears.
3). Modal frequencies and modal shapes between0-5000Hz of the large marine gearbox system are analyzed utilizing modal analysis theories. By means of simulated tests before real modal experiments, frequency responses of different parts on the box to force-hammer pulse excitation are extracted to provide a reference of location choices for the real tests. Then hammering method of modal experiments is adopted for modal tests of the large marine gearbox system. The theoretical modal analysis data are compared with experimental modal analysis data, to verify the effectiveness of the theoretical model.
4). Based on rotor dynamics, gear system dynamics and finite element method, the inner and outside excitations are studied for the large marine gearbox system. Then, based on modal superposition method of vibration theories, the dynamic response simulation is carried out. By means of comparing the theoretically analyzed response data and experimental vibration data, the rationality of the theoretical model is proved. On this basis, the main vibration frequencies are analyzed, and then the vibration intensity and structural noise are assessed for the gearbox system.
5). Based on calculation method of military specification, combined with the vibration parameters of the large marine gearbox system, DDAM design shock spectrum of natural frequencies is produced. Then the DDAM design shock spectrum was fitting into dual-polyline shock response spectrum, which is exerted as excitation of under-water explosion to the foundation of the gearbox system. After that, the response peak values of acceleration, velocity, displacement and stress for the marine gearbox of vertical, athwartship and fore-aft loading directions are computed.
6). Mapping relationship between nodes and elements of each sub-system and entire assembly finite element system is established. Synthetic method is derived to combine the static stress under normal working condition and dynamic stress obtained from response spectrum analysis. Then, this method is used to assess the safety performance for the gearbox system under under-water explosion. At last, damping sinusoid method is used to fitting the time domain explosion shock signal from the shock response spectrum, and the time domain signal is utilized to analyze the transient response characteristics of the gearbox system.
7). Topology optimization technology was introduced to improve the structural design and optimization for the gearbox. The objective function of dynamic response was derived according to the actual operation condition and dynamic performance analysis method. Multi-constraint and multi-objective optimized model was established according to the SIMP algorithm optimization criteria. After optimization analysis, optimized improvement was done to the gearbox structure.
引文
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