土压平衡盾构机主减速器三级行星齿轮系统动力学
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摘要
土压平衡盾构机(Shield Tunnelling Machine, STM)是盾构法掘进施工中的关键装备,其刀盘驱动系统在掘进施工中起着驱动刀盘切割岩土的作用,它包括液压马达、主减速器、小齿轮/大齿圈减速单元。主减速器是盾构机刀盘驱动系统的核心部件,采用三级行星齿轮传动,结构复杂且功率密度高,动力学特性较为复杂。该主减速器多级行星齿轮的耦合振动会加速其疲劳失效,其动态性能对系统可靠性及整机运行稳定性有较大影响。基于动力学理论研究主减速器振动特性,并通过型式试验分析评价其动态性能,是开展盾构机整机试验及产品批量投产前的重要工作。
本课题结合国家863计划资助项目(2007AA041802)——“土压平衡盾构大功率减速器”的研究任务,并考虑到盾构机的实际工况要求和项目指南所规定的具体指标,针对土压平衡盾构机三级行星减速器的动力学问题开展了较全面深入的研究。主要研究内容包括以下方面:
①盾构机主减速器三级行星齿轮传动系统动力学
基于齿轮啮合理论和Lagrange方程,运用集中参数法建立了多级行星齿轮系统的扭转动力学模型,计算了三级行星齿轮传动系统的固有特性。采用梯形波表示啮合刚度的时变特征,分析行星齿轮啮合过程中的相位关系,计算了三级行星齿轮不同啮合位置的扭转振动结构频率。针对齿轮啮合误差特点,采用轴频和齿频叠加的谐波函数表示行星齿轮传递误差,考虑受啮合相位关系影响的行星齿轮系统时变刚度,系统地分析了多级行星齿轮传动的内部激励特征。基于某施工标段盾构机的统计负载,考虑系统的内外部激励,求解了三级行星齿轮系统的动态响应,并对齿轮振动频谱特性进行了分析。通过计算减速器不同转速下系统构件的动态响应,研究了齿轮振动与盾构机减速器输入转速的关系,为盾构机驱动系统运行工况的选择提供了依据。
②主减速器多级行星齿轮——箱体耦合动力学研究
考虑各级齿圈的扭转支撑刚度,采用集中参数法建立了多级行星齿轮—箱体的耦合扭转动力学模型。运用有限元方法获取了各齿圈的扭转支撑刚度,并在分析行星齿轮啮合相位和主要内部激励特征的基础上,求解了系统动态响应,分析了各级齿圈振动的时频特性和齿轮传动系统——箱体的耦合振动机理。
③盾构机主减速器齿轮传动系统变载工况下的动态响应
建立了土压平衡盾构机的刀盘力学模型,分析了掘进时的刀盘载荷特性。利用盾构机监控系统采集的掘进过程中刀盘承受的扭矩数据,得到主减速器的外部载荷。依据载荷数据的变化规律,运用随机插值和数据拟合得到主减速器的连续载荷谱。求解了盾构机刀盘驱动主减速器三级行星齿轮传动系统在变载荷工况下的动态响应,分析了其振动特征,并研究了主减速器传动系统振动响应与盾构机刀盘转速之间的关系。
④主减速器箱体模态分析与实验
建立了主减速器箱体的有限元模型,计算了其特征值问题,获取了箱体的低阶固有频率及相应振型。开展了主减速器箱体的模态实验,运用最小二乘复频域法分析了模态数据,得到了箱体的固有特性,并通过模态置信判据验证了实验模态参数。通过对比理论分析结果和实验数据,验证了模态参数识别的可靠性和有效性。根据模态分析结果确定了箱体的薄弱环节,为结构优化提供了依据。
⑤盾构机主减速器动态性能测试与分析
根据实验模态分析方法,进行了主减速器的模态实验,获取了系统的频响函数及模态频率。依据盾构机三级行星减速器大传动比的工作特性,采用背靠背能量回馈的试验台架,设计了动态性能测试方案。测量了多种工况载荷下主减速器的振动加速度,分析了其振动特性,计算了主减速器的1/3倍频程结构噪声。采用数值积分法计算了主减速器的振动速度和振动烈度,对主减速器的动态性能进行综合评价。对比分析了各级齿圈的振动计算结果和测试数据,验证了所建立的多级行星齿轮—箱体耦合扭转动力学模型的正确有效性。在采用隔声罩降低背景噪声的条件下,运用声压法进行了主减速器的噪声测试和声压级确定,同时采用声强法对主减速器台架运行的噪声强度分布进行了测量。
Earth pressure balance (EPB) shield tunnelling machine (STM) is a key equipment in shield excavation project, and its main driving system is to drive the cutter head cutting rock and soil, which includes hydraulic motor, main reducer and pinion-ring unit. The main reducer with three-stage planetary gears train (PGT) is the primary part of the driving system. The dynamic behaviors of main reducer are more complex because of the demand for high power density, and the coupling vibration would accelerate its fatigue failure, which has a great effect on system reliability and whole performance. It is an important work before production to study the vibration property of main reducer by dynamic theory and testing.
According to the research task of national 863 program (2007AA041802)“EPB STM high-power reducer”, and considering the practical operating condition of STM and the guide line of project, for the three-stage planetary gearbox used in EPB STM, the dynamic problems are investigated fairly comprehensively and deeply in this dissertation. The main researches are as following:
①Dynamics of 3-stage planetary gears train of STM main reducer
According to gear mesh theory and Lagrange equation, the torsional dynamic model for multi-stage PGT is developed by lumped-parameter method, and the natural characteristics of 3-stage PGT are computed. Trapezoid waves are used to express the time-varying mesh stiffness, and the mesh phasing relations among planetary gears are analyzed. For the 3-stages planetary gears of shield tunnelling machine, the torsional vibration frequencies are calculated at the different mesh position of sun-planet-ring gearing. According to the characteristics of the gears mesh errors, the harmonic waves with composite shaft frequencies and mesh frequencies are presented to describe the transmission errors of the planetary gears. Considering the time-varying mesh stiffness with different mesh phases of planet gears, the inner excitations of 3-stages planetary gears are analyzed systematically. The dynamic responses of the 3-stages planetary gears are simulated under the inner and external excitation got from a statistical load, and the spectrum properties of gears vibration are also analyzed. The dynamic response of system components are calculated under different speeds for the reducer, and the relationship between gears vibration and the rotational speed of the reducer is studied, which provides the base for choosing the suitable operating condition of driving system of the shield tunnelling machine.
②Coupling dynamics of multi-stage PGT—housing of main reducer
Considering the torsional support stiffnesses of ring gears, the coupling torsional dynamic model for multi-stage PGT-housing is developed by lumped-parameter method. The torsional support stiffnesses of ring gears are obtained by using the FE method. Based on the analysis of mesh phase and inner excitations, the system dynamic response and time-frequency characteristics of ring gears are analyzed, and then realize the vibration coupling mechanism between gears train and housing.
③The gears train dynamic response of STM main reducer under variable load
The load characteristics of cutter head are analyzed by developing the mechanical model for the cutter head of EPB shield tunnelling machine. The external load of main reducer is obtained through the torque data of cutter head from the STM control system. According to the fluctuating range and randomness of the load data, the continuous load data are simulated by using the IVS (Insert-value stochastically) and data fitting. The dynamic responses of three-stage PGT of main reducer are computed, moreover, the vibration property and the relationship between the system response and the speed of STM cutter head are investigated.
④Experimental and theoretical modal analysis on main reducer housing
The eigenvalue problem is solved by developing the FE model for the gearbox housing, and the low order natural frequencies and corresponding modes are extracted. The modal testing is made for the gearbox housing. The least-squares complex frequency-domain (LSCF) estimation method is used to analyze the modal data, and the natural characteristics of housing are obtained. According to the modal assurance criterion (MAC), the experimental modal parameters are validated. The experimental data is coincided with analytical results, which indicates the accuracy of modal parameters. Modal analysis shows the weak position, which provides a basis for structural optimization.
⑤Testing and analysis on dynamic performance of STM main reducer
The frequency responses and natural frequencies of the gearbox are obtained by modal experiment on the basis of the experimental modal analysis method. According to the large speed ratio of 3-stage planetary gearbox, the experimental project of back-to-back power circulation set-up is developed, and the test scheme is designed. The vibration properties of the gearbox are analyzed by using the acceleration data tested under different operating condition, and 1/3 octave structural borne noise have been calculated. The vibration velocities are computed, and the vibration severity is valuated synthetically. The ring gear responses from the theoretical and experimental method are successfully compared, which validates the rationality and validity of the analytical model for multi-stage PGT-housing. The sound pressure level is obtained by sound pressure testing under background noise suppressed through using the acoustic enclosure. At the same time, the sound intensity measurement is also carried out, and the sound intensity distribution is understood.
本课题结合国家863计划资助项目(2007AA041802)——“土压平衡盾构大功率减速器”的研究任务,并考虑到盾构机的实际工况要求和项目指南所规定的具体指标,针对土压平衡盾构机三级行星减速器的动力学问题开展了较全面深入的研究。主要研究内容包括以下方面:
①盾构机主减速器三级行星齿轮传动系统动力学
基于齿轮啮合理论和Lagrange方程,运用集中参数法建立了多级行星齿轮系统的扭转动力学模型,计算了三级行星齿轮传动系统的固有特性。采用梯形波表示啮合刚度的时变特征,分析行星齿轮啮合过程中的相位关系,计算了三级行星齿轮不同啮合位置的扭转振动结构频率。针对齿轮啮合误差特点,采用轴频和齿频叠加的谐波函数表示行星齿轮传递误差,考虑受啮合相位关系影响的行星齿轮系统时变刚度,系统地分析了多级行星齿轮传动的内部激励特征。基于某施工标段盾构机的统计负载,考虑系统的内外部激励,求解了三级行星齿轮系统的动态响应,并对齿轮振动频谱特性进行了分析。通过计算减速器不同转速下系统构件的动态响应,研究了齿轮振动与盾构机减速器输入转速的关系,为盾构机驱动系统运行工况的选择提供了依据。
②主减速器多级行星齿轮——箱体耦合动力学研究
考虑各级齿圈的扭转支撑刚度,采用集中参数法建立了多级行星齿轮—箱体的耦合扭转动力学模型。运用有限元方法获取了各齿圈的扭转支撑刚度,并在分析行星齿轮啮合相位和主要内部激励特征的基础上,求解了系统动态响应,分析了各级齿圈振动的时频特性和齿轮传动系统——箱体的耦合振动机理。
③盾构机主减速器齿轮传动系统变载工况下的动态响应
建立了土压平衡盾构机的刀盘力学模型,分析了掘进时的刀盘载荷特性。利用盾构机监控系统采集的掘进过程中刀盘承受的扭矩数据,得到主减速器的外部载荷。依据载荷数据的变化规律,运用随机插值和数据拟合得到主减速器的连续载荷谱。求解了盾构机刀盘驱动主减速器三级行星齿轮传动系统在变载荷工况下的动态响应,分析了其振动特征,并研究了主减速器传动系统振动响应与盾构机刀盘转速之间的关系。
④主减速器箱体模态分析与实验
建立了主减速器箱体的有限元模型,计算了其特征值问题,获取了箱体的低阶固有频率及相应振型。开展了主减速器箱体的模态实验,运用最小二乘复频域法分析了模态数据,得到了箱体的固有特性,并通过模态置信判据验证了实验模态参数。通过对比理论分析结果和实验数据,验证了模态参数识别的可靠性和有效性。根据模态分析结果确定了箱体的薄弱环节,为结构优化提供了依据。
⑤盾构机主减速器动态性能测试与分析
根据实验模态分析方法,进行了主减速器的模态实验,获取了系统的频响函数及模态频率。依据盾构机三级行星减速器大传动比的工作特性,采用背靠背能量回馈的试验台架,设计了动态性能测试方案。测量了多种工况载荷下主减速器的振动加速度,分析了其振动特性,计算了主减速器的1/3倍频程结构噪声。采用数值积分法计算了主减速器的振动速度和振动烈度,对主减速器的动态性能进行综合评价。对比分析了各级齿圈的振动计算结果和测试数据,验证了所建立的多级行星齿轮—箱体耦合扭转动力学模型的正确有效性。在采用隔声罩降低背景噪声的条件下,运用声压法进行了主减速器的噪声测试和声压级确定,同时采用声强法对主减速器台架运行的噪声强度分布进行了测量。
Earth pressure balance (EPB) shield tunnelling machine (STM) is a key equipment in shield excavation project, and its main driving system is to drive the cutter head cutting rock and soil, which includes hydraulic motor, main reducer and pinion-ring unit. The main reducer with three-stage planetary gears train (PGT) is the primary part of the driving system. The dynamic behaviors of main reducer are more complex because of the demand for high power density, and the coupling vibration would accelerate its fatigue failure, which has a great effect on system reliability and whole performance. It is an important work before production to study the vibration property of main reducer by dynamic theory and testing.
According to the research task of national 863 program (2007AA041802)“EPB STM high-power reducer”, and considering the practical operating condition of STM and the guide line of project, for the three-stage planetary gearbox used in EPB STM, the dynamic problems are investigated fairly comprehensively and deeply in this dissertation. The main researches are as following:
①Dynamics of 3-stage planetary gears train of STM main reducer
According to gear mesh theory and Lagrange equation, the torsional dynamic model for multi-stage PGT is developed by lumped-parameter method, and the natural characteristics of 3-stage PGT are computed. Trapezoid waves are used to express the time-varying mesh stiffness, and the mesh phasing relations among planetary gears are analyzed. For the 3-stages planetary gears of shield tunnelling machine, the torsional vibration frequencies are calculated at the different mesh position of sun-planet-ring gearing. According to the characteristics of the gears mesh errors, the harmonic waves with composite shaft frequencies and mesh frequencies are presented to describe the transmission errors of the planetary gears. Considering the time-varying mesh stiffness with different mesh phases of planet gears, the inner excitations of 3-stages planetary gears are analyzed systematically. The dynamic responses of the 3-stages planetary gears are simulated under the inner and external excitation got from a statistical load, and the spectrum properties of gears vibration are also analyzed. The dynamic response of system components are calculated under different speeds for the reducer, and the relationship between gears vibration and the rotational speed of the reducer is studied, which provides the base for choosing the suitable operating condition of driving system of the shield tunnelling machine.
②Coupling dynamics of multi-stage PGT—housing of main reducer
Considering the torsional support stiffnesses of ring gears, the coupling torsional dynamic model for multi-stage PGT-housing is developed by lumped-parameter method. The torsional support stiffnesses of ring gears are obtained by using the FE method. Based on the analysis of mesh phase and inner excitations, the system dynamic response and time-frequency characteristics of ring gears are analyzed, and then realize the vibration coupling mechanism between gears train and housing.
③The gears train dynamic response of STM main reducer under variable load
The load characteristics of cutter head are analyzed by developing the mechanical model for the cutter head of EPB shield tunnelling machine. The external load of main reducer is obtained through the torque data of cutter head from the STM control system. According to the fluctuating range and randomness of the load data, the continuous load data are simulated by using the IVS (Insert-value stochastically) and data fitting. The dynamic responses of three-stage PGT of main reducer are computed, moreover, the vibration property and the relationship between the system response and the speed of STM cutter head are investigated.
④Experimental and theoretical modal analysis on main reducer housing
The eigenvalue problem is solved by developing the FE model for the gearbox housing, and the low order natural frequencies and corresponding modes are extracted. The modal testing is made for the gearbox housing. The least-squares complex frequency-domain (LSCF) estimation method is used to analyze the modal data, and the natural characteristics of housing are obtained. According to the modal assurance criterion (MAC), the experimental modal parameters are validated. The experimental data is coincided with analytical results, which indicates the accuracy of modal parameters. Modal analysis shows the weak position, which provides a basis for structural optimization.
⑤Testing and analysis on dynamic performance of STM main reducer
The frequency responses and natural frequencies of the gearbox are obtained by modal experiment on the basis of the experimental modal analysis method. According to the large speed ratio of 3-stage planetary gearbox, the experimental project of back-to-back power circulation set-up is developed, and the test scheme is designed. The vibration properties of the gearbox are analyzed by using the acceleration data tested under different operating condition, and 1/3 octave structural borne noise have been calculated. The vibration velocities are computed, and the vibration severity is valuated synthetically. The ring gear responses from the theoretical and experimental method are successfully compared, which validates the rationality and validity of the analytical model for multi-stage PGT-housing. The sound pressure level is obtained by sound pressure testing under background noise suppressed through using the acoustic enclosure. At the same time, the sound intensity measurement is also carried out, and the sound intensity distribution is understood.
引文
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