载荷分流式多级行星齿轮传动参数优化设计（“研究生论坛”稿件）

提出了一种风电增速箱用载荷分流式两级行星齿轮新型传动机构,应用转化机构法和行星齿轮传动构件速度间的普遍公式,求得了该新型传动机构的总传动比公式。研究表明,传动比随着两级行星排特性参数的取值的增加而增大,在区间[3,8]之间传动比最大取值为73。在此基础上对载荷分流三级行星传动系统的参数优化问题进行了研究。结果表明,给出的优化设计方法和得到的优化设计参数,能够显著的降低载荷分流式风电增速箱多级传动系统的体积。     

同轴对转行星齿轮传动系统的固有特性

以同轴对转行星齿轮传动系统为研究对象,为揭示其固有特性,基于齿轮系统动力学和Lagrange方程建立了同轴对转系统的平移-耦合动力学模型。根据同轴对转系统的相关参数进行特征值问题的求解,得到系统的固有频率与振型矢量。分析结果表明系统存在3种不同的振动模式:定轴轮系振动模式、差动轮系振动模式和耦合振动模式。同时讨论了随着差动轮系行星轮个数的增加,系统固有频率的重根数与差动轮系行星轮个数的关系。最后分析了耦合刚度对系统振动特性的影响。     

级间耦合刚度对行星传动系统灵敏度的影响分析

考虑行星传动中内齿圈的弹性变形及其切向和径向刚度约束的弹性基,通过级间耦合的方法建立了某混合动力系统中两级行星齿轮机构在弹性支承下的刚柔耦合混合动力学模型,基于所建模型,采用有限差分法并结合模态能量研究了四行星轮传动系统的固有频率对级间耦合刚度的灵敏度,研究结果表明:Ⅰ/Ⅱ级耦合扭转振动模式的固有频率随着第Ⅰ级内齿圈与第Ⅱ级行星架间耦合刚度、第Ⅰ级太阳轮与第Ⅱ级太阳轮间耦合刚度变化而变化,且固有频率的灵敏度程度随级间耦合刚度的增大而减小,其他各振动模式的固有频率均保持不变;模态能量分析验证了上述结论.     

单齿裂纹行星轮系合成刚度的劣化特性

行星轮系由于结构复杂,其齿面损伤对系统动态特性的影响不易评估,因而为行星轮系的故障诊断带来很大障碍.以某NGW21型行星齿轮减速器为研究对象,在内齿圈固定的前提下,研究了健康轮系的刚度合成方法以及齿面损伤条件下的刚度劣化行为.采用能量法获得了行星轮与太阳轮和内齿圈单独啮合时的刚度分布曲线,进而基于轮系内部的运动关系和各行星轮之间的相位关系,建立了多点同时啮合工况下的轮系刚度合成方法.针对太阳轮、内齿圈分别存在不同深度裂纹的情况,探讨了裂纹齿轮与行星轮单独啮合时的刚度分布,并最终对同一行星轮参与的内、外啮合刚度进行了合成.结果表明:太阳轮裂纹引起的整体刚度劣化更为明显,将更显著地影响行星轮系的响应特性.     

风电增速箱行星轮系瞬态接触动力学分析

增速箱是风电装备中的关键部件,其传动方式多为复合行星轮系传动,行星轮系接触应力影响增速箱的工作性能。设计了功率分流式行星差动结构的5.5 MW增速箱,利用UG对低速级斜齿行星轮系进行模型简化处理,利用ANSYS Workbench建立了刚柔混合有限元模型,设置了合理的运动副和接触关系,完成了瞬态接触动力学分析,对计算得到的接触应力进行了分析,并与许用应力值850 MPa进行了比较,验证了行星轮系的结构设计满足要求。     

考虑多体承载啮合斜齿行星齿轮动载特性分析

斜齿行星传动在高速重载场合中应用越来越广泛,其动载特性研究对减振降噪具有重要意义。正确地描述行星齿轮系统的啮合刚度和啮合误差是进行动力学分析的前提,为此,紧密结合齿轮几何分析与力学分析,提出行星齿轮承载接触分析技术,获得各齿轮副的耦合时变啮合刚度,并计算其啮合冲击力,为行星齿轮动力学深入分析奠定基础;其次,应用集中参数法建立考虑齿轮副安装误差、刚度激励及啮合冲击激励的斜齿行星传动啮合型弯-扭-轴动力学模型,采用数值法求解系统的动载特性。表明：考虑啮合冲击激励时,随转速的增加动载荷增加更为明显;共振转速附近,啮合冲击对动态啮合力的影响较小;安装误差特别是中心距误差是引起各齿轮副啮合刚度不同的主要原因,其进一步导致了系统的共振转速变多;行星轮浮动可以明显降低共振转速处的动载荷,由于各外（内）齿轮副刚度的不同,随转速的增加行星轮浮动使得部分齿轮副的动态啮合力明显降低。     

空间机械臂用多级2K-H行星传动系统模块化动力学研究

多级行星传动系统的动力学研究多采用整体式建模方法,此种方法不便于通过动态性能分析快速选取传动方案,而且模型不具有通用性,传动形式改变,需要重建系统动力学模型。为克服整体式建模方法的缺点,提出了模块化思想,将多级行星传动系统划分为4个分级子模块,综合考虑啮合刚度、阻尼和行星轮支撑刚度等因素,建立了各级子模块的动力学模型,通过各级模块的集成,得到了多级行星传动系统非线性动力学方程。以空间机械臂关节用多级行星传动系统为例,通过调用各级模块,形成4级行星传动系统动力学微分方程组,对其进行数值求解,得到了系统的时域及频域响应特性。通过与整体式建模方法所得响应结果进行对比,验证了模块化建模方法的同一性和有效性。     

双电机耦合驱动系统低速档扭转振动特性分析

以某新型双电机耦合驱动系统为研究对象,考虑齿轮副综合啮合刚度、各构件惯量、中心构件的扭转支撑刚度等因素,推导并建立了双电机耦合驱动系统的纯扭转动力学模型.通过求解特征值的方法获取系统固有特性.对系统整体扭转振动模式和轴系扭转振动模式下的固有特性进行分析,发现系统固有特性具有一种不完全的对称性.对系统固有频率的主要影响因素进行了研究,分析了系统共振点与车速之间的对应关系.建立了双输入双输出机电耦合系统振动特性分析方法,为双电机耦合驱动系统的扭振抑制控制方法的研究奠定了基础.     

基于有限元的齿轮传动系统动力修改研究

建立了考虑轮齿啮合刚度的斜齿轮传动系统弯-扭-轴-摆耦合振动有限元模型,阐述了基于有限元的动态特性灵敏度分析及结构动力修改方法.对斜齿轮传动系统耦合振动有限元模型进行了模态分析,在此基础上对系统进行了动态特性灵敏度分析,提出了一种改善动态特性的齿轮传动系统动力修改方法,为结构动力修改理论在工程实践中的应用作了有益的尝试.     

齿轮传动系统扭振特性的灵敏度分析

本文研究了齿轮传动系统扭振固有频率及频响函数的设计灵敏度问题。对齿轮传动系统扭振动力学控制方程中时变的齿轮啮合刚度进行了分解．推导了系统扭振固有频率及频响函数相对于设计参数的灵敏度计算公式，这些设计参数可以是轴的扭转刚度、齿轮平均啮合刚度、阻尼及齿轮转动惯量等。这一方法可用于齿轮传动系统动力学优化设计。     

Structure vibration characteristics of two stage double helical tooth planetary gear trains with unequally spaced planets and stars

A computational model of two stage double helical tooth planetary gear set is employed to built the lateral torsional coupling dynamic governing equations. Base on the dynamic equation, the free vibration properties of the system with unequally spaced planets and stars are analyzed. The vibration modes are classified into three types: star mode, planet mode, and coupling mode. For each of the modes, the relation between inherent frequency and vibration amplitude is investigated in detail by the eigenvalue and mode characteristics.     

Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train

A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.     

Analysis of the Relationship Between the Meshing Stiffness and the Inherent Characteristics of Planetary Gear Transmission Mechanism

According to the relationship between the meshing stiffness and the inherent characteristics of a seven-speed three-row coupled planetary transmission mechanism, a equivalent concentrated mass dynamics model of the planetary transmission mechanism is established. The natural frequency of the planetary gear train at a specific gear is calculated and extracted. The relationship between the meshing stiffness of each row and the natural frequency of the system is analyzed, thereby avoiding possible resonance behavior by changing the meshing stiffness. These results show that the meshing stiffness, in its range of possible values, has nearly no effect on the low order natural frequency (<4.000.Hz), and that the time-varying meshing stiffness mainly affects the natural frequencies of the higher- and middle-order parts of the system. Changes of the natural frequencies lead to the change of the system''s corresponding vibration mode, which will change the vibration situation of the system.     

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton''s second law, the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established. According to the principle of tooth profile modification, the tooth profile modification is considered as time-varying gear backlash function acting along the line of action. Then the dynamic functions are solved by using Runge-Kutta numerical method. After analyzing the effect of tooth profile modification quantity(TPMQ) and relative tooth profile modification length(TPML) to the nonlinear dynamic characteristics of power split gear transmission, the following conclusions are drawn: ①The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage, and the coupling effect between two stages can be ignored usually in the modification design; ②If the first stage TPMLs are less than 0.3, the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration, or else both the first and second stage TPMLs affect the first stage transmission vibration largely. The same is true for the second stage TPMLs, and the cutoff value is 0.2; ③The TPMQ affects the vibration of power split gear transmission system more principally than the TPML, and should be top-priority in the modification design.     

斜齿圆柱齿轮传动的固有振动特征

在综合考虑斜齿轮啮合刚度、轮辐弯扭刚度以及传动轴－轴承支承刚度的基础上,建立了斜齿轮副的耦合振动模型,介绍了系统刚度的计算方法,分析了系统的固有振动特征及其螺旋角的影响,实例分析结果表明：螺旋角不仅引起斜齿轮复杂的耦合振动,而且它的变化将会造成斜齿轮轴向、扭摆共振频率比较大的改变,而对径向共振频率的影响不大;斜齿轮的径向和扭转共振会造成齿轮很大的动载荷,而轴向共振的这种影响则不显著。     

Theoretical and experimental study on non-linear vibration characteristic of gear transmission system

In order to investigate the vibration of gear transmission system with clearance, a vibratory test-bed of the gear transmission system was designed. The non-linear dynamic model of the system was presented, with consideration of the effects of nonlinear dynamic gear mesh excitation, flexible rotors and bearings. Integration method was used to investigate the non-linear dynamic response of the system. The results imply that when the mesh frequency is near the natural frequency of gear pair, it is the first primary resonance, the bifurcation appears, and the vibration becomes to be chaotic motion rapidly. When the speed is close to the natural frequency of the first-order bending vibration, it is the second primary resonance, the periodic motion changes to chaos by period doubling bifurcation. The vibratory measurement of test-bed of the gear transmission system was performed. Accelerometers were employed to measure the high frequency vibration. Experimental results show that the vibration acceleration of the gear transmission system includes mesh frequency and sideband. The numerical calculation results of low speed can be validated by experimental results basically. It means that the presented non-linear dynamic model of the gear transmission system is right.     

含弹性支撑的船用减速器箱体动态特性

为分析弹性支承对船用减速器动态特性的影响,提高其动态性能,综合考虑齿轮时变啮合刚度、齿轮偏心误差及啮合误差等因素的影响,依据各零件作用力传递关系,建立传动系统动力学模型,计算系统动态激励．采用有限元法构建齿轮箱稳态动响应分析模型,应用弹簧单元对其底部支撑进行模拟,依据自编制动响应求解流程,对齿轮箱在系统动激励作用下的稳态响应进行求解,得到齿轮箱节点振动加速度响应时域历程及其频谱．引入齿轮箱隔振系统频率比概念,分析支撑刚度对齿轮箱振动传递及倾斜变形的影响,发现当频率比为2～3时可达到较好的支撑效果,为齿轮箱的设计提供了理论依据．