功率分流行星齿轮传动系统动态及均载特性研究
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摘要
功率分流行星齿轮传动系统是船舶后传动装置的重要组成部分。整个传动系统由差动轮系和星型轮系组合而成，是船舶设备中的主要噪声源之一，研究该传动系统的功率分流及动态特性对降低船舶振动噪声、改善动态特性具有重要意义。
本文建立了功率分流行星齿轮传动系统多自由度耦合非线性动力学模型。在系统动力学建模过程中充分考虑了各齿轮啮合副的时变啮合刚度、啮合误差以及阻尼等非线性因素，同时考虑了各支撑轴承的支撑刚度，利用集中质量参数法建立了行星传动系统的非线性动力学模型。文中研究了齿轮副啮合刚度和啮合误差激励的计算方法，并通过行星传动系统的静态啮合刚度试验，对啮合刚度的计算方法进行试验验证；啮合综合误差通过啮合线增量的形式来描述。系统动力学模型的建立为后续研究工作的开展奠定了理论基础。
本文在行星传动系统动力学模型的基础上，对功率分流行星传动系统的分流特性进行了研究。文中研究了系统静态均载系数和动态均载系数的计算方法，研究了制造误差和安装误差对传动系统各级之间的均载系数的影响，获得了各种误差在影响系统均载特性中的影响比重，为提高均载特性提供理论依据；最后研究了系统输入功率、输入转速、行星轮个数变化时对各级均载系数的影响。
本文采用Runge-Kutta数值积分法对无量纲化后的动力学方程进行求解，应用时域历程响应、相图、Poincare映射和分岔图等分析手段，对传动系统的非线性动力学响应进行了深入研究，得到了各种稳态响应相互间的转化规律，重点研究了啮合刚度、啮合误差及阻尼比等因素对动态特性的影响。
本文在行星齿轮传动系统修形研究方面，首先对单对轮齿进行轮齿接触分析，在此基础上，以系统传动误差最小为目标函数对轮齿进行优化修形研究，文中应用齿轮修形试验进行试验验证。
文中最后将上述修形理论应用于行星齿轮传动系统，分析修形对行星传动系统动态特性的影响，分析结果表明，修形后齿轮系统的传动误差波动得到明显降低，这使得行星齿轮传动系统的动态特性得到明显改善。
The split power planetary gear transmission system is one of the most importantcomponents in the ship drive sysyem. The entire system is composed of a differential stage anda closed stage gear transmission system; gear transmission is the important noise source. It hasan important signification to research dynamic and split power to reduce noise of warship.
The multiple degrees of freedom coupling nonlinear dynamics model of the split powerplanetary gear transmission system is constructed. The process of dynamics model constructionconsiders the nonlinear element of transmission system; the nonlinear element includestime-varying mesh stiffness, meshing error, damping and bearing support stiffness and so on,the nonlinear dynamics model is builded of the entire transmission system by the lumped massparameter method. The mesh stiffness and meshing error excitations of gear train must becomputed in process of dynamics analysis. The static stiffness experiment is carried out of theplanetary transmission to test and verify the stiffness computing method; the time varyingmeshing error can be expressed by the increment method of mesh action line. The constructionof system dynamics model is the foundation to the following research.
The power distribution characteristics are researched of split power planetary geartransmission system on the basis of the system dynamics model. In the paper, the statics loadsharing characteristics and dynamics sharing characteriscs are studied firstly. The relation isresearched between manufacture errors, assembly error and the transmission system loadsharing coefficient and some valuable conclusion will be obtained. At last, the influence isstudied of input power, input speed, the number of planet gear to load sharing coefficient ofsub-system.
The dimensionless dynamics differential equation is solved by the Runge-Kutta numericalintegral method, the nonlinear dynamics response of the transmission system is researchedprofoundly by the displacement of the time domain response, phase diagram, Poincare map andbifurcation diagram. The system parameters include mesh stiffness, mesh error and dampingratio.
The contact analysis of single gear train is studied on the gear modification research of planetary transmission system and the gear optimization modification is researched accordingto transmission error lowest on the basis of structure characteristic. Modification experiment iscarried out of the helical gear to testify validity of the modification method.
At last, the optimization modification method is applied to planetary gear transmissionsystem and the dynamics characteristics are compared of differential class transmission systemunder gear modified and unmodified. The results show that transmission error fluctuation isreduced when gear is modified, it can improve obviously dynamics characteristics of gearsystem, they include mesh stiffness and mesh dynamics load and gear surface stress and so on.
本文建立了功率分流行星齿轮传动系统多自由度耦合非线性动力学模型。在系统动力学建模过程中充分考虑了各齿轮啮合副的时变啮合刚度、啮合误差以及阻尼等非线性因素，同时考虑了各支撑轴承的支撑刚度，利用集中质量参数法建立了行星传动系统的非线性动力学模型。文中研究了齿轮副啮合刚度和啮合误差激励的计算方法，并通过行星传动系统的静态啮合刚度试验，对啮合刚度的计算方法进行试验验证；啮合综合误差通过啮合线增量的形式来描述。系统动力学模型的建立为后续研究工作的开展奠定了理论基础。
本文在行星传动系统动力学模型的基础上，对功率分流行星传动系统的分流特性进行了研究。文中研究了系统静态均载系数和动态均载系数的计算方法，研究了制造误差和安装误差对传动系统各级之间的均载系数的影响，获得了各种误差在影响系统均载特性中的影响比重，为提高均载特性提供理论依据；最后研究了系统输入功率、输入转速、行星轮个数变化时对各级均载系数的影响。
本文采用Runge-Kutta数值积分法对无量纲化后的动力学方程进行求解，应用时域历程响应、相图、Poincare映射和分岔图等分析手段，对传动系统的非线性动力学响应进行了深入研究，得到了各种稳态响应相互间的转化规律，重点研究了啮合刚度、啮合误差及阻尼比等因素对动态特性的影响。
本文在行星齿轮传动系统修形研究方面，首先对单对轮齿进行轮齿接触分析，在此基础上，以系统传动误差最小为目标函数对轮齿进行优化修形研究，文中应用齿轮修形试验进行试验验证。
文中最后将上述修形理论应用于行星齿轮传动系统，分析修形对行星传动系统动态特性的影响，分析结果表明，修形后齿轮系统的传动误差波动得到明显降低，这使得行星齿轮传动系统的动态特性得到明显改善。
The split power planetary gear transmission system is one of the most importantcomponents in the ship drive sysyem. The entire system is composed of a differential stage anda closed stage gear transmission system; gear transmission is the important noise source. It hasan important signification to research dynamic and split power to reduce noise of warship.
The multiple degrees of freedom coupling nonlinear dynamics model of the split powerplanetary gear transmission system is constructed. The process of dynamics model constructionconsiders the nonlinear element of transmission system; the nonlinear element includestime-varying mesh stiffness, meshing error, damping and bearing support stiffness and so on,the nonlinear dynamics model is builded of the entire transmission system by the lumped massparameter method. The mesh stiffness and meshing error excitations of gear train must becomputed in process of dynamics analysis. The static stiffness experiment is carried out of theplanetary transmission to test and verify the stiffness computing method; the time varyingmeshing error can be expressed by the increment method of mesh action line. The constructionof system dynamics model is the foundation to the following research.
The power distribution characteristics are researched of split power planetary geartransmission system on the basis of the system dynamics model. In the paper, the statics loadsharing characteristics and dynamics sharing characteriscs are studied firstly. The relation isresearched between manufacture errors, assembly error and the transmission system loadsharing coefficient and some valuable conclusion will be obtained. At last, the influence isstudied of input power, input speed, the number of planet gear to load sharing coefficient ofsub-system.
The dimensionless dynamics differential equation is solved by the Runge-Kutta numericalintegral method, the nonlinear dynamics response of the transmission system is researchedprofoundly by the displacement of the time domain response, phase diagram, Poincare map andbifurcation diagram. The system parameters include mesh stiffness, mesh error and dampingratio.
The contact analysis of single gear train is studied on the gear modification research of planetary transmission system and the gear optimization modification is researched accordingto transmission error lowest on the basis of structure characteristic. Modification experiment iscarried out of the helical gear to testify validity of the modification method.
At last, the optimization modification method is applied to planetary gear transmissionsystem and the dynamics characteristics are compared of differential class transmission systemunder gear modified and unmodified. The results show that transmission error fluctuation isreduced when gear is modified, it can improve obviously dynamics characteristics of gearsystem, they include mesh stiffness and mesh dynamics load and gear surface stress and so on.
引文
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