Effects of eccentricity defect on the nonlinear dynamic behavior of the mechanism clutch-helical two stage gear

This paper investigates the nonlinear dynamic behavior of an automotive clutch coupled with a helical two stage gear system. The nonlinear dynamic model is simulated by twenty seven degrees of freedom and including three types of nonlinearity: dry friction path, double stage stiffness and spline clearance. The utility of the proposed nonlinear model is illustrated by the industrial need to clearly identify the dynamic behavior of mechanical elements (shafts, bearings, gears, flywheel, pressure plate, hub of the clutch…) and reduce vibration. The governing nonlinear time varying motion equation formulated is resolved by the analytic Runge Kutta method.Then the modeling of the eccentricity defect located on the gear and the flywheel of the clutch is done. The effect of this defect on the nonlinear dynamic behavior of the system is investigated.     

双离合变速器预选档策略下齿轮敲击动力学分析

双离合自动变速器（Dual clutch transmission,DCT）在预选档状态下具有换档无动力中断和换档平顺等优点,然而在预选档策略下双离合自动变速器的齿轮敲击问题更加突出。以某型湿式双离合变速器为研究对象,分别建立变速器1档无预选以及预选2档下的齿轮敲击动力学模型。模型中各空套齿轮拖曳力矩包括齿轮搅油阻力矩、轴承阻力矩以及同步器阻力矩,此外,模型还考虑了变速器非功率流中未结合状态下离合器所产生的拖曳力矩。齿轮接触模型在考虑齿面弹性接触的基础上,计入了由润滑效应引起的齿隙间非线性油膜力。运用龙格库塔算法对模型求解,获得各齿轮副的动态响应。通过变速器敲击台架试验验证了动力学模型的可行性,计算结果与试验结果具有较好的一致性。对变速器齿轮动力学响应的研究结果表明：在一定角加速度激励下,变速器中空套齿轮存在明显的双面敲击现象;预选档位并不会对无预选状态下已发生敲击的齿轮副产生影响,但是预选档后,变速器非功率流分支发生改变,变速器内空套齿轮数量增多,整体上使变速器敲击问题更加突出。     

基于离散傅里叶变换与谐波平衡法的行星齿轮系统非线性动力学分析

研究了多间隙作用下行星齿轮系统的强非线性动力学行为。考虑齿轮啮合误差和时变啮合刚度,建立了2K—H型行星齿轮传动的弯扭耦合非线性动力学模型。利用离散Fourier变换(DFT)及其逆变换(IDFT)处理方程中非线性恢复力与位移坐标之间的函数关系,发展了一种可以求解多阶谐波响应的数值谐波平衡法,并用Broyden方法求解其形成的代数平衡方程组。用该方法分析齿轮非线性动力学稳态解时,啮合刚度与激励可以是任意的周期函数形式,不仅可以包含多次谐波响应,而且还可以求解系统的次谐波响应。克服了传统的解析谐波平衡法基于描述函数进行而难以求解一般周期响应和次谐波响应的缺点。作为算例,用该方法分析了行星齿轮传动的非线性频响特性,并与相应的线性系统进行了比较。     

用Lyapunov指数研究单对齿轮间隙非线性系统的动力学行为

在间隙函数为分段线性函数的单对齿轮系统非线性微分方程量纲一化的基础上，给出院 系统的精确解析解，直接从Lyapunov指数的定义出发，给出了计算最大Lyapunov指数的数值方法，作出了系统随激励频率变化时的Lyapunov指数图，并扰此判别了系统中所存在的周期和混沌吸引子，研究结果表明，Lyapunov指数确是判定齿轮系统非线性动力学状态的一种可靠的特征指标。     

Influences of stochastic perturbation of parameters on dynamic behavior of gear system

Gear systems are commonly used in vehicles, and the vibration of the gear system was paid more attention in recent years. In this paper, the dynamic behavior of gear system with stochastic perturbation of system parameters was analyzed. A stochastic nonlinear dynamic model of gear system, with consideration of the stochastic perturbation of system parameters, was established. The influences of stochastic perturbation of system parameters, such as excitation frequency, damping ratio, and backlash, on the dynamic behavior of the system were discussed. It was found that when the perturbation intensity is weak, the topological structure of the system solutions will not change, and there is no transition of the attractors. But if the perturbation intensity increases further, there will be transition between the attractors. In general, for single-DOF gear system, the multi-periodic attractor will jump to the quasi-period-1 attractor. But the quasi-period-1 attractor will not jump to other attractors. If the perturbation intensity is considerable great, bi-directional transition will occur. Yet, the probability of transition from multi-periodic attractor to quasi-period-1 attractor is greater than the probability of transition from multi-periodic attractor to other attractors. Which provide theoretical basis for effective vibration control of gear system.     

两级行星轮系分岔与混沌特性研究

建立了某设备两级行星齿轮传动系统非线性纯扭转动力学模型,模型在综合考虑时变啮合刚度、齿侧间隙与综合啮合误差等强非线性因素的基础上,推导出系统在广义坐标下的量纲一动力学方程,并采用数值积分方法对方程组进行求解,得到了系统的非线性动态响应结果,综合运用分岔图、相空间轨线和Poincáre截面研究了激励频率、啮合阻尼比对系统分岔与混沌特性的影响。结果表明：多级行星轮系在高速轻载工况下,由于齿侧间隙与时变啮合刚度等非线性因素的耦合作用使其具有丰富的非线性动力学特性;系统随激励频率的变化出现简谐运动、非简谐周期运动、拟周期运动和混沌运动等多种运动状态;系统通过Hopf分岔等多种途径由周期运动进入混沌运动;增大系统啮合阻尼比可使系统复杂运动状态区间缩小,稳定周期运动状态区间扩大。     

自动调整臂单向离合环模态分析

针对自动调整臂的自调失效现象,以单向离合器为研究对象,使用ANSYS软件对单向离合环进行模态分析,研究其固有振动特性。分析得到的低阶固有振动频率和主振型,反映了单向离合环的动力学性能。在自调系统的设计中使工作频率远离单向离合环的固有频率,避免发生共振,为自动调整臂减少自调失效、增加使用寿命提供了理论依据。     

Effect of manufacturing and assembly defects on two-stage gear systems vibration

The modeling of the dynamic behavior of a two-stage gear system is made for a general configuration of wheels location. The excitation is induced by the periodic variation of the mesh stiffness. This case describes the real working of the gearings. The variation of the mesh phasing is related to the number of teeth and also to the wheels location. We developed a plane model of a two-stage gear system. The modal analysis of the system was then treated. The calculation of the dynamic response was done by a step-by-step time integration method (Newmark algorithm). Three cases of wheels location are treated. The solutions are presented both in the frequency domain and in the time domain. Three types of geometric defects of the toothed wheels are introduced in the model: defect of eccentricity, profile error and assembly defect. An analysis of the effects of these defects on the gear system dynamic behavior is then treated.     

Nonlinear dynamic analysis of coupled gear-rotor-bearing system with the effect of internal and external excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.     

齿侧间隙对齿轮系统动力学行为的影响

为分析齿轮传动系统在齿侧间隙变化条件下的非线性动力学变化机理,对不同齿侧间隙参数下非线性齿轮传动系统的动力学行为进行了研究,建立了全齿齿侧间隙变化的齿轮传动系统非线性动力学模型,探讨了不同齿侧间隙参数条件下齿轮传动系统吸引子的变化。研究表明,齿侧间隙的变化不仅能够影响齿轮传动系统振动幅值的变化,同时,齿侧间隙的变化也能够显著改变齿轮传动系统的动力学行为,使齿轮传动系统在混沌状态与周期状态间发生跃变。研究结果能够为齿轮传动系统的设计和故障诊断提供一定的参考。     

齿轮系统周期运动稳定性研究

针对含间隙的强非线性齿轮系统动力学模型，用数值方法研究了当系统参数和初始条件变化时周期运动的稳定性。基于Floquet分岔理论将预测一校正算法用于讨论参数变化时周期解的稳定性，得到精确的分岔点参数值；通过胞映射法求得周期吸引子的吸引域，引入稳定性品质因子用以定量分析初始条件变化时周期运动的稳定性。该研究结果可为非线性动力学行为的分析和齿轮系统的设计提供参考。     

超声激励下弧齿锥齿轮研齿系统动态研磨力分析

在综合考虑超声激励和齿面几何传动误差激励的情况下，建立了有间隙的两自由度周向振动的弧齿锥齿轮研齿动力学模型，得到了齿面间动态研磨力的计算公式。通过算例分析表明，与普通研齿效果对比，超声激励增大了齿面间的动态研磨力，使齿面在啮合过程中出现了碰撞，当超声激励振幅值为16．5N·m时，超声研齿系统由周期运动进入到混沌状态。     

含时变啮合刚度的间隙非线性齿轮系统的混沌控制

基于含时变啮合刚度和间隙非线性单级齿轮系统的动力学模型,分析了系统响应的动态特性。针对系统在部分参数区域发生的混沌运动,运用OGY控制原理,以混沌吸引子内部不稳定周期轨道为目标,通过对系统的外激励参数实施连续的小扰动,使系统的轨道始终落在未加扰动的鞍点轨道的稳定流形上,从而实现了系统运动的稳定化。     

随机内外激励对齿轮系统动态特性的影响分析

考虑时变啮合刚度、齿侧间隙等因素的影响,建立了单对齿轮系统纯扭转非线性动力学模型。将齿轮综合传递误差波动和外部载荷作为随机变量,利用数值仿真方法对系统模型进行了求解,通过统计分析得到了系统各响应量和动态啮合力的统计特征。结果表明:外部激励的随机性对齿轮系统振幅和动态啮合力的影响比综合传递误差波动随机时明显;综合传递误差及外部激励随机波动离散程度的增加会导致系统振幅和动态啮合力不稳定性加剧。     

多因素条件下单级齿轮系统的非线性特性

考虑啮合刚度、齿侧间隙和轴承支撑间隙等因素,运用集中质量法建立了三自由度直齿圆柱齿轮副弯扭耦合非线性振动模型,并据此研究了各参数对齿轮系统非线性振动特性的影响。结果表明：齿侧间隙一定时,随着频率的升高,系统由周期运动通过激变直接进入混沌,然后又由混沌通过激变变为周期运动;在周期运动中,系统经过倍周期分岔,由双周期运动变为四周期运动,然后又通过逆倍周期分岔,由四周期运动变为双周期运动,之后又由双周期运动变为单周期运动;不同的输入转频条件下,间隙变化使系统表现出不同分岔特性,在某些特定频率下,间隙变化只增加系统响应能量变化,并不改变其动力学特性。     

对自动变速器中单向离合器消除降档冲击的功能分析

针对自动变速器在自动变换档位时的冲击问题进行研究,简要介绍变速原理,并在此基础上对如何采用单向离合器消除换档特别是降档时的冲击问题进行了详细阐述,并提出了消除换档冲击的几种方法。     

含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究

齿面侧隙和时变啮合刚度等因素的存在,将导致弧齿锥齿轮传动系统在工作过程中呈现典型的非线性特性;置于转子上的弧齿锥齿轮传动系统被等效处理为8自由度动力学模型,借助动态相对传动误差,使两轮转动自由度合并,建立了7自由度的非线性振动方程。采用A算符算法获得了不同工况下弧齿锥齿轮系统的扭转、横向及轴向的振动位移和速度,发现随着啮合频率的变化,系统经倍周期分岔进入混沌,而随着支承刚度的变化,系统经拟周期分岔进入混沌振动,在啮合频率的变化过程中,系统存在跳跃现象。     

齿轮系统倍周期分岔和混沌层次结构的研究

针对考虑间隙和时变啮合刚度的强非线性齿轮系统动力学模型,讨论了混乱带中倍周期分岔现象及混沌的层次结构问题。利用频谱分析法对周期运动和混沌运动进行判断,并对嵌于不同混乱带中的周期轨道进行区分。运用分频采样法求解强非线性齿轮系统主倍周期分岔序列与混沌带合并序列,以及混沌带中周期窗口和混沌窗口共存的层次结构问题。通过分析揭示了强非线性齿轮系统存在着复杂的分岔结构和普适规律,并为深入研究机械系统非线性动力学行为的性态提供参考。     

Gear rattle analysis of a torsional system with multi-staged clutch damper in a manual transmission under the wide open throttle condition

Vibro-impacts of a manual transmission in vehicle systems occur normally at the location of unloaded gear pairs, correlated with firing strokes from the engine. These vibro-impacts are possibly simulated by modeling the nonlinear dynamic characteristics and then, the problems can be resolved by efficiently designing multi-staged clutch dampers. For the sake of understanding rattle phenomena, a practical manual transmission with a front-engine and front-wheel drive configuration is investigated. First, the dynamic characteristics of the given system is examined on the basis of a modal analysis. Second, the nonlinear simulation model is developed under the wide open throttle condition by focusing on the third gear pair engaged and fifth gear pair unloaded case. Third, specific multi-staged clutch damper is examined using linear and nonlinear models, and rattle phenomena are investigated by employing a multi-staged clutch dampers with single- and dual-mass flywheels. Finally, estimation on the drag torque is conducted by assuming that the vehicle system is under the steady state condition. Thus, the rattle phenomena can be simulated under different driving conditions with the known input torque profiles.     

星形齿轮传动系统分岔与混沌的研究

迄今,未有文献详细研究复杂齿轮系统在强非线性因素激励下的混沌与分岔性态。建立了星形齿轮传动的间隙型非线性动力学模型并用数值解法进行了求解。研究了系统在改变激振频率或者齿轮副啮合阻尼比时产生的种类分岔以及通向混沌的途径。利用Poincare映射和分岔图详细描述了系统在倍周期分岔和拟周期分岔道路上吸引子由规则运动到混沌运动深化过程。发现了因变化阻尼比引起的周期倍化道路上存在的吸引子突变现象。从而首次从理论上揭示了星形齿轮系统非线性动力学行为的复杂性态。