考虑温度因素的单级直齿圆柱齿轮系统动态特性研究

发布时间：2018-03-25 07:36

  本文选题：圆柱齿轮　切入点：非线性动力学　出处：《兰州交通大学》2016年博士论文

【摘要】：齿轮系统是机械装备中应用广泛的传动装置之一,它具有结构紧凑、传动效率高、传动平稳等优点。齿轮系统的振动对其所在机械系统的稳定性、可靠性和疲劳寿命有重要的影响。研究齿轮振动产生的机理和影响齿轮振动的力学因素,对于机械设备的减振降噪,提高机械设备的使用寿命和可靠性具有重要的科学意义和工程价值。本文以某车辆系统中使用的单级直齿圆柱齿轮传动系统为研究对象,综合考虑齿轮啮合时的齿侧间隙、时变刚度、综合传递误差和齿面摩擦等因素,由简单到复杂,对单自由度齿轮扭转振动系统、齿轮-转子系统、考虑支承的三自由度齿轮系统和齿轮-转子-轴承等四种系统,分别建立不考虑温度因素和考虑温度因素两种情况下的非线性动力学模型,研究系统动态特性。主要研究内容如下:1.根据齿轮系统的特点,提出了一种改进的胞映射法。该算法根据胞映射法将所要研究的连续状态空间划分为离散的胞空间,采用简单胞映射法建立胞与胞之间的映射关系,实现对胞的初步分组;用逃逸时间算法,检验陷胞的真伪,并对陷胞的周期性重新分组;通过点映射方法检验周期胞的真伪。该改进胞映射法通过祛除陷胞影响数值计算过程,从而得到任意范围内所考察系统的精确吸引域,提高程序的计算精度,对于非光滑系统可以避免系统在切换时出现伪解和胞流扩张。2.建立综合考虑时变啮合刚度、齿面摩擦、齿侧间隙和综合传递误差等因素的单自由度齿轮系统的扭转振动动力学模型。通过计算系统最大幅值波动云图、考察参数条件下的系统位移时间映像图,分析该单自由度齿轮系统在参数平面内的动态特性。结合系统单初值分岔图、多初值分岔图和最大Lyapunov指数谱,利用改进的胞映射法分析不同参数对该系统的全局和局部动力学特性的影响。3.基于Blok闪温理论,推导出齿面接触温度随时间变化的表达式,计算主、从动齿轮的齿面闪温,计算由齿面接触温度变化导致的齿廓变形;根据Hertz接触理论,推导出啮合刚度随齿面接触温度变化的表达式。构建温度刚度,以便将温度的影响引入齿轮系统动力学模型。4.建立综合考虑齿面接触温度、时变啮合刚度、齿面摩擦、齿侧间隙和综合传递误差等因素的单自由度直齿圆柱齿轮系统非线性动力学模型。通过计算不同参数关联下的齿面最大闪现温度云图和齿面闪温随啮合点变化趋势图,分析齿面接触温度对系统动态特性的影响。结合系统单初值分岔图、多初值分岔图、相图和Poincaré映射图,利用改进的胞映射法分析不同参数对考虑温度因素的单自由度齿轮系统局部和全局动力学特性的影响。对比分析温度因素对单自由度齿轮系统的动力学特性的影响。5.将连接在齿轮输入输出轴上的电机等其他部件抽象为与齿轮轴连接的转子,建立齿轮-转子系统非线性动力学模型,计算系统动力学参数,分析啮合频率、时变刚度和综合传递误差等因素对系统非线性动力学特性的影响。将温度刚度引入该系统,建立考虑温度影响的齿轮转子系统模型,分析系统分岔、混沌运动及其动态特性。6.考虑主从动轴上轴承对齿轮的作用力及其位移,建立三自由度单级齿轮系统的扭转振动模型,借助分岔图、最大Lyapunov指数谱、Poincaré映射图和FFT频谱图等,分析系统的动力学特性。将温度刚度引入该系统,考察系统的动态特性,分析系统的动力学行为。7.建立齿轮-转子-轴承耦合系统的非线性动力学模型,分析系统的分岔与混沌、吸引子共存和动态特性。建立考虑温度因素的齿轮-转子-轴承耦合系统的非线性动力学模型,分析系统的分岔与混沌、齿面闪温变化及其动态特性。对比分析温度对该系统动力学特性的影响。研究发现系统存在Hopf分岔、擦切分岔等多种分岔形式。其中擦切运动包括齿面擦切和轴承接触面擦切等多种形式,这些擦边运动有的仅改变系统的运动轨迹而不会引起系统的运动形式的拓扑改变,有的则会引起系统发生分岔;该系统中存在大量的吸引子共存现象;系统在误差较大时的扭转振幅值较大,而选择合理的间隙能够明显减小系统的扭转振幅;如果综合传递误差系数取值也较大,系统的扭转振幅将突然增加,说明综合传递误差系数和时变刚度波动系数具有强烈的非线性耦合影响。研究发现,温度因素是齿轮系统非线性动力学研究不可忽略的因素。齿面闪温最低点位于节点附近;主动轮从齿根部分啮入和齿顶附近即将啮出时,出现较高的齿面闪温。随着频率和摩擦系数的增大,齿面最大闪温随之增大,且在啮入和啮出时出现的齿面最大闪温变化幅值也随之增大;本体温度对系统最大振幅的影响较小,而频率的变化会引起系统最大振幅的复杂变化。本文所建立的齿面闪温计算方法能够在一定程度上反映齿轮啮合时的温度变化和滑动情况,该方法在计算齿面温度变化时其基本规律是正确的。本文的研究结果对齿轮系统优化设计及参数选择具有一定的参考价值和理论意义。
[Abstract]:The gear transmission system is one of the most widely used in mechanical equipment, it has the advantages of compact structure, high transmission efficiency, has the advantages of stable transmission. The stability of vibration of gear system on the mechanical system, has an important impact on the reliability and fatigue life of gear vibration. The formation mechanism and influence of gear vibration for mechanical factors. Vibration and noise of mechanical equipment, has important scientific significance and engineering value to improve the life of machinery and equipment use and reliability. Based on a vehicle system in a single-stage spur gear transmission system as the research object, considering the tooth side gear meshing clearance, time-varying stiffness, transmission error and tooth comprehensive surface friction and other factors, from simple to complex vibration system of single degree of freedom gear reverse gear rotor system, considering the three degree of freedom gear system and gear - rotor - bearing support The four systems were established, without considering the temperature factors of the nonlinear dynamics model of two kinds of situations and considering the temperature factors and the dynamic characteristics of the system. The main contents are as follows: 1. according to the characteristics of the gear system, put forward a kind of improved cell mapping method. The algorithm is based on continuous state space division cell mapping method to study for the discrete cell space, mapping relationship between using simple cell mapping method to establish the cell and the cell, to achieve the initial grouping of cells; using the escape time algorithm and test in the cell of authenticity, and the periodical in the cell groups; through the point mapping method test periodic authenticity. The improved cell mapping method the effect of the process of numerical calculation in removing cell, to obtain a precise system of domain of attraction within any range, improve the accuracy of the program, for the non smooth system can avoid system when switching artifacts Solution and cell expansion of.2. is established considering time-varying mesh stiffness, tooth surface friction, the torsional vibration dynamic model of single degree of freedom gear system with backlash and integrated transmission error and other factors. By calculating the maximum amplitude fluctuation of cloud system parameters under the condition of displacement time map, analysis of dynamic characteristics the parameter plane of the single degree of freedom gear system. Combined with the system of a single initial bifurcation diagram, multiple initial bifurcation and the maximum Lyapunov exponent spectrum, analysis the influence of different parameters on the system of global and local dynamics of the.3. Blok flash temperature theory based on cell mapping method is improved, is derived. The tooth contact temperature change over time to calculate the main driven gear tooth surface, the flash temperature, calculate the temperature change caused by tooth contact tooth surface deformation; based on Hertz contact theory, the meshing stiffness with the tooth surface contact temperature is derived The change of expression. In order to construct temperature stiffness, the influence of temperature into the gear system dynamics model of.4. is established considering the tooth contact temperature, time-varying mesh stiffness, tooth surface friction, single degree of freedom gear system nonlinear dynamic model of gear backlash and transmission error and other factors. Through the calculation of different parameters of tooth surface maximum flash temperature charts and surface flash temperature trends with the meshing point changes, influence analysis of tooth contact temperature on the dynamic characteristics of the system. Combined with the system of a single initial bifurcation diagram, multiple initial bifurcation diagram, phase diagram and Poincar maps, analysis of the influence of different parameters on the consideration of local and global free single the degree of gear system dynamics characteristics of temperature factors using the cell mapping method improved. Comparative analysis of effect of temperature on the dynamic characteristics of single degree of freedom gear system.5. will be connected to the gear The input on the output shaft of the motor and other components are abstracted as rotor is connected with the gear shaft, a gear nonlinear dynamics of rotor system model, system dynamics calculation parameters, analysis of meshing frequency, time-varying stiffness and transmission error of comprehensive factors such as nonlinear dynamic characteristics of the system. The temperature stiffness is introduced into the system, the establishment of gear the rotor system model considering the influence of temperature, analysis the bifurcation, chaotic motion and dynamic characteristics of.6. driving force and its displacement considering the shaft bearing of the gear, we establish three degree of freedom gear torsional vibration model of the system, the bifurcation diagram, the largest Lyapunov exponent, Poincar maps and FFT spectrum. Analysis of dynamic characteristics of the system. The temperature stiffness is introduced into the system, the dynamic characteristics of the system, the.7. dynamic behavior analysis system to establish gear - rotor - bearing coupling The nonlinear dynamic model of the system, bifurcation and chaos analysis system, attractors and dynamic characteristics. The nonlinear dynamics model is established by considering the temperature factors of the gear rotor bearing system, bifurcation and chaos analysis system, surface flash characteristics and its dynamic changes in temperature. Comparative analysis of the influence of temperature on the dynamic characteristics of the system. The study found that the system has a Hopf bifurcation, tangent bifurcation and other clean forms. The clean cut bifurcation motion including tooth cutting and rubbing contact surface clean cut and other forms, these edge movement some only change the system's motion trajectory without causing the movement of the system in the form of topology changes, some will cause the system bifurcation; a large number of attractors phenomenon exists in the system; the system is greater in torsion of large amplitude error, and the choice of reasonable gap torsion can obviously reduce the system If the transmission error amplitude; comprehensive coefficient is larger, the torsion amplitude system will suddenly increase, indicating that transmission is strongly influenced by the nonlinear coupling coefficient and the time-varying stiffness fluctuation coefficient. It is found that the temperature factors are nonlinear dynamics of gear system research can not be ignored. The surface flash temperature lows in the node near the driving wheel; from the root of meshing and tooth meshing is near the top, high surface flash temperature. With the increase of frequency and coefficient of friction of tooth surface, maximum flash temperature increases, and the meshing and meshing tooth surface when the maximum flash temperature change amplitude increases smaller; the body temperature affects the system maximum amplitude, and frequency variation will cause complex changes of the system maximum amplitude. Calculation method of tooth surface of the flash temperature can reflect the temperature when the gears are engaged in a certain extent The basic law of the method is correct when calculating the change of tooth surface temperature. The results of this study have some reference value and theoretical significance for gear system optimization design and parameter selection.

【学位授予单位】：兰州交通大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH132.41
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本文编号：1662146