【作者】 李文良；

【导师】 王黎钦；

【作者基本信息】 哈尔滨工业大学 ， 机械设计及理论， 2013， 博士

【摘要】 齿轮是机械系统中重要的传递运动和动力的机械元件，随着传动系统的高速、高效、精密、可靠、低振动、低噪声、轻量化的要求越来越高，齿轮的工作性能对整个传动系统的影响也会越来越大。在航空航天、舰船、机械等行业，齿轮正朝着高速、重载方向发展，其动态特性引起研究人员的广泛关注。由于我国齿轮行业的振动噪声等动态特性不足较发达国家的严重，因此传动系统中尤其斜齿轮的动态特性研究是现阶段工程实际中急需要解决的问题，但在该领域中国内的研究更多的忽略了齿面摩擦对动态特性的影响，国外近年研究表明齿面摩擦对齿轮传动动态特性的影响是不可忽略的。本文主要以斜齿轮传动作为研究对象，分析在考虑齿面摩擦时斜齿轮的动态特性。研究结果对于认识复杂的斜齿轮传动的动态性能、进行动态优化设计具有重要的理论和实际应用价值，也为齿轮传动及其转子系统的动态特性分析提供理论基础，为传动系统的可靠性以及减振降噪分析提供技术支持。本文首先根据齿轮啮合理论推导出计算斜齿轮时变接触线的改进数值算法，该算法突破了文献计算时变接触线的限制条件，扩大了数值计算斜齿轮时变接触线的适用范围，算法准确、快速、方便实用，为时变摩擦力、时变摩擦转矩以及时变啮合刚度的计算和频响分析、误差分析等动态特性分析奠定基础。分析斜齿轮时变接触线的变化规律并揭示出接触线总长度变化最小的条件：初始时刻当L1(啮合起始时刻接触线上端距离啮合区右端最短距离)和端面齿距相等，且L2(啮合起始时刻接触线上端距离啮合区左端最短距离)和L4(啮合起始时刻接触线下端距离啮合区右端最短距离)相等时，接触线总长度不变。在时变接触线长度算法基础上考虑齿轮的混合弹流润滑状态下的摩擦影响，采用分片直齿轮法构建计算斜齿轮齿面摩擦力以及齿面摩擦转矩的算法。研究结果表明：时变接触线的波动是齿面摩擦力以及齿面摩擦转矩波动的重要原因。在本文所选的参数范围内，当螺旋角为20°时，时变接触线长度的波动、齿面摩擦力的波动和齿面摩擦转矩的波动最小。时变接触线以及齿面摩擦力、摩擦转矩的算法为齿轮的参数优化以及动态特性分析提供了更准确的基础。以能量最小原理构建了渐开线齿轮时变接触线载荷分布的数学模型，得到了齿轮沿接触线的载荷分布。直齿轮在啮合周期内双齿啮合时载荷分配率在0.33~0.67之间变化。斜齿轮沿接触线的载荷分布较直齿轮平缓，没有载荷突变。在轮齿的变形计算中考虑齿面摩擦力对变形的影响，研究结果表明：齿面摩擦对齿轮的弯曲效应随着齿廓参数的变大其影响也变得较为明显，由于节点的摩擦力方向改变，节点产生了变形突变。在此基础上计算斜齿轮的时变啮合刚度，给出考虑齿面摩擦时斜齿轮的时变啮合刚度曲线，以及时变啮合刚度的变化对振动位移的影响程度，为谐波共振分析以及齿轮传动误差分析提供了较为真实的时变啮合刚度。考虑齿面摩擦情况下构建斜齿轮动力学方程，分析了主频共振响应、2阶超频共振响应以及1/2阶次频共振响应的动力学频响特性，分析结果表明：齿面摩擦对共振幅值有抑制作用，随着摩擦系数的变大，共振幅值随之降低，共振频率略有增大。在考虑齿面摩擦情况下，动、静态载荷引起的共振幅值较无摩擦时明显的降低，静态载荷较大时发生共振的频率较无摩擦时明显变小；动态载荷、阻尼系数所引起的共振幅值较无摩擦时明显减小，但共振频率变化不大。采用整体误差理论并考虑齿面摩擦以及时变啮合刚度构建斜齿轮动力学方程。在变转速的情况下，分析载荷、阻尼对齿轮传动误差、最大啮合力以及动载系数的影响。研究结果表明：误差激励对重载齿轮的动态响应的影响较小，对高速齿轮的动态响应的影响较大，阻尼对降低误差激励引起的动态响应的影响效果较为明显。最后在传动误差引起的啮合冲击模型中考虑进齿面摩擦引起的啮合变形，给出基节误差、齿距偏差以及由齿形误差反映的齿轮精度等级对齿轮振动噪声的影响。更多还原

【Abstract】 Gears are very impoint element for motion and power transmission in mechanicalsystems. The gear dynamics performance have great influence on entire transmissionsystem, with the increasing of performance such as fast, efficient, precise, reliable, lowvibration, low noise and lightweight. With the development of aerospace, machinery,electronics and ship industries, the performance of gear look forward to high-speed,overloaded. The study of dynamic characteristics was extensive concerned by theresearchers. Noise, vibration and dynamic characteristics of the gear are more seriousthan the performance of foreign. So transmission system, especially gear dynamiccharacteristics are an urgent engineering problem to be solved. But, most researchneglect the influence of tooth friction, with the further studies the researcher realize theimportance of tooth friction and can not be ignored in recent years. This paper focuseson the helical gear pair and analyzes the dynamics performance considering the toothfriction. The results have theoretical and practical significance for complex helical geardynamic performance, and also provide a theoretical basis for dynamic performance oftransmission system and technical support in order to reduce vibrations and noise.An improved numerical algorithm is proposed in order to calculate time-varyingcontact line according to gear meshing theory. The algorithm has broken through thecalculation restrictions of numerical from literature published abroad in recent years andexpands numerical calculation application range of the conference. The algorithm has somany advantages such as accurate, fast, convenient and practical. Analyze the changelaw of time-varying and reveal the minimum fluctuation conditions of the time-varyingcontact line. The results show the fluctuation of contact line is the smallest when thelength of L1(the smallest distance from the top of contact line to the right end surface)is a transverse pitch and L2(the smallest distance from the top of contact line to the leftend surface) equal L4(the shortest distance from the bottle of contact line to the rightend surface). The gear runs stably when the change law satisfies with the minimumfluctuation conditions. An algorithm is given about the calculation of tooth frictionforce and tooth friction torque condiering the friction coefficient of elastohydrodynamiclubrication. The change laws are obtained about tooth friction force and friction torque.The results shown that the fluctuation of time-varying contact line is very importantfactor for the fluctuation of tooth friction force and tooth torque. Within the selectedparameters scope of this article the fluctuation of tooth friction force and friction torqueare small when helix angle is20°. The conclusions will provide theoretical basis todesign gears and dynamic analysis of future work of this paper. The load distribution model of involute gear was constructed along thetime-varying contact line based on the energy minimization principle. The model wasused to calculate the load distribution along the contact line. The distribution rate is0.33~0.67when spur gear run at double contact zone. The load distribution of helicalgear is smoothly then spur gear. There is no load mutation of helical gear. The contactdeformation was calculated considering the tooth friction force. The analysis resultsshow the bending effect become larger with the increasing profile parameter. There is adeformation motion at pitch point, because the direction is changed of tooth frictionforce at pitch point. According to the above work the time-varying stiffness is calculatedand analyzed considering the tooth friction force. The calculation results providetheorial basis for frequency spectrum analysis and foundation for transmission error anddynamics analysis.The dynamic function of helical gear was built considering the tooth friction force.Main frequency resonance response,1/2order frequency resonance response and2orderfrequency resonance response were analyzed. The results show the tooth friction canreduce the resonance amplitude. The resonance amplitude will decrease with increasingof friction coefficient, but the resonance frequency will become large. The resonanceamplitude of static load obviously reduces when considering the tooth friction force. Thedynamic load and damping factor can reduce effectively the resonance amplitude, but theinfluence on resonance frequency is not obvious.In this paper, the integrate error and tooth friction are considered to constructdynamic equation of helical gear pair. The results about the maximum dynamictransmission error, maximum meshing force and maximum dynamic factor are obtainedwith the different speeds. The results show that error excitations are not important forheavy-duty gear. But, error excitations are important element for heavy-duty gear. Thedamping has obviously effect for reducing the dynamic response. Finally, the noise wasanalyzed considering different tooth base error、individual circular pitch error、pitchcumulative error and gear precision when the meshing impact was caused bytransmission error.更多还原