多种载荷下齿轮弯曲强度与齿面摩擦因数的计算方法研究

【作者】 周长江；

【导师】 钟志华； 韩旭；

【作者基本信息】 湖南大学 ， 机械工程， 2013， 博士

【摘要】 齿轮是重要的基础件，其设计与制造水平影响到机械装备的性能和可靠性。开展齿轮强度和齿面摩擦的计算与试验研究，对于增大承载能力、提高疲劳寿命、减少摩擦磨损、改善传动性能等具有显著的意义。关于齿轮弯曲强度和齿面摩擦的计算和试验研究较多，以下问题值得探索：多种荷载下齿轮弯曲强度计算的精确建模方法，齿根应力和轮齿变形的数值计算；能够表征齿面多样的摩擦润滑性态及其变化规律的过程模型，齿面关键摩擦参数的普适计算方法；基于啮合理论与摩擦学、接触动力学等交叉的齿面冲击摩擦机理及定量计算等。基于上述问题的思考并结合作者承担的相关课题，提出了本论文的研究论题。重点研究三个问题：多种荷载下齿轮弯曲强度计算的精确建模方法；齿面摩擦润滑的多态性模型与计算方法；齿面摩擦力与摩擦因数的普适量化计算方法。主要研究内容和创新点如下：1.对齿轮有限元精确建模与弯曲强度计算方法进行了研究，通过比较研究验证了上述方法的正确性。根据齿轮展成加工原理和坐标系矩阵变换法推导出齿形曲线，基于纯文本数据文件的APDL与MATLAB的混合建模方法，实现了齿轮几何模型的精确建模。基于含误差与变形的计算模型，推导出弯曲强度计算力点的位置判别式，可作为弯曲强度计算力点选取的参考。研究了齿轮弯曲强度有限元计算的多种有效荷载，通过对不同荷载下齿根峰值应力和轮齿变形的比较研究发现：按集中力、线分布力、Hertz接触面分布力、静态接触力的次序，计算结果的精确性不断提高；移动负荷的动载等效分析，较难体现啮合冲击效应。2.研究了齿间载荷叠加效应、齿高及齿宽方向的载荷分布及轮齿变形和齿根最大拉/压分布规律。研究显示：（1）相邻齿对啮合引起的力叠加效应，在齿轮强度精确计算中不能忽略，啮合力叠加效应对中心齿受压侧的影响大于受拉侧，并使轮齿最大变形进一步增大。（2）均布荷载、三角分布和三次抛物线分布荷载作用下，齿宽方向的齿根峰值应力和接触区域轮齿变形的变化规律，验证了齿端刚度效应和轮齿变形及应力分布的连续性；齿向荷载的不均匀性和齿端刚度效应，使得齿根最大压/拉应力有所增大，接触区域的最大变形略有下降。3.基于虚拟仪器集成平台，提出了通过无线应变采集卡和路由器传输齿根应变数据的新方法，设计了齿根动应力无线测试台。通过多点平均法消除随机电噪声获取待测数据，将输入端和输出端的转速和转矩取平均值，作为计算模型的加载工况，保证了计算模型力边界与试验条件的一致性。测得的齿根应力变化曲线比较准确地反映了单/双啮区交变、啮合冲击及相邻啮合齿对的影响；测得的最大齿根应力与有限元计算结果及其他研究者的结论比较一致，验证了本文提出的无线测量方法及上述有限元计算模型的正确性。获取了齿面摩擦因数反求需要用到的试验样本数据，即测量应力。4.提出了齿面摩擦润滑的多态性模型。将啮合传动理论与摩擦学理论相结合，对齿轮传动中的多种摩擦润滑性态（弹流润滑、边界润滑、混合润滑、干摩擦、冲击摩擦等）的形成机理、特征及存在条件等进行了研究。结合齿轮系统的复杂性和传动中出现的摩擦过渡特性，提出了齿轮传动摩擦润滑的多态性概念和过程模型。根据齿面是否出现局部干摩擦，提出将混合润滑分为Ⅰ型（不含局部干摩擦）和Ⅱ型（含局部干摩擦）。最后，研究了混合润滑Ⅰ型的构成模型及其齿面摩擦力/摩擦因数的计算方法。5.提出了基于齿根计算应力和测量应力的齿面摩擦因数反求方法。研究发现，轮齿在单啮上界点啮合时，齿根非接触区的最大拉/压应力对齿面摩擦具有较高的灵敏性，其中最大拉应力的灵敏度比压应力高出近1倍。在此基础上，提出了以计算应力和测试应力为变量构建优化目标函数，利用隔代映射小种群遗传算法与有限单元程序，反求干摩擦状态下的齿面摩擦因数。根据反求的齿面摩擦因数，研究了齿面摩擦对齿根应力和轮齿变形的影响。6.提出了将线外啮入冲击阶段分为冲击、刮行和正常啮合三个阶段，基于齿轮啮合原理与数值反推技术，计算含系统误差和轮齿变形的线外啮入冲击几何位置、冲击速度及冲击摩擦因数。主要研究结论：（1）考虑到影响啮入冲击的主要误差项、轮齿变形和齿面载荷均沿啮合作用线方向，提出了在该方向上构建“系统等效误差－轮齿综合变形”计算模型。（2）按统计分布规律将基节偏差、法向侧隙和齿廓修形量沿啮合线合成为系统等效误差；将弯曲、压缩、剪切、接触等变形沿作用线合成为轮齿综合变形；再将系统等效误差与轮齿综合变形进行二次合成，用以判断线外啮入冲击点的初始几何位置。（3）根据轮齿变形－载荷历程曲线按搜索法反推出线外啮入冲击点的轮齿综合变形，据此推算出线外啮入初始点的位置和冲击力；建立线外啮入冲击摩擦模型和计算冲击摩擦因数。更多还原

【Abstract】 Gear transmission, as a key mechanical part, may affect the performance andreliability of machinery and equipment, which relate to gear design and manufacture.The theoretical and experimental researches on gear strength and friction have asignificant meaning for increasing the carrying capacity, improved fatigue life, andto reduce friction and wear, to improve the transmission performance.Many researches are devoted to gear bending strength and friction by usingtheoretical and experimental methods. However, there are many intractabilityproblems about exactly calculating or testing the bending strength and friction, andneed to be studied further:(1) Accurate finite element model and numericalsimulation method for calculating root stress and tooth compliance under differentloads;(2) the realistic model for describing the friction and lubrication states andchange rules on the tooth surface, and pervasive calculating methods for toothfriction parameters;(3) Impact friction mechanism and quantitative calculationbased on interdisciplinary such as theory of gear, tribology, contact dynamics.Above all, the main motivations of the present paper are:(1) Accurate finiteelement model and numerical simulation method for bending strength;(2)polymorphism model and calculating method of gear friction and lubrication;(3)pervasive calculating methods for friction force and coefficient of tooth surface.Main works and innovation points are listed as follows.1. The research is about the accurate FEM modeling of gear pair and thecalculation method of bending, which are validated by comparative research. Thetooth curve is deduced based on the gear generating method and coordinatetransformation, and the accurate geometrical modeling of gear profile isaccomplished by the co-modeling method of APDL and MATLAB with text data files.Due to the calculation model including error and deformation, the calculationequation of bending strength is deduced, which may be a criterion to determine theselection of calculation points. The effective loads are studied with the FEM of gearbending strength. The peak stress value of dedendum and deformation of gear toothunder varying loads are compared and conclude that the accuracy of calculation isincreased along with the order of concentrated force, line loads, distribution force onHertz contact interface and static contact force. Dynamic characteristic analyses of moving load cannot exhibit the impact effects easily.2. The additive effects of tooth load, load distribution in the direction of toothdepth and tooth width are exhibited in the research. Moreover, the deformation ofgear tooth and the distribution discipline of maximum pull/press force are deserved.The research shows:(1) the additive effect of adjacent gear tooth meshing cannot beignored in the accurate calculation of gear strength, press sides are more affectedthan pull sides, eventually the maximum deformation of gear tooth is increased.Under the influence of even load, triangular distribution and cubic parabola loaddistribution, the varying disciplines of peak stress of dedendum in the gear widthdirection and tooth deformation in the contact zones are displayed. Moreover, it isvalidated about the gear end stiffness effect, gear tooth deformation and continuationof stress. Overall, the maximum press or pull stress of dedendum is increasedaccording to the irregularity of tooth load and effect of gear end stiffness, whereasthe maximum deformation of contact zones is decreased.3. Based on the virtual integration platform, a new method of stress is conductedcombined with wireless strain acquisition card and stress data transmitted by router.Further, the wireless test rig of dynamic strain in dedendum is designed. The dataunmeasured is acquired with the elimination of random electrical noise by averagemethod. And the input and output of speeds and torques are averaged to be regard asworking conditions, which can be coordinated with the boundary of calculatingmodel and experimental conditions. The tested variation curve of strain ondedendum reflect the phenomenon of single and double tooth gear meshing, gearmeshing impact and the impact of adjacent gear tooth. The measured maximumstrain on dedendum is coordinated with the results of FEM model and conclusionsderived by other researchers, which means the reliability and correction of methodreferred in the thesis and the FEM model as well as the results deduced. At last, thetest samples, namely measuring stresses, used in the fiction coefficient reverse ofgear tooth are acquired reliable.4. The polymorphism model of gear friction and lubrication is proposed. Theforming-mechanisms, characteristics and existing conditions of multiple gearfriction and lubrication behaviors (including elastohydrodynamic lubrication,boundary lubrication, mixed lubrication, dry friction, impact friction) in drivingprocess are investigated combining mesh theory with tribology. Then thepolymorphism model is proposed in consideration of the tribology systemcomplexity of gear drive and the friction transient phenomenon of teeth contact. The mixed lubrication can be devided into typeⅠ(not including local dry friction) andtype Ⅱ (including local dry friction). Finally, the composition model of mixedlubricationⅠand calculating method of friction coefficient are studied.5. The reverse method for coefficient of friction on surfaces on gear teeth isproposed by IP-uGA based on the numerical solution and test value of maximumtooth root stress. The sensibility of the tooth root stress to profile friction force andcoefficient is investigated when loaded on the upper point of single gear engagement.The sensitivity of the maximum tensile stress is twice as much as the maximumcompressive stress. The objective function considering calculating stress, testingstress and friction force as variables is gained and the dry friction coefficient isreversed by the genetic algorithm and FEM program. The effects of tooth surfacefriction on tooth root stress and tooth deformation are studied based on the frictioncoefficient reversed.6. Corner contact is devided into impact, scrape and normal engagement stages.Combining gear theory with numerical backstepping, the method for modelling andcalculating of impact friction caused by corner contact in gear transmissionconsidering the system error and tooth deformation is proposed. Main conclusionsinclude:(1) The work law of the main system errors, teeth deformation and loads onthe line of action is studied, which influences corner contact. Then the calculationmodel including gear equivalent error—combined deformation is established on theline of action.(2) According to the distributive rule, gear equivalent error issynthesized by base pitch error, normal backlash and tooth profile modification onthe line of action, and combined deformation is synthesized by bending, compressive,shearing and contact compliances. Combining the secondarily equivalent error withthe combined deformation, the position standard of the point situated at cornercontact is established.(3) The combined tooth compliance of the first point lying incorner contact before the normal path is backstepped, on basis of the curve of toothsynthetic compliance&load-history curve. After the impact position and force arecalculated accurately, the impact friction model is estabilshed and the impact frictioncoefficient is calculated.更多还原