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

发布时间：2018-06-23 22:46

本文选题：齿轮弯曲强度 + 齿面摩擦因数　；参考：《湖南大学》2013年博士论文

【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。
[Abstract]:The gear is an important foundation. Its design and manufacturing level affects the performance and reliability of the mechanical equipment. The calculation and test of the gear strength and the friction of the tooth surface have significant significance for increasing the bearing capacity, improving the fatigue life, reducing the friction and wear, and improving the transmission performance. There are many problems in calculation and experiment. The following problems are worth exploring: the exact modeling method for calculating the bending strength of gears under various loads, the numerical calculation of the tooth root stress and the deformation of the gear teeth; the process model which can characterize the variety of friction lubrication state and the changing law of the tooth surface, and the universal calculation method of the key friction parameters of the tooth surface; Friction mechanism and quantitative calculation of tooth surfaces such as meshing theory, tribology, contact dynamics and so on.
Based on the thinking of the above problems and combining the related topics of the author, this paper puts forward the research topic of this thesis. It focuses on three problems: the accurate modeling method of the calculation of the bending strength of gear under various loads; the polymorphism model and calculation method of the friction lubrication of the tooth surface; the universal quantitative calculation method of the friction force and the friction factor of the tooth surface The main research contents and innovation points are as follows:
1. the precise modeling of the gear finite element and the calculation method of the bending strength are studied. The correctness of the method is verified by comparison and research. The tooth profile is derived from the principle of gear forming and the coordinate system matrix transformation. The geometric model of the gear is realized by the mixed modeling method of APDL and MATLAB based on the pure text data file. Based on the calculation model with error and deformation, the position discriminant of the calculation force point of bending strength is derived, which can be used as a reference for the calculation of the force point of the bending strength. The various effective loads of the finite element calculation of the bending strength of the gear are studied, and the comparison of the peak stress and the tooth deformation of the tooth root under different loads is found. According to the concentration force, the line distribution force, the distribution force of the Hertz contact surface, the order of the static contact force and the accuracy of the calculation result, the dynamic load equivalent analysis of the moving load is difficult to reflect the impact effect of the meshing.
2. the load distribution between the teeth, the load distribution in the direction of tooth height and tooth width, and the distribution of the tooth deformation and the maximum tension / pressure distribution of the tooth root are studied. The study shows: (1) the force superposition effect caused by the engagement of the adjacent teeth can not be ignored in the accurate calculation of the gear strength, and the effect of the superposition effect of the meshing force on the compression side of the central tooth is greater than that of the tension side, and the effect of the superposition of the meshing force is greater than that of the tension side. The maximum deformation of the gear tooth is further increased. (2) the variation of tooth root peak stress and tooth deformation in the contact area under the action of uniform load, triangular distribution and three parabolic load. The stiffness effect of the tooth and the continuity of the tooth deformation and stress distribution, the inhomogeneity of the tooth load and the effect of the tooth end stiffness are verified. The maximum pressure / tensile stress of the tooth root is increased, and the maximum deformation of the contact area decreases slightly.
3. based on the virtual instrument integration platform, a new method of transmitting the tooth root strain data through the wireless strain acquisition card and router is proposed. The tooth root dynamic stress wireless test table is designed. The multipoint averaging method is used to eliminate the random electrical noise to obtain the data to be measured, and the speed and torque of the input and output ends are taken as the calculation model. The force boundary of the calculated model is consistent with the test conditions. The measured tooth root stress change curve accurately reflects the influence of the alternating of single / double meshing, the impact of meshing and the adjacent meshing tooth pairs, and the maximum root stress measured by the finite element method is in agreement with the results of the finite element calculation and the other researchers. The wireless measurement method and the correctness of the above finite element calculation model are obtained. The test data, that is, the measurement stress, is obtained from the reverse calculation of the friction coefficient of the tooth surface.
4. a polymorphic model of friction lubrication of tooth surface is proposed. The mechanism, characteristics and conditions of various frictional states (elastohydrodynamic lubrication, boundary lubrication, mixed lubrication, dry friction and impact friction) in gear transmission are studied by combining the meshing transmission theory with the tribological theory, and the complexity of the gear system and the complexity of the gear system are also studied. The concept and process model of the polymorphism of friction lubrication in gear transmission are proposed in the transmission. According to the local dry friction of the tooth surface, it is proposed to divide the mixed lubrication into type I (without local dry friction) and type II (including local dry friction). Finally, the composition model of the mixed lubrication type I and its tooth surface friction are studied. The calculation method of force / friction factor.
5. the inverse method of the tooth surface friction factor based on the tooth root calculation stress and the measurement stress is proposed. It is found that the maximum tensile / pressure stress of the tooth root non contact area has high sensitivity to the tooth surface friction, and the maximum tensile stress sensitivity is nearly 1 times higher than the compressive stress when the tooth is meshing at the upper boundary point of the single Rog. The optimization objective function is constructed by calculating the stress and the test stress, and the friction factor of the tooth surface in the dry friction condition is calculated by using the small population genetic algorithm and the finite element program, and the effect of the tooth surface friction on the tooth root stress and the tooth deformation is studied.
6. it is proposed that the stage of out of line meshing impact is divided into three stages: impact, scraping and normal meshing. Based on the gear meshing principle and numerical backstepping technology, the geometric position, impact velocity and impact friction factor of the external meshing, the impact velocity and the impact friction factor are calculated. The main conclusions are as follows: (1) the main errors that affect the meshing impact are taken into account. The difference term, the tooth deformation and the load of the tooth surface are all along the direction of the rodent cooperating line, and the calculation model of the "system equivalent error - the comprehensive deformation of the gear tooth" is proposed in this direction. (2) according to the statistical distribution law, the base section deviation, the normal side gap and the tooth profile modification amount are synthesized into the system equivalent error along the meshing line, and the bending, compression, shear, contact and so on are changed. The composite deformation of the gear tooth is formed along the line of action, and then the equivalent error of the system and the comprehensive deformation of the tooth are synthesized two times to judge the initial geometric position of the impact point. (3) according to the tooth deformation load course curve, the comprehensive deformation of the gear tooth is deduced from the search method, and the outer rodent is calculated. The location and impact force of the initial point are established, and the impact friction model is calculated and the impact friction factor is calculated.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH132.41

【参考文献】