【作者】 李秀莲；

【导师】 王贵成；

【作者基本信息】 江苏大学 ， 动力机械及工程， 2012， 博士

【摘要】 齿轮是动力机械装备的主要传动零件之一。非对称齿轮是一种为了提高轮齿的抗弯曲强度而提出的新型齿轮。该齿轮具有承载能力大、体积小、重量轻、使用寿命长等优点,开展非对称齿轮的研究,对航天、航空等场合下重载、高速齿轮的应用具有重要的理论指导和现实意义。本文采用理论分析、数值模拟和实验测试相结合的方法,以非对称渐开线齿轮为对象,研究齿面摩擦下单、双模数非对称齿轮的传动性能,探索提高非对称齿轮传动性能的新方法、新理论和新技术,主要研究工作如下：1.阐述了非对称渐开线斜(圆锥)齿轮齿廓曲面的生成原理,推导出单、双模数非对称渐开线齿条刀具的参数方程根据非对称齿轮的结构特点,阐述了非对称渐开线斜(圆锥)齿轮齿廓曲面的生成原理,为进一步推广非对称齿轮奠定了理论基础；为了加快单、双模数非对称齿轮的研究和应用,结合单、双模数非对称齿轮的特点,推导出单、双模数非对称渐开线齿条刀具的参数方程。2.建立齿面摩擦下非对称渐开线齿轮齿面接触应力和齿根弯曲应力的数学模型在考虑齿面摩擦影响的情况下,通过建立轮齿受力的数学模型,推导出单、双模数非对称渐开线齿轮齿面接触应力和齿根弯曲应力的数学模型,为提高齿面接触强度和齿根弯曲强度提供了理论依据。3.建立齿面摩擦下非对称渐开线齿轮支座反力的数学模型通过对轮齿受力进行分析,在引入齿间载荷分配因数的情况下,建立齿面摩擦作用下单、双模数非对称渐开线齿轮支座反力的数学模型,给出了表征齿轮支座反力波动程度的评价指标,为提高齿轮传动平稳性提供了理论参考。4.建立非对称渐开线齿轮齿廓滑动系数的数学模型利用啮合齿廓接触点的公法线矢量和接触点相对运动速度方向的法曲率,推导出空间啮合状态下,单、双模数非对称渐开线齿轮齿廓滑动系数的矢量计算公式；以及单、双模数非对称渐开线直齿圆柱齿轮齿廓滑动系数的简化计算公式；为揭示齿轮摩擦、磨损的机理提供了理论依据。5.实现了非对称渐开线齿轮啮合效率的预测在引入轮齿啮合点齿廓曲率半径的条件下,通过对轮齿的单、双齿啮合情况进行受力分析,建立任意齿间载荷分配因系数下单、双模数非对称渐开线齿轮啮合效率的数学模型,并对各种条件下齿轮啮合效率进行了预测,为非对称渐开线齿轮传动效率的确定,提供了一种快速、便捷的方法。6.非对称渐开线齿轮传动系统的测试及实验设计设计了非对称渐开线齿轮传动系统的测试平台,进行了齿轮传动装置噪声和振动加速度的测试,分析了对称齿轮和非对称齿轮在不同啮合状态下的动态性能。研究表明,在非对称渐开线齿轮齿面接触应力和齿根弯曲应力的计算中不可忽视齿面摩擦的影响；非对称渐开线齿轮在轮齿强度、齿廓滑动系数、啮合效率、振动、噪声等方面的性能指标均优于对称渐开线齿轮；相对于单模数对称渐开线齿轮,双模数非对称渐开线齿轮不仅可节省材料、减轻重量、提高齿面接触强度和齿根弯曲强度,而且由于齿廓滑动系数值较小,齿面磨损也较轻。与对称渐开线齿轮相比,非对称渐开线齿轮齿面接触应力可降低28.86%,齿根弯曲应力可降低6.37%。在考虑齿面摩擦的情况下,非对称渐开线齿轮齿面接触应力将增大7.51%,齿根弯曲应力将增大7.12%。与单模数对称渐开线齿轮相比,双模数非对称渐开线齿轮齿面接触应力可降低34.74%。对于单模数非对称齿轮,增大压力角,齿顶滑动系数可降低17.42%,齿根滑动系数可降低40.28%。对于双模数非对称齿轮,增大压力角,齿顶滑动系数可降低21.81%,齿根滑动系数可降低34.75%。对称渐开线齿轮的啮合效率为97.73%,而同等条件下非对称渐开线齿轮的啮合效率为98.24%。对称渐开线齿轮的噪声为83.685.0 dB,而非对称渐开线齿轮噪声72.6—73.7 dB。对称渐开线齿轮的振动加速度峰—峰值为4.49 G—-4.29 G,而非对称渐开线齿轮的振动加速度峰—峰值为1.02G—-1.08 G。研究表明,采用非对称齿轮能显著提高齿轮的传动性能,对于高速、重载、大功率齿轮传动场合具有非常重要的意义。本文的研究得到了国家自然科学基金资助(No.51075192)。更多还原

【Abstract】 Gear is one of the driving parts of power machinery and equipment. In order to improve the bending strength at the tooth root of gear, a kind of new gear,namely, asymmetric gear was put forward. The advantages of this kind of gear have larger carrying capacity, smaller volume, lighter weight and longer life. The study of asymmetric gear has important theoretical direction and realized significance to the application of the heavy load and high-speed gear for aerospace. The methods of theory analysis combined numerical simulation and experimental test are used in the paper. The asymmetric involute gear was used as object, the transmission performance of the single & double moduli asymmetric involute gear is researched under the friction force between teeth.The new technique, the new theory,and the new methods, of improving the transmission performance are explored. The main works are as follows:1. The generated principles of the tooth profile curved surface of asymmetric involute gear are stated, the parametric equation of single & double moduli asymmetric involute rack tools is deducedAccording to the structural features of asymmetric involute gear, the generated principles of the tooth profile curved surface of asymmetric involute gear are stated, this will establish the theory basis for popularizing the asymmetric involute gear. To accelerate the study and application of single & double moduli asymmetric involute gear, the parametric equation of single & double moduli asymmetric involute rack tools are deduced according to the characteristic of single & double moduli asymmetric involute gear.2. The mathematic models on tooth face contact stress and tooth root bending stress of asymmetric involute gear are established under friction force between teethThe mathematic models on tooth face contact stress and tooth root bending stress of asymmetric involute gear with double pressure angles are deduced by through fully analyzing the forces exerted on the driving gear of asymmetric spur gear drive under the action of sliding friction. Simulation results provide a theoretical basis to improve the tooth face contact strength and tooth root bending strength of asymmetric involute gear with double pressure angles.3. The mathematic models of gear supports of asymmetric gear driving system are established under the sliding friction forceThe author of the paper deduced the calculation equation of the gear supports reaction, under the action of the sliding friction between teeth, through fully analyzing the forces exerted on the driving gear of reducing-speed asymmetric spur gear drive system with double pressure angles in the single & double gears meshing range. And presented the index of gear supports reaction fluctuation in the condition of the random interteeth load.Simulation results provide the theoretical references for improving the transmission smoothness of the asymmetric gear with double pressure angles. 4. Establish the mathematical model of the sliding coefficient of asymmetric involute gear tooth profileThe vector calculation formula of tooth profile sliding coefficient of single & double moduli asymmetric involute gear was deduced by using the normal curvature of meshing point relative velocity direction and the common normal line vector of meshing point on the contac tooth profile under the spatial meshing state.And the simplified formula of tooth profile sliding coefficient of single & double moudli asymmetric involute spur gear was also deduced. Simulation results provide the theoretical references for revealing the working principle of friction and wear of the asymmetric gear with double pressure angles.5. Prediction of meshing efficiency on asymmetric gear with double pressure anglesThe author of the paper deduced the calculation equation of the gear mesh efficiency in the condition of the random interteeth load, under the action of the sliding friction between teeth, making use of the radii of teeth outline curvature at the mating points, through fully analyzing the forces exerted on the gears’teeth of single or double moduli asymmetric involute spur gear drive system with double pressure angles in the single & double gears meshing range.And, calculation of the mating efficiency was carried out by changing the sliding interteeth friction, pressure angle, modulus and gear’s rotating speed ratio on the diving & driven gears of single or double moduli asymmetric spur gear drive system with double pressure angles. And provides a fast, convenient way in order to determine the transmission efficiency of asymmetric spur gear drive system with double pressure angles.6. Testing and experimental design of the asymmetric involute gear drive system with double pressure angles.The test platform of the asymmetric involute gear driving system with double pressure angles was designed, the noise and vibration acceleration of gear driving equipment was tested,and the dynamic performance of both unsymmetric gear and symmetric gear are analyzed under different meshing states in this paper.The results show that the effect of the sliding friction between teeth can not be neglected in the tooth root bending stress calculation and tooth face contact stress calculation of asymmetric involute gear with double pressure angles. The performance index of noise and vibration, meshing efficient, tooth profile sliding coefficient,and gear strength,of asymmetric involute gear are superior to symmetric involute gear. Compared to single modulus symmetrical involute gear,dual modulus asymmetric involute gear can not only save material, reduce weight, improve tooth surface contact strength and root bending strength, and because of the smaller sliding coefficient of tooth profile, tooth wear lighter. Compared with the symmetric involute gear, asymmetric involute gear tooth face contact stress can be reduced 28.86%, tooth root bending stress can be reduced 6.37%. Considering the tooth surface friction, asymmetric involute gear tooth surface contact stress will increase to 7.51%, the tooth root bending stress will increase to 7.12%.The tooth face contact stress of double moduli asymmetric involute gear can reduce to 34.74% comparing with single modulus symmetric involute gear. Tooth profile Sliding coefficient of tooth addendum can reduce to 17.42%, Sliding coefficient of tooth root can reduce to 40.28% by increasing the pressure angle for single modulus asymmetric involute gear. Tooth profile sliding coefficient of tooth addendum can reduce to 21.81%, Sliding coefficient of tooth root can reduce to 34.75% by increasing the pressure angle for double moduli asymmetric involute gear.The meshing efficiency of symmetric involute gear is 97.73%, but the meshing efficient of symmetric involute gear is 98.24% under the same conditions.The noise of symmetric involute gear is from 83.6 to 85.0 dB, but the noise of asymmetric involute gear is from 72.6 to 73.7 dB, The vibration acceleration peak-peak of symmetric involute gear is from 4.49 G to -4.29G, while on the asymmetric involute gear is from 1.02 G to -1.08 G. The results show that the asymmetric gear can significantly improve the transmission performance of the gear, has very important significance for the high-speed, overload, high-power gear working environment.The dissertation is supported by National Natural Science Foundation (No.51075192).更多还原