正交面齿轮的啮合仿真与插齿加工
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摘要
面齿轮传动是一种圆柱齿轮与圆锥齿轮相啮合的齿轮传动形式,当两轮轴线正交时,圆锥齿轮的轮齿将分布在一个圆平面上,泛称为面齿轮传动。面齿轮传动由于其在分流—汇流传动中的独特性,使其在航空领域的应用有着潜在的优势。目前国外在这方面的理论研究和应用上已经较为全面深入,但由于面齿轮传动技术应用的军事背景,形成了技术封锁与技术壁垒。所以,立足于自主创新和国产化,对面齿轮传动展开研究,提高其传动性能、啮合质量与可靠性,对公共安全和国防都有着重要的意义。本论文主要研究内容和结论如下:
研究了面齿轮传动的几何原理,齿面接触区的局部化及其修形方法。建立了圆柱插齿刀具加工面齿轮的数学模型,推导了正交面齿轮的齿面方程。根据面齿轮的展成原理,建立了面齿轮不根切和齿顶不变尖的临界条件,确定面齿轮不根切的最小内半径和齿顶不变尖的最大外半径。以两套面齿轮为例,进行了几何参数计算和齿坯设计。
推导了面齿轮齿面旋转投影面内网格节点的坐标计算公式;根据旋转投影关系,构建了理论齿面数据,并用数值算法进行求解;最后利用UG软件对计算得到的理论齿面进行三维仿真。三维仿真结果验证理论推导和几何设计的正确性。
建立了面齿轮副啮合的TCA分析数学模型,通过对数学模型的求解,得到面齿轮副的接触路径。分析了安装偏置距、安装误差变形角和轴向位移三种安装误差对正交面齿轮副啮合传动的影响。最后根据TCA分析结果,计算了面齿轮副的重合度。
根据面齿轮与圆柱齿轮的啮合原理,设计了插齿加工的工装,对现有的514型插齿机的工作台进行改造。进行了面齿轮插削加工试验,切制了若干对面齿轮,并在Y9550型锥齿轮滚检机上进行滚检和噪声试验。试验基本上达到预期的目的,验证了本文的理论研究结果。
Face gear drive is a type of transmission which is a spur pinion mating a bevel gear. When the two axes of the spur pinion and the bevel gear are orthogonal, the tooth of bevel gear will distribute in a disk, so that it is called generally the face gear drive. With the specificity of the pair of face gear in the split/combination drive of power, it shows its potential advantage in the application of aviation area. At the present, the overseas research and application on face gears have already been in the more depth. Since internationally the face gear drive has been used in the military, it is self-evident that the technique is blockaded on our country. Therefore, the transmission technology of face gear drive must be established in the domestic research and development. The researchs on the face gear drive to increase its transmission performance and meshing quality and reliability are very necessary and important for the public secruity and national defense. In this dissertation the main contents and the conclusions are following as:
The researchs on the geometrical principle of face gear drive, the localization of contact bearing and the correction of the tooth flank form have been done. The mathematical model generating face gear using shaping cutter has been established to obtain the theoretical equations of the orthogonal face gear. Based on the generating theory of face gears, the critical conditions of the teeth non-undercutting and non-pointing of face gears have been set up, then the internal radius and outer radius have been determined. Then two pairs of face gears being taken as examples, the calculation of the gear geometric parameter and the blank design have been carried out.
The computing formulas of the coordinate grids in the rotary projection of face gear tooth surfaces have been derived, and according to the relationship of rotary projection, the data of theoretical tooth surface have been solved by the numerical alonrithm. Finally, the 3-D simulation of the object model of the theoretical tooth surface has been carried out by using the UG software. The 3-D modelling proves that the above theoretical derivation and the geometric design on the face gears are right.
set up, and then the contact path of the pair of face gears has been obtained by the sovling of the model. The analysis have been done on the fluences of the three kinds of installing errors on the transmission performance of the orthogonal face gears, refering to the offset errors, the angle errors of deformation and the axial displacement errors. Then based on the analysis results of TCA, the calculation of the contact ratio of the face gear drive has been done.
According to meshing theory of the face gear and the spur pinion, the design of the gear shaping fixture has been done, and then the worktable of the present type of 514 gear slotting machine-tool has been rebuilded. Then the tests of the face gear shaping have been carried out, and a serial of pairs of face gears have been slotted. Then noise tests of inspection on a type of Y9550 inspectiong machine-tool have been done. The above tests basically achieving the expected results proves the theoretical researchs in this dissertation.
研究了面齿轮传动的几何原理,齿面接触区的局部化及其修形方法。建立了圆柱插齿刀具加工面齿轮的数学模型,推导了正交面齿轮的齿面方程。根据面齿轮的展成原理,建立了面齿轮不根切和齿顶不变尖的临界条件,确定面齿轮不根切的最小内半径和齿顶不变尖的最大外半径。以两套面齿轮为例,进行了几何参数计算和齿坯设计。
推导了面齿轮齿面旋转投影面内网格节点的坐标计算公式;根据旋转投影关系,构建了理论齿面数据,并用数值算法进行求解;最后利用UG软件对计算得到的理论齿面进行三维仿真。三维仿真结果验证理论推导和几何设计的正确性。
建立了面齿轮副啮合的TCA分析数学模型,通过对数学模型的求解,得到面齿轮副的接触路径。分析了安装偏置距、安装误差变形角和轴向位移三种安装误差对正交面齿轮副啮合传动的影响。最后根据TCA分析结果,计算了面齿轮副的重合度。
根据面齿轮与圆柱齿轮的啮合原理,设计了插齿加工的工装,对现有的514型插齿机的工作台进行改造。进行了面齿轮插削加工试验,切制了若干对面齿轮,并在Y9550型锥齿轮滚检机上进行滚检和噪声试验。试验基本上达到预期的目的,验证了本文的理论研究结果。
Face gear drive is a type of transmission which is a spur pinion mating a bevel gear. When the two axes of the spur pinion and the bevel gear are orthogonal, the tooth of bevel gear will distribute in a disk, so that it is called generally the face gear drive. With the specificity of the pair of face gear in the split/combination drive of power, it shows its potential advantage in the application of aviation area. At the present, the overseas research and application on face gears have already been in the more depth. Since internationally the face gear drive has been used in the military, it is self-evident that the technique is blockaded on our country. Therefore, the transmission technology of face gear drive must be established in the domestic research and development. The researchs on the face gear drive to increase its transmission performance and meshing quality and reliability are very necessary and important for the public secruity and national defense. In this dissertation the main contents and the conclusions are following as:
The researchs on the geometrical principle of face gear drive, the localization of contact bearing and the correction of the tooth flank form have been done. The mathematical model generating face gear using shaping cutter has been established to obtain the theoretical equations of the orthogonal face gear. Based on the generating theory of face gears, the critical conditions of the teeth non-undercutting and non-pointing of face gears have been set up, then the internal radius and outer radius have been determined. Then two pairs of face gears being taken as examples, the calculation of the gear geometric parameter and the blank design have been carried out.
The computing formulas of the coordinate grids in the rotary projection of face gear tooth surfaces have been derived, and according to the relationship of rotary projection, the data of theoretical tooth surface have been solved by the numerical alonrithm. Finally, the 3-D simulation of the object model of the theoretical tooth surface has been carried out by using the UG software. The 3-D modelling proves that the above theoretical derivation and the geometric design on the face gears are right.
set up, and then the contact path of the pair of face gears has been obtained by the sovling of the model. The analysis have been done on the fluences of the three kinds of installing errors on the transmission performance of the orthogonal face gears, refering to the offset errors, the angle errors of deformation and the axial displacement errors. Then based on the analysis results of TCA, the calculation of the contact ratio of the face gear drive has been done.
According to meshing theory of the face gear and the spur pinion, the design of the gear shaping fixture has been done, and then the worktable of the present type of 514 gear slotting machine-tool has been rebuilded. Then the tests of the face gear shaping have been carried out, and a serial of pairs of face gears have been slotted. Then noise tests of inspection on a type of Y9550 inspectiong machine-tool have been done. The above tests basically achieving the expected results proves the theoretical researchs in this dissertation.
引文
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[7]中国齿轮网.深入分析我国齿轮传动制造行业的发展现状[R].网址:http://www.subcon.cn/chs/news/2009-08-04/1249372479d10523.html
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[9] Hendrik Kuiken,Emmeloord,Netherlands.“Face Gear Transmission”,United States Patetnt,No.4744263,May 17,1998.
[10] F.L.Litvin.Gear Geometry and Applied Theory[M]. Englewood Cliffs: Prentice Hall, Inc.,1994, 490-525.
[11] Heath,G.F.,and Bossler,R.B..Advanced Rotorcraft Transmission(ART) Program-Final Report[J],NASA CR-191057,Army Research Laboratory ARL-CR-14,January 1993.
[12] Robert R.Filler,Gregory F.Heath,Stephen C. Slaughter,David G.Lewicki.Torque Splotting by a Concentric Face Gear Transmission[J]. The American Helicopter Society 58th Annual Forum,2002,6:11-22.
[13] Faydor L. Litvin,Alfonso Fuentes,Claudio Zanzi,Matteo Pontiggia.Design,generation,and stress analysis of two versions of geometry of face-gear drives,Mechanism and Machine Theory , 2002, 37:1179-1211.
[14] Shuo-Hung Chang,Tsang-Dong Chung,Shui-Shong Lu.Tooth Contact Analysis of Face-gear Drives. Mechnical Sciences, 2000, 42:487-502.
[15] Faydor L.Litvin,Alfonso Fuentes,Claudio Zanzi,Matteo Pontiggia.Design,generation, and stress analysis of two versions of geometry of face-gear drives[J]. Mechanism and Mechine Theory , 2002, 37:1179-1211.
[16] Faydor L.Litvin,Ignacio Gonzalez-Perez,Alfonso Fuentes,Daniele Vecchiato,Bruce D.Hansen,David Binney.Generation and stress analysis of face-gear drive with helical pinion[J]. Computer methods in applied mechaics andengineering , 2005, 194:3870-3901.
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