FA型摆线针轮行星传动齿形优化方法与相关理论的研究
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摘要
摆线针轮行星传动具有传动比范围大、结构紧凑、可靠性高和寿命长等显著特点,因而获得了广泛的应用,研究也不断深入。该传动不仅广泛应用于通用传动领域,而且在微机械、机械人传动装置、精密机械传动、超小型传动、宇航设备,测量仪器、住宅智能化和高技术设备等方面有诱人的应用潜力。
在摆线针轮行星传动家族中,FA型摆线针轮行星传动变速器是一种新的传动装置。与一般的摆线针轮行星传动相比,它具有体积小、重量轻、传动比范围大、传动比的多样性、寿命长、刚度大、回转精度高、精度保持稳定、效率高、传动平稳等一系列的优点。该传动设计采用了许多先进的理念和技术,应用一种创新的结构形式,因此该种FA型针摆传动有效地克服了传统的结构不足,提高了传递的功率和容量,提高了传递的精度。
论文对此进行了系统的综述和分析,并提出了论文的主要研究内容。针对该传动的结构特点,论文从理论上和实际应用两方面研究并解决了以下几个问题:
1.在摆线针轮行星传动摆线轮和针齿齿面受力分析理论方面,提出了一种更加适用于工程实际的齿面有隙啮合受力分析的方法。该方法可以比较精确地计算在整个传递过程中针齿和摆线轮齿面接触力的大小和变化范围。该方法既有效地克服了按标准齿形进行理论受力分析计算误差大的缺点,又证明文献[1]中提出的理论只计算了整个传递过程中针齿和摆线轮齿面接触力的其中一个位置,是本文方法的一种特例。
2.通过对摆线轮和针齿齿面受力分析有限元计算,证明了本文提出的受力分析方法的正确性。两种受力分析计算结果在针齿的受力、同时接触针齿、接触应力的数值分布上均呈现了一致性,且两者最大接触应力的误差在5%左右。
3.在销孔式输出机构受力分析方面,首次提出了一种采用有隙啮合原理进行柱销与摆线轮上的柱销孔之间接触力的计算理论与方法,并推导出一套完整的计算公式,利用该理论比较准确地获得了柱销在整个转动过程中受力的变化区间,以及各个针齿的参与传递扭矩区间。计算结果表明了本文的计算方法更加接近于工程实际。
4.齿面修形理论与方法是国外保密的核心技术,本文在调研各种修形方法的基础上,基于齿面接触状态最佳的原则,首次提出了“反弓齿廓”概念,并给出了利用“负移距+正等距”简单组合修形方法获得反弓齿廓的条件,反弓齿廓初始间隙的计算方法,并采用优化理论获得了最佳的反弓齿廓所需要的“负移距+正等距”组合修形量。受力分析计算结果表明,最佳的反弓齿廓的接触状态可以达到最佳的受力状态。
5.在对FA型针摆传动几何回差和动态回差深入分析的基础上,针对高精传动的特点,本文提出了采用“负等距+正移距”的修形方法可以获得“弓背齿廓”的方法,而“弓背齿廓”的回差可以通过选择不同的修形量来满足。本文还提出了通过搜索计算获得满足许用回差的“弓背齿廓”修形量的计算方法。
6.在FA型摆线针轮行星传动变速器的研究方面,利用本文所提出的理论和研究成果,采用优化设计理论,对FA型针摆传动中的结构主要参数进行优化设计,编制了相关参数优化软件,并以FA45-59型号为例进行了产品设计,并由合作厂生产出样机。整机性能实际试验的结果表明了本文研究方法的正确性。
The cycloid drive has the essential advantages such as wide range of transmission ratio, compact structure, high reliability and long working life, so it gets broad application and its research goes deep constantly. The drive has been not only applied to traditional transmission field but also has alluring application in the aspects of micro machine, robot gear, precision machine transmission, super mini cycloid drive, astronaut equipment, measurement apparatus, tenement intelligence and high-tech equipment.In the family of the cycloid drive, the FA cycloid-pin wheel planetary drive reducer is a new transmission device. Compared with the common cycloid drive, it has a series of advantages such as small volume, lightweight, wide range of transmission, diversity transmission, long life time, high rigidity, high slewing precision, stable precision, high efficiency and stable transmission. The design of the drive adopts a lot of advanced theories and technology methods and uses a kind of innovation structure, so the FA drive has overcome the defect of the traditional structure, enhanced the transmission efficiency, volume, and the transmission precision.It has summarized and analyzed the FA cycloid-pin wheel planetary drive systematically and put forward the main research content in the paper. Aiming for the structure character, the paper has studied and solved the following problems in the two aspects of both the theory and the practical application.1. In the aspect of the force analysis of the cycloid and pin wheel of the cycloid-pin wheel planetary drive, a force analysis method of mesh with initial clearance is put forward, which is more accord with the actual engineering. The method can calculate the contact force and its change range between the pin gear and the cycloid during the whole transmission more precisely. The method has overcome efficiently the deficiency of the big calculation error in the force analysis of the standard gear profile, also has proved that the one position of the touch force between the gear and the cycloid during whole transmission which put forward by literature [1] is a special case of the paper.2. Though the finite element calculation of the force analysis of the cycloid and the pin gear surface, it has been proved that the method put forward by the paper is correct. The two force analysis calculation results are consistent in the pin gear force, the touch pin gear at the same time and the touch stress value distribution, and the biggest error of touch stress between them is less than 5 percent.3. In the force analysis of the pin-hole-output mechanism, based on the principle of mesh with initial clearance, a method has been put forward to calculate the touch stress between the pin and the pin-hole in the cycloid disk for the first time, and a set of calculation formulas has been deduced too. Using the theory the pin force variation range during whole transmission and the pin gear transmitting force area has been obtained correctly. The calculation result shows that the calculation method in this paper is more near to the actual engineering.
4. The teeth profile modification theory is the confidential core technology outside. On the base of investigating all kinds of the profile modification methods, and on the principle of optimum teeth touching surface, the concept of Inverse Arch-shaped Teeth Profile is been brought forward for the first time. It has also provided the method to get the Inverse Arch-shaped Teeth Profile with the combining modification method of 'plus equidistant + minus radial-moving' and the calculation method of the initial clearance of the Arch-shaped Teeth Profile. With the optimization theory the optimum inverse arch-shaped teeth profile is obtained. The calculation results about the various modification methods have showed that the touch state of the optimum inverse arch-shaped teeth profile can get the best stress.5. On the base of analyzing the geometry return difference and the dynamic return difference of the FA cycloid drive deeply, aiming for the character of the high precision drive, the Arch Back Teeth profile is obtained through the modification of the minus equidistant and plus radial-moving. While the return difference of the Arch Back Teeth profile can be satisfied by means of selecting different modification value. The calculation method of the modification value of the Arch Back Teeth profile of the allowable difference is also obtained by searching calculation.6. In the aspect of the FA cycloid-pin wheel planetary drive reducer, using the theory and research results put forward by the paper and adopting the optimized design theory, the main structure parameters in FA drive are optimized, the parameter optimization software is programmed, and taking the case of the type FA45-59 the product is designed and the sample machine is produced by the corporate factory. The practical test result of the whole sample function shows that the research methods of the paper are correct.7. According to the research results above, the serial software package of the FA cycloid-pin wheel planetary drive with three cycloids has been developed with the Visual C++ 6.0. The serial software concentrates the study result of the paper. The serial software is openness, and it can help users to design the main parameters of the FA cycloid-pin wheel planetary drive by providing the ordered transmission ratio. The software is able to provide all sets of technology information for cycloid drive manufactures and it can short the exploit cycle of the new products and economize the design costs.
在摆线针轮行星传动家族中,FA型摆线针轮行星传动变速器是一种新的传动装置。与一般的摆线针轮行星传动相比,它具有体积小、重量轻、传动比范围大、传动比的多样性、寿命长、刚度大、回转精度高、精度保持稳定、效率高、传动平稳等一系列的优点。该传动设计采用了许多先进的理念和技术,应用一种创新的结构形式,因此该种FA型针摆传动有效地克服了传统的结构不足,提高了传递的功率和容量,提高了传递的精度。
论文对此进行了系统的综述和分析,并提出了论文的主要研究内容。针对该传动的结构特点,论文从理论上和实际应用两方面研究并解决了以下几个问题:
1.在摆线针轮行星传动摆线轮和针齿齿面受力分析理论方面,提出了一种更加适用于工程实际的齿面有隙啮合受力分析的方法。该方法可以比较精确地计算在整个传递过程中针齿和摆线轮齿面接触力的大小和变化范围。该方法既有效地克服了按标准齿形进行理论受力分析计算误差大的缺点,又证明文献[1]中提出的理论只计算了整个传递过程中针齿和摆线轮齿面接触力的其中一个位置,是本文方法的一种特例。
2.通过对摆线轮和针齿齿面受力分析有限元计算,证明了本文提出的受力分析方法的正确性。两种受力分析计算结果在针齿的受力、同时接触针齿、接触应力的数值分布上均呈现了一致性,且两者最大接触应力的误差在5%左右。
3.在销孔式输出机构受力分析方面,首次提出了一种采用有隙啮合原理进行柱销与摆线轮上的柱销孔之间接触力的计算理论与方法,并推导出一套完整的计算公式,利用该理论比较准确地获得了柱销在整个转动过程中受力的变化区间,以及各个针齿的参与传递扭矩区间。计算结果表明了本文的计算方法更加接近于工程实际。
4.齿面修形理论与方法是国外保密的核心技术,本文在调研各种修形方法的基础上,基于齿面接触状态最佳的原则,首次提出了“反弓齿廓”概念,并给出了利用“负移距+正等距”简单组合修形方法获得反弓齿廓的条件,反弓齿廓初始间隙的计算方法,并采用优化理论获得了最佳的反弓齿廓所需要的“负移距+正等距”组合修形量。受力分析计算结果表明,最佳的反弓齿廓的接触状态可以达到最佳的受力状态。
5.在对FA型针摆传动几何回差和动态回差深入分析的基础上,针对高精传动的特点,本文提出了采用“负等距+正移距”的修形方法可以获得“弓背齿廓”的方法,而“弓背齿廓”的回差可以通过选择不同的修形量来满足。本文还提出了通过搜索计算获得满足许用回差的“弓背齿廓”修形量的计算方法。
6.在FA型摆线针轮行星传动变速器的研究方面,利用本文所提出的理论和研究成果,采用优化设计理论,对FA型针摆传动中的结构主要参数进行优化设计,编制了相关参数优化软件,并以FA45-59型号为例进行了产品设计,并由合作厂生产出样机。整机性能实际试验的结果表明了本文研究方法的正确性。
The cycloid drive has the essential advantages such as wide range of transmission ratio, compact structure, high reliability and long working life, so it gets broad application and its research goes deep constantly. The drive has been not only applied to traditional transmission field but also has alluring application in the aspects of micro machine, robot gear, precision machine transmission, super mini cycloid drive, astronaut equipment, measurement apparatus, tenement intelligence and high-tech equipment.In the family of the cycloid drive, the FA cycloid-pin wheel planetary drive reducer is a new transmission device. Compared with the common cycloid drive, it has a series of advantages such as small volume, lightweight, wide range of transmission, diversity transmission, long life time, high rigidity, high slewing precision, stable precision, high efficiency and stable transmission. The design of the drive adopts a lot of advanced theories and technology methods and uses a kind of innovation structure, so the FA drive has overcome the defect of the traditional structure, enhanced the transmission efficiency, volume, and the transmission precision.It has summarized and analyzed the FA cycloid-pin wheel planetary drive systematically and put forward the main research content in the paper. Aiming for the structure character, the paper has studied and solved the following problems in the two aspects of both the theory and the practical application.1. In the aspect of the force analysis of the cycloid and pin wheel of the cycloid-pin wheel planetary drive, a force analysis method of mesh with initial clearance is put forward, which is more accord with the actual engineering. The method can calculate the contact force and its change range between the pin gear and the cycloid during the whole transmission more precisely. The method has overcome efficiently the deficiency of the big calculation error in the force analysis of the standard gear profile, also has proved that the one position of the touch force between the gear and the cycloid during whole transmission which put forward by literature [1] is a special case of the paper.2. Though the finite element calculation of the force analysis of the cycloid and the pin gear surface, it has been proved that the method put forward by the paper is correct. The two force analysis calculation results are consistent in the pin gear force, the touch pin gear at the same time and the touch stress value distribution, and the biggest error of touch stress between them is less than 5 percent.3. In the force analysis of the pin-hole-output mechanism, based on the principle of mesh with initial clearance, a method has been put forward to calculate the touch stress between the pin and the pin-hole in the cycloid disk for the first time, and a set of calculation formulas has been deduced too. Using the theory the pin force variation range during whole transmission and the pin gear transmitting force area has been obtained correctly. The calculation result shows that the calculation method in this paper is more near to the actual engineering.
4. The teeth profile modification theory is the confidential core technology outside. On the base of investigating all kinds of the profile modification methods, and on the principle of optimum teeth touching surface, the concept of Inverse Arch-shaped Teeth Profile is been brought forward for the first time. It has also provided the method to get the Inverse Arch-shaped Teeth Profile with the combining modification method of 'plus equidistant + minus radial-moving' and the calculation method of the initial clearance of the Arch-shaped Teeth Profile. With the optimization theory the optimum inverse arch-shaped teeth profile is obtained. The calculation results about the various modification methods have showed that the touch state of the optimum inverse arch-shaped teeth profile can get the best stress.5. On the base of analyzing the geometry return difference and the dynamic return difference of the FA cycloid drive deeply, aiming for the character of the high precision drive, the Arch Back Teeth profile is obtained through the modification of the minus equidistant and plus radial-moving. While the return difference of the Arch Back Teeth profile can be satisfied by means of selecting different modification value. The calculation method of the modification value of the Arch Back Teeth profile of the allowable difference is also obtained by searching calculation.6. In the aspect of the FA cycloid-pin wheel planetary drive reducer, using the theory and research results put forward by the paper and adopting the optimized design theory, the main structure parameters in FA drive are optimized, the parameter optimization software is programmed, and taking the case of the type FA45-59 the product is designed and the sample machine is produced by the corporate factory. The practical test result of the whole sample function shows that the research methods of the paper are correct.7. According to the research results above, the serial software package of the FA cycloid-pin wheel planetary drive with three cycloids has been developed with the Visual C++ 6.0. The serial software concentrates the study result of the paper. The serial software is openness, and it can help users to design the main parameters of the FA cycloid-pin wheel planetary drive by providing the ordered transmission ratio. The software is able to provide all sets of technology information for cycloid drive manufactures and it can short the exploit cycle of the new products and economize the design costs.
引文
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