超声珩齿非谐振单元变幅器的设计理论与实验研究
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摘要
齿轮是机械动力传递的最主要的元器件,齿轮传动由于其传动功率范围大,传动效率高、传动比准确、寿命长、安全可靠等特点,具有其它传动不可替代的优势,得到广泛应用。以齿轮为代表的基础零部件不仅是我国装备制造业的基础性产业,也是我国国民经济建设各领域的重要基础。
为了提高齿轮的承载能力和缩小传动装置的尺寸,各国普遍采用硬齿面技术。而当前我国的硬齿面齿轮精加工技术明显落后于发达国家。将超声振动引入传统的珩齿工艺中进行超声辅助复合加工是硬齿面齿轮精加工技术的一种新的探索和尝试,其目的在于利用超声振动的特点改进传统珩齿技术的不足,充分发挥珩齿在硬齿面齿轮精加工中的优势,从而实现高质量、高效率、低成本的齿轮精密加工的目标。
超声辅助珩齿的关键技术之一是振动系统的设计,这也是后续所有研究工作的基础,为此,2009年国家自然科学基金资助了本课题组提出的“非谐振单元变幅器设计理论及其齿轮超声剃珩应用”(No.50975191)项目。本文瞄准“非谐振单元变幅器设计理论”这一关键问题进行了创新性研究,目的是解决不同结构、尺寸齿轮的振动系统的设计问题,使齿轮的振动模态、振动频率、振幅等满足超声珩齿加工的要求。本文主要完成以下研究工作：
(1)纵向振动变幅器的设计
对于小直径的齿轮,在变幅杆的推动下主要表现为一维纵向振动,其弯曲振动和径向振动可以忽略不计。将小直径齿轮简化为等截面圆柱杆,则由齿轮、固定螺母及变幅杆组成的变幅器的结构形式、振动特点与复合变幅杆相同。应用复合变幅杆的设计原理设计了纵向振动变幅器,并得到较准确的计算结果。分析比较了提高纵振变幅器振幅的措施,提出了针对大输出端变幅杆应用场合的改进式级联变幅杆。
(2)齿轮及圆板、环板的弯曲振动
齿轮的弯曲振动理论是设计弯曲振动变幅器的基础。将齿轮简化为与其分度圆等径的圆板或环板,应用Mindlin中厚板振动理论计算齿轮的弯曲振动,通过与有限元分析结果的比较,说明采用中厚板理论虽然计算复杂,但计算精度高,远优于经典薄板理论。针对沿径向阶梯变厚度齿轮、沿径向任意变厚度圆板、环板、带均布减重孔的齿轮,基于Mindlin中厚板振动理论创新性的提出了计算其弯曲振动频率的方法,通过与有限元分析结果的比较,证明了所提出的方法能够得到较准确的计算结果。
(3)弯曲振动变幅器的设计
弯曲振动变幅器是超声珩齿非谐振单元变幅器的主要形式。基于中厚板振动理论,深入分析了弯曲振动变幅器的振动特点,提出了多种数学模型和计算方法,结合实验,确定了合理可行的弯曲振动变幅器设计理论和方法。在此基础上对弯曲振动变幅器的振幅分布特性做了分析,提出了提高变幅器振幅的措施。此外,对弯曲振动变幅器有限元模态分析方法做了探讨。
(4)由二分之一波长变幅杆组成的弯曲振动
理论和实验都表明,在弯曲振动变幅器中,固定螺母的长度会对变幅器的频率产生影响,固定螺母越长则变幅器频率越低,反之变幅器频率越高。另外,在弯曲振动变幅器中加入固定板单元也会对变幅器频率产生影响。据此提出由二分之一波长变幅杆组成的弯曲振动变幅器的设计思想,变幅杆按二分之一波长设计,通过改变螺母或固定板的尺寸来调节变幅器频率。从理论上对这种结构的变幅器做了初步的探索研究。
(5)径向振动变幅器的设计
径向振动变幅器是超声珩齿非谐振单元变幅器的第三种形式。对于大孔径的齿轮,相应的变幅杆直径也大,变幅器的径向振动增强。如果齿轮做纯径向振动,则这也是一种轴对称的振动模态,可以用来进行齿轮的超声复合加工。基于纵、径耦合振动理论提出了径向振动变幅器的设计理论和数学模型,利用有限元分析方法验证了设计结果的准确性。此外对径向振动变幅器的频率特性和振幅特性做了分析,并提出了径向振动变幅器的改进结构。
通过以上理论与实验研究,形成了超声珩齿非谐振单元变幅器较为完善的设计理论体系,满足了超声珩齿加工的要求,为今后更深层次的超声珩齿理论研究和实验研究提供了基础。
Gear is the most important component of the mechanical power transmission. It has the advantages of wide range power, high transmission efficiency, accurate drive ratio, long life and safety so as to irreplaceable and extensive use. The gear as the basic components of machinery products is the foundational industry in the national economy development.
To raise bearing capacity of gears and reduce the size of transmission devices, hardened-tooth gears are widely used in many countries. However china's precision finishing technology of hardened-tooth gears is significantly behind the developed countries. It is a new attempt to introduce the ultrasonic vibration to traditional gear honing processing, the purpose is to use the advantages of the ultrasonic vibration cutting to overcome the traditional honing disadvantage, give full play to the advantage of gear honing in the precision finishing technology, and achieve the goal of gear machining at high quality, high efficient and low cost.
The design of vibration system is one of the key technologies in ultrasonic gear honing, and also is the further study base. Just for this reason, the project proposed by our research team, named "design theory of transformer with non-resonance structure and its application in ultrasonic gear honing and shaving"(No.50975191) was supported by national natural science foundation in2009. The key problem of "design theory of transformer with non-resonance structure" is focused to be solved and innovative research is carried out in this paper, its purpose is to solve the resonance of vibration system composed of gear and horn, and to make vibration mode and frequency and amplitude of gear meet the ultrasonic machining requirements. The following contents are mainly researched in this paper:
(1) The design of longitudinal vibration transformer
For small-diameter gear, its vibration mode of gear is one-dimensional longitudinal vibration driven by ultrasonic horn, its radial vibration and bending vibration can be neglected. The small diameter gear is simplified as a cylindrical rod, and then the system formed by the gear and fixing nut and transformer show the same features as compound ultrasonic horn. The longitudinal vibration transformer is designed using the design principle of the composite horn, and a more accurate calculation is obtained. In the last, the amplitude of longitudinal vibration transformer is also analyzed, and a new cascade horn is proposed to increases the amplitude of longitudinal vibration, it is suitable for the application of the large output horn.
(2) Axisymmetric flexural vibration of gear and circular plate, annular plate
Gear axisymmetric flexural vibration is fundamental of design the flexural vibration transformer. Gear is simplified as a circular plate which diameter is equal to gear's pitch circle diameter, and then Mindlin theory of moderately-thick plate vibration is used in the calculation of the gear flexural vibration. The comparison between the calculated results with FEM analysis results show it is more reasonable and accurate to analyze the vibration of gear using Mindin theory than using thin plate theory. Based on Mindlin theory, respectively methods are proposed to calculate the vibration frequency of circular plates with variable thickness along the radial and circular plates with circumferencially distributed holes. Comparisons of calculated results with FEM results prove that this method is reasonably accurate.
(3) The design of gear flexural vibration transformer
Gear flexural vibration transformer is the main vibration form of transformer with non-resonance structure in ultrasonic gear honing. Based on Mindlin theory, through in-depth analysis of vibration characteristics of the gear flexural vibration transformer, multiple computational model is proposed, and then the reasonably practicable design theories and methods of the flexural vibration transformer are identified binding experiments. Furthermore, amplitude distribution characters is analyzed and the measures to increase amplitude is raised. In some extend, the analysis of flexural vibration transformer with FEM is explored.
(4) Flexural vibration transformer composed by half-wavelength horn
Theories and experiments have shown that the length of nut will have an impact to the frequency of the transformer in flexural vibration amplitude transformer. The longer the fixed nut is, the lower frequency the transformer has, and on the contrary the amplitude transformer will have higher frequency. In addition, the adding of the fixed plate element to flexural vibration amplitude transformer will exert influence over the frequency of the transformer. Based on the results, we put forward a design idea of flexural vibration transformer composed by half-wavelength amplitude transformer. The amplitude transformer is designed as half wavelength and it adjusts the frequency by changing the size of the nut or fixed plate. Theoretically, a preliminary exploration is done on the transformer with this kind of structure.
(5) The design of radial vibration transformer
Radial vibration amplitude transformer is the third vibration form of the ultrasonic gear honing transformer with non-resonant Structure. The greater the aperture of gears is, the greater the diameter of horns, and the stronger the radial vibration of transformer. The gear's pure radial vibration is also a kind of axisymmetric vibration modes that can be used for compound ultrasonic machining of gears. Based on the longitudinal and radial coupled vibration theory, we present a design theory and mathematical model of radial vibration transformer and verify the accuracy of the design results using finite element analysis method. In addition, an analysis of frequency characteristics and amplitude characteristics of the radial vibration amplitude transformer is also conducted and the improved structure of it is proposed.
The above theoretical and experimental studies could help shape a fairly complete design theoretical system of ultrasonic gear honing transformer with non-resonant structure, meets the requirements of the ultrasonic gear honing. These creative researches will have set up a basis for the further theoretical and experimental studies on ultrasonic gear honing in the future.
为了提高齿轮的承载能力和缩小传动装置的尺寸,各国普遍采用硬齿面技术。而当前我国的硬齿面齿轮精加工技术明显落后于发达国家。将超声振动引入传统的珩齿工艺中进行超声辅助复合加工是硬齿面齿轮精加工技术的一种新的探索和尝试,其目的在于利用超声振动的特点改进传统珩齿技术的不足,充分发挥珩齿在硬齿面齿轮精加工中的优势,从而实现高质量、高效率、低成本的齿轮精密加工的目标。
超声辅助珩齿的关键技术之一是振动系统的设计,这也是后续所有研究工作的基础,为此,2009年国家自然科学基金资助了本课题组提出的“非谐振单元变幅器设计理论及其齿轮超声剃珩应用”(No.50975191)项目。本文瞄准“非谐振单元变幅器设计理论”这一关键问题进行了创新性研究,目的是解决不同结构、尺寸齿轮的振动系统的设计问题,使齿轮的振动模态、振动频率、振幅等满足超声珩齿加工的要求。本文主要完成以下研究工作：
(1)纵向振动变幅器的设计
对于小直径的齿轮,在变幅杆的推动下主要表现为一维纵向振动,其弯曲振动和径向振动可以忽略不计。将小直径齿轮简化为等截面圆柱杆,则由齿轮、固定螺母及变幅杆组成的变幅器的结构形式、振动特点与复合变幅杆相同。应用复合变幅杆的设计原理设计了纵向振动变幅器,并得到较准确的计算结果。分析比较了提高纵振变幅器振幅的措施,提出了针对大输出端变幅杆应用场合的改进式级联变幅杆。
(2)齿轮及圆板、环板的弯曲振动
齿轮的弯曲振动理论是设计弯曲振动变幅器的基础。将齿轮简化为与其分度圆等径的圆板或环板,应用Mindlin中厚板振动理论计算齿轮的弯曲振动,通过与有限元分析结果的比较,说明采用中厚板理论虽然计算复杂,但计算精度高,远优于经典薄板理论。针对沿径向阶梯变厚度齿轮、沿径向任意变厚度圆板、环板、带均布减重孔的齿轮,基于Mindlin中厚板振动理论创新性的提出了计算其弯曲振动频率的方法,通过与有限元分析结果的比较,证明了所提出的方法能够得到较准确的计算结果。
(3)弯曲振动变幅器的设计
弯曲振动变幅器是超声珩齿非谐振单元变幅器的主要形式。基于中厚板振动理论,深入分析了弯曲振动变幅器的振动特点,提出了多种数学模型和计算方法,结合实验,确定了合理可行的弯曲振动变幅器设计理论和方法。在此基础上对弯曲振动变幅器的振幅分布特性做了分析,提出了提高变幅器振幅的措施。此外,对弯曲振动变幅器有限元模态分析方法做了探讨。
(4)由二分之一波长变幅杆组成的弯曲振动
理论和实验都表明,在弯曲振动变幅器中,固定螺母的长度会对变幅器的频率产生影响,固定螺母越长则变幅器频率越低,反之变幅器频率越高。另外,在弯曲振动变幅器中加入固定板单元也会对变幅器频率产生影响。据此提出由二分之一波长变幅杆组成的弯曲振动变幅器的设计思想,变幅杆按二分之一波长设计,通过改变螺母或固定板的尺寸来调节变幅器频率。从理论上对这种结构的变幅器做了初步的探索研究。
(5)径向振动变幅器的设计
径向振动变幅器是超声珩齿非谐振单元变幅器的第三种形式。对于大孔径的齿轮,相应的变幅杆直径也大,变幅器的径向振动增强。如果齿轮做纯径向振动,则这也是一种轴对称的振动模态,可以用来进行齿轮的超声复合加工。基于纵、径耦合振动理论提出了径向振动变幅器的设计理论和数学模型,利用有限元分析方法验证了设计结果的准确性。此外对径向振动变幅器的频率特性和振幅特性做了分析,并提出了径向振动变幅器的改进结构。
通过以上理论与实验研究,形成了超声珩齿非谐振单元变幅器较为完善的设计理论体系,满足了超声珩齿加工的要求,为今后更深层次的超声珩齿理论研究和实验研究提供了基础。
Gear is the most important component of the mechanical power transmission. It has the advantages of wide range power, high transmission efficiency, accurate drive ratio, long life and safety so as to irreplaceable and extensive use. The gear as the basic components of machinery products is the foundational industry in the national economy development.
To raise bearing capacity of gears and reduce the size of transmission devices, hardened-tooth gears are widely used in many countries. However china's precision finishing technology of hardened-tooth gears is significantly behind the developed countries. It is a new attempt to introduce the ultrasonic vibration to traditional gear honing processing, the purpose is to use the advantages of the ultrasonic vibration cutting to overcome the traditional honing disadvantage, give full play to the advantage of gear honing in the precision finishing technology, and achieve the goal of gear machining at high quality, high efficient and low cost.
The design of vibration system is one of the key technologies in ultrasonic gear honing, and also is the further study base. Just for this reason, the project proposed by our research team, named "design theory of transformer with non-resonance structure and its application in ultrasonic gear honing and shaving"(No.50975191) was supported by national natural science foundation in2009. The key problem of "design theory of transformer with non-resonance structure" is focused to be solved and innovative research is carried out in this paper, its purpose is to solve the resonance of vibration system composed of gear and horn, and to make vibration mode and frequency and amplitude of gear meet the ultrasonic machining requirements. The following contents are mainly researched in this paper:
(1) The design of longitudinal vibration transformer
For small-diameter gear, its vibration mode of gear is one-dimensional longitudinal vibration driven by ultrasonic horn, its radial vibration and bending vibration can be neglected. The small diameter gear is simplified as a cylindrical rod, and then the system formed by the gear and fixing nut and transformer show the same features as compound ultrasonic horn. The longitudinal vibration transformer is designed using the design principle of the composite horn, and a more accurate calculation is obtained. In the last, the amplitude of longitudinal vibration transformer is also analyzed, and a new cascade horn is proposed to increases the amplitude of longitudinal vibration, it is suitable for the application of the large output horn.
(2) Axisymmetric flexural vibration of gear and circular plate, annular plate
Gear axisymmetric flexural vibration is fundamental of design the flexural vibration transformer. Gear is simplified as a circular plate which diameter is equal to gear's pitch circle diameter, and then Mindlin theory of moderately-thick plate vibration is used in the calculation of the gear flexural vibration. The comparison between the calculated results with FEM analysis results show it is more reasonable and accurate to analyze the vibration of gear using Mindin theory than using thin plate theory. Based on Mindlin theory, respectively methods are proposed to calculate the vibration frequency of circular plates with variable thickness along the radial and circular plates with circumferencially distributed holes. Comparisons of calculated results with FEM results prove that this method is reasonably accurate.
(3) The design of gear flexural vibration transformer
Gear flexural vibration transformer is the main vibration form of transformer with non-resonance structure in ultrasonic gear honing. Based on Mindlin theory, through in-depth analysis of vibration characteristics of the gear flexural vibration transformer, multiple computational model is proposed, and then the reasonably practicable design theories and methods of the flexural vibration transformer are identified binding experiments. Furthermore, amplitude distribution characters is analyzed and the measures to increase amplitude is raised. In some extend, the analysis of flexural vibration transformer with FEM is explored.
(4) Flexural vibration transformer composed by half-wavelength horn
Theories and experiments have shown that the length of nut will have an impact to the frequency of the transformer in flexural vibration amplitude transformer. The longer the fixed nut is, the lower frequency the transformer has, and on the contrary the amplitude transformer will have higher frequency. In addition, the adding of the fixed plate element to flexural vibration amplitude transformer will exert influence over the frequency of the transformer. Based on the results, we put forward a design idea of flexural vibration transformer composed by half-wavelength amplitude transformer. The amplitude transformer is designed as half wavelength and it adjusts the frequency by changing the size of the nut or fixed plate. Theoretically, a preliminary exploration is done on the transformer with this kind of structure.
(5) The design of radial vibration transformer
Radial vibration amplitude transformer is the third vibration form of the ultrasonic gear honing transformer with non-resonant Structure. The greater the aperture of gears is, the greater the diameter of horns, and the stronger the radial vibration of transformer. The gear's pure radial vibration is also a kind of axisymmetric vibration modes that can be used for compound ultrasonic machining of gears. Based on the longitudinal and radial coupled vibration theory, we present a design theory and mathematical model of radial vibration transformer and verify the accuracy of the design results using finite element analysis method. In addition, an analysis of frequency characteristics and amplitude characteristics of the radial vibration amplitude transformer is also conducted and the improved structure of it is proposed.
The above theoretical and experimental studies could help shape a fairly complete design theoretical system of ultrasonic gear honing transformer with non-resonant structure, meets the requirements of the ultrasonic gear honing. These creative researches will have set up a basis for the further theoretical and experimental studies on ultrasonic gear honing in the future.
引文
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