摘要
硬齿面齿轮的广泛应用,满足了现代工业对齿轮传动提出的结构紧凑、噪音小、性能稳定的使用要求。珩齿是一种对淬硬齿轮进行精加工的工艺方法,可作为硬齿面齿轮的最终精加工工序。传统珩齿工艺存在加工效率低、珩轮易堵塞、修形能力差等缺点。可以考虑从提高珩削速度、减小珩削力、缩短磨粒切削长度、减少珩轮堵塞等方面改进珩齿工艺。现代超声波加工理论和技术为这一构想提供了理论基础和技术支撑。超声珩齿将超声振动切削技术应用于珩齿加工,其高频振动能有效减小珩磨力,切削液的超声空化作用可以对珩轮进行动态清洗,有效减小珩轮堵塞,提高加工效率,可充分发挥硬珩齿工艺特点。超声珩齿振动系统是超声珩齿工艺系统的核心,其性能直接影响着工件质量。目前,在超声加工振动系统设计中,普遍采用谐振单元的全谐振设计理论：而齿轮的振动频率由其结构决定,不能按照超声波发生器的工作频率进行谐振设计,是非谐振单元。因此,课题组提出了非谐振单元变幅器的设计理论,解决了薄环盘类圆柱齿轮的超声珩齿振动系统的设计问题。但工程应用中,大多数齿轮的厚径比在中厚板范围内,还带有轮毂、辐板、轮缘、减重孔等结构,超声珩齿振动系统的设计,不能直接应用中厚板的振动求解理论。这制约了超声珩齿技术的发展与应用,为此,超声珩齿振动系统的设计理论和实验研究,已成为超声珩齿加工中亟待解决的问题。
本论文以建立中小模数(小于10mm),分度圆直径在300mm左右的不同结构、尺寸的齿轮与变幅杆两非谐振单元组成的超声珩齿振动系统的非谐振设计理论为目标,研究振动系统的全谐振设计与非谐振设计之间的联系与区别。从理论和实验角度证明：振动系统的全谐振设计是非谐振设计的特例,非谐振设计涵盖了全谐振设计,是超声振动系统设计理论的扩展和深化。提出了齿轮与变幅杆两非谐振单元超声珩齿振动系统的非谐振设计理论。其实质是根据齿轮结构特点,合理简化其振动模型,联合建立齿轮和变幅杆的振动系统模型,通过振动耦合的位移、力、弯矩等连续条件和边界条件建立系统的振动频率方程,进而确定满足谐振频率和振动模态的系统形状尺寸参数。
按照振动系统利用变幅杆与齿轮的耦合振动形式,超声珩齿振动系统可分为：纵向、纵向—弯曲、纵向—径向三种耦合振动形式。圆柱齿轮横向弯曲振动的统一求解模型的建立与求解,是纵—弯齿轮变幅器非谐振设计的理论基础。将齿轮等效为与其分度圆等径的中厚环盘,利用Mindlin中厚板振动求解理论,通过齿轮轮毂、辐板、轮缘三个环盘单元的耦合振动连续条件和边界条件,并结合三个环盘单元的厚度尺寸关系,建立了圆柱齿轮的横向弯曲振动求解的统一模型,为超声珩齿振动系统的设计奠定了理论基础。
阻抗特性和谐振特性是超声珩齿振动系统的两个重要性能指标。以阻抗分析仪和激光测振仪为基础,建立了振动系统的阻抗特性和谐振特性参数测量系统,可以精确测量齿轮端面不同位置的振幅,为非谐振单元齿轮超声加工振动系统的精确设计和谐振特性检测提供了一种新的测试方法。
对不同振动方式齿轮变幅器所适应齿轮参数范围给出定量描述。加工分度圆直径小于100mm,厚径比大于0.3的中小模数齿轮,适宜利用纵向振动方式设计振动系统；加工分度圆直径大于100mm,且厚径比小于0.3的齿轮,适宜利用纵弯耦合振动方式设计振动系统。推导出各类型纵向、纵弯谐振变幅器的频率方程,通过多种变幅器的设计、有限元分析验证、谐振特性实验,表明：对于分度圆直径一定,不同的中小模数、齿数圆柱齿轮的变幅器设计,非谐振设计理论是有效的,它将非谐振单元变幅器的设计理论从薄环盘理论拓展到了中厚环盘理论。为工程中不同结构参数的圆柱齿轮超声珩齿振动系统的设计提供了设计理论和技术支撑。
应用三维振动里兹数值求解方法,统一了圆锥、指数形和悬链线形变幅杆的扭转、纵向、弯曲振动的求解方法；结果表明：三维振动里兹数值法求解比一维振动理论求解准确,方便了大截面变幅杆的设计。统一了径向变厚度环盘横向弯曲和径向振动的求解方法,为变厚度齿轮动态分析建模、振动特性分析提供了一种新的求解分析方法。为超声珩齿振动系统的精确建模和三维振动求解分析提供了研究基础。
综合应用上述设计理论和实验方法研制了高速超声珩齿装置,在Y4650珩齿机上构建了超声珩齿实验系统,实现了超声珩齿。与传统珩齿相比,超声珩齿的工艺优势在于：可以获得更理想的齿面质量、更高的珩削效率,且齿面加工纹理复杂,齿轮的齿形、齿向、径向跳动、周节累积偏差有不同程度的减小,尤其齿向偏差减小更明显。为利用超声振动增大珩齿的修形能力,提高齿轮加工精度,提供了实验依据。
上述研究工作得到了国家自然科学基金项目“非谐振单元变幅器设计理论及其齿轮超声剃珩应用(50975191)”和山西省研究生优秀创新项目“齿轮超声加工振动系统设计理论与实验验证(20113027)”的资助。通过以上设计理论和实验研究,确立了超声珩齿振动系统的非谐振设计理论,拓展和完善了超声加工振动系统的设计理论体系。超声珩齿振动系统的非谐振设计方法同样适合于超声滚齿、剃齿、研齿等齿轮超声加工振动系统的设计,为超声加工在齿轮精密制造中的发展与应用奠定了理论和实验基础。
Modern gear transmissions must be compact, noiseless and stable in performance, so the most primary need is hardened gear with high precision. Gear honing process used in the finial process of quench-hardening gear is a surface finishing machining. However, traditional gear honing was inefficient and poor ability of modification, while honing wheel was jammed usually. Gear honing was restricted within these drawbacks. Ultrasonic vibration can reduce honing forces obviously and ultrasonic cavitations of machining liquid can implement dynamic washing during the machining process, which decreases the jam of honing wheel and increases the honing efficience. So the ultrasonic gear honing has a bright future to apply. Gear resonance system is the core of gear ultrasonic honing system, which has significant effect on gear ultrasonic machining quality. Most of the researchers designed ultrasonic resonance system in resonant way. Otherwise, gear is a inharmnoic unit. The inherent vibration frequency of gear is decided by its own stcture and paremeters according to engineering application. It is reasonable to design gear ultrasonic resonance system in inharmnoic design method rather than resonant design. Therefore, it brought forward a inharmonic design theory of gear amplitude transformer, which can design resonant system of thin plate helical gear in ultrasonic honing. However, the ratio of thickness to reference diameters of most gear in engineering application falls into that of moderate plate. At the same time, there are hub, web, rim, weight reducing holes structures in most gear. It can't adopt moderate plate theory straightway to design resonance system in ultrasonic gear honing, which restricts the development and application of ultrasonic gear honing. There are no consummate design theories of gear ultrasonic resonance system. It is important to set up design theory system of ultrasonic resonance system composed of inharmonic units. The inharmonic design theory is essential for small and moderate modulus gear with different structure feature in ultrasonic honing.
It is compulsory to present design theory of resonant system composed of two inharmonic units such as gear and horn. In ultrasonic gear honing, the gear's modulus is less than10mm and the reference circle diameter is about300mm. It also laid more emphasis on the distinguish and affiliation of whole-resonance and inharmonic design theories. Through theoretical and experimental view, it proved that the whole-resonance design theory is a special case of the inharmonic design theory, the inharmonic design theory covers the whole-resonance design theory, which is the expansion and deepening of the ultrasonic vibration system design theory. It presented a inharmonic design approach to design transformer in ultrasonic gear honing. Firstly, it brought out a simplified vibration analytical model that was equivalent to the gear, according to gear structure characteristic. Secondly, it set up a united analytical model of vibration system composed of gear and horn. Therefore, frequency equation was achieved in this way based on kinetic equation, force and displacement coupling, and boundary condition. The unknown parameter and mode shape have been solved in the theory with the help of Matalab201IRa.
There are three kinds of vibration style such as longitudinal mode, longitudinal-flexural mode, and longitudinal-radial mode in ultrasonic gear honing, according to the coupling vibration style of the two inharmonic units. An analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. The natural boundary conditions that traverse displacement, rotation angle, shear force and flexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is quite consistent. The model has certain theoretical significance to guide designing a vibration system in ultrasonic gear honing.
Mechanical impedance and resonance characteristic are two key guideline to design resonant system in ultrasonic gear honing. Impedance characteristic measure system was set up based on impedance analyzer. Polytec Laser Doppler Vibrometers OFV-505and lathe C6140were used to precisely measure mechanical vibrations amplitude of different location in gear of resonant system, which will be helpful for accurate design and experiment of resonant system.
Furthermore it pointed out that these gear parameters range was suit to certain vibration style of resonance system. During the machining process of the gear with middle or small modulus, it could be appropriate for the gear with less than100millimeter diameter of reference circle and the ratio of thickness to radial dimension more than0.3to use the amplitude transformer with longitudinal vibration mode. It also could be appropriate for the gear with more than100millimeter diameter of reference circle and the ratio of thickness to radial dimension less than0.3to use the amplitude transformer with longitudinal and flexural vibration mode. A novel design method was derived from a uniform analyzed model of gear with wheel hub, web and rim based on the Mindlin moderate plate theory. The uniform analytical model of resonant system in longitudinal-lexural vibration was set up based on kinetic equation, force and displacement coupling, and boundary condition of horn and gear. The natural boundary conditions that traverse displacement, rotation angle, shear force and flexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. Therefore, frequency equation was achieved in this way. Comparisons were made with the frequencies and displacement arised from the presented method, finite elements method, and resonant vibration experiment. The result derived from these three ways is very identical, which validates the design method of transformer in longitudinal-flexural vibration mode. The design method of resonant system composed of two units in gear flexural vibration was brought forward, which can extend the transformer design range from gear including thin annular plate to gear including moderate annular plate. The inharmonic design theory will provided theoretical and technical support for resonant system of helical gear with different structure and parameters.
It presented the Ritz method in Energy-variational principle based on three dimensional elasticity kinetics equations. Three vibration modes such as longitudinal, bending and torsional vibration inherent frequencies and mode shapes for conical, exponential and catenary horns could be solved. Analytical solutions based on the three dimensional elastic vibration theories produce more accurate answers than ones that are based on the classical Euler-Bernoulli theory. Axisymmetric free vibration such as transverse flexural and radial vibration inherent frequencies and mode shapes for annular disk with non-uniform thickness cross section could be solved. The present work proposes a new approach to vibrational characteristics analysis of the annular disks with non uniform cross-section. The conclusion has certain theoretical guidance and engineering application significance to design the vibration system of ultrasonic gear machining.
The high speed ultrasonic gear honing device was developed with the help of the above design theory, furthermore, the ultrasonic gear honing experimental system in gear honing machine Y4650was established. The contrast experiment of using the longitudinal, longitudinal and transversal amplitude transformer in ultrasonic gear honing to the traditional gear honing was also accomplished. At the same time, surface roughness, revolution mark, honing cutting efficiency and the gear machining precision have been contrastive analyzed. It can achieve better gear roughness and two times cutting efficiency through the ultrasonic honing method than it in the traditional method. At last, the tooth precision through the direction of ultrasonic vibration becomes better, which provides a experimental proof that it is possible to improve gear honing precision and enforce modification possibility by gear ultrasonic vibration.
The dissertation was supported by the national natural science foundation project of China (Grant No.50975191) of China and the outstanding innovation project (Grant No.20113027) of Shanxi province foundation for graduate student. The above theory and experiment form the inharmonic design theory of resonant system in ultrasonic gear honing, which enriches and perfects the design theory of ultrasonic machining vibration system. The inharmonic design theory is suitable for resonant system in gear ultrasonic hobbing, shaving and lapping. The experiment about the comparison between the result of ultrasonic honing and that of traditional honing laids a solid theoretical and experimental foundation of the research and application of gear ultrasonic machining.
引文
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