【作者】 郭芳；

【导师】 方宗德； 张永振；

【作者基本信息】 西北工业大学 ， 机械设计及理论， 2020， 博士

【摘要】 因齿轮加工需要经过多道工序、多次离线(或在线)测量,产生加工偏差是无法避免的。齿轮加工偏差形成机理复杂、种类繁多,影响齿轮的传动精度和传动平稳性,是齿轮传动系统产生振动和噪声的主要原因之一,在高速和重载工况下可能会造成轮齿失效的严重后果。因此,齿轮加工偏差不容忽视,准确地描述齿轮加工偏差、对含加工偏差的实际齿轮传动系统进行动力学仿真分析具有重要的应用价值。本文系统地提出了考虑确定性齿轮加工偏差的齿轮传动系统动力学分析方法,该方法基于实测齿面偏差数据,将齿轮加工偏差的影响全面、真实地引入齿轮传动系统动力学仿真模型中。基于齿轮加工偏差具有随机性的特点,应用上述考虑确定性齿轮加工偏差的理论分析方法,统计分析了随机性齿轮加工偏差对齿轮系统内部激励及动态响应的影响规律,并基于统计结果对含加工偏差的齿轮进行齿面修形6σ稳健优化设计。本文的主要内容和研究成果如下:(1)提出了含确定性加工偏差的实际齿面接触仿真分析方法。该方法采用双三次B样条曲面拟合不规则分布的实测齿面偏差数据,细致地将齿面微小波动呈现于偏差曲面中。基于偏差曲面和理论齿面构建实际齿面,并对实际齿面进行几何接触分析和承载接触分析,获得了含确定性加工偏差的实际齿面静态啮合特性(包括几何传动误差、齿面接触印痕、承载传动误差等),体现了各项齿面加工偏差的影响。(2)基于实际齿面的几何接触分析和承载接触分析,提出了确定性齿轮加工偏差影响下齿轮系统内部激励的计算方法。大周期静态几何传动误差激励包括啮合周期(即齿频)误差激励和大、小轮的转动周期(即转频)误差激励。综合时变啮合刚度激励基于齿轮副的几何传动误差、承载传动误差和综合承载变形之间的关系而确定。提出了实际齿面在非全齿面接触时发生线外接触具体位置的判定方法,计算了啮入冲击激励。三种内部激励均基于考虑加工偏差的齿轮副实际啮合过程计算而得。(3)考虑上述三种内部激励,建立了含确定性齿轮加工偏差的斜齿轮传动弯-扭-轴耦合动力学仿真模型。在拟静态和动态两种工况下,对齿轮系统进行了动力学性能仿真分析。深入探索了齿轮系统动态响应随小轮转速的变化规律,确定了系统的共振转速,并与ISO标准进行对比验证。对比分析了三种内部激励对齿轮系统动态响应的影响。本文提出的考虑确定性齿轮加工偏差的齿轮系统动力学分析方法真实、合理地将加工偏差的影响引入动力学仿真模型中。(4)以用于齿面检测的斜齿轮副作为试验件,搭建封闭功率流式齿轮传动试验台,在拟静态和动态两种工况下进行齿轮传动性能测试试验,并与理论仿真结果进行对比分析,以验证本文所提理论分析方法的可行性和准确性。(5)基于考虑确定性齿轮加工偏差的齿轮系统动力学分析方法,提出了考虑随机性加工偏差的齿轮传动系统动力学特性统计分析方法。深入研究了随机性单项齿面偏差以及随机性综合齿面偏差对齿轮系统内部激励及动态响应的影响规律,对比分析了不同形式的齿面偏差特征对齿轮传动性能的影响程度。(6)选取对齿轮传动性能影响最恶劣的齿面偏差特征,采用6σ稳健优化设计方法和确定性优化设计方法,对含此类偏差特征的齿轮系统进行减振优化设计。利用蒙特卡罗模拟方法对修形优化方案进行随机抽样,对含修形参数抽样值和齿面偏差的齿轮传动系统进行动力学计算,对比分析两种优化设计方法所得修形优化方案的可行性以及修形优化后的齿轮系统动态性能的稳健性。研究表明:在考虑加工偏差的条件下,6σ稳健优化设计方法保证修形方案的可行性概率达到6σ水平,有效提高了齿轮系统传动性能的稳健性。更多还原

【Abstract】 Due to multiple processes and offline(or online)measurements in the gear processing,gear machining deviation will occur inevitably.Its formation mechanism is complex and it covers a great variety species.The gear machining deviation affects the transmission accuracy and transmission stability of gear,which is one of the main causes of vibration and noise of gear transmission system.Under the condition of high speed and heavy load,it may cause the failure of gear teeth.Hence,the machining deviation of gears can never be ignored.The accurate description of the gear machining deviation and the dynamic simulation analysis on the actual gear transmission system with machining deviation have great applied value.This paper presents a dynamic analysis method of gear transmission system considering the deterministic gear machining deviation.In this method,the influence of the gear machining error is fully and realistically introduced into the dynamic simulation model of gear transmission system based on the measured tooth surface deviation.Because of the randomness of gear machining deviation,the statistical analysis on the effect law of the random gear processing deviation on the internal excitations and dynamic response of gear system is done by use of the above theoretical analysis method for the deterministic gear machining deviation.According to the statistical results,the tooth surface modification design of gear with processing deviation is done by the method of six-sigma robust optimization design.The main contents and results of this paper are as follows:(1)A contact simulation method for real tooth surface with deterministic machining deviation is presented.In this method,the measured tooth surface deviation data with irregular distribution is fitted as an error curved surface by using the bicubic B-spline curved surface,and the minor fluctuations of the tooth surface are presented in it in detail.Based on the theoretical tooth surface and the deviation surface,the real tooth surface is constructed and the gear tooth contact analysis and loaded tooth contact analysis are done on it.The static meshing characteristics(including geometric transmission error and tooth contact pattern,loaded transmission error,etc.)of real tooth surface with deterministic processing deviation are obtained,which reflect the influence of the tooth surface processing deviation.(2)Based on the gear tooth contact analysis and the loaded tooth contact analysis on the real tooth surface,the calculation method of the internal excitations of the gear system is proposed under the action of the deterministic gear machining deviation.The large period static geometric transmission error excitation includes the error excitation of meshing period(i.e.tooth frequency)and the error excitation of rotation period of pinion and gear(i.e.rotation frequency).The comprehensive time-varying meshing stiffness excitation is determined based on the relationship between the geometric transmission error,loaded transmission error and comprehensive elastic deformation of the gear pair.A judgment method about the exact position of meshing-in point when the non-full tooth contact of the real tooth surface happens is presented.By using this method the meshing-in impact excitation is calculated.The three internal excitations are all calculated based on the actual meshing process of gear pair considering the machining deviation.(3)Considering the above three kinds of internal excitation,a dynamic simulation model with coupled lateral-torsional-axial is established for the helical gear transmission system with the deterministic machining deviation.The dynamic simulation analysis of the gear drive system is carried out under the quasi-static and dynamic conditions.The variation of the dynamic response of gear system with the rotation speed of pinion is explored deeply.The resonance speed of gear system is determined and it is demonstrated by ISO standard.The effects of three internal excitations on the dynamic response of gear system are compared and analyzed.The dynamic analysis method of gear system considering the deterministic gear machining deviation introduces the influence of gear machining deviation into the dynamic simulation model in a real and reasonable way.(4)Taking the helical gear pair used for tooth surface detection as the test piece,a power cycling test bed is built to test the gear transmission,and the gear transmission performance test is carried out under the quasi-static and dynamic conditions.The results are contrasted between the experiment and theoretical simulation to verify the feasibility and accuracy of the theoretical analysis method proposed in this paper.(5)Based on the dynamic analysis method of gear system with the deterministic gear machining deviation,a statistical analysis method for the dynamic characteristics of gear transmission system considering the random machining deviation is presented.The method has deeply studied the influence law of the single random tooth surface deviation and the comprehensive random tooth surface deviation on the internal excitation and the dynamic response of gear system.The influence on the gear transmission performance between deferent forms of tooth surface deviation is compared and analyzed.(6)Selecting the tooth surface deviation characteristic with the worst influence on the gear transmission performance,the vibration reduction optimization for gear system with such deviation characteristic is done by the six sigma robust optimization design method and the deterministic optimization design method.The random sampling of the modification optimization scheme is conducted by using the Monte Carlo Simulation method.Considering the modification parameter sampling values and the tooth surface deviation,the dynamic calculation of the gear transmission system is carried out.The feasibility of the modification optimization scheme obtained by the two optimization design methods and the robustness of the dynamic performance of gear system after the modified optimization are analyzed and compared.The results show that,considering the machining deviation,the six sigma robust optimization design method ensures a six sigma level of feasibility probability for the modification design scheme and strengthen the robustness of the transmission performance of the gear system effectively.更多还原