直齿面齿轮啮合性能预控及碟形砂轮磨齿关键技术研究
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摘要
面齿轮传动作为一种新型的机械传动形式,具有结构紧凑、安装方便、单级传动比高、重合度大等优点,特别是在分流—汇流传动中表现出来的优势,使其近年来逐渐成为欧美各国相关研究机构关注的热点,其中的典型代表是美国DARPA在TRP计划中成功设计了先进的面齿轮分流装置,该设计与弧齿锥齿轮传动机构相比,重量减轻约50%,动力传输密度提高35%。
在齿轮传动中,齿面接触性能是衡量传动质量的主要指标,在不考虑安装误差的情况下,齿面的三维拓扑形状是影响齿面接触性能的关键因素,通过对齿轮的齿面拓扑修形以避免边缘接触,改善接齿面接触性能一直是国内外相关学者追踪的目标,面齿轮也同样存在相似问题。
目前,面齿轮传动在螺旋翼飞行器的主传动系统中已得到应用,并表现出了优异特性；但由于国外相关的技术封锁和保密,我国的面齿轮加工研究一直处于初级阶段,特别是面齿轮的硬齿面精加工,还处于理论分析及试验阶段。
根据上述情况,本文在面齿轮齿坯设计,齿面修形及啮合性能预控,面齿轮的碟形砂轮磨齿技术等方面做了系统研究,解决了面齿轮的蝶形砂轮磨齿的相关理论问题及机床加工方案。主要成果包括：
(1)研究了偏置面齿轮齿面结构及特性。根据齿轮啮合理论及面齿轮插齿加工原理,建立了面齿轮的切削模型,推导了面齿轮齿面方程,根据面齿轮齿根发生根切及齿顶变尖的条件,获得了面齿轮的最小内半径,最大外半径和齿宽系数的计算公式,讨论了设计参数对三种系数的影响规律；并在上述推导基础上编制了偏置面齿轮齿坯的参数化设计软件,避免了重复编程,使设计过程灵活高效。
(2)提出了面齿轮副三维拓扑修形原理及啮合性能的预控方法。基于TCA原理,研究了基于小轮齿面三维拓扑修形理论,根据齿轮啮合及磨削修形原理,推导了二阶和高阶抛物线修形的小轮齿面方程,通过控制齿廓和齿向两个方向的5个修形因数,实现了对面齿轮啮合性能的预控,改善了齿面接触印痕的方向和位置,得到了抛物线形状的传动误差曲线,减小了传动误差幅值,同时降低面齿轮副对安装误差的敏感性,使啮合印痕和传动误差得到较好的控制。
(3)根据蝶形砂轮产成磨削面齿轮的原理,提出了三种而齿轮磨削方案及产形机床的运动关系模型,推导了五轴联动加工中心磨削面齿轮的插补运动公式,并对加工过程做了数控仿真。推导了蝶形砂轮的产成齿面方程,通过推导砂轮轴截面廓形的等距曲线,计算了金刚轮修整砂轮的运动轨迹,编制了蝶形砂轮磨齿加工及砂轮修整程序,并提出了多片砂轮廓形的展成修整法。研究了小轮的成形磨齿修形的方法,以及成形磨齿修形运动规律,研究了小轮修形量的求解及其变化规律,编制相关磨齿加工程序及砂轮修整程序。
(4)研究了面齿轮的磨削加工齿面误差及补偿方法。首先分析了而齿轮的蝶形砂轮磨削误差产生机理,确定了砂轮安装误差种类；建立了蝶形砂轮磨削加工面齿轮的数学模型,推导了包含蝶形砂轮安装误差的而齿轮误差曲面方程,通过规划齿面网格点,计算了网格点法向误差,分析了砂轮安装误差对齿面啮合区平均法向误差值的影响,提出了砂轮安装误差对面齿轮齿面误差影响的敏感方向,确定了两类误差敏感方向的计算方法,在此基础上分析了砂轮安装误差对而齿轮齿形误差的影响规律,利用分析结果对砂轮安装参数进行调整,实现了对面齿轮齿面误差的补偿。
(5)完成了面齿轮蝶形砂轮磨削加工及齿轮副滚检试验。利用砂轮修整程序和面齿轮磨削加工程序,在五轴联动磨齿机上完成了面齿轮磨削试验,对齿面进行了测量及修正；进行了小轮双向修形磨齿试验及检测,完成了齿轮滚检及噪声对比试验,试验及检测结果显示,通过调整小轮的修形因数,可以实现对血齿轮副啮合性能的预控。试验结果验证了基于TCA分析的面齿轮副性能预控理论和蝶形砂轮磨削理论的正确性及工程可行性。
Face-gear drive is a new developing type of transmission form. Compared with general spiral bevel gears, the face-gear drive has many advantages such as compact structure, high gear ratio, big contact ratio, alignment convenience. Particularly, the advantages of application of face gears are the possibility of split and the convergence of the torque, it has become focus of related research body in Europe and the United States in recent years, Typical representation is that an advanced split transmission equipment has been successful designed by America DARPA in TRP program using the face gear, reduced the quality of gear box by50%, enhance its power transmission density by35%.
The meshing behavior is an important item to evaluate the transmission quality of face gear, and the3D topology shape of the tooth surface is the key factor to meshing behavior, such improvement of the meshing behavior is the research target of relevant scholars by means of tooth surface modification.
At present, the face gear drive has been applied in main transmission system of rotorcraft in overseas, but processing technology of face gear is still in the initial stage in our country because of the blockade and security of technologies, especially the harden Gear Grinding technology is in theoretical analysis and experimental stage.
This paper presented investigations such as gear blank design, tooth surface modification and meshing behavior pre-control, as well as the grinding technology by using grinding disk. The main results include:
(1) Tooth geometry design of face gear is studied. Generating model of face gear was built and the tooth surface equation is derived based on differential geometry, gear meshing principle and shaping processing of face gear. The conditions of undercutting and pointing for an offset face-gear in the generation process were studied, the expressions of approximate and exact solution for inner radius and outer radius to avoid undercutting and pointing are provided, respectively. According to the study above, Parametric design program of face gear is compiled.
(2)3D topology modification theory of face gear drive are studied and the pre-control method for meshing behavior is proposed. According to the principle of grinding, the tooth surface equation of modification parabolic has been obtained. Based on the principle of TCA, the position and orientation of the contact path of tooth face can be pre-control by changing modification parabola coefficient of tooth profile and tooth direction, reaching the purpose of reducing the sensitivity of the gear drive to the misalignments. At same time, the predesigned parabolic function of transmission errors can be obtained, which reducing noise and vibrations of the face-gear drive efficiently.
(3) According to the generation theory and grinding disk motion of face gear ground by grinding disk, there grinding schemes are proposed and the model of the machine tool are set up. Based on the processing Principle of5-axis machining center, the gerneral equation of interpolated point coordinates is derivated, and NC manufacturing simulation is realized. Diamond roller motion trajectory for dressing grinding disk is calculation, which is consistent with the equidistant curve of grinding disk axis section profile. The pinion forming-grinding method is studied and the processing scheme of pinion double crowned modification is proposed, grinding wheel dressing program and cutter grinding program are completed.
(4) The single indexing grinding of face gear is discussed. Contributing factors of gear machining errors are analyzed. Mathematical model for grinding face gear is built and the tooth surface equation is derived based on application of grinding disk, the theoretical tooth surface and real tooth surface are obtained. The relationship between grinding disk installation errors and tooth surface errors is researched. The analytical results are helpful to compensation of the tooth surface errors.
(5) A face gear is ground by grinding disk and meshing experiments are finished. Grinding experiment of face gear has been completed on5-axis cnc grinding machine using grinding wheel dressing program and grinding program. The distribution situation of tooth face error is obtained based on using CNC gear measuring center and the error sources of tooth surface are analyzed. Pinion double crowned modification experiment has been completed, meshing behavior pre-control has been realized through the optimization of modification coefficients. The experimental results show that the performance pre-control theory based on TCA and grinding disk theory of the face gear are correct.
在齿轮传动中,齿面接触性能是衡量传动质量的主要指标,在不考虑安装误差的情况下,齿面的三维拓扑形状是影响齿面接触性能的关键因素,通过对齿轮的齿面拓扑修形以避免边缘接触,改善接齿面接触性能一直是国内外相关学者追踪的目标,面齿轮也同样存在相似问题。
目前,面齿轮传动在螺旋翼飞行器的主传动系统中已得到应用,并表现出了优异特性；但由于国外相关的技术封锁和保密,我国的面齿轮加工研究一直处于初级阶段,特别是面齿轮的硬齿面精加工,还处于理论分析及试验阶段。
根据上述情况,本文在面齿轮齿坯设计,齿面修形及啮合性能预控,面齿轮的碟形砂轮磨齿技术等方面做了系统研究,解决了面齿轮的蝶形砂轮磨齿的相关理论问题及机床加工方案。主要成果包括：
(1)研究了偏置面齿轮齿面结构及特性。根据齿轮啮合理论及面齿轮插齿加工原理,建立了面齿轮的切削模型,推导了面齿轮齿面方程,根据面齿轮齿根发生根切及齿顶变尖的条件,获得了面齿轮的最小内半径,最大外半径和齿宽系数的计算公式,讨论了设计参数对三种系数的影响规律；并在上述推导基础上编制了偏置面齿轮齿坯的参数化设计软件,避免了重复编程,使设计过程灵活高效。
(2)提出了面齿轮副三维拓扑修形原理及啮合性能的预控方法。基于TCA原理,研究了基于小轮齿面三维拓扑修形理论,根据齿轮啮合及磨削修形原理,推导了二阶和高阶抛物线修形的小轮齿面方程,通过控制齿廓和齿向两个方向的5个修形因数,实现了对面齿轮啮合性能的预控,改善了齿面接触印痕的方向和位置,得到了抛物线形状的传动误差曲线,减小了传动误差幅值,同时降低面齿轮副对安装误差的敏感性,使啮合印痕和传动误差得到较好的控制。
(3)根据蝶形砂轮产成磨削面齿轮的原理,提出了三种而齿轮磨削方案及产形机床的运动关系模型,推导了五轴联动加工中心磨削面齿轮的插补运动公式,并对加工过程做了数控仿真。推导了蝶形砂轮的产成齿面方程,通过推导砂轮轴截面廓形的等距曲线,计算了金刚轮修整砂轮的运动轨迹,编制了蝶形砂轮磨齿加工及砂轮修整程序,并提出了多片砂轮廓形的展成修整法。研究了小轮的成形磨齿修形的方法,以及成形磨齿修形运动规律,研究了小轮修形量的求解及其变化规律,编制相关磨齿加工程序及砂轮修整程序。
(4)研究了面齿轮的磨削加工齿面误差及补偿方法。首先分析了而齿轮的蝶形砂轮磨削误差产生机理,确定了砂轮安装误差种类；建立了蝶形砂轮磨削加工面齿轮的数学模型,推导了包含蝶形砂轮安装误差的而齿轮误差曲面方程,通过规划齿面网格点,计算了网格点法向误差,分析了砂轮安装误差对齿面啮合区平均法向误差值的影响,提出了砂轮安装误差对面齿轮齿面误差影响的敏感方向,确定了两类误差敏感方向的计算方法,在此基础上分析了砂轮安装误差对而齿轮齿形误差的影响规律,利用分析结果对砂轮安装参数进行调整,实现了对面齿轮齿面误差的补偿。
(5)完成了面齿轮蝶形砂轮磨削加工及齿轮副滚检试验。利用砂轮修整程序和面齿轮磨削加工程序,在五轴联动磨齿机上完成了面齿轮磨削试验,对齿面进行了测量及修正；进行了小轮双向修形磨齿试验及检测,完成了齿轮滚检及噪声对比试验,试验及检测结果显示,通过调整小轮的修形因数,可以实现对血齿轮副啮合性能的预控。试验结果验证了基于TCA分析的面齿轮副性能预控理论和蝶形砂轮磨削理论的正确性及工程可行性。
Face-gear drive is a new developing type of transmission form. Compared with general spiral bevel gears, the face-gear drive has many advantages such as compact structure, high gear ratio, big contact ratio, alignment convenience. Particularly, the advantages of application of face gears are the possibility of split and the convergence of the torque, it has become focus of related research body in Europe and the United States in recent years, Typical representation is that an advanced split transmission equipment has been successful designed by America DARPA in TRP program using the face gear, reduced the quality of gear box by50%, enhance its power transmission density by35%.
The meshing behavior is an important item to evaluate the transmission quality of face gear, and the3D topology shape of the tooth surface is the key factor to meshing behavior, such improvement of the meshing behavior is the research target of relevant scholars by means of tooth surface modification.
At present, the face gear drive has been applied in main transmission system of rotorcraft in overseas, but processing technology of face gear is still in the initial stage in our country because of the blockade and security of technologies, especially the harden Gear Grinding technology is in theoretical analysis and experimental stage.
This paper presented investigations such as gear blank design, tooth surface modification and meshing behavior pre-control, as well as the grinding technology by using grinding disk. The main results include:
(1) Tooth geometry design of face gear is studied. Generating model of face gear was built and the tooth surface equation is derived based on differential geometry, gear meshing principle and shaping processing of face gear. The conditions of undercutting and pointing for an offset face-gear in the generation process were studied, the expressions of approximate and exact solution for inner radius and outer radius to avoid undercutting and pointing are provided, respectively. According to the study above, Parametric design program of face gear is compiled.
(2)3D topology modification theory of face gear drive are studied and the pre-control method for meshing behavior is proposed. According to the principle of grinding, the tooth surface equation of modification parabolic has been obtained. Based on the principle of TCA, the position and orientation of the contact path of tooth face can be pre-control by changing modification parabola coefficient of tooth profile and tooth direction, reaching the purpose of reducing the sensitivity of the gear drive to the misalignments. At same time, the predesigned parabolic function of transmission errors can be obtained, which reducing noise and vibrations of the face-gear drive efficiently.
(3) According to the generation theory and grinding disk motion of face gear ground by grinding disk, there grinding schemes are proposed and the model of the machine tool are set up. Based on the processing Principle of5-axis machining center, the gerneral equation of interpolated point coordinates is derivated, and NC manufacturing simulation is realized. Diamond roller motion trajectory for dressing grinding disk is calculation, which is consistent with the equidistant curve of grinding disk axis section profile. The pinion forming-grinding method is studied and the processing scheme of pinion double crowned modification is proposed, grinding wheel dressing program and cutter grinding program are completed.
(4) The single indexing grinding of face gear is discussed. Contributing factors of gear machining errors are analyzed. Mathematical model for grinding face gear is built and the tooth surface equation is derived based on application of grinding disk, the theoretical tooth surface and real tooth surface are obtained. The relationship between grinding disk installation errors and tooth surface errors is researched. The analytical results are helpful to compensation of the tooth surface errors.
(5) A face gear is ground by grinding disk and meshing experiments are finished. Grinding experiment of face gear has been completed on5-axis cnc grinding machine using grinding wheel dressing program and grinding program. The distribution situation of tooth face error is obtained based on using CNC gear measuring center and the error sources of tooth surface are analyzed. Pinion double crowned modification experiment has been completed, meshing behavior pre-control has been realized through the optimization of modification coefficients. The experimental results show that the performance pre-control theory based on TCA and grinding disk theory of the face gear are correct.
引文
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