面齿轮齿面创成方法及啮合特性研究
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摘要
摘要：面齿轮传动是一种由圆柱齿轮与圆锥齿轮相啮合演变而来的新型齿轮传动,与锥齿轮传动相比,具有体积小、质量轻、承载能力高、噪声低、可靠性高、寿命长等诸多特点。尤其是其在武装直升机主减装置中的独特分流特性,引起了业界的高度关注。目前,面齿轮传动正逐步替代螺旋锥齿轮而成为武装直升机传动系统中最重要的核心零件。
本文以高强度、低噪声的高质量面齿轮设计为目标,对其齿面创成方法及啮合特性进行相关研究,主要研究内容如下：
1.基于范成加工的面齿轮齿面生成及接触迹特征研究
根据面齿轮啮合原理,建立了齿面工作区及过渡区的曲面方程,对轮齿外圈出现齿顶变尖和内圈产生齿根根切的原因进行了分析,获得了满足齿根不产生根切及齿顶不变尖的面齿轮最小内半径和最大外半径系数的变化曲线,为面齿轮参数设计提供了方便；推导了齿面接触迹方程,并获得了齿面接触迹分布规律图；对不同模数、齿数差条件下的齿面接触迹进行了仿真,发现齿面接触迹与齿数差、模数及传动比有关,其中传动比对接触迹影响较大。同时发现,如果模数变大将引起齿高和齿长变大,而齿数增加将引起齿宽变大,但齿高则变小；建立了考虑安装偏差的面齿轮传动坐标系,对安装过程中出现的偏置距偏差、轴向偏差和轴向夹角偏差等三种偏差之间的联系进行讨论,发现通过控制安装偏差可以改变面齿轮传动在啮合过程中的接触区域位置,以便进行接触轨迹的调整。
2.面齿轮齿面创成几何方法及磨齿物理场研究
对面齿轮齿面采用蜗杆磨削所需的运动进行分析,建立了面齿轮齿面蜗杆磨削机床的几何模型。根据蜗杆砂轮包络过程坐标系,推导了由插齿刀齿面包络蜗杆砂轮齿面时的坐标变换矩阵,建立了用于磨削面齿轮的蜗杆砂轮模型；并对采用所设计的蜗杆砂轮模型仿真加工出的面齿轮的齿面与理论齿面进行对比,进行面齿轮磨削齿面接触及误差分析；对面齿轮磨削过程中的热力耦合及工艺参数对面齿轮磨削物理场影响的程度进行了分析,得到了齿面磨削时的温度、应力及应变的分布图。结果表明：磨削速度高和磨削深度小,对面齿轮齿面磨削是有益的,而进给速度对齿面磨削应力和应变等影响不明显,因此,可适当提高面齿轮的磨削进给速度。
3.面齿轮啮合温度场与振动特性分析
对齿面啮合点处的相对滑动速度、接触压力、齿面摩擦因数、摩擦热流量沿啮合面的分布规律及影响因素进行了分析,结果表明：大的压力角降低齿面摩擦热流量有利；对不同啮合位置的齿面温升进行了分析,发现齿面温度最高点位于齿顶边缘附近区域；分别就齿数差、压力角、模数、转数及负载等因素对面齿轮啮合性能的影响进行分析,结果表明：面齿轮传动系统中的主要振动来源于从动轮面齿轮。压力角为20°或者25°、齿数差为3时系统振动最小。增大模数对改善系统振动有益,但输入转速增加、负载增大,系统的振动则加剧。
4.面齿轮传动啮合实验研究
为了验证面齿轮传动啮合性能仿真结果的正确性,在面齿轮检查机上,对三种齿数差的面齿轮传动接触迹、传动误差及振动进行了测试,测试结果表面：齿数差对接触迹有一定的影响,但不明显。传动比对齿面接触迹的影响比较大,在一定范围内,传动比越大,接触迹越靠近轮齿的中部；振动测试实验研究发现：圆柱齿轮的齿数差为1时,面齿轮传动的误差最小。但齿数差为2时的面齿轮传动,其啮合性能较好；圆柱齿轮和面齿轮在x轴方向的振动受转速的影响都比较大,而z轴方向的振动则很小,但面齿轮较圆柱齿轮在z轴方向的振动受转速的影响要更敏感。图133幅,表19,参考文献181。
Abstract:Face-gear transmission is a new-type gear transmission.It evolves from the transmission with cylindrical gear and bevel gear wheel.Compared with bevel gear drive, it has many advantages, for example, small size, light weight, high bearing capacity, low noise, high reliability, long life.Especially, it used in the main decelerator of armed helicopter, because of its distinctive split-flow characteristic which has been paid close attention. At present, face-gear transmission are taking the place of spiral bevel gears and becoming top-drawer key components in the drive system of armed helicopters.
The tooth surface generating and meshing characteristics of face gears were studied for the purpose of designing high-quality face-gear with high strength and low noise. The main contents are as follows:
1. The tooth surface generating of face-gear based on generating cutting and the research on the contact trace
According to the face-gear meshing theory, equations of the working tooth surface and transition curved surface were derived. And the reasons that the outside of tooth appears the tooth top sharpens and the inner side of tooth appears the tooth root undercuts were analyzed.Finally,the change curves of minimum inner radius and maximum external radius' coefficient which can keep unsharpened tooth top and disundercuted tooth root, which provides convenience for the parameter design of face gear. The equation of contact track on the tooth surface was derived, by which can obtain the distribution map of contact trace. Based on the simulations on tooth surface contact were proceeded under conditions of different modules and tooth number, found that the tooth contact trace is related to the difference of number of teeth, modulus and transmission ratio, and the influence of transmission ratio is larger. And,if the modulus is increased,the height and length of the tooth will increase. While if the number of tooth is increased,width of the tooth will increase,the height of the tooth will decrease.Face-gear transmission coordinate system considering installing deviation is established.The relation among offset deviation, axial deviation and axis shaft deviation that exist during installation is discussed.It was found that controlling the deviation can change the position of the contact area on surface in the meshing process of face-gear drive, and it can adjust the contact trace.
2. The research on the geometric method of face-gear tooth surface generating and the physical field of face-gear teeth grinding
The movement was analyzed in process of face-gear grinding by worm grinding wheel, and the geometric model of grinding machine for face-gear tooth surface grinding by worm grinding wheel was built. On the basis of the coordinate system of the worm grinding wheel enveloping process, the coordinate transformation matrix when the tooth surface of shaping cutters enveloped worm grinding wheel tooth surface was derived, and the model of worm grinding wheel was built for face-gear grinding. With the model of worm grinding wheel designed,the surface of face-gear is simulation processed.By comparison of it and theoretical tooth surface, contact and deviation were analyzed in the process of face-gear grinding.Thermo-mechanical coupling and the influence of process parameters on face-gear grinding physical field were analyzed.The distribution diagram of temperature, stress and strain in process of tooth surface grinding were obtained.The results showed that, higher grinding speed and lower grinding depth are beneficial for the tooth surface grinding of face-gear, but the feeding speed's influence on the tooth surface grinding stress is not obvious. So, it may be appropriate to properly increase the speed of face gear grinding feed.
3. Analysis on the temperature field and vibration characteristics of face-gear meshing
Absolute and relative slipping velocity, contact pressure, tooth surface friction coefficient of the meshing points,and the distribution law and the influencing factors of frictional heat flux along meshing surface have been analyzed.And we got conclusions that larger pressure angle is good for the decrease of the frictional heat flux. The analysis on the temperature rise of tooth surface with the variation of meshing position in the meshing process of face-gear drive was conducted. The study found that the highest temperature point is in the region near the top edge.The influences of factors such as tooth number difference, pressure angle, modulus, rotation speed and load on face-gear meshing performance was analyzed. The study found that the main source of surface vibration of face-gear drive is the slave wheel, i.e. face-gear. The vibration of system is the least when the pressure angle is20degree or25degree, the difference of number of teeth is3.Larger modulus is beneficial to the improvement of vibration of system,while larger input speed and load will increase the vibration of the system.
4. The research on the experiments on the meshing performance of face-gear drive
In order to verify the correctness of the simulation results of face-gear drive meshing performance, the contact trace and transmission errors of the face-gear drive that a face-gear meshing with three cylindrical gears of1-3tooth difference respectively, were tested on a face-gear tester. The test results showed that the influence of the difference of the number of tooth on contact trace is not obvious, but the transmission ratio's is large. Larger transmission ratio, within a certain range, can make the contact trace near the middle of tooth. Experimental study on the vibration testing found that the difference of number of teeth is1, least error of face gear drive, but when the difference of number of teeth is2, meshing performance of face-gear drive is better. The influence of rotation on vibration of cylindrical gear and face-gear in the X axis direction are larger than in the Z axis. But the influence of rotation on vibration of face-gear in the Z axis direction is larger than more sensitive than cylindrical gear.
本文以高强度、低噪声的高质量面齿轮设计为目标,对其齿面创成方法及啮合特性进行相关研究,主要研究内容如下：
1.基于范成加工的面齿轮齿面生成及接触迹特征研究
根据面齿轮啮合原理,建立了齿面工作区及过渡区的曲面方程,对轮齿外圈出现齿顶变尖和内圈产生齿根根切的原因进行了分析,获得了满足齿根不产生根切及齿顶不变尖的面齿轮最小内半径和最大外半径系数的变化曲线,为面齿轮参数设计提供了方便；推导了齿面接触迹方程,并获得了齿面接触迹分布规律图；对不同模数、齿数差条件下的齿面接触迹进行了仿真,发现齿面接触迹与齿数差、模数及传动比有关,其中传动比对接触迹影响较大。同时发现,如果模数变大将引起齿高和齿长变大,而齿数增加将引起齿宽变大,但齿高则变小；建立了考虑安装偏差的面齿轮传动坐标系,对安装过程中出现的偏置距偏差、轴向偏差和轴向夹角偏差等三种偏差之间的联系进行讨论,发现通过控制安装偏差可以改变面齿轮传动在啮合过程中的接触区域位置,以便进行接触轨迹的调整。
2.面齿轮齿面创成几何方法及磨齿物理场研究
对面齿轮齿面采用蜗杆磨削所需的运动进行分析,建立了面齿轮齿面蜗杆磨削机床的几何模型。根据蜗杆砂轮包络过程坐标系,推导了由插齿刀齿面包络蜗杆砂轮齿面时的坐标变换矩阵,建立了用于磨削面齿轮的蜗杆砂轮模型；并对采用所设计的蜗杆砂轮模型仿真加工出的面齿轮的齿面与理论齿面进行对比,进行面齿轮磨削齿面接触及误差分析；对面齿轮磨削过程中的热力耦合及工艺参数对面齿轮磨削物理场影响的程度进行了分析,得到了齿面磨削时的温度、应力及应变的分布图。结果表明：磨削速度高和磨削深度小,对面齿轮齿面磨削是有益的,而进给速度对齿面磨削应力和应变等影响不明显,因此,可适当提高面齿轮的磨削进给速度。
3.面齿轮啮合温度场与振动特性分析
对齿面啮合点处的相对滑动速度、接触压力、齿面摩擦因数、摩擦热流量沿啮合面的分布规律及影响因素进行了分析,结果表明：大的压力角降低齿面摩擦热流量有利；对不同啮合位置的齿面温升进行了分析,发现齿面温度最高点位于齿顶边缘附近区域；分别就齿数差、压力角、模数、转数及负载等因素对面齿轮啮合性能的影响进行分析,结果表明：面齿轮传动系统中的主要振动来源于从动轮面齿轮。压力角为20°或者25°、齿数差为3时系统振动最小。增大模数对改善系统振动有益,但输入转速增加、负载增大,系统的振动则加剧。
4.面齿轮传动啮合实验研究
为了验证面齿轮传动啮合性能仿真结果的正确性,在面齿轮检查机上,对三种齿数差的面齿轮传动接触迹、传动误差及振动进行了测试,测试结果表面：齿数差对接触迹有一定的影响,但不明显。传动比对齿面接触迹的影响比较大,在一定范围内,传动比越大,接触迹越靠近轮齿的中部；振动测试实验研究发现：圆柱齿轮的齿数差为1时,面齿轮传动的误差最小。但齿数差为2时的面齿轮传动,其啮合性能较好；圆柱齿轮和面齿轮在x轴方向的振动受转速的影响都比较大,而z轴方向的振动则很小,但面齿轮较圆柱齿轮在z轴方向的振动受转速的影响要更敏感。图133幅,表19,参考文献181。
Abstract:Face-gear transmission is a new-type gear transmission.It evolves from the transmission with cylindrical gear and bevel gear wheel.Compared with bevel gear drive, it has many advantages, for example, small size, light weight, high bearing capacity, low noise, high reliability, long life.Especially, it used in the main decelerator of armed helicopter, because of its distinctive split-flow characteristic which has been paid close attention. At present, face-gear transmission are taking the place of spiral bevel gears and becoming top-drawer key components in the drive system of armed helicopters.
The tooth surface generating and meshing characteristics of face gears were studied for the purpose of designing high-quality face-gear with high strength and low noise. The main contents are as follows:
1. The tooth surface generating of face-gear based on generating cutting and the research on the contact trace
According to the face-gear meshing theory, equations of the working tooth surface and transition curved surface were derived. And the reasons that the outside of tooth appears the tooth top sharpens and the inner side of tooth appears the tooth root undercuts were analyzed.Finally,the change curves of minimum inner radius and maximum external radius' coefficient which can keep unsharpened tooth top and disundercuted tooth root, which provides convenience for the parameter design of face gear. The equation of contact track on the tooth surface was derived, by which can obtain the distribution map of contact trace. Based on the simulations on tooth surface contact were proceeded under conditions of different modules and tooth number, found that the tooth contact trace is related to the difference of number of teeth, modulus and transmission ratio, and the influence of transmission ratio is larger. And,if the modulus is increased,the height and length of the tooth will increase. While if the number of tooth is increased,width of the tooth will increase,the height of the tooth will decrease.Face-gear transmission coordinate system considering installing deviation is established.The relation among offset deviation, axial deviation and axis shaft deviation that exist during installation is discussed.It was found that controlling the deviation can change the position of the contact area on surface in the meshing process of face-gear drive, and it can adjust the contact trace.
2. The research on the geometric method of face-gear tooth surface generating and the physical field of face-gear teeth grinding
The movement was analyzed in process of face-gear grinding by worm grinding wheel, and the geometric model of grinding machine for face-gear tooth surface grinding by worm grinding wheel was built. On the basis of the coordinate system of the worm grinding wheel enveloping process, the coordinate transformation matrix when the tooth surface of shaping cutters enveloped worm grinding wheel tooth surface was derived, and the model of worm grinding wheel was built for face-gear grinding. With the model of worm grinding wheel designed,the surface of face-gear is simulation processed.By comparison of it and theoretical tooth surface, contact and deviation were analyzed in the process of face-gear grinding.Thermo-mechanical coupling and the influence of process parameters on face-gear grinding physical field were analyzed.The distribution diagram of temperature, stress and strain in process of tooth surface grinding were obtained.The results showed that, higher grinding speed and lower grinding depth are beneficial for the tooth surface grinding of face-gear, but the feeding speed's influence on the tooth surface grinding stress is not obvious. So, it may be appropriate to properly increase the speed of face gear grinding feed.
3. Analysis on the temperature field and vibration characteristics of face-gear meshing
Absolute and relative slipping velocity, contact pressure, tooth surface friction coefficient of the meshing points,and the distribution law and the influencing factors of frictional heat flux along meshing surface have been analyzed.And we got conclusions that larger pressure angle is good for the decrease of the frictional heat flux. The analysis on the temperature rise of tooth surface with the variation of meshing position in the meshing process of face-gear drive was conducted. The study found that the highest temperature point is in the region near the top edge.The influences of factors such as tooth number difference, pressure angle, modulus, rotation speed and load on face-gear meshing performance was analyzed. The study found that the main source of surface vibration of face-gear drive is the slave wheel, i.e. face-gear. The vibration of system is the least when the pressure angle is20degree or25degree, the difference of number of teeth is3.Larger modulus is beneficial to the improvement of vibration of system,while larger input speed and load will increase the vibration of the system.
4. The research on the experiments on the meshing performance of face-gear drive
In order to verify the correctness of the simulation results of face-gear drive meshing performance, the contact trace and transmission errors of the face-gear drive that a face-gear meshing with three cylindrical gears of1-3tooth difference respectively, were tested on a face-gear tester. The test results showed that the influence of the difference of the number of tooth on contact trace is not obvious, but the transmission ratio's is large. Larger transmission ratio, within a certain range, can make the contact trace near the middle of tooth. Experimental study on the vibration testing found that the difference of number of teeth is1, least error of face gear drive, but when the difference of number of teeth is2, meshing performance of face-gear drive is better. The influence of rotation on vibration of cylindrical gear and face-gear in the X axis direction are larger than in the Z axis. But the influence of rotation on vibration of face-gear in the Z axis direction is larger than more sensitive than cylindrical gear.
引文
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