双圆弧谐波齿轮传动基本齿形的研究

在研究圆弧齿廓谐波齿轮传动啮合原理的基础上,提出了双圆弧谐波齿轮传动柔轮和刚轮基本齿廓设计方法。通过三维CAD设计软件SolidWorks查看柔轮和刚轮的配合情况,并用有限元法研究柔轮齿形的位移变形,模拟波发生器下柔轮的弹性变形过程,通过仿真结果验证柔轮齿形设计的合理性。     

考虑柔轮空间变形的谐波齿轮传动齿形设计方法

为了解决基于平面设计的轮齿在柔轮空间变形影响下的齿廓干涉问题,提出了一种考虑柔轮空间变形的双向共轭法.该方法分别在柔轮轮齿前后端截面对预设柔轮凸圆弧进行共轭计算,得到刚轮的双圆弧齿廓,用刚轮凸圆弧在前端截面反向共轭计算柔轮凹圆弧齿廓,并与预设凸圆弧结合得到柔轮齿廓.基于三维有限元分析进行谐波齿轮传动啮合仿真,证明了将柔轮空间变形引入齿形设计可以有效避免齿廓干涉.     

高精度谐波传动刚轮柔轮的检测

高精度谐波传动刚轮、柔轮的制作,不仅要解决轮齿的精加工工艺问题,而且必须解决高精度刚轮、柔轮轮齿的工艺检测方法和精度鉴定问题。谐波传动装置中的刚轮和柔轮常常是非渐开线型内齿和外齿的直齿圆柱齿轮。由于选用齿形角近于30°的直线型齿廓,因而在刚轮、柔轮的检测方法上,特别是齿形误差的检测方法必须特殊考虑。本文介绍5～3级高精度谐波传动刚轮、柔轮的检测方法,着重探讨了直线型齿廓齿形误差的检测方法。一、直线型齿廓内齿齿型误差的测量     

谐波减速器传动机构的动态仿真研究

为了研究谐波减速器在实际工作状态下的变形情况,利用Adams对模型进行动态仿真.谐波减速器齿轮均采用双圆弧齿形,因此首先对齿形进行设计,并通过solidworks建立谐波传动装置各零部件的模型.然后在AnsysWorkbench中对柔轮进行静力学分析,查看柔轮的应力分布以及变形情况.最后利用Adams建立谐波减速器的刚柔混合模型,实现柔轮和刚轮的动态仿真.通过仿真分析可以看到谐波减速器的传动过程比较平稳,柔轮与刚轮轮齿之间的啮合情况良好,因此可以说明减速器的传动机构设计合理.     

用B矩阵法建立谐波齿轮啮合基本方程

利用文献［１］提出的建立啮合方程的Ｂ矩阵法，建立了谐波齿轮传动的理论啮合方程，求出了任意变形形状时谐波齿轮传动Ｂ矩阵的一般形式。设计者只须给出齿形方程及其法线方程，而无须在改变齿形时重新计算啮合点的相对速度（对应包络法中的各个偏导数）。计算了具有余弦凸轮波发生器的谐波齿轮传动中，与渐开线柔轮齿廓共轭的刚轮齿廓及形成共轭的发生器转角区间。得出在这种变形形状下，在柔轮齿的啮入侧或啮出侧分别有两个共轭区间，在发生器转角为±３９°附近的第二条共轭曲线是由柔轮的内齿廓包络形成     

接转化啮合再现法设计加工谐波传动柔轮

本文所探讨的“转化啮合再现法”，其要点为（１）使柔轮处在与刚轮空载啮合时相同的变形条件下进行范成加工；（２）加工装置中的波发生器固定不动，切齿刀具与刚轮存在着对应关系”；（３）按柔轮的当量齿轮法进行设计计算，将当量齿轮的分度圆取在柔轮中线上，并使该对齿轮假想的节圆与分度国重合。按上述原理设计加工出的谐波传动齿轮副能够符合齿廓啮合基本定理。柔轮轮齿加工装置结构简单，生产率高。     

双圆弧谐波齿轮传动柔轮齿廓参数对侧隙的影响

在谐波齿轮传动中,空载啮合侧隙对其传动性能有显著影响。基于谐波传动共轭精确求解方法,研究了谐波齿轮传动共轭区间、刚轮理论共轭齿廓和侧隙随柔轮齿廓参数的变化规律。研究结果表明,柔轮齿廓参数对啮合共轭区间、刚轮理论共轭齿廓和侧隙具有决定性作用。减少凸齿廓圆弧半径有利于增加啮合共轭区间,但不利于减小侧隙;凹齿廓圆弧半径对共轭区间影响不明显,对侧隙影响较大;减小公切线倾角有利于增加共轭区间,也有利于减小侧隙值和改善侧隙分布;凸齿廓、凹齿廓圆弧半径对刚轮齿廓参数影响明显,公切线倾角对刚轮齿廓参数几乎无影响。合理选择柔轮齿廓参数能够获得更大的共轭区和更均匀的侧隙分布,从而提高承载能力和传动性能。     

基于包络精确算法的渐开线齿廓谐波齿轮侧隙计算

啮合侧隙大小是影响谐波齿轮传动工作性能的重要指标之一。为了更准确计算渐开线谐波齿轮的侧隙,应用基于柔轮装配变形的共轭精确算法确定变形后柔轮齿的位置,计算渐开线齿廓柔轮的共轭齿廓,用曲线拟合的方法获得刚轮渐开线齿廓的变位系数,并进行侧隙计算。侧隙计算结果发现:渐开线齿廓谐波齿轮的最小侧隙出现在柔轮齿顶或刚轮齿顶。在柔轮最大变形左侧,最小侧隙出现在刚轮齿顶处,而在右侧则出现在柔轮齿顶处。     

圆弧齿廓谐波齿轮齿廓设计和啮合侧隙优化

以圆弧齿廓谐波齿轮为研究对象,建立柔轮节曲线上任意点的切向方程和法向方程,并将柔轮节曲线上各点的切向位移与法向位移拟合,计算出装入椭圆凸轮波发生器时的柔轮齿廓曲线。根据柔轮坐标系到刚轮坐标系的变换矩阵及所求出的柔轮齿廓曲线,得到刚轮齿廓上离散点的坐标,从而拟合出与柔轮齿廓共轭的刚轮齿廓。建立了柔轮和刚轮间的侧隙模型,并以啮合侧隙为目标函数,选取柔轮齿面与刚轮齿面接触点的压力角、柔轮齿廓的全齿高、柔轮轮齿的法向转角及柔轮齿面接触线的弧长增量,这4个变量作为侧隙优化的设计变量,使侧隙量在满足约束方程的条件下最小。针对椭圆波发生器的谐波齿轮,通过其圆弧齿廓设计和啮合侧隙优化的实例,验证了理论模型的正确性。     

谐波齿轮传动的齿形设计

基于曲线映射理论,阐述谐波齿轮传动非干涉且大范围啮合齿形的设计方法。先根据柔轮中线上点的运动轨迹,确定近似齿形;然后考虑柔轮齿倾斜和运动轨迹改变的情况,对近似齿形进行适当修正,得到最终齿形。     

端面谐波齿轮传动啮合性能的分析

端面谐波齿轮传动较径向谐波齿轮传动有不同的特点,它是在轴向变形力的作用下迫使端面齿柔轮变形使其与端面齿刚轮啮合并产生相对运动。对端面谐波齿轮传动来说,啮入深度、齿侧间隙等是分析和评价其啮合性能的质量指标,而齿形角、柔轮的变形规律和变形量的大小,又是影响啮入深度和齿侧间隙的主要因素。为此本文利用已建立的啮合分析计算方法,通过计算机绘出的图形,着重分析齿形角、最大变形量等对啮入深度和齿侧间隙的影响,并从中获得了一些有实用价值的结论,从而为端面谐波齿轮传动选取合理的啮合参数和结构参数提供了依据。     

变齿厚渐开线齿轮包络环面蜗杆传动啮合性能分析

为准确掌握变齿厚渐开线齿轮包络环面蜗杆传动的宏微观啮合性能及各设计参数对啮合性能的影响,建立了传动副数学模型,推导出啮合几何学方程,研究了螺旋角、传动比、法向模数及压力角等主要设计参数对啮合性能的影响规律;综合考虑选取优化设计参数并进行传动副样件加工,通过传动副对检试验考察了接触斑点的分布情况。分析结果表明：在满足环面蜗杆喉部中径强度和刚度要求的情况下,适当螺旋角、较大传动比、较大法向模数和较大压力角会获得优异的接触线分布、接触区域和较优的微观啮合质量;右侧的微观啮合质量优于左侧的微观啮合质量;传动副样件接触斑点与理论分析结果一致,右侧齿面接触斑点分布更好,验证了分析方法的正确性。     

变轴交角渐开线齿轮啮合理论和设计

为了提供合理的变轴交角渐开线齿轮传动设计方法,基于双自由度齿轮啮合理论,对这种传动进行了研究。在轴交角变动范围内,由相配齿轮2齿面无根切导出两轮支座摆动轴线位置和相配齿轮2工作齿宽的计算公式,得到支座摆动轴线与渐开线齿轮1轴线间距l1的许用最小值l1min和最大值l1max;得到不同轴交角 时的重合度计算公式;推导出啮合点瞬时接触椭圆参数的计算公式。研究表明：取l1接近l1max时,相配齿轮2工作齿宽最大;轴交角| |为最大时重合度ε最大,=0时ε最小;相配齿轮2中断面分度圆啮合点处的瞬时接触椭圆参数接近其余各点的平均值,可由该点来评价接触质量,使计算大为简化。为这种传动的几何设计,提供一套详尽的计算方法。     

Geometric design of involute spur gear drives with symmetric and asymmetric teeth using the Realized Potential Method

The index gear drive potential is defined for the estimation of the quality of spur gear drives as a maximum contact ratio obtained at the contact of teeth profiles along the full line of action. In this paper, a new method is proposed for the geometric design of symmetric and asymmetric involute meshing in which the contact ratio of the gear drive is equal to its potential. This method is appropriate for the geometric design of spur gears with a small teeth number and is based on the generalized model of involute meshing. The gear drive potential is assigned as an input value, from which, after appropriate calculations, the geometry of rack-cutters, gears and involute meshing can be determined. Using the proposed method, the areas of the realized potential and the areas of the existence of involute gear drives are defined. In addition, many numerical examples are solved. In the cases of symmetric and asymmetric meshing, the minimum teeth number is obtained when the gear drive potential is larger than one.     

齿轮副端面重合度统一定义及其计算式

针对各种齿轮传动提出端面重合度的统一定义,并且推导其计算表达式,进一步讨论了渐开线齿轮副、微线段齿轮副和正弦齿廓齿轮副的端面重合度的计算问题。齿轮副的端面重合度定义为齿轮作用角（即一对轮齿从进入啮合到脱离啮合过程中齿轮所转过的角度）与齿轮的齿距转角的比值。根据齿轮啮合原理,由基本齿条的轮廓曲线能够获得其啮合线方程。根据所获得的啮合线方程,以及给定的齿轮副齿顶线方程,就能够根据本文的计算式得到齿轮副的重舍度。对于渐开线齿轮副,该定义与众所周知的“啮合线长度与基节之比”的结果相同。该定义同样适用于非渐开线齿轮副,例如微线段齿轮副、正弦齿廓齿轮副等,而且计算结果更可靠。     

Geometric design of a face gear drive with a helical pinion

The application of face gear drives, which have been used recently instead of bevel and hypoid gears for helicopter transmission, has resulted in renewed interest in such drives. A helical pinion must be utilized to change the composition of the contact surface freely. In this work, the problem of where to place the pinion with respect to a gear is solved by defining a reference point. The effect of the helix angle on the composition of the surface contact lines is clarified. A geometric design method that recognizes meshing singularity is proposed. Two unique lines on which specific sliding becomes infinite are regarded as design indexes. Results show that the contribution of the surface contact lines changes significantly depending on the helix angle, and the offset distances influence the effective tooth width of the gear.     

具有啮合齿面接触对的谐波传动有限元模型建立与分析

现有谐波传动有限元分析模型过于简化,与实际情况差别较大,为此,在ANSYS中建立带有整圈轮齿的刚轮和柔轮模型,利用其接触分析要素在啮合齿面间定义面-面接触对,使得各对轮齿在啮合时产生作用力,从而提出了一种与实际较接近的谐波传动有限元模型建模方法;以50机型为例,用该方法得到了负载作用下柔轮的等效应力、变形、各啮合齿面接...     

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-to-weight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.     

行星分度凸轮机构瞬心线的研究

根据少齿差行星齿轮传动中的三环传动原理,提出了一种新型机构———行星分度凸轮机构Ⅳ型结构。推导了行星分度凸轮机构凸轮和针轮的瞬心线方程以及凸轮理论廓线的法线方程,得出如下结论:凸轮与针轮的瞬心线是封闭的、连续的,但由于机构输出是间歇运动,故其瞬心线封闭在无穷远处,在机构的停歇期,两轮瞬心P沿直线ObOg在无穷远处;在凸轮与针轮啮合的瞬时,各针齿与凸轮啮合点处,凸轮理论廓线的法线交汇于该瞬时凸轮与针轮的速度瞬心,符合齿形啮合基本定理。     

Contact finite element method for dynamic meshing characteristics analysis of continuous engaged gear drives

The dynamic meshing characteristics of gear drives have been a major concern in the design of power transmission systems as they affect vibration, acoustic noise, durability and efficiency. Gaining a more comprehensive understanding of the dynamic meshing characteristics of continuous engaged gear drives is a key to the development of power transmission systems. In this paper, a dynamic contact finite element analysis method, considering the variation of the engaged teeth pairs, the loaded elastic and contact deformations, and the sliding friction, is presented for the dynamic meshing characteristics analysis of continuous and elastic engaged gear drives. Various kinds of continuous engaged gear models under low and high speed condition are simulated and compared using the presented method. The tooth profile modification was designed based on the simulation results. Moreover, the effects of the tooth profile modification, the sliding friction and the time-varying meshing stiffness upon the dynamic meshing characteristics of continuous engaged gear drives are discussed in detail. The results show that the method is not only effective in designing and evaluating the tooth profile modification, but also in studying the dynamic meshing characteristics of continuous engaged gear drives with realistic time-varying meshing stiffness and tooth sliding friction. The present method could provide an effective tool for vibration mechanism study and dynamic design of the continuous engaged gear drives considering more influence factors.