外文翻译--变圆弧齿轮的形成原理及特性.doc

Variable Arc Gear Principle and the Formation of Abstract To a class of variable arc gear. Use of deviation function, given the tooth profile of the structural integrity of the process, proved its tooth profile engagement to meet the basic law of tooth profile equation derived basic formula, discussed the changing arc of the gear, given the changing arc tooth Profile examples; such gear has a high carrying capacity, especially for high-speed, high-precision CNC machining, it will be occasions in the heavy transmission applications. Keywords：gear, profile, deviation function, engagement principle, gear strength Introduction With the development of science and technology, to drive the requirements have been increased, particularly in the area of heavy and small is particularly prominent. At present, the gear used in the design of a involutes line, and cycloid arc tooth profile three of them, involutes gear due to manufacturing simple deviation from the Centre not sensitive to the advantages of widely used, but it bearer Less and less for heavy transmission; cyclonical gear contact stress small, tooth profile of the coincidence of large and is conducive to the improvement of bending strength, but the meshing of gears precision manufacturing and assembly higher; last century 1950s the arc gear bending strength is not high, in order to achieve continuous contact to be made generally helical gears, and small manufacturers in the area have been greatly restricted. In order to increase the carrying capacity of gears, the researchers put forward a number of new tooth profile, for example: micro-segment gear profile, dual-band involutes gear, the gear increase the intensity could play a role, but these new teeth Profile in the manufacturing or assembly areas there are still certain deficiencies. This deviation from the concept of function, a new type of gear - gear change arc. The paper introduced the arc gear change the formation of principle, derived Tooth formula, discussed the changing arc of the gear is given tooth profile examples. 1 A variable arc tooth profile of a principle 1.1 Variable arc tooth profile of a principle Below D. C. H. Yang according to American scholars, such as the deviation function (DF), variable arc tooth profile on the formation of principle. P1 is a radius of a circle of the gear section, 1 for the corner to e(1) radius, evenly distributed in the center of a round, painted a series of round, as shown in Figure 1 (here for e(11) = COS(21); When e(1) bound to meet certain conditions, this series of round envelope can to smooth the tooth profile g1 (1), can be seen from the map, e1 (1) = | | P (1) - g (1)| |, said e (1) for the deviation function and we will meet the above principle of formation of a tooth profile collectively referred to as variable envelope arc tooth profile, referred to as variable arc tooth profile, It constitutes a change of gear known as the Arc gear. When the deviation from function e（1）= r1cos（）, the change is the common arc tooth profile of the involutes tooth profile, and when the deviation function for Then changed the arc tooth profile Cycloid is the tooth profile, and the general arc gear, the equivalent of deviation function e(1) only in certain discrete points value. 1.2 arc tooth profile change the calculation Can be seen from Figure 2, the component that coordinates with the gear change arc tooth profile of the equation for P1 (1) (2) - In, defined as the point g tooth profile of the normal line with the angle between the x-axis, which is a function of 1 from Figure 2 that （3） In order to get the tooth profile to the practical application, the deviation must also function e(1) the choice to do certain restrictions (1) To ensure the tooth profile of non-crossing to （4）(2) To ensure that equation (3) Solution for （5） (3) To ensure the contour of C continuous, in the section with a round p1 Tooth g1 at the intersection of Cp, e() must be zero. (4) To ensure Tooth fairing, in e(1) minimum, between the maximum change must be monotonous. (5) In order to gear teeth N1 for integer and ensuring that a certain overlap factor , the meeting point between the point of view of the 1 should meet. 2 gear change arc tooth profile of the engagement principle For a change of gear arc tooth profile of mutual engagement, as shown in Figure 3, in one instant, this conjugate gear and s Tooth and g point in the mesh, according to tooth profile engagement principle, Conjugate tooth profile equation can be written （6） （7） （8） （9） （10） （11） - In, g1x, g1y, g2x and g2y are engaging point g in gear with the Cartesian coordinates of and in the coordinates of weight, and is 2 gear 1 and the corner, and 1 and 2 tooth profile is in g The normal line with the two points x coordinate axis angle. Meshing the two tooth profile in the course of maintaining contact with the condition that the Tooth c1g points on the speed and vgn1 Tooth c2g points on the normal line speed vgn2 in the direction of the rate of weight equal to that vgn1=vgn2; generated from the tooth profile of principle We can see that the two gear tooth profile at any point g meshing of the existence of public law n-n even with the TAC in the heart of node P, from and respectively, to the point n-n for vertical, the TAC in n1, n2 and, Figure 3, the transmission ratio for the (12) Therefore, we concluded: Arc gear change can be achieved than the constant speed drive. Variable Arc gear tooth profile of the relative speed of sliding （13） （14）Under normal circumstances, and change the arc gear with the gear pressureangle corner of the variables, the involutes tooth profile line, e(1) = r1cos (), the pressure angle into the formula available e = a. 3 Arc gear profile change the characteristics of In theory, change gears arc, including meshing of gears and meshing gear.Because of the meshing of the involutes gear has created a simple, is not sensitive to the advantages of error, therefore, discussed below the arc gear changeis raising gear strength for the purpose of the occasion for heavy protruding-concave Internal arc gear change . Shown in Figure 4, to a round of the interface can be changed arc tooth profile split into convex teeth a, a and b, b teeth in two parts, a , b is a, b mirror, a and b of the deviation can use different functions were designed, it must be in the circle of the intersection and to ensure that the Nodal Agency for at least one band. Gear failure is the main form of broken teeth and pitting, to reflect their performance indicators include: tooth root bending strength and intensity of contact with the surface; tooth root bending stress for the approximate calculation formula （15） - In, for the tooth width, h and b, respectively force Ft role points to the distance between the tooth root and tooth width. According to Hertz contact stress theory, assuming that two gear the same materials, Internal Tooth g point of contact in the contact stress is calculated as （16） Type in g1 g2 were two tooth profile at contact points in the radius of curvature, their formula for （17） （18） From the above formula we can see that tooth contact stress and the size of the contact point difference is directly proportional to the radius of curvature, tooth root bending stress and tooth contact with the stress generated tooth profile of the deviation function, therefore, change through a rational design of Arc gear The deviation function, we can get the tooth root bending strength and intensity of contact with the surface. Variable Arc gear in a state of instantaneous meshing of gears and double arc similar, but ordinary double arc in order to achieve continuous transmission gear must be made in the form of helical gears, here on the arc gear change is through a series of different radius Arc the envelope, straight teeth in the circumstances, to achieve a continuous arc gear transmission. Variable Arc gear undercut phenomenon does not exist, the smallest teeth can do two teeth. Can achieve high-precision, low-cost manufacturing is the limit of non-involutes gear of one of the main reasons, if we are to node for the origin, election gear corner, the error function e () and the pressure angle for a three-axis feed , Then, in NC interpolation processing, the tool radius compensation law to become very simple addition, the type (3) with Minkowski Gougu-speed curve in the form of easy to achieve high-speed, high-precision CNC Machining This is a very important variable gear arc of advantage. Internal Gear and other similar arc gear change error also sensitive to such issues. 4 Arc gear change profile, for example Variable Arc gear design are the main contents of geometric constraints in certain conditions, designed to meet the requirements of the strength of gear tooth profile. Arc gear change the design of the whole into four steps 1) to determine gear parameters, such as: gear material properties, the transmission ratio, the coincidence factor module, the center distance and load torque, and so on. 2) to form a deviation function. 3) Construction tooth profile. 4) The assessment of performance gear. Meet the requirements of the end, otherwise, to 2. Below is a deviation function method used in the design of the meshing of gears are changed arc. Located away from the center of gear for the l, with a radius of a round for the l / 2, deviation function election （19） （20） Figure 5 depicts the profile of the gear for protruding-concave contact characteristics, the coincidence factor of 1.2. Owing to space constraints, the gear change arc of other content and design methods in the future in an article for further briefing. 5 Conclusion This paper presents a new type of variable arc gear, such gear on the design of the new method for tooth profile research has provided new ideas and more extensive research on space. Derived from the above, demonstration and calculate the following conclusions can be drawn: Variable Arc gear transmission gear to meet the basic conditions, it mainly uses protruding-concave in the meshing of the forms of transmission for heavy transmission occasions. By optimizing the design deviation function, and change gears arc can be excellent performance of the gear tooth profile, in particular, can tooth root bending stress and surface contact stress significantly reduced. It also has a compact structure, the smallest gear teeth may be two advantages. Tooth design clear physical meaning, the formula is simple and easy to optimize the design, computer-aided design and manufacturing, in particular, it can easily achieve tool radius compensation and high-speed, high-precision CNC machining. Tooth point for the arc-shaped mesh gear transmission. There are usually two forms of engagement: gear for small convex arc tooth profile, big gear for the concave arc tooth profile, the circular said single-gear transmission; big small gear in their respective sections outside the circle of the teeth are made convex arc Profile in the section within the circle are made part of the Au arc tooth profile, said double arc gear transmission. Arc-gear transmission gear of the small convex teeth tooth profile in the work of a round, the Tooth in the central section circle; Au teeth of the gear tooth profile work in a round section, the Tooth in the central section slightly incline outside the circle. Because of the large gear tooth profile radius p2 more than small gear tooth profile radius p1, so when the two tooth profile to the K, its normal line through the node c, the tooth will contact immediately isolated, but it is O the other end of the Tooth immediately contacted, that is, two teeth K1 K1, K2 K2 K3 K3 points followed along the lines mesh contact. Therefore, the arc gear concave surface of the end Tooth Profile convex only for instantaneous meshing. A new circular gear in theory is instantaneous point engagement, the circular drive is often called the meshing gear transmission point arc. After running-gear, in fact tooth profile to high gear along with a rather long period of exposure. Arc gear transmission is characterized by: (1) comprehensive than the radius of curvature involutes gear transmission much bigger, than the intensity of their contact with involutes gear transmission of about 0.5 to 1.5 times (2) two teeth along the direction of the meshing Rolling great speed, easy-tooth surface of a Film, transmission more efficient, generally up to 0.99 to 0.995 (3) arc high gear along the direction of tooth wear uniform, and easy to run a (4) the arc gear without undercutting Phenomenon, the smallest teeth can be less. But for Gear arc from the center of spiral Cutting depth and angle of error of great sensitivity, the three errors on a greater impact on carrying capacity, the circular gear on the manufacture and installation of high accuracy. In addition, single-arc Gear bending strength weak same-cutting large number of small gear, needed two different hob. Double arc gear transmission work, from one end, the first tooth of the Au initiative to promote the Department of the Ministry of convex follower of the tooth, left, and then to its convex promote each others Department of the Ministry of Au, the double arc in theory Gear At the same time there are two points of contact, the running-in, such transmission in fact there are two contact line, so the teeth can achieve more and more engagement. In addition, because of its greater thickness of the tooth root, not only double arc gear transmission capacity than the single-gear transmission arc of about 30% higher above, and drive more stable, less vibration and noise, and the same can be used to match the processing hob The two gears. Therefore, heavy high-speed, double-arc replace the single-gear transmission with the trend of Arc Gear As such tooth profile in the drive to be point-to-point counterparts, thus creating more sensitive and assembly error, the tooth profile to use high-precision CNC machining; gear such other nature pending further study. References 1 Wuxutang made an order of the court. Gearing principle. Beijing: Machinery Industry Press, 1984 2 Taiyuan Engineering Research Center for the gear. Arc gear. Beijing: Machinery Industry Press, 1992变圆弧齿轮的形成原理及特性摘要：提出了一类变圆弧齿轮。利用偏差函数法，给出了齿廓的完整构造过程，证明了它满足齿廓啮合基本定律；推导了齿廓方程等基本公式，讨论了变圆弧齿轮的特性，给出了变圆弧齿廓的实例；这种齿轮具有较高的承载能力，特别便于高速、高精度数控加工，它将在重载传动场合得到应用。关键词：齿轮 齿廓 偏差函数 啮合原理 齿轮强度 引言 随着科学技术的发展，对齿轮传动的要求也不断提高，特别在重载和小型化方面尤为突出。目前，在齿轮设计中常用的有渐开线、摆线和圆弧3种齿廓；其中，渐开线齿轮由于制造简单，对中心距偏差不敏感等优点，得到广泛使用，但是，它承载能力较差，较少用于重载传动中；摆线齿轮接触应力小，齿廓的重合度较大，有利于弯曲强度的改善，但对啮合齿轮的制造和装配精度要求较高；上世纪50年代出现的圆弧类齿轮弯曲强度不高，为了实现连续接触，一般需做成斜齿轮，在制造和小型化方面受到了极大地限制。为了提高齿轮的承载能力，研究人员提出了许多新型齿廓，例如：微线段齿轮齿廓，分阶式双渐开线齿轮等，对提高齿轮的强度能起到一定作用，但是，这些新齿廓在制造或装配等方面还存在某些不足。本文从偏差函数概念出发，提出了一种新型齿轮变圆弧齿轮。文中介绍了变圆弧齿轮的形成原理，推导了齿廓计算公式，讨论了变圆弧齿轮的特性，给出了齿廓实例。1变圆弧齿廓的形成原理1.1变圆弧齿廓的形成原理 下面根据美国学者D. C. H. Yang等提出的偏差函数（DF）法，介绍变圆弧齿廓的形成原理。设P1是半径为1的齿轮节圆，1为转角，以e（1）为半径，圆心均匀分布在节圆上，画出一系列的圆，如图1所示（这里取e（1）=r0cos（21）,当e（1）满足一定的约束条件时，这一系列的圆可以包络出光滑的齿廓g1（1），从图中可看出，e1（1）=|P（1）-g（1）|，称e（1）为偏差函数。我们将满足上述生成原理的一类齿廓统称为变圆弧包络齿廓，简称为变圆弧齿廓，由它构成的齿轮副称为变圆弧齿轮副。 当取偏差函数e（1）=r1cos(）时，变圆弧齿廓就是常见的渐开线齿廓；而当偏差函数取 时，这时的变圆弧齿廓就是摆线齿廓；而对于普通圆弧齿轮来说，相当于偏差函数e（1）只在某些离散点取值。1.2变圆弧齿廓的计算 从图2可以看出，用坐标分量表示的变圆弧齿轮齿廓P1的方程为 (1) (2) 式中，定义为在g点齿廓的法线与x轴之间的夹角，它是1的函数，由图2知 （3） 为了使获得的上述齿廓能够实际应用，还必须对偏差函数 e(1）的选择做某些限制（1）为保证齿廓曲线不相交，要求 （4）（2）为确保方程式（3）有解，要求 （5）（3）为保证轮廓曲线C连续，在节圆p1与齿廓g1的交叉点Cp处，e（）必须等于零。（4）为了保证齿廓光顺，在e（1）最小、最大值之间必须单调变化。（5）为了使齿轮齿数N1取整数并且保证有一定的重合系数 ，两个交汇点之间的角度范围1应满足2变圆弧齿轮齿廓的啮合原理 设一对变圆弧齿轮的齿廓相互啮合，如图3所示，在某一瞬时，这对共轭齿轮O1和O2的齿廓c1和c2在g点处啮合，根据齿廓啮合原理，共轭齿廓方程可写成 （6） （7） （8） （9） (10） （11）式中，g1x，g1y，g2x和g2y分别是啮合点g在齿轮随体直角坐标系0l和02中的坐标分量，O1和O2是齿轮1和2的转角，而1和2是齿廓在g点的法线与两个x坐标轴的夹角。两齿廓啮合过程中保持接触的条件是齿廓c1上的g点速度Vg1和齿廓c2上的g点速度Vg2在公法线方向的速度分量相等，即vgn1=vgn2；从齿廓的生成原理可知，两齿轮的齿廓在任意啮合点g处存在公法线n-n它与连心线O1O2交于节点P，由O1和O2点分别向n-n作垂线，交于n1和n2点，则， 如图3，则传动比为 （12）因此，我们得出结论：变圆弧齿轮能够实现恒定转速比传动。变圆弧齿轮副齿廓间的相对滑动速度为 （13） （14）一般情况下，变圆弧齿轮的压力角是与齿轮转角有关的变量，对渐开线齿廓，e（1）=r1cos（），带入上述压力角计算公式可得e=a。 3变圆弧齿