【正文】 h will contact immediately isolated, but it is O the other end of the Tooth immediately contacted, that is, two teeth K1 ﹑ K39。1, K2 ﹑ K39。2 ﹑ K3 ﹑ K39。3…… 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 runninggear, in fact tooth profile to high gear along with a rather long period of exposure. Arc gear transmission is characterized by: (1) prehensive than the radius of curvature involutes gear transmission much bigger, than the intensity of their contact with involutes gear transmission of about to times (2) two teeth along the direction of the meshing Rolling great speed, easytooth surface of a Film, transmission more efficient, generally up to to (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, singlearc Gear bending strength weak samecutting ﹑ 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 other39。s Department of the Ministry of Au, the double arc in theory Gear At the same time there are two points of contact, the runningin, 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 singlegear 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 highspeed, doublearc replace the singlegear transmission with the trend of Arc Gear As such tooth profile in the drive to be pointtopoint counterparts, thus creating more sensitive and assembly error, the tooth profile to use highprecision 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 變圓弧齒輪的形成原理及特性 摘要： 提出了一類變圓弧齒輪。利用偏差函數(shù)法，給出了齒廓的完整構(gòu)造過程，證明了它滿足齒廓嚙合基本定律；推導(dǎo)了齒廓方程等基本公式，討論了變圓弧齒輪的特性，給出了變圓弧齒廓的實(shí)例；這種齒輪具有較高的承載能力，特別便于高速、高精度數(shù)控加工，它將在重載傳動場合得到應(yīng)用。 關(guān)鍵詞： 齒輪 齒廓 偏差函數(shù) 嚙合原理 齒輪 強(qiáng)度 引言 隨著科學(xué)技術(shù)的發(fā)展，對齒輪傳動的要求也不斷提高，特別在重載和小型化方面尤為突出。目前，在齒輪設(shè)計(jì)中常用的有漸開線、擺線和圓弧 3 種齒廓；其中，漸開線齒輪由于制造簡單，對中心距偏差不敏感等優(yōu)點(diǎn)，得到廣泛使用，但是，它承載能力較差，較少用于重載傳動中；擺線齒輪接觸應(yīng)力小，齒廓的重合度較大，有利于彎曲強(qiáng)度的改善，但對嚙合齒輪的制造和裝配精度要求較高；上世紀(jì) 50 年代出現(xiàn)的圓弧類齒輪彎曲強(qiáng)度不高，為了實(shí)現(xiàn)連續(xù)接觸，一般需做成斜齒輪，在制造和小型化方面受到了極大地限制。為了提高齒輪的承載能力， 研究人員提出了許多新型齒廓，例如：微線段齒輪齒廓，分階式雙漸開線齒輪等，對提高齒輪的強(qiáng)度能起到一定作用，但是，這些新齒廓在制造或裝配等方面還存在某些不足。本文從偏差函數(shù)概念出發(fā)，提出了一種新型齒輪 —— 變圓弧齒輪。文中介紹了變圓弧齒輪的形成原理，推導(dǎo)了齒廓計(jì)算公式，討論了變圓弧齒輪的特性，給出了齒廓實(shí)例。 1 變圓弧齒廓的形成原理 變圓弧齒廓的形成原理 下面根據(jù)美國學(xué)者 D. C. H. Yang 等提出的偏差函數(shù)（ DF）法，介紹變圓弧齒廓的形成原理。 設(shè) P1是半徑為 1 的齒輪節(jié)圓， θ1為轉(zhuǎn)角，以 e（ θ1）為半徑，圓心均勻分布在節(jié)圓上，畫出一系列的圓，如圖 1 所示（這里取 e（ θ1） =r0cos（ 2θ1） ,當(dāng) e（ θ1）滿足一定的約束條件時(shí)，這一系列的圓可以包絡(luò)出光滑的齒廓 g1（ θ1），從圖中可看出， e1（ θ1） =||P（ θ1） g（ θ1） ||，稱 e（ θ1）為偏差函數(shù)。我們將滿足上述生成原理的一類齒廓統(tǒng)稱為變圓弧包絡(luò)齒廓，簡稱為變圓弧齒廓，由它構(gòu)成的齒輪副稱為變圓弧齒輪副。 當(dāng)取偏差函數(shù) e（ θ 1） =r1cosα (θ ） 時(shí)，變圓弧齒廓就是常見的漸開線齒廓；而當(dāng)偏差函數(shù)取 )2sin(2)( 10101 ?? rrre ? 時(shí)，這時(shí)的變圓弧齒廓就是擺線齒廓；而對于普通圓弧齒輪來說，相當(dāng)于偏差函數(shù) e（ θ1）只在某些離散點(diǎn)取值。 變圓弧齒廓的計(jì)算 從圖 2 可以看出，用坐標(biāo)分量表示的變圓弧齒輪齒廓 P1的方程為 )c o s ()c o s ( 1111 ?? erg x ?? (1) )s i n ()s i n ( 1111 ?? erg y ?? (2) 式中， ψ 定義為在 g 點(diǎn)齒廓的法線與 x 軸之間的夾角，它是 θ1的函數(shù)，由圖 2知 139。39。 ?? ??ee 139。1 ?? ??rL )(tan 239。2139。1erebac??? ? bacoaooao ??????? 11111 )( ???? )2/0( 1 ?? ?? （ 3） 為了使獲得的上述齒廓能夠?qū)嶋H應(yīng)用，還必須對偏差函數(shù) e(θ1）的選擇做某些限制 （ 1）為保證齒廓曲線不相交，要求 |)cos(| 11 ?re? （ 4） （ 2）為確保方程式（ 3）有解，要求 21239。 re?