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1、附錄 1 The Introduction of the gears In the force analysis of spur gears,the forces are assumed to act in a single plance.We shall study gears in which the forces have three dimensions.The reason for this ,in the case of helical gears,is that the teeth are not [arallel to the axis of rotation.And i

2、n the case of bevel gears. the rotational axes are not parallel to each other.There are also other reasons,as we shall learn. Helical gears are used to transmit motion between parallel shafts.The helix angle is the same on each gear, but one gear must have a right-hand helix and the other a left-h

3、and helix.The shape of the tooth is an involute helicoid.If a piece of paper cut in the shape of a parallelogram is wrapped around a cylinder,the angular edge of the paper becomes a helic.If we unwind this paper ,each point on the angular edge generates an onvolute curve.The surface obtained when ev

4、eru point on the edge generates an involute is called an involute helicoid. The initial contact of spur-gear teeth is a line extending all the way across the face of the tooth. The initial contact of helical gear teeth is a point ,which changes into a line as the teeth come into more engagement.In

5、 spur gears the line of contact is parallel to jthe axis of the rotation;in helied gears the ability to transmit heavy loads at high loads at high speeds.Helical gears subject the shaft bearings to both radial and thrust loads.When the thrust loads brcome high or are objectionable for other reasons,

6、it may be desirable to use double helical grars.A double helical gear(herringbone)is equitcalent to two helical gears of opposite hand, mounted side by side on the same shaft.They develop opposite thrust reactions and thus cancel out the thrust load.When two or more single helical gears are mounted

7、on the same shaft, the hand of the gears should be selected so as to produce the minimum thrust load. Crossed-helical,or spiral,gears are those in which the shaft centerlines are neither parallel nor intersecting. The teeth of crossed-helical fears have point cntact with each other, which changes

8、to line contact as the gears wear in.For this reason they will carry out very small loads and are mainly for instrumental applications,and are definitely not crossed helical gear and a helical gear until they are mounted in mesh with each other. They are manufactured in the same way. A pair of meshe

9、d crossed helical gears usually of crossed-helical gears,the minimum sliding velocity is obtained when the helix angle are equal.However,when the helix angle are not equal,the gear with the larger helix angle should be used as the driver if both gears have the same hand. Worm gears are similar to

10、crossed helical gears.The pinion or worm has a small number of teeth,ususlly one to four,and since they completely wrap around the pitch cylinder they are called thteads.Tts mating gear is called a worm gear, which is not a true helical gear.A worm and gear are uesd to provide a high angular-velocit

11、y reduction between nouintersecting shafts which are usually at right angle.The worm gear is not a helical gear because its face is point contact. However,a disadvantage of worm gearing is the high sliding velocities across the teech, the same as with crossed helical gears. Worm gearing are either

12、 single or double enveloping. A single-enveloping gearing is one in which the gear wraps around or partially encoloses the norm.A gearing in which each element partially encoloses the other is,of course,a double-enveloping worm gearing.The important difference between the two is that area contact ex

13、ists between the teeth of double-enveloping gears while only line contact between those of single-enveloping gears.The worn and worm gears while only line contact between those of single-enveloping gears.The worm and worm gear of a set have the same hand of helix as for crossed helical gears,but the

14、 helix angles are usually quite different.The helix angle on the worm is generally quite large, and that on the gear very small .Bwcause of the worm helic angle.and the helix angle on the gear;the two angles are equal for a 90-deg.Shaft angle. When gears are to be used to transmit motion between i

15、ntersecting shaft,some of bevel gear is requited. Although bevel gear are usually made for a shaft angle of 90 deg.They may be produced for almost any shaft angle.The teeth may be east,milled,or generated.Only the generated teeth may be classed as accurate.In a typical bevel gear mouning,one of the

16、gear is often mounted outboard of the bearing.This means that shaft detlection can be more pronounced and have a greater effect on the contact of teeth. Another difficulty,which occurs in predicting the stress in becel-gear teeth, is the fact the teeth are tapered. Straight bevel gears are easy to

17、design and simple to manufacture and give veru good results in service if they are mounted and positively.As in the case of squr gears, however,they become noisy at higher values of the pitch-line velocity.In these cases it is oftern good design practice to go to the spiral bevel gears give a much s

18、moother tooth action than straight bevel gears, and hence are useful where high speed are encountered. It is frequently desirable,as in the case of automotive differential appplicarions,to have gearing similar to bevel gears but with the shaft offset.Such gears are called hypoid gears because thei

19、r pitch surfaces are hyperboloids of revolution.The tooth action between such gears is a combination of rolling and sliding along a straight line and has much in common with that of worm gears. 2 齒輪簡介 在直齒園柱齒輪的受力分析中，是假定各力作用在單一平面的。我們將研究作用力具有三維坐標(biāo)的齒輪。因在，在斜齒輪的情況下，其齒向是不平行于回轉(zhuǎn)軸線的。而在錐齒輪的情況中

20、各回轉(zhuǎn)軸線互相不平行。像我們要討論的那樣，尚有其他道理需要學(xué)習(xí)，掌握。 斜齒輪用于傳遞平行軸之間的運(yùn)動(dòng)。傾斜角度每個(gè)齒輪都一樣，但一個(gè)必須右旋斜齒，而另一個(gè)必須是左旋斜齒。齒的形狀是一漸開線螺旋面，如果一張被剪成平行四邊形(矩形)的紙張包圍在齒輪圓柱體上，紙上印出齒的角刃邊就變成斜線。如果我展開這張紙，在血角刃邊上的每一個(gè)點(diǎn)久發(fā)生一漸開線曲線。 直齒圓柱齒輪輪齒的初始接觸處是跨過整個(gè)齒面而伸展開來的線。斜齒輪輪齒的初始接觸是一點(diǎn)，當(dāng)齒進(jìn)入更多的嚙合時(shí)，它就變成線。在直齒圓柱齒輪中，接觸是平行于回轉(zhuǎn)軸線的。在斜齒輪中，該先是跨過齒面的對(duì)角線。它是齒輪逐漸進(jìn)行嚙合并平穩(wěn)的從一個(gè)齒到另一個(gè)齒傳遞

21、運(yùn)動(dòng)，那樣就使斜齒輪具有高速重載下平穩(wěn)傳遞運(yùn)動(dòng)的能力。斜齒輪使軸的軸承承受徑向和軸向力。當(dāng)軸向推力變的大了或由于別的原因而產(chǎn)生某些影響時(shí)，那就可以使用人字齒輪。雙斜齒輪（人字齒輪）是與反向的并排地裝在同一軸上的兩個(gè)斜齒輪等效。他們產(chǎn)生相反的軸向推力作用，這樣就消除了軸向推力。當(dāng)兩個(gè)或更多個(gè)單向齒斜齒輪被在同一軸上時(shí)，齒輪的齒向應(yīng)作選擇。以便產(chǎn)生最小的軸向推力。 交錯(cuò)軸斜齒輪或螺旋齒輪，他們是軸中心線既不相交也不平行，交錯(cuò)軸斜齒輪的齒彼此之間發(fā)生點(diǎn)接觸，它隨著齒輪的磨合而變成線接觸。因此他們只能傳遞小的載荷和主要用于儀器設(shè)備中，而且肯定不能推薦在動(dòng)力傳動(dòng)中使用。交錯(cuò)軸斜齒輪之間在被安裝后互相捏

22、合之前是沒有任何區(qū)別的。它們是以同樣的方法制造。一對(duì)相嚙合的交錯(cuò)軸斜齒輪通常具有同樣的齒向，即左旋主動(dòng)齒輪跟右旋從動(dòng)齒輪相嚙合。在交錯(cuò)軸斜齒輪設(shè)計(jì)中，當(dāng)該齒的斜角相等時(shí)所產(chǎn)生滑移速度最小。但當(dāng)該齒輪的斜角不相等時(shí)，如果兩個(gè)齒輪具有相同齒向的話，大斜角齒輪應(yīng)用作主動(dòng)齒輪。 渦輪與交錯(cuò)軸斜齒輪相似。小齒輪即蝸桿具有較小的齒數(shù)，通常是一到四齒，由于它們完全纏繞在節(jié)圓柱上，因此它們被稱為螺紋齒。與其相配的齒輪叫做蝸桿齒輪不是真正的斜齒輪。蝸桿和渦輪通常是用于向垂直相交軸之間的傳動(dòng)提供大的角速度減速比。渦輪不是斜齒輪。因?yàn)槠潺X頂面做成中凹形狀以適配蝸桿曲率，目的是要形成線接觸而不是點(diǎn)接觸。然而蝸桿渦輪

23、傳動(dòng)機(jī)構(gòu)中存在齒間有較大滑移速度的缺點(diǎn)，正像交錯(cuò)軸斜齒輪那樣。 蝸桿渦輪機(jī)構(gòu)有單包圍和雙包圍機(jī)構(gòu)，單包圍機(jī)構(gòu)就是渦輪包裹著蝸桿的一種機(jī)構(gòu)。當(dāng)然，如果每個(gè)構(gòu)件各自局部地包圍著對(duì)方的渦輪機(jī)構(gòu)就是雙包圍渦輪蝸桿機(jī)構(gòu)。這兩者之間的重要區(qū)別是，在雙包圍渦輪組的齒輪間有面接觸，而是單包圍的渦輪組的輪齒間有有線接觸。一個(gè)裝置中的蝸桿和渦輪正像交錯(cuò)軸斜齒輪那樣具有相同的齒向，但是其斜齒輪角的角度是極不相同的。蝸桿上的齒斜角度通常很大，而蝸桿上的則極小，因此習(xí)慣常規(guī)定蝸桿的導(dǎo)角，那就是蝸桿齒斜角的余角；也規(guī)定了渦輪上的齒斜角，該兩角之和就等于90度得軸線交角。 當(dāng)齒輪要用來傳遞相交軸之間的運(yùn)動(dòng)時(shí)，就需要某種

24、形式的錐齒輪。雖然錐齒輪通常制造成能構(gòu)成90度軸交角。但它們也可產(chǎn)生任何角度的軸交角。齒輪可以鑄出，銑制或滾切加工，僅就滾齒而言就可達(dá)一級(jí)精度。在典型的錐齒輪安裝中，其中一個(gè)錐齒輪常常裝于支承的外側(cè)。這意味著軸的撓曲情況更加明顯而使在輪齒接觸上具有更大的影響。 另外一個(gè)難題，發(fā)生在難于預(yù)示錐齒輪輪齒上的應(yīng)力，實(shí)際上是由于齒輪被加工成錐狀造成的。 直齒錐齒輪易于設(shè)計(jì)且制造簡單，如果他們安裝的精密而確定，在運(yùn)轉(zhuǎn)中會(huì)產(chǎn)生良好效果。然而在直齒圓柱齒輪情況下，在節(jié)線速度較高時(shí)，他們將發(fā)出噪音。在這些情況下，螺旋錐齒輪比直齒輪能產(chǎn)生平穩(wěn)的多的嚙合作用，因此碰到高速運(yùn)轉(zhuǎn)的場合那是很有用的。當(dāng)在汽車的各種不同用途中，有一個(gè)帶偏心軸的類似錐齒輪的機(jī)構(gòu)，那是常常所希望的。這樣的齒輪機(jī)構(gòu)叫做準(zhǔn)雙曲面齒輪機(jī)構(gòu)，因?yàn)樗鼈兊墓?jié)面是雙曲面回轉(zhuǎn)面。這種齒輪之間的輪齒作用是沿著一根直線上產(chǎn)生滾動(dòng)與滑動(dòng)相結(jié)合的運(yùn)動(dòng)并和蝸桿渦輪作用有著更多的共同之處。 第 5 頁 共 5 頁