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外文資料翻譯
翻譯資料名稱(外文) GEARS
翻譯資料名稱(中文) 齒輪
院 （系）： 機械工程系
專 業(yè)： 機械設(shè)計制造及其自動化
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齒輪
齒輪是成對運轉(zhuǎn)的直接接觸體，它們通過連續(xù)嚙合的稱作齒的突出物把運動和力從一根轉(zhuǎn)軸傳遞帶另一根轉(zhuǎn)軸上，或從一根轉(zhuǎn)軸傳遞到齒條上。圖7所示是四種主要的齒輪（正齒輪、斜齒輪、蝸輪和錐齒輪）以及齒條小齒輪.
齒廓 齒輪齒的接觸面必須排列得使傳動是流暢的，即所傳遞的負載決不能依賴摩擦接觸。正如在分析直接接觸體時所指出的，這要求接觸面上的公法線一定既不能通過主動輪的樞軸，也不能通過從動輪的樞軸。
大多數(shù)齒輪的齒廓還要求具有能使齒輪的速比保持不變的那樣一種外形（本文只討論這種齒輪，除非另作說明）。這就要求公法線必須與兩齒輪樞軸的連線在一定點相交。
正如在討論直接接觸體的那一節(jié)所指出的，擺線好漸開線齒廓不但能保證流暢傳動而且能獲得等速比，即共軛作用。
我們已經(jīng)列舉了漸開線用作齒輪齒廓的一些優(yōu)點。評價齒輪齒廓時所要考慮的因素包括制造的難易程度、對調(diào)整不良的敏感性以及承受負載的能力。在所有這幾方面，漸開線都優(yōu)于或比得上擺線。然而，漸開線不適用于只有六、七個齒每齒能轉(zhuǎn)六十度角的從動齒輪齒。這是鐘表齒輪的要求。由于擺線齒或近似于尖拱形（圓弧形）的齒能滿足這一點，所以它們用于鐘表和小型儀表中。另一類用于鐘表裝置的小齒輪是鈍齒小齒輪，或者稱為針齒輪。這種齒是由固定在兩塊端板之間的許多段很短的經(jīng)過拋光的硬質(zhì)鋼絲制作，和它配合的齒輪上的齒呈現(xiàn)共軛外擺線形。利用滾柱來代替固定的針齒，可以減少摩擦力。
最近在某些國家，建議對齒輪采用圓形齒廓。因為互相接觸的一對漸開線都是凸形 的，其接觸應(yīng)力比圓形齒廓所能獲得的一對凹凸形齒廓的應(yīng)力要大。盡管圓形齒廓的接觸面承載能力比較高，然而這種齒輪使用的比較少。因為它們沒有漸開線齒輪所具有的那種齒廓互換性，并且難于制造，對中心距的變化也非常敏感。
盡管也存在某些缺點，漸開線仍然是最常用的齒輪齒廓。就傳遞運動而論，一對齒輪的齒無論具有什么形狀都無關(guān)重要，只要這些齒是互相嚙合就行，也就是說，只要能以等速比傳遞運動就行。需要著重考慮 的問題是制造的方便程度和互換性。
蝸杠及其嚙合齒輪是不可分的，切削該齒輪所用的刀具（滾齒刀）基本上同蝸桿是完全一樣的東西。英國某些制造廠比較喜歡采用漸開線齒廓的蝸桿；在美國，這種類型的齒輪很少采用漸開線。
基本關(guān)系 一對齒輪中比較小的一個叫小齒輪，較大的一個叫大齒輪。如果小齒輪在主動軸上，這對齒輪起減速裝置的作用；如果大齒輪裝在主動軸上，這對齒輪起加速裝置的作用。齒輪裝置較常用語減速而不是用于加速。
如果一個齒數(shù)為N的齒輪的轉(zhuǎn)速為n轉(zhuǎn)/分，則乘積Nn的量綱是“每分鐘齒數(shù)”。這一乘積對于互配的兩個齒輪來說必須是相等的，如果在通過嚙合區(qū)時想讓每一個齒都能從互陪齒輪獲得一個互陪齒的話。對于各種類型的嚙合齒輪來說，齒輪傳動比和轉(zhuǎn)速比都是根據(jù)大齒輪的齒數(shù)同小齒輪的齒數(shù)的比值得出來的。如果大齒輪的齒數(shù)為100，互配小齒輪的齒數(shù)為20則比值5.所以不管大齒輪的轉(zhuǎn)速如何，小齒輪的轉(zhuǎn)速都是大齒輪的5倍。
如果兩根軸是平行的，該大齒輪和小齒輪可以用一對速度比與這對齒輪相同的通過純滾動接觸傳遞運動的圓柱體來代替。在這兩個齒輪上，稱這兩個假想的圓柱體的圓稱作節(jié)圓；這兩個節(jié)圓可供分析齒輪的參數(shù)之用。這兩個圓的切點稱作節(jié)點，因為節(jié)點位于中心線上，所以節(jié)點是兩個齒輪純滾動接觸的唯一的一點。兩根軸上不平行，不相交的一對齒輪也有節(jié)圓，但滾動節(jié)圓的概念對它是不適用的。
齒輪的型式主要取決于軸的布置；此外，某幾種類型的齒輪比其它幾種更適用于速度變化很大的場合。這意味著如果對軸的布置有某種特殊的要求，齒輪的型式或多或少也就確定了。反之，若果所需要的某種速度變化要求某種型式的齒輪，那么軸的位置也就確定了。
直齒輪和斜齒輪 齒輪其輪齒與軸平行的齒輪稱作直齒輪。一對直齒輪只能用來連接平行軸。然而，平行軸也可以用其他型式的齒輪來連接，并且一個直齒輪可以同一個不同形式的齒輪互配。 在圖6中，如果互配的漸開線直齒輪的一對齒的齒廓都是漸開線，那么，因為接觸在r點開始并在s點結(jié)束，為了獲得連續(xù)傳動，一對齒在s點脫離接觸之前，另一對齒必須在r點開始接觸。這種情況是否出現(xiàn)取決于吃的間距和直線rs的長度，而rs的長度取決于齒伸出節(jié)圓上下的量。這些尺寸的使用值已經(jīng)標準化了。
因為節(jié)圓是純滾動的，互配齒輪兩個節(jié)圓上齒的距離必須相等。這個距離記做p，他是齒的尺寸的計量參數(shù)，是相鄰的兩個齒在節(jié)圓上相應(yīng)的兩點之間的距離。
為了避免由于熱膨脹而出現(xiàn)的卡頓現(xiàn)象，為了潤滑，為了補償在制造是不可避免的誤差，所有傳遞動力的齒輪必須具有側(cè)向間隙。這意味著在互配齒輪的節(jié)圓上，小齒輪的間隙寬度必須稍大于大齒輪的寬度，反之亦然。在儀表齒輪上，可以利用中部分開的配合齒輪來消除側(cè)向間隙，它的一半可相對于另一半轉(zhuǎn)動。彈簧迫使配合齒輪的齒占滿小齒輪的間隙的整個空間。
如果一個漸開線直齒小齒輪是用橡皮做的，并且被均勻扭轉(zhuǎn)使其兩端面繞軸線相對轉(zhuǎn)動，則原來是直的、其方向同軸線平行的輪齒素線就會變成螺旋線。那么這個小齒輪實際上就會變成一個斜齒輪。
斜齒輪具備某些有點，例如，當連接兩根平行軸時，斜齒輪比齒數(shù)相同并用相同刀具切削出來的直齒輪具有較高的承載能力。由于齒輪的重疊作用工作比較平穩(wěn)，并且與直齒輪相比能以比較高的節(jié)線速度運轉(zhuǎn)。節(jié)線速度是節(jié)圓的速度。因為齒輪傾斜于旋轉(zhuǎn)軸的方向，所以斜齒輪會產(chǎn)生軸向推力。如果單個使用，這一推力必須有軸承來承受。推力問題可以通過在同一培件上切削兩列方向相反的斜齒的方法來克服。根據(jù)制造方法的不同，齒輪可以做成連續(xù)人字形的，或者做成雙斜齒形的，在兩列斜齒之間留一間隙以便讓切削刀具通過。雙斜齒輪非常適用于高速高效的傳遞動力。這種齒輪的一個重要用途是用在船舶上的齒輪蝸輪傳動。在一條排水量八萬噸的客輪上，有四個單級減速人字齒輪箱，從每分鐘1500轉(zhuǎn)和1050轉(zhuǎn)的幾臺渦輪機把總功率160000馬力傳遞到每分鐘180轉(zhuǎn)的螺旋槳軸上。每個大型從動齒輪的直徑接近于13.5英尺。
斜齒輪也能用來連接不平行也不相交的相互成任何角度的軸。90度是這種齒輪最常用的角度。當兩根軸平行時，互配齒輪的輪齒之間的接觸是“線接觸”，不管齒輪是直齒輪還是斜齒輪。當軸傾斜時，接觸就變成了“點接觸”。因此，交叉軸（不平行也不相交）斜齒輪的承載能力就不及平行軸斜齒輪。然而，交叉軸斜齒輪不易調(diào)整，所以常用于只有摩擦力是唯一阻礙運動的力的儀表和定位機構(gòu)上。
如上所述，適用于平行軸齒輪的滾動節(jié)圓的概念，不適用于不平行也不相交的軸。這意味著一對齒輪當它們的軸相互交叉時，比相互平行時更容易獲得大的速比，比如100。在平行軸的情況下，小齒輪的節(jié)徑應(yīng)是大齒輪節(jié)徑的1/100，這個比較不現(xiàn)實。在交叉軸的情況下，小齒輪只要有一個斜齒就行其大小要適應(yīng)足夠的強度的需要。這個小齒輪看上去就像一個螺旋。而大齒輪則有一百個牙。
蝸輪蝸桿和錐齒輪 為了使交叉軸斜齒輪獲得線接觸并且改進他的承載能力，可以把大齒輪做成彎曲的，部分包在小齒輪上，有點像螺母套在螺絲上一樣。結(jié)果就形成一個柱形蝸桿和蝸輪。蝸桿也可以做成沙漏形（即兩端粗中間細，象計量時間用的沙漏的形狀）而不是圓柱形的，以便部分包在小輪上。這就導致承載能力的進一步提高。
蝸輪蝸桿提供了獲得一對大速比齒輪的最簡單的方法。然而，蝸輪蝸桿的效率通常低于平行軸齒輪，因為沿輪齒方向會產(chǎn)生額外的滑動。由于它們的類似性蝸輪蝸桿的效率也同樣取決于影響螺紋效率的那些因素。大直徑的單線蝸桿的導角很小并且效率很低。多線蝸桿的導角較大并且效率也比較高。如果導角約為15度，摩擦系數(shù)小于0.15，則其效率約為55%至95%不等，渦輪就能驅(qū)動蝸桿。這樣的組合可以組成結(jié)構(gòu)緊湊的增速裝置；它們已經(jīng)用來驅(qū)動飛機發(fā)動機的增壓器。在自鎖式蝸輪蝸桿中，蝸輪不能驅(qū)動蝸桿，并且效率而已低于50%。
為了使傳遞的轉(zhuǎn)動和扭轉(zhuǎn)能轉(zhuǎn)一個角度，常常使用傘齒輪。所連接的兩根軸如果延長后其軸線就會相交，它們彼此通常（但不是必須）相交成90度。傘齒輪的節(jié)面是滾動的截錐，而在厚度和高度上都必須逐漸減小的輪齒即可以是直的，也可以是弧形的。雖然弧齒傘齒輪稱作螺旋傘齒輪，但輪齒的曲線通常是一個圓弧。輪齒的曲率可以導致輪齒重疊工作從而使動力的傳遞比直齒平穩(wěn)。對于高轉(zhuǎn)速和高扭矩來說，螺旋傘齒輪由于直齒傘齒輪，很象在兩軸平行的情況下，斜齒輪優(yōu)于正齒輪一樣。
適用于兩軸不相交的螺旋傘齒輪稱作偏軸錐齒輪。這種齒輪的節(jié)面不是滾動的，并且它們的平均直徑比不等于速比。因此，小齒輪的齒數(shù)可以比較小，并使其大小能適應(yīng)承載的需要。這就使之比兩軸相交有更高的速比，正向交叉軸斜齒輪和蝸輪蝸桿能比平行軸斜齒輪提供更高的速比一樣。不需要成比例的滾動節(jié)面是一個有利之處。
螺旋錐齒輪在汽車上用來連接驅(qū)動軸和后軸。驅(qū)動軸上的小齒輪的軸線低于大齒輪的軸線，這就使發(fā)動機和車子的重心得以降低。因為軸不相交，所以從安裝在一根小齒輪軸上的幾個小齒輪可以驅(qū)動幾根輪軸，像卡車的傳動軸那樣。
錐齒輪的齒廓不是漸開線形，它們的形狀使切齒輪刀具比漸開線刀具更易于制造和維修。因為錐齒輪都是成對供應(yīng)的，只要它們的相互嚙合的，它們就不需要同齒數(shù)的其他齒輪嚙合。
齒輪系和減速器 一對齒輪能獲得的最大傳動比因齒輪的類型和用途而異。各種類型的齒輪在平均負載條件下最大傳動比的近似值如下：直齒輪：8；平行軸斜齒輪：10；直齒錐齒輪：6；螺旋錐齒輪：8；直角交錯齒輪：12；蝸輪蝸桿：80。對輕載齒輪、儀表齒輪和定位齒輪來說，這一比值還可以更大點。用類似于和偏軸傘齒輪嚙合的錐形蝸桿的齒輪裝置可以獲得高達400或400以上的傳動比。對于重載齒輪，上述比值可能太高，這會造成這樣一種情況，即傳動比過高找不到合適的小齒輪。
因為一對齒輪的傳動比是齒數(shù)的商，并且因為一對適用的齒輪的齒數(shù)的最大值和最小值通常都有一個極限，因此一對齒輪所能獲得的傳動比值也有一定限度。為了擴大其比值范圍，必須采用幾對齒輪或齒輪輪系。齒輪系的總速比是每對齒輪的速比的乘積。在某些情況下，用齒輪不能獲得精確的速比，但采用兩對或幾對齒輪，就能使所要求的速比接近任何精確度。
為了使機械制造者和使用者方便起見，根據(jù)工業(yè)通用的式樣，制造了各種不同類型，結(jié)構(gòu)，速比和能力的成套減速器；這些減速器有一個外殼，外殼里面裝有軸承，軸，齒輪，潤滑劑和油封。增速器通常是定做的。
在連續(xù)運轉(zhuǎn)的情況下，由于輪齒，潤滑劑，軸承和油封中的摩擦作用，所有減速器都會發(fā)熱。如果發(fā)熱的速度比散發(fā)到大氣中速度快，潤滑劑就會變質(zhì)，齒輪或軸承就會損壞。
GEARS
Gears are direct-contact bodies , operating in pairs, that transmit motion and force from one rotating shaft to another , or from a shaft to a slide (rack), by means of successively engaging projections called teeth . The four main types of gears ( spur , helical, worm ,and bevel) and a rack and pinon are shown in Figure 7.
Tooth profiles. The contacting surfaces of gear teeth must be aligned in such a way that the drive is positive ; the load transmitted must not depend on frictional contact . As shown in the treatment of direct-contact bodies , this requires that the common normal to the surfaces must not passs through the follower .
Most gears are also required to hae tooth proflies of such a shape that the velocity ratio of the gears remains constant (unless otherwise noted ,this article will deal with such gears only ).thid requires that the common nomarl must cut the line between the pivots at a fixed point.
As shown in the section on direct-contact bodies,cycloidal and involute profiles provide both a positive drive and a uniform velocity ration; i.e. , conjugate action .
Some of the adantage of the involute as a geartooth profile have already been enumerated. The factors to be consided in evaluating a gear-tooth profile include ease of manufacture, sensitivity to maladjustment , and load-carrying capicity . On all of these counts the involute is superior or equal to the cycloid . Involutes , however ,are unsuitable for the teeth of driven gears having as few as six or seven teeth and capable of action through 60 degrees of rotation.This is a requirement for watch and clock gears , and since they can supply it , cycloidal teeth or ogival (circular are )approximations thereto are used on watches ,clocks, and small instrucments. Another type of pionn used in clockwork is the lantern pinon , or pin gear .The teeth are short lengths of hard ,polished ,steel wire held between two end plates, and the teeth on the mating gear are conjugate epicycloids.By using rollers in place of fixed pins , the friction is reduced.
Circular profile have proposed for gears , most recently in some countires . Since contacting involutes are both convex , the contact stresses are higher than in a convex-concave pair such as can be obtained with circular-profile gears are seldom used,because they lack the profile interchangeability of involute gears , are difficult to manufacture ,and are sensitive to centre-distance variations.
In spite of some deficiencies , the involute is still the most commonly used gear-tooth profile . As far as the transmition of motion is concerned , it does not matter what shape the teeth on a gear pair have as long as they are conjugate to one another ;i,e, transmit the motion with a uniform velocity ration . The dominating considerations are manufacturing convenience and interchangability .
A worm and its mating gear are inseparable , and the gear is cut with a tool that is basically a replical of the worm . Some British manufactures prefer the involute profile for worms ; in the United States, involutes are seldom used for this type of gear .
Basic relations . The smaller of a gear pair is called the pinion and the larger is the gear. When the pinion is on the driving shaft the pair acts is a speed reducer ; when the gear drives , the pair is a speen increaser . Gears are more frequently used to reduce speed to increace it .
If a gear having N teeth rotates at n revoltions per minute , the product Nn has the dimension “teeth per miute ” This product must be the same for both members of a mating pair if each tooth is to acquire a partner from the mating gear as it passes through the region of tooth engagement.
For conjugate gears of all ypes the gear ration and the speed ration are both given by the ration of the number of teeth on the gear to the number of teeth on the pinion. If a gear has 100 teeth and a mating pinion 20, the ratio is 5 . Thus the pinion rotates five times as fast as the gear , regardless of the speed of the gear .
If the shaft are parllel , the gear and the pinion could be replacled by a pair of cylinders that would tranmit the motion by pure rolling contact at the same speed ration as the gears . On the gears , the circles that represent these imaginary cylinders are called the pitch circles ; these are useful for reference purposes in the analysis of gears . Their point of tangency is called the pitch point , and since it lies on the line of centres , it is the only point at which the tooth profiles have pure rolling contact , Gears on nonparallel , non-intersecting shafts also have pitch circles, but the rolling –pitch-circle concept is not valid .
Gear types are determined largely by the disposition of the shafts ; in addition , certain types are better suited than others for large speed changes.This means that if a specifical disposition of the shafts is required,the type of gear is more or less fixed .On the other hand ,if a required speed change demands a certain type, the shaft position are fixed .
Spur and helical gears . A gear having tooth elements that are straight and parallel to its axis is known as a spur gear . A spur pair can be used to connect parallel shafts only .Parallel shafts ,hoewever , can also be connected by gears of another type , and a spur can be mated with a gear of a different type .
In figure 6 , if the involutes are a single pair of teeth on mating involute spur gears ,then ,since contact begins at r and ends at s , to obtain continuous transmission of motion , a pair must come into contact at r beforce the preceding pair goes out of contact at s . Wheather this does or does not occur depends on the tooth spacing and the length of the line rs ,which depends on the amounts that the teeth project above and below the pitch circles , Satisfactory values of dimendions have been standardized .
Since the pitch circles roll on one another ,the spcing of the teeth on these circles on a mating pair must be equal . This spacing , which is known as the circular pitch p and is a measure of tooth size , is the distance between corresponding points on adjacent teeth , measured on the pitchcircle .
To prevent jamming as a result of thermal expansion ,to aid lubrication , and to compensate for unavoidable inaccuracies ,all power-transmitting gears must have backlash.This means that on the pitch circkes of a mating pair ,the space width on the pinion must be slightly greter than the tooth thickness on the gear , and vice versa.. On instrument gears , backlash can be eliminated by using a gear split down its middle , noe half being rotatable relative to the other . A spring force the split gear teeth to occupy the full width of the pinion space .
If an involute spur pinion were made of rubber and twisted uniformly so that the ends rotated about the ais relative to one another ,the elements of the teeeth , initially straight and parallel to the axis ,would become helices.The pinion then in effect would become a helical gear .
Helical gears have certain advantages; for examples , when connecting parallel shafts they have a higher load-carrying capacity than spur gears with the same tooth numbers and cut with the same cutter . because of the overlapping action of the teeth , they are smoother in action and can opeerate at higher pitch-line velocities than spur gears . The pitch-line velocity is the velocity of the pitch circle . Since the teeth are inclined to the axis of rotation , helical gears create an axial thrust. If used singly ,shis thrust must be obsorbed in the shaft bearings. The thrust problem can be overcome by cutting two sets of opposed helical teeth on the same blank . Depending on the method of manufacture , the gear may be of the continuous-tooth herringbone variety or a double-helical gear with a space between the two halves to permit the cutting tool to run out .Double-helical gears are well suited for the efficient transmission of such gears is for geard-turbine shipdrives. On a passager liner of 80,000 tons displacement , there are four single-reduction , double-helical gearboxes transmitting a total of 160,000 horsepower from turbines rotating at 1,500 and 1,050 revolutions per minute to a propeller shaft rotating at 180 revolutions per minute . Each large driven gear was approximately 13.5 feet in diameter.
Helical gears can also be used to connect nonparallel , non-intersecting shafts at any angle to one another .Ninety degrees is the commonest angle at which such gears are used . When the shafts are parallel , the contact between the teeth on mating gears is “ line contact ” regarless of whether the teeth are straight ao helical . When the shafts are inclined , the contact becomes “point contact . ” For shis reason , crossed-axis helical gears do not have as much load-carring capacity as parallel-shaft helicals . They are relatively insensitive to misalignment , however, and are frequently employed in instrument and positioning mechanisms where friction is the only force opposing their motion.
As stated above , the rolling-pitch-circle concept , which applies to gears on parallel shafts , does not apply to gears on nonparallel , non-intersecting shafts . This means that a large speed ration on one pair of geara , 100 for example , is more easily obtained when the axes are crossed than when they are parallel . With parallel shafts ,the pinion pitch dimmeter would have to be of the gear pitch diamater , an impracticalproportion . With crossed axes , the pinion could have only one helical tooth – or – thread – and be as large as necessary for adequate strength .The pinion would look like a screw , and the gear would have 100 teeth .
Worm and bevel gears . In order to achieve line contact and improve the load – carrying capacitiy of the crossed – axis helical gears ,the gear can be made to curve paritially around the pinion , in somewhat the same way that a nut envelops a screw . The result would be a cylindrical worm and gear. Worms are also made in the shape of an hourglass , instead of cylindrical , so that they partially envelop the gear . This results in a further increase in load-carring capicity .
Worm gears provide the simplest means of obtaing large ratios in a single pair . they are usually less efficient than parallel-shaft gears ,however ,because of an additional sliding movement a;ong the teeth .Becaude of their similicity , the efficiency of a worm and gear depends on the same factors as the efficiency of a screw . Single –thread worms of large diameter have small lead angles and low efficiency . Multipie-thread worms have larger lead angles and higher efficiencies . For lead angles of about 15 degrees and a coefficient of friction less than 0.15 ,the efficiency ranges from about 55 percent to 95 percent , and the gear can drive the worm .Such units make compact speed increases ; they have been used for driving superchargers on aircraft engines , In self-locking worms , the gear cannot drive the worm , and the efficiency is less than 50 percent .
For transmitting rotary motion and torque around corners , beveal gears are commonly used . The connected shafts.whose axes would intersect if extended ,are usually but not necessarily at right angles to one another .The pitch surface of bevel gears are rolling ,truncated cones , and the teeth , which must be tapered in both thickness and height , are either straight or curved . Although curved –tooth bevel gears are called spiral beel gears ,the curve of the teeth is usually a circular one .The curvature of the teeth results in overlapping tooth action and a smoother transmission of power than with straight teeth. For high speeeds and torpues ,spiral bevel gears are superior to straight beveal gears in much the same way that helical gears are superior to spur gears for connecting parallel shafts.
When adapted for shafts that do not intersect , spiral beveal gears are called hypoid gears .The pitch surfaces of these gears are not rolling cones , and the ratio of their mean diameters is not equal to the speed ratio .Consequently ,the pinion may have few teeth and be made as large as necessary to carry the load . This permits higer speed ratios than with intersecting axes , just as crossed axis helicals and worm gears can provide higher eatios than parallel helicals .The abseence of the proportionsl rolling –pitch surface requirement is a benefit .
Hypoid gears are used on automobiles to connect the drive shaft is to the rear axles .The axis of the pinion on the drive shaft is below the gear axis ehich permits lowering of the engine and the center of gravity of the vehicle . Since the shafts do not intersect , several gear shafts may be driven from pinions mounted on a single pinion shaft ,as in tandem axles for trucks.
The profiles of the teeth on bevel gears are not involutes ;they are such a shape that the tools for cutting the teeth are easier to make and maintain than involute cutting tools . Since bevel gears come in pairs , as long as they are conjugate to one another they need not be conjugate to one another they need not be conjugate to other gears with different tooth numbers.
Gear trains and reducers .The maxiimum gear ratio obtainable with a single pair of gears varies with the type of gear and the application . The following are aproximate maxima for the various types for average load conditions : spur 8 ; parallel-shaft helical , 10 ; straight bevel 6 ; spiral bevel , 8 ; hypoid , 12 ; and worm , 80 .For lightly loaded ,instrument , and positioning gears , these ratios can be obtained with gears that resembe tapered worms meshing with hypoid gears . For heavily loaded gears , the given ratios may be so high that a reasonable gear size precludes a satisfactory pinion.
Since the ratio in a single pair of gears is the quotient of the tooth numbers , and since there usually are limitation on both the minimum and maximum numbers of teeth on the available gears , follows that the number of ratios obtainable in a single pair is limited . To enlarge the coverage it is necessary to use multiple pairs , or trains . the overall speed ratio in a train is the product of the ratios in each pair . In certain cases an exact ratio cannot be obtained with gears , but by using two or more pairs , the desired ratio can be approximated to any degree of precision .
As a convenience for machine builders and users , packaged speed reducer , following an industry – accepted pattern , are manufactured in a wide variety of types , configurations ,speed ratios , and capacities ; these consist of a box or housing containing bearings , shafts , gears , lubricant , and shaft oil seals. Speed increasers are usually custom built.
All speed reducer when operating continuously become hot because of friction in the teeth , in the lubricant , in the bearings , and in the oil seals . If the heat is generated at a faster rate than it can be dissipated to the atmosphere , the lubricant may determined and the gears or bearings fail