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Gear mechanisms
Gear mechanisms are used for transmitting motion and power from one shaft to another by means of the positive contact of successively engaging teeth. In about 2,600B.C., Chinese are known to have used a chariot incorporating a complex series of gears like those illustrated in Fig.2.7. Aristotle, in the fourth century B .C .wrote of gears as if they were commonplace. In the fifteenth century A.D., Leonardo da Vinci designed a multitude of devices incorporating many kinds of gears. In comparison with belt and chain drives ,gear drives are more compact ,can operate at high speeds, and can be used where precise timing is desired. The transmission efficiency of gears is as high as 98 percent. On the other hand, gears are usually more costly and require more attention to lubrication, cleanliness, shaft alignment, etc., and usually operate in a closed case with provision for proper lubrication.
Gear mechanisms can be divided into planar gear mechanisms and spatial gear mechanisms. Planar gear mechanisms are used to transmit motion and spatial gear mechanisms. Planar gear mechanisms are used to transmit motion and power between parallel shafts ,and spatial gear mechanisms between nonparallel shafts.
Types of gears
(1) Spur gears. The spur gear has a cylindrical pitch surface and has straight teeth parallel to its axis as shown in Fig. 2.8. They are used to transmit motion and power between parallel shafts. The tooth surfaces of spur gears contact on a straight line parallel to the axes of gears. This implies that tooth profiles go into and out of contact along the whole facewidth at the same time. This will therefore result in the sudden loading and sudden unloading on teeth as profiles go into and out of contact. As aresult, vibration and noise are produced.
(2) Helical gears. These gears have their tooth elements at an angle or helix to the axis of the gear(Fig.2.9). The tooth surfaces of two engaging helical gears inn planar gear mechanisms contact on a straight line inclined to the axes of the gears. The length of the contact line changes gradually from zero to maximum and then from maximum to zero. The loading and unloading of the teeth become gradual and smooth. Helical gears may be used to transmit motion and power between parallel shafts[Fig. 2.9(a)]or shafts at an angle to each other[Fig. 2.9(d)]. A herringbone gear [Fig. 2.9(c)] is equivalent to a right-hand and a left-hand helical gear placed side by side. Because of the angle of the tooth, helical gears create considerable side thrust on the shaft. A herringbone gear corrects this thrust by neutralizing it , allowing the use of a small thrust bearing instead of a large one and perhaps eliminating one altogether. Often a central groove is made around the gear for ease in machining.
(3) Bevel gars. The teeth of a bevel gear are distributed on the frustum of a cone. The corresponding pitch cylinder in cylindrical gears becomes pitch cone. The dimensions of teeth on different transverse planes are different. For convenience, parameters and dimensions at the large end are taken to be standard values. Bevel gears are used to connect shafts which are not parallel to each other. Usually the shafts are 90 deg. to each other, but may be more or less than 90 deg. The two mating gears may have the same number of teeth for the purpose of changing direction of motion only, or they may have a different number of teeth for the purpose of changing both speed and direction. The tooth elements may be straight or spiral, so that we have plain and spiral bevel gears. Hypoid comes from the word hyperboloid and indicates the surface on which the tooth face lies. Hypoid gears are similar to bevel gears, but the two shafts do not intersect. The teeth are curved, and because of the nonintersection of the shafts, bearings can be placed on each side of each gear. The principal use of thid type of gear is in automobile rear ends for the purpose of lowering the drive shaft, and thus the car floor.
(4) Worm and worm gears. Worm gear drives are used to transmit motion and ower between non-intersecting and non-parallel shafts, usually crossing at a right angle, especially where it is desired to obtain high gear reduction in a limited space. Worms are a kind of screw, usually right handed for convenience of cutting, or left handed it necessary. According to the enveloping type, worms can be divided into single and double enveloping. Worms are usually drivers to reduce the speed. If not self-locking, a worm gear can also be the driver in a so called back-driving mechanism to increase the speed. Two things characterize worm gearing (a) large velocity ratios, and (b) high sliding velocities. The latter means that heat generation and power transmission efficiency are of greater concern than with other types of gears.
(5) Racks. A rack is a gear with an infinite radius, or a gear with its perimeter stretched out into a straight line. It is used to change reciprocating motion to rotary motion or vice versa. A lathe rack and pinion is good example of this mechanism.
Geometry of gear tooth
The basic requirement of gear-tooth geometry is the provision of angular velocity rations that are exactly constant. Of course, manufacturing inaccuracies and tooth deflections well cause slight deviations in velocity ratio; but acceptable tooth profiles are based on theoretical curves that meet this criterion.
The action of a pair of gear teeth satisfying this requirement is termed conjugate gear-tooth action, and is illustrated in Fig. 2.12. The basic law of conjugate gear-tooth action states that as the gears rotate, the common normal to the surfaces at the point of contact must always intersect the line of centers at the same point P called the pitch point.
The law of conjugate gear-tooth can be satisfied by various tooth shapes, but the only one of current importance is the involute, or, more precisely, the involute of the circle. (Its last important competitor was the cycloidal shape, used in the gears of Model T Ford transmissions.) An involute (of the circle) is the curve generated by any point on a taut thread as it unwinds from a circle, called the base circle. The generation of two involutes is shown in Fig. 2.13. The dotted lines show how these could correspond to the outer portion of the right sides of adjacent gear teeth. Correspondingly, involutes generated by unwinding a thread wrapped counterclockwise around the base circle would for the outer portions of the left sides of the teeth. Note that at every point, the involute is perpendicular to the taut thread, since the involute is a circular arc with everincreasing radius, and a radius is always perpendicular to its circular arc. It is important to note that an involute can be developed as far as desired outside the base circle, but an involute cannot exist inside its base circle.
Let us now develop a mating pair of involute gear teeth in three steps: friction drive, belt drive, and finally, involute gear-tooth drive. Figure 2.14 shows two pitch circles. Imagine that they represent two cylinders pressed together. If slippage does not occur, rotation of one cylinder (pitch circle) will cause rotation of the other at an angular velocity ratio inversely proportional to their diameters. In any pair of mating gears, the smaller of the two is called the pinion and the larger one the gear. (The term “gear” is used in a general sense to indicate either of the members, and also in a specific sense to indicate the larger of the two.) Using subscripts p and g to denote pinion and gear, respectively.
In order to transmit more torque than is possible with friction drive alone, we now add a belt drive running between pulleys representing the base circles, as in Fig 2.15. If the pinion is turned counterclockwise a few degrees, the belt will cause the gear to rotate in accordance with correct velocity ratio. In gear parlance, angle Φ is called the pressure angle. From similar triangles, the base circles have the same ratio as the pitch; thus, the velocity ratio provided by the friction and belt drives are the same.
In Fig. 2.16 the belt is cut at point c, and the two ends are used to generate involute profiles de and fg for the pinion and gear, respectively. It should now be clear why Φ is called the pressure angle: neglecting sliding friction, the force of one involute tooth pushing against the other is always at an angle equal to the pressure angle. A comparison of Fig. 2.16 and Fig.2.12 shows that the involute profiles do indeed satisfy the fundamental law of conjugate gear-tooth action. Incidentally, the involute is the only geometric profile satisfying this law that maintains a constant pressure angle as the gears rotate. Note especially that conjugate involute action can take place only outside of both base circles.
Nomenclature of spur gear
The nomenclature of spur gear (Fig .2.17) is mostly applicable to all other type of gears.
The diameter of each of the original rolling cylinders of two mating gears is called the pitch diameter, and the cylinder’s sectional outline is called the pitch circle. The pitch circles are tangent to each other at pitch point. The circle from which the involute is generated is called the base circle. The circle where the tops of the teeth lie is called the dedendum circle. Similarly, the circle where the roots of the teeth lie is called the dedendum circle. Between the addendum circle and the dedendum circle, there is an important circle which is called the reference circle. Parameters on the reference circle are standardized. The module m of a gear is introduced on the reference circle as a basic parameter, which is defined as m=p/π. Sizes of the teeth and gear are proportional to the module m.
The addendum is the radial distance from the reference circle to the addendum circle. The dedendum is the radial distance from the reference circle to the dedendum circle. Clearance is the difference between addendum and dedendum in mating gears. Clearance prevents binding caused by any possible eccentricity.
The circular pitch p is the distance between corresponding side of neighboring teeth, measured along the reference circle. The base pitch is similar to the circular pitch is measured along the base circle instead of along the reference circle. It can easily be seen that the base radius equals the reference radius times the cosine of the pressure angle. Since, for a given angle, the ratio between any subtended arc and its radius is constant, it is also true that the base pitch equals the circular pitch times the cosine of the pressure angle. The pressure angle is the angle between the normal and the circumferential velocity of the point on a specific circle. The pressure angle on the reference circle is also standardized. It is most commonly 20o(sometimes 15o).
The line of centers is a line passing through the centers of two mating gears. The center distance (measured along the line of centers) equals the sum of the pitch radii of pinion and gear.
Tooth thickness is the width of the tooth, measured along the reference circle, is also referred to as tooth thickness. Width of space is the distance between facing side of adjacent teeth, measured along the reference circle. Tooth thickness plus width of space equals the circular pitch. Backlash is the width of space minus the tooth thickness. Face width measures tooth width in an axial direction.
The face of the tooth is the active surface of the tooth outside the pitch cylinder. The flank of the tooth is the active surface inside the pitch cylinder. The fillet is the rounded corner at the base of the tooth. The working depth is the sum of the addendum of a gear and the addendum of its mating gear.
In order to mate properly, gears running together must have: (a) the same module; (b) the same pressure angle; (c) the same addendum and dedendum. The last requirement is valid for standard gears only.
Rolling-Contactbearings
The rolling-contact bearing consists of niier and outer rings sepatated by a number of rolling elements in the form of balls ,which are held in separators or retainers, and roller bearings have mainly cyinndrical, conical , or barrelcage.The needles are retainde by integral flanges on the outer race,
Bearigs with rolling contact have no skopstick effect,low statting torqeu and running friction,and unlike as in journal bearings. The coefficient of friction varies little with load or opeed.Probably the outstanding of a rolling-contant beating over a sliding bearing is its low statting friction.The srdinary sliding bearing starts from rest with practically metal to metal contact and has a high coefficient of friction as compared with that between rolling members.This teature is of particular important in the case of beatings whcch vust carry the same laode at test as when tunning,for example.less than one-thirtieth as much force is required to start a raliroad freight car equopped with roller beatings as with plain journal bearings.However.most journal bearing can only carry relatively light loads while starting and do not become heavily loaded until the speed is high enough for a hydrodynamic film to be built up.At this time the friction id that in the luvricant ,and in a properly designed journal bearing the viscous friction will be in the same order of magnitude ad that for a that for a rolling-conanct bearing.
齒輪機(jī)構(gòu)
齒輪機(jī)構(gòu)用來(lái)傳遞運(yùn)動(dòng)和動(dòng)力，通過(guò)連續(xù)嚙合輪齒的正確接觸，從一根軸傳動(dòng)到另一根軸。大約公元前2600年，中國(guó)人就能夠使用一系列戰(zhàn)車而聞名復(fù)雜的齒輪機(jī)構(gòu)而構(gòu)成的。公元前4世紀(jì)，亞里士多德寫的齒輪好象推動(dòng)的是平凡的。在公元15世紀(jì)，Leonardo da Vinci 設(shè)計(jì)了能與許多種類的齒輪樞結(jié)合的大量裝置。與皮帶和鏈傳動(dòng)相比較，齒輪傳動(dòng)裝置更加緊湊，能高速運(yùn)行，也能夠被運(yùn)用在要求準(zhǔn)確定時(shí)的場(chǎng)合。齒輪傳動(dòng)的傳動(dòng)效率高達(dá)98％。另一方面，齒輪傳動(dòng)機(jī)構(gòu)成本高，而且要求注意潤(rùn)滑、清潔度、軸的對(duì)中等等，經(jīng)常用在提供準(zhǔn)確箱體潤(rùn)滑的閉式情況下。
齒輪機(jī)構(gòu)能被分為平面齒輪機(jī)構(gòu)和空間齒輪機(jī)構(gòu)。平面齒輪機(jī)構(gòu)被用于傳遞運(yùn)動(dòng)和動(dòng)力，而平行軸間的運(yùn)動(dòng)和動(dòng)力空間齒輪機(jī)構(gòu)用于傳遞不平行軸間的運(yùn)動(dòng)和動(dòng)力。
齒輪的分類：
1、 直齒輪 直齒輪有節(jié)輪表面和平行于輪的軸線的直齒輪，如圖2.8所示。它們用于傳遞兩平行軸間的運(yùn)動(dòng)和動(dòng)力。兩配合的直接齒面嚙合在一條平行于其軸線的直線上，這意味著整個(gè)齒寬在同一時(shí)刻嚙合脫開，這樣在齒面上導(dǎo)致加載或卸載，當(dāng)齒輪嚙合或脫開時(shí)，結(jié)果推動(dòng)和噪聲就產(chǎn)生了。
（1） 斜齒輪 這種齒輪的輪齒有一位角度或與其軸線旋轉(zhuǎn)一定角度在平面齒輪機(jī)構(gòu)中相互嚙合，斜齒輪齒面相嚙合于一條傾斜于軸承的直線上，嚙合線的長(zhǎng)度從0逐漸變化到最大再?gòu)淖畲笞兓?，輪齒的加載和卸載變得平穩(wěn)均勻的運(yùn)動(dòng)和動(dòng)力。人字齒輪相當(dāng)于右旋齒輪和左旋齒輪并在一起，因?yàn)檩嘄X存在一定角度，斜齒輪產(chǎn)生相當(dāng)大的軸間推力，人字齒輪通過(guò)相互抵消糾正了這一推力，允許其使用以推力軸承代替大推力軸承，或不同推力軸承，為了加工方便經(jīng)常沿著齒輪加工一個(gè)中心槽。
（2） 傘狀齒輪 傘狀齒輪是依據(jù)平截頭圓錐體分配的。圓柱齒輪的節(jié)圓柱成為分圓錐，齒輪的齒的橫剖面的尺寸是不同的。為了方便起見，錐齒輪的大頭端部的參數(shù)和尺寸作為標(biāo)準(zhǔn)值。習(xí)慣上錐齒輪相互作用的軸彼此不是平行的，通常兩軸線彼此成為90度，有時(shí)會(huì)比90度或多或少。兩個(gè)相互嚙合的齒輪僅僅為了變向或許有一樣的齒數(shù)，又或者為了改變速度和方向而齒數(shù)不同。錐齒輪可能是直齒的也可能是螺旋形齒輪，以便我們有簡(jiǎn)單的和螺旋形的齒輪。準(zhǔn)雙曲面來(lái)自于雙曲面和齒面的放置的表面。準(zhǔn)雙曲面的齒輪屬于錐齒輪，但是兩軸不能橫斷，因?yàn)檩S的材料，它的齒是曲線的，軸承可以位于各齒輪的各個(gè)側(cè)面。這種齒輪主要用在汽車后方末端是為了降低傳動(dòng)軸并且用在汽車踏板處。
（3） 蝸輪蝸桿齒輪 蝸輪傳動(dòng)慣于傳遞動(dòng)力和功率，它的軸既不相交也不平行，通常都是垂直的，尤其是要求獲得高的齒輪減速在一定的極限運(yùn)算范圍內(nèi)。蝸桿是螺旋的，通常為了方便起見都是順時(shí)針?lè)较虻?，如果需要的話也可是左旋方向的。按照類型，可以是單螺旋的也可以是雙螺旋的，螺桿通常用來(lái)降低速度的，即使不自動(dòng)鎖住，螺桿也能夠被驅(qū)動(dòng)，所以稱作回力驅(qū)動(dòng)機(jī)構(gòu)，為了提高速度。下面是蝸輪蝸桿傳動(dòng)裝置的兩個(gè)特點(diǎn)：（a）有很高的傳動(dòng)速度（b）后者意思指和其它種類的齒輪相比中心有高的發(fā)熱性和電力傳輸效率。
齒輪輪齒形狀
輪齒幾何形狀的基本要求提供一個(gè)準(zhǔn)確不變的角速度，當(dāng)然制造端差和輪齒變形將會(huì)在速度比上產(chǎn)生微小的偏差，然而可接受的齒形依據(jù)基于滿足這一判劇的理論曲線得出的。
滿足這要求的一對(duì)配合齒輪的運(yùn)動(dòng)被稱為共軛齒輪傳動(dòng)。如圖2.12所示，共軛齒輪傳動(dòng)的基本定律論述為當(dāng)齒輪轉(zhuǎn)動(dòng)時(shí)，接觸點(diǎn)表面的公法線總是與中心線交于一點(diǎn)P，這點(diǎn)叫節(jié)點(diǎn)。
共軛齒輪傳動(dòng)原則能被各種齒形適應(yīng)，目前最重要的一種是漸開線齒輪更精確地說(shuō)一個(gè)圓的漸開線（與它相近的重要的競(jìng)爭(zhēng)者是擺線齒輪，它被用在福特汽車廠模式中）是條曲線，當(dāng)從一個(gè)基圓滿開時(shí)，張緊線上每一點(diǎn)所形成的，兩條漸近線輪齒右外形相對(duì)應(yīng)，相應(yīng)地，通過(guò)逆時(shí)針?lè)较蛘归_預(yù)先在右基圓上的線所產(chǎn)生的漸開線會(huì)形成輪齒左邊的外形，該點(diǎn)在每一點(diǎn)上，漸開線始終垂直于這條張緊線，因?yàn)闈u開線理一條半徑不斷增加的圓弧，值得注意的是漸開線能夠在基圓外部產(chǎn)生并繪制，而不能在基圓里面。
用以下三個(gè)步驟研究一對(duì)相配合的齒輪：摩擦傳動(dòng)，帶傳動(dòng)和漸開線齒輪傳動(dòng)。如圖2.14所示兩個(gè)節(jié)圓，假設(shè)他們是兩個(gè)壓在一起的圓柱，如果不發(fā)生打滑，一個(gè)圓柱的旋轉(zhuǎn)會(huì)引起另一個(gè)圓柱以一定角速度旋轉(zhuǎn)，且這個(gè)速比反比于他們的直徑比，任何一對(duì)相嚙合的齒輪，兩個(gè)中較小的叫小齒輪，較大的叫大齒輪，用下標(biāo)p和g分別指明。
為了使傳動(dòng)的扭矩比摩擦傳動(dòng)產(chǎn)生的扭矩大，要附加一個(gè)帶有基圓的皮帶辦的皮帶驅(qū)動(dòng)裝置。如圖2.15所示，如圖，小齒輪逆時(shí)針旋轉(zhuǎn)一個(gè)小角度，皮帶將帶動(dòng)大齒輪以相應(yīng)的速比旋轉(zhuǎn)，在齒輪傳動(dòng)中，角度Ψ為壓力角，人相似三角形得，把基圓具有相同速度的點(diǎn)稱為節(jié)點(diǎn)。
如圖2.16中皮帶在c點(diǎn)被切斷，兩端分別形成了大齒輪和大齒輪上的漸開線齒形DE和FG，現(xiàn)在應(yīng)該清楚了為什么稱Ψ為壓力角，忽略滑動(dòng)摩擦，一個(gè)齒輪作用于另一個(gè)齒輪的力總是形成一個(gè)與壓力角相同的角度。圖2.16和2.12的比較表明了漸開線齒輪強(qiáng)調(diào)滿足共軛齒輪傳動(dòng)的基本原則，附帶的漸開線齒輪只是幾何形狀滿足當(dāng)齒輪旋轉(zhuǎn)時(shí)壓力角多產(chǎn)生這一原則，特別注意共軛漸開線齒輪傳動(dòng)只能發(fā)生在兩基圓外面，從而摩擦傳動(dòng)和皮帶傳動(dòng)所提供的速度三角開相同。
直齒輪的專用術(shù)語(yǔ)
直齒輪的術(shù)語(yǔ)大部分可用于其它種類的齒輪。
兩個(gè)相配合的齒輪的每個(gè)最初的圓柱直徑被稱為中徑，并且圓柱體的橫截面外形被稱為節(jié)圓，兩個(gè)節(jié)圓相切于節(jié)點(diǎn)。產(chǎn)生漸開線的圓稱為基圓。位于齒的頂部的圓稱為齒頂圓，同樣的，位于齒的根部的圓稱為齒根圓，在齒頂圓和齒根圓之間的重要的圓稱為分度圓，分度圓的參數(shù)是標(biāo)準(zhǔn)化了的。用在齒輪分度圓的模數(shù)作為基本參數(shù)，m=p/π,齒和齒輪的尺寸正比于模數(shù)m。
齒頂是指由分度圓到齒頂圓的徑向距離，齒根是指由分度圓到齒根圓的徑向距離。相互嚙合的齒輪的齒頂和齒根之間的間隙是有差異的，此間隙的存在是為了防止兩齒輪相互嚙合引起偏心。
周節(jié)p是指相鄰齒的相應(yīng)邊之間的距離，它是沿分度圓測(cè)量的。類似于周節(jié)的基節(jié)沿分度圓測(cè)量代替分度圓。很容易看出來(lái)基圓半徑等于分度圓半徑乘上壓力角的余弦，因?yàn)閷?duì)于給定的角度，任一相對(duì)的弧和半徑之比為常數(shù)，它確實(shí)是基圓節(jié)距等于圓的節(jié)距乘上壓力角的余弦。壓力角是一確定的圓上法線和圓周速度相交點(diǎn)所在的角。在分度圓上的壓力角是標(biāo)準(zhǔn)化的，它通常是20o（有時(shí)15o）。
中心線是指通過(guò)相互嚙合齒輪的中心線的那條線。中心距（沿中心線測(cè)量）等于小齒輪和大齒輪節(jié)圓半徑的和。
齒厚是指齒的寬度，是沿著分度圓測(cè)量的這段距離稱之為齒厚。齒間寬是沿著分度圓測(cè)量相鄰齒相對(duì)邊之間的距離，齒厚加上齒間寬等于節(jié)距，齒側(cè)是齒間寬減去齒厚的距離。齒面寬是沿軸線上測(cè)量出齒的寬度。
齒頂面是在節(jié)圓作用之外的齒的作用面，齒根面是在節(jié)圓之內(nèi)的作用面。齒根圓角是齒的根部處的圓角，工作深度是大齒輪齒頂高與其相嚙合的齒輪的齒頂高之和。
為了正確嚙合，齒輪共同運(yùn)轉(zhuǎn)的準(zhǔn)則是：（a）具有相同的模數(shù)；（b）有相同的壓力角；（c）有相同的齒頂高和相同的齒根高。最后的一條準(zhǔn)則只適用于標(biāo)準(zhǔn)齒輪。
滾動(dòng)軸承
滾動(dòng)軸承包含了內(nèi)外尾圈，他由許多滾動(dòng)元件分開，如滾珠，圓柱或圓錐滾子，或者滾針。滾珠軸承具有球狀滾動(dòng)元件，他被保持在隔圈和保持架之間，棍子軸承主要由圓柱的，圓錐的，鼓形的磙子代替。球行的滾針軸承通常即設(shè)內(nèi)滾道也設(shè)保持架。滾針被外圈滾道上構(gòu)成整體的必須法點(diǎn)固定。
具有滾動(dòng)軸承的滾道軸，不具有滑動(dòng)粘著效應(yīng)，低啟動(dòng)扭矩和速度摩擦力，不像滑動(dòng)軸承，摩擦系數(shù)遂在和和速度變化不大，滾動(dòng)接觸軸承優(yōu)于滑動(dòng)軸承的有點(diǎn)是他的啟動(dòng)扭矩，普通滑動(dòng)軸承從靜止開始實(shí)際上伴隨著金屬的接觸，和滾動(dòng)元件之間的摩擦具有高摩擦系數(shù)，在軸承帶恒定負(fù)荷啟動(dòng)的情況下，這個(gè)特點(diǎn)相當(dāng)重要。