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【20160409】Gears: Kinematic Analysis and Selection
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INTRODUCTION
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In general, the function of a gear is to transmit motion from one rotating shaft to another. In addition to transmitting the motion, gears are often used to increase or reduce speed, or change the direction of motion from one shaft to the other." |* n1 E; Y( [) h4 x7 q' Q9 j2 {
通常來說,齒輪的功能是在一個(gè)轉(zhuǎn)動(dòng)軸與另一個(gè)之間傳遞運(yùn)動(dòng)。除此之外,齒輪也常用于增速或降速,或者改變兩軸的運(yùn)動(dòng)方向。% b: i' h3 Y3 c1 K* A Z. B
. S9 `' T& L) b6 p) gFriction rollers or disks that are also designed to transmit motion are less costly than complex gear configurations, but they may not be able to generate sufficient frictional forces and thus will slip under larger loads. To remedy the possibility of slipping, a gear is formed such that the smooth surfaces of the disks are replaced by teeth. The teeth provide a positive engagement and eliminate slipping., ~" k% B$ {3 t( P9 k& y( }
盡管摩擦輪也可傳遞運(yùn)動(dòng),而且比復(fù)雜的齒輪配置更加經(jīng)濟(jì),但可能因摩擦力不足而導(dǎo)致打滑。為彌補(bǔ)這一缺陷,帶齒齒輪取代摩擦輪成為了主流。帶齒齒輪嚙合更好,并能減少打滑現(xiàn)象。
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TYPES OF GEARS
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Spur gears are simplest and, hence, the most common type of gear. The teeth of a spur gear are parallel to the axis of rotation. Spur gears are used to transmit motion between parallel shafts, which encompasses the majority of applications. A pair of mating spur gears is illustrated in Figure 10.3a.
# t* g+ U, ^2 K7 O! Q直齒輪最簡單,應(yīng)用也最廣。直齒輪的齒與轉(zhuǎn)動(dòng)軸平行(指邊)。直齒輪用于傳遞兩平行軸之間的運(yùn)動(dòng),這占了實(shí)際生產(chǎn)中的大多數(shù)情況。圖a為一對(duì)配合的直齒輪。6 I( W7 S J+ V/ s
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A rack is a special case of spur gear where the teeth of the rack are not formed around a circle, but laid flat. The rack can be perceived as a spur gear with an infinitely large diameter.When the rack mates with a spur gear, translating motion is produced. A mating rack and gear are illustrated in Figure 10.3b. J8 E4 S0 e0 n& `9 f
齒條是直齒輪的特例,齒條的齒不是繞圓,而是平鋪形成的。齒條可以看做是無限直徑的圓。齒輪和齒條配合時(shí)產(chǎn)生平移運(yùn)動(dòng)。圖b為一對(duì)配合的齒輪齒條。
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) ^: C& w8 d4 G' r! B9 ~/ Y, k6 EInternal or annular gears have the teeth formed on the inner surface of a circle. When mating with a spur gear, the internal gear has the advantage of reducing the distance between the gear centers for a given speed variation. An internal gear mating with a traditional spur gear is illustrated in Figure 10.3c.
% Q" k ^3 c) J, H l內(nèi)齒輪的齒在圓的內(nèi)表面形成。與直齒輪嚙合時(shí),在給定的速度下,內(nèi)齒輪能有效減少兩齒輪中心的距離。圖c為內(nèi)齒輪與普通直齒輪配合。* D# u& H# |3 j" X9 z, p! M3 H
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Helical gears are similar to, and can be used in the same applications as, spur gears. The difference is that the teeth of a helical gear are inclined to the axis of rotation. The angle of inclination is termed the helix angle, . This angle provides a more gradual engagement of the teeth during meshing and produces less impact and noise. Because of this smoother action, helical gears are preferred in high-speed applications. However, the helix angle produces thrust forces and bending couples, which are not generated in spur gears. A pair of mating helical gears is illustrated in Figure 10.3d.# o3 E( i1 I7 V1 |/ K- q5 F) V4 l
斜齒輪與直齒輪有很多類似之處,不同的是它的齒與轉(zhuǎn)軸有一定夾角,稱為螺旋角。螺旋角使配合更平穩(wěn),產(chǎn)生的壓力和噪音也更小。因此高速場合多用斜齒輪。然而螺旋角會(huì)產(chǎn)生軸向力與彎曲偶,直齒輪卻不會(huì)產(chǎn)生。圖d為喻隊(duì)配合的斜齒輪。
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$ R( Q) p) Y- `( SHerringbone gears are used in the same applications as spur gears and helical gears. In fact, they are also referred to as double helical gears. The herringbone gear appears as two opposite-hand helical gears butted against each other. This complex configuration counterbalances the thrust force of a helical gear. A herringbone gear is shown in Figure 10.3e.% g! c* y6 `8 `4 z. q
人字齒的用途與直齒輪、斜齒輪類似。實(shí)際上也把它叫做雙斜齒輪。人字齒有兩個(gè)相反方向的螺線。這種復(fù)雜的配置平衡了螺旋角的軸向力。圖e為人字齒。
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Bevel gears have teeth formed on a conical surface and are used to transmit motion between nonparallel shafts. Although most of their applications involve connecting perpendicular shafts, bevel gears can also be used in applications that require shaft angles that are both larger and smaller than 90°. As bevel gears mesh, their cones have a common apex. However, the actual cone angle of each gear depends on the gear ratio of the mating gears. Therefore, bevel gears are designed as a set, and replacing one gear to alter the gear ratio is not possible. A pair of mating bevel gears is illustrated in Figure 10.3f. J1 m, P% K7 W8 a
圓錐齒輪的齒在圓錐表面上形成。用于傳遞不平行軸之間的運(yùn)動(dòng)。大多數(shù)情況下圓錐齒輪用于傳遞垂直軸間的運(yùn)動(dòng),但也可傳遞成任意角度的軸之間的運(yùn)動(dòng)。圓錐齒輪配合時(shí)錐頂重合。然而錐角決定于齒數(shù)比。因此圓錐齒輪一般成套設(shè)計(jì),通過改變一個(gè)齒輪來改變齒數(shù)比是不現(xiàn)實(shí)的。圖f是一對(duì)配合的圓錐齒輪。8 C7 \) @5 x) B6 O5 @- O
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% W6 A8 p/ U* X oMiter gears are a special case of bevel gears where the gears are of equal size and the shaft angle is 90°. A pair of mating miter gears is illustrated in Figure 10.3g.: S! S' @; c$ K0 r
等齒數(shù)整角錐齒輪副是圓錐齒輪的特例,兩齒輪有相同的尺寸,并且兩軸成90°。圖g為一對(duì)配合的等齒數(shù)整角錐齒輪副。# V) m; B5 u) J' h- r) W& O. ]
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A worm and worm gear is used to transmit motion between nonparallel and nonintersecting shafts. The worm has one tooth that is formed in a spiral around a pitch cylinder. This one tooth is also referred to as the thread because it resembles a screw thread. Similar to the helical gear, the spiral pitch of the worm generates an axial force that must be supported. In most applications, the worm drives the worm gear to produce great speed reductions. Generally, a worm gear drive is not reversible. That is, the worm gear cannot drive the worm. A mating worm and worm gear are shown in Figure 10.3h.& u3 Q1 E" B; F" Y* C7 N! t
蝸輪蝸桿用于傳遞不平行不相交軸之間的運(yùn)動(dòng)。蝸桿是指具有一個(gè)或幾個(gè)螺旋齒,并且與蝸輪嚙合而組成交錯(cuò)軸齒輪副的齒輪。這一螺旋齒也被稱作螺紋。與斜齒輪類似,蝸桿的螺線產(chǎn)生軸向力。絕大多數(shù)情況下,由蝸桿驅(qū)動(dòng)渦輪產(chǎn)生巨大的減速。一般來說渦輪驅(qū)動(dòng)是不可逆的,也就是說,渦輪不能驅(qū)動(dòng)蝸桿。圖h為一對(duì)配合的蝸輪蝸桿。8 G- u" x# P! T) z; O* b
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