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1、XXX大學(xué)郵電與信息工程學(xué)院 外文文獻(xiàn)翻譯 文 獻(xiàn) 名 Planetary Gears 文獻(xiàn)譯名 行星齒輪結(jié)構(gòu) 專業(yè)班級 學(xué) 號 學(xué)生姓名 指導(dǎo)教師

2、指導(dǎo)教師職稱 學(xué) 部 名 稱 完成日期： 年 5 月 21日 英文原文 Planetary Gears Introduction The Tamiya planetary gearbox is driven by a small DC motor that runs at about 10,500 rpm on 3.0V DC and draws about 1.0A. The maximum speed ratio is

3、1:400, giving an output speed of about 26 rpm. Four planetary stages are supplied with the gearbox, two 1:4 and two 1:5, and any combination can be selected. Not only is this a good drive for small mechanical applications, it provides an excellent review of epicycle gear trains. The gearbox is a ver

4、y well-designed plastic kit that can be assembled in about an hour with very few tools. The source for the kit is given in the References. Lets begin by reviewing the fundamentals of gearing, and the trick of analyzing epicyclic gear trains. Epicyclic Gear Trains A pair of spur gears is rep

5、resented in the diagram by their pitch circles, which are tangent at the pitch point P. The meshing gear teeth extend beyond the pitch circle by the addendum, and the spaces between them have a depth beneath the pitch circle by the dedendum. If the radii of the pitch circles are a and b, the distanc

6、e between the gear shafts is a + b. In the action of the gears, the pitch circles roll on one another without slipping. To ensure this, the gear teeth must have a proper shape so that when the driving gear moves uniformly, so does the driven gear. This means that the line of pressure, normal to the

7、tooth profiles in contact, passes through the pitch point. Then, the transmission of power will be free of vibration and high speeds are possible. We wont talk further about gear teeth here, having stated this fundamental principle of gearing. If a gear of pitch radius a has N teeth, then the dist

8、ance between corresponding points on successive teeth will be 2πa/N, a quantity called the circular pitch. If two gears are to mate, the circular pitches must be the same. The pitch is usually stated as the ration 2a/N, called the diametral pitch. If you count the number of teeth on a gear, then the

9、 pitch diameter is the number of teeth times the diametral pitch. If you know the pitch diameters of two gears, then you can specify the distance between the shafts. The velocity ratio r of a pair of gears is the ratio of the angular velocity of the driven gear to the angular velocity of the drivi

10、ng gear. By the condition of rolling of pitch circles, r = -a/b = -N1/N2, since pitch radii are proportional to the number of teeth. The angular velocity n of the gears may be given in radians/sec, revolutions per minute (rpm), or any similar units. If we take one direction of rotation as positive,

11、then the other direction is negative. This is the reason for the (-) sign in the above expression. If one of the gears is internal (having teeth on its inner rim), then the velocity ratio is positive, since the gears will rotate in the same direction. The usual involute gears have a tooth shape th

12、at is tolerant of variations in the distance between the axes, so the gears will run smoothly if this distance is not quite correct. The velocity ratio of the gears does not depend on the exact spacing of the axes, but is fixed by the number of teeth, or what is the same thing, by the pitch diameter

13、s. Slightly increasing the distance above its theoretical value makes the gears run easier, since the clearances are larger. On the other hand, backlash is also increased, which may not be desired in some applications. An epicyclic gear train has gear shafts mounted on a moving arm or carrier that

14、 can rotate about the axis, as well as the gears themselves. The arm can be an input element, or an output element, and can be held fixed or allowed to rotate. The outer gear is the ring gear or annulus. A simple but very common epicyclic train is the sun-and-planet epicyclic train, shown in the fig

15、ure at the left. Three planetary gears are used for mechanical reasons; they may be considered as one in describing the action of the gearing. The sun gear, the arm, or the ring gear may be input or output links. If the arm is fixed, so that it cannot rotate, we have a simple train of three gears. T

16、hen, n2/n1 = -N1/N2, n3/n2 = +N2/N3, and n3/n1 = -N1/N3. This is very simple, and should not be confusing. If the arm is allowed to move, figuring out the velocity ratios taxes the human intellect. Attempting this will show the truth of the statement; if you can manage it, you deserve praise and fam

17、e. It is by no means impossible, just invoved. However, there is a very easy way to get the desired result. First, just consider the gear train locked, so it moves as a rigid body, arm and all. All three gears and the arm then have a unity velocity ratio. The trick is that any motion of the gear t

18、rain can carried out by first holding the arm fixed and rotating the gears relative to one another, and then locking the train and rotating it about the fixed axis. The net motion is the sum or difference of multiples of the two separate motions that satisfies the conditions of the problem (usually

19、that one element is held fixed). To carry out this program, construct a table in which the angular velocities of the gears and arm are listed for each, for each of the two cases. The locked train gives 1, 1, 1, 1 for arm, gear 1, gear 2 and gear 3. Arm fixed gives 0, 1, -N1/N2, -N1/N3. Suppose we wa

20、nt the velocity ration between the arm and gear 1, when gear 3 is fixed. Multiply the first row by a constant so that when it is added to the second row, the velocity of gear 3 will be zero. This constant is N1/N3. Now, doing one displacement and then the other corresponds to adding the two rows. We

21、 find N1/N3, 1 + N1/N3, N1/N3 - N1/N2. The first number is the arm velocity, the second the velocity of gear 1, so the velocity ratio between them is N1/(N1 + N3), after multiplying through by N3. This is the velocity ratio we need for the Tamiya gearbox, where the ring gear does not rotate, the s

22、un gear is the input, and the arm is the output. The procedure is general, however, and will work for any epicyclic train. One of the Tamiya planetary gear assemblies has N1 = N2 = 16, N3 = 48, while the other has N1 = 12, N2 = 18, N3 = 48. Because the planetary gears must fit between the sun and

23、ring gears, the condition N3 = N1 + 2N2 must be satisfied. It is indeed satisfied for the numbers of teeth given. The velocity ratio of the first set will be 16/(48 + 16) = 1/4. The velocity ratio of the second set will be 12/(48 + 12) = 1/5. Both ratios are as advertised. Note that the sun gear and

24、 arm will rotate in the same direction. The best general method for solving epicyclic gear trains is the tabular method, since it does not contain hidden assumptions like formulas, nor require the work of the vector method. The first step is to isolate the epicyclic train, separating the gear trai

25、ns for inputs and outputs from it. Find the input speeds or turns, using the input gear trains. There are, in general, two inputs, one of which may be zero in simple problems. Now prepare two rows of the table of turns or angular velocities. The first row corresponds to rotating around the epicyclic

26、 axis once, and consists of all 1s. Write down the second row assuming that the arm velocity is zero, using the known gear ratios. The row that you want is a linear combination of these two rows, with unknown multipliers x and y. Summing the entries for the input gears gives two simultaneous linear

27、equations for x and y in terms of the known input velocities. Now the sum of the two rows multiplied by their respective multipliers gives the speeds of all the gears of interest. Finally, find the output speed with the aid of the output gear train. Be careful to get the directions of rotation corre

28、ct, with respect to a direction taken as positive. The Tamiya Gearbox Kit The parts are best cut from the sprues with a flush-cutter of the type used in electronics. The very small bits of plastic remaining can then be removed with a sharp X-acto knife. Carefully remove all excess plastic, as

29、 the instructions say. Read the instructions carefully and make sure that things are the right way up and in the correct relative positons. The gearbox units go together easily with light pressure. Note that the brown ones must go together in the correct relative orientation. The 4mm washers are t

30、he ones of which two are supplied, and there is also a full-size drawing of one in the instructions. The smaller washers will not fit over the shaft, anyway. The output shaft is metal. Use larger long-nose pliers to press the E-ring into position in its groove in front of the washer. There is a pict

31、ure showing how to do this. There was an extra E-ring in my kit. The three prongs fit into the carriers for the planetary gears, and are driven by them. Now stack up the gearbox units as desired. I used all four, being sure to put a 1:5 unit on the end next to the motor. Therefore, I needed the lo

32、ng screws. Press the orange sun gear for the last 1:5 unit firmly on the motor shaft as far as it will go. If it is not well-seated, the motor clip will not close. It might be a good idea to put some lubricant on this gear from the tube included with the kit. If you use a different lubricant, test i

33、t first on a piece of plastic from the kit to make sure that it is compatible. A dry graphite lubricant would also work quite well. This should spread lubricant on all parts of the last unit, which is the one subject to the highest speeds. Put the motor in place, gently but firmly, wiggling it so th

34、at the sun gear meshes. If the sun gear is not meshed, the motor clip will not close. Now put the motor terminals in a vertical column, and press on the motor clamp. The reverse of the instructions show how to attach the drive arm and gives some hints on use of the gearbox. I got an extra spring p

35、in, and two extra 3 mm washers. If you have some small washers, they can be used on the machine screws holding the gearbox together. Enough torque is produced at the output to damage things (up to 6 kg-cm), so make sure the output arm can rotate freely. I used a standard laboratory DC supply with va

36、riable voltage and current limiting, but dry cells could be used as well. The current drain of 1 A is high even for D cells, so a power supply is indicated for serious use. The instructions say not to exceed 4.5V, which is good advice. With 400:1 reduction, the motor should run freely whatever the o

37、utput load. My gearbox ran well the first time it was tested. I timed the output revolutions with a stopwatch, and found 47s for 20 revolutions, or 25.5 rpm. This corresponds to 10,200 rpm at the motor, which is close to specifications. It would be easy to connect another gearbox in series with th

38、is one (parts are included to make this possible), and get about 4 revolutions per hour. Still another gearbox would produce about one revolution in four days. This is an excellent kit, and I recommend it highly. Other Epicyclic Trains A very famous epicyclic chain is the Watt sun-and-planet g

39、ear, patented in 1781 as an alternative to the crank for converting the reciprocating motion of a steam engine into rotary motion. It was invented by William Murdoch. The crank, at that time, had been patented and Watt did not want to pay royalties. An incidental advantage was a 1:2 increase in the

40、rotative speed of the output. However, it was more expensive than a crank, and was seldom used after the crank patent expired. Watch the animation on Wikipedia. The input is the arm, which carries the planet gear wheel mating with the sun gear wheel of equal size. The planet wheel is prevented fro

41、m rotating by being fastened to the connecting rod. It oscillates a little, but always returns to the same place on every revolution. Using the tabular method explained above, the first line is 1, 1, 1 where the first number refers to the arm, the second to the planet gear, and the third to the sun

42、gear. The second line is 0, -1, 1, where we have rotated the planet one turn anticlockwise. Adding, we get 1, 0, 2, which means that one revolution of the arm (one double stroke of the engine) gives two revolutions of the sun gear. We can use the sun-and-planet gear to illustrate another method fo

43、r analyzing epicyclical trains in which we use velocities. This method may be more satisfying than the tabular method and show more clearly how the train works. In the diagram at the right, A and O are the centres of the planet and sun gears, respectively. A rotates about O with angular velocity ω1,

44、 which we assume clockwise. At the position shown, this gives A a velocity 2ω1 upward, as shown. Now the planet gear does not rotate, so all points in it move with the same velocity as A. This includes the pitch point P, which is also a point in the sun gear, which rotates about the fixed axis O wit

45、h angular velocity ω2. Therefore, ω2 = 2ω1, the same result as with the tabular method. The diagram at the left shows how the velocity method is applied to the planetary gear set treated above. The sun and planet gears are assumed to be the same diameter (2 units). The ring gear is then of diamete

46、r 6. Let us assume the sun gear is fixed, so that the pitch point P is also fixed. The velocity of point A is twice the angular velocity of the arm. Since P is fixed, P must move at twice the velocity of A, or four times the velocity of the arm. However, the velocity of P is three times the angular

47、velocity of the ring gear as well, so that 3ωr = 4ωa. If the arm is the input, the velocity ratio is then 3:4, while if the ring is the input, the velocity ratio is 4:3. A three-speed bicycle hub may contain two of these epicyclical trains, with the ring gears connected (actually, common to the tw

48、o trains). The input from the rear sprocket is to the arm of one train, while the output to the hub is from the arm of the second train. It is possible to lock one or both of the sun gears to the axle, or else to lock the sun gear to the arm and free of the axle, so that the train gives a 1:1 ratio.

49、 The three gears are: high, 3:4, output train locked; middle, 1:1, both trains locked, and low, 4:3 input train locked. Of course, this is just one possibility, and many different variable hubs have been manufactured. The planetary variable hub was introduced by Sturmey-Archer in 1903. The popular A

50、W hub had the ratios mentioned here. Chain hoists may use epicyclical trains. The ring gear is stationary, part of the main housing. The input is to the sun gear, the output from the planet carrier. The sun and planet gears have very different diameters, to obtain a large reduction ratio. The Mo

51、del T Ford (1908-1927) used a reverted epicyclic transmission in which brake bands applied to the shafts carrying sun gears selected the gear ratio. The low gear ratio was 11:4 forward, while the reverse gear ratio was -4:1. The high gear was 1:1. Reverted means that the gears on the planet carrier

52、shaft drove other gears on shafts concentric with the main shaft, where the brake bands were applied. The floor controls were three pedals: low-neutral-high, reverse, transmission brake. The hand brake applied stopped the left-hand pedal at neutral. The spark advance and throttle were on the steerin

53、g column. The automotive differential, illustrated at the right, is a bevel-gear epicyclic train. The pinion drives the ring gear (crown wheel) which rotates freely, carrying the idler gears. Only one idler is necessary, but more than one gives better symmetry. The ring gear corresponds to the pla

54、net carrier, and the idler gears to the planet gears, of the usual epicyclic chain. The idler gears drive the side gears on the half-axles, which correspond to the sun and ring gears, and are the output gears. When the two half-axles revolve at the same speed, the idlers do not revolve. When the hal

55、f-axles move at different speeds, the idlers revolve. The differential applies equal torque to the side gears (they are driven at equal distances by the idlers) while allowing them to rotate at different speeds. If one wheel slips, it rotates at double speed while the other wheel does not rotate. Th

56、e same (small) torque is, nevertheless, applied to both wheels. The tabular method is easily used to analyze the angular velocities. Rotating the chain as a whole gives 1, 0, 1, 1 for ring, idler, left and right side gears. Holding the ring fixed gives 0, 1, 1, -1. If the right side gear is held f

57、ixed and the ring makes one rotation, we simply add to get 1, 1, 2, 0, which says that the left side gear makes two revolutions. The velocity method can also be used, of course. Considering the (equal) forces exerted on the side gears by the idler gears shows that the torques will be equal. Refe

58、rences Tamiya Planetary Gearbox Set, Item 72001-1400. Edmund Scientific, Catalog No. C029D, item D30524-08 ($19.95). C. Carmichael, ed., Kents Mechanical Engineers Handbook, 12th ed. (New York: John Wiley and Sons, 1950). Design and Production Volume, p.14-49 to 14-43. V. L. Doughtie, Elemen

59、ts of Mechanism, 6th ed. (New York: John Wiley and Sons, 1947). pp. 299-311. Epicyclic gear. Wikipedia article on epicyclic trains. Sun and planet gear. Includes an animation. 英文譯文 行星齒輪機(jī)構(gòu) 介紹 Tamiya行星輪變速箱由一個約 10500 r/min, 3. 0V

60、， 1. 0A 的直流電機(jī)運行。 最大傳動比 1: 400，輸出速度為 26r/min。 四級行星輪變速箱由兩個 1: 4 和兩個 1: 5 的傳動級組成， 并可以任意選擇組合。 對于小的機(jī)械應(yīng)用程序這不僅是一個良好的驅(qū)動器， 而且還提供了一個出色檢驗的行星齒輪系。 這種齒輪變速箱是一種設(shè)計非常精心的塑料套件， 可在約一個小時用很少的工具裝配完成。 參考文獻(xiàn)中給出了裝備資料。 下面讓我們來開始檢驗齒輪傳動裝置的基本原理和分析行星輪系的技巧。 行星輪系 一對直齒圓柱齒輪的由節(jié)圓表示在圖表中， 它們相切與節(jié)點 P 點， 嚙合齒輪的輪齒齒頂超出了節(jié)圓半徑， 在節(jié)圓與齒齒頂之間有一齒頂間隙，

61、。 若節(jié)圓半徑分別為 a 和 b， 齒輪軸之間的距離就是 a + b。 為了確保齒輪傳動中， 一個節(jié)圓在另一個節(jié)圓上沒有滑動， 必須得有適當(dāng)?shù)男螤畲_保從動輪與主動輪的運動一致。 這就意味著接觸線以正常接觸齒廓的形式通過節(jié)點。 這時， 動力傳遞脫離高速震動達(dá)到可能。 在這里我們不會進(jìn)一步談?wù)擙X輪輪齒， 以及上述有提到的傳動裝置的基本原理。 如果一個齒輪節(jié)圓半徑上有 N 個齒， 這時在兩個連續(xù)的齒間的距離， 我們稱的齒間距將會是 2π a/N。 如果兩個齒輪相嚙合， 他們之間的齒距必須是相同的。 他們之間的節(jié)距通常以 2a/N 來表示，我們稱為模數(shù)。 如果你計算一個齒輪的齒數(shù)， 這時節(jié)圓直徑的

62、大小是模數(shù)的倍數(shù)， 而倍數(shù)則是齒數(shù)。如果你知道兩個齒輪的節(jié)圓直徑， 那么你就能夠得出兩齒輪軸之間的距離。 一對齒輪的傳動比 r 驅(qū)動輪與從動輪之間的角速度之比。 因為分度圓之間旋轉(zhuǎn)方向的限制條件， r =-a / b =-N 1 /N 2,， 因此它們之間的節(jié)圓半徑比與齒數(shù)成正比。 齒輪角速度 n 可以用轉(zhuǎn)/秒，轉(zhuǎn)/分， 或者任何類似的單位表示。 如果以一齒輪的旋轉(zhuǎn)方向為正， 此時另外一個的方向則為負(fù)。 這就是上面的表達(dá)式中的 (-) 標(biāo)志的由于原因。 如果其中一個是內(nèi)齒（齒在齒圈內(nèi)部） ， 這時傳動比為正， 因此它們的傳動方向一致。 常用漸開線齒輪的牙形能夠允許軸線之間一定的變位 ，

63、 所以即使它們之間的距離不是很精確也能夠順利的運行。 齒輪的傳動比并不依賴于該軸的精確的間距， 而是輪齒或者節(jié)圓諸如此類之間的 安裝。 稍微增加高于其理論值的距離， 能夠使運行更容易。 因為其游隙較大的齒輪， 在另一方面 齒隙 也增加， 它可能不是我們在某些應(yīng)用上所希望的。 一個行星輪系包含了固定在齒輪軸上的轉(zhuǎn)臂和行星架以及齒輪和旋轉(zhuǎn)的齒輪軸。 一個移動的 手臂 或 承運人 的有關(guān)該的軸以及齒輪自己可以旋轉(zhuǎn)的齒輪軸。 轉(zhuǎn)臂可以是一個輸入或輸出構(gòu)件而且可被固定固定或可旋轉(zhuǎn)。 最外面的齒輪為內(nèi)齒輪。 一個簡單常見的行星輪是如左圖所示的太陽-行星輪系。 這是三個行星齒輪輪系用于機(jī)械領(lǐng)域的原因 ；

64、 他們可能被認(rèn)為是在描述該傳動裝置的操作之一。 太陽輪、 轉(zhuǎn)臂或內(nèi)齒輪可能成為輸入或輸出的鏈接。 如果轉(zhuǎn)臂被固定， 就不能旋轉(zhuǎn)， 一個簡單的三行星輪輪系嗎有 n 2 /n 1 =-N 1 /N 2， n 3 /n 2 = + N 2 /N 3， 和 n 3 /n 1 =-N 1 /N 3。 這是非常簡單， 不應(yīng)令人困惑。 如果轉(zhuǎn)臂允許移動， 算出速度比彰顯出了人類的智慧。 嘗試這將顯示該陳述的真實性 ； 如果你能做到， 你應(yīng)得到贊揚和聲譽(yù)。 這并不意味這將不可能， 只是比較復(fù)雜罷了。 不過， 有一個非常簡單的方法獲得所需的結(jié)果。 首先， 把這輪系假定認(rèn)為是鎖定的， 因此把轉(zhuǎn)臂和所有的作為剛

65、體、 。 所有的三個齒輪和手臂然后有一個統(tǒng)一的速度比。 行星齒輪任何運動的特點是可以被第一個固定支撐轉(zhuǎn)臂和相對于另外一個旋轉(zhuǎn)的齒輪實現(xiàn)， 然后鎖定輪系并關(guān)于固定的軸旋轉(zhuǎn)。 凈運動總和或兩個不同的獨立的分離運動來滿足這問題的條件 （通常一個構(gòu)件被固定） 。 若要進(jìn)行此程序， 構(gòu)造的齒輪和轉(zhuǎn)臂臂的角速度列出兩例的每個表。 鎖定的輪系給定的 N1, N2, N3 為齒輪 1、 齒輪 2 和齒輪 3。 固定轉(zhuǎn)臂為 0， 1， -N 1 /N 2， -N 1 /N 3。 假定我們想知道齒輪 1 與轉(zhuǎn)臂之間的傳動比, 當(dāng)齒輪 3 固定時， 輪 1 時齒輪 3 固定的。 第一行乘以常量中， 以便在添加第二

66、行時， 齒輪 3 的速度將為零。 此常量為 N 1 /N 3。 現(xiàn)在， 做一個位移， 然后另對應(yīng)于添加這兩行。 我們發(fā)現(xiàn) N 1 /N 3， 1 + N 1 /N 3， N 1 /N 3-N 1 /N 2。 第一個數(shù)字是揮臂速度， 第二個數(shù)字是齒輪 1 的速度， 因此， 它們之間的速度比是 N 1 /(N1 + N3) ，再用這個結(jié)果乘以 N 3。 這就是我們需要的田宮變速器的速度比， 在變速器里面， 環(huán)齒輪不會旋轉(zhuǎn)，太陽齒輪是輸入端， 揮臂速度則是輸出值。 這是個通用過程， 但可以為任何行星齒輪系服務(wù)。 田行星齒輪組件之一有 N 1 = N 2 = 16， N 3 = 48， 而另有 N 1 = 12， N 2 = 18， N 3 = 48。 因為行星齒輪必須剛好位于太陽和環(huán)齒輪之間， N 3 = 2N 1 + N2 這個條件必須得到滿足。 事實上， 這個條件得滿足給定齒輪的數(shù)目。 第一個組件的速度比將是 16 /(48 + 16) = 1/4。 第二個組件的速度比將是 12 /(48 + 12) = 1/5。 這兩個比率如同廣告中介紹的那樣。 請注意， 太