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1、2012級 機械設計制造及其自動化 312012080301721 尹明摘自:制造工程與技術(機加工)(英文版) Manufacturing Engineering and Technology-Machining 機械工業(yè)出版社,2004年3月第一版 P560564頁 美 s. 卡爾帕基安(Serope kalpakjian) s.r 施密德(Steven R.Schmid)中文譯文齒輪的加工方法加工齒輪輪齒有兩種基本的方法:產(chǎn)生過程和形成過程。當一個輪齒產(chǎn)生時,工件和切削或磨削工具,是不斷嚙合在一起的,輪齒的形式是由刀具決定的。換句話說,工件和刀具是共軛的。滾齒機,成型切割機,剃齒機,磨床
2、都使用這個原理。當一個輪齒形成時,該刀具是呈正被加工出來的空間的形狀的。一些磨床使用此原理,與一個指示裝置配套在一起使輪齒一個挨一個形成。刀就是同時加工所有輪齒形成刀具的例子。成型 成型本質(zhì)上是與平面圖類似的,但采用了圓形的切削刀具替代了齒條,由此產(chǎn)生的往復慣性的減少,允許更高的行程速度:現(xiàn)代的成型切割汽車齒輪可以以每分鐘2000切割行程運行。切削刀具的形狀大致是與漸開線齒輪相同的,但輪齒的頂端是圓形的。切削刀具和工件之間的發(fā)電驅(qū)動器之間不涉及機架或連接螺釘 ,因為只有圓周運動在涉及的范圍內(nèi)。切割機每走一個行程,工具和工件通常在切線方向移動0.5毫米。在返回的行程中,刀具必須被縮進約1毫米留有
3、間隙,否則就會產(chǎn)生摩擦,馬上發(fā)生故障。這類型機床的速度被限制,保證大約50千克重的切割機和軸承可移動1毫米的距離。加速度所涉及的扭矩可增加5000N的力,但必須保持高的精度。成型機的優(yōu)點是生產(chǎn)效率相對較高,可能在齒頂上切出直角。不幸的是,對于斜齒輪,螺旋導向器需要在直線運動中施加旋轉(zhuǎn)運動,這種螺旋導向器不容易生產(chǎn),也不便宜。所以該方法只適合在斜齒輪上的長距離,因為對每個不同的螺旋角就要生產(chǎn)特殊的刀具和導向器。成型機的一個很大的優(yōu)點,是它可以生產(chǎn)環(huán)形齒輪,例如那些需要大型epicyclie周轉(zhuǎn)圓的驅(qū)動器。非常高的精確度是十分重要的,而成型切割機的不準確性也是相當要緊的。因為它們可能轉(zhuǎn)移到削減齒輪
4、。很明顯側(cè)面的錯誤將轉(zhuǎn)移,但比起離心機或破碎機給予的特點, “掉落的輪齒” ,是相當不明顯的。對于掉齒有幾個原因,但它發(fā)生最頻繁的是,當工件的直徑大約是刀具直徑的一半,1.5倍或2.5倍時。如果刀具開始在高點,在最后完成漸開線齒輪期間結(jié)束在低點,在刀具上峰與峰的偏心誤差發(fā)生在最后的漸開線切割齒輪的第一個和最后一個齒輪之間。當?shù)毒叩睦鄯e螺距誤差可能剛好超過25微米時,切割輪齒時就會有一個突然的這個數(shù)量的螺距誤差。在機床上切割的下一個齒輪可能在鄰近的節(jié)圓上是好的,如果在切割機上最后的切割碰巧發(fā)生在一個有利的位置。各種嘗試已經(jīng)作出,防止這種效應,特別是通過連續(xù)旋轉(zhuǎn),沒有任何進一步的刀料,但如果成型機
5、是不是很堅固,刀具不是很尖銳,然后沒有進一步的切割發(fā)生,誤差將不會被消除。滾齒滾齒是最常用的金屬切削方法,使用機架產(chǎn)生的原理,但避免了由在旋轉(zhuǎn)切削機上增加許多齒條引起的緩慢的往復運動。齒條在軸線方向上替換為切口蝸桿。 齒條不能為整個輪齒的工作長度產(chǎn)生正確的漸開線形狀,因為他們在圓弧軌跡上移動,所以滾刀緩慢地沿輪齒走刀,在軸向或法向或傾斜的滾齒機螺旋線方向上。金屬去除率高,因為螺旋銑刀或工件沒有做往復運動的需要,所以40m/min的切割速度可用于傳統(tǒng)的滾刀,切割速度高達150m/min的用于硬質(zhì)合金滾刀。通常一個直徑為100毫米的滾刀轉(zhuǎn)速達到100rpm ,所以20個齒的工件以每分鐘5轉(zhuǎn)的速度旋
6、轉(zhuǎn)。工件的每個旋轉(zhuǎn)運動將對應于0.75毫米的進給量,所以滾刀會提前通過工件約每分鐘4毫米。對于汽車生產(chǎn),近似多頭開始的滾刀,可用于每轉(zhuǎn)3毫米的粗糙進給量,以便在切割機上達到100rpm的速度,一個兩頭開始的滾刀和20個齒的齒輪可提供每分鐘30毫米的進給速率。粗糙進給速率的缺點是在工件上會留下明顯的標志,尤其是在齒根,每轉(zhuǎn)在進給速率的空間顯示一種圖案。齒側(cè)標記的表面波紋比齒跟要少,當有一個隨后的整理操作時,如剃齒或磨削,這一點就不重要了。當沒有進一步的操作時,每轉(zhuǎn)的進給量必須加以限制,保證粗糙度在一個界限以下,通常這決定于潤滑條件。齒根上波紋的高度指定乘以每轉(zhuǎn)的進給量,然后除以滾刀直徑的4倍。1
7、毫米的進給量和100毫米的直徑可產(chǎn)生2.5微米高的波紋。對齒側(cè)波紋大約跟cos70一樣大,即約0.85微米。滾齒機的精度對齒距和螺旋線來說,通常很高,假設機床維持不變,漸開線單單決定于滾刀齒廓的精度。漸開線的形式隨著滾刀的切入產(chǎn)生,在滾刀上留有裂痕時,漸開線是不真實的。但是,如果說有14條切線產(chǎn)生在曲率半徑約20毫米的齒側(cè),從真實的漸開線分離,僅僅大約0.5微米。滾刀的制造和安裝誤差可以超過10微米。使用兩頭開始的滾刀或斜滾齒機可增加誤差水平,因為滾刀的齒距誤差的轉(zhuǎn)移到切割齒輪上。拉削 拉削不被用于斜齒輪,但對內(nèi)齒直齒輪時十分有用的。聯(lián)系全局來看,拉削的最重要的用途是用任何其他的方
8、法都不容易加工的內(nèi)花鍵。跟所有的拉削方法一樣,這種方法對批量生產(chǎn)是經(jīng)濟的,因為安裝成本較高。 拉削技術對內(nèi)齒斜齒輪主要的應用是由Gleasons在其G-TRAC機床上。這臺機器的運作,增加滾齒切割機的有效半徑至無限遠,使刀具的每一個齒都能在一條直線上轉(zhuǎn)動,而不是對在一個半徑上。這使得切割行為延長超過齒輪的整個端面寬度,替代了傳統(tǒng)的滾刀每轉(zhuǎn)0.75毫米的進給量。由此產(chǎn)生的過程中提供了非常高的生產(chǎn)率,更適合于美國,美國的產(chǎn)量在整個歐洲來說,相對較低,盡管初始成本高,但非常具有競爭力。拉削提供了較高的精確度和良好的表面光潔度,但象所有切削過程一樣,僅限于 “軟”材料,必須隨后進行表面淬火或熱處理,使
9、其變形。剃齒剃齒切割機看起來像一個在齒根有著額外間隙的齒輪,齒側(cè)有槽,提供切削邊緣。它是運行在網(wǎng)格與粗糙齒輪軸交叉處,以便與做剩余運動的輪齒的相對速度有理論聯(lián)系點。該剃齒刀的輪齒相對靈活的彎曲,所以當它們在兩個齒輪的輪齒間兩兩接觸時,只有有效地運作。齒輪和刀具橫向在工作面以高轉(zhuǎn)速運轉(zhuǎn)時,大約100毫米的材料被去除。周期時間可以少于半分鐘,機床并不昂貴,但刀具是精密的,很難制造。在剃齒機邊緣容易對齒廓作出調(diào)整,然后凸緣能被利用。剃齒可以使用刀具在凸肩處完成,向下到某一深度,無軸向運動。這種方法速度快,但需要更復雜的刀具設計。磨削磨削是非常重要的,因為它是硬化正在加工的齒輪的主要途徑。當要求高精度
10、時,熱處理不足以使其變形,那么,磨削是很必要的。磨削的最簡單的方法往往被稱為orcutt方法。車輪的輪廓使用單點鉆石精確的裝飾使其變形,被模板切割控制到所需要的真實形狀。一個縮放儀6:1的比例是常用的。車輪的輪廓然后沿齒輪作軸向往復運動,齒輪旋轉(zhuǎn)允許受螺旋角的影響。當一個齒形已經(jīng)完成,通常包括100微米的金屬去除,齒輪被指引到下一個齒的空間。這種方法可清楚查看,但一貫有著高的精度要求。安裝尺寸過長,因為如果模數(shù),齒數(shù),螺旋角或齒廓校正線改變時,需要不同的裝飾模板。最快的磨削方法跟滾齒機使用相同的原理,但取代了憑借磨削輪增加切口和減輕的蝸桿,磨削輪是機架上的一節(jié)。由于高的表面速度的需求,砂輪的直
11、徑被增大,使直徑為0.5米的砂輪可以超過2000 rpm的速度運轉(zhuǎn),給予必要的1000米/分鐘的速度。只有單頭蝸桿可在砂輪上切削,但齒輪轉(zhuǎn)速很高,通常情況下 為100rpm。因此很難設計驅(qū)動系統(tǒng)提供精度和剛度。該過程的精度是在合理的高水平,雖然在磨削期間有砂輪和工件的轉(zhuǎn)向變化的一種傾向。所以砂輪的形式可能需要補償機床撓度的影響。磨削輪上一代蝸桿的形狀是一個緩慢的進程,因為裝飾的鉆石或滾子,不僅要形成機架上的輪廓,而且當砂輪旋轉(zhuǎn)時必須做軸向運動。一旦砂輪已經(jīng)形成,齒輪必須被快速的磨削,直到要求再做調(diào)整。這就是用小齒輪創(chuàng)造高生產(chǎn)率的最流行的方法,通常被稱為reishauer方法。大型齒輪通常由Ma
12、ag方法產(chǎn)生,與其方法中的規(guī)劃相似,但使用大直徑的磨削輪,形成側(cè)面的理論嚙合齒條。非常大的直徑的齒輪不能被輕易移動,所以齒輪基本上是平穩(wěn)的,而磨削輪的活動部分在螺旋線方向上作往復運動。磨削輪只在斜齒輪的端面上有一小部分是接觸的,所以,當在一年內(nèi)制造這個齒數(shù)的幾個齒輪時,這并不重要。與形成磨削相同,磨削后,一對側(cè)面的齒輪被指引到下一對。類似的方法用于中等大小的齒輪,這種齒輪有固定的輪子,而粗糙的齒輪是走過了車輪下。齒輪相應的旋轉(zhuǎn)運動由輪上的皮帶控制,這條皮帶從一圓柱體的節(jié)圓直徑上散開,使齒輪相對齒條的運動是正確的。 另一種方法,尼羅河的做法,采用了車輪,它被形成提供了理論上的嚙合機架,而不是象M
13、aag方法一樣用兩個杯輪子。這種做法最適合在小齒輪上中等精度的工作,速度介于reishauer方法和Maag方法之間。所有磨削加工與切削加工相比,是緩慢和昂貴的,因此只用于精度要求至關重要的條件下。一個粗略的經(jīng)驗法則是,磨削會增加齒輪的切削成本,這是10個因素之一,但輪齒的成本,往往只占變速箱總費用的一小部分。令人驚訝地是,可獲得的精度不是非常取決于齒輪的大小,齒輪的直徑是5米或50米,可獲得的節(jié)圓漸開線和螺旋線的精度是預想的5微米或更好,比起任何其他因素,更取決于操作工和檢查員的技術和耐心。它往往是假定磨削將去除在粗的階段產(chǎn)生的所有誤差。不幸的是,磨床是較靈活的,所以砂輪有一個按照以往誤差的
14、趨勢。誤差將因此減少,但并沒有完全消除,除非很多切削方法被使用。任何時候磨削過程給出的都一致的結(jié)果,這是可在粗切的階段檢測精度是可取的。唯一的例外是磨削的形成過程,將不跟隨漸開線誤差,但仍允許螺旋線和節(jié)圓誤差。英文原文Gear manufacturing methodsThere are two basic methods of manufacturing gear teeth: the generating process and the forming process. when a gear tooth is generated, the workpiece and the cuttin
15、g or grinding tool are in continuous mesh and the tooth form is generated by the tool. In other words, the work and the tool are conjugated to each other. hobbing :machines, shaper cutters, shaving machines, and grinders use this principle.When a gear tooth is formed, the tool is in the shape of the
16、 space that is being machined out. Some grinding machines use this principle with an indexing mechianism which allows the gear teeth to be formed tooth by tooth. Broaches are examples of form tools that machine all the gear teeth simultaneously.shaping Shaping is inherently similar to planning but u
17、ses a circular cuttrer instead of rack and the resulting reduction in the reciprocating inertia allows much higher stroking speeds: modern shapers cutting car gears can run at 2,000 cutting strokes per minmute. The shape of the cutter is roughly the same as an involute gear but the tips of the teeth
18、 are rounded. The generating drive between cutter and workpiece does not involve a rack or leadscrew since only circular motion in involved. The tool and workpiece move tangential typically 0.5 mm for each stroke of the cutter. On the return stroke the cutter must be retracted about 1 mm to give cle
19、arance otherwise tool rub occurs on the backstroke and failure is rapid. The speed on this type of machine is limited by the rate at which some 50kg of cutter and bearings can be moved a distance of 1 mm. the accelerations involved tequire forces of the order of 5000N yet high accuracy must be maint
20、ained. The advantages of shaping are that production rates are relatively high and that it is possible to cut right up to a shoulder. Unfortunately, for helical gears, a helical guide is required to impose a rotational motion on the stroking motion; such helical guides cannot be produced easily or c
21、heaply so the method is only suitable for long runs with helical gears since special cutters and guides must be manufactured for each different helix angle. A great advantage of shaping is its ability to annular gears such as those required for large epicyclie drives. When very high accuracy is of i
22、mportance the inaccuracies in the shaping cutter matter since they may transfer to the cut gear. It is obvious that profile errors will transfer but it is less obvious than an eccentrically mounted or ground cutter will give a characteristic “dropped tooth”. There are several causes for “dropped too
23、th” but it occurs most commonly when the diameter of the workpiece is about half, one and half, two and a half, etc, times the cutter diameter. If the cutter starts on a high point and finishes on a low point during the final finishing revolution of the gear the peak to peak eccentricity errors in t
24、he cutter occurs between the last and the first tooth of the final revolution of the cut gear; as the cumulative pitch error of the cutter may well be over 25 microns there is a sudden pitch error of this amount on the cut gear. The next gear cut on the machine may however be very good on adjacent p
25、itch if the final cut happened to start in a favorable position on the cutter. Various attempts have been made to prevent this effect, in particular by continuing rotation without any further cutter infeed but if the shaping machine is not very rigid and the cutter very sharp then no further cutting
26、 will occur and the error will not be removed. hobbingHobbing, the most used metal cutting method, uses the rack generating principle but avoids slow reciprocation by mounting many “racks ” on a rotating cutter. The “racks” are displaced axially to form a gashed worm. The “racks” do not generate the
27、 correct involute shape for the whole length of the teeth since they are moving on a circular path and so the hob is fed slowly along the teeth either axially in normal or in the direction of the helix in “oblique” hobbing.Metal removal rates are high since no reciprocation of hob or workpiece is re
28、quired and so cutting speeds of 40 m/min can be used for conventional hobs and up to 150m/min for carbide hobs. Typically with a 100mm diameter hob the rotation speed will be 100rpm and so a twenty tooth workpiece will rotate at 5 rpm. Each revolution of the workpiece will correspond to 0.75mm feed
29、so the hob will advance through the workpiece at about 4mm per minute. For car production roughing multiple start hobs can be used with coarse feeds of 3mm per revolution so that 100 rpm on the cutter, a two-start hob and a 20 tooth gear will give a feed rate of 30mm/minute.The disadvantage of a coa
30、rse feed rate is that a clear marking is left on the workpiece, particularly in the root, showing a pattern at a spacing of the feed rate per revolution. This surface undulation is less marked on the flanks than in the root and is not important when there is a subsequent finishing operation such as
31、shaving or grinding. When there are no further operations the feed per revolution must be restricted to keep the undulations below a limit which is usually dictated by lubrication conditions. The height of the undulations in the root of the gear is given by squaring the feed per revolution and divid
32、ing by four times the diameter of the hob; 1 mm feed and 100mm diameter gives 2.5 micron high undulations in the root. On the gear flank the undulation is roughly cos70 as large, i.e., about 0.85 micron.Accuracy of hobbing is normally high for pitch and for helix, provided machines are maintained; i
33、nvolute is dependent solely on the accuracy of the hob profile. As the involute form is generated by as many cuts as there are gashes on the hob the involute is not exact, but if there are, say, 14 tangents generating a flank of 20 mm radius curvature about 4 mm high the divergence from a true invol
34、ute is only about half a micron; hob manufacturing and mounting errors can be above 10 microns. Use of twostart hobs or oblique hobbing gives increased error levels since hob errors of pitching transfer to the cut gear.broaching Broaching is not used for helical gears but is useful for internal spur
35、 gears; the principal use of broaching in this context is for internal splines which cannot easily be made by any other method. As with all broaching the method is only economic for large quantities since setup costs are high. The major application of broaching techniques to helical external gears i
36、s that used by Gleasons in their G-TRAC machine .this machine operates by increasing the effective radius of a hobbing cutter to infinity so that each tooth of the cutter is traveling in a straight line instead of on a radius. This allows the cutting action to extend over the whole facewidth of a ge
37、ar instead of the typical 0.75 mm feed per revolution of hobbing. The resulting process gives a very high production rate , more suitable for U.S.A. production volumes than for the relatively low European volumes and so, despite a high initial cost ,is very competitive.Broaching give high accuracy a
38、nd good surface finish but like all cutting processes is limited to “soft” materials which must be subsequently casehardened or heat treated, giving distortion. shaving A shaving cutting cutter looks like a gear which has extra clearance at the root and whose tooth flanks have been grooved to give c
39、utting edges. It is run in mesh with the rough gear with crossed axes so that there is in theory point contact with a relative velocity along the teeth giving scraping action. The shaving cutter teeth are relatively flexible in bending and so will only operate effectively when they are in double con
40、tact between two gear teeth. The gear and cutter operate at high rotational speeds with traversing of the workface and about 100 mm micron of material is removed. Cycle times can be less than half a minute and the machines are not expensive but cutters are delicate and difficult to manufacture. It i
41、s easy to make adjustments of profile at the shaving stage and crowning can be applied. Shaving can be carried out near a shoulder by using a cutter which is plunged in to depth without axial movement; this method is fast but requires more complex cutter design.grinding Grinding is extremely importa
42、nt because it is the main way hardened gear are machined. When high accuracy is required it is not sufficient to pre-correct for heat treatment distortion and grinding is then necessary.The simplest approach to grinding, often termed the Orcutt method. The wheel profile is dressed accurately to shap
43、e using single point diamonds which are controlled by templates cut to the exact shape required; 6:1 scaling with a pantograph is often used. The profile wheel is then reciprocated axially along the gear which rotates to allow for helix angle effects; when one tooth shape has been finished, involvin
44、g typically 100 micron metal removal the gear is indexed to the next tooth space. This method is fairly show but gives high accuracy consistently. Setting up is lengthy because different dressing templates are needed if module, number of teeth, helix angle, or profile correction are changed.The fast
45、est grinding method uses the same principle as hobbing but replaces a gashed and relieved worm by a grinding wheel which is a rack in section. Since high surface speeds are needed the wheel diameter is increased so that wheels of 0.5 m diameter can run at over 2000 rpm to give the necessary 1000 m/m
46、in. only single start worms are cut on the wheel but gear rotation speeds are high,100 rpm typically, so it is difficult to design the drive system to give accuracy and rigidity. Accuracy of the process is reasonably high although there is a tendency for wheel and workpiece to deflect variably durin
47、g grinding so the wheel form may require compensation for machine deflection effects. Generation of a worm shape on the grinding wheel is a slow process since a dressing diamond or roller must not only form the rack profile but has to move axially as the wheel rotates. Once the wheel has been trued,
48、 gears can be ground rapidly until redressing is required. This is the most popular method for high production rates with small gear and is usually called the Reishauer method.Large gears are usually generated by the Maag method which is similar to planning in its approach but uses cup grinding whee
49、ls of large diameter to form the flanks of the theoretical mating rack. Gears of very large diameter cannot easily be moved so the gear is essentially stationary while the grinding wheel carriage reciprocates in the direction of the helix. The wheel is only in contact over a small part of the facewi
50、dth in helical gears so this is not important when only a few gears of this size are made in a year. As with form grinding, after grinding a pair of flanks the gear is indexed to the next pair.A similar method used for medium size gears has stationary wheels, while the rough gear is traversed under the
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