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軸、聯(lián)軸器、材料的選擇及傳動(dòng)方式
June, 1992 by Keith Briere
軸和聯(lián)軸器
實(shí)際上, 幾乎所有的機(jī)器中都裝有軸。 軸的最常見的形狀是圓形,其截面可以是實(shí)心的,也可以是空心的(空心軸可以減輕重量).有時(shí)也采用矩形2軸,例如,螺絲起子的頭部, 套筒扳手和控制旋鈕的桿。
為了在傳遞扭矩時(shí)不發(fā)生過載，軸應(yīng)該具有適當(dāng)?shù)目古ぞ囟?。軸還應(yīng)該具有足夠的抗扭剛度，以使在同一個(gè)軸上的兩個(gè)傳動(dòng)零件之間的相對(duì)轉(zhuǎn)角不會(huì)過大。一般說(shuō)來(lái)，在長(zhǎng)度等于軸的直徑的202倍時(shí)，軸的扭轉(zhuǎn)角不應(yīng)該超過1度。軸安裝在軸承中，通過齒輪，皮帶輪，凸輪和離合器等零件傳遞動(dòng)力。通過這些零件傳來(lái)的力可能會(huì)使軸產(chǎn)生彎曲變形。因此，軸應(yīng)該有足夠的剛度以防止支撐軸承受力過大。總而言之，在兩個(gè)軸承支撐之間，軸在每英尺長(zhǎng)度上的彎曲變形不應(yīng)該超過0.01英寸。
此外，軸還必須能夠承受彎矩和扭矩的組合作用。因此。要考慮扭矩與彎矩的當(dāng)量載荷。因?yàn)榕ぞ睾蛷澗貢?huì)產(chǎn)生交變應(yīng)力，在需用應(yīng)力中也應(yīng)該有一個(gè)考慮疲勞現(xiàn)象的安全系數(shù)。
直徑小于3英寸的軸可以采用含炭量大約為0.4％的冷軋鋼，直徑在3～5英寸之間的軸卡一采用冷軋鋼或鍛造毛坯。當(dāng)直徑大于5英寸時(shí)，則要采用鍛造毛坯，然后機(jī)械加工到所要求得尺寸。輕載時(shí)，廣泛采用塑料軸。由于塑料是電的不良導(dǎo)體，在電器中采用塑料比較安全。
齒輪和皮帶輪等零件通過鍵聯(lián)接在軸上。在鍵及軸上與之相對(duì)應(yīng)的鍵槽的設(shè)計(jì)中。必須進(jìn)行認(rèn)真的計(jì)算。例如，軸上的鍵槽會(huì)引起應(yīng)力集中，由于鍵槽的存在會(huì)使軸的橫截面積減小，會(huì)進(jìn)一步減弱軸的強(qiáng)度。
如果軸以臨界速度傳動(dòng)，將會(huì)發(fā)生強(qiáng)烈的振動(dòng)，可能會(huì)毀壞整臺(tái)機(jī)器。知道這些臨界速度的大小是很重要的，因?yàn)檫@樣可以避開它。一般憑經(jīng)驗(yàn)來(lái)說(shuō)，工作速度與臨界速度之間至少應(yīng)該相差20％
許多軸需要三個(gè)或更多的軸承來(lái)支撐，這就意味著它是一個(gè)超靜定問題。材料力學(xué)教科書介紹了求解這類問題的方法。但是，設(shè)計(jì)工作應(yīng)該與特定場(chǎng)合的經(jīng)濟(jì)性相符合。例如，需要一根由三個(gè)或更多個(gè)軸承來(lái)支撐的主傳動(dòng)軸，可以對(duì)力矩做出保守的假定，按照靜定軸對(duì)其進(jìn)行設(shè)計(jì)，其成本可能會(huì)更低一些。由于軸的尺寸增加的成本可能會(huì)比進(jìn)行復(fù)雜，精細(xì)的設(shè)計(jì)分析工作所多花費(fèi)的成本要低一些。
軸的設(shè)計(jì)工作中的另一個(gè)重要方面是一根軸與另一根軸之間的直接聯(lián)接方法。這是由剛性或者彈性聯(lián)軸來(lái)實(shí)現(xiàn)的。
聯(lián)軸器是用來(lái)把相鄰的兩個(gè)軸端聯(lián)接起來(lái)的裝置。在機(jī)械機(jī)構(gòu)中，聯(lián)軸器被用來(lái)實(shí)現(xiàn)相鄰的兩根軸之間的半永久性聯(lián)接。在機(jī)器的正常使用期間內(nèi)，這種聯(lián)接一般不必拆開，在這種意義上，可以說(shuō)聯(lián)軸器的聯(lián)接是永久性聯(lián)接。但是在緊急情況下 或者在需要更換已磨損的零件時(shí)，可以先把聯(lián)軸器拆開，然后再聯(lián)接上。
聯(lián)軸器有幾種類型，它們的特性隨其用途而定。如果制造工廠中或者船舶的螺旋槳需要一根特別長(zhǎng)的軸，可以采用分段的方式將其制造出來(lái)，然后采用剛性聯(lián)軸器將各段聯(lián)接起來(lái)。一種常用的聯(lián)軸器是由兩個(gè)配對(duì)的法蘭盤組成。這兩個(gè)法蘭盤借助靠鍵傳動(dòng)的軸套聯(lián)接到相鄰兩節(jié)軸的兩端。然后用螺栓穿過法蘭盤聯(lián)接起來(lái)形成剛性接頭。相互聯(lián)接的兩根軸通常是靠法蘭面上的槽口來(lái)對(duì)準(zhǔn)的。
在把屬于不同的設(shè)備（例如一個(gè)電動(dòng)機(jī)和一個(gè)變速箱）的軸聯(lián)接起來(lái)的時(shí)候，要把這些軸精確地對(duì)準(zhǔn)是比較困難的，此時(shí)可以采用彈性聯(lián)軸器聯(lián)接軸的方式可以把由于被聯(lián)接的軸之間的軸線的不重合所造成的有害影響減少到最低程度。彈性聯(lián)軸器也允許被聯(lián)接的軸在它們各自的載荷系統(tǒng)作用下產(chǎn)生偏斜或在軸線方向自由移動(dòng)（浮動(dòng)）而不致于產(chǎn)生相互干擾。彈性聯(lián)軸器也可以用來(lái)減輕從一根軸到另一根軸的沖擊載荷和振動(dòng)的強(qiáng)度。
滾動(dòng)軸承
對(duì)于求軸承和滾子軸承，一個(gè)機(jī)器設(shè)計(jì)人員應(yīng)該考慮下面五個(gè)方面：（a）壽命與載荷的關(guān)系；（b）剛度，也就是在載荷作用下的變形；（c）摩擦；（d）磨損；（e）噪聲。對(duì)于中等載荷和轉(zhuǎn)速，根據(jù)額定負(fù)荷選擇一個(gè)標(biāo)準(zhǔn)軸承，通常都可以保證其具有令人滿意的工作性能。當(dāng)載荷較大時(shí)，軸承零件的變形，盡管它通常小于軸和其他與軸承一起工作的零部件的變形，將會(huì)變的重要起來(lái)。在轉(zhuǎn)速高的場(chǎng)合需要有專門的冷卻裝置，而著可能會(huì)增大摩擦阻力。磨損主要是由于污染物的進(jìn)入引起的，必須選用密封裝置以防止周圍環(huán)境的不良影響。因?yàn)榇笈可a(chǎn)這種方式就決定了球軸承和滾子軸承不但質(zhì)量高而且價(jià)格低，因而機(jī)器設(shè)計(jì)人員的任務(wù)是選擇而不是設(shè)計(jì)軸承。滾動(dòng)接觸軸承通常是采用硬度約為900HV、整體淬火的鋼來(lái)制造。但在許多機(jī)構(gòu)上不使用專門的套圈，而將相互作用的表面淬硬到600HV。滾動(dòng)軸承由于在工作中會(huì)產(chǎn)生高的壓力，其主要失效形式是金屬疲勞，這一點(diǎn)并不奇怪，目前正在進(jìn)行大量的工作以求改進(jìn)這種軸承的可靠性。軸承設(shè)計(jì)可以基于能夠被人們所接受的壽命值來(lái)進(jìn)行。在軸承行業(yè)中，通常將軸承的承載能力定義為這樣的值，即所承擔(dān)載荷小于這個(gè)值時(shí)，一批軸承中將會(huì)有90%的軸承具有超過一百萬(wàn)轉(zhuǎn)的壽命。
盡管球軸承和滾子軸承的基本設(shè)計(jì)責(zé)任在生產(chǎn)廠家，機(jī)器設(shè)計(jì)人員必須對(duì)軸承所要完成的任務(wù)進(jìn)行正確的評(píng)價(jià)，不僅要考慮軸承的選擇，而且還要考慮軸承的正確的安裝條件。軸承套圈與軸或軸承座的配合非常重要，因?yàn)樗鼈冎g的配合不僅應(yīng)該保證所需的過盈量，而且也應(yīng)該保證軸承的內(nèi)部間隙。不正確的過盈量會(huì)產(chǎn)生微動(dòng)腐蝕從而導(dǎo)致嚴(yán)重的故障。內(nèi)圈通常是通過緊靠在軸肩上進(jìn)行周詳定位的。軸肩處的圓弧半徑主要是未了避免應(yīng)力集中。在軸承內(nèi)圈上加工一個(gè)圓弧或倒角，用來(lái)提供軸肩處圓弧半徑的空間。
在使用壽命不是設(shè)計(jì)中決定因素的場(chǎng)合，統(tǒng)稱根據(jù)軸承受災(zāi)何時(shí)產(chǎn)生的變形量來(lái)確定其最大載荷。因此“靜態(tài)載荷能力”這個(gè)概念可以理解為對(duì)處于靜止?fàn)顟B(tài)或進(jìn)行緩慢轉(zhuǎn)動(dòng)的軸承所能夠施加的載荷。這個(gè)載荷在軸承隨后進(jìn)行的旋轉(zhuǎn)運(yùn)動(dòng)時(shí)的質(zhì)量沒有不利影響。按照實(shí)踐經(jīng)驗(yàn)確定，靜載承載能力是這樣一個(gè)載荷，當(dāng)他作用在軸承時(shí)，滾動(dòng)體與滾道在一個(gè)接觸點(diǎn)處的總變形量不超過滾動(dòng)體直徑的0.01%。這相當(dāng)于直徑為25 mm 的球產(chǎn)生0.0025mm的永久變形。
只有將軸承與周圍的環(huán)境適當(dāng)?shù)母綦x開，許多軸承才能成功地實(shí)現(xiàn)他們的功能。在某些情況下，必須保護(hù)環(huán)境，使其不受潤(rùn)滑劑和軸承表面摩擦生成物的污染。軸承設(shè)計(jì)的一個(gè)重要組成部分實(shí)施密封裝置起到應(yīng)有的作用。此外，對(duì)摩擦學(xué)研究人員來(lái)說(shuō)，未料任何目的而應(yīng)用于運(yùn)動(dòng)零部件上的密封裝置都是他們感興趣的。因?yàn)槊芊庋b置是軸承的一部分，只有根據(jù)適當(dāng)?shù)妮S承理論才能使基礎(chǔ)令人滿意的密封系統(tǒng)。雖然他們很重要，與軸承其它方面的研究工作相比，在密封裝置研究方面所作的工作還是比較少的。
齒輪
齒輪是從一個(gè)軸相另一個(gè)軸傳遞旋轉(zhuǎn)運(yùn)動(dòng)在幾乎所能想象的每一種機(jī)器都存在。齒輪便是能夠用來(lái)傳遞這種運(yùn)動(dòng)的最好方法之一。
齒輪實(shí)際上是帶有精確成型齒的輪子。這些齒與另一個(gè)齒輪的齒嚙合，因而就提供拉強(qiáng)制運(yùn)動(dòng)的驅(qū)動(dòng)。裝有一對(duì)齒輪的軸間的傳速比取決于齒輪的齒數(shù)。例如，一個(gè)２０齒的齒輪，驅(qū)動(dòng)一個(gè)５０齒的齒輪，較小的齒輪轉(zhuǎn)２.５圈，可使較大的齒輪轉(zhuǎn)一圈。
為了不同的用途，人們已經(jīng)研制不同類型的齒輪。如果兩個(gè)軸平行可采用直齒圓柱齒輪、斜齒輪或人字齒輪三類齒輪中任意一種。直齒圓柱齒輪是最簡(jiǎn)單和最便宜的，它一般用在需要中速驅(qū)動(dòng)的裝置。錐齒輪用在兩個(gè)交叉軸之間的傳遞動(dòng)力。在希望一個(gè)零件的旋轉(zhuǎn)運(yùn)動(dòng)轉(zhuǎn)換為其他零件的線性運(yùn)動(dòng)時(shí)采用齒條和小齒輪驅(qū)動(dòng)，反之亦然。
直齒圓柱齒輪用于平行軸之間傳遞旋轉(zhuǎn)運(yùn)動(dòng)，他們通常是圓柱形的，且齒是直的并且平行與旋轉(zhuǎn)軸。
齒輪常用術(shù)語(yǔ)定義：
（１） 分度圓是一個(gè)假想圓柱的正截面（節(jié)圓柱），帶齒的齒輪要考慮替換。分度圓的直徑為節(jié)徑。
（２） 齒頂圓是經(jīng)過所有齒端的圓，齒頂高是齒頂圓與分度圓之間的徑向距離。
（３） 齒根高和齒根圓限制拉齒間的間隙，分度圓和齒根圓之間的距離成為齒根高。
（４） 一個(gè)齒輪的齒根高和嚙合齒輪的齒頂高之間的公差是間隙配合。
（５） 一個(gè)齒的頂面、底面分別稱為頂端面、底端面。
（６） 齒面是分度圓柱和齒頂圓柱之間的齒的一部分沿齒向?qū)挾确Q為齒面寬。
（７） 齒的齒根面是節(jié)圓柱和齒根圓柱之間的齒的一部分。
（８） 齒厚是沿著節(jié)度圓弧測(cè)量的齒的厚度。
（９） 齒槽寬是沿著節(jié)圓測(cè)量的兩連續(xù)齒間的齒距。
（１０） 齒隙是一個(gè)齒輪的齒槽寬與配合齒輪齒厚之間的間隙。
（１１） 周節(jié)距ＰＣ是沿著節(jié)圓測(cè)量的齒厚與齒槽寬之和。如果Ｄ表示節(jié)圓直徑，Ｔ是一個(gè)齒輪的齒數(shù)， 周節(jié)距Ｐc由（３－１）來(lái)計(jì)算。
ＰＣ＝３.１４Ｄ/Ｔ ?。ǎ常保?
（１２）分度周節(jié)?。衐是單位分度圓直徑齒輪的齒數(shù)，由式（３－２）計(jì)算。
Ｐd＝Ｔ/Ｄ ?。ǎ常玻?
分度周節(jié)?。衐的倒數(shù)是齒輪模數(shù)m。
由上兩式可知節(jié)圓和直徑節(jié)圓之間的關(guān)系由（３－３）獲得。
ＰＣＰd＝３.１４ ?。ǎ常常?
（１３）小齒輪是嚙合齒輪副小的齒輪。
（１４）節(jié)點(diǎn)是一對(duì)嚙合節(jié)圓相切的點(diǎn)，公切線是在節(jié)點(diǎn)處切于節(jié)圓的一條切線。
（１５）嚙合線是接觸點(diǎn)處兩嚙合輪廓的法線。
（１６）接觸嚙合路徑是連接接觸節(jié)點(diǎn)的路徑。
（１７）壓力角是公切線與嚙合線之間的角度。
材料的選擇
近些年來(lái)，工程材料的選擇已經(jīng)顯得非常重要。此外，選擇過程應(yīng)該是一個(gè)對(duì)材料的連續(xù)不斷得重新評(píng)價(jià)過程。新材料不斷出現(xiàn)，而一些原有的材料的可以被利用的數(shù)量可能會(huì)減少。環(huán)境污染，材料的回收利用，工人的健康及安全等方面經(jīng)常會(huì)對(duì)材料的選擇附加新的限制條件。為了減輕重量或者節(jié)約能源，可能要求使用不同的材料。來(lái)自國(guó)內(nèi)和國(guó)際的競(jìng)爭(zhēng)，對(duì)產(chǎn)品維修保養(yǎng)方便性要求的提高和顧客的反饋等方面的壓力，都會(huì)促使人們對(duì)材料進(jìn)行重新評(píng)價(jià)。由于材料選擇不當(dāng)造成的產(chǎn)品責(zé)任訴訟，已經(jīng)產(chǎn)生深刻的影響。此外，材料與材料加工之間的相互依賴關(guān)系已經(jīng)被人們認(rèn)識(shí)的更清楚。新的加工方法的出現(xiàn)，通常會(huì)促使人們對(duì)被加工材料進(jìn)行重新評(píng)價(jià)。因此，為了能在合理的成本和確保質(zhì)量的前提下，獲得滿意的結(jié)果，設(shè)計(jì)工程師和制造工程師都必須認(rèn)真仔細(xì)的選擇，確定和使用材料。
制造任何產(chǎn)品的第一部工作都是設(shè)計(jì)。設(shè)計(jì)通?？梢苑譃閹讉€(gè)明確的階段：（a）概念設(shè)計(jì)；(b)功能設(shè)計(jì)；（c）生產(chǎn)設(shè)計(jì)。在概念設(shè)計(jì)階段，設(shè)計(jì)者著重考慮產(chǎn)品應(yīng)該具有的功能。 通常要設(shè)想和考慮幾個(gè)方案做進(jìn)一步的改進(jìn)。在此階段，關(guān)于材料選擇唯一需要考慮的問題是：是否有性能符合要求的材料可供選擇；如果沒有的話，是否有較大的把握在和時(shí)間都允許的限度內(nèi)研制出一種新材料。
在功能設(shè)計(jì)或工程設(shè)計(jì)階段，要做出一個(gè)切實(shí)可行的設(shè)計(jì)。在這個(gè)階段需要繪制相當(dāng)完整的圖紙，選擇并且確定各種零件的材料。通常要制造出樣機(jī)或者實(shí)物模型，并對(duì)其進(jìn)行試驗(yàn)，評(píng)價(jià)產(chǎn)品的功能，可靠性，外觀和維修保養(yǎng)性等。雖然這種試驗(yàn)可能表明，在產(chǎn)品進(jìn)入生產(chǎn)階段之前，應(yīng)該更換某些材料，但是，絕對(duì)不能將這一點(diǎn)作為不認(rèn)真選擇材料的借口。應(yīng)該結(jié)合產(chǎn)品的功能，認(rèn)真仔細(xì)的考慮產(chǎn)品的外觀，成本和可靠性。一個(gè)很有成就的公司在制造所有樣機(jī)時(shí)，所選用的材料應(yīng)該和其在生產(chǎn)中使用的材料相同，并盡可能使用同樣的技術(shù)。這樣做，對(duì)公司是很有好處的。功能完備的樣機(jī)如果不能根據(jù)預(yù)期的銷售量經(jīng)濟(jì)地制造出來(lái)，或者樣機(jī)與正式生產(chǎn)的裝置在質(zhì)量和可靠性方面有很大不同，則這種樣機(jī)就沒有多大的價(jià)值。設(shè)計(jì)工程師最好能在這一階段全部完成材料的分析，選擇和確定工作，而不是將其留到生產(chǎn)設(shè)計(jì)階段去做。因?yàn)椋谏a(chǎn)設(shè)計(jì)階段材料的更換是由其他人進(jìn)行的，這些人對(duì)產(chǎn)品的所有功能的了解可能不如設(shè)計(jì)工程師。
在生產(chǎn)設(shè)計(jì)階段中，與材料有關(guān)的主要問題是應(yīng)該把材料完全確定下來(lái)，使他們與現(xiàn)有的設(shè)備相適應(yīng)，能夠利用現(xiàn)有設(shè)備經(jīng)濟(jì)地進(jìn)行加工，而且材料的數(shù)量能夠比較容易地保證供應(yīng)。在制造過程中，不可避免地會(huì)出現(xiàn)對(duì)使用中的材料做一些更改的情況。經(jīng)驗(yàn)表明，可以采用某些便宜材料作為替代品。然而，大多數(shù)情況下，在進(jìn)行生產(chǎn)以后改換材料比在開始生產(chǎn)前改換材料所花費(fèi)的代價(jià)要高。在生產(chǎn)設(shè)計(jì)階段做好材料選擇工作，可以避免大多數(shù)的這種材料更換情況。在生產(chǎn)制造開始后出現(xiàn)了可供使用的新材料是更換材料的最常見的原因。當(dāng)然，這些新材料可能降低成本，改進(jìn)產(chǎn)品性能。但是，必須對(duì)新材料進(jìn)行認(rèn)真的評(píng)價(jià)，以確保其所有性能都被人們所了解。應(yīng)當(dāng)時(shí)刻牢記，新材料的性能和可靠性很少能像現(xiàn)有的材料那樣為人們所了解。大部分的產(chǎn)品失效和產(chǎn)品責(zé)任事故案件是由于在選用新材料作為替代材料之前，沒有真正了解它們的長(zhǎng)期使用性能而引起的。
產(chǎn)品的責(zé)任訴訟迫使設(shè)計(jì)人員和公司在選材料時(shí)，采用最好的程序。在材料選擇過程中，五個(gè)最常見的問題：（a）不了解或者未能利用關(guān)于材料應(yīng)用方面的最新和最好的信息資料；（b）未能預(yù)見和考慮產(chǎn)品可能的合理用途（若有可能，設(shè)計(jì)人員還應(yīng)進(jìn)一步預(yù)測(cè)和考慮由于產(chǎn)品使用方法不當(dāng)造成的后果。在近年來(lái)的許多產(chǎn)品責(zé)任訴訟案件中，由于錯(cuò)誤的使用產(chǎn)品而受到傷害的原告控告生產(chǎn)廠家， 并且贏得判決）；（c）所使用的材料的數(shù)據(jù)不全或者有些數(shù)據(jù)不確定，尤其當(dāng)其長(zhǎng)期性能數(shù)據(jù)是如此的時(shí)候；（d）質(zhì)量控制方法不適當(dāng)和未經(jīng)驗(yàn)證；（e）由一些完全不稱職得人員選擇材料。
通過對(duì)上述五個(gè)問題的分析，可以得出這些問題是沒有充分理由存在的結(jié)論。對(duì)這些問題的分析和研究可以給避免這些問題的出現(xiàn)指明方向。盡管采用最好的材料選擇辦法爺不能避免發(fā)生產(chǎn)品責(zé)任訴訟，設(shè)計(jì)人員和工作界按照適當(dāng)?shù)某绦蜻M(jìn)行材料選擇，可以大大減少訴訟的數(shù)量。
從上面的討論可以看出，選擇材料的人們應(yīng)該對(duì)材料的性質(zhì)，特點(diǎn)和加工方法有一個(gè)全面而基本的了解。
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SHAFTS、COUPLINGS、MATERIAL SELECTION AND
TRANSMISSION METHOD
June, 1992 by Keith Briere
Shafts and couplings
Virtually all machines contain shafts. The most common shape for shafts is circular and the cross section can be either solid or hollow (hollow shafts can result in weight savings). Rectangular shafts are sometimes used ,as in screw driver blades, socket wreches and control knob stems.
A shaft must have adequate torsional strength to transmit torque and not be over stressed . It must also be torsionally stiff enough so that one mounted component does not deviat excessively from its original angular position relative to a second component mounted on the same shaft . Generally speaking , the angle of twist should ont exceed one degree in a shaft length equal to 20 diameters.
Shafts are mounted in bearings and transmit power through such devices as gears , pulleys , cams and clutches .These devices introduce forces which attempt to bend the shaft ; bence , the bending deflection of a shaft should ont exceed 0.01 in per ft of length between bearing supports .
In addition , the shaft must be able to sustain a combination of bending and torsional loads . Thus an equivalent load must be considered which takes into account both torsion and bending . Also , the allowable stress must contain a factor of safety which includes fatigue , since torsional and bending stress reversaks occur .
For diameters less than 3 in. , the usual shaft material is cold-rolled steel containing about 0.4 percent xarbon . Shafts are either cold-rolled or forged in size . Plastic shafts are widely used for light load applications . One advantage of using plastic is safely in electrical applications , since plastic is a poor conductor of electricity .
Components such as gears and pulleys are mounted on shafts by means of key . The design of the key and the corresponding keyway in the shaft must be properly evaluated . For example ,stress concentrations occur in shafts due to keyways , and the material removed to form the keyway further weakens theshaft .
If shafts are run at critical speeds , severe vibrations can occur which can seriously damage a machine . It is important to know the magnitude of these critical speeds so that they can be avoided . As a general rule of thumb , the diference between the oprating speed and the critical speed should be at least 20 percent .
Many shafts are supported by three or more bearings , which means that the problem is statically indeterminate . Texts on strength of materials give methods of solving such problems . The design effort should be in keeping with the economics of a given situation . For example , if one line shaft supported by three or more bearings is needed , it probably would be cheaper to make conservative assumptions as to moments and design it as though it were determinate . The extra cost of an oversize shaft may be less than the extra cost of an elaborate design analysis .
Another important aspect of shaft design is the method of directly connecting one shaft to another . This is accomplished by devices such as rigid and flexible couplings.
A coupling is a device for connecting the ends of adjacent shafts . In machine construction , couplings are used to effect a semipermanent connection between adjacent rotating shafts . The connection is permanent in the sense that it is not meant to be broken during the useful life of the machine , but it can be broken and restored in an emergency or when worn parts are replaced .
There are several types of shaft couplings , their characteristics depend on the purpose for which they are used . If an exceptionally long shaft is required in a manufacturing plant or a propeller shaft on a ship , it is made in sections that are coupled together with rigid couplings . A common type of rigid coupling consists of two mating radial flanges (disk) that are attached by key driven hubs to the ends of adjacent shaft sections and bolted together through the flanges to form a rigid connection .Alignment of the connected shafts is usually effected by means of a rabbet joint on the face of the flanges .
In connecting shafts belonging to separate devices (such as electric motor and a gearbox ) , precise aligning of the shafts is difficult and a flrxible coupling is used . This coupling connects the shafts in such a way as to minimize the harmful effects of shaft misalignment . Flexible couplings also permit the shafts to deflect under their separate systems of loads and to move freely (float) in the axial direction without interfering with one another . Flexible coupling can also serve to reduce the intensity of shock loads and vibrations transmitted from one shaft to another .
Rolling Contact Bearing
The concern of a machine designer with ball and rolling bearings is fivefold as follows:(a) life in relation to load; (b) stiffness, i.e. deflections under load;(c) friction; (d) wear; (e) noise. For moderate loads and speeds the correct selection of a standard bearing on the basis of load rating will usually secure satisfactory performance. the deflection of the bearing elements will become important where load are high, although this is usually of less magnitude than that of the shafts or other components associated with the bearing. Where speeds are high special cooling arrangements become necessary which may increase frictional drag. Wearing is primarily associated with the introduction of contaminants, and sealing arrangements must be chosen with regard to the hostility of the environment.
Because the high quality and low price of the ball and roller bearings depends on quantity production, the task of the machine designer becomes one of selection rather than design. Rolling-contact bearings are generally made with steel which is through-hardened to about 900 HV, although in many mechanisms special races are not provided and the interacting surfaces are hardened to about 600 HV. It is not surprising that , owing to the high stresses involved, a predominant form of failure should be metal fatigue, and a good deal of work is currently in progress intended to improve the reliability of this type of bearing. Design can be based on accepted values of life and it is general practice in the bearing industry to define to define the load capacity of the bearing as that value below which 90 per cent of a batch will exceed a life of one million revolutions.
Notwithstanding the fact that responsibility for the basic design of ball and roller bearings rests with the bearing manufacturer, the machine designer must form a correct appreciation of the duty to be performed by the bearing and be concerned not only with bearing selection but with the conditions for correct installation.
The fit of the bearing races onto the shaft or onto the housings is of critical importance because of their combined effect on the internal clearance of the bearing as well as preserving the desired degree of interference fit. Inadequate interference can induce serious trouble from fretting corrosion. The inner race is frequently located axially by abutting against a shoulder. A radius at this point is essential for the avoidance of stress concentration and ball races are provided with a radius or chamfer to allow space for this.
Where life is not the determining factor in design, it is usual to determine maximum loading by the amount to which a bearing will deflect under load. Thus the concept of” static load-carrying capacity” is understood to mean the load that can be applied to a bearing which is either stationary or subject to slight swiveling motions, without impairing its running qualities for subsequent rotational motion. This has been determined by practical experience as the load which when applied to a bearing result in a total deformation of the rolling element and raceway at any point of contact not exceeding 0.01 per cent of the rolling-element diameter. This would correspond to a permanent deformation of 0.0025 mm for a ball 25 mm in diameter.
The successful functioning of many bearings depends upon providing them with adequate protection against their environment, and in some circumstances the environment must be protected from lubricants or products of deterioration of the bearing surfaces. Achievement of the correct functioning of seals is an essential part of bearing design. Moreover, seals which are applied to moving parts for any purpose are of interest to tribologists because they are components of bearing systems and can only be designed satisfactorily on the basis of the appropriate bearing theory.
Notwithstanding their importance, the amount of research effort that has been devoted to the understanding of the behavior of seals has been small when compared with that devoted to other aspects of bearing technology.
Gears
The transmission of rotary motion from one shaft to another occurs in nearly every machine one can imagine. Gears constitute one of the best of the various means available for transmitting this motion.
A gear is virtually a wheel with very accurately shaped teeth. These teeth mesh with teeth of another gear, thus providing as positive-motion drive. The speed ratio between shafts carrying a pair of gears depends upon the numbers of teeth in the gear. For example, a 20tooth gear drives a gear of 50 teeth, the smaller gear will have to turn 2.5 times to cause the larger one to make 1 turn.
Various types of gearing have been developed for different purposes. If the shafts are parallel, any of these types may be used, spur, bevel, or herring-bone. Spur gears are the simplest and least expensive type. They are generally used on drives requiring moderate speeds. Bevel gears serve to transmit power between tow intersecting shafts. Rack-and-pinion drives are used where it is desirable to transform the rotary motion of one part into linear motion for the other part or vice versa.
Spur gears are used to transmit rotary motion between parallel shafts; they are usually cylindrical, and the teeth are straight and parallel to the axis of rotation.
The following are definitions for some common terms used in study of gears.
(1) The pitch circle is a right section of an imaginary cylinder (pitch cylinder), that the toothed gear may be considered for replacement. The diameter of the circle is called pitch diameter.
(2) The addendum circle is a circle which passes through all the tooth ends, and the addendum is the radial distance between the pitch circle and addendum circle.
(3) The dedendum or root circle bounds the spaces between the teeth, and the distance between the pitch circle and the dedendum circle is termed as dedendumm.
(4) The tolerate between the dedendum of one gear and addendum of the mating gear is the clearance.
(5) The top and bottom surfaces of a tooth are known as top land and bottom land respectively.
(6) The face of the tooth is the part of the tooth between the pitch cylinder and addendum cylinder, and its width along the tooth element is known as face width.
(7) The flank of the tooth is the part of the tooth lying between pitch cylinder and addendum cylinder。
(8) The tooth thickness is the thickness of the tooth measured along the arc of the pitch circle.
(9) The tooth space is the circular distance between two successive teeth measured along the pitch circle.
(10) Back ash is the difference between the tooth space of one gear and tooth thickness of the mating gear.
(11) The circular pitch, Pc is the sum of tooth thickness and tooth space, measured along the pitch circle. If D is the pitch diameter, and T is the number of the teeth of a gear, the circular pitch Pc is given by Eqs (3-1)
Pc=3.14D/T (3-1)
(12) The diametral pitch, Pd is the number of the teeth of a gear per unit pitch diameter.Hence by Eqs
Pd=T/D (3-2)
The inverse of diametric pitch Pd is called module m of the gear.
From Eqs (3-1) and (3-2), the relation between circular and diametric pitches can be obtained as (3-3)
Pc Pd =3.1415926 (3-3)
(13) The pinion is the smaller gear of a mating gear pair.
(14) The pitch point is the point of tangency of the pitch circles ora pair of mating gear wheels, and the common tangent is a tangent to the pitch circles at the pitch point.
(15) The line of action is a line normal to both the mating profiles at the contact point.
(16) The path of contact is the path traced by the contact point.
(17) The pressure angle between the common tangent and line of action.
Material Selection
During recent years the selection of engineering materials has assumed great importance . Moreover , the process should be one of continual reevaluation . New materials often become available and there may be a decreasing availability of others . Concerns regarding environmental pollution , recycling and worker health and safety often impose new constraints .The desire for weight reduction or energy savings may dictate the use of different materials . Pressures from domestic and foreign competition , increased serviceability requirements , and customer feedback may all promote materials reevaluation . The extent of product liability actions , often the result of improper material use , has had a marked impact .In addition , the interdependence between materials and their processing has become better recognized . The development of new processes often forces reevaluation of the materials being processed . Therefore , it is imperative that design and manufacturing engineers exercise considerable care in selecting , specifying ,and utilizing materials if they are to achieve satisfactory results at reasonable cost and still assure quality .
The first step in the manufacture of any product is design , which usually takes place in several distinct stages : (a) conceptual ;(b) functional ;(c) production . During the conceptual-design stage , the designer is concerned primarily with the functions the product is to fulfill .Usually several concepts are visualized and considered ,and a decision is made either that the idea is not practical or that the idea is sound and one or more of the conceptual designs should be developed further . Here ,the only concern for materials is that materials exist that can provide the desired properties . If no such materials are available ,consideration is given as to whether there is a reasonable prospect that new one could be developed within cost and time limitations .
At the functional or engineering-design stage , a practical ,workable design is developed .Fairly complete drawings are made , and materials are selected and specified for the various components . Often a prototype or working model is made that can be tested to permit evaluation of the product as to function ,reliability , appearance , serviceability , and so on . Although it is expected that such testing might show that some changes may have to be made in materials before the product is advanced to the product is advanced to the production-design stage ,this should not be taken as an excuse for not doing a thorough job of material selection . Appearance , cost ,and reliability factors should be considered in detail , together with the functional factors . There is much merit to the practice of one very successful company which requires that all prototypes be built with the same materials that will be used in production and ,insofar as possible , with the same manufacturing techniques . It is of little value to have a perfectly functioning prototype that cannot be manufactured economically in the expected sales volume , or one that is substantially different from what the production units will be in regard to quality and reliability . Also , it is much better for design engineers to do a complete job of material analysis , selection , and specification at the development stage of design rather than to leave it to the production-design stage , where changes may be made by others , possibly less knowledgeable about all of the functional aspects of the product .
At the production-design stage , the primary concern relative to materials should be that they are specified fully , that they are compatible with , and can be processed economically by , existing equipment , and that they are readily available in the needed quantities .
As manufacturing progresses , it is inevitable that situations will arise that may require modifications of the materials being used . Experience may reveal that substitution of cheaper materials can be made . In most cases , however , changes are much more costly to make after manufacturing is in progress than before it starts . Good selection during the production-design phase will eliminate the necessity for this type of change . The more common type of change that occurs after manufacturing starts is the result of the availability of new materials .these , of course , present possibilities for cost reduction and improved peformance . However , new materials must be evaluated very carefully to make sure that all their characteristics are well established . One should always remember that it is indeed rare that as much is known about the properties and reliability of a new material as about those of an existing one . A large proportion of product failure and product liability cases have resulted from new materials being substituted before their long-term properties were really known .
Product liability actions have made it imperative that designers and companies employ the very best procedures in selecting materials . The five most common faults in material selection have been : (a) failure to know and use the latest and best information available about the materials utilized ; (b) failure to foresee , and take into account the reasonable uses for the product (where possible , the designer is further advised to foresee and account for misuse of the product , as there have been many product liability cases in recent years where the claimant , injured during misuse of the product , has sued the manufacturer and won ) ;(c) the use of materials about which there was insufficient or uncertain data , particularly as to its long-term properties ; (d) inadequate , and unverified , quality control procedures ; and (e) material selection made by people who are completely unqualified to do so .
An examination of the faults above will lead one to conclude that there is no good reason why they should exist . Consideration of them provides guidance as to how they can be eliminated . While following the very best methods in material selection nay not eliminate all product-liability claims , the use of proper procedures by designers and industries can greatly reduce their numbers . From the previous discussion , it is apparent that those who select materials should have a broad , basic understanding of the nature and properties of materials and their processing .
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