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黃河科技學院畢業(yè)設計(文獻翻譯） 第 7 頁
軸、聯(lián)軸器、材料的選擇及傳動方式
June, 1992 by Keith Briere
軸和聯(lián)軸器
實際上, 幾乎所有的機器中都裝有軸。 軸的最常見的形狀是圓形,其截面可以是實心的,也可以是空心的(空心軸可以減輕重量).有時也采用矩形2軸,例如,螺絲起子的頭部, 套筒扳手和控制旋鈕的桿。
為了在傳遞扭矩時不發(fā)生過載，軸應該具有適當?shù)目古ぞ囟?。軸還應該具有足夠的抗扭剛度，以使在同一個軸上的兩個傳動零件之間的相對轉角不會過大。一般說來，在長度等于軸的直徑的202倍時，軸的扭轉角不應該超過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力。通過這些零件傳來的力可能會使軸產生彎曲變形。因此，軸應該有足夠的剛度以防止支撐軸承受力過大。總而言之，在兩個軸承支撐之間，軸在每英尺長度上的彎曲變形不應該超過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量載荷。因為扭矩和彎矩會產生交變應力，在需用應力中也應該有一個考慮疲勞現(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。當直徑大于5英寸時，則要采用鍛造毛坯，然后機械加工到所要求得尺寸。輕載時，廣泛采用塑料軸。由于塑料是電的不良導體，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應的鍵槽的設計中。必須進行認真的計算。例如，軸上的鍵槽會引起應力集中，由于鍵槽的存在會使軸的橫截面積減小，會進一步減弱軸的強度。
如果軸以臨界速度傳動，將會發(fā)生強烈的振動，可能會毀壞整臺機器。知道這些臨界速度的大小是很重要的，因為這樣可以避開它。一般憑經(jīng)驗來說，工作速度與臨界速度之間至少應該相差20％
許多軸需要三個或更多的軸承來支撐，這就意味著它是一個超靜定問題。材料力學教科書介紹了求解這類問題的方法。但是，設計工作應該與特定場合的經(jīng)濟性相符合。例如，需要一根由三個或更多個軸承來支撐的主傳動軸，可以對力矩做出保守的假定，按照靜定軸對其進行設計，其成本可能會更低一些。由于軸的尺寸增加的成本可能會比進行復雜，精細的設計分析工作所多花費的成本要低一些。
軸的設計工作中的另一個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)軸來實現(xiàn)的。
聯(lián)軸器是用來把相鄰的兩個軸端聯(lián)接起來的裝置。在機械機構中，聯(lián)軸器被用來實現(xiàn)相鄰的兩根軸之間的半永久性聯(lián)接。在機器的正常使用期間內，這種聯(lián)接一般不必拆開，在這種意義上，可以說聯(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，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的軸，可以采用分段的方式將其制造出來，然后采用剛性聯(lián)軸器將各段聯(lián)接起來。一種常用的聯(lián)軸器是由兩個配對的法蘭盤組成。這兩個法蘭盤借助靠鍵傳動的軸套聯(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對準的。
在把屬于不同的設備（例如一個電動機和一個變速箱）的軸聯(lián)接起來的時候，要把這些軸精確地對準是比較困難的，此時可以采用彈性聯(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)作用下產生偏斜或在軸線方向自由移動（浮動）而不致于產生相互干擾。彈性聯(lián)軸器也可以用來減輕從一根軸到另一根軸的沖擊載荷和振動的強度。
滾動軸承
對于求軸承和滾子軸承，一個機器設計人員應該考慮下面五個方面：（a）壽命與載荷的關系；（b）剛度，也就是在載荷作用下的變形；（c）摩擦；（d）磨損；（e）噪聲。對于中等載荷和轉速，根據(jù)額定負荷選擇一個標準軸承，通常都可以保證其具有令人滿意的工作性能。當載荷較大時，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，將會變的重要起來。在轉速高的場合需要有專門的冷卻裝置，而著可能會增大摩擦阻力。磨損主要是由于污染物的進入引起的，必須選用密封裝置以防止周圍環(huán)境的不良影響。因為大批量生產這種方式就決定了球軸承和滾子軸承不但質量高而且價格低，因而機器設計人員的任務是選擇而不是設計軸承。滾動接觸軸承通常是采用硬度約為900HV、整體淬火的鋼來制造。但在許多機構上不使用專門的套圈，而將相互作用的表面淬硬到600HV。滾動軸承由于在工作中會產生高的壓力，其主要失效形式是金屬疲勞，這一點并不奇怪，目前正在進行大量的工作以求改進這種軸承的可靠性。軸承設計可以基于能夠被人們所接受的壽命值來進行。在軸承行業(yè)中，通常將軸承的承載能力定義為這樣的值，即所承擔載荷小于這個值時，一批軸承中將會有90%的軸承具有超過一百萬轉的壽命。
盡管球軸承和滾子軸承的基本設計責任在生產廠家，機器設計人員必須對軸承所要完成的任務進行正確的評價，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，因為它們之間的配合不僅應該保證所需的過盈量，而且也應該保證軸承的內部間隙。不正確的過盈量會產生微動腐蝕從而導致嚴重的故障。內圈通常是通過緊靠在軸肩上進行周詳定位的。軸肩處的圓弧半徑主要是未了避免應力集中。在軸承內圈上加工一個圓弧或倒角，用來提供軸肩處圓弧半徑的空間。
在使用壽命不是設計中決定因素的場合，統(tǒng)稱根據(jù)軸承受災何時產生的變形量來確定其最大載荷。因此“靜態(tài)載荷能力”這個概念可以理解為對處于靜止狀態(tài)或進行緩慢轉動的軸承所能夠施加的載荷。這個載荷在軸承隨后進行的旋轉運動時的質量沒有不利影響。按照實踐經(jīng)驗確定，靜載承載能力是這樣一個載荷，當他作用在軸承時，滾動體與滾道在一個接觸點處的總變形量不超過滾動體直徑的0.01%。這相當于直徑為25 mm 的球產生0.0025mm的永久變形。
只有將軸承與周圍的環(huán)境適當?shù)母綦x開，許多軸承才能成功地實現(xiàn)他們的功能。在某些情況下，必須保護環(huán)境，使其不受潤滑劑和軸承表面摩擦生成物的污染。軸承設計的一個重要組成部分實施密封裝置起到應有的作用。此外，對摩擦學研究人員來說，未料任何目的而應用于運動零部件上的密封裝置都是他們感興趣的。因為密封裝置是軸承的一部分，只有根據(jù)適當?shù)妮S承理論才能使基礎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
齒輪是從一個軸相另一個軸傳遞旋轉運動在幾乎所能想象的每一種機器都存在。齒輪便是能夠用來傳遞這種運動的最好方法之一。
齒輪實際上是帶有精確成型齒的輪子。這些齒與另一個齒輪的齒嚙合，因而就提供拉強制運動的驅動。裝有一對齒輪的軸間的傳速比取決于齒輪的齒數(shù)。例如，一個２０齒的齒輪，驅動一個５０齒的齒輪，較小的齒輪轉２.５圈，可使較大的齒輪轉一圈。
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單和最便宜的，它一般用在需要中速驅動的裝置。錐齒輪用在兩個交叉軸之間的傳遞動力。在希望一個零件的旋轉運動轉換為其他零件的線性運動時采用齒條和小齒輪驅動，反之亦然。
直齒圓柱齒輪用于平行軸之間傳遞旋轉運動，他們通常是圓柱形的，且齒是直的并且平行與旋轉軸。
齒輪常用術語定義：
（１） 分度圓是一個假想圓柱的正截面（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寬度稱為齒面寬。
（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)度圓弧測量的齒的厚度。
（９） 齒槽寬是沿著節(jié)圓測量的兩連續(xù)齒間的齒距。
（１０） 齒隙是一個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)圓測量的齒厚與齒槽寬之和。如果Ｄ表示節(jié)圓直徑，Ｔ是一個齒輪的齒數(shù)， 周節(jié)距Ｐc由（３－１）來計算。
ＰＣ＝３.１４Ｄ/Ｔ （３－１）
（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)點是一對嚙合節(jié)圓相切的點，公切線是在節(jié)點處切于節(jié)圓的一條切線。
（１５）嚙合線是接觸點處兩嚙合輪廓的法線。
（１６）接觸嚙合路徑是連接接觸節(jié)點的路徑。
（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，工程材料的選擇已經(jīng)顯得非常重要。此外，選擇過程應該是一個對材料的連續(xù)不斷得重新評價過程。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)常會對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。來自國內和國際的競爭，對產品維修保養(yǎng)方便性要求的提高和顧客的反饋等方面的壓力，都會促使人們對材料進行重新評價。由于材料選擇不當造成的產品責任訴訟，已經(jīng)產生深刻的影響。此外，材料與材料加工之間的相互依賴關系已經(jīng)被人們認識的更清楚。新的加工方法的出現(xiàn)，通常會促使人們對被加工材料進行重新評價。因此，為了能在合理的成本和確保質量的前提下，獲得滿意的結果，設計工程師和制造工程師都必須認真仔細的選擇，確定和使用材料。
制造任何產品的第一部工作都是設計。設計通?？梢苑譃閹讉€明確的階段：（a）概念設計；(b)功能設計；（c）生產設計。在概念設計階段，設計者著重考慮產品應該具有的功能。 通常要設想和考慮幾個方案做進一步的改進。在此階段，關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間都允許的限度內研制出一種新材料。
在功能設計或工程設計階段，要做出一個切實可行的設計。在這個階段需要繪制相當完整的圖紙，選擇并且確定各種零件的材料。通常要制造出樣機或者實物模型，并對其進行試驗，評價產品的功能，可靠性，外觀和維修保養(yǎng)性等。雖然這種試驗可能表明，在產品進入生產階段之前，應該更換某些材料，但是，絕對不能將這一點作為不認真選擇材料的借口。應該結合產品的功能，認真仔細的考慮產品的外觀，成本和可靠性。一個很有成就的公司在制造所有樣機時，所選用的材料應該和其在生產中使用的材料相同，并盡可能使用同樣的技術。這樣做，對公司是很有好處的。功能完備的樣機如果不能根據(jù)預期的銷售量經(jīng)濟地制造出來，或者樣機與正式生產的裝置在質量和可靠性方面有很大不同，則這種樣機就沒有多大的價值。設計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設計階段去做。因為，在生產設計階段材料的更換是由其他人進行的，這些人對產品的所有功能的了解可能不如設計工程師。
在生產設計階段中，與材料有關的主要問題是應該把材料完全確定下來，使他們與現(xiàn)有的設備相適應，能夠利用現(xiàn)有設備經(jīng)濟地進行加工，而且材料的數(shù)量能夠比較容易地保證供應。在制造過程中，不可避免地會出現(xiàn)對使用中的材料做一些更改的情況。經(jīng)驗表明，可以采用某些便宜材料作為替代品。然而，大多數(shù)情況下，在進行生產以后改換材料比在開始生產前改換材料所花費的代價要高。在生產設計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。當然，這些新材料可能降低成本，改進產品性能。但是，必須對新材料進行認真的評價，以確保其所有性能都被人們所了解。應當時刻牢記，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。大部分的產品失效和產品責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期使用性能而引起的。
產品的責任訴訟迫使設計人員和公司在選材料時，采用最好的程序。在材料選擇過程中，五個最常見的問題：（a）不了解或者未能利用關于材料應用方面的最新和最好的信息資料；（b）未能預見和考慮產品可能的合理用途（若有可能，設計人員還應進一步預測和考慮由于產品使用方法不當造成的后果。在近年來的許多產品責任訴訟案件中，由于錯誤的使用產品而受到傷害的原告控告生產廠家， 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，尤其當其長期性能數(shù)據(jù)是如此的時候；（d）質量控制方法不適當和未經(jīng)驗證；（e）由一些完全不稱職得人員選擇材料。
通過對上述五個問題的分析，可以得出這些問題是沒有充分理由存在的結論。對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)生產品責任訴訟，設計人員和工作界按照適當?shù)某绦蜻M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，選擇材料的人們應該對材料的性質，特點和加工方法有一個全面而基本的了解。
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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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