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故障的分析、尺寸的決定以及凸輪的分析和應(yīng)用 前言介紹： 作為一名設(shè)計(jì)工程師有必要知道零件如何發(fā)生和為什么會(huì)發(fā)生故障，以便通過進(jìn)行最低限度的維修以保證機(jī)器的可靠性。有時(shí)一次零件的故障或者失效可能是很嚴(yán)重的一件事情，比如，當(dāng)一輛汽車正在高速行駛的時(shí)候，突然汽車的輪胎發(fā)生爆炸等。另一方面，一個(gè)零件發(fā)生故障也可能只是一件微不足道的小事，只是給你造成了一點(diǎn)小麻煩。一個(gè)例子是在一個(gè)汽車?yán)鋮s系統(tǒng)里的暖氣裝置軟管的松動(dòng)。后者發(fā)生的這次故障造成的結(jié)果通常只不過是一些暖氣裝置里冷卻劑的損失，是一種很容易被發(fā)現(xiàn)并且被改正的情況。 能夠被零件進(jìn)行吸收的載荷是相當(dāng)重要的。一般說來，與靜載重相比較，有兩個(gè)相反方向的動(dòng)載荷將會(huì)引起更大的問題，因此，疲勞強(qiáng)度必須被考慮。另一個(gè)關(guān)鍵是材料是可延展性的還是脆性的。例如，脆的材料被認(rèn)為在存在疲勞的地方是不能夠被使用的。 很多人錯(cuò)誤的把一個(gè)零件發(fā)生故障或者失效理解成這樣就意味著一個(gè)零件遭到了實(shí)際的物理破損。無論如何，一名設(shè)計(jì)工程師必須從一個(gè)更廣泛的范圍來考慮和理解變形是究竟如何發(fā)生的。一種具有延展性的材料，在破裂之前必將發(fā)生很大程度的變形。發(fā)生了過度的變形，但并沒有產(chǎn)生裂縫，也可能會(huì)引起一臺(tái)機(jī)器出毛病，因?yàn)榘l(fā)生畸變的零件會(huì)干擾下一個(gè)零件的移動(dòng)。因此，每當(dāng)它不能夠再履行它要求達(dá)到的性能的時(shí)候，一個(gè)零件就都算是被毀壞了（即使它的表面沒有被損毀）。有時(shí)故障可能是由于兩個(gè)兩個(gè)相互搭配的零件之間的不正常的磨擦或者異常的振動(dòng)引起的。故障也可能是由一種叫蠕變的現(xiàn)象引起的，這種現(xiàn)象是指金屬在高溫下時(shí)一種材料的塑性流動(dòng)。此外，一個(gè)零件的實(shí)際形狀可能會(huì)引起故障的發(fā)生。例如，應(yīng)力的集中可能就是由于輪廓的突然變化引起的，這一點(diǎn)也需要被考慮到。當(dāng)有用兩個(gè)相反方向的動(dòng)載荷，材料不具有很好的可延展性時(shí)，對(duì)應(yīng)力考慮的評(píng)估就特別重要。 一般說來，設(shè)計(jì)工程師必須考慮故障可能發(fā)生的全部方式，包括如下一些方面： ——壓力 ——變形 ——磨損 ——腐蝕 ——振動(dòng) ——環(huán)境破壞 ——固定設(shè)備松動(dòng) 在選擇零件的大小與形狀的時(shí)候，也必須考慮到一些可能會(huì)產(chǎn)生外部負(fù)載影響的空間因素，例如幾何學(xué)間斷性，為了達(dá)到要求的外形輪廓及使用相關(guān)的連接件，也會(huì)產(chǎn)生相應(yīng)的殘余應(yīng)力。 凸輪是被應(yīng)用的最廣泛的機(jī)械結(jié)構(gòu)之一。凸輪是一種僅僅有兩個(gè)組件構(gòu)成的設(shè)備。主動(dòng)件本身就是凸輪，而輸出件被稱為從動(dòng)件。通過使用凸輪，一個(gè)簡單的輸入動(dòng)作可以被修改成幾乎可以想像得到的任何輸出運(yùn)動(dòng)。常見的一些關(guān)于凸輪應(yīng)用的例子有： ——凸輪軸和汽車發(fā)動(dòng)機(jī)工程的裝配 ——專用機(jī)床 ——自動(dòng)電唱機(jī) ——印刷機(jī) ——自動(dòng)的洗衣機(jī) ——自動(dòng)的洗碗機(jī) 高速凸輪(凸輪超過1000 rpm的速度)的輪廓必須從數(shù)學(xué)意義上來定義。無論如何，大多數(shù)凸輪以低速(少于500 rpm)運(yùn)行而中速的凸輪可以通過一個(gè)大比例的圖形表示出來。一般說來，凸輪的速度和輸出負(fù)載越大，凸輪的輪廓在被床上被加工時(shí)就一定要更加精密。 材料的設(shè)計(jì)屬性 當(dāng)他們與抗拉的試驗(yàn)有關(guān)時(shí)，材料的下列設(shè)計(jì)特性被定義如下。 靜強(qiáng)度： 一個(gè)零件的強(qiáng)度是指零件在不會(huì)失去它被要求的能力的前提下能夠承受的最大應(yīng)力。因此靜強(qiáng)度可以被認(rèn)為是大約等于比例極限，從理論上來說，我們可以認(rèn)為在這種情況下，材料沒有發(fā)生塑性變形和物理破壞。 剛度： 剛度是指材料抵抗變形的一種屬性。這條斜的模數(shù)線以及彈性模數(shù)是一種衡量材料的剛度的一種方法。 彈性： 彈性是指零件能夠吸收能量但并沒有發(fā)生永久變形的一種材料的屬性。吸收的能量的多少可以通過下面彈性區(qū)域內(nèi)的應(yīng)力圖表來描述出來。 韌性： 韌性和彈性是兩種相似的特性。無論如何，韌性是一種可以吸收能量并且不會(huì)發(fā)生破裂的能力。因此可以通過應(yīng)力圖里面的總面積來描述韌性，就像用圖2.8 b 描繪的那樣。顯而易見，脆性材料的韌性和彈性非常低，并且大約相等。 脆性： 一種脆性的材料就是指在任何可以被看出來的塑性變形之前就發(fā)生破裂的材料。脆性的材料一般被認(rèn)為不適合用來做機(jī)床的零部件，因?yàn)楫?dāng)遇到由軸肩，孔，槽，或者鍵槽等幾何應(yīng)力集中源引起的高的應(yīng)力時(shí)，脆性材料是無法來產(chǎn)生局部屈服的現(xiàn)象以適應(yīng)高的應(yīng)力環(huán)境的。 延展性： 一種延展性材料會(huì)在破裂之前表現(xiàn)出很大程度上的塑性變形現(xiàn)象。延展性是通過可延展的零件在發(fā)生破裂前后的面積和長度的百分比來測量的。一個(gè)在發(fā)生破裂的零件，其伸長量如果為5%，則認(rèn)為該伸長量就是可延展性和脆性材料分界線。 可鍛性： 可鍛性從根本上來說是指材料的一種在承受擠壓或壓縮是可以發(fā)生塑性變形的能力，同時(shí)，它也是一種在金屬被滾壓成鋼板時(shí)所需金屬的重要性能。 硬度： 一種材料的硬度是指它抵抗擠壓或者拉伸它的能力。一般說來，材料越硬，它的脆性也越大，因此，彈性越小。同樣，一種材料的極限強(qiáng)度粗略與它的硬度成正比。 機(jī)械加工性能（或切削性）： 機(jī)械加工性能是指材料的一種容易被加工的性能。通常，材料越硬，越難以加工。 壓應(yīng)力和剪應(yīng)力 除抗拉的試驗(yàn)之外，還有其它一些可以提供有用信息的靜載荷的實(shí)驗(yàn)類型。 壓縮測試： 大多數(shù)可延展材料大約有相同特性，當(dāng)它們處于受壓狀態(tài)的緊張狀態(tài)時(shí)。極限強(qiáng)度，無論如何，不能夠被用于評(píng)價(jià)壓力狀態(tài)。當(dāng)一件具有可延展性的樣品受壓發(fā)生塑性變形時(shí)，材料的其它部分會(huì)凸出來，但是在這種緊張的狀態(tài)下，材料通常不會(huì)發(fā)生物理上的破裂。因此，一種可延展的材料通常是由于變形受壓而損壞的，并不是壓力的原因。 剪應(yīng)力測試： 軸，螺釘，鉚釘和焊接件被用這樣一種方式定位以致于生產(chǎn)了剪應(yīng)力。一張抗拉試驗(yàn)的試驗(yàn)圖紙就可以說明問題。當(dāng)壓力大到可以使材料發(fā)生永久變形或發(fā)生破壞時(shí)，這時(shí)的壓力就被定義為極限剪切強(qiáng)度。極限剪切強(qiáng)度，無論如何，不等于處于緊張狀態(tài)的極限強(qiáng)度。例如，以鋼的材料為例，最后的剪切強(qiáng)度是處于緊張狀態(tài)大約極限強(qiáng)度的75%。當(dāng)在機(jī)器零部件里遇到剪應(yīng)力時(shí)，這個(gè)差別就一定要考慮到了。 動(dòng)力載荷 不會(huì)在各種不同的形式的力之間不停發(fā)生變化的作用力被叫作靜載荷或者穩(wěn)定載荷。此外，我們通常也把很少發(fā)生變化的作用力叫作靜載荷。在拉伸實(shí)驗(yàn)中，被分次、逐漸的加載的作用力也被叫作靜載荷。 另一方面，在大小和方向上經(jīng)常發(fā)生變化的力則被稱為動(dòng)載荷。動(dòng)載荷可以被再細(xì)分為以下的3種類型。 變載荷： 所謂變載荷，就是說載荷的大小在變，但是方向不變的載荷。比如說，變載荷會(huì)產(chǎn)生忽大忽小的張應(yīng)力，但不會(huì)產(chǎn)生壓應(yīng)力。 周期性載荷： 像這樣的話，如果大小和方向同時(shí)改變，則就是說這種載荷會(huì)反復(fù)周期性的產(chǎn)生變化的拉應(yīng)力和壓應(yīng)力，這種現(xiàn)象往往就伴隨著應(yīng)力在方向和大小上的周期性變化。 沖擊載荷： 這類載荷是由于沖擊作用產(chǎn)生的。一個(gè)例子就是一臺(tái)升降機(jī)墜落到位于通道底部的一套彈簧裝置上，這套裝置產(chǎn)生的力會(huì)比升降機(jī)本身的重量大上好幾倍。當(dāng)汽車的一個(gè)輪胎碰撞到道路上的一個(gè)突起或者路上的一個(gè)洞時(shí)，相同的沖擊荷載的類型也會(huì)在汽車的減震器彈簧上發(fā)生。 疲勞失效－疲勞極限線圖 正如圖2.10a所示，如果材料的某處經(jīng)常會(huì)產(chǎn)生大量的周期性作用力，那么在材料的表面就很可能會(huì)出現(xiàn)裂縫。裂縫最初是在應(yīng)力超過它極限壓力的地方開始出現(xiàn)的，而通常這往往是有微小的表面缺陷的地方，例如有一處材料出現(xiàn)瑕疵或者一道極小的劃痕。當(dāng)循環(huán)的次數(shù)增加時(shí)，最初的裂縫開始在軸的周圍的逐漸產(chǎn)生許多類似的裂縫。所以說，第一道裂縫的意義就是指應(yīng)力集中的地方，它會(huì)加速其它裂縫的產(chǎn)生。一旦整個(gè)的外圍斗出現(xiàn)了裂縫，裂縫就會(huì)開始向軸的中心轉(zhuǎn)移。最后，當(dāng)剩下的固體的內(nèi)部地區(qū)變得足夠小，且當(dāng)壓力超過極限強(qiáng)度時(shí)，軸就會(huì)突然發(fā)生斷裂。對(duì)斷面的檢查可以發(fā)現(xiàn)一種非常有趣的圖案，如圖2.13中所示。外部的一個(gè)環(huán)形部分相對(duì)光滑一些，因?yàn)樵瓉肀砻嫔舷嗷ソ诲e(cuò)的裂縫之間不斷地發(fā)生磨擦導(dǎo)致了這種現(xiàn)象的產(chǎn)生。無論如何，中心部分是粗糙的，表明中心是突然發(fā)生了斷裂，類似于脆性材料斷裂時(shí)的現(xiàn)象。 這就表明了一個(gè)有趣的事實(shí)。當(dāng)正在使用的機(jī)器零件由于靜載荷的原因出現(xiàn)問題時(shí)，由于材料具有的延展性，他們通常會(huì)發(fā)生一定程度的變形。 盡管許多地由于靜壓力導(dǎo)致的零件故障可以通過頻繁的做實(shí)際的觀察并且替換全部發(fā)生變形的零件來避免。不管怎樣，疲勞失效有助于起到警告的作用。汽車中發(fā)生故障的零件中的90%的原因都是因?yàn)槠诘淖饔谩? 一種材料的疲勞強(qiáng)度是指在壓力的反復(fù)作用下的抵抗產(chǎn)生裂縫的能力。持久極限是用來評(píng)價(jià)一種材料的疲勞強(qiáng)度的一個(gè)重要參數(shù)。進(jìn)一步說明就是，持久極限就是指在無限循環(huán)的作用力下不引起失效的壓力值。 讓我們回頭來看在圖2.9 所示的疲勞試驗(yàn)機(jī)器的。試驗(yàn)是這樣被進(jìn)行的：一件小的重物被插入，電動(dòng)機(jī)被啟動(dòng)。在試樣的失效過程中，由計(jì)算寄存器記錄下循環(huán)的次數(shù)N，并且彎曲壓力的相應(yīng)最大量由第2.5 方程式計(jì)算。然后用一個(gè)新的樣品替換掉被毀壞的樣品，并且將另一個(gè)重物插入以增加負(fù)荷量。壓力的新的數(shù)值再次被計(jì)算，并且相同的程序再次被重復(fù)進(jìn)行，直到零件的失效只需要一個(gè)完整周期時(shí)為止。然后根據(jù)壓力值和所需的循環(huán)的次數(shù)來繪制一個(gè)圖。正如圖表2.14a所示圖形，該圖被稱為持久極限曲線或者S-N 曲線。由于這需要的前提是要進(jìn)行無限次的循環(huán)，所以我們可以以100萬個(gè)循環(huán)用來作循環(huán)參考單位。因此，持久極限可以從圖表2.14a那里看到，該材料是在承受了100萬個(gè)循環(huán)后而沒有發(fā)生失效的。 用圖2.14 描繪的關(guān)系對(duì)于鋼的材料來說更為典型，因?yàn)楫?dāng)N 接近非常大的數(shù)字時(shí)，曲線就會(huì)變得水平。因此持久極限等于曲線接近一條水平的切線時(shí)的壓力水平。由于包含了大量的循環(huán)，在繪圖時(shí)，N通常會(huì)被按照對(duì)數(shù)標(biāo)度來畫，如圖2.14 b中所示。當(dāng)采用這樣的方法做時(shí)，水平的直線就可以更容易發(fā)現(xiàn)材料的持久極限值。對(duì)于鋼的材料來說，持久極限值大約等于極限強(qiáng)度的50%。無論如何，已經(jīng)加工完成的表面如果不是一樣的光滑，持久極限的值就會(huì)被降低。例如，對(duì)于鋼材料的零件來說，63 微英寸（ μin ）的機(jī)械加工的表面，零件的持久極限占理論的持久極限的百分比降低到了大約40%。而對(duì)于粗糙的表面來說 （300μin，甚至更多），百分比可能降低到25%左右的水平。 最常見的疲勞損壞的類型通常是由于彎曲應(yīng)力所引起的。其次就是扭應(yīng)力導(dǎo)致的失效，而由于軸向負(fù)載引起的疲勞失效卻極少發(fā)生。彈性材料通常使用從零到最大值之間變化的剪應(yīng)力值來做實(shí)驗(yàn)，以此來模擬材料實(shí)際的受力方式。 就一些有色金屬而論，當(dāng)循環(huán)的次數(shù)變得非常大時(shí)，疲勞曲線不會(huì)隨著循環(huán)次數(shù)的增大而變得水平。，而疲勞曲線的繼續(xù)變小，表明不管作用力有多么的小，多次的應(yīng)力反復(fù)作用都會(huì)引起零件的失效。這樣的一種材料據(jù)說沒有持久極限。對(duì)于大多數(shù)有色金屬來說，它們都有一個(gè)持久極限，數(shù)值大小大約是極限強(qiáng)度的25%。 溫度對(duì)屈服強(qiáng)度和彈性模數(shù)的影響 一般說來，當(dāng)在說明一種擁有特殊的屬性的材料時(shí)，如彈性模數(shù)和屈服強(qiáng)度，表示這些性能在室溫環(huán)境下就可以存在。在低的或者較高的溫度下，材料的特性可能會(huì)有很大的不同。例如，很多金屬在低溫時(shí)會(huì)變得更脆。此外，當(dāng)溫度升高時(shí)，材料的彈性模數(shù)和屈服強(qiáng)度都會(huì)變差。圖2.23 顯示了低碳鋼的屈服強(qiáng)度在從室溫升高到1000oC過程中被降低了大約70%。 當(dāng)溫度升高時(shí)，圖2.24顯示了低碳鋼在彈性模數(shù)E方面的削減。正如從圖上可以看見的那樣，彈性模數(shù)在從室溫升高到1000oC過程中大約降低了30%。從這張圖表中，我們也能看到在室溫下承受了一定載荷而不會(huì)發(fā)生變形的零件卻可能在高溫時(shí)承受相同載荷時(shí)發(fā)生永久變形。 蠕變： 一種塑性變形的現(xiàn)象 由于溫度效應(yīng)的影響，金屬中產(chǎn)生了一種被稱為蠕變的現(xiàn)象，一個(gè)承受了一定的載荷的零件的塑性變形是按照一個(gè)時(shí)間函數(shù)來逐漸增加的。蠕變現(xiàn)象在室溫的條件下也是存在的，但它發(fā)生的過程是如此之慢，以致于很少變得像在預(yù)期壽命中溫度被升高到300oC或更多時(shí)那樣顯著，逐漸增加的塑性變形可能在一段短的時(shí)期內(nèi)變得很明顯。材料的抗蠕變強(qiáng)度是指材料抵抗蠕變的屬性，并且抗蠕變強(qiáng)度的數(shù)據(jù)可以通過處理長期的蠕變試驗(yàn)(模擬實(shí)際零件的操作條件)來獲得。在試驗(yàn)的過程中，給定的材料在規(guī)定的溫度下的塑性應(yīng)變被被進(jìn)行了實(shí)時(shí)監(jiān)控。 由于蠕變是一種塑性變形現(xiàn)象，發(fā)生了蠕變的零件的尺寸可能就會(huì)被永久的改變。因此，如果一個(gè)零件是在很強(qiáng)的強(qiáng)度下運(yùn)轉(zhuǎn)的話，那么設(shè)計(jì)工程師必須精確地預(yù)言將在機(jī)器的使用壽命期間可能發(fā)生的蠕變的次數(shù)。否則，與此伴隨的或者相關(guān)的問題就可能發(fā)生。 在高溫下，當(dāng)螺栓被用來緊固零件時(shí)，蠕變就可能變成一個(gè)必須解決的問題。處在壓力狀態(tài)下的螺釘，蠕變是按照一個(gè)時(shí)間函數(shù)來發(fā)生的。因?yàn)樽冃问撬苄缘?，夾緊力的損失將可能導(dǎo)致螺紋連接件的意外松動(dòng)。像這種特殊的現(xiàn)象，通常被稱為松弛，我們可以通過進(jìn)行適當(dāng)?shù)娜渥儚?qiáng)度時(shí)測試來確定是不是發(fā)生了蠕變。 圖2.25顯示了三種承受了恒定的張緊力的低碳鋼零件的典型的蠕變曲線。從中，我們可以注意到在高溫條件下，蠕變發(fā)生的速度逐漸加速，直到零件失效。從圖表里的時(shí)間軸上(x軸)，我們可以描述在10年的時(shí)間里，這種產(chǎn)品的預(yù)期壽命。 總結(jié) 機(jī)器設(shè)計(jì)者必須理解進(jìn)行抗拉的靜止強(qiáng)度的測試目的。這種試驗(yàn)可以確定被在設(shè)計(jì)方程式過程中使用的許多金屬的機(jī)械特性。像彈性模數(shù)，比例極限，屈服強(qiáng)度，彈性，以及延展性等等可以根據(jù)抗拉試驗(yàn)來決定它們的特性。 動(dòng)載荷是指那些，在大小和方向上發(fā)生變化并且可能需要對(duì)機(jī)器零件在抵抗失效能力上的研究。由于應(yīng)力的反復(fù)作用，允許使用的安全應(yīng)力是基于材料的持久極限而不是基于屈服強(qiáng)度或者是極限強(qiáng)度。 壓力集中在機(jī)器零件改變尺寸的位置發(fā)生，例如在一塊平的金屬板上的一個(gè)孔或者一塊平板、一個(gè)溝槽、一個(gè)圓軸上的皮帶在寬度方向上的突然變化。尤其是在一塊平板上或一塊條板上有一個(gè)孔的情況下，當(dāng)孔的大小減少時(shí)，最大應(yīng)力的值相對(duì)于平均應(yīng)力變得大得多。減少的壓力集中影響的方法通常就是使在形狀上的變化更有規(guī)律性。 被設(shè)計(jì)出來的機(jī)械零件被用于在低于屈服強(qiáng)度或者極限強(qiáng)度的一些允許的環(huán)境下使用。這種方法可以用來照顧到在加工期間像材料屬性的變化和殘余應(yīng)力的產(chǎn)生這樣的未知因素， 以及用來做近似而不是精確計(jì)算的方程式。根據(jù)屈服強(qiáng)度或者極限強(qiáng)度來確定安全系數(shù)以決定安全應(yīng)力的大小。 溫度能影響金屬的機(jī)械特性。溫度的增加可能會(huì)引起金屬的熱脹和蠕變，并且還可能降低它的屈服強(qiáng)度和它的彈性模數(shù)。如果大多數(shù)金屬不被允許在溫度發(fā)生變化時(shí)發(fā)生膨脹或者收縮，那么壓力就會(huì)被當(dāng)做載荷來看待。這現(xiàn)象在依靠干涉配合來進(jìn)行零件裝配時(shí)是有益的。一個(gè)轂或者孔的內(nèi)徑比與它相配的軸或者圓柱的直徑小一點(diǎn)。先將轂加熱后，由于熱脹冷縮，此時(shí)可以輕松的將軸插入其中。當(dāng)它冷卻以后，同樣由于熱脹冷縮，它的內(nèi)孔直徑會(huì)變小，從而對(duì)插入其中的軸產(chǎn)生了很大的摩擦力，有效的防止了軸的松動(dòng)。 計(jì)算機(jī)輔助制造構(gòu)造的類型 盤形凸輪. 這類凸輪是最受歡迎的類型之一，因?yàn)檫@種凸輪的設(shè)計(jì)和制造是比較簡單和容易的。如圖6.1所示的盤形凸輪?？梢宰⒁獾綇膭?dòng)件移動(dòng)到了與凸輪的旋轉(zhuǎn)軸垂直的位置。所有的凸輪都按照兩個(gè)不同的實(shí)體在運(yùn)轉(zhuǎn)時(shí)不會(huì)互相碰撞的基本原理來運(yùn)行。因此，隨著凸輪的旋轉(zhuǎn)（在這種情況下，一般是逆時(shí)針轉(zhuǎn)），從動(dòng)件要么向上移動(dòng)要么就接受適當(dāng)?shù)募s束。我們應(yīng)該把注意力集中于防止從動(dòng)件發(fā)生粘接和使從動(dòng)件的運(yùn)動(dòng)滿足生產(chǎn)的要求。當(dāng)從動(dòng)件向下移動(dòng)時(shí)，彈簧需要使從動(dòng)件的棍子和凸輪的輪廓保持。棍子是被用來減少齒輪接觸表面的磨擦力的。對(duì)于凸輪的每次旋轉(zhuǎn)來說，從動(dòng)件通過對(duì)凸輪底部死點(diǎn)的沖擊使其移動(dòng)到頂端。 圖6.2 所示的是一個(gè)帶有一個(gè)尖頂從動(dòng)件的盤形凸輪。復(fù)雜的動(dòng)作可以通過這類從動(dòng)件產(chǎn)生，因?yàn)橐粋€(gè)點(diǎn)能夠精確地跟隨著凸輪輪廓的任何突然變化。無論如何，這種設(shè)計(jì)局限于負(fù)荷是非常小的應(yīng)用里；否則兩個(gè)實(shí)體的接觸點(diǎn)將會(huì)被磨損掉，從而導(dǎo)致一系列的問題出現(xiàn)。 盤形凸輪的兩個(gè)另外的變量分別是旋轉(zhuǎn)的從動(dòng)件和從動(dòng)件的偏移量，如圖6.3所示。當(dāng)需要的是旋轉(zhuǎn)的運(yùn)動(dòng)時(shí)，一個(gè)旋轉(zhuǎn)的從動(dòng)件就會(huì)被使用。關(guān)于從動(dòng)件的偏移量，我們需要注意從動(dòng)件的偏移量的大小是取決于像壓力角和凸輪外輪廓等參數(shù)的，這兩個(gè)參數(shù)稍后將會(huì)被介紹。沒有偏移量的從動(dòng)件被稱作同軸心的從動(dòng)件。 傳遞動(dòng)力的凸輪：如圖6.4 所描繪的被用來傳遞動(dòng)力的凸輪。當(dāng)凸輪朝著水平的方向傳遞運(yùn)動(dòng)時(shí)，從動(dòng)件會(huì)產(chǎn)生上下滑動(dòng)。從這里我們可以看出，一個(gè)旋轉(zhuǎn)的從動(dòng)件和一個(gè)滑動(dòng)的從動(dòng)件都可以被使用。這種類型的動(dòng)作通常會(huì)被用在一些生產(chǎn)用于凸輪上的產(chǎn)品的專用機(jī)床上。這種設(shè)計(jì)上的變化在旋轉(zhuǎn)和傳輸動(dòng)力的三維的凸輪上體現(xiàn)了出來。例如，一塊手工制造的步槍原料被放在一臺(tái)專用車床上。這塊原料的形狀是要求能夠?qū)崿F(xiàn)以各凸輪所要達(dá)到的功能。當(dāng)它旋轉(zhuǎn)并傳輸動(dòng)力時(shí)，從動(dòng)件就可以控制用來把一塊木材加工成生產(chǎn)步槍原料的機(jī)床。 主動(dòng)凸輪：在上述的凸輪設(shè)計(jì)中，凸輪和從動(dòng)件之間在往返運(yùn)動(dòng)中保持接觸是通過彈簧力的作用來保證的。無論如何，處于高速運(yùn)轉(zhuǎn)中的凸輪，用來保持凸輪和從動(dòng)件之間的接觸的彈簧力可能會(huì)變得很大，這是由于凸輪在高速運(yùn)動(dòng)中的加速度會(huì)產(chǎn)生額外的動(dòng)作用力，接觸的位置可能會(huì)發(fā)生變形。在這種情況下，接觸面可能產(chǎn)生過大的壓力，這樣將會(huì)導(dǎo)致零件過早的被磨損。主動(dòng)凸輪是不需要彈簧的，因?yàn)閺膭?dòng)件被迫在兩個(gè)方向上與凸輪接觸。這樣的主動(dòng)凸輪可以分為4類：圓柱形的凸輪，開槽的盤形凸輪(也叫表面凸輪)，分型板凸輪，以及共軛凸輪。 圓柱形凸輪：如圖6.5所示，圓柱形凸輪可以使從動(dòng)件實(shí)現(xiàn)不斷的往復(fù)運(yùn)動(dòng)。圖6.6所示的是一個(gè)旋轉(zhuǎn)的從動(dòng)件的應(yīng)用實(shí)例。通過凸輪上槽溝的設(shè)計(jì)，我們可以實(shí)現(xiàn)使用幾個(gè)凸輪軸來完成從動(dòng)件的圓周分布。 開槽的盤形凸輪：在圖6.8上，我們可以看到一個(gè)帶有旋轉(zhuǎn)的從動(dòng)件的分型板凸輪，但是這樣的設(shè)計(jì)也可以被用于傳遞動(dòng)力的從動(dòng)件上面。凸輪E和F一起繞著凸輪軸B旋轉(zhuǎn)。凸輪E始終保持與滾筒C接觸，而凸輪F則一直和滾筒D保持著接觸。滾筒C和滾筒D都被安裝在一根直角杠桿上，而這個(gè)直角杠桿是繞著點(diǎn)A 擺動(dòng)的從動(dòng)件。當(dāng)凸輪F提供個(gè)滾筒D的需要的動(dòng)作時(shí)，凸輪E則被用于給滾筒C提供需要的動(dòng)作。 共軛凸輪．這種類型的凸輪，正如圖表6.9描述的那樣，由一個(gè)被安裝在凸輪軸偏心處的圓凸輪組成。從動(dòng)件每次的擺度等于兩倍的凸輪的偏心矩e。這樣的凸輪會(huì)生產(chǎn)簡諧振運(yùn)動(dòng)而沒有保留時(shí)間。下面更進(jìn)一步的討論一下第6.8 部分。 計(jì)算機(jī)輔助制造的專有名詞 在我們涉及凸輪的設(shè)計(jì)之前，我們很有必要知道各種各樣被用于鑒別凸輪的重要的設(shè)計(jì)參數(shù)?？匆幌孪聢D6.11中的術(shù)語。如果你把凸輪想像成是不動(dòng)的，而從動(dòng)件是繞著凸輪轉(zhuǎn)動(dòng)的，那么，你將更容易理解對(duì)凸輪的描述。 軌跡點(diǎn)：是指尖頂從動(dòng)件的終點(diǎn)或者輥?zhàn)又行幕蛘咻佔(zhàn)又惖膹膭?dòng)件的終點(diǎn)。 凸輪輪廓：凸輪的實(shí)際形狀。 基圓：是指能夠畫出來的且與凸輪的輪廓線相切的最小的圓。它的中心也就是凸輪軸的中心。凸輪軸里的最小的半徑就是基圓的半徑。 嚙合曲線：假定凸輪是固定不動(dòng)的，從動(dòng)件繞著凸輪旋轉(zhuǎn)的，那么，軌跡點(diǎn)的路徑就是嚙合曲線。 優(yōu)圓：優(yōu)圓是指與嚙合曲線相切，且它的中心也在分配軸的中心的圓。 壓力角：壓力角是指從動(dòng)件的運(yùn)動(dòng)方向與節(jié)圓上輥?zhàn)拥闹行乃诘狞c(diǎn)之間的角度。 凸輪外形：與凸輪輪廓相同。 BDC：是Bottom Dead Center的縮寫，是指從動(dòng)件離凸輪中心最近的位置。 行程：是指從動(dòng)件在BDC 和TDC之間走過的路程的長度。 高度上的行程：是指從動(dòng)件從BDC轉(zhuǎn)到TDC的時(shí)高度的變化值。 返程：是指從動(dòng)件從TDC轉(zhuǎn)到BDC時(shí)所需時(shí)間。 輪廓平行線：是指當(dāng)凸輪在轉(zhuǎn)動(dòng)時(shí)，從動(dòng)件可以和凸輪的中心保持恒定的距離不變的軌跡。 我們可以通過圖6.12獲得對(duì)壓力角的意義有一個(gè)更清楚、更深刻的理解。在這里，F(xiàn)T是影響輥?zhàn)拥囊粋€(gè)合力。在任何一個(gè)接觸點(diǎn)的地方，它一定是與表面垂直的。FT的方向顯而易見不與從動(dòng)件運(yùn)動(dòng)的方向平行。相反，它時(shí)通過壓力角α來表明從動(dòng)件的運(yùn)動(dòng)的方向的。因此，力FT可以被分解為水平方向的力FH和垂直方向的力FV兩部分。垂直分量是向上驅(qū)動(dòng)從動(dòng)件的那個(gè)力，因此，忽略了摩擦力，就等于從動(dòng)件所受的力。水平方向的力沒有座有用功，但是它仍然是不可或缺的。事實(shí)上，它試圖使從動(dòng)件能夠沿著它的方向走。這樣就可能會(huì)損壞從動(dòng)件或者使從動(dòng)件被卡死。很明顯，我們希望壓力角能夠盡可能的減小測向力的大小。一個(gè)實(shí)際的經(jīng)驗(yàn)法則是設(shè)計(jì)凸輪輪廓時(shí)，應(yīng)使壓力角的度數(shù)不超過30o 。壓力角的大小，一般說來，取決于從動(dòng)件的以下四個(gè)參數(shù)： ——基圓的大小。 ——從動(dòng)件相對(duì)主動(dòng)件的圓心的偏移量的大小。 ——滾筒直徑的大小。 ——凸輪輪廓平面(取決于使用的從動(dòng)件運(yùn)動(dòng)的從動(dòng)件行程和類型)。 如果凸輪的要求沒有改變，那么前面提到的一些參數(shù)就不能被改變。例如空間的限制。在我們已經(jīng)學(xué)習(xí)過了如何設(shè)計(jì)凸輪之后，我們將學(xué)到減小壓力角的各種各樣的方法。 湘潭大學(xué)興湘學(xué)院 畢業(yè)論文（設(shè)計(jì)）任務(wù)書 論文（設(shè)計(jì)）題目： 絞肉機(jī)的設(shè)計(jì) 學(xué)號(hào)：2006183822 姓名：李昌席 專業(yè)：機(jī)械設(shè)計(jì)制造及其自動(dòng)化 指導(dǎo)教師： 系主任： 一、主要內(nèi)容及基本要求 原料:肉類 生產(chǎn)動(dòng)力: 螺旋供料器的轉(zhuǎn)速n＝326r/min 要求:繪制總裝備圖A01張,其他元件圖周拆合為1.5A0圖 說明書1份 10000字以上 全部激光打印 翻譯資料1份 3000字符 光盤2張 二、重點(diǎn)研究的問題 絞肉機(jī)的結(jié)構(gòu)，工作原理以及完成對(duì)中等復(fù)雜程度機(jī)械的計(jì)算、結(jié)構(gòu)設(shè)計(jì)等工作. 三、進(jìn)度安排 序號(hào) 各階段完成的內(nèi)容 完成時(shí)間 1 熟悉題目 調(diào)研 收集材料 第1-2周 2 方案設(shè)計(jì) 論證 第3-4周 3 總體設(shè)計(jì) 機(jī)械設(shè)計(jì)計(jì)算 第5-7周 4 繪制裝備圖 元件圖 第8-11周 5 撰寫說明書 翻譯資料 第12-13周 6 修改圖紙 打圖 第14周 四、應(yīng)收集的資料及主要參考文獻(xiàn) 1 吳宗澤主編．機(jī)械設(shè)計(jì)實(shí)用手冊[M]．第一版．北京：化學(xué)工業(yè)出版社．1999 2 濮良貴、紀(jì)名剛主編．機(jī)械設(shè)計(jì)[M]．第七版．北京：高等教育出版社．2001 3 張?jiān)Ｖ兄骶帲称芳庸ぜ夹g(shù)裝備[M]．第一版．北京：中國輕工業(yè)出版社．2000 4 無錫輕工業(yè)學(xué)院、天津輕工業(yè)學(xué)院編．食品工廠機(jī)械與設(shè)備[M]．第二版．北京：輕工業(yè)出版社．1985 5 胡繼強(qiáng)主編．食品機(jī)械與設(shè)備[M]．第一版．北京：中國輕工業(yè)出版社．1999 6李興國主編．食品機(jī)械學(xué)（下冊）V．第一版．四川：四川教育出版社．1992 7中國農(nóng)業(yè)機(jī)械化科學(xué)研究院編．實(shí)用機(jī)械設(shè)計(jì)手冊（下）[M]．北京：中國農(nóng)業(yè)機(jī)械出版社．1985 8成大先主編．機(jī)械設(shè)計(jì)手冊（第4卷）[M]．第四版．北京：化學(xué)工業(yè)出版社．2002 9毛謙德、李振清主編．袖珍機(jī)械設(shè)計(jì)師手冊[M]．第二版．北京：機(jī)械工業(yè)出版社．2002 10馬曉湘、鐘均祥主編．畫法幾何及機(jī)械制圖[M]．第二版．華南理工大學(xué)出版社1992 11張萬昌主編．熱加工工業(yè)基礎(chǔ)V．第一版．北京:高等教育出版社．1997 Failure Analysis， Dimensional Determination And Analysis， Applications Of Cams INTRODUCTION It is absolutely essential that a design engineer know how and why parts fail so that reliable machines t hat require minimum maintenance can be designed． Sometimes a failure can be serious， such as when a tire blows out on an automobile traveling at high speed． On the other hand， a failure may be no more t han a nuisance． An example is the loosening of the radiator hose in an automobile cooling system． The consequence of this latter failure is usually the loss of some radiator coolant， a condition that is readily detected and corrected． The type of load a part absorbs is just as significant as the magnitude． Generally speaking， dynamic loa ds with direction reversals cause greater difficulty than static loads， and therefore， fatigue strength must be considered． Another concern is whether the material is ductile or brittle． For example， brittle material s are considered to be unacceptable where fatigue is involved． Many people mistakingly interpret the word failure to mean the actual breakage of a part． However， a d esign engineer must consider a broader understanding of what appreciable deformation occurs． A ductile material， however will deform a large amount prior to rupture． Excessive deformation， without fracture， may cause a machine to fail because the deformed part interferes with a moving second part． Therefore， a part fails(even if it has not physically broken)whenever it no longer fulfills its required function． Somet imes failure may be due to abnormal friction or vibration between two mating parts． Failure also may be due to a phenomenon called creep， which is the plastic flow of a material under load at elevated tempe ratures． In addition， the actual shape of a part may be responsible for failure． For example， stress conc entrations due to sudden changes in contour must be taken into account． Evaluation of stress consideratio ns is especially important when there are dynamic loads with direction reversals and the material is not very ductile． In general， the design engineer must consider all possible modes of failure， which include the following． —— Stress —— Deformation —— Wear —— Corrosion —— Vibration —— Environmental damage —— Loosening of fastening devices The part sizes and shapes selected also must take into account many dimensional factors that produce ext ernal load effects， such as geometric discontinuities， residual stresses due to forming of desired contours， and the application of interference fit joints． Cams are among the most versatile mechanisms available． A cam is a simple two-member device． The i nput member is the cam itself， while the output member is called the follower． Through the use of cams， a simple input motion can be modified into almost any conceivable output motion that is desired． Some of the common applications of cams are —— Camshaft and distributor shaft of automotive engine —— Production machine tools —— Automatic record players —— Printing machines —— Automatic washing machines —— Automatic dishwashers The contour of high-speed cams (cam speed in excess of 1000 rpm) must be determined mathematicall y． However， the vast majority of cams operate at low speeds(less than 500 rpm) or medium-speed cams can be determined graphically using a large-scale layout． In general， the greater the cam speed and outp ut load， the greater must be the precision with which the cam contour is machined． DESIGN PROPERTIES OF MATERIALS The following design properties of materials are defined as they relate to the tensile test． Figure 2.7 Static Strength． The strength of a part is the maximum stress that the part can sustain without losing i ts ability to perform its required function． Thus the static strength may be considered to be approximatel y equal to the proportional limit， since no plastic deformation takes place and no damage theoretically is done to the material． Stiffness． Stiffness is the deformation-resisting property of a material． The slope of the modulus line an d， hence， the modulus of elasticity are measures of the stiffness of a material． Resilience． Resilience is the property of a material that permits it to absorb energy without permanent d eformation． The amount of energy absorbed is represented by the area underneath the stress-strain diagra m within the elastic region． Toughness． Resilience and toughness are similar properties． However， toughness is the ability to absorb energy without rupture． Thus toughness is represented by the total area underneath the stress-strain diagr am， as depicted in Figure 2． 8b． Obviously， the toughness and resilience of brittle materials are very l ow and are approximately equal． Brittleness． A brittle material is one that ruptures before any appreciable plastic deformation takes plac e． Brittle materials are generally considered undesirable for machine components because they are unable to yield locally at locations of high stress because of geometric stress raisers such as shoulders， holes， n otches， or keyways． Ductility． A ductility material exhibits a large amount of plastic deformation prior to rupture． Ductility is measured by the percent of area and percent elongation of a part loaded to rupture． A 5%elongation a t rupture is considered to be the dividing line between ductile and brittle materials． Malleability． Malleability is essentially a measure of the compressive ductility of a material and， as suc h， is an important characteristic of metals that are to be rolled into sheets． Figure 2.8 Hardness． The hardness of a material is its ability to resist indentation or scratching． Generally speakin g， the harder a material， the more brittle it is and， hence， the less resilient． Also， the ultimate strength of a material is roughly proportional to its hardness． Machinability． Machinability is a measure of the relative ease with which a material can be machined． I n general， the harder the material， the more difficult it is to machine． COMPRESSION AND SHEAR STATIC STRENGTH In addition to the tensile tests， there are other types of static load testing that provide valuable informati on． Compression Testing． Most ductile materials have approximately the same properties in compression as in tension． The ultimate strength， however， can not be evaluated for compression． As a ductile specime n flows plastically in compression， the material bulges out， but there is no physical rupture as is the cas e in tension． Therefore， a ductile material fails in compression as a result of deformation， not stress． Shear Testing． Shafts， bolts， rivets， and welds are located in such a way that shear stresses are produ ced． A plot of the tensile test． The ultimate shearing strength is defined as the stress at which failure oc curs． The ultimate strength in shear， however， does not equal the ultimate strength in tension． For exam ple， in the case of steel， the ultimate shear strength is approximately 75% of the ultimate strength in ten sion． This difference must be taken into account when shear stresses are encountered in machine compon ents． DYNAMIC LOADS An applied force that does not vary in any manner is called a static or steady load． It is also common practice to consider applied forces that seldom vary to be static loads． The force that is gradually applied during a tensile test is therefore a static load． On the other hand， forces that vary frequently in magnitude and direction are called dynamic loads． Dyn amic loads can be subdivided to the following three categories． Varying Load． With varying loads， the magnitude changes， but the direction does not． For example， t he load may produce high and low tensile stresses but no compressive stresses． Reversing Load． In this case， both the magnitude and direction change． These load reversals produce a lternately varying tensile and compressive stresses that are commonly referred to as stress reversals． Shock Load． This type of load is due to impact． One example is an elevator dropping on a nest of sp rings at the bottom of a chute． The resulting maximum spring force can be many times greater than the weight of the elevator， The same type of shock load occurs in automobile springs when a tire hits a bu mp or hole in the road． FATIGUE FAILURE-THE ENDURANCE LIMIT DIAGRAM The test specimen in Figure 2.10a．， after a given number of stress reversals will experience a crack at the outer surface where the stress is greatest． The initial crack starts where the stress exceeds the strengt h of the grain on which it acts． This is usually where there is a small surface defect， such as a materia l flaw or a tiny scratch． As the number of cycles increases， the initial crack begins to propagate into a continuous series of cracks all around the periphery of the shaft． The conception of the initial crack is it self a stress concentration that accelerates the crack propagation phenomenon． Once the entire periphery b ecomes cracked， the cracks start to move toward the center of the shaft． Finally， when the remaining so lid inner area becomes small enough， the stress exceeds the ultimate strength and the shaft suddenly brea ks． Inspection of the break reveals a very interesting pattern， as shown in Figure 2.13． The outer annula r area is relatively smooth because mating cracked surfaces had rubbed against each other． However， the center portion is rough， indicating a sudden rupture similar to that experienced with the fracture of brittle materials． This brings out an interesting fact． When actual machine parts fail as a result of static loads， they norma lly deform appreciably because of the ductility of the material． Figure 2.13 Thus many static failures can be avoided by making frequent visual observations and replacing all defor med parts． However， fatigue failures give to warning． Fatigue fail mated that over 90% of broken autom obile parts have failed through fatigue． The fatigue strength of a material is its ability to resist the propagation of cracks under stress reversal s． Endurance limit is a parameter used to measure the fatigue strength of a material． By definition， the endurance limit is the stress value below which an infinite number of cycles will not cause failure． Let us return our attention to the fatigue testing machine in Figure 2.9． The test is run as follows： A s mall weight is inserted and the motor is turned on． At failure of the test specimen， the counter registers the number of cycles N， and the corresponding maximum bending stress is calculated from Equation 2. 5． The broken specimen is then replaced by an identical one， and an additional weight is inserted to inc rease the load． A new value of stress is calculated， and the procedure is repeated until failure requires o nly one complete cycle． A plot is then made of stress versus number of cycles to failure． Figure 2.14a shows the plot， which is called the endurance limit or S-N curve． Since it would take forever to achieve an infinite number of cycles， 1 million cycles is used as a reference． Hence the endurance limit can be found from Figure 2.14a by noting that it is the stress level below which the material can sustain 1 mil lion cycles without failure． The relationship depicted in Figure 2.14 is typical for steel， because the curve becomes horizontal as N a pproaches a very large number． Thus the endurance limit equals the stress level where the curve approac hes a horizontal tangent． Owing to the large number of cycles involved， N is usually plotted on a logari thmic scale， as shown in Figure 2.14b． When this is done， the endurance limit value can be readily det ected by the horizontal straight line． For steel， the endurance limit equals approximately 50% of the ulti mate strength． However， if the surface finish is not of polished equality， the value of the endurance limi t will be lower． For example， for steel parts with a machined surface finish of 63 microinches ( μin． )， the percentage drops to about 40%． For rough surfaces (300μin． or greater)， the percentage may be as l ow as 25%． The most common type of fatigue is that due to bending． The next most frequent is torsion failure， whe reas fatigue due to axial loads occurs very seldom． Spring materials are usually tested by applying variab le shear stresses that alternate from zero to a maximum value， simulating the actual stress patterns． In the case of some nonferrous metals， the fatigue curve does not level off as the number of cycles bec omes very large． This continuing toward zero stress means that a large number of stress reversals will ca use failure regardless of how small the value of stress is． Such a material is said to have no endurance l imit． For most nonferrous metals having an endurance limit， the value is about 25% of the ultimate stre ngth． EFFECTS OF TEMPERATURE ON YIELD STRENGTH AND MODULUS OF ELASTICITY Generally speaking， when stating that a material possesses specified values of properties such as modulus of elasticity and yield strength， it is implied that these values exist at room temperature． At low or elev ated temperatures， the properties of materials may be drastically different． For example， many metals are more brittle at low temperatures． In addition， the modulus of elasticity and yield strength deteriorate as the temperature increases． Figure 2.23 shows that the yield strength for mild steel is reduced by about 7 0% in going from room temperature to 1000oF． Figure 2.24 shows the reduction in the modulus of elasticity E for mild steel as the temperature increase s． As can be seen from the graph， a 30% reduction in modulus of elasticity occurs in going from room temperature to 1000oF． In this figure， we also can see that a part loaded below the proportional limit at room temperature can be permanently deformed under the same load at elevated temperatures． Figure 2.24 CREEP: A PLASTIC PHENOMENON Temperature effects bring us to a phenomenon called creep， which is the increasing plastic deformation o f a part under constant load as a function of time． Creep also occurs at room temperature， but the proce ss is so slow that it rarely becomes significant during the expected life of the temperature is raised to 3 00oC or more， the increasing plastic deformation can become significant within a relatively short period o f time． The creep strength of a material is its ability to resist creep， and creep strength data can be obt ained by conducting long-time creep tests simulating actual part operating conditions． During the test， the plastic strain is monitored for given material at specified temperatures． Since creep is a plastic deformation phenomenon， the dimensions of a part experiencing creep are perman ently altered． Thus， if a part operates with tight clearances， the design engineer must accurately predict t he amount of creep that will occur during the life of the machine． Otherwise， problems such binding or interference can occur． Creep also can be a problem in the case where bolts are used to clamp tow parts together at elevated te mperatures． The bolts， under tension， will creep as a function of time． Since the deformation is plastic， loss of clamping force will result in an undesirable loosening of the bolted joint． The extent of this parti cular phenomenon， called relaxation， can be determined by running appropriate creep strength tests． Figure 2.25 shows typical creep curves for three samples of a mild steel part under a constant tensile loa d． Notice that for the high-temperature case the creep tends to accelerate until the part fails． The time li ne in the graph (the x-axis) may represent a period of 10 years， the anticipated life of the product． Figure 2.25 SUMMARY The machine designer must understand the purpose of the static tensile strength test． This test determines a number of mechanical properties of metals that are used in design equations． Such terms as modulus o f elasticity， proportional limit， yield strength， ultimate strength， resilience， and ductility define properties that can be determined from the tensile test． Dynamic loads are those which vary in magnitude and direction and may require an investigation of the machine part’s resistance to failure． Stress reversals may require that the allowable design stress be based on the endurance limit of the material rather than on the yield strength or ultimate strength． Stress concentration occurs at locations where a machine part changes size， such as a hole in a flat plate or a sudden change in width of a flat plate or a groove or fillet on a circular shaft． Note that for the case of a hole in a flat or bar， the value of the maximum stress becomes much larger in relation to the average stress as the size of the hole decreases． Methods of reducing the effect of stress concentration us ually involve making the shape change more gradual． Machine parts are designed to operate at some allowable stress below the yield strength or ultimate stren gth． This approach is used to take care of such unknown factors as material property variations and resid ual stresses produced during manufacture and the fact that the equations used may be approximate rather that exact． The factor of safety is applied to the yield strength or the ultimate strength to determine the allowable stress． Temperature can affect the mechanical properties of metals． Increases in temperature may cause a metal t o expand and creep and may reduce its yield strength and its modulus of elasticity． If most metals are n ot allowed to expand or contract with a change in temperature， then stresses are set up that may be add ed to the stresses from the load． This phenomenon is useful in assembling parts by means of interference fits． A hub or ring has an inside diameter slightly smaller than the mating shaft or post． The hub is th en heated so that it expands enough to slip over the shaft． When it cools， it exerts a pressure on the sh aft resulting in a strong frictional force that prevents loosening． TYPES OF CAM CONFIGURATIONS Plate Cams． This type of cam is the most popular type because it is easy to design and manufacture． F igure 6． 1 shows a plate cam． Notice that the follower moves perpendicular to the axis of rotation of th e camshaft． All cams operate on the principle that no two objects can occupy the same space at the sam e time． Thus， as the cam rotates ( in this case， counterclockwise )， the follower must either move upwa rd or bind inside the guide． We will focus our attention on the prevention of binding and attainment of t he desired output follower motion． The spring is required to maintain contact between the roller of the f ollower and the cam contour when the follower is moving downward． The roller is used to reduce frictio n and hence wear at the contact surface． For each revolution of the cam， the follower moves through t wo strokes-bottom dead center to top dead center (BDC to TDC) and TDC to BDC． Figure 6.2 illustrates a plate cam with a pointed follower． Complex motions can be produced with this t ype of follower because the point can follow precisely any sudden changes in cam contour． However， th is design is limited to applications in which the loads are very light； otherwise the contact point of both members will wear prematurely， with subsequent failure． Two additional variations of the plate cam are the pivoted follower and the offset sliding follower， which are illustrated in Figure 6.3． A pivoted follower is used when rotary output motion is desired． Referring to the offset follower， note that the amount of offset used depends on such parameters as pressure angl e and cam profile flatness， which will be covered later． A follower that has no offset is called an in-lin e follower． Figure 6.3 Translation Cams． Figure 6.4 depicts a translation cam． The follower slides up and down as the cam tr anslates motion in the horizontal direction． Note that a pivoted follower can be