2609 多軸鉆床設(shè)計(jì),鉆床,設(shè)計(jì) 河南理工大學(xué)萬方科技學(xué)院本科畢業(yè)設(shè)計(jì)開題報(bào)告題目名稱 多軸鉆床設(shè)計(jì)學(xué)生姓名 陳浩 專業(yè)班級(jí) 08 機(jī)制 3 班 學(xué)號(hào) 0828070004一、 選題的目的和意義：1.了解多軸鉆床的結(jié)構(gòu)及工作原理，掌握其設(shè)計(jì)方法；2.掌握設(shè)計(jì)計(jì)算的基本原理和方法,提高設(shè)計(jì)計(jì)算的能力；3.加深領(lǐng)會(huì)計(jì)算的基本理論和深化所學(xué)的理論知識(shí)；4.樹立正確的設(shè)計(jì)思想，為以后在工作中遇到相關(guān)問題提供解決依據(jù)。通過本次畢業(yè)設(shè)計(jì)，讓我將所學(xué)的理論知識(shí)在實(shí)際的設(shè)計(jì)工作中得以綜合應(yīng)用；鍛煉搜集整理資料的能力，本次畢業(yè)設(shè)計(jì)，讓我們能夠熟練應(yīng)用有關(guān)參考資料、計(jì)算圖表、手冊(cè)；熟悉有關(guān)的國(guó)家標(biāo)準(zhǔn)，為以后成為優(yōu)秀的工程技術(shù)人員打下良好的基礎(chǔ)。、、 國(guó)內(nèi)外研究現(xiàn)狀簡(jiǎn)述：多軸鉆床是一種孔加工的機(jī)床，它被廣泛用于加工多孔工件。它在生產(chǎn)中的應(yīng)用，解決了普通鉆床加工多孔工件時(shí)逐孔加工浪費(fèi)時(shí)間和人工這兩個(gè)重要問題。多軸鉆床是伴隨著經(jīng)濟(jì)的飛速發(fā)展和工業(yè)現(xiàn)代化的需要而產(chǎn)生的。其被應(yīng)用與許多方面，像汽車零部件的加工、農(nóng)用機(jī)械的零部件的加工以及其它大批量生產(chǎn)加工生產(chǎn)多孔零件的地方。多軸鉆床在加工業(yè)中有著很大的優(yōu)勢(shì)。它的使用使加工速度提高，因?yàn)楫?dāng)一個(gè)工件在同一個(gè)方向上有數(shù)個(gè)孔時(shí)，用普通鉆床加工時(shí)就要加工一個(gè)孔后又挪動(dòng)工件加工另一個(gè)孔，這樣就需要專人搬動(dòng)工件，對(duì)于小型工件可以采用這種方法，但當(dāng)工件很大時(shí)再采用這種方法就很落后，生產(chǎn)率很低，成本增加。所以，我們?cè)谂柯暽a(chǎn)多孔工件時(shí)就需要一種專門的機(jī)床來加工，所以就產(chǎn)生了由單臂鉆床衍生而來的多軸鉆床。多軸鉆床與普通鉆床的不同是多軸鉆床的主軸箱是像太陽系一樣，繞中間軸均部排列的主軸被中間軸帶動(dòng)轉(zhuǎn)動(dòng)，主軸帶動(dòng)刀具轉(zhuǎn)動(dòng)，完成切削工作。這樣多孔工件被一次加工成形，從而使勞動(dòng)強(qiáng)度大大減小，加工時(shí)間大大縮短，提高了勞動(dòng)生產(chǎn)率，降低了產(chǎn)品成本。用多軸鉆床加工零件具有以下優(yōu)越性：1． 加工速度塊快。使用多軸鉆床加工輪輻，較之采用普通搖臂鉆床，平均功效提高 30％。2． 加工質(zhì)量好。采用該鉆床加工的空組，孔的位置尺寸誤差小，工件互換性好，從未出現(xiàn)過因孔位置尺寸部隊(duì)而反攻報(bào)廢的情況。3． 多軸鉆造價(jià)低廉，維修方便，技術(shù)難度不高。多軸鉆的形式也是多種多樣的。根據(jù)多軸鉆的結(jié)構(gòu)可吧多軸鉆分為內(nèi)嚙合多軸鉆和為嚙合多軸鉆。內(nèi)嚙合多軸鉆是指齒輪傳動(dòng)為內(nèi)嚙合式，外嚙合多軸鉆式指齒輪傳動(dòng)為外嚙合式。根據(jù)鉆頭形式可分為臥式和立式兩種?？傊?，多軸鉆床在我們的工業(yè)生產(chǎn)中有著重要的意義。它大大的提高了我們的勞動(dòng)生產(chǎn)率，提高了多孔工件加工的精度，減少了工人的勞動(dòng)強(qiáng)度，也推動(dòng)了我國(guó)生產(chǎn)行業(yè)的迅速發(fā)展。我們應(yīng)該加強(qiáng)對(duì)多軸鉆床領(lǐng)域的開發(fā)。 三、畢業(yè)設(shè)計(jì)（論文）所采用的研究方法和手段：1.畢業(yè)設(shè)計(jì)所用的方法是：類比設(shè)計(jì)、優(yōu)化設(shè)計(jì)、經(jīng)驗(yàn)設(shè)計(jì)以及數(shù)據(jù)計(jì)算法等方法。在資料和信息獲取過程中進(jìn)行了實(shí)地考察和調(diào)研。2.在學(xué)校圖書館查閱相關(guān)資料；3.在工廠的實(shí)踐畢業(yè)實(shí)習(xí)；4.通過老師和工程師的指導(dǎo)；5.通過對(duì)相關(guān)資料和數(shù)據(jù)的理論計(jì)算和分析；6.整理，繪圖，寫設(shè)計(jì)說明書及畢業(yè)論文；四、主要參考文獻(xiàn)與資料獲得情況：[1]馮辛安主編 機(jī)械制造裝備設(shè)計(jì) 北京：機(jī)械工業(yè)出版社 1998[2]吳相憲 王正為主編 實(shí)用機(jī)械手冊(cè) 徐州：中國(guó)礦業(yè)大學(xué)出版社 2001（9）[3]機(jī)械工程手冊(cè) 電機(jī)工程手冊(cè)編輯委員會(huì) 機(jī)械工程手冊(cè) 第 2 版 北京：機(jī)械工業(yè)出版社 1997[4]機(jī)械設(shè)計(jì)手冊(cè)編寫組 機(jī)械設(shè)計(jì)手冊(cè) 第二冊(cè)（上下冊(cè)）[5]上海紡織工學(xué)院 哈爾濱工業(yè)大學(xué) 天津大學(xué)主編 機(jī)床課程設(shè)計(jì)圖冊(cè) 上海：上?？茖W(xué)技術(shù)出版社[6]徐灝主編 新編機(jī)械設(shè)計(jì)師手冊(cè) 上冊(cè) 北京：機(jī)械工業(yè)出版社 1995[7]專用機(jī)床設(shè)計(jì)與制造編寫組 專用機(jī)床設(shè)計(jì)與制造 下冊(cè) 第二版 黑龍江人民出版社[8]濮良貴 紀(jì)名剛主編 機(jī)械設(shè)計(jì) 第七版 北京：高等教育出版社 2001(2004重印)[9]機(jī)械設(shè)計(jì)便覽編寫組 機(jī)械設(shè)計(jì)便覽 天津科學(xué)技術(shù)出版社[10]李天無主編 簡(jiǎn)明機(jī)械工程師手冊(cè) 上冊(cè) 云南科技出版社 1988 年 5 月第一版五、畢業(yè)設(shè)計(jì)（論文）進(jìn)度安排（按周說明）：第 1-4 周 進(jìn)行畢業(yè)實(shí)習(xí)，收集整理資料，完成實(shí)習(xí)報(bào)告以及英文文獻(xiàn)翻譯。第 5-7 周 完成開題報(bào)告.實(shí)習(xí)報(bào)告，總體方案設(shè)計(jì)，初步完成設(shè)計(jì)算第 8-13 周完成總裝圖及零件圖的繪制，進(jìn)行中期檢查，并完成中期檢查報(bào)告，寫設(shè)計(jì)說明書。第 14-15 周整理并完善設(shè)計(jì)說明書以及零件圖，并檢查所有圖紙。第 16 周 打印圖紙進(jìn)行歸納整理，進(jìn)行答辯。六、指導(dǎo)教師審批意見（對(duì)選題的可行性、研究方法、進(jìn)度安排作出評(píng)價(jià)，對(duì)是否開題作出決定）： 指導(dǎo)教師： （簽名）年 月 日 中文翻譯：軸承的振動(dòng)分析Dr. S. J. Lacey舍夫勒(英國(guó))有限公司工程經(jīng)理摘要：在生產(chǎn)過程中,滾動(dòng)軸承振動(dòng)產(chǎn)生的復(fù)雜幾何缺陷可能會(huì)導(dǎo)致滾動(dòng)表面上的缺陷或相關(guān)組件的幾何誤差。噪音和振動(dòng)在所有類型的設(shè)備中正變得越來越關(guān)鍵,因?yàn)樗３１徽J(rèn)為是質(zhì)量的代名詞并常被用于預(yù)測(cè)和維護(hù)。這篇文章是關(guān)于一些軸承振動(dòng)的不同來源是如何隨著缺陷的頻率特征而展現(xiàn)出來的。文中給出了一些例子來說明了如何利用振動(dòng)來進(jìn)一步分析探測(cè)機(jī)器狀態(tài)的惡化。關(guān)鍵詞：軸承振動(dòng)，維修工程，可靠性工程，振動(dòng)探測(cè)。介紹：幾乎所有類型的旋轉(zhuǎn)機(jī)械都要用到滾動(dòng)接觸軸承，他們的可靠性依賴于軸承選定的類型以及所有相關(guān)組件的精度,即軸、墊片、螺帽等。在假定軸承正確安裝、操作和維護(hù)時(shí)，軸承工程師一般使用疲勞和正常的失效模式。今天，由于制造工藝和材料的改進(jìn)，一般情況下軸承疲勞壽命（與表面應(yīng)力相關(guān)）并不是限制因素而且不必考慮那些不足3%的誤差。不過，盡管許多軸承因?yàn)槲廴?、?rùn)滑不良、極端溫度、惡劣的裝修、不平衡和不合理的維修而過早失效，所有這些因素導(dǎo)致軸承振動(dòng)的增加，而且在使用了多年之后的狀態(tài)監(jiān)測(cè)仍然會(huì)對(duì)軸承造成災(zāi)難性失效(與停工期的相關(guān)費(fèi)用或身體機(jī)器其他部位的重大損害)。滾動(dòng)軸承通常被用于噪聲敏感的電器中，如家電用電動(dòng)機(jī)往往使用中小型軸承。因此軸承振動(dòng)不論是從它對(duì)機(jī)器質(zhì)量的重要性方面，還是從環(huán)境方面考慮，它都變得越來越重要?，F(xiàn)在人們普遍認(rèn)為安靜的運(yùn)行形式是滾動(dòng)接觸表面光潔度的代名詞。因此，軸承制造商已經(jīng)開發(fā)它們作為衡量質(zhì)量和振動(dòng)試驗(yàn)的有效方法。一個(gè)常用的方法是把它安裝在一個(gè)安靜運(yùn)行的主軸軸承上和對(duì)軸承的外圈點(diǎn)和三個(gè)頻段，分別是徑向速度。 50-300，300-1800和1800-10000赫茲。軸承必須符合三個(gè)頻段的均方根速度的限制。由于軸承振動(dòng)信號(hào)是由機(jī)械結(jié)構(gòu)修改的，所以在大多數(shù)情況下軸承振動(dòng)不能被直接測(cè)量。這種情況下因?yàn)槠渌O(shè)備（如電動(dòng)馬達(dá)，齒輪，皮帶）的振動(dòng)進(jìn)一步復(fù)雜化，會(huì)使那些未受過訓(xùn)練的專家很難對(duì)振動(dòng)數(shù)據(jù)做出解釋，在某些情況下會(huì)導(dǎo)致誤診斷，造成不必要的停機(jī)時(shí)間和成本增加。振動(dòng)源：滾動(dòng)軸承振動(dòng)是一個(gè)復(fù)雜的系統(tǒng)，其組成部分包括：滾動(dòng)體，內(nèi)滾道，外圈滾道和籠，相互作用產(chǎn)生復(fù)雜的振動(dòng)。雖然滾動(dòng)軸承是采用高精密機(jī)床加工，進(jìn)行嚴(yán)格的質(zhì)量控制和清潔，像其他制成品一樣，通過互動(dòng)的滾動(dòng)和滑動(dòng)組合，他們有缺陷且表面產(chǎn)生震動(dòng)。如今，雖然表面缺陷的幅度在納米級(jí)別，仍然可以在整個(gè)可聽頻率范圍（20赫茲- 20千赫）內(nèi)產(chǎn)生顯著的振動(dòng)。該振動(dòng)水平將取決于許多因素，包括沖擊能量，在哪個(gè)振動(dòng)測(cè)量點(diǎn)和軸承的結(jié)構(gòu)。變量合規(guī)： 即使軸承有非常完美的幾何外形，在承受徑向載荷下，軸承振動(dòng)也是滾動(dòng)軸承的固有特點(diǎn)，而非質(zhì)量差的原因。這樣的振動(dòng)類型通常被稱為變量合規(guī)，而且外部負(fù)載發(fā)生的原因是其位置由一個(gè)方面的負(fù)荷隨時(shí)間不斷變化造成的。（見圖1）圖1變剛度振動(dòng)嚴(yán)重依賴于配套的滾動(dòng)體外所加的負(fù)載數(shù)目，滾動(dòng)體的數(shù)量越多，它的振動(dòng)就越小。由于徑向加載或錯(cuò)位軸承的游隙決定了外部負(fù)載區(qū)域，因此，一般情況下隨著間隙變合規(guī)，運(yùn)行間隙不應(yīng)與徑向內(nèi)部游隙（里克）相混淆，由于過盈配合運(yùn)行中的內(nèi)、外圈熱膨脹的原因，前者通常是低于里克。變剛度振動(dòng)水平可以比粗糙度和表面波紋度的滾動(dòng)產(chǎn)生的更高。然而，在應(yīng)用中至關(guān)重要的是振動(dòng)可以通過使用正確的水平軸向預(yù)緊力來減少到一個(gè)可以忽略的水平。幾何缺陷：由于生產(chǎn)過程中使用的性質(zhì)，生產(chǎn)軸承零件的幾何缺陷將始終存在，其不同程度根據(jù)軸承精度等級(jí)而定。對(duì)于受壓球軸承在中等速度運(yùn)行下的臨界軋制表面形式和表面光潔度是軸承的噪音和振動(dòng)的最大來源。因此控制部件波紋和在生產(chǎn)過程中的表面光潔度是至關(guān)重要的，因?yàn)樗赡懿粌H有顯著影響，而且振動(dòng)可能會(huì)影響軸承的使用壽命。為方便起見，考慮到滾動(dòng)體，滾道的接觸寬度不完善之處幾何缺陷的波長(zhǎng) 被稱為粗糙表面特征，而波長(zhǎng)較長(zhǎng)的特點(diǎn)被稱為波紋（見圖2）。圖2 表面粗糙度：表面粗糙度是振動(dòng)的一個(gè)重要的來源，當(dāng)其表面粗糙度高時(shí)，在滾動(dòng)體與滾道的接觸處（見圖2）產(chǎn)生較厚的潤(rùn)滑油膜。在此條件下表面粗糙可以突破潤(rùn)滑膜，并與對(duì)方互動(dòng)的表面，造成金屬與金屬的接觸。由此產(chǎn)生的振動(dòng)，組成了一個(gè)激發(fā)所有的軸承和支撐結(jié)構(gòu)的自然模式隨機(jī)序列。表面粗糙度產(chǎn)生的振動(dòng)主要發(fā)生在六十次頻率軸承轉(zhuǎn)速上。因此頻譜的高頻部分通常顯示為一個(gè)系列的共振。用于估計(jì)相互作用的粗程度一個(gè)常見的參數(shù)是 lambda 比（Λ）。這是復(fù)合潤(rùn)滑膜厚度，表面粗 糙度糙度比率，由表達(dá)式給出Λ = h (σЪ 2 + σr 2)0.5 其中 Λ=粗糙程度的相互作用h=油膜厚度σЪ=粗糙度球σr=滾道表面粗糙度 圖3如果我們假定滾道表面光潔度是滾動(dòng)體的兩倍，那么對(duì)于一個(gè)典型的潤(rùn)滑油膜厚度為0.3μm 的表面飾面比0.06微米更加需要實(shí)現(xiàn)三 Λ值和較低的相互作用發(fā)生率。如需0.1_m 表面潤(rùn)滑油膜厚度比0.025_m完成須達(dá)到 Λ= 3。 Λ 對(duì)軸承的壽命的影響見圖3。如果 Λ 小于1，軸承將因破損而不可能達(dá)到估計(jì)的設(shè)計(jì)使用年限，這可能迅速導(dǎo)致滾動(dòng)表面疲勞破壞。一般來說，Λ 比值大于三顯示完整的表面分離。從全彈流（彈流潤(rùn)滑）過渡到混合潤(rùn)滑（有些粗糙接觸彈流潤(rùn)滑膜部分）發(fā)生在1至3Λ 范圍。波紋：對(duì)于更長(zhǎng)波長(zhǎng)的表面特征，與赫茲觸點(diǎn)相比峰值是低的，滾動(dòng)運(yùn)動(dòng)是隨著表面輪廓與滾動(dòng)體相連續(xù)的。表面間的幾何形狀和振動(dòng)水平的關(guān)系是復(fù)雜的，視軸承和接觸幾何以及載荷和速度情況而定。波紋能夠產(chǎn)生振動(dòng)頻率高達(dá)約三百次的旋轉(zhuǎn)速度，但通常是低于六十次的頻率轉(zhuǎn)速為主。上限是由于滾動(dòng)體的滾道接觸的有限區(qū)域最終得到更短特點(diǎn)的平均波長(zhǎng)。在滾動(dòng)方向上，接觸時(shí)彈性變形減輕對(duì)簡(jiǎn)單的諧波波形接觸寬度見圖4。 圖4在極限情況下，波長(zhǎng)隨衰減水平的減小而提高，直到一個(gè)波長(zhǎng)等于接觸寬度，波紋幅度在理論上是零。接觸長(zhǎng)度也是短波長(zhǎng)的衰減表面特征。通常較差的相關(guān)性可能存在于平行面之間高度的軌道，在不同的點(diǎn)抽取不同的配置文件，并全波紋度測(cè)量幅值平均值低一級(jí)。對(duì)于典型的軸承表面的平行面只有在更短的波長(zhǎng)存在較差的相關(guān)性。即使是現(xiàn)代精密加工技術(shù)波紋也不能被完全消除，盡管在相對(duì)較低的水平，但波紋元素將始終存在。對(duì)于軸承本身，相關(guān)的零部件的質(zhì)量也會(huì)影響軸承的振動(dòng)而且任何軸的幾何外徑的誤差，可能在振動(dòng)軸承的滾道中反映出來。因此，需要特別注意形式和所有相關(guān)的軸承零件的精度。離散缺陷：而表面粗糙度和波紋度的結(jié)果直接從軸承零部件生產(chǎn)制造工藝，離散的缺陷是指表面的滾動(dòng)由于污染，操作，安裝，保養(yǎng)不善等而造成的過大的損害。這些缺陷可能會(huì)非常小，難以察覺，但可能對(duì)振動(dòng)的關(guān)鍵設(shè)備產(chǎn)生重大影響或可能導(dǎo)致軸承壽命降低。此類缺陷可能有很多種類的形式。壓痕，劃痕和整個(gè)沿軋制表面，坑，碎片及潤(rùn)滑油中的顆粒。軸承制造商對(duì)成品缺陷的檢測(cè)都采用簡(jiǎn)單的振動(dòng)測(cè)量，但這些往往受到軸承的類型和大小的限制。這方面的一個(gè)類型的測(cè)量例子如圖5（a）和5（b）所示，與一個(gè)良好的軸承相比，在軸承外圈滾道離散損害產(chǎn)生了典型的脈沖振動(dòng)，具有較高的峰值/有效值比。圖5（a）圖5（b）在大量的缺陷發(fā)生個(gè)別峰值處不具有很明確的定義，但在 RMS 振動(dòng)水平數(shù)倍于通常與軸承相關(guān)的良好條件的總和。參考文獻(xiàn)1.Harris T A, Rolling Bearing Analysis (4th Ed), Wiley, New York, 2001.2.Lacey S J, Vibration monitoring of the internal centreless grinding process, Part 1: mathematical models. Proc Instn Mech Engrs. Vol 24. 1990.3.Lacey S J, Vibration monitoring of the internal centreless grinding process, Part 2: experimental results. Proc Instn Mech Engrs. Vol 24. 1990.4.Wardle F P and Lacey S J, Vibration Research in RHP. Acoustics Bulletin.外文資料：An Overview of Bearing Vibration AnalysisDr. S. J. LaceyEngineering Manager, Schaeffler (UK) Ltd AbstractVibration produced by rolling bearings can be complex and can result from geometrical imperfections during the manufacturing process, defects on the rolling surfaces or geometrical errors in associated components. Noise and vibration is becoming more critical in all types of equipment since it is often perceived to be synonymous with quality and often used for predictive maintenance. In this article the different sources of bearing vibration are considered along with some of the characteristic defect frequencies that may be present. Some examples of how vibration analysis can be used to detect deterioration in machine condition are also given.Keywords: Bearing Vibration, maintenance engineering, reliability engineering, Vibration detectionINTRODUCTIONRolling contact bearings are used in almost every type of rotating machinery whose successful and reliable operation is very dependent on the type of bearing selected as well as the precision of all associated components, i.e. shaft, housing, spacers, nuts etc. Bearing engineers generally use fatigue as the normal failure mode, on the assumption that the bearings are properly installed, operated and maintained. Today, because of improvements in manufacturing technology and materials, it is generally the case that bearing fatigue life, which is related to sub-surface stresses, is not the limiting factor and probably accounts for less than 3% of failures in service.Unfortunately though, many bearings fail prematurely in service because of contamination, poor lubrication, temperature extremes, poor fitting/fits, unbalance and misalignment. All these factors lead to an increase in bearing vibration and condition monitoring has been used for many years to detect degrading bearings before they catastrophically fail (with the associated costs of downtime or significant damage to other parts of the machine).Rolling element bearings are often used in noise sensitive applications, e.g. household appliance electric motors which often use small to medium size bearings. Bearing vibration is therefore becoming increasingly important from both an environmental consideration and because it is synonymous with quality.It is now generally accepted that quiet running is synonymous with the form and finish of the rolling contact surfaces. As a result, bearing manufacturers have developed vibration tests as an effective method for measuring quality. A common approach is to mount the bearing on a quiet running spindle and measure the radial velocity at a point on the bearing’s outer ring and in three frequency bands, viz. 50-300, 300-1800 and 1800-10000 Hz. The bearing must meet RMS velocity limits in all three frequency bands.in most situations bearing vibration cannot be measured directly and so the bearing vibration signature is modified by the machine structure, this situation being further complicated by vibration from other equipment on the machine, i.e. electric motors, gears, belts, hydraulics, structural resonances etc. This often makes the interpretation of vibration data difficult other than by a trained specialist and can in some situations lead to a mis-diagnosis, resulting in unnecessary machine downtime and costs.In this paper the sources of bearing vibration are discussed along with the characteristic vibration frequencies that are likely to be generated.SOURCES OF VIBRATIONRolling contact bearings represents a complex vibration system whose components – i.e. rolling elements, inner raceway, outer raceway and cage – interact to generate complex vibration signatures. Although rolling bearings are manufactured using high precision machine tools and under strict cleanliness and quality controls, like any other manufactured part they will have degrees of imperfection and generate vibration as the surfaces interact through a combination of rolling and sliding. Nowadays, although the amplitudes of surface imperfections are in the order of nanometres, significant vibrations can still be produced in the entire audible frequency range (20 Hz – 20 kHz).The level of the vibration will depend upon many factors, including the energy of the impact, the point at which the vibration is measured and the construction of the bearing.Variable complianceUnder radial and misaligning loads bearing vibration is an inherent feature of rolling bearings even if the bearing is geometrically perfect and is not therefore indicative of poor quality. This type of vibration is often referred to as variable compliance and occurs because the external load is supported by a discrete number of rolling elements whose position with respect to the line of action of the load continually changes with time (see Figure 1).圖 1Variable compliance vibration is heavily dependent on the number of rolling elements supporting the externally applied load; the greater the number of loaded rolling elements, the less the vibration. For radially loaded or misaligned bearings ‘running clearance’ determines the extent of the load region, and hence, in general, variable compliance increases with clearance. Running clearance should not be confused with radial internal clearance (RIC), the former normally being lower than the RIC due to interference fit of the rings and differential thermal expansion of the inner and outer rings during operation.Variable compliance vibration levels can be higher than those produced by roughness and waviness of the rolling surfaces. However, in applications where vibration is critical it can be reduced to a negligible level by using ball bearings with the correct level of axial pre-load.Geometrical imperfectionsBecause of the very nature of the manufacturing processes used to produce bearing components geometrical imperfections will always be present to varying degrees depending on the accuracy class of the bearing. For axially loaded ball bearings operating under moderate speeds the form and surface finish of the critical rolling surfaces are generally the largest source of noise and vibration. Controlling component waviness and surface finish during the manufacturing process is therefore critical since it may not only have a significant effect on vibration but also may affect bearing life.It is convenient to consider geometrical imperfections in terms of wavelength compared with the width of the rolling element-raceway contacts. Surface features of wavelength of the order of the contact width or less are termed roughness, whereas longer wavelength features are termed waviness (see Figure 2).圖 2SURFACE ROUGHNESSSurface roughness is a significant source of vibration when its level is high compared with the lubricant film thickness generated between the rolling element-raceway contacts (see Figure 2). Under this condition surface asperities can break through the lubricant film and interact with the opposing surface, resulting in metal-to-metal contact. The resulting vibration consists of a random sequence of small impulses which excite all the natural modes of the bearing and supporting structure.Surface roughness produces vibration predominantly at frequencies above sixty times the rotational speed of the bearing. Thus the high frequency part of the spectrum usually appears as a series of resonances.A common parameter used to estimate the degree of asperity interaction is the lambda ratio (Λ ). This is the ratio of lubricant film thickness to composite surface roughness and is given by the expressionΛ = h (σЪ 2 + σr 2)0.5 where Λ = degree of asperity interactionh = the lubricant film thicknessσЪ = RMS roughness of the ballσr = RMS roughness of the racewayIf we assume that the surface finish of the raceway is twice that of rolling element, then for a typical lubricant film thickness of 0.3μm surface finishes better than 0.06 μm are required to achieve a Λ value of three and a low incidence of asperity interaction. For a lubricant film thickness of 0.1_m surface finishes better than 0.025 _m are required to achieve Λ=3. The effect of Λ on bearing life is shown in Figure 3.圖 3If Λ is less than unity it is unlikely that the bearing will attain its estimated design life because of surface distress, which can lead to a rapid fatigue failure of the rolling surfaces. In general, Λ ratios greater than three indicate complete surface separation. A transition from full EHL (elastohydrodynamic lubrication) to mixed lubrication (partial EHL film with some asperity contact) occurs in the Λ range .WavinessFor longer wavelength surface features, peak curvatures are low compared with that of the Hertzian contacts and rolling motion is continuous with the rolling elements following the surface contours. The relationship between surface geometry and vibration level is complex, being dependent upon the bearing and contact geometry as well as conditions of load and speed. Waviness can produce vibration at frequencies up to approximately three hundred times rotational speed but is usually predominant at frequencies below sixty times rotational speed. The upper limit is attributed to the finite area of the rolling element raceway contacts which average out the shorter wavelength features.In the direction of rolling, elastic deformation at the contact attenuates simple harmonic waveforms over the contact width (see Figure 4).圖 4The level of attenuation increases as wavelength decreases until, in the limit, for a wavelength equal to the contact width, waviness amplitude is theoretically zero. The contact length also attenuates short wavelength surface features. Generally poor correlation can exist between parallel surface height profiles taken at different points across the tracks and this averages measured waviness amplitudes to a low level. For typical bearing surfaces poor correlation of parallel surface heights profiles only exists at shorter wavelengths.Even with modern precision machining technology waviness cannot be eliminated completely and an element of waviness will always exist albeit at relatively low levels. As well as the bearing itself, the quality of the associated components can also affect bearing vibration and any geometrical errors on the outside diameter of the shaft or bore of the housing can be reflected on the bearing raceways with the associated increase in vibration. Therefore, careful attention is required to the form and precision of all associated bearing components. Discrete defectsWhereas surface roughness and waviness result directly from the bearing component manufacturing processes, discrete defects refer to damage of the rolling surfaces due to assembly, contamination, operation, mounting, poor maintenance etc. These defects can be extremely small and difficult to detect and yet can have a significant impact on vibration-critical equipment or can result in reduced bearing life. This type of defect can take a variety of forms, viz. indentations, scratches along and across the rolling surfaces, pits, debris and particles in the lubricant. Bearing manufacturers have adopted simple vibration measurements on the finished product to detect such defects but these tend to be limited by the type and size of bearing. An example of this type of measurement is shown in Figures 5(a) and 5(b) where, compared to a good bearing, the discrete damage on a bearing outer ring raceway has produced a characteristically impulsive vibration which has a high peak/RMS ratio. Where a large number of defects occurs individual peaks are not so clearly defined but the RMS vibration level is several times greater than that normally associated with a bearing in good conditio圖 5（a）圖 5（b）Bearing characteristic frequenciesAlthough the fundamental frequencies generated by rolling bearings are expressed by relatively simple formulas they cover a wide frequency range and can interact to give very complex signals. This is often further complicated by the presence on the equipment of other sources of mechanical, structural or electro-mechanical .REFERENCES1.Harris T A, Rolling Bearing Analysis (4th Ed), Wiley, New York, 2001.2.Lacey S J, Vibration monitoring of the internal centreless grinding process, Part 1: mathematical models. Proc Instn Mech Engrs. Vol 24. 1990.3.Lacey S J, Vibration monitoring of the internal centreless grinding process, Part 2: experimental results. Proc Instn Mech Engrs. Vol 24. 1990.4.Wardle F P and Lacey S J, Vibration Research in RHP. Acoustics Bulletin.