旋轉(zhuǎn)機(jī)械轉(zhuǎn)子的平衡外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯

旋轉(zhuǎn)機(jī)械轉(zhuǎn)子的平衡外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯,旋轉(zhuǎn),機(jī)械,轉(zhuǎn)子,平衡,外文,文獻(xiàn),翻譯,中英文 附錄一 旋轉(zhuǎn)機(jī)械轉(zhuǎn)子的平衡 轉(zhuǎn)子平衡的目的是，當(dāng)在現(xiàn)場安裝，實(shí)現(xiàn)令人滿意的運(yùn)行。這意味著不大于振動(dòng)的可接受大小是由留在轉(zhuǎn)子的不平衡決定的。在轉(zhuǎn)子靈活的情況下，這也意味著不大于偏轉(zhuǎn)的可接受大小便發(fā)生在轉(zhuǎn)子以任何速度達(dá)到最大的服務(wù)的速度。 大多數(shù)的轉(zhuǎn)子是整機(jī)組裝之前的平衡，因?yàn)槭潞螅锌赡苤挥杏邢薜脑L問轉(zhuǎn)子。 ISO按照自己的平衡要求分類轉(zhuǎn)子，并建立剩余不平衡的評定方法。在ISO還演示了如何在平衡設(shè)施使用的標(biāo)準(zhǔn)可能源自對組裝和安裝機(jī)器或由轉(zhuǎn)子不平衡指定限額規(guī)定的振動(dòng)限制。 如果這種限制可用，它可以由ISO10876和ISO7919在振動(dòng)性上得到，并從在允許的剩余平衡方面的ISO1940-1。 （見ISO11342平衡柔性轉(zhuǎn)子的方法） 轉(zhuǎn)子不平衡的原因 制造業(yè) - 原因 許多原因被列為有助于不平衡狀況，包括材料的問題，如密度，孔隙率，空隙和氣孔。制造問題，如畸形鑄件，偏心加工和裝配差。失真的問題，如旋轉(zhuǎn)應(yīng)力，空氣動(dòng)力學(xué)和溫度的變化。甚至固有轉(zhuǎn)子的設(shè)計(jì)標(biāo)準(zhǔn)是無法避免的。在機(jī)器的操作壽命期間許多這些發(fā)生在制造過程中，其他人。雖然一些更正偏心可以平衡抵消，這是一種妥協(xié)。動(dòng)平衡不應(yīng)該是替代加工不良或其他妥協(xié)的生產(chǎn)實(shí)踐。 在制造過程中，如果不采取適當(dāng)?shù)恼樟希源_保鑄件是健全的，并加工是同心的，那么它遵循兩個(gè)軸和裝配的轉(zhuǎn)子將在平衡（里昂，1998）的狀態(tài)下 裝配 - 原因 如前所述，當(dāng)轉(zhuǎn)子正在制造的不平衡發(fā)生原因很多。在這些原則是公差的堆疊起來。當(dāng)一個(gè)均衡軸和一個(gè)良好平衡轉(zhuǎn)子。 必要的裝配公差可允許徑向位移，這將產(chǎn)生一個(gè)徹頭徹尾的平衡狀態(tài)。添加鍵和鍵槽的增加的問題。雖然ISO標(biāo)準(zhǔn)確實(shí)存在的軸和裝修主要公約（見ISO8821），在實(shí)踐中，不同廠家按照自己的程序。一些使用全鍵，一些使用半鍵，一些在無鑰匙 因此，當(dāng)一個(gè)單元被組裝和永久鍵被添加，不平衡往往會(huì)的結(jié)果。通過ISO規(guī)定的現(xiàn)代化平衡公差，API，ANSI等，迫使，在ISO標(biāo)準(zhǔn)中列出的約定執(zhí)行。如果不這樣做將意味著，在這些標(biāo)準(zhǔn)中規(guī)定的低層次的平衡公差就不可能實(shí)現(xiàn)（里昂，1998年）。 安裝機(jī) - 原因 當(dāng)轉(zhuǎn)子已經(jīng)在服務(wù)了一段時(shí)間，各種其他因素可以向平衡狀態(tài)。這些包括腐蝕，磨損，變形，和沉積積聚。存款也可以折斷不均勻，從而導(dǎo)致嚴(yán)重的不平衡。這特別適用于風(fēng)機(jī)，鼓風(fēng)機(jī)，壓縮機(jī)等旋轉(zhuǎn)設(shè)備的處理過程的變量。例行檢查和清潔可以最小化的效果，但最終的機(jī)器將必須從服務(wù)中移除用于平衡。 當(dāng)然大的不平衡，需要重量大的校正并且除非小心，這可能對轉(zhuǎn)子的完整性產(chǎn)生不利影響。濃縮的重調(diào)整（是否添加或帶走）在給定的點(diǎn)可以削弱轉(zhuǎn)子。這可能會(huì)導(dǎo)致它當(dāng)在操作速度紡絲偏轉(zhuǎn)，從而誘導(dǎo)對軸承和造紙機(jī)框架（里昂，1998）有害的振動(dòng)。 其他原因 不平衡的另一個(gè)原因，是不是顯而易見，是轉(zhuǎn)子類型之間的差異。有兩種不同的類型 - 剛性和柔性。 如果轉(zhuǎn)子是在70％以下操作 - 其臨界速度的75％，可以認(rèn)為是（諧振發(fā)生在其中，即其自然頻率的速度）是一種靈活的轉(zhuǎn)子。如果工作溫度低于這個(gè)速度它被認(rèn)為是剛性的。 剛性轉(zhuǎn)子可以是在兩個(gè)端平面平衡和將留在平衡服務(wù)時(shí)。一個(gè)靈活的轉(zhuǎn)子將需要多平面平衡。如果轉(zhuǎn)子低速動(dòng)平衡機(jī)假定它是剛性的平衡，然后在服務(wù)變得靈活，那么失衡，因而高振動(dòng)，會(huì)是這個(gè)結(jié)果。 典型的機(jī)器，它適合這一類，包括蒸汽和燃?xì)鉁u輪機(jī)，??多級離心式泵，壓縮機(jī)和紙卷。在造紙行業(yè)尤其是，??利用滾動(dòng)平衡方法時(shí)，造紙機(jī)均在低速運(yùn)行的滿意，現(xiàn)在是不夠的。由于舊機(jī)器加快，并安裝了新的高速機(jī)，精密軋輥平衡是強(qiáng)制性的。如果不這樣做會(huì)導(dǎo)致卷變形，可影響產(chǎn)品的質(zhì)量，甚至造成結(jié)構(gòu)損壞。用于生產(chǎn)具有最小偏轉(zhuǎn)或拉桿在其運(yùn)行速度范圍內(nèi)，平衡軸的方法。是一種多面的技術(shù)。沿輥的長度是至關(guān)重要的平衡平面的選擇（里昂 1998年）。 平衡旋轉(zhuǎn)部件 檢查靜態(tài)平衡的方法 有測試旋轉(zhuǎn)部分的站立或靜平衡的幾種方法。即有時(shí)用于飛輪等的簡單方法，通過該圖中，圖2所示。 1.精確的軸 通過成品輪，然后將其安裝在仔細(xì)拉平“緯線”A.如果車輪處于不平衡狀態(tài)的孔中插入時(shí)，它會(huì)變成直到重側(cè)是向下。當(dāng)站在任何位置制衡和降低重心部分的結(jié)果，它被說成是在站立或靜態(tài)平衡。 另一個(gè)測試其用于盤形零件示于圖。 2以下。盤D被安裝在附連到一個(gè)可調(diào)節(jié)的橫滑板B.后者由表C，其是攜帶的垂直軸 由一個(gè)刀刃狀軸承支撐。具有調(diào)節(jié)-能夠螺桿重量W在其下端擺動(dòng) 從橫滑動(dòng)B.懸浮為了測試盤D的靜態(tài)平衡，滑動(dòng)B被調(diào)整，直到擺錘指針E固定到刻度F.盤D然后接通中途不移動(dòng)滑動(dòng)圍繞的中心重合，如果指示燈保持靜止，則說明該磁盤是平衡這個(gè)特殊的位置上。測試，然后重復(fù)10或12的其他位置，并且重側(cè)減小，通常通過鉆出所需的金屬量。其他一些設(shè)備，用于測試靜態(tài)平衡是在這個(gè)同樣的原則設(shè)計(jì)的。 檢查動(dòng)平衡的方法 圓柱形轉(zhuǎn)子的靜態(tài)平衡，而不是處于平衡狀態(tài)時(shí)，在高速旋轉(zhuǎn)。如果部件是在一個(gè)薄的磁盤，靜平衡，如果小心做的，也許準(zhǔn)確高速的形式。然而，如果旋轉(zhuǎn)部分是長相對于其直徑，以及不平衡部中是在相對端或在不同的平面的平衡，以抗衡充當(dāng)這些重部件的離心力，當(dāng)它們被快速旋轉(zhuǎn)。這個(gè)過程被稱為一個(gè)正在運(yùn)行的平衡或動(dòng)態(tài)均衡。 為了說明，如果一個(gè)重的部分位于的H（圖3），并且為H 1的另一重的部分，可以確切地抵消了其它氣缸是固定的，并且該靜態(tài)平衡可能是足夠的一部分剛性安裝并旋轉(zhuǎn)以相對慢的速度;但是當(dāng)速度是非常高的，如在渦輪轉(zhuǎn)子等，重群眾H和H 1中，在不同的平面之中，在由于離心力的作用，這會(huì)導(dǎo)致過度的應(yīng)變和損害性不平衡狀態(tài)振動(dòng)。 理論上，以獲得完美的運(yùn)行平衡，重的部分的精確位置應(yīng)通過減少其重量，或者通過添加實(shí)現(xiàn)平衡 配重相對各部分和在適當(dāng)?shù)陌霃降耐黄矫嫔?但是，如果旋轉(zhuǎn)部分 剛性地安裝在剛性軸上，正在運(yùn)行的平衡是足夠精確的實(shí)際用途可以通過位于參考不平衡零件比較少制衡加權(quán)裝置得到。 平衡機(jī) 平衡機(jī)用于檢測在轉(zhuǎn)子的不平衡質(zhì)量的量和位置。它是旋轉(zhuǎn)的一組彈簧的安裝軸承的轉(zhuǎn)子的裝置。與軟軸承，任何不平衡將導(dǎo)致轉(zhuǎn)子移動(dòng)至約作為它旋轉(zhuǎn)。機(jī)器測量運(yùn)動(dòng)的相位角和振幅，并計(jì)算其必須存在以使運(yùn)動(dòng)的不平衡。適當(dāng)?shù)男拚涂梢杂刹僮髡撸ú悸搴眨π粮瘢?008）進(jìn)行。 平衡的基本方法 轉(zhuǎn)子可以通過與軸承中心（諾菲爾德，2006）對準(zhǔn)的轉(zhuǎn)子質(zhì)量平衡。 轉(zhuǎn)子是對稱的，除了不平衡米的半徑r：U= M* R= M* E U = M *?因此E = U / M = M * R / M 不平衡質(zhì)量m半徑r等于ü轉(zhuǎn)子不平衡。由轉(zhuǎn)子質(zhì)量分這和我們得到 “e”的，這是一種衡量不平衡的，獨(dú)立于轉(zhuǎn)子質(zhì)量。它被稱為質(zhì)量偏心，或 具體的不平衡。它是從軸承中心的質(zhì)量中心的位移。 質(zhì)量軸 當(dāng)我們強(qiáng)迫一個(gè)目的是旋轉(zhuǎn)約一個(gè)限定軸承軸線有用于旋轉(zhuǎn)軸的固定參考（軸承軸）。如果質(zhì)量不能均勻分布有關(guān)固定軸，然后我們有不平衡。關(guān)于該質(zhì)量均勻分布的軸被定義為質(zhì)心軸 質(zhì)量偏心的'e'是不平衡的，在質(zhì)譜軸的位移和軸承方面軸的量度。單位是線性的；英寸，毫米。偏心乘以轉(zhuǎn)子質(zhì)量給出不平衡。單位是質(zhì)量和偏心組合。 平衡定義 轉(zhuǎn)子要旋轉(zhuǎn)關(guān)于它的質(zhì)量軸，但我們希望它旋轉(zhuǎn)約軸承軸線。結(jié)果是軸承上的力，軸承的振動(dòng)或兩者的組合（諾菲爾德，2006）。 它被定義為，通過該轉(zhuǎn)子的質(zhì)量分布進(jìn)行檢查，并在必要的步驟，以確保調(diào)整該軸承上的頻率對應(yīng)于服務(wù)的速度的刊物和/或力的振動(dòng)是在規(guī)定范圍內(nèi)（ISO 1925）。 對于給定的不平衡狀態(tài)的振動(dòng)是負(fù)相關(guān)，并且在軸承的力有直接關(guān)系，該軸承的剛度（ISO 1925）。不平衡不是由外部外觀，但由振動(dòng)示或強(qiáng)制產(chǎn)生。轉(zhuǎn)子可能會(huì)鉆在外面一個(gè)洞。這可能是有以校正不平衡，而不是作為不平衡（諾菲爾德，2006）的原因。 平衡機(jī)是米為不平衡，并使得轉(zhuǎn)子條件真實(shí)測量。 轉(zhuǎn)子剛度 有若干轉(zhuǎn)子的分類，這取決于靈活性，操作速度，和其他因素（ISO 5243）的。 1類是剛性轉(zhuǎn)子 - 這包括90％的應(yīng)用 類2是轉(zhuǎn)子不在剛性或具有質(zhì)量分布的特點(diǎn)，但是，可以使用改進(jìn)的均衡技術(shù)（選擇的校正平面的是這里的關(guān)鍵）進(jìn)行平衡。 3級和4是撓性轉(zhuǎn)子 注意一些電機(jī)需要在特定的速度進(jìn)行平衡，以兩種速度甚至熱的時(shí)候。熱效應(yīng)可以引起失真，這反過來會(huì)導(dǎo)致不平衡，這可能會(huì)導(dǎo)致更多的失真。 靜不平衡 它被定義為通過所述轉(zhuǎn)子的質(zhì)量中心和由定義可以在單個(gè)位置通過添加或符合質(zhì)量中心去除材料來校正作用。質(zhì)量軸要保持平行于軸承軸線?？稍诓恍D(zhuǎn)該轉(zhuǎn)子（諾菲爾德，2006年）來檢測靜態(tài)失衡。 平衡在刀刃可以校正為靜態(tài)失衡，但沒有不平衡的剩余量中的任何質(zhì)量測量 - 取決于摩擦，風(fēng)，軸的直徑，轉(zhuǎn)子的質(zhì)量等，這不面對檢查不平衡對已知標(biāo)準(zhǔn)的基本定義。大多數(shù)單機(jī)平衡做的旋轉(zhuǎn)（離心式）平衡機(jī)。非旋轉(zhuǎn)（引力）平衡用于大批量生產(chǎn)轉(zhuǎn)子粗寬容。 （這些測量彈簧或使用兩個(gè)稱重傳感器的偏移力的校正偏差。） 偶不平衡 偶不平衡是當(dāng)你平衡的刀刃，不糾正失衡的真正根源是什么，你得到的。下圖顯示了一個(gè)轉(zhuǎn)子有一個(gè)不平衡的一端是靜態(tài)的平衡與矯正結(jié)束不平衡相反的。結(jié)果是，它看起來不錯(cuò)的刀刃，但會(huì)動(dòng)搖像瘋了似的，只要它旋轉(zhuǎn)。需要注意的是質(zhì)量軸交叉于中心幾何軸線所以沒有靜態(tài)失衡 動(dòng)態(tài)不平衡，在不同平面的平衡機(jī)，校正程序 有跡象表明，我們能夠平衡公差準(zhǔn)則中使用的國際標(biāo)準(zhǔn)，但他們本質(zhì)上是非常普遍的。僅僅依靠對這些標(biāo)準(zhǔn)的人可以給你一個(gè)寬容是一個(gè)相當(dāng)遙遠(yuǎn)的最佳。 需要的是最具效益的無軸承過早失效或過度振動(dòng)來執(zhí)行。正確的方法來確定理想的平衡寬容度采取了一批良好制造轉(zhuǎn)子，平衡他們盡可能的低，然后運(yùn)行它們，并逐步增加直至不平衡的表現(xiàn)僅僅是可以接受的?，F(xiàn)在的不平衡可以測量和限制確定提供了良好的結(jié)果，這些轉(zhuǎn)子也應(yīng)的運(yùn)行條件下檢查振動(dòng)信號進(jìn)行分類什么其它的振動(dòng)可能會(huì)影響性能。 一個(gè)其它變量需要在生產(chǎn)過程中要考慮的 - 由于裝配平衡后發(fā)生并疊起的公差變化。電樞是平衡，然后軸承相加。電動(dòng)機(jī)配有一個(gè)驅(qū)動(dòng)皮帶輪或飛輪，其具有寬松的公差。其結(jié)果是在組件的百分比高振動(dòng)。 標(biāo)準(zhǔn) ISO 1940是基于機(jī)械振動(dòng)速度的測量中的ANSI規(guī)范是相同的，由美國國家標(biāo)準(zhǔn)協(xié)會(huì)打印。 API規(guī)范被寫入圍繞在石油化學(xué)工業(yè)泵的要求和不平衡水平轉(zhuǎn)子質(zhì)量和操作速度（諾菲爾德，2006）的功能分類。 ISO 1940是著名的在G代碼方面的振動(dòng)分級，雖然很多人不知道他們的意思很容易弄清楚，G2.5是一個(gè)嚴(yán)格的公差比G6.3。注意選詞這里，緊縮不一定好。 G2.5指為2.5毫米/秒特定條件下的振動(dòng)速度。不幸的是，它是理論值假定轉(zhuǎn)子紡紗在自由空間，以便它不涉及到實(shí)際操作條件。 ISO 1940采用的是一套標(biāo)準(zhǔn)，以可接受的振動(dòng)等級分類 - 低速船用柴油機(jī)具有粗級，而高速磨削主軸有一個(gè)非常嚴(yán)格的等級。最嚴(yán)格的等??級要求平衡在它自己的軸承和服務(wù)條件下的轉(zhuǎn)子。 得到的數(shù)字的例子 UPER =平衡寬容度 G可從下表中可以得到（ISO1940） 平衡質(zhì)量等級的不同群體的代表剛性電機(jī) API 610 API 610是基于下述式（使用SI單位）： T = 6350W / N ?公斤W =轉(zhuǎn)子重量 ?N =速度RPM ?T =寬容公斤 注意公式不起作用100％。對于高速泵，寬容可以得到可笑緊。 一個(gè)非常具體的問題的API規(guī)范，它不作任何津貼平衡工具的錯(cuò)誤，并承擔(dān)間隙的喬木。這樣做是為了平衡到平衡器，以便允許裝配誤差。其結(jié)果是，一個(gè)高振動(dòng)泵可被剝離下來，并在葉輪平衡檢查才發(fā)現(xiàn)高不平衡（實(shí)際上由于非重復(fù)性安裝的）。再平衡和重新組裝后仍可能存在高的不平衡，或相反，它可能是確定。次要的結(jié)果可能是運(yùn)營商失去信心，平衡機(jī)和模具。 （對于轉(zhuǎn)子）最后，店鋪測試的機(jī)器，組裝有平衡轉(zhuǎn)子，在其最大連續(xù)速度，或在特定的運(yùn)行速度范圍內(nèi)的任何其他速度操作期間，峰值向未過濾的振動(dòng)，在任何平面上的峰值振幅，上相鄰并相對于每個(gè)徑向軸承，可能不超過以下的值（基于SI）或2.0密耳（50微米）的軸測量的，取以下（布洛赫·辛格，2008年）： ?A =振幅未經(jīng)過濾的振動(dòng)，密爾（微米）峰峰值 ?N =最大連續(xù)轉(zhuǎn)速，轉(zhuǎn)/分（RPM） 實(shí)際的例子： 如果我們有一個(gè)轉(zhuǎn)子的質(zhì)量為235公斤，420毫米在半徑，以及運(yùn)行在3000 RPM的速度，通過2軸承支撐。 基于ISO 1940的圖表或公式G1允許的平衡，電子會(huì)被解讀為3 g.mm/kg，這給了我們705 g.mm（后次由轉(zhuǎn)子質(zhì)量獲得U）。 基于API 610，6350xMass /速度= 497gmm。 允許不平衡質(zhì)量（次半徑）會(huì)為1.6g。 基于API 610，1.2克。 （ISO定義建議核實(shí)平衡機(jī)操作進(jìn)行每年一次或每3個(gè)月為航空應(yīng)用。） UPER分配到校正平面（IRD平衡，2009年） 校正平面：垂直到平衡校正軸的任何平面上。計(jì)算公差ú在不同的平面上，請參考ISO 1940-1中使用的方法。 UPER必須分配給平衡校正平面用于根據(jù)轉(zhuǎn)子的尺寸平面。 對于轉(zhuǎn)子在一個(gè)校正平面平衡，所有的UPER的適用于校正平面。 對于轉(zhuǎn)子在兩個(gè)矯正平面平衡，UPER必須分配給基于轉(zhuǎn)子的配置和尺寸的每個(gè)校正平面。 對稱轉(zhuǎn)子（IRD平衡，2009） 規(guī)則對稱轉(zhuǎn)子： ?修正平面是軸承之間。 ?距離“B”大于1/3“D”。 ?校正平面是從重心等距。 UPER左= UPER右= UPER/2 當(dāng)校正平面不是從重心，然后等距離 UPER左= UPER（HR/ B）UPER右= UPER（HL/ B） 注意UPER向左或向右UPER應(yīng)不超過30％或70％以上。 轉(zhuǎn)子與出站校正平面（IRD平衡，2009年） 兩個(gè)校正平面舷外軸承。 B>D 調(diào)整UPER由D / B值（減少UPER） UPER= UPER（D/ B）UPER=調(diào)整后的價(jià)值 當(dāng)校正平面不是從重心，然后等距離 UPER左= UPER（HR/ B）UPER右= UPER（HL/ B） 狹窄的轉(zhuǎn)子 規(guī)則懸臂和狹窄的轉(zhuǎn)子“ ?校正平面之間的距離是小于1/3的軸承之間的距離。 B<0.33e ?假設(shè)等于允許動(dòng)態(tài)軸承負(fù)荷 ?動(dòng)態(tài)改正的180?除了在各自的平面 ?分配UPER靜態(tài)和動(dòng)態(tài)剩余不平衡如下： 標(biāo)準(zhǔn)比較 該報(bào)告比較了三個(gè)標(biāo)準(zhǔn)：ISO（G6.3，G2.5，G1.0），MIL-STD和API。結(jié)論是，API標(biāo)準(zhǔn)要求的低殘余不平衡水平，并與該轉(zhuǎn)子的軸承較小不平衡力負(fù)荷。然而，為了達(dá)到這樣的結(jié)果不可能總是具有成本效益（IRD平衡，2009年）。 彎 曲 軸的軸是直的。在室溫下可能彎曲在滿負(fù)荷運(yùn)行時(shí)，尤其是如果有不均勻的加熱效果。過度的皮帶張力可以彎曲軸（也可導(dǎo)致快速軸承失效）。較長軸會(huì)下垂，如果他們沒有保持緩慢轉(zhuǎn)動(dòng)。另一軸的問題可導(dǎo)致加工誤差。它并非罕見叉車下車課程和所造成的影響的損害可能是致命的設(shè)備（諾菲爾德，2006）。 甲細(xì)長轉(zhuǎn)子，如驅(qū)動(dòng)軸，將彎曲高速。這不是不平衡的變化，但轉(zhuǎn)子的變形問題。不平衡耐受性和不平衡校正位置必須選擇，以確保安全運(yùn)行的運(yùn)行速度范圍。 平衡軸和裝配的關(guān)鍵 它往往是不可能的或經(jīng)濟(jì)上不可行，他們已組裝后，以平衡轉(zhuǎn)子和生產(chǎn)設(shè)備。因此，分別平衡。適當(dāng)?shù)钠胶馊莶畋皇┘?，使得?dāng)轉(zhuǎn)子側(cè)端都與相應(yīng)的鍵連接在一起，該組件將符合所要求的平衡容差和振動(dòng)嚴(yán)重性級別。然而，如果平衡的軸或轉(zhuǎn)子用于平衡配件之一時(shí)不同的密鑰約定已被使用，這是很可能的是，組合件的平衡誤差超過容許殘余不平衡（請參考ISO 8821平衡方法）。  附錄二 Rotating Machinery Rotor Balancing The aim of rotor balancing is to achieve satisfactory running when installed on site. It means no more than an acceptable magnitude of vibration is caused by the unbalance remaining in the rotor. In the case of a flexible rotor, it also means that not more than an acceptable magnitude of deflection occurs in the rotor at any speed up to the maximum service speed. Most rotors are balanced before machine assembly because afterwards, there may be only limited access to the rotor. ISO classifies rotor in accordance with their balancing requirements and establishes methods of assessment of residual unbalance. The ISO also shows how criteria for use in the balancing facility maybe derived from vibration limits specified for the assembled and installed machine or unbalance limits specified by the rotor. If such limits are not available, it may be derived from ISO 10876 and ISO 7919 in terms of vibration, and from ISO 1940-1 in terms of permissible residual balance. (See ISO 11342 for methods of balancing flexible rotor) ……………………………………………………………………………………………………… Causes of rotor unbalance Manufacturing - Causes Many causes are listed as contributing to an unbalance condition, including material problems such as density, porosity, voids and blowholes. Fabrication problems such as misshapen castings, eccentric machining and poor assembly. Distortion problems such as rotational stresses, aerodynamics and temperature changes. Even inherent rotor design criteria that cannot be avoided. Many of these occur during manufacture, others during the operational life of the machine. Whilst some corrections for eccentricity can be counteracted by balancing, it is a compromise. Dynamic balancing should not be a substitute for poor machining or other compromise manufacturing practices. In the manufacturing process, if proper care is taken to ensure that castings are sound and machining is concentric, then it follows that the two axis will coincide and the assembled rotor will be in a state of balance (Lyons, 1998). Assembly - Causes As previously stated, there are many reasons why unbalance occurs when a rotor is being fabricated. Principle among these is a stack up of tolerances. When a well-balanced shaft and a well-balanced rotor are united, the necessary assembly tolerances can permit radial displacement, which will produce an out of balance condition. The addition of keys and keyways adds to the problem. Although an ISO standard does exist for Shaft and Fitment Key Conventions (refer to ISO 8821), in practice, different manufacturers follow their own procedures. Some use a full key, some a half key and some no key at all. Thus, when a unit is assembled and the permanent key is added, unbalance will often be the result. The modern balancing tolerances specified by ISO, API, ANSI and others make it imperative that the conventions listed in the ISO standard be followed. Failure to do so will mean that the low-level balance tolerances specified in these standards will be impossible to achieve (Lyons, 1998). Installed Machines - Causes When a rotor has been in service for some time, various other factors can contribute to the balance condition. These include corrosion, wear, distortion, and deposit build up. Deposits can also break off unevenly, which can lead to severe unbalance. This particularly applies to fans, blowers, compressors and other rotating devices handling process variables. Routine inspection and cleaning can minimize the effect, but eventually the machines will have to be removed from service for balancing. Large unbalances will of course require large weight corrections and unless care is taken, this can have a detrimental effect on the integrity of the rotor. Concentrating a weight adjustment (whether adding or taking away) at a given point can weaken the rotor. For example paper rolls are fabricated from tubing and large additions or removal of weight can affect the strength of the walls of the roll. This may cause it to deflect when spinning at operating speed and thus induce harmful vibrations on the bearings and paper machine frame (Lyons, 1998). Other Causes Another cause of unbalance that is not readily apparent, is the difference between types of rotors. There are two distinct types - rigid and flexible. If a rotor is operating within 70% - 75% of its critical speed (the speed at which resonance occurs, i.e. its natural frequency) it can be considered to be a flexible rotor. If it is operating below that speed it is considered rigid. A rigid rotor can be balanced at the two end planes and will stay in balance when in service. A flexible rotor will require multi-plane balancing. If a rotor is balanced on a low speed balancing machine assuming it is rigid and then in service becomes flexible, then unbalance and thus high vibration, will be the result. Typical machines, which fit this category, include steam and gas turbines, multistage centrifugal pumps, compressors and paper rolls. In the paper industry particularly, use of roll balancing methods that were satisfactory when paper machines were running at low speed, are now inadequate. As older machines speed up and new high-speed machines are installed, precision roll balancing is mandatory. Failure to do so will result in roll deflections which can effect product quality and even cause structural damage. The method used to produce a balanced roll with minimum deflection or whip over its operating speed range is a multi-plane technique. The choice of the balancing planes along the length of the roll is vital (Lyons, 1998). Balancing rotating parts Methods to check for static balancing There are several methods of testing the standing or static balance of a rotating part. A simple method that is sometimes used for flywheels, etc., is illustrated by the diagram, Fig. 1. An accurate shaft is inserted through the bore of the finished wheel, which is then mounted on carefully leveled “parallels” A. If the wheel is in an unbalanced state, it will turn until the heavy side is downward. When it will stand in any position as the result of counterbalancing and reducing the heavy portions, it is said to be in standing or static balance. Another test which is used for disk-shaped parts is shown in Fig. 2 below. The disk D is mounted on a vertical arbor attached to an adjustable cross-slide B. The latter is carried by a table C, which is supported by a knife-edged bearing. A pendulum having an adjust-able screw-weight W at the lower end is suspended from cross-slide B. To test the static balance of disk D, slide B is adjusted until pointer E of the pendulum coincides with the center of a stationary scale F. Disk D is then turned halfway around without moving the slide, and if the indicator remains stationary, it shows that the disk is in balance for this particular position. The test is then repeated for ten or twelve other positions, and the heavy sides are reduced, usually by drilling out the required amount of metal. Several other devices for testing static balance are designed on this same principle. Methods to check for dynamic balancing A cylindrical maybe in perfect static balance and not be in a balanced state when rotating at high speed. If the part is in the form of a thin disk, static balancing, if carefully done, maybe accurate at high speeds. However if the rotating part is long in relative to its diameter, and the unbalanced portion are at opposite ends or in different planes. The balancing must be done so as to counter act the centrifugal force of these heavy parts when they are rotating rapidly. This process is known as a running balance or dynamic balancing. To illustrate, if a heavy section is located at H (Fig. 3), and another correspondingly heavy section at H 1 , one may exactly counterbalance the other when the cylinder is stationary, and this static balance may be sufficient for a part rigidly mounted and rotating at a comparatively slow speed; but when the speed is very high, as in turbine rotors, etc., the heavy masses H and H 1 , being in different planes, are in an unbalanced state owing to the effect of centrifugal force, which results in excessive strains and injurious vibrations. Theoretically, to obtain a perfect running balance, the exact positions of the heavy sections should be located and the balancing effected either by reducing their weight or by adding counterweights opposite each section and in the same plane at the proper radius; but if the rotating part is riidly mounted on a stiff shaft, a running balance that is sufficiently accurate for practical purposes can be obtained by means of comparatively few counterbalancing weights located with reference to the unbalanced parts. Balancing machine A balance machine is used to detect the amount and location of the unbalanced masses on a rotor. It is a device that spins the rotor a set of spring mounted bearings. With the soft bearings, any imbalance will cause the rotor to move about as it spins. The machine measures the phase angle and amplitude of the movement, and computes the unbalance which must be present to cause the motion. Appropriate corrections can then be made by the operator (Bloch & Singh, 2008). Basic methods of balancing Rotor can be balanced by aligning the rotor mass with the bearing centers (Norfield, 2006) The rotor is symmetrical except for the unbalanced m at radius r: U = m*r = M*e U = M*e so e = U/M = m*r/M The unbalance mass m times its radius r equals U Rotor unbalance. Divide this by rotor mass and we get ‘e’, which is a measure of unbalance that is independent of rotor mass. It is called mass eccentricity, or specific unbalance. It is the displacement of the mass center from the bearing center. Mass axis When we force an object to spin about a defined bearing axis there is a fixed reference for the rotation axis (bearing axis). If the mass is not evenly distributed about that fixed axis then we have unbalance. The axis about which the mass is evenly distributed is defined as the mass axis. The mass eccentricity ‘e’ is the measure of the unbalance in terms of the displacement of the mass axis and the bearing axis. Units are linear – inches or mm. The eccentricity multiplied by the rotor mass gives the unbalance. The units are the combination of mass and eccentricity – ounce.inches or gram.millimeter. Balancing defined The rotor wants to spin about its mass axis but we want it to spin about the bearing axis. The results are force on the bearings, vibration of the bearings or a combination of both (Norfield, 2006). It is defined as a procedure by which the mass distribution of a rotor is checked and, if necessary, adjusted in order to ensure that the vibration of the journals and/or forces on the bearings at a frequency corresponding to service speed are within specified limits (ISO 1925). For a given unbalance condition the vibration is inversely related, and force on the bearings is directly related, to the bearing stiffness (ISO 1925). Unbalance is not shown by the external appearance but by the vibration or force it generates. A rotor may have a hole drilled in the outside. That may be there to correct the unbalance rather than being the cause of the unbalance (Norfield, 2006). The balancing machine is the meter for unbalance, and makes real measurements of the rotor condition. Rotor rigidity There are a number of classifications of rotors, depending on flexibility, operating speed, and other factors (ISO 5243). Class 1 is rigid rotors – this covers 90% of application Class 2 is rotors that are not rigid or that have special characteristics of mass distribution but that can be balanced using a modified balancing technique (choice of correction planes is the key here). Class 3 and 4 are flexible rotors Note some motors need to be balanced at specific speeds, at two speeds or even when hot. Thermal effect can cause distortion that in turn causes unbalance, which can cause more distortion. Static unbalance It is defined as acting through the mass center of the rotor and by definition can be corrected at a single location by adding or removing material in line with the center of mass. Implicit in the definition is that the mass axis remains parallel to the bearing axis. Static unbalance can be detected without spinning the rotor (Norfield, 2006). Balancing on knife edges can correct for static unbalance but without any qualitative measurement of the remaining amount of unbalance – depends on friction, wind, shaft diameter, rotor mass, etc. This does not confront the basic definition of checking the unbalance against a known standard. Most single plane balancing is done on rotating (centrifugal) balancing machines. Non-rotating (gravitational) balancers are used for high volume production of rotors with coarse tolerance. (These measure the calibrated deflection of a spring or the offset force using two load cells.) Couple unbalance Couple unbalance is what you get when you balance on knife edges and don’t correct the real source of unbalance. The image below shows a rotor that had an unbalance at one end and was static balanced with correction of the end opposite the unbalance. Result is that