中英文文獻(xiàn)翻譯研磨機(jī)的最佳優(yōu)化設(shè)計(jì)

1、研磨機(jī)的最佳優(yōu)化設(shè)計(jì)摘要：研磨機(jī)的制造商正在盡量的減少傳動(dòng)給低振動(dòng)，高生產(chǎn)率的研磨機(jī)所增加的壓力。然而，實(shí)際上，運(yùn)行研磨的過(guò)度磨損的發(fā)生，研磨孔附近的裂縫的發(fā)展都可能帶來(lái)脫離的破碎和造成災(zāi)難性的結(jié)果。振動(dòng)等級(jí)的增加已經(jīng)在很多的新型研磨機(jī)中有所發(fā)現(xiàn)。現(xiàn)有的設(shè)計(jì)方法對(duì)于這種現(xiàn)象的解釋是不可靠的。本文能夠表述一種新的研磨機(jī)的設(shè)計(jì)方法，并寫(xiě)能夠很好的阻礙振動(dòng)的增加和不必要的磨損。最后，提供了研磨機(jī)的較好的設(shè)計(jì)方法。關(guān)鍵字：研磨機(jī) 過(guò)度磨損 破碎 振動(dòng) 新設(shè)計(jì) 標(biāo)注單位 c 聯(lián)結(jié)的扭力硬度 離心力 慣性力 滑塊慣性 電動(dòng)馬達(dá)轉(zhuǎn)子的兩極滑塊的慣性 研磨機(jī)的兩極滑塊的慣性 徑向支持的硬度 動(dòng)能 研磨區(qū)和引力

2、的中心之間的距離 徑向支持的距離 研磨齒或槌集合重量 瞬時(shí)慣性 槌的頻率交換振動(dòng) 潛在能量 推力 圓盤(pán)的半徑 重量 槌的引力中心的換置 鼓輪軸支持的換置 側(cè)軸或槌的坐標(biāo)的角度換置 圓盤(pán)的坐標(biāo)角度 初始頻率 鼓輪的旋轉(zhuǎn)速度 研磨的扭力震動(dòng)的天然頻率磨細(xì)傳輸一 介紹研磨機(jī)廣泛地被用于食物和谷粒工業(yè)。研磨機(jī)的一個(gè)典型結(jié)構(gòu)被顯示在圖 1.它由一個(gè)電動(dòng)馬達(dá)所組成 (1),這個(gè)馬達(dá)帶動(dòng)鼓輪聯(lián)結(jié)(2)。鼓輪包括一個(gè)圓盤(pán)(3)在輪軸上轉(zhuǎn)動(dòng)。(4)輪軸靠?jī)蓚€(gè)徑向支撐所支持。(5)它有二組桿: 一組桿(6)運(yùn)送槌,而另一組桿（7)運(yùn)送緩沖裝置。它們用來(lái)限制那槌搖擺按某一角度轉(zhuǎn)動(dòng)。(8)槌被聚集在一個(gè)桿上(6)，舉

3、例來(lái)說(shuō)五支槌,然后四支槌,在圓盤(pán)的相反邊上的等等,不同的槌被安裝( 舉例來(lái)說(shuō)在一邊上有五個(gè)，在另一邊上則有四個(gè)).那槌在外形上是矩形的并且有三個(gè)外部的邊緣被焊接在材料表面上面。他們被間隔的裝置所分開(kāi)。在研磨機(jī)被安置好之前，這個(gè)裝置是通過(guò)增加自己的重量來(lái)保持平衡的。一些公司甚至選擇槌以便它的總重量裝置在一支桿對(duì)所有的桿是相同的。整個(gè)的結(jié)構(gòu)集合在一個(gè)金屬包裝中被附上( 不在圖 1 中顯示).被供應(yīng)的谷物在包裝的頂端打開(kāi)。替換槌擊中落下的谷粒, 打碎它,并且磨細(xì)了碎片在包裝的底部從滑槽被收集。鼓旋轉(zhuǎn)的方向時(shí)常被顛倒用以證實(shí)槌的邊緣的磨損。在研磨機(jī)的操作中, 桿所連接的槌沒(méi)有與谷粒的直接接觸或磨細(xì)碎片

4、, 因?yàn)槟莻€(gè)桿被槌及其周?chē)臻g包圍。 與此同時(shí),周?chē)臻g的外部表面在與磨細(xì)的碎片直接的接觸中,不表示任何磨平的警告。在實(shí)際中，嚴(yán)格的震動(dòng)通常發(fā)生在相對(duì)較新的研磨機(jī)上。 深的裂縫在圓盤(pán)上通常會(huì)發(fā)展到洞附近。 裂縫以 45 度被定向到半徑和向圓盤(pán)的周邊部份 (見(jiàn)到圖 2),可能會(huì)造成脫離破碎的危險(xiǎn)。不平順的穿越在槌的竿上發(fā)生。深的凹槽在圓筒形的表面上發(fā)展到桿上.(見(jiàn)到圖 3) 槌上的洞會(huì)逐漸的變?yōu)闄E圓形這是由于圓形的邊緣。 槌的兩側(cè)表面在這個(gè)洞的附近會(huì)有一個(gè)沖擊負(fù)荷力來(lái)警示從其間隔中所具有的裝置。在槌上的離心力要比圓盤(pán)上的應(yīng)力小上好幾倍。 竿上的凹槽和槌上的橢圓形洞證明實(shí)際的連絡(luò)壓迫力超過(guò)生產(chǎn)壓迫

5、力,并且在槌上邊緣的沖擊標(biāo)志表明那槌正在被搖動(dòng)和旋轉(zhuǎn)?，F(xiàn)有的設(shè)計(jì)方法已經(jīng)證明和解釋這一種現(xiàn)象的不可能性。 要減少震動(dòng)的程度,人們不得不減少鼓的旋轉(zhuǎn)工作速度, 而這樣做必將會(huì)影響到生產(chǎn)效率。2 對(duì)于傳統(tǒng)研磨機(jī)的弱表現(xiàn)力的理論解釋和存在的問(wèn)題當(dāng)一個(gè)研磨機(jī)被裝配的時(shí)候, 通常36個(gè)槌以一種盤(pán)環(huán)的樣式被安裝在一個(gè)桿上。由于槌有不同的組成部分，因此,槌的分配沿著桿是不平順的。 當(dāng)鼓快速旋轉(zhuǎn)的時(shí)候,離心力會(huì)沿著半徑指向槌。由于不平順的槌的分配和槌的交錯(cuò)打在地面上 (五個(gè)槌在圓盤(pán)直徑的一邊上而另外的四個(gè)槌則在相反的方向上),由于離心力的分配不均發(fā)生,這將引起整個(gè)的鼓震動(dòng)。 這個(gè)鼓在兩個(gè)軸承的支持下保持穩(wěn)定,

6、 從動(dòng)態(tài)的觀點(diǎn)來(lái)分析，它被認(rèn)為是在兩個(gè)相同的彈力支持下作為一個(gè)整體。 當(dāng)做為兩個(gè)自由的振動(dòng)系統(tǒng)時(shí),它有二個(gè)模態(tài):(a) 當(dāng)槌在徑向方向上振動(dòng)時(shí), 它是跳躍振動(dòng);(b) 當(dāng)槌的一端輪軸移動(dòng)向上的和另一端移動(dòng)向下時(shí)，它是搖擺振動(dòng)。第一個(gè)模態(tài)有助于槌的搖擺振動(dòng)( 將會(huì)在以后被討論),而第二個(gè)模態(tài)對(duì)于槌擺脫其旋轉(zhuǎn)方向的不穩(wěn)定是有幫助的。 槌的搖動(dòng)作用在一個(gè)沖擊負(fù)荷的間隔裝置中,引起表面過(guò)度的磨損,而且槌的搖動(dòng)也造成連接槌和桿的面積的減少。 這就解釋桿 (凹槽) 和槌孔的過(guò)度磨損(邊緣區(qū)域的橢圓形形狀)。 問(wèn)題在于鼓的振動(dòng)共嗚來(lái)自傳輸?shù)倪^(guò)度沖擊。當(dāng)槌替換的時(shí)候,槌受制于離心力和他們自己的重量(見(jiàn)到圖 4

7、)。當(dāng)槌被垂直地排列的時(shí)候,沿著半徑的重量和離心力就會(huì)帶動(dòng)鼓運(yùn)動(dòng)。 當(dāng)槌被水平地排列的時(shí)候,離心力， fcf 的合量， fr和重量w,在鼓的一個(gè)旋轉(zhuǎn)方向上傾斜 , 在相反的方向中其他的也是同樣的。 因此，就引起了槌的搖擺振動(dòng)。這一種情形在工作速度 (鼓旋轉(zhuǎn)) 的共振,槌的跳躍振動(dòng)或傳輸?shù)呐ちφ駝?dòng)的共振的條件下，可能會(huì)變的很危險(xiǎn)。所有的這些可能性都被現(xiàn)存的設(shè)計(jì)方法給忽略了。磨碎谷物的碎片用于研磨相互接觸的表面磨損或者研磨桿和樞軸的孔洞,這樣做是不大可能的，因?yàn)榍逑锤綦x環(huán)和槌之間的相對(duì)較大的磨碎碎片是非常難的。它沒(méi)有清洗隔離環(huán)表面的研磨磨損，而這確是磨碎碎片主要的藏身之處。3 研磨機(jī)的固有振動(dòng)頻率

8、的決定條件如早前所討論的那樣, 鼓輪被認(rèn)為是有兩個(gè)自由度的擺動(dòng)系統(tǒng)。（見(jiàn)圖 5) 當(dāng)一鼓輪由于 m 和瞬時(shí)慣性 j合成振動(dòng)時(shí)(側(cè)軸水平的通過(guò)其中心c)振動(dòng),它表現(xiàn)為直線(xiàn)運(yùn)動(dòng): 它的中心 c沿著垂直線(xiàn)運(yùn)動(dòng) (換置 xc) 并且它繞者水平軸旋轉(zhuǎn)(角度換置). 作為一個(gè)有兩個(gè)自由度的系統(tǒng)，它能是被兩個(gè)獨(dú)立的參數(shù)x1和x2所表示，分別被兩個(gè)彈性硬度k1和k2支撐（齒輪支撐）發(fā)生偏轉(zhuǎn)。xc和p可以用x1和x2來(lái)表示： （1）運(yùn)動(dòng)的公式來(lái)源于拉格朗日等式: i=1,2,3,n ( 2 )對(duì)于在圖 5 中被顯示的保守系統(tǒng),沒(méi)有阻力和外加力, 這時(shí)其合力為q=0, 動(dòng)能的表達(dá)式k,和潛能p, 能依次寫(xiě)為下式:

9、 (3) (4)由公式（3）和（4）來(lái)引出并且替代它們進(jìn)入公式（2）,下列的兩個(gè)微分方程式能被如下獲得: (5) (6)這些能被從整理到下列公式中: (7) (8)x1和x2能用下式來(lái)取代： (9)由公式（9）來(lái)引出并且替代它們進(jìn)入公式（7）和（8），下列公式包含有圓周率w: (10)對(duì)于公式 (10) 的解決能被寫(xiě)成為： (11)4 槌的固有頻率的搖擺振動(dòng)的決定因素槌 (見(jiàn)到圖 6) 繞著a點(diǎn)旋轉(zhuǎn)并且它有兩種運(yùn)動(dòng)的類(lèi)型:以一定的角速度繞著圓盤(pán)上的o點(diǎn)旋轉(zhuǎn),并且旋轉(zhuǎn)振動(dòng)指向a點(diǎn)。盤(pán)的角度位置取決于坐標(biāo)，而且槌的角度位置通過(guò)角度坐標(biāo)表現(xiàn)出來(lái)。因此，槌是一個(gè)有離心作用的鐘擺。在科學(xué)文獻(xiàn)中有一組關(guān)于

10、離心作用的鐘擺的自然頻率振動(dòng)的統(tǒng)計(jì)數(shù)據(jù)。在有關(guān)機(jī)械振動(dòng)的書(shū)籍中，有一些實(shí)例被討論。例如, 在叁考文獻(xiàn)中1 中，有一個(gè)離心鐘擺的減振裝置被討論。 在叁考文獻(xiàn)2中，雙向轉(zhuǎn)動(dòng)的離心鐘擺被討論，并且它還指出了如何選出那些減少圓盤(pán)扭轉(zhuǎn)振動(dòng)的參數(shù)。在叁考文獻(xiàn)3中，雙重鐘擺的理論也被表現(xiàn)出來(lái)。然而,第一個(gè)鐘擺沒(méi)有指出一個(gè)完全的旋轉(zhuǎn)方式。 因此，它不能夠被認(rèn)為是一個(gè)離心鐘擺。所以,在理論的發(fā)展中，槌的自然頻率的理論研究是很必要的。在一般的情形中,離心鐘擺一個(gè)非線(xiàn)性的系統(tǒng)。然而, 如果槌搖擺角度能被假定是很小的時(shí)候，它就可以被考慮為一個(gè)線(xiàn)性的系統(tǒng)。如圖 4 所示,槌受制于兩種力的作用: 離心力 fcf 和自身重

11、力w。從現(xiàn)在的研磨機(jī)可以看出，它的離心力fcf至少要超過(guò)其自身重力w500牛頓，這作為一個(gè)因素。因此，槌的搖擺角度將小于1度，而且線(xiàn)性系統(tǒng)才是有效的。槌的運(yùn)動(dòng)公式來(lái)源于槌的動(dòng)態(tài)平衡的情況(在槌上a點(diǎn)的所有力的合成為0).圓盤(pán)的中心o和槌的質(zhì)心的距離是l, 而且它能用公式表示成： （12）槌的運(yùn)動(dòng)受制于下列各項(xiàng)的力:(見(jiàn)到圖 6) 離心力 fcf 導(dǎo)致離心加速度 acf的存在,慣性力 fi導(dǎo)致槌ai的線(xiàn)性加速度的存在,并且瞬時(shí)慣量導(dǎo)致了槌繞著a點(diǎn)的旋轉(zhuǎn)。這些力和慣量能用下列公式所表示: ， ， （13）槌的動(dòng)態(tài)平衡條件是： (14)a點(diǎn)的瞬時(shí)力（13），動(dòng)態(tài)平衡條件公式(14)能被表示成： (1

12、5)把公式（13）代入公式（15），可寫(xiě)為下式: (16)角度可以根據(jù)a點(diǎn)，c點(diǎn)，o點(diǎn)的距離表示成： (17)x 是從質(zhì)心 c 到半徑 oa的垂直距離, 它實(shí)際上是槌的質(zhì)心擺動(dòng)的振幅。把公式(17)代入公式(16)，可以得到以下等式： (18)對(duì)于小的振動(dòng)，它可以被假定成： (19)并且把公式(19)代入和公式(18)中,其最后的公式可以表達(dá)成： (20)從振動(dòng)的理論4可以知道,x的第二個(gè)條件表示為固有頻率的平方， 它可以用公式表示為： (21)從公式(21)中可以看到，固有頻率p是wo的一部分，因?yàn)樵诟?hào)之下的線(xiàn)性和慣性參數(shù)是常數(shù)。這意謂著,轉(zhuǎn)動(dòng)速度w的增加或者減少,使得固有頻率p也將會(huì)增加

13、或者減少，并且保持不變的比率。 這可能引起槌的固有頻率和鼓的固有頻率一起發(fā)生共振。 如果這一個(gè)共振不發(fā)生在工作運(yùn)行當(dāng)中,它可能會(huì)在啟動(dòng)或者切斷狀態(tài)時(shí)發(fā)生。因?yàn)檠心C(jī)的旋轉(zhuǎn)方向經(jīng)常是變換的，以防止槌的磨損。 如果啟動(dòng)時(shí)間需要 3 3.5秒的話(huà),那么切斷時(shí)就需要持續(xù)20秒甚至更長(zhǎng)的時(shí)間, 這要視軸承的情況而定。雖然共振只會(huì)發(fā)生在一秒到幾秒，但是它還是會(huì)加速損害到桿和槌，這樣槌的旋轉(zhuǎn)方向的經(jīng)常變換會(huì)嚴(yán)重的縮短它們的壽命。這也是一種槌在傳動(dòng)當(dāng)中扭力振動(dòng)所引起共振的可能性。5 在運(yùn)動(dòng)中決定扭矩振動(dòng)的固有頻率的因素研磨機(jī)的傳動(dòng)在示圖1中展示出來(lái)，它由兩個(gè)大規(guī)模的旋轉(zhuǎn)式噴灌器所組成: 電動(dòng)機(jī)的轉(zhuǎn)子和研磨機(jī)的

14、鼓, 它們被連接耦合器所連接。這是一個(gè)系統(tǒng)的例子, 也被稱(chēng)為無(wú)限制或者退化的系統(tǒng)4。這個(gè)系統(tǒng)的第一個(gè)固有頻率為0,第二個(gè)固有頻率可由下式4表示: 和 （22）這里c=耦合器的扭轉(zhuǎn)硬度j1 和 j2=轉(zhuǎn)子和鼓的瞬時(shí)轉(zhuǎn)動(dòng)慣性第一個(gè)固有頻率為0意味著這個(gè)系統(tǒng)在這兩個(gè)大規(guī)模的旋轉(zhuǎn)式噴灌器的相對(duì)運(yùn)動(dòng)速度為0（主要部分的轉(zhuǎn)換）。第二個(gè)固有頻率決定了在啟動(dòng)和斷開(kāi)時(shí)的扭轉(zhuǎn)振動(dòng)頻率和共振時(shí)的運(yùn)轉(zhuǎn)速度，例如，槌的搖擺振動(dòng)或者鼓的擺動(dòng)振動(dòng)。由以上的論述可知,槌的搖擺振動(dòng)的固有頻率是一部分的運(yùn)轉(zhuǎn)速度。 這意謂著共振的發(fā)生更加可能。例如,在鼓以不同的速度旋轉(zhuǎn)時(shí)它的斷開(kāi)模式,因此,鼓 的固有頻率也是改變的。槌的搖擺振動(dòng)的

15、扭轉(zhuǎn)共振尤其危險(xiǎn)因?yàn)樗芤鸸牡臄[動(dòng)。6 數(shù)字舉例對(duì)于數(shù)字計(jì)算，一個(gè)典型的研磨機(jī)的運(yùn)轉(zhuǎn)計(jì)算由下列叁數(shù)確定:槌的重量 m =0.768 kg支點(diǎn)處的瞬時(shí)慣量j= 2.713* kg樞軸的中點(diǎn)和鼓的重心之間的距離l=0.0883 m鼓的半徑 r=0.44 m鼓的側(cè)軸的瞬時(shí)轉(zhuǎn)動(dòng)慣量 j= 144 kg鼓的總重量m=1018 kg軸承的支撐硬度 k1=k2=2.12 * n/m軸承支撐之間的距離 l=0.85 m電動(dòng)機(jī)轉(zhuǎn)子兩極的瞬時(shí)轉(zhuǎn)動(dòng)慣量 j1=65 kg鼓兩側(cè)的瞬時(shí)慣量 j2=140 kg聯(lián)軸器的扭轉(zhuǎn)硬度c=3.6 * nm/rad聯(lián)軸器的扭轉(zhuǎn)硬度和軸承支撐硬度是根據(jù)所選的參考書(shū)所確定的5.把這些

16、數(shù)據(jù)代入(11)(21)和(22)中，就可以得到固有頻率的數(shù)據(jù):鼓的固有頻率和鼓旋轉(zhuǎn)的角速度0-1450r/min或者是鼓的擺動(dòng)振動(dòng)的固有頻率在傳動(dòng)中的扭轉(zhuǎn)振動(dòng)的固有頻率7 實(shí)際考慮的因素從上面的數(shù)據(jù)結(jié)果可以看出, 工作速度與任意的固有頻率都不一致。然而, 當(dāng)研磨機(jī)被翻轉(zhuǎn)時(shí),它就會(huì)被停止然后再被啟動(dòng)。 它的角速度將會(huì)逐漸的由152 rad/s轉(zhuǎn)變到0，然后在從 0 到 152 rad/s。 在一個(gè)很短的時(shí)間內(nèi) (直到好幾秒) 角速度會(huì)等于鼓的擺動(dòng)固有頻率的四分之一,也就是393/4=98.25 rad/s,而且能量的進(jìn)入使得鼓搖擺,引起槌擺動(dòng)。 與此同時(shí),槌擺動(dòng)的固有頻率與扭轉(zhuǎn)振動(dòng)的固有頻率是

17、相符的,以此來(lái)增加槌的擺動(dòng)角度。盡管這一種現(xiàn)象發(fā)生在很短的時(shí)間,但是研磨機(jī)的經(jīng)常的回轉(zhuǎn)還是會(huì)引起機(jī)器損害的積累。為了減少損害,就必須盡快的繞過(guò)這個(gè)共振地帶, 舉例來(lái)說(shuō),使用帶有剎車(chē)裝置的電動(dòng)機(jī)。在啟始模態(tài)下, 在沒(méi)有電動(dòng)機(jī)增加動(dòng)力的情況下加速度的時(shí)間是不能被減少的,這一點(diǎn)是很重要的。然而,通過(guò)參考文獻(xiàn)2中對(duì)雙向驅(qū)動(dòng)裝置的介紹，振動(dòng)的振幅還是應(yīng)該被減少的。沿著桿方向的大批的槌的分配和在圓盤(pán)直徑相反方向上的槌的錯(cuò)位排列導(dǎo)致了沿著桿方向上的離心力的不均勻的分配,這就不可避免的引起了鼓的振動(dòng)和槌的擺動(dòng)。為了預(yù)防這一點(diǎn),相同數(shù)目的槌就必須被安裝在圓盤(pán)直徑上相反的位置上, 例如 5 和 5,4 和 4,

18、等等 (這并不是錯(cuò)排的方式)。然后，槌必須被選擇以便在一支桿上所有的槌總數(shù)目和所有桿上的數(shù)目是一樣的,而且較重的槌應(yīng)被安裝在桿的中央部位上,較輕的桿被安裝在桿的邊緣上。這根本的解決方法是使得在較重一邊的鉆孔上的所有的槌的重量是相等的,而且整個(gè)研磨機(jī)的安裝必須是在動(dòng)態(tài)平衡的條件下進(jìn)行(不僅僅是在沒(méi)有槌的鼓上進(jìn)行)。為了減少軸承的接觸壓力,就必須增加槌上樞軸孔的直徑,并且槌必須是被裱好的而不是被直接的安裝在桿上,在這情況下它通常被設(shè)計(jì)成襯套的形式。 (見(jiàn)到圖 7) 磨破的間隔環(huán)是比較便宜的用來(lái)代替桿。8 結(jié)論 現(xiàn)有的研磨機(jī)的設(shè)計(jì)方法已經(jīng)被呈現(xiàn)出來(lái)。研磨機(jī)損害的主要原因是槌的擺動(dòng)導(dǎo)致了大量的不均勻的

19、分配和共振。一種新的研磨機(jī)的設(shè)計(jì)方法已經(jīng)被表達(dá),它對(duì)于研磨機(jī)的設(shè)計(jì)作出了一些新的改進(jìn)方案。詳情如下:(a) 取代了錯(cuò)排的設(shè)計(jì)方案,它把一個(gè)相等的數(shù)目的槌安置在圓盤(pán)的相反位置上；(b) 它平衡了整個(gè)的裝置，不僅僅是鼓；(c) 縮短了切斷時(shí)間以避免延長(zhǎng)共嗚；(d) 介紹了一種新型間隔環(huán)并且把槌安裝在此上面，它取代了把槌直接安裝在桿上，這種方法增加了接觸面積而且減少了接觸壓力，并且很好的限制了擺動(dòng)角度；(e) 在設(shè)計(jì)階段, 檢查了發(fā)生共嗚的可能性而且采取了措施來(lái)預(yù)防它們的出現(xiàn)。參考文獻(xiàn)：1 thomson, w. t. theory of vibration with application, 4t

20、h edition, 1993, p. 152 (prentice-hall, englewood cliffs, new jersey). 2 panovko, j. g. fundamental s of applied theory of vibrations, (in russian ), 3rd edition, 1976, p. 28 (mashinostroyenie, st petersburg, russia). 3 timoshenko , s. vibrations problem in engineering, 1955 (d. van nostrand, toront

21、o/new york/london). 4 singiresu s. rao. mechanical vibration s, 2nd edition, 1990 (addison-wesley). 5 leshenko, v. a. (ed.)metal cutting machines with cnc (in russian ), 2nd edition, 1988 (mashinostroyenie, moscow)附錄二design of hammer mills for optimum performanceabstract: hammer mill manufacturers a

22、re under increasing pressure to deliver mills of high productivity with a reduced level of vibrations. however, in practice, excessive wear of the rods carrying the hammers takes place, and cracks develop in the vicinity of the holes holding the rods with the hammers , with the possibility of breaka

23、way fracture and disastrous consequences . an increase d level of vibrations has been found on many new mills. existing design approaches have proved to be incapable of explaining this phenomenon. this paper present s a new approach to hammer mill design and enables the prevention of increase d vibr

24、ations and uneven wear and, finally, provides better performance of hammer mills. keywords: hammer mill, excess ive wear, fracture , vibrations, new design notation c torsional stiffness of the coupling (n m/rad) centrifugal force (n) inertia force (n) j mass moment of inertia (kg m2) polar moment o

25、f inertia of the rotor of the electric motor (kg m2) polar moment of inertia of the hammer mill drum (kg m2) radial stiffness of the drum bearing support s (n/m) k kinetic energy (j) distance between the hammer pivot and its centre of gravity (m) l distance between the bearing support s (m) m mass d

26、rum or hammer (kg) inertia moment (n m) p natural frequency of the hammer swinging oscillations (rad/s) p potential energy (j) generalized force (n) r radius of a disc (distance between drum axis and hammer pivot) (m) w weight (n) displacement of the drum centre of gravity (m) displacements of the d

27、rum axle at the bearing supports (m) angular displacement of the drum about the lateral axis or angular coordinate of hammer (rad) angular coordinate of a disc (rad) natural frequency (rad/s) angular velocity of rotation of the drum (rad/s) natural frequencies of torsional vibrations in the hammer m

28、ill transmission (rad/s) 1 introduc tion hammer mills are widely used in the food and grain industries . a typical layout of a hammer mill is shown in fig. 1. it consist s of an electric motor (1), which drives a drum through a coupling (2). the drum includes a set of discs (3) . fixed on the axle (

29、4). the axle rests on two bearing supports (5). there are two groups of rods: one group of rods (6) carrying hammers, and another group (7) carrying buffer rods. they are used to restrict the hammer swing angle. the hammers (8) are grouped in a staggered manner along the rods (6), e.g. five hammers

30、, then four hammers , etc.on opposite sides of the disc diameter, a different number of hammer s are installed (e.g. . fve on one side, and four on the other side). the hammer s are rectangular in shape and have three extern l edges welded up with wear-resistant material. they are separate d by spac

31、er rings. a drum is carefully balance d by adding weights to the side discs before the hammer s are installed. some companies even select hammers so that the total weight of the hammers installed on one rod is the same for all rods. the whole assembly is enclosed in a sheet metal casing (not shown i

32、n fig. 1). grain is supplied through the opening at the top of the casing. the rotating hammers hit the falling grain, crushing it, and milled fragments are collected from the chute at the bottom of the casing. the direction of the drum rotation is frequently reverse d to provide even wear of the ha

33、mmer edges. during hammer mill operation , the rods carrying the hammers do not have direct contact with the grain or milled fragments, which might cause abrasive wear, because the rods are surrounded by hammers and space-rings . in the meantime, the external surfaces of the space rings, which are i

34、n direct contact with milled fragments , do not show any sign of abrasive wear. in practice , severe vibration s occur even on relatively new hammer mills. deep cracks develop on the discs in the vicinity of the holes holding the rods with the hammers. cracks are oriented at 45 to the radius and pro

35、pagate towards the peripheral part of the disc (see fig. 2), creating the danger of breakaway fracture . uneven wear takes place on the rods holding the hammers. deep groove s develop on the cylindrical surfaces of the rods (see fig. 3). the holes in the hammers that embrace the rods become elliptic

36、ally in shape with rounded edges. the side surface s of the hammer s in the vicinity of the holes have strong signs of an impact load from the spacer rings. the centrifugal force s acting on the hammer s and rods are several times smaller than that required to induce fracture in the discs. grooves o

37、n the rods and elliptically shaped holes in the hammer s prove that the actual contact stresses exceed the yield stress, and impact marks on the hammer side surface s indicate that the hammers are wobbling out of the plane of rotation . existing design approaches have proved to be incapable of expla

38、ining this phenomenon . to decrease the level of vibrations , consumers are force d to reduce the working speed of rotation of the drum, which affects the productivity. 2 hypotheses explaining the poor performance of conv entional hammer mills and existing problems when a hammer mill is assembled, u

39、sually 36 hammers are installed on a rod in a staggered manner . the hammers have different mass. thus, the mass distribution along the rod is uneven. when the drum spins, centrifugal force s align the hammer s along the radius . owing to the uneven mass distribution and staggered hammer layout (. f

40、ive hammers on one side of the disc diameter and four on the opposite side), uneven distribution of centrifugal forces takes place, which induces vibrations of the whole drum. since the drum rests on two bearing supports, from the dynamic standpoint it can be considered as a solid body suspended on

41、two identical springs . as a two-degree-of-freedom (2 dof) oscillating system, it has two modes: (a) bouncing oscillations , when the drum oscillates in the radial direction ; (b) rocking oscillations, when one end of the drum axle moves upwards and the other end moves downwards. the .first mode con

42、tribute s to hammer swinging oscillation s (which will be discussed later), and the second mode induces hammer wobbling out of the plane of rotation. wobbling hammers apply an impact load to the spacer rings, causing excessive wear of the side surfaces, and hammer wobbling also results in a reduced

43、contact area of the hammers and rods. this explains the excessive wear of the rods (grooves ) and hammer holes (elliptically shaped with rounded edges). the problem worsens in the case of resonance of the drum oscillations with the excitation from the transmission . when the drum rotates , the hamme

44、r s are subjected to the action of a centrifugal force and their own weight (see fig. 4). when the hammer s are aligned vertically, the weight and the centrifug l force act along the radius of the drum. when the hammer s are aligned horizontally, the resultant , fr, of the centrifugal force, fcf, an

45、d the weight, w, tilt them in the direction of rotation of the drum on one side, and in the opposite direction on the other side. thus, hammer swinging oscillations are induced. this situation may become dangerous in the case of resonance with the working speed (drum rotation), resonance with the dr

46、um bouncing oscillations or resonance with the torsional oscillations in the transmission. all these possibilities were overlooked by the existing design methods . it is very unlikely that milled grain fragment s can contribute to abrasive wear of the contacting surfaces or rods and pivot holes in h

47、ammer s because the clearance s between the spacer rings and hammer s are too small for relatively large milled fragments to get through.there was no indication of abrasive wear of the external surfaces of the space rings, which are in direct contact with milled fragments . 3 determination of the na

48、tural frequencies of hammer mill drum oscillationsas discussed earlier, the drum can be considered as a 2 dof oscillating system (see fig. 5). when a drum with mass m and mass moment of inertia j (about the lateral axis draw n horizontally through its centroidc) oscillates, it perform s translationa

49、l motion : its centroidc moves along the vertical line (displacement xc) and it rotate s about the lateral horizontal axis (angular displacement ). as a 2 dof oscillating system, it can be described by two independent parameters , x1 and x2 the deflection of the spring supports (bearing supports) of

50、 stiffness k1 and k2 respectively. parameters xc and can be expressed in term of x1 and x2 as follows: (1)equation s of motion can be derived from lagrange s equations: i=1,2,3,n (2)for the conservative system shown in fig.5, without damping and external forces, the force qi=0, and the expressions f

51、or kinetic energy, k, and potential energy, p , can be written as follows: (3) (4)taking derivative s from expression s (3) and (4) and substituting them into (2), the following system of two differential equations can be obtained: (5) (6)these can be rearranged into the following equationd: (7) (8)

52、displacements x1 and x2 can be sought in the form (9)taking derivatives from equation s (9) and substituting them into equation s (7) and (8) yields the following algebraic equation with respect to circular frequency w: (10)the solution to equation (10) can be written as: (11)4 determination of the

53、natural frequencies of hammer swinging oscillations a hammer (see fig. 6) is pivoted to a disc at point a and performs two kinds of motion: rotation with the disc about point o with an angular velocity , and rotation (oscillation ) about point a. the angular position of the disc is determined by the coordinate ., and th