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齒輪噪聲的結(jié)構(gòu)傳動(dòng)裝置和變速箱的作用
Sne?ana ?iri? Kosti?
Teaching Assistant
Faculty of Mechanical Engineering - KraljevoUniversity of Kragujevac
Milosav Ognjanovi?
Professor
Faculty of Mechanical Engineering University of Belgrade
該齒輪組（變速箱）的噪音取決于（齒輪嚙合，軸承運(yùn)轉(zhuǎn)等等）和箱體的絕熱性能和配合形式。當(dāng)然箱體的輕微振動(dòng)可以預(yù)防或根據(jù)改進(jìn)設(shè)計(jì)參數(shù)。噪音的傳播可以通過開展對大功率傳動(dòng)機(jī)構(gòu)結(jié)構(gòu)中的能量釋放過程和通過對外殼進(jìn)行模態(tài)測試了解的機(jī)械裝置這是令人興奮。在對模態(tài)測試結(jié)果和噪聲測試結(jié)果的對比中表明噪聲的識別可能性結(jié)構(gòu)來自變速箱的選擇。對結(jié)果的比較和分析獲得了導(dǎo)致齒輪傳動(dòng)單元全部光譜的創(chuàng)造性原因的精確測定。
關(guān)鍵詞：變速箱外殼，齒輪，振動(dòng)，噪聲，模態(tài)測試
1、概述：
在齒輪傳動(dòng)單元中，噪音是齒輪輪齒的嚙合和滾動(dòng)軸承產(chǎn)生的。沖擊聲，滑動(dòng)，滾動(dòng)等等。安裝有彈性結(jié)構(gòu)的機(jī)械零件可以通過它的整體結(jié)構(gòu)吸收干擾的能量和傳輸。內(nèi)表面這種能源的一部分以噪聲的形式排放到周圍環(huán)境中。另一部分經(jīng)過衰減轉(zhuǎn)化為熱能。圖1顯示了擾動(dòng)結(jié)構(gòu)，阻尼和噪聲排放到齒輪傳動(dòng)單元。這一進(jìn)程的主要部分如下：
●初級聲波直接造成齒輪網(wǎng)進(jìn)入齒輪單元的內(nèi)部。這些波穿透外殼壁的周圍環(huán)境。波能量的一部分被減速機(jī)的壁所抑制。
●該傳動(dòng)裝置的彈性結(jié)構(gòu)零件（齒輪，軸，外殼等）吸收能量的主要干擾。這種能量以波的形式移動(dòng)在這些裝置中并且它很大的衰減。這部分的外表面噴出的次級聲波。
●干擾能量在機(jī)體積振動(dòng)可激發(fā)創(chuàng)造聲波的自然能。
●該外殼的任務(wù)是雙重的。它可以是初級和次級的絕緣體，同時(shí)也是高等聲波的放大器。貝爾格萊德機(jī)械工程學(xué)院。所有版權(quán)都認(rèn)為，噪音的產(chǎn)生機(jī)制在變速箱外殼方面的作用。這是文件[2]的一個(gè)延續(xù)，其中包含一個(gè)模式結(jié)構(gòu)的數(shù)值分析和自然振動(dòng)。該模態(tài)方式激發(fā)的簡歷通過調(diào)查激發(fā)模態(tài)振動(dòng)。其他論文呈現(xiàn)數(shù)值預(yù)報(bào)的噪聲（參考文獻(xiàn)[1]和[3]）的可能性，以及通過幾何形狀的齒輪對經(jīng)過處理[10]和[9]優(yōu)化降低變速箱的噪音。變速箱聲音強(qiáng)度的服務(wù)情況的影響已被Oswald, James, Zakrajsek等在參考文獻(xiàn) [6]證明了。由于工作速度的提升，影響聲音強(qiáng)度的加劇，Oswald, Choy等人開發(fā)出了一種為使用變速箱動(dòng)態(tài)仿真的全球性動(dòng)態(tài)模型[7]，然后一個(gè)計(jì)算聲強(qiáng)的程序[8]，他們所顯示的變速箱噪聲譜在一變形方殼一起振動(dòng)。在那個(gè)例子中，然而，對一般噪音標(biāo)準(zhǔn)影響最大的是輪齒在嚙合時(shí)產(chǎn)生的頻率。此外，Sellgren和Akerblom的測試，為“沃爾沃”[9]和哈里斯等人的需要在[11]從事實(shí)出發(fā)觀察問題，該外殼是不是有足夠的剛性承載嚙合齒的影響（傳動(dòng)時(shí)的增長誤差）。這當(dāng)然導(dǎo)致擾動(dòng)和噪聲分別地加劇。在參考文獻(xiàn)[12]中，通過使用FEM和BEM，為減少震動(dòng)，通過對現(xiàn)有外殼簡單形狀的優(yōu)化，考慮到四舍五入對上部半徑的影響。 本文的目的是確定噪聲經(jīng)過外殼壁所的發(fā)出結(jié)構(gòu)，確立外殼壁和噪聲發(fā)出之間的關(guān)系。
圖1一般結(jié)構(gòu)中的干擾能量轉(zhuǎn)化過程
2、通過系統(tǒng)結(jié)構(gòu)的能量傳送
干擾能量的傳遞從齒嚙合地區(qū)到外殼壁是通過齒輪機(jī)構(gòu)，軸和軸承（圖2）實(shí)現(xiàn)的。能源是通過這些部分的波動(dòng)被分散的。一個(gè)部分能源很大大的損失是通過連接被傳送的（接觸面）。一個(gè)值得注意的問題是能源在通過齒輪到軸上時(shí)損失了大部分。這種程度的減輕類似于從軸到軸承或是從軸承到外殼壁。球軸承的接觸面這是相當(dāng)于增加了能源的損失。所以，這指的是從嚙合到外殼表面?zhèn)鬏數(shù)姆绞接邢喈?dāng)大的聯(lián)系。齒嚙合中聲的功率Ws和擾動(dòng)能量Wd之間的比例可以被定義作為擾動(dòng)能源通過系統(tǒng)結(jié)構(gòu)的傳輸因子。
圖2 通過齒輪傳動(dòng)結(jié)構(gòu)的能源傳輸
聲音的功率（Ws1）一部分代表的一部分穿過墻壁來的內(nèi)聲能。這種能量的傳輸通過彈性波穿過墻壁的厚度實(shí)現(xiàn)的。聲音的衰減是和聲音的頻率和墻的厚度成正比的。另一部分聲輻射的傳輸從齒輪到的外殼壁的表面閉并以彈性波的形式釋放到環(huán)境中（Ws2）。這兩個(gè)部分的聲功率造成輻射到周圍環(huán)境的外墻的彈性結(jié)構(gòu)中聲音的被迫波。聲音功率的第三部分是自然的自由振動(dòng)的結(jié)果，也就是外殼壁（Ws3）的彈性波。通過使用測量模態(tài)阻尼，活躍能模態(tài)可以通過有限元方法計(jì)算得出。在這種情況下，總動(dòng)能等于某些干擾的所有形式的總能Ekj。如果這種干擾是由齒輪嚙合引起的，振動(dòng)模態(tài)引起的能量是
wn=j=1qwnj=j=1qEkjfnj (1)
其中q - 對模態(tài)形狀的數(shù)量 。 fnj - 自然頻率?？梢詫⒖偣β蕚鬏斠蜃樱▊鬟f）分為兩部分：
st=wswd=wswdwvwv=wvwdwswv=sT1sT2 (2)
Wv是總壁振動(dòng)能量。
傳輸因子的第一部分是振動(dòng)功率成比例的，ζT1= Wv Wd，另一個(gè)因素是ζT2聲音輻射和墻壁震動(dòng)成正比。如果周圍環(huán)境的物質(zhì)密度ρ2比壁密度小，傳遞因子ζT2變小。
該外殼壁是用高密度ρ1的鑄鐵或鋼和高彈性波速cw1構(gòu)成。聲學(xué)空間提出了較小密度ρ2和波速度為空氣的cw2。
干擾功率從外殼傳輸?shù)街車h(huán)境的簡化的公式是 [參考文獻(xiàn)14]（圖2）
sT2=wswv=11+14p2cw2p1cw1+p1cw1p2cw22 (3)
通過使用這個(gè)公式和密度與鋼鐵的波動(dòng)速度和空氣的關(guān)系，我們可以得到聲功率和壁振動(dòng)功率之間的比值。這就意味著一個(gè)非常小的振動(dòng)能量是以聲音能量被傳輸?shù)?，即聲功率傳輸?
3、外殼壁振動(dòng)的模態(tài)
外殼壁被擾動(dòng)產(chǎn)生自激，這種擾動(dòng)通過軸承和軸，來自于齒嚙合區(qū)，以自然頻率振蕩的[2]。自然振蕩和彈性變形的波動(dòng)是復(fù)雜的。主體部分激勵(lì)振蕩的過程也是復(fù)雜的，以及對振動(dòng)能量的級別決定的，就是激發(fā)能量和釋放能源之間所產(chǎn)生的比。為這種原因準(zhǔn)確定義導(dǎo)致某些方式的震動(dòng)，可能的震蕩形式及自然振蕩頻率，通過FEM理論首先做出定義，，然后通過在變速箱外殼測試模態(tài)完成。結(jié)果表明，只有一小部分模型在觀察范圍可達(dá)3000赫茲下產(chǎn)生自激的方式。結(jié)果的分析，得到了振蕩模態(tài)和模態(tài)一致，則震蕩模態(tài)會(huì)被激發(fā)：
●變形方向，
●如在激發(fā)行為的最大點(diǎn)發(fā)生變化并且，
●如果相應(yīng)模態(tài)形狀的激勵(lì)頻率等于自然頻率。
然而，振蕩模態(tài)形狀也可以被激勵(lì)當(dāng)激勵(lì)頻率與自然頻率不一樣時(shí)。某些方式的復(fù)雜機(jī)制激發(fā)，和數(shù)值模態(tài)分析和測試模態(tài)齒輪傳動(dòng)外殼的結(jié)果一樣，在[2，13]有詳細(xì)的對待方式。
4、振動(dòng)與噪音測量與分析
在圖1中提出的變速箱已被用作測試項(xiàng)目。振動(dòng)和噪音的測量與分析已經(jīng)通過PULSE-system的應(yīng)用被執(zhí)行，B&K。傳輸單元壁的模態(tài)測試已通過脈沖激勵(lì)的手段被提出- 模態(tài)錘（圖3），并已通過FFT的頻譜分析儀分析振動(dòng)測量措施。一些選擇結(jié)果在圖4中。振動(dòng)已經(jīng)在軸承領(lǐng)域被提出，通過使用壓電加速度計(jì)（圖3）沖擊力（錘模態(tài)的沖擊）已應(yīng)用于外殼壁正交在壁上。
圖3變速箱住房模態(tài)測試
在圖4，列出相對振動(dòng)反應(yīng)在薄壁區(qū)域的沖擊所造成的影響（圖3）。這種反應(yīng)在約2.4千赫的高密集自然頻率時(shí)非常集中的。對于軸承領(lǐng)域的影響（薄壁區(qū)），該頻率響應(yīng)較低（反應(yīng) 圖 – 4b）。下一個(gè)響應(yīng)圖（c-圖4）通過在齒輪齒上的響應(yīng)獲得的。沖擊能（干擾能）必須傳播經(jīng)齒輪機(jī)構(gòu)，通過軸和軸承各地，然后它激發(fā)外殼壁的自然振動(dòng)。一個(gè)非常高的水平干擾耗能由于非常低的水平的自然振動(dòng)引起的，但它得到高數(shù)值的自然頻率的響應(yīng)。
圖4外殼模態(tài)測試的頻率響應(yīng)
1）影響了殼壁頂點(diǎn)，2）在軸承區(qū)域受到的影響，3）齒輪的影響.
能量傳送單元已被放入一鏜孔里（圖5），使聲壓可以用于分析。麥克風(fēng)已放在變速箱的上面，0.5米的距離。
圖5 現(xiàn)場檢測
變速箱驅(qū)動(dòng)器已通過電動(dòng)變速器從次門相室到其相鄰鏜孔室的旋轉(zhuǎn)速度的手段實(shí)現(xiàn)。目前已進(jìn)行了測量使用激勵(lì)從缺陷齒輪（圖6A），并已達(dá)到目的。對于精確確定的外殼壁的影響，當(dāng)上部（覆蓋）的部分已被覆蓋時(shí)實(shí)現(xiàn)測量，（圖6B）及它已被關(guān)閉的情況（圖6c中）。輸入軸轉(zhuǎn)速已被更改在每分鐘140到1100的范圍內(nèi)。 180°下的兩個(gè)角缺陷對已由驅(qū)動(dòng)齒輪彌補(bǔ)，擺脫哪一個(gè)是小，另一個(gè)是更大。一個(gè)強(qiáng)烈的沖擊在這些齒的入口處實(shí)現(xiàn)了，并成為加強(qiáng)在齒更大的缺陷。在這些變速箱測試狀態(tài)的照片。
圖6變速箱測試：1）齒輪的缺陷，b）無蓋室，三）封閉的室
4.1模態(tài)反應(yīng)和室振動(dòng)之間的相關(guān)性
該室模態(tài)響應(yīng)（圖7A）已被在變速箱下部軸承室的軸的兩個(gè)大洞外側(cè)測量，并已通過一個(gè)錘模式獲得脈沖激勵(lì)，這在方式意味著影響軸承的支持點(diǎn)的影響，即點(diǎn)在實(shí)際操作軸承引入的干擾點(diǎn)。通過此響應(yīng)結(jié)果與模態(tài)分析比較，通過FEM手段執(zhí)行，可以得出結(jié)論，通信時(shí)令人滿意的，除了一定的偏差。數(shù)值和試驗(yàn)?zāi)B(tài)響應(yīng)的對比并不是這篇文章的主題 - 在模態(tài)試驗(yàn)的室反應(yīng)譜對在同一測點(diǎn)的振動(dòng)光譜（圖7b中），在與齒輪嚙合的缺陷，在轉(zhuǎn)數(shù)n=500° /分。振動(dòng)頻率和兩個(gè)頻譜基本相同。因此，它可以得出結(jié)論，變速箱室的震動(dòng)是自然振蕩的結(jié)果，而振動(dòng)響應(yīng)的強(qiáng)度（圖7B條）與模態(tài)測試強(qiáng)度大致相同（圖7A）。其中的差異目前仍然是其他主題，更廣泛的考慮。
圖7齒輪箱室的振動(dòng)光譜：1）在模態(tài)測試，b）在齒輪嚙合與缺損
第三個(gè)結(jié)論，可在振動(dòng)頻譜圖7的基礎(chǔ)上提出，是對指激勵(lì)頻率。在激勵(lì)頻率為為16Hz的旋轉(zhuǎn)500 ° /分鐘，及缺陷驅(qū)動(dòng)齒輪。該振動(dòng)頻率的強(qiáng)度是主要的，但不是最重要。進(jìn)入彈性結(jié)構(gòu)取決于干擾能源的強(qiáng)度。
4.2齒輪箱振動(dòng)和噪音之間的相關(guān)性
接下來的實(shí)驗(yàn)應(yīng)確認(rèn)的論點(diǎn)是：噪音通過變速箱排放到周圍環(huán)境是室自然振蕩的結(jié)果。為此，圖8給出了兩個(gè)噪聲譜，1指出軸的瑕疵/損失，在500°/min（圖8A）及另一個(gè)指封閉齒輪變速箱具有相同齒輪和相同的旋轉(zhuǎn)速度（圖8B項(xiàng)）。通過比較這些頻譜，及對比在圖7中振動(dòng)的頻譜，可以得出結(jié)論如下：
*開放式齒輪已取得復(fù)雜噪音的頻譜。他們主要是初級聲音波和已出現(xiàn)較高的諧波由齒的缺陷所影響
*室壁以自然頻率振蕩并發(fā)出聲波進(jìn)入周圍環(huán)境并進(jìn)入自己室的內(nèi)部。該聲壓強(qiáng)表示成m Pa（圖8B號）已被測量在封閉變速箱0.5米的距離上。頻率水平等于室自然頻率強(qiáng)調(diào)在這個(gè)頻譜上。這證實(shí)了上述論斷，室的自然頻率占聲音頻譜的支配地位。
此外，其隔離室應(yīng)造成聲壓水平降低，與無室（圖8A）款齒輪相對比。然而，這并沒有發(fā)生。噪音水平得到了顯著提高。在室內(nèi)，有一個(gè)相當(dāng)大的開孔。外殼已充當(dāng)諧振器框。
該傳動(dòng)軸的角速度也速度顯著影響的噪聲排放水平。速度的改變導(dǎo)致激勵(lì)頻率，吸收干擾能量變化和噪音的水平對外殼的自然頻率的改變。
5、結(jié)論
對發(fā)射機(jī)噪聲結(jié)構(gòu)的識別方法論已經(jīng)研制成功。
最初的假說已被證實(shí)，能量傳輸室的自然振蕩模態(tài)結(jié)構(gòu)和噪聲發(fā)射頻譜的全面關(guān)系。
在輸電系統(tǒng)（齒輪，軸振動(dòng)，軸承）的齒嚙合激勵(lì)震蕩中的干擾能源，以及外殼的自然振動(dòng)。外殼壁作為基層聲音主要絕緣體，為次級和第三級聲波透射作為一個(gè)傳動(dòng)裝置。這些聲波可以詳細(xì)的分離通過對該頻譜結(jié)構(gòu)的深入分析。
圖8 傳輸單元噪聲頻譜 1）開啟變速箱 2）封閉變
參考文獻(xiàn)
[1]Sabot, J.: Integrated Vibroacoustic Approach to Compute and Reduce Gear Transmissions Noise,- Proceedings of the International Conference on Power Transmission,Paris,pp.2039-2050,1999.
[2]Ciric Kostic, S., Ognjanovic M.: Excitation of Modal Vibration in Gear Housing Walls, FME Transactions,Vol.34,No.1,pp.21-28,2006.
[3]Houser, D.R., Sorenson, J.D., Harianto, J., ect.: Comparison of Analytical Predictions with Dynamic Noise and Vibration Measurements for a Simple Gearbox, Proc. Intl. Conf. on gears, Munich pp.995-1002,2002.
[4] Kartik, V., Houser, D.R.: An Investigation of Shaft Dynamic Effects on Gear Vibration andNoise Excitation, SAE Transactions,Vol.112, pp.1737-1746,2003.
[5]Genechte, B.V., Pluymers,B., Vanmaele, C., ect.: On the coupling of Wave Based Models withModally Reduced Finite Element Models for Structural-Acoustic Analysis,Proceedings of ISMA Conf.,Leuven,pp.2383-2403,2006.
[6]Oswald,F.B,Zakrajsek J.J.,Atherton,W.,Lin H.: H.Effect of Operating Conditions on Gearbox Noise, ASME Publication DE-Vol.43-2,pp.669-674,1992.
[7]Choy,F.K.,Ruan,Y.F.,Zakrajsek J.J.,Oswald,F. B.:Modal Simulation of Gearbox Vibration with Experimental Correlation,Journal of Propulsion and Power,Vol.9,No.2,pp.301-306,1993.
[8]Oswald,F.B.,Seybert,A.F.,Wu,T.W.,Atherton, W.:Comparison of Analysis and Experiment for Gearbox Noise,Proceedings of the International Power Transmission and Gearing Conference,Phoenix,Vol.2,pp.675-679,1992.
[9]Sellgren,U.,Akerblom,M.:A Model-based Design Study of gearbox Induced Noise,Proceedings of the International Design Conference-Design2004, Dubrovnik,Croatia,pp.1337-1342,2004.
[10]Chung,C.H.,Steyer,G.ect.:Gear Noise Reduction through Transmission Error ControlandGearBlankDynamicTuning,SAETransactions,Vol.108(2),No.6,pp.2829-2837,1999.
[11]Harris,O.J.,James,B.M.,Woolley,A.M.: Predicting the Effects of Housing Flexibility and Bearing Stiffness on Gear Misalignment and Transmission Noise Using a Fully Coupled Non-Linear Hyperstatic Analysis,Romax Technology Preview Paper-Vehicle Noise&Vibration,88-NVH-AN-0299-1,2000.
[12]Inoue,K.:Shape Optimization of Gearbox Housing for Low Vibration,Proceedings of the International Conference on Power Transmission,Paris,pp2053-2064,1999.
[13]Ciric Kostic,S.,Ognjanovic M.:Gear Disturbance Energy Transmission through the Gear System and Frequency Spectrum,Proceedings of the International Conference Power Transmission, Novi Sad-Serbia,pp.167-172,2006.
[14]Ognjanovic M.:The noise generation in machine systems,Faculty of Mechanical Engineering, University of Belgrade,Monography,Belgrade,1995.(in Serbian)
[15]Ognjanovic M.,Ciric-Kostic S.:Effects of Gear Housing Modal Behaviour at the Noise Emission,- Proceedings of the International Conference on Gears,Munich VDI-Berichte 1904-02,pp.1767-1772,2005.
The Noise Structure of Gear Transmission Units and the Role of Gearbox Walls
The noise emission of gear units(gearboxes)depends both on the disturbances(gear meshing, bearing operation, etc)and on the insulating capabilities and modal behavior of the housing. Natural vibrations of the housing walls can be prevented or intensified depending on design parameters. The mechanism of exciting and emission of transmission noise is defined by carrying out the process of propagation of excitation energy through the structure of power transmitters and by modal testing of the housing. The results of vibration and noise testing in comparison to the results of modal testing give the possibility of identification of noise structure for the chosen gearbox. Comparison and analysis of the results obtained lead to precise determination of the causes of creation of the total spectrum of gear transmission units.
Keywords: gearbox housing, gears, vibration, noise, modal testing
1.INTRODUCTION
In gear transmission units, sound is generated by excitation in gear teeth meshes and in rolling bearings. Impacts, sliding, rolling, etc. absorb disturbance energy in the elastic structure of machine parts and transmit it through the whole structure. Interior surfaces emit a part of this energy into the surroundings in the form of noise. Another part is converted into heat by damping. Figure 1 shows the structure of disturbance, damping and noise emission in gear transmission units. Some of the main parts of this process are as follows:
● Primary sound waves are caused directly in gear meshes and emitted into the interior of the gear unit. These waves penetrate through the housing walls into the surroundings. A part of the wave energy is damped in the gear unit walls.
● The elastic structure of the transmission unit parts (gears, shafts, housing, etc) absorb the dominant part of disturbance energy. This energy moves in the form of waves within these parts and a lot of it is damped. Exterior surfaces of the parts emit secondary sound waves inside the housing.
● Disturbance energy in the volume of the machine part may excite natural vibrations which can create tertial sound waves.
● The role of the housing is dual. It can simultaneously be the insulator of primary and secondary sound waves and the amplifier of the tertiary ones.
The acoustic emission of gear transmission units has been treated in a number of papers but this one
Faculty of Mechanical Engineering, Belgrade . All rights reserved considers the mechanism of noise generation and the role of the gear box housing. This is a continuation of paper [2], which contains a numerical analysis of modal structure and natural vibrations. The manner of modal excitation is established by investigating excitation of modal vibration. Other papers present the possibility of numerical prediction of noise (papers [1]and[3]), and the reduction of gearbox noise by optimization of geometry of gear pairs has been treated in[10]and[9]. The effects of service conditions on sound intensity of the gearbox have been shown by Oswald, James, Zakrajsek and others in paper[6].Due to the increasing working speeds, which affects intensification of sound intensity, Oswald, Choy and others have developed a global dynamic model which they use for simulation of gearbox dynamics [7], then a programme for calculation of sound intensity[8] and they have shown, on a housing with one deformable side, that its vibrations participate in the spectrum of gearbox noise. In that example, however, the biggest influence on the general level of noise is made by the frequency of gear teeth meshing. Further, Sellgren and Akerblom, in testing for the needs of "Volvo"[9]and Harris and others in[11] observe the problem by starting from the fact that the housing which is not rigid enough can have significant influence on teeth meshing(increase of transmission error).This certainly leads to intensification of disturbances in meshes and intensification of noise separately. In [12], Inoue has, by using FEM and BEM, and for the purpose of reducing vibrations, worked on optimization of simple shapes of the housing by considering the influence of the radius of rounding of the upper part. This paper aims at determining the structure of noise emitted by the housing walls and establishing the correlation between the housing vibrations and the noise emitted. The noise structure in comparison with disturbance conditions (gear meshing) defines the main phenomenon in the mechanism of noise generation
Figure 1.General structure of the process of disturbance energy transformation
2.TRANSMISSION OF ENERGY THROUGH THE SYSTEM STRUCTURE
Transmission of disturbance energy from the zone of teeth meshing to the housing walls is realized through the gear bodies, shafts and bearings(Fig.2). Energy is distributed through these parts by wave motion. A part of the energy is transmitted through the joints (contiguous surfaces) with considerable losses. A significant amount is lost at the passage of the energy from the gear to the shaft. The degree of reduction is similar at the passage from the shaft to the bearing and from the bearing to the housing. It is considerably increased at the passage of disturbance energy over the contiguous surfaces of the bearing balls. So, this refers to a relatively high number of contacts on the way of transmission from the teeth mesh to the housing surface. The ratio between the sound power Ws and the disturbance power in the teeth meshes Wd can be defined as a factor of transmission (transmissibility) of disturbance energy through the system structure.
Figure 2.Transmission of energy through the gear transmission structure
One part of the sound power (Ws1) represents a part of the inside sound energy which comes through the walls. This energy transmission is realized by elastic waves through the wall thickness. The sound reduction is proportional to the sound frequency and the wall thickness.
Another part of sound radiation is transmitted from the gear contacts to the surfaces of the housing walls and emitted in the form of elastic waves into the surroundings (Ws2).
The first two parts of the sound power create forced waves in the elastic structure of the walls which radiate sound into the surroundings.
The third part of the sound power is a result of natural free vibrations, i.e. elastic waves of the housing walls(Ws3).By using the measured modal damping, the modal kinetic energy can be calculated by means of FEM method. In this case, the total kinetic energy is equal to the sum of the kinetic energy Ekj of all modal shapes for a certain disturbance. If this disturbance is caused by gear meshing, the power of modal vibration is
where q– the number of modal shapes and fnj - the natural frequency. It is possible to divide the total power transmission factor (transmissibility) into two parts:
Where Wv is the total wall vibration power.
The first part of the transmission factor is proportional to the vibration power ratio ζT1= Wv Wd, and the second one ζT2 is proportional to the sound radiation in comparison with the wall vibration. The transmission factor ζT2 is smaller if the material density ρ2 of the surroundings is smaller in comparison with the wall density.
The housing walls are made of cast iron or steel with the high level of density ρ1 and with the high elastic wave speed cw1. Acoustic space is presented with the much smaller density ρ2 and the wave speed cw2 for the air.
The simplified formula [14] of disturbance power transmission from the walls into the surroundings (Fig.2) is
By using this formula and the values of density and wave speed for steel and for the air, we obtain the ratio between the sound power and the wall vibration power.This means that an extremely small part of vibration energy is transmitted into sound energy, i.e. sound power.
3. MODAL VIBRATION OF THE HOUSING
The housing walls excited by disturbances which, through the bearings and shafts, come from the zone of teeth meshing, oscillate with natural frequencies [2]. Elastic deformations at wave motion and natural oscillation are complex. The process of excitation of main shapes of oscillation is also complex, as well as determination of levels of oscillation energy, that is the ratio between the excitation energy and the emitted energy. For the purpose of accurate definition of the causes leading to excitation of certain modes, possible shapes of oscillation and natural frequencies have been firstly defined by applying the FEM method, and then modal testing of the gearbox housing has been performed. The results show that only a small number of modes have been excited in the observed range of up to 3000 Hz. The analysis of the results obtained shows that modal oscillation will be excited if it is coincided by modal:
●directions of deformations,
●if the excitation acts at the point of the biggest deformations and
●if the excitation frequency is equal to the natural frequency of the corresponding modal shape.
However, the modal shape of oscillation can also be excited when the excitation frequency is not identical with the natural frequency. The complex mechanism of excitation of certain modes as well as the results of numerical modal analysis and the results of modal testing of the gear transmission housing are treated in a detailed manner in [2,13].
4. MEASURING AND ANALYSIS OF VIBRATION AND NOISE
The gearbox presented in Fig.1 has been used as the subject of testing. Measuring and analysis of vibrations and noise have been performed by the application of the PULSE-system, B&K. Modal testing of the transmission unit housing has been carried out by means of impulse excitation–the modal hammer(Fig.3),and by measuring of vibrations which has been analyzed by using a FFT frequency analyzer. Some of the chosen results are presented in Figure 4.Vibration has been carried out in the area for bearings, by using a piezoelectric accelerometer(Fig.3). Impact force (impact of the modal hammer) has been applied around the housing walls orthogonal on the wall.
Figure 3.Gearbox housing modal testing
In Figure 4,diagram(a)presents relative vibration response caused by impact in the area of the thin wall (Fig.3).The response is very intensive for the high natural frequency of about 2.4 kHz. For impact in the area of bearings (area of thick wall),the response for that frequency is less(response diagram–4b).The next response diagram(c-Fig.4)is obtained by using impact in the gear tooth. Impact energy (disturbance energy) has to be transmitted through the gear body, through the shafts and across bearings, and then it excites natural vibrations of the housing walls. A very high level of disturbance energy dissipation causes very low level of responded natural vibrations, but it is obtained response of high number of natural frequencies.
Figure 4.Frequency response of housing modal testing: a)impact on the top wall of the housing, b)impact on the housing in the area of bearings, c)impact on the gears
The power transmission unit has been placed into an anehoic chamber (Fig.5) so that acoustic pressure could be used for the analysis. The microphone has been placed above the gearbox , at the distance of 0.5m.
The gearbox drive has been realized by means of an electric variator with the rotation speed from the next door room in relation to the anehoic chamber. Measuring has been performed by using the excitation from the gears with defects (Fig.6a) which have been caused on purpose. For the purpose of determining the effects of the housing walls, measuring has been performed when the upper part (cover) of the housing has been removed(Fig.6b)and in the situation when the housing has been closed(Fig.6c).The rotation speed of the input shaft has been varied within the range of 140-1100 min-1.Two defects under the angle of 1800 have been made on the teeth of the driving gear, out of which one is smaller and the other one is bigger. An intense impact is realized at the entrance of these teeth, and it becomes intensified at coming of the tooth with a bigger defect. The photographs of the gearbox in the state of testing are presented in Figure 5
Figure 5.Gearbox testing: a) gears with defects, b)housing without cover, c)closed housing
4.1 Correlation between modal response and vibrations of the housing
The modal response of the housing (Fig.7a) has been measured at the lateral side between two bigger holes for the bearings on the lower part of the gearbox housing, and it has been obtained by impulse excitation by means of a modal hammer, which means by the impact at the point where the bearing is supported, i.e. at the point where real disturbance at bearing operation is introduced. By comparing this response with the results of the modal analysis performed by means of
FEM, it can be concluded that correspondence is satisfactory but that there are certain deviations. The comparison between numerical and experimental modal responses is not the subject of this paper–it compares the spectrum of housing responses at modal testing with the spectrum of vibrations measured at the same point (Fig.7b) at meshing of gears with defects, at the number of revolutions n=500 o/min. Frequencies of vibrations are mostly the same in both spectrums. Therefore, it can be concluded that the gearbox housing vibrations are the consequence of natural oscillation and that the intensities of vibration responses (Fig.7b) approximately correspond to the intensities of response at modal testing (Fig.7a).The differences which are still present can be the subject of other, broader considerations.
Figure 6.Spectrums of gearbox housing vibrations:
Figure 6.Spectrums of gearbox housing vibrations: a) at modal testing, b) at meshing of gears with defect
The third conclusion which can be made on the basis of the spectrum of vibrations in Figure 7b refers to the frequency of excitation. The frequency of excitation is 16Hz for the rotation speed of 500 o/min and for two defects at the driving gear. The intensity of vibrations for this frequency is important but not the highest one. The intensity of disturbance energy which is entered into the elastic structure depends upon it.
4.2 Correlation between gearbox housing vibrations and noise
The next experiment should confirm the thesis that the noise emitted into the surroundings by the gearbox is the consequence of natural oscillation of the housing. For that purpose, Figure 8 presents two spectrums of noise, one referring to gears with defects/damages, at 500o/min(Fig.8a)and the other one referring to the closed gearbox with the same gears and the same speed of rotation(Fig.8b).By comparing these spectrums with each other and with the spectrums of vibrations in Figure 7,the following can be concluded:
A very complex spectrum of noise of open gears has been obtained. They are mainly primary sound waves and their higher harmonics that have arisen by impact of teeth with defects
The housing walls oscillate with natural frequencies and emit sound waves both into the surroundings and into the interior of the housing itself. The spectrum of acoustic pressure expressed in m Pa (Fig.8b) has been measured at the distance of 0.5 m above the closed gearbox. The levels for the frequencies equal to the natural frequencies of the housing are emphasized in this spectrum. This confirms the above mentioned thesis that natural frequencies of the housing are dominant in the sound spectrum.
Besides, the housing with its insulation should lead to reduction of the level of acoustic pressure in comparison with the noise of the gear without the housing (Fig.8a). However, this has not happened. Significantly increased noise levels have been obtained. At the housing, there is a considerably big open hole. The housing has acted as a resonator Box.
The angle speed of the driving shaft also significantly influences the level of the noise emitted. The change of speed results in the change of excitation frequency, the change of disturbance energy absorbed and the change of the level of noise for corresponding natural frequencies of the housing.
5. CONCLUSION
The methodology of identification of the power transmitter noise structure has been developed.
The initial hypothesis has been confirmed that the modal structure of natural oscillation of the power transmitter housing and the spectrum of the noise emitted are in full correlation.
Disturbance energy in teeth meshes excites vibrations of the transmission system (gears, shafts, bearings)as well as natural vibrations of the housing. The housing walls act as an insulator of primary sound waves, as transmission of secondary sound waves and as a generator of tertiary (structural)sound waves. Detailed separation of these sound waves can be performed by a deeper analysis of the structure of the spectrums presented.
Figure 7.Spectrums of transmission unit noise: a)open gearbox, b)closed gearbox
REFERENCES
[1]Sabot, J.: Integrated Vibroacoustic Approach to Compute and Reduce Gear Transmissions Noise,- Proceedings of the International Conference on Power Transmission,Paris,pp.2039-2050,1999.
[2]Ciric Kostic, S., Ognjanovic M.: Excitation of Modal Vibration in Gear Housing Walls, FME Transactions,Vol.34,No.1,pp.21-28,2006.
[3]Houser, D.R., Sorenson, J.D., Harianto, J., ect.: Comparison of Analytical Predictions with Dynamic Noise and Vibration Measurements for a Simple Gearbox, Proc. Intl. Conf. on gears, Munich pp.995-1002,2002.
[4] Kartik, V., Houser, D.R.: An Investigation of Shaft Dynamic Effects on Gear Vibration and
Noise Excitation, SAE Transactions,Vol.112, pp.1737-1746,2003.
[5]Genechte, B.V., Pluymers,B., Vanmaele, C., ect.: On the coupling of Wave Based Models with
Modally Reduced Finite Element Models for Structural-Acoustic Analysis,Proceedings of ISMA Conf.,Leuven,pp.2383-2403,2006.
[6]Oswald,F.B,Zakrajsek J.J.,Atherton,W.,Lin H.: H.Effect of Operating Conditions on Gearbox Noise, ASME Publication DE-Vol.43-2,pp.669-674,1992.
[7]Choy,F.K.,Ruan,Y.F.,Zakrajsek J.J.,Oswald,F. B.:Modal Simulation of Gearbox Vibration with Experimental Correlation,Journal of Propulsion and Power,Vol.9,No.2,pp.301-306,1993.
[8]Oswald,F.B.,Seybert,A.F.,Wu,T.W.,Atherton, W.:Comparison of Analysis and Experiment for Gearbox Noise,Proceedings of the International Power Transmission and Gearing Conference,Phoenix,Vol.2,pp.675-679,1992.
[9]Sellgren,U.,Akerblom,M.:A Model-based Design Study of gearbox Induced Noise,Proceedings of the International Design Conference-Design2004, Dubrovnik,Croatia,pp.1337-1342,2004.
[10]Chung,C.H.,Steyer,G.ect.:Gear Noise Reduction through Transmission Error Control and
Gear Blank Dynamic Tuning,SAE Transactions,Vol.108(2),No.6,pp.2829-2837,1999.
[11]Harris,O.J.,James,B.M.,Woolley,A.M.: Predicting the Effects of Housing Flexibility and Bearing Stiffness on Gear Misalignment and Transmission Noise Using a Fully Coupled Non-Linear Hyperstatic Analysis,Romax Technology Preview Paper-Vehicle Noise&Vibration,88-
NVH-AN-0299-1,2000.
[12]Inoue,K.:Shape Optimization of Gearbox Housing for Low Vibration,Proceedings of the International Conference on Power Transmission,Paris,pp2053-2064,1999.
[13]Ciric Kostic,S.,Ognjanovic M.:Gear Disturbance Energy Transmission through the Gear System and Frequency Spectrum,Proceedings of the International Conference Power Transmission, Novi Sad-Serbia,pp.167-172,2006.
[14]Ognjanovic M.:The noise generation in machine systems,Faculty of Mechanical Engineering, University of Belgrade,Monography,Belgrade,1995.(in Serbian)
[15]Ognjanovic M.,Ciric-Kostic S.:Effects of Gear Housing Modal Behaviour at the Noise Emission,- Proceedings of the International Conference on Gears,Munich VDI-Berichte 1904-02,pp.1767-1772,2005.