錘片式粉碎機(jī)轉(zhuǎn)子結(jié)構(gòu)動(dòng)態(tài)優(yōu)化設(shè)計(jì)

1、振 動(dòng) 與 沖 擊第29卷第5期JOURNAL OF VI BRATIO N AND S HOCKVol .29N o .52010錘片式粉碎機(jī)轉(zhuǎn)子結(jié)構(gòu)動(dòng)態(tài)優(yōu)化設(shè)計(jì) 收稿日期:2009-04-17第一作者王曉博女,碩士生,1984年生王曉博1,3,謝瑞清2,丁武學(xué)1,王栓虎1(1.南京理工大學(xué)機(jī)械工程學(xué)院,南京 210094;2.成都精密光學(xué)工程研究中心,成都 610041;3.西南交通大學(xué)牽引動(dòng)力國(guó)家重點(diǎn)實(shí)驗(yàn)室,成都 610031摘 要:運(yùn)用有限元法對(duì)錘片式粉碎機(jī)進(jìn)行了動(dòng)力學(xué)分析,得到了轉(zhuǎn)子的固有頻率、模態(tài)振型及不平衡響應(yīng)等動(dòng)態(tài)特性參數(shù)。利用靈敏度分析技術(shù)研究了各結(jié)構(gòu)參數(shù)對(duì)轉(zhuǎn)子動(dòng)態(tài)性能的影響

2、程度。以轉(zhuǎn)子重量和不平衡振動(dòng)響應(yīng)為狀態(tài)變量,以轉(zhuǎn)子的固有頻率為目標(biāo)函數(shù)對(duì)結(jié)構(gòu)進(jìn)行了動(dòng)態(tài)優(yōu)化設(shè)計(jì)。優(yōu)化結(jié)果表明,轉(zhuǎn)子動(dòng)態(tài)性能得到明顯改善,為解決粉碎機(jī)的振動(dòng)問(wèn)題提供了有效的途徑。關(guān)鍵詞:錘片式粉碎機(jī);優(yōu)化設(shè)計(jì);靈敏度分析;動(dòng)力學(xué)分析;有限元法中圖分類號(hào):TH 133 文獻(xiàn)標(biāo)識(shí)碼:A錘片式粉碎機(jī)是目前飼料工業(yè)中應(yīng)用最廣泛的一種粉碎機(jī)機(jī)型,它主要利用高速旋轉(zhuǎn)的錘片對(duì)物料產(chǎn)生強(qiáng)烈的沖擊和摩擦來(lái)達(dá)到對(duì)物料破碎的目的,具有結(jié)構(gòu)簡(jiǎn)單、通用性好、適應(yīng)性強(qiáng)、生產(chǎn)率高的特點(diǎn)。但由于是在高速旋轉(zhuǎn)工況下的機(jī)械,這類粉碎機(jī)普遍存在振動(dòng)和噪音較大的問(wèn)題。目前國(guó)內(nèi)外對(duì)錘片式粉碎機(jī)的研究主要集中在,諸如轉(zhuǎn)子直徑、粉碎室寬度、

3、錘片末端線速度、錘篩間隙、錘片數(shù)量、錘片厚度、錘片排列方式以及吸風(fēng)量等因素對(duì)粉碎機(jī)工作效率的影響上,其研究目的多在于提高粉碎效率,節(jié)能降耗1-5。但對(duì)錘片式粉碎機(jī)的動(dòng)態(tài)特性及其影響因素的研究則相對(duì)較少,關(guān)于錘片式粉碎機(jī)結(jié)構(gòu)動(dòng)態(tài)優(yōu)化設(shè)計(jì)的研究則幾乎空白。本文利用有限元分析軟件ANSYS ,對(duì)錘片式粉碎機(jī)轉(zhuǎn)子-軸承系統(tǒng)進(jìn)行了動(dòng)力學(xué)分析,得到了系統(tǒng)的固有頻率、振型以及不平衡振動(dòng)響應(yīng)。基于靈敏度分析原理分析各結(jié)構(gòu)參數(shù)對(duì)系統(tǒng)動(dòng)態(tài)特性的影響,并根據(jù)現(xiàn)代機(jī)械優(yōu)化設(shè)計(jì)理論對(duì)轉(zhuǎn)子結(jié)構(gòu)進(jìn)行優(yōu)化,可為相似類型的旋轉(zhuǎn)機(jī)械的動(dòng)態(tài)優(yōu)化設(shè)計(jì)提供參考。1 轉(zhuǎn)子-軸承系統(tǒng)有限元模型及動(dòng)力學(xué)分析1 1 錘片式粉碎機(jī)轉(zhuǎn)子的基本結(jié)構(gòu)

4、圖1為錘片式粉碎機(jī)轉(zhuǎn)子的CAD 模型。錘片式粉碎機(jī)的轉(zhuǎn)子主要由主軸、錘架板、定位套筒、錘片、銷軸、錘片隔套,以及其他一些標(biāo)準(zhǔn)件(如鍵、開(kāi)口銷、圓螺母、止推墊圈等組成。錘片式粉碎機(jī)轉(zhuǎn)子不同于一般機(jī)械設(shè)備中常見(jiàn)的內(nèi)部無(wú)活動(dòng)部件的轉(zhuǎn)子,其執(zhí)行粉碎的主要部件 錘片,是懸掛在均布于轉(zhuǎn)子錘架板的銷軸上的,錘片與銷軸的聯(lián)接方式屬于鉸接,各錘片可繞銷軸自由轉(zhuǎn)動(dòng)。圖1 錘片式粉碎機(jī)轉(zhuǎn)子-軸承系統(tǒng)CAD 模型1 2 有限元模型根據(jù)轉(zhuǎn)子的實(shí)際結(jié)構(gòu),在不影響計(jì)算精度的前提下,建立轉(zhuǎn)子有限元模型過(guò)程中進(jìn)行了以下簡(jiǎn)化:(1將主軸和定位套筒合并為一個(gè)幾何實(shí)體,采用BEAM 188梁?jiǎn)卧獊?lái)模擬。對(duì)于主軸的變截面結(jié)構(gòu),可以通過(guò)

5、定義不同的梁截面來(lái)模擬。(2錘架板、擋圈、錘片、銷軸、錘片隔套等零件隨著主軸一同旋轉(zhuǎn),將其簡(jiǎn)化為三維質(zhì)量單元MASS21。(3對(duì)起彈性支承作用的滾動(dòng)軸承用COMB I N 14彈簧單元來(lái)模擬。由于COMB I N 14是一維彈簧單元,所以考慮在主軸的水平和垂直方向分別設(shè)置2個(gè)C OM BI N14單元,來(lái)分別模擬滾動(dòng)軸承在這兩個(gè)方向的彈性。在主軸與聯(lián)軸節(jié)連接處,考慮存在彈性連接,所以在水平和垂直方向上也設(shè)置兩個(gè)彈簧單元,來(lái)模擬聯(lián)軸節(jié)對(duì)主軸的支承作用。通過(guò)以上的簡(jiǎn)化處理,設(shè)定好材料參數(shù),劃分網(wǎng)格并建立約束,最后建立的錘片式粉碎機(jī)轉(zhuǎn)子-軸承系統(tǒng)有限元模型如圖2所示。整個(gè)模型共有節(jié)點(diǎn)150個(gè),BEA

6、M 188梁?jiǎn)卧?37個(gè),C OM B I N E14彈簧單元12個(gè),MASS21質(zhì)量單元11個(gè)。 圖2 錘片式粉碎機(jī)轉(zhuǎn)子-軸承系統(tǒng)有限元模型1.3 模態(tài)分析模態(tài)分析用于確定結(jié)構(gòu)的振動(dòng)特性,如固有頻率、振型等。利用ANSYS10.0軟件的B lock Lanczos法對(duì)上述模型進(jìn)行分析求解,即可得到了轉(zhuǎn)子的各階固有頻率(見(jiàn)表1和模態(tài)振型(如圖3。為了保證機(jī)器安全運(yùn)行和正常工作,在機(jī)械設(shè)計(jì)中應(yīng)使旋轉(zhuǎn)軸的工作轉(zhuǎn)速n離開(kāi)其各階臨界轉(zhuǎn)速一定范圍。一般的要求是,工作轉(zhuǎn)速n不能超過(guò)一階臨界轉(zhuǎn)速nc的75%。由于本文所研究的錘片式粉碎機(jī)其工作轉(zhuǎn)速在3000 r/m i n左右,低于危險(xiǎn)工作轉(zhuǎn)速60 84.7

7、23 0.75= 3812.535r/m i n,所以其工作轉(zhuǎn)速的設(shè)計(jì)是合理的。表1 轉(zhuǎn)子的前5階固有頻率模態(tài)階數(shù)12345 9圖3 錘片式粉碎機(jī)轉(zhuǎn)子前三階模態(tài)振型圖圖4 工作頻率范圍內(nèi)轉(zhuǎn)子各部位動(dòng)態(tài)位移對(duì)頻率曲線1.4 諧響應(yīng)分析錘片式粉碎機(jī)工作時(shí),由于轉(zhuǎn)子質(zhì)心偏移現(xiàn)象的存在,受慣性的作用,會(huì)產(chǎn)生一個(gè)不平衡離心力,此不平衡力將通過(guò)主軸傳遞到軸承及機(jī)座上,從而引起粉碎機(jī)的振動(dòng)6?；谵D(zhuǎn)子不平衡振動(dòng)的特點(diǎn),應(yīng)用ANSYS諧響應(yīng)分析模塊來(lái)求解轉(zhuǎn)子-軸承系統(tǒng)的不平衡響應(yīng)。假設(shè)不平衡出現(xiàn)在轉(zhuǎn)子的中間部位,按錘片式粉碎機(jī)轉(zhuǎn)子的最大許用不平衡度7,取轉(zhuǎn)子質(zhì)心偏心距為0.052mm,不平衡力幅值為1315N

8、。選用Fu ll法(完全法,對(duì)轉(zhuǎn)子進(jìn)行其工作頻率范圍(約49.5H z的低頻激振,得到在不平衡載荷作用下轉(zhuǎn)子中部、左端軸承、右端軸承等處的徑向振動(dòng)響應(yīng)(如圖4所示。從圖4可以看出,在工作轉(zhuǎn)速下轉(zhuǎn)子中部的振幅(39.2 m大于兩端的振幅,左、右兩端軸承處的不平衡振幅基本相等(20 m。2 轉(zhuǎn)子結(jié)構(gòu)動(dòng)態(tài)靈敏度分析及優(yōu)化設(shè)計(jì)錘片式粉碎機(jī)的結(jié)構(gòu)復(fù)雜,設(shè)計(jì)變量很多,為了有效地進(jìn)行結(jié)構(gòu)的動(dòng)態(tài)優(yōu)化設(shè)計(jì),必須了解哪些物理參數(shù)對(duì)結(jié)構(gòu)的動(dòng)態(tài)特性影響較大,即研究結(jié)構(gòu)的動(dòng)態(tài)特性對(duì)這些結(jié)構(gòu)參數(shù)的敏感程度。在靈敏度分析基礎(chǔ)之上,有目的地修改結(jié)構(gòu),從而達(dá)到最佳的優(yōu)化結(jié)果。2 1 目標(biāo)函數(shù)的確定轉(zhuǎn)子優(yōu)化的目標(biāo)是提高轉(zhuǎn)子的動(dòng)態(tài)

9、特性,以降低錘片式粉碎機(jī)的振動(dòng)水平。由于ANSYS只能求解極小值問(wèn)題8,所以定義轉(zhuǎn)子優(yōu)化的目標(biāo)函數(shù)為:m i nf(x=10000f21+f22+f23式中:f1、f2、f3為轉(zhuǎn)子的前三階固有頻率。2 2 狀態(tài)變量的確定在優(yōu)化過(guò)程中,應(yīng)對(duì)轉(zhuǎn)子的重量和轉(zhuǎn)子在工作轉(zhuǎn)速下的不平衡響應(yīng)振幅加以控制。所以優(yōu)化模型的狀態(tài)變量選為轉(zhuǎn)子重量(W T和工作轉(zhuǎn)速下的左端軸承處的不平衡響應(yīng)振幅(RESP_LEFT2.3 設(shè)計(jì)變量的確定對(duì)轉(zhuǎn)子各結(jié)構(gòu)參數(shù)(如錘架板直徑、轉(zhuǎn)子主軸各軸148振動(dòng)與沖擊 2010年第29卷段的直徑和長(zhǎng)度進(jìn)行靈敏度分析,然后根據(jù)靈敏度分析結(jié)果確定設(shè)計(jì)變量。轉(zhuǎn)子各結(jié)構(gòu)參數(shù)如圖4所示,其中D1=D

10、5,D2=D4,L1=L5,L2=L4 。圖5 轉(zhuǎn)子優(yōu)化結(jié)構(gòu)參數(shù)2.4 轉(zhuǎn)子結(jié)構(gòu)靈敏度分析利用ANSYS 的最優(yōu)梯度法分別計(jì)算出轉(zhuǎn)子的各結(jié)構(gòu)參數(shù)對(duì)目標(biāo)函數(shù)和狀態(tài)變量的的靈敏度Sf 、S WT 、SRESP ,計(jì)算結(jié)果如表2所示。表2 轉(zhuǎn)子結(jié)構(gòu)靈敏度分析結(jié)果變量名稱靈敏度S f靈敏度S RESP靈敏度S WT S f32.65-0.0646729.991.0887從靈敏度分析結(jié)果可以看出,各設(shè)計(jì)變量對(duì)目標(biāo)函數(shù)及性能約束的影響程度不同,其中對(duì)轉(zhuǎn)子固有頻率影響最敏感的設(shè)計(jì)變量依次為D3>D7>L1>L6>L7>L3>L2>D6>D1>D2;對(duì)轉(zhuǎn)子

11、不平衡響應(yīng)振幅影響最敏感的依次為D3>L2>L3>D2>D1>L1>D7>L6>L7>D6;對(duì)轉(zhuǎn)子重量變化最敏感的依次為D3>D2>D1>L2>L3>D7>L1>D6>L6>L7;提高相同固有頻率值但付出重量代價(jià)較小的設(shè)計(jì)變量依次為L(zhǎng)7>L6>D7>L1>D6>L3>L2>D3。綜合以上分析,為了提高優(yōu)化效率,選取D3、D6、D7、L1、L2、L3、L6、L7為最終優(yōu)化模型的設(shè)計(jì)變量。2.5 轉(zhuǎn)子結(jié)構(gòu)的優(yōu)化結(jié)果轉(zhuǎn)子優(yōu)化模型設(shè)計(jì)變量、狀態(tài)變量、目標(biāo)

12、函數(shù)的設(shè)定及最優(yōu)結(jié)果見(jiàn)表3。轉(zhuǎn)子優(yōu)化方案經(jīng)過(guò)17次迭代后收斂,最優(yōu)結(jié)果為序列18。目標(biāo)函數(shù)f (x 及f 1、f 2、f 3的 收斂情況如圖6、圖7所示。表3 轉(zhuǎn)子結(jié)構(gòu)優(yōu)化過(guò)程優(yōu)化變量代號(hào)初值最小允許值最大允許值收斂誤差優(yōu)化結(jié)果u m RESP _L EF T0.110.090.112.0E-40.090041圖6 目標(biāo)函數(shù)f (x 的優(yōu)化收斂曲線圖7 轉(zhuǎn)子前三階固有頻率的優(yōu)化收斂曲線從優(yōu)化結(jié)果可以看出,目標(biāo)函數(shù)f (x 從22.56下降到17.999,下降了20.22%,其中轉(zhuǎn)子的第1階固有頻率從84.72H z 上升到90.295H z ,第2階固有頻率從183.2H z 上升到189.4

13、8H z ,第3階固有頻率從394.5H z 上升到514.41H z ;轉(zhuǎn)子的不平衡響應(yīng)19.75um 下(下轉(zhuǎn)第161頁(yè)149第5期 王曉博等:錘片式粉碎機(jī)轉(zhuǎn)子結(jié)構(gòu)動(dòng)態(tài)優(yōu)化設(shè)計(jì)端振動(dòng)值要小一些,但相差不大,所有鋪位均屬二級(jí)舒適度水平,但是下鋪和中鋪要比上鋪舒適。5 結(jié) 論鐵道車輛振動(dòng)舒適性是反映鐵道車輛運(yùn)行品質(zhì)的重要指標(biāo)。為較精確地仿真臥姿狀態(tài)下的人體振動(dòng)響應(yīng)特性,采用三自由度臥姿人體阻抗模型,對(duì)人體頭部、臀部和腳部的振動(dòng)進(jìn)行模擬?？紤]臥姿人體振動(dòng)響應(yīng)特性以及臥鋪的隔振作用,在傳統(tǒng)車輛二系懸掛動(dòng)力學(xué)模型基礎(chǔ)上,建立了 人-鋪-車輛 空間垂向耦合動(dòng)力學(xué)模型,并推導(dǎo)出臥姿人體振動(dòng)方程和臥姿人體

14、不同部位對(duì)8個(gè)車輪位移激勵(lì)的總頻響函數(shù),從而為鐵路臥鋪客車人體振動(dòng)舒適性仿真提供了理論模型。以 臥姿人體全身振動(dòng)舒適性的評(píng)價(jià) 國(guó)家標(biāo)準(zhǔn)為依據(jù),建立了鐵路臥鋪客車人體振動(dòng)舒適性仿真流程。該流程考慮通過(guò)對(duì)頭-臀兩部位加速度1/3倍頻程均方根值先后進(jìn)行部位計(jì)權(quán)和頻率計(jì)權(quán),得到臥姿人體垂向振動(dòng)舒適性綜合評(píng)價(jià)指標(biāo),進(jìn)而實(shí)現(xiàn)鐵路臥鋪客車的乘用舒適性分析仿真。根據(jù)文中建立的鐵路臥鋪客車人體振動(dòng)舒適性仿真理論模型和仿真流程,以M atlab為工具開(kāi)發(fā)軟件實(shí)現(xiàn)了鐵路人體振動(dòng)舒適性仿真,從而簡(jiǎn)化繁瑣的計(jì)算工作,大大提高了仿真計(jì)算的效率。論文研究工作為鐵路臥鋪客車人體振動(dòng)舒適性分析以及車輛參數(shù)優(yōu)化提供了有效手段。參

15、考文獻(xiàn)1俞展猷.鐵道車輛舒適性評(píng)價(jià)方法的發(fā)展與研究現(xiàn)狀J.鐵道車輛,2004,42(3:1-7.2徐國(guó)宇,梅雪松,吳序堂.多自由度人體-車輛-道路系統(tǒng)的建模與模擬J.機(jī)械工程學(xué)報(bào),1999,35(2:105-109.3魏 朗,陳蔭三,龔國(guó)慶.公路臥鋪客車的車-鋪-人系統(tǒng)平順性模擬計(jì)算J.中國(guó)公路學(xué)報(bào),1999,12(11:102-104.4王巖松,何 輝,耿艾莉.車輛-人體系統(tǒng)振動(dòng)時(shí)域模擬及懸架非線性分析J.振動(dòng)與沖擊,2007,26(12:36-39.5N ag aiM,Y osh i da H,Tohtake T.Coup led v i bration of passeng er and

16、 ligh t w e i ght ca r body i n consi derati on o f hu m an body b i om echan icsJ.V eh icle Syste m D yna m i cs,2006,44(1:601-611.6W e i L,G r iffi n M J.M athe m atica l m ode ls f o r the apparen tmass o f t he seated hu m an body exposed to vertical v i brati onJ.Journal o f Sound and V i brati

17、on,1998,212(5:855-874.7Ca rl bo m P,Berg M.P assenge rs,seats and carbody i n ra il vehicle dyna m icsJ.V eh i c le Syste m Dyna m ics.2003,37(S U PPL.:290-300.8張濟(jì)民,胡用生,陸正剛.軌道車輛運(yùn)行過(guò)程中人體振動(dòng)仿真研究J.振動(dòng)與沖擊,2007,26(10:76-80.9劉炳坤.人體沖擊動(dòng)力學(xué)模型研究中的若干問(wèn)題J.航天醫(yī)學(xué)與醫(yī)學(xué)工程,1996,9(5:381-384.10GB16440-1996.振動(dòng)與沖擊-人體機(jī)械驅(qū)動(dòng)點(diǎn)阻抗S.11

18、翟婉明.車輛-軌道耦合動(dòng)力學(xué)M.第三版.北京:科學(xué)出版社,2007:185-187.12王福天.車輛系統(tǒng)動(dòng)力學(xué)M.北京:中國(guó)鐵道出版社,1994:4-5.13龐勝明.公路與鐵路臥鋪客車臥位振動(dòng)舒適性試驗(yàn)與空間數(shù)值模擬D.西安:長(zhǎng)安大學(xué),2002:26-27.14GB/T18368-2001.臥姿人體全身振動(dòng)舒適性的評(píng)價(jià)S.(上接第149頁(yè)降為18.937u m;優(yōu)化后的轉(zhuǎn)子的重量為268.41kg,僅增加了1.29%。可見(jiàn),優(yōu)化后轉(zhuǎn)子的重量和不平衡響應(yīng)變化控制在較小范圍,但動(dòng)態(tài)性能得到明顯提高,優(yōu)化效果非常顯著。3 結(jié) 論以ANSYS軟件為平臺(tái),建立了錘片式粉碎機(jī)轉(zhuǎn)子有限元分析模型,對(duì)轉(zhuǎn)子進(jìn)行

19、了動(dòng)力學(xué)分析,得到了轉(zhuǎn)子固有頻率、模態(tài)振型、不平衡響應(yīng)等重要?jiǎng)討B(tài)性能參數(shù)。在此基礎(chǔ)上,對(duì)轉(zhuǎn)子結(jié)構(gòu)進(jìn)行靈敏度分析并完成了結(jié)構(gòu)的動(dòng)態(tài)優(yōu)化設(shè)計(jì)。經(jīng)過(guò)優(yōu)化,錘片式粉碎機(jī)轉(zhuǎn)子的動(dòng)態(tài)性能得到了明顯提高,為錘片式粉碎機(jī)的改進(jìn)提供了行之有效的解決辦法,并為相似類型的旋轉(zhuǎn)機(jī)械的動(dòng)態(tài)優(yōu)化設(shè)計(jì)提供有益的參考。參考文獻(xiàn)1朱新化,田沛玉.錘片式粉碎機(jī)的理論分析和結(jié)構(gòu)改進(jìn)措施探討J.西北農(nóng)業(yè)大學(xué)學(xué)報(bào),1999,27(1:108-111.2A jay iO A,C larke B.H i gh V e l oc ity I mpact of M aize K erne l sJ.Journal of A gr i cult

20、ural Eng ineer i ng R eseach,1997,67(2:97-107.3Fengn i an S,K o j ov ic T,Esterle J S,D av i d D.A n energy-based m ode l for s w i ng hamm er m ill sJ.Inte rnati onal Journa l o fM i neral P rocessi ng,22,2003,71(1-4:147-166. 4劉曼茹.錘式粉碎機(jī)的研究J.農(nóng)業(yè)機(jī)械學(xué)報(bào),1990,(3:54-58.5鄧潔紅,曹樂(lè)平.錘式粉碎機(jī)的優(yōu)化設(shè)計(jì)J.糧油食品科技,2005,13(3

21、:14-15.6宗 力,徐紅梅.錘片式粉碎機(jī)錘片磨損機(jī)理初探J.飼料工業(yè),2005,25(9:5-7.7J B/T9822.1-1999,錘片式飼料粉碎機(jī)技術(shù)條件S.北京:機(jī)械科學(xué)研究院,1999.12.8李黎明.ANSY S有限元分析實(shí)用教程M.北京:清華大學(xué)出版社.2005,1.161第5期 湯小紅等:鐵路臥鋪客車人體振動(dòng)舒適性建模與仿真246 J OURNAL OF V IBRAT I ON AND S HOCK V o.l29N o.52010data than those fro m the traditi o na l linear theoretic m ode.lK ey w

22、ords:m odeling;o il da mp i n g;para m eter i d entification;test(pp:133-135W enchuan8.0rank eart hquake acceleration peakattenuation curve based on a four area elliptical m odelY ANG F an1,LUO Q i f e ng2(1.Institute o f structurea l Eng i neer i ng and D isaster P reventi on,T ong jiU n i v.,Shang

23、ha i200092,Ch i na;2.Shangha i Institute o f D i saster P revention and R e lie,f Shangha i200092,Ch i naAbstract: A t presen,t an equal d istance circ le m odel is genera lly used for directly fitting acceleration peak attenua ti o n curve,ep icen tra l d i s tance o r focal distance is only the co

24、o r d i n ate statisti c al para m e ter for a seis m ic observation sta ti o n.For large eart h quake w ith a l o ng fau l,t the isoseis m ic curves of the equa l d istance c ircle m ode l ex ist serious dev iation fro m realistic isose i s m ic curves.There is enor m ous d ifferences bet w een the

25、 acceleration peak attenuati o n c urve along the long ax is and t h at a l o ng the short ax is.An four area elli p tica lm odelw as proposed here dividing seis m ic observation sta ti o ns into f o ur areas according to the long ax is and t h e short ax is.Every e lliptica l acceleration isose is

26、m ic curve in four are asw as respecti v ely figured out using i n terpo lation i n re lati o n to seis m ic i n tensity i s oseis m ic curves.On this basis,W en chuan earthquake acceleration peak attenuation cur ve w as derived a l o ng t w o l o ng se m iaxes and t w o short se m iaxes.Co m pari n

27、 g W enchuan8.0rank earthquake acceleration peak attenuation curve usi n g the four area elliptica lm ode lw it h that u si n g the circ le m ode,l the for m er w asm ore close to the rea l situati o n and it cou l d reflect t h e hang ing and foo tw all effect o f fault and the d irection e ffect o

28、 f eart h quake.K ey w ords:attenuation curve;four area e llipticalm ode;l equa l distance circ le m ode;l acce lerati o n peak(pp:136-140Analysis of iced trans m ission line galloping and effect of anti gallopingSU N Zhen mao,LOU W en juan(Instit ute o f Structural Eng i neeri ng,Zhe jiang U n i ve

29、 rs i ty,H ang z hou310058,ChinaAbstract: The non li n ear d ifferential equations of i c ed trans m issi o n li n e ga ll o ping w ere derived w ith Lag range equa ti o n for the fixed fi x ed trans m i s sion li n es insta lled w ith m asses or det u ning pendul u m s.The m ethod to calcu late the

30、 cr itical w ind velocity w as proposed.The non linear d ifferenti a l equati o ns w ere so lved by Runge Kutta m ethod to get the gall o ping response i n ti m e do m a i n.A tested trans m ission li n e w as calcu lated and analyzed as an exa m p l e.The results sho w ed that t h e torsional gall

31、o ping can cause lateral gallop i n g when their v ibrati o n frequencies are c l o se to each other;the a m plitude o f gall o ping is relatively large when t h e w ind ve l o c ity is in a certa i n range;the ga ll o ping a m plitude changesw ith the conduc to r sag sign ificantly and there ex ist

32、s t h e w orst sag to cause the lar gest ga ll o ping a m plitude;t h e m ethod to prevent gall o ping w it h m asses can reduce but not suppress the a m plitude of ga ll o ping;but t h e m e t h od to prevent ga llopi n g w ith detuning pendul u m s can e li m i n ate gallop i n g co m p letely.K e

33、y w ords:ga ll o ping;trans m ission li n e;anti gallop i n g;critica lw i n d ve l o c ity(pp:141-146Struct ural dyna m ic opti m al design for a ha mm er m ill s rotorWANG X iao bo1,X I E Rui qing2,D ING W u xue1,WA NG Shuan hu1(1.Schoo l o fM echanical Eng i nee ri ng,N anji ng U n i ve rsity o f

34、 Sc ience&T echnology,N anji ng210094,China;2.F ine O ptica l Eng i neer i ng R esearch Center,Chengdu610041,Ch i na;3.T racti on P o w er State K ey L aboratory of Sou t hwest Jiaotong U n i versity,Chengdu610031Ch i naAbstract: Dyna m ic ana l y sis o f a ha mm er m illw as carried out using F

35、E M,and dyna m ic c haracteristic para m e ters, such as,natural frequencies,v i b ration m odes,and unba lance responses w ere obta i n ed.The vari o us str uctural para m eters effect on the dyna m ic characteristic of t h e r o tor w ere ana l y zed based on sensitive ana l y sis.Taking the we i

36、g ht o f the r o tor and unba l a nce v i b ration responses as the state variab les,and the natural frequencies of the rotor as the objective func ti o ns,t h e rotor s structure w as opti m ized.The results o f the opti m a l desi g n i n d icated t h at the dyna m ic perfo r m ance o f theV o . 2

37、9 N o 5 2010 l . JOU RNAL OF V IBRAT I ON AND SHO CK 247 roto r is sig nifican tly i proved T he resu lts prov id ed an effect iv e m ethod to solve th e v ib rat ion prob lem o f a hamm er m il.l m . K ey w ord s hamm er m il;l opti al design sensitiv e ana ly sis dyna ic analysis; FE : m ; ; m M (

38、 pp 147- 149 161 : , Analysis of stick ing m otion in a vibro im pact syste w ith mu ltip le constrain ts m LI F ei, D I G W ang ca i N ( Schoo l ofM echa tron ic Eng ineering L anzhou Jiaotong U niversity Lanzhou 730070, China , , Ab stract : A tw o DOF v ibro i pact syste w ith mu lti constra in t

39、 w as estab lished A ccord in g to the number o f st ick m m . ing oscillators the m ode l w as divided in to four m ov ing system s w hose mo tions w ere analyzed si u ltaneously W ith cer , , m . tain para eters different k inds of period ic stick ing m otions appeared due to the d ifferent num be

40、r o f sticking oscillators and m , th e different start and end ti e of sticking m otion. H ere the sw itchover and transit io n conditions am ong the four m oving m , system s w ere studied T he temporary stilln ess appeared w hen a ll the oscillators of the system w ere in st icking state at . th

41、e sam e ti e. By ana lyzing the forces exerted to the oscillators on the i pact surface it w as discovered that w hen the m m , constra in ts are arranged on different sid es of the t o osc illato rs the forces of the tw o oscillators can t sat isfy the sticking w , conditions si u ltaneously so the

42、 si ultaneous stick w on t happen and th e proof is g iven by alterin g the param eters, tem m , m ; porary st illness w ill appearw hen constraints are p laced on the sam e sid es o f th e tw o osc illators F ina lly, num erical si . m u lation is g iv en and the results are a lso analyzed , . K ey

43、 w ord s v ibro i pac; m u ltiple constraints; period ic st icking m otion cha tter : m t ; ( pp 150- 156 : M odeling and si u lation of vibration com fort of human body in a railw ay sleeper carriage m TANG X iao hong , YANG Yue , PENG Bo 12 , 2 2 ( 1. Schoo l of E lectrical and M echan ica l Eng i

44、neer ing C entra l South U niversity of Fo restry and T echno logy Chang sha 410004, Ch ina , , ; 2. Schoo l o f T raffic and T ransportation Eng inee ring Cen tra l South U n iversity Chang sha 410075, Ch ina , , Abstract : T he whole body v ibratio n o f a recum bent passenger in a ra ilw ay sleep

45、er carriage is them ajor effect on the com fort feeling. T he vertical v ibratio n m odel o f a sup in e hum an body w as stu died B ased on the secondary suspensio n dy . nam ic m ode l of rail ay vehic les, a 14 DOF s hum an berth veh icle spatial vertica l coupled dynam ic m ode l w as estab w li

46、shed considering the vibration iso la tio n effect of the sleep ing berth and th e vert ic al vibration characteristics of th e supine hu an body Under the random irregular excitation o f track on the coupled dynam ic m ode,l the vertica l v ib ration respon m . ses of the sup in e hu an body w ere

47、stud ied at different tra in speeds W ith the evaluat io n criterion o f the v ib rat io n com fort m . of hum an body in supine position the si ulat ion program for the v ib ra tio n com fort of hum an body in a rail ay sleeper car , m w riage w as established The root m ean square acce lera tio ns o f head and buttock w ere w e