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      科學技術論文

      高階振型振動實驗裝置研制與教學應用

      時間:2019年06月05日 所屬分類:科學技術論文 點擊次數:

      摘要:針對振動學相關課程中高階振動實驗裝置偏少,學生對高階振型和固有頻率難以理解等問題,設計并制作了一種用于教學的高階振型振動實驗裝置。該裝置通過基于柔度法編寫的Matlab程序、基于錘擊法的自由振動實驗以及以激振器作為激勵振源的受迫振動實驗,

        摘要:針對振動學相關課程中高階振動實驗裝置偏少,學生對高階振型和固有頻率難以理解等問題,設計并制作了一種用于教學的高階振型振動實驗裝置。該裝置通過基于柔度法編寫的Matlab程序、基于錘擊法的自由振動實驗以及以激振器作為激勵振源的受迫振動實驗,實現了對高階振動的固有頻率和振型的理論計算和實驗測試,通過頻閃儀可以直觀地觀察到各階頻率的振型。實驗測得的各階頻率與相應的理論值的最大相對誤差分別為6.88%、5.40%和2.01%。該裝置已在教學中得到應用,并收到了良好的效果。

        關鍵詞:振動裝置;固有頻率;實驗教學;柔度矩陣

      機電一體化

        振動學涉及機械類的多門專業課程,高階振動系統又是振動學中的一類研究對象。為了使學生對振動現象有更深刻的認識,加深對理論知識的理解,各種振動實驗裝置及教學系統相繼開發。江蘇大學的李建康等[1]建立了多自由度系統模態振型實驗臺,用于研究在頻率可變的水平激勵下各個質量塊的振型狀態;中國礦業大學的張曉光等[2]搭建了含有故障的齒輪減速器振動實驗裝置;華中科技大學的何嶺松[3]設計了用于描述多自由度振動模型的仿真系統。

        蔣志峰[4]等、張予等[5]利用Matlab對單自由度系統受不同激振頻率的受迫振動響應進行了仿真分析;付志一等[6]設計了三自由度扭振實驗裝置,研究系統本身的振型及附加質量和剛度對于系統振型的影響;梁慶等[7]基于Lab-VIEW開發了多自由度懸臂梁振動實驗教學系統,可實現單自由度、兩自由度和三自由度等多種實驗方案,并利用有限元軟件對模型進行模態分析與比較;張蔚波等[8]研制了簡支梁形式的振動實驗教學裝置,分析了不同性質激勵下的響應;李兆軍等[9]研制了包含離散質量、連續梁、軸和組合結構的綜合振動實驗裝置。

        上述的振動實驗裝置及教學系統,有的局限于單自由度的振動研究,有的則專門針對某一實體部件而進行研究,有關高階振動的振型可視化及固有頻率的計算則涉及非常少,能夠在理論和實驗兩方面都能激發學生的學習興趣、增強學生的理解能力的裝置更少。為此本文研制了一套適用于高階振型振動系統教學的實驗裝置。該裝置可實現對固有頻率的理論計算和實驗測試,可直接觀察不同階次的振型。該實驗裝置可根據需要設計為不同的階數,本文以三階系統為例進行介紹。

        1實驗裝置結構設計

        本實驗裝置主要由主體框架、振動傳感器、千分表、磁性表座、立柱、定滑輪、激振器、信號發生器、數據采集儀和頻閃儀等組成。主體框架為3層鋼架結構,由空心鋼管和側板固接;振動傳感器為加速度傳感器,固定在主體框架的頂層側板上;千分表主要用來測量框架受到靜力作用時各層的位移變化量;立柱用于固定測算振動體柔度矩陣的定滑輪;激振器為主體框架提供受迫振動的激勵,通過信號發生器改變其振動頻率,經實驗驗證,激振器與主體框架的連接位置對系統的固有頻率沒有影響,為了方便安裝,本文將激振器與底層側板相連;數據采集儀主要將測得的振動信號傳遞給安裝有動態分析軟件的上位機,以此來實時顯示振動信號的時域及頻域波形圖,便于學生更為直觀地了解振動信號的固有頻率及振幅。

        2實驗方案

        主要包括理論計算、自由振動實驗、受迫振動實驗3部分。理論計算通過重物在主體框架的某個節點上作用一定的載荷,使得各層鋼管產生一定的變形,由千分表測得位移變化量并輸入基于柔度法編寫的Matlab程序中,從而在理論上計算出各階振動的固有頻率及振型。實驗方法分別通過錘擊法模擬自由振動,和由激振器模擬的強迫振動,使得主體框架產生振動,由加速度傳感器將振動信號傳遞給數據采集儀和安裝有DHDAS動態信號采集分析軟件的上位機,以此來直觀地觀察高階振動的各階固有頻率及振幅變化。

        利用頻閃儀可觀察到受迫振動時各階頻率的振型,并與理論計算結果進行比較,檢驗模型和算法的準確性。該實驗裝置的主要目的在于給學生提供一個能夠對高階振動的振型及固有頻率產生一種直觀印象的實驗平臺。通過理論計算方法和實驗方法,學生不僅可以從理論上掌握求解相關高階振動的固有頻率及其振型的方法,而且還可以運用所學的理論知識,通過實驗測得和觀察高階振動的固有頻率及振型,加深對高階振動的理解。

        3理論計算方法

        本文基于柔度法計算固有頻率及振型。根據柔度影響系數aij的定義,在j點上作用的單位載荷所引起的i點的位移,可以通過施加在主體框架上力的大小以及各層框架的位移變化量來計算出該系統的柔度矩陣,進而求出固有頻率及振型。

        4實驗結果分析

        按照理論計算方法的步驟,將各層質量及位移變化量輸入到程序中。一階振型均為正值,表明各層之間沒有從負向正的節點變化;二階振型底層和中層為負值,頂層為正值,表明中層與頂層之間存在節點;三階振型的中間層為負值,其余兩層為正值,表明底層與中層、中層與頂層之間分別存在一個節點。

        理論計算、自由振動實驗和受迫振動實驗得到的3層框架結構振動體的固有頻率。實驗與理論計算之間存在誤差,其中一階固有頻率的相對誤差最大,三階固有頻率的相對誤差最小。產生誤差的原因主要是由于千分表的測量誤差、主體框架材料的剛度較大以及加速度傳感器質量的影響。

        5結語

        機械類專業課程都會涉及到振動學,高階振型振動實驗裝置可用于機械振動學、機械故障診斷、理論力學、機械動力學以及機械工程控制基礎等課程的實驗教學。利用高階振型振動實驗裝置,學生從理論和實驗兩個方面獲取高階振動體的固有頻率,并觀測其振型的變化,從而加深了對高階振動系統的認識。該實驗裝置完善了振動學的教學實驗內容,在教學應用中收到了良好的教學效果,提高了學科教學質量。

        參考文獻(References)

        [1]李建康,肖同亮,蔡東升,等.多自由度系統模態振型創新型教學實驗的設計與實現[J].實驗技術與管理,2006,23(2):16-18.

        [2]張曉光,趙志科,陳瑩瑩.基于齒輪減速器的振動實驗裝置研制[J].實驗技術與管理,2014,31(1):55-59.

        [3]何嶺松.多自由度振動模型仿真和在教學中的應用[J].實驗室研究與探索,2005,24(5):5-7.

        [4]蔣志峰,樓易.用MATLAB進行單自由度系統機械振動試驗[J].力學與實踐,2004(26):86-88.

        [5]張予,楊福運,呂紹棣,等.基于MATLAB的單自由度振動系統的數學仿真實驗[J].華東交通大學學報,2002,19(1):28-30.

        [6]付志一,張平,余蓮英.三自由度扭振綜合性實驗裝置的設計與應用[J].實驗技術與管理,2009,26(10):49-51.

        [7]梁慶,任利惠,賀經緯.一種多自由度懸臂梁振動實驗教學系統[J].機電一體化,2015(2):67-70.

        機電工程師評職刊物:機電一體化(月刊)創刊于1995年,由上海圖書館、上海科技情報研究所主管,上海科學技術文獻出版社主辦,中國電工技術學會機電一體化專業委員會協辦。

        

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