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螺桿真空泵轉子熱形變分析及轉子優化

2017-10-17  來自: 真(zhen)空技術網 瀏覽次數(shu):721

建立180L/s 轉子溫度場有限元模型,得到其溫度場和熱形變分布情況,結合熱形變結果推導出泵腔內各點冷配合間隙。利用分析結果對螺桿真空泵轉子形狀進行優化設計。分析結果顯示:180L/s 螺桿真空泵兩轉子之間間隙應大于0.28mm,泵腔和轉子之間間隙應大于0.20mm。結合所述分析結果對轉子形狀進行優化,優化后的轉子可以減少原有22%冷配合間隙,一定程度上降低泵工作過程中返流量。

  螺(luo)(luo)桿(gan)真空泵(beng)(beng)轉(zhuan)(zhuan)子(zi)(zi)的(de)裝(zhuang)(zhuang)配間(jian)隙取決于(yu)工(gong)作(zuo)(zuo)狀(zhuang)態下(xia)轉(zhuan)(zhuan)子(zi)(zi)每一(yi)個嚙合位置的(de)熱形(xing)變量(liang)。工(gong)作(zuo)(zuo)狀(zhuang)態下(xia)轉(zhuan)(zhuan)子(zi)(zi)徑向熱形(xing)變量(liang)較(jiao)大,需要預(yu)留一(yi)定裝(zhuang)(zhuang)配間(jian)隙,這些間(jian)隙很(hen)大程(cheng)(cheng)度上影響了泵(beng)(beng)的(de)抽氣性能。環境溫度較(jiao)低的(de)工(gong)況下(xia),工(gong)作(zuo)(zuo)前(qian)需要對螺(luo)(luo)桿(gan)真空泵(beng)(beng)進行(xing)(xing)預(yu)熱,使轉(zhuan)(zhuan)子(zi)(zi)膨脹一(yi)定程(cheng)(cheng)度以彌補較(jiao)大的(de)冷配合間(jian)隙,泵(beng)(beng)才能正常工(gong)作(zuo)(zuo)。很(hen)多學者曾(ceng)對螺(luo)(luo)桿(gan)真空泵(beng)(beng)轉(zhuan)(zhuan)子(zi)(zi)型線(xian)(xian)和轉(zhuan)(zhuan)子(zi)(zi)熱形(xing)變情況進行(xing)(xing)研究,為螺(luo)(luo)桿(gan)真空泵(beng)(beng)轉(zhuan)(zhuan)子(zi)(zi)型線(xian)(xian)和熱學分析做出許多貢獻。本(ben)研究對螺(luo)(luo)桿(gan)真空泵(beng)(beng)轉(zhuan)(zhuan)子(zi)(zi)進行(xing)(xing)熱形(xing)變分析,并結合分析結果對轉(zhuan)(zhuan)子(zi)(zi)曲線(xian)(xian)的(de)軸截(jie)面形(xing)狀(zhuang)進行(xing)(xing)優化設計,一(yi)定程(cheng)(cheng)度上減(jian)少(shao)了轉(zhuan)(zhuan)子(zi)(zi)的(de)裝(zhuang)(zhuang)配間(jian)隙。

1、有限元模型的建立

  選擇180L/s 螺桿真空(kong)泵作為(wei)研究對象,其幾何參數如表1 所示。建立(li)主動、從(cong)動轉(zhuan)子的簡化三維(wei)模型。轉(zhuan)子端面型線如圖1 所示。

表1 螺桿泵(beng)轉子幾何參數

螺桿真空泵轉子熱形變分析及轉子優化

螺桿真空泵轉子熱形變分析及轉子優化

圖1 轉子型(xing)線方程

螺桿真空泵轉子熱形變分析及轉子優化

  將模型(xing)(xing)導入有(you)限元分析軟件。熱分析涉及的(de)三(san)維(wei)實體單元有(you)SOLID87、SOLID70 和SOLID90,選擇20 個節點的(de)分析單元類型(xing)(xing)SOLID90。因不(bu)銹鋼螺桿難以加工(gong),目前大多數螺桿真(zhen)空泵(beng)轉子(zi)材料采用鑄鐵,其(qi)物性(xing)參(can)數如表2 所(suo)示。考慮到(dao)螺桿轉子(zi)的(de)幾何形(xing)狀較為復雜,對轉子(zi)進行(xing)自由(you)網格(ge)劃分,得(de)到(dao)螺桿真(zhen)空泵(beng)轉子(zi)的(de)有(you)限元模型(xing)(xing)。

表2 轉(zhuan)子(zi)物性參數

螺桿真空泵轉子熱形變分析及轉子優化

2、熱載荷的施加

2.1、熱邊界條件的選取

  進(jin)行(xing)熱分(fen)析之前(qian),需要確定單值(zhi)性條件(jian),包(bao)括幾何參(can)數、物性參(can)數和邊(bian)界(jie)條件(jian)。幾何參(can)數和物性參(can)數上文已經給出。邊(bian)界(jie)條件(jian)的(de)選取是單值(zhi)性條件(jian)的(de)關(guan)鍵。

  熱(re)學(xue)分(fen)(fen)析邊(bian)界條件有三類,本文采用(yong)施加(jia)第三類邊(bian)界條件,即施加(jia)轉(zhuan)(zhuan)子(zi)接觸的(de)流(liu)(liu)體介(jie)質溫度(du)和對流(liu)(liu)換(huan)熱(re)系數。根據轉(zhuan)(zhuan)子(zi)運轉(zhuan)(zhuan)過程中(zhong)每一級封閉腔流(liu)(liu)體介(jie)質狀態不同,轉(zhuan)(zhuan)子(zi)熱(re)邊(bian)界條件按照導(dao)程劃(hua)分(fen)(fen)為(wei)四部分(fen)(fen)。

2.2、邊界(jie)條件的確定

  螺桿真空泵(beng)工作過(guo)程中所產生(sheng)的熱量主要來源于后一(yi)級運輸腔(qiang)壓縮氣體做功。后一(yi)級運輸腔(qiang)涉及到的熱力學表達式為:

Q-W=ΔU (1)

  式中:Q 為(wei)(wei)后一級(ji)運(yun)輸腔與外(wai)界交換的(de)熱量;W 為(wei)(wei)對(dui)外(wai)所作(zuo)膨脹功;ΔU 為(wei)(wei)熱力學能變(bian)化(hua)。由文(wen)獻中轉(zhuan)子溫度的(de)實驗結果(guo)可(ke)知,轉(zhuan)子前三段溫度每一級(ji)溫度可(ke)近似為(wei)(wei)線性分布(bu)。螺桿泵(beng)工作(zuo)時的(de)氣體(ti)運(yun)輸可(ke)以近似為(wei)(wei)管道流動過(guo)程,故(gu)選擇管內(nei)受迫流動準則方程確定傳熱系(xi)數。

Nu=0.023Re 0.8 Pr 0.3 (2)

  式中Nu 為(wei)(wei)努塞(sai)爾數;Re 為(wei)(wei)雷諾數;Pr 為(wei)(wei)普(pu)朗數。

  反映對(dui)流(liu)換(huan)熱強弱的努塞(sai)爾數公式(shi)為:

Nu=ad/λ (3)

  式中a 為對(dui)流換熱(re)系數;d 為當量(liang)直(zhi)徑;λ 為流體(ti)的導(dao)熱(re)系數。

  由式(2)和(he)(3)聯立可得(de)

a=0.023Re 0.8 Pr 0.3 d/λ (4)

  根據每一級不同流(liu)體狀(zhuang)態,得(de)到陰陽轉子的對流(liu)換熱系(xi)數和(he)當(dang)量(liang)溫度。

3、分析結果

3.1、溫(wen)度場分(fen)布

  本研究(jiu)分析的(de)是所(suo)抽(chou)氣體溫(wen)度為30℃,螺桿真空泵(beng)正(zheng)常工作時的(de)穩(wen)態溫(wen)度場分布。將計算得到的(de)邊界條件施加在轉(zhuan)子表面,得到主、從動(dong)轉(zhuan)子溫(wen)度場分布如(ru)圖2 所(suo)示。

  從(cong)圖2(a)、(b)可以得知主(zhu)動(dong)轉(zhuan)(zhuan)子(zi)和從(cong)動(dong)轉(zhuan)(zhuan)子(zi)的溫(wen)度(du)沿(yan)軸(zhou)向從(cong)進(jin)氣端至(zhi)排(pai)氣端逐(zhu)漸增高(gao)。主(zhu)動(dong)轉(zhuan)(zhuan)子(zi)的進(jin)氣端為112.50℃, 排(pai)氣端溫(wen)度(du)為179.57℃;從(cong)動(dong)轉(zhuan)(zhuan)子(zi)的進(jin)氣端溫(wen)度(du)為110.65℃,排(pai)氣端溫(wen)度(du)為178.46℃。

螺桿真空泵轉子熱形變分析及轉子優化

圖2 轉(zhuan)子(zi)溫度場分布云圖

3.2、熱形變分析

  基于溫度場分(fen)析(xi)結果求得(de)轉子(zi)熱形變(bian)(bian)(bian)(bian)(bian)量。圖3 顯示了轉子(zi)工作(zuo)狀態下(xia)齒(chi)(chi)(chi)頂圓(yuan)(yuan)、齒(chi)(chi)(chi)根圓(yuan)(yuan)徑向熱形變(bian)(bian)(bian)(bian)(bian)量大(da)小。由圖可(ke)知,齒(chi)(chi)(chi)頂圓(yuan)(yuan)、齒(chi)(chi)(chi)根圓(yuan)(yuan)徑向熱形變(bian)(bian)(bian)(bian)(bian)量從進(jin)氣端(duan)至排氣端(duan)逐漸增大(da)。齒(chi)(chi)(chi)頂圓(yuan)(yuan)熱形變(bian)(bian)(bian)(bian)(bian)量為(wei)0.198mm,小熱形變(bian)(bian)(bian)(bian)(bian)量為(wei)0.078mm;齒(chi)(chi)(chi)根圓(yuan)(yuan)熱形變(bian)(bian)(bian)(bian)(bian)量為(wei)0.074mm,小熱形變(bian)(bian)(bian)(bian)(bian)量為(wei)0.03mm。

螺桿真空泵轉子熱形變分析及轉子優化

圖3 轉子各點徑向熱形變量

  如果不(bu)考(kao)慮(lv)轉(zhuan)子(zi)端面間(jian)(jian)(jian)隙(xi)(xi),泵(beng)腔(qiang)內存在四處(chu)間(jian)(jian)(jian)隙(xi)(xi),α 處(chu)為一個(ge)轉(zhuan)子(zi)齒頂(ding)(ding)圓與(yu)另一個(ge)齒根(gen)圓的(de)間(jian)(jian)(jian)隙(xi)(xi),β 處(chu)為兩轉(zhuan)子(zi)型線中(zhong)cd、de 段之(zhi)間(jian)(jian)(jian)的(de)間(jian)(jian)(jian)隙(xi)(xi),γ 處(chu)轉(zhuan)子(zi)齒頂(ding)(ding)圓與(yu)泵(beng)腔(qiang)之(zhi)間(jian)(jian)(jian)間(jian)(jian)(jian)隙(xi)(xi),ε 處(chu)為兩轉(zhuan)子(zi)型線中(zhong)ab 段之(zhi)間(jian)(jian)(jian)的(de)間(jian)(jian)(jian)隙(xi)(xi),如圖4 所(suo)示。轉(zhuan)子(zi)的(de)齒頂(ding)(ding)圓與(yu)另一轉(zhuan)子(zi)的(de)齒根(gen)圓嚙合,通過圖3 齒頂(ding)(ding)圓與(yu)齒根(gen)圓徑向(xiang)(xiang)熱(re)(re)形(xing)變(bian)曲線可以確(que)定α 處(chu)間(jian)(jian)(jian)隙(xi)(xi)值應該不(bu)小于0.28mm。由于兩轉(zhuan)子(zi)軸向(xiang)(xiang)熱(re)(re)形(xing)變(bian)量(liang)(liang)(liang)差別不(bu)大,一般不(bu)考(kao)慮(lv)轉(zhuan)子(zi)熱(re)(re)形(xing)變(bian)量(liang)(liang)(liang)對(dui)兩轉(zhuan)子(zi)軸向(xiang)(xiang)間(jian)(jian)(jian)隙(xi)(xi)的(de)影響。工作狀態下泵(beng)腔(qiang)熱(re)(re)形(xing)變(bian)量(liang)(liang)(liang)很(hen)小,所(suo)以γ 處(chu)泵(beng)腔(qiang)與(yu)齒頂(ding)(ding)圓間(jian)(jian)(jian)隙(xi)(xi)可由齒頂(ding)(ding)圓熱(re)(re)形(xing)變(bian)量(liang)(liang)(liang)決定,應該不(bu)小于0.20mm。α 處(chu)間(jian)(jian)(jian)隙(xi)(xi)與(yu)兩轉(zhuan)子(zi)軸向(xiang)(xiang)間(jian)(jian)(jian)隙(xi)(xi)值確(que)定后間(jian)(jian)(jian)接可以推斷出β和ε 處(chu)裝配間(jian)(jian)(jian)隙(xi)(xi)值。

螺桿真空泵轉子熱形變分析及轉子優化

圖4 泵腔內裝配間隙帶位置(zhi)

4、優化設計

  針(zhen)對轉(zhuan)(zhuan)子(zi)(zi)各點(dian)(dian)徑向(xiang)熱形(xing)變量(liang)存在的(de)(de)(de)差異(yi),從(cong)轉(zhuan)(zhuan)子(zi)(zi)形(xing)狀入手,加工轉(zhuan)(zhuan)子(zi)(zi)時對其熱形(xing)變量(liang)大的(de)(de)(de)位置(zhi)進(jin)(jin)行(xing)切削,提前預留出(chu)工作過程中轉(zhuan)(zhuan)子(zi)(zi)熱形(xing)變對間(jian)隙(xi)(xi)的(de)(de)(de)補(bu)償值,達(da)到減小裝(zhuang)配間(jian)隙(xi)(xi)的(de)(de)(de)目的(de)(de)(de)。通過分析結果(guo)可以(yi)看出(chu)轉(zhuan)(zhuan)子(zi)(zi)徑向(xiang)熱形(xing)變量(liang)從(cong)進(jin)(jin)氣(qi)端至(zhi)排氣(qi)端呈線性遞增,因此(ci)優化思路為加工轉(zhuan)(zhuan)子(zi)(zi)時將整個轉(zhuan)(zhuan)子(zi)(zi)外(wai)形(xing)做成(cheng)錐形(xing),進(jin)(jin)氣(qi)端較粗,排氣(qi)端較細(xi),真空(kong)技術網(wang)(http://www.chvacuum.com/)認為可以(yi)一(yi)(yi)定程度上(shang)減小兩(liang)轉(zhuan)(zhuan)子(zi)(zi)之間(jian)的(de)(de)(de)冷配合間(jian)隙(xi)(xi),降低泵(beng)工作過程中的(de)(de)(de)返流量(liang),達(da)到提高螺桿真空(kong)泵(beng)的(de)(de)(de)抽氣(qi)性能的(de)(de)(de)效果(guo)。型線的(de)(de)(de)特征為轉(zhuan)(zhuan)子(zi)(zi)ab 段于另一(yi)(yi)轉(zhuan)(zhuan)子(zi)(zi)的(de)(de)(de)a 點(dian)(dian)嚙合,轉(zhuan)(zhuan)子(zi)(zi)cd 段和另一(yi)(yi)轉(zhuan)(zhuan)子(zi)(zi)的(de)(de)(de)e 點(dian)(dian)嚙合,de 段和另一(yi)(yi)轉(zhuan)(zhuan)子(zi)(zi)的(de)(de)(de)d 點(dian)(dian)嚙合。e 點(dian)(dian)在齒頂圓上(shang),d 點(dian)(dian)在節圓位置(zhi)上(shang)。

  因(yin)此(ci)(ci)優化設計(ji)的(de)方案是將粗加工(gong)好轉子(zi)(zi)的(de)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)切削(xue)量從進(jin)氣(qi)(qi)端(duan)(duan)(duan)的(de)0mm 線性(xing)增大(da)至排(pai)氣(qi)(qi)端(duan)(duan)(duan)的(de)0.12mm,使得加工(gong)出(chu)的(de)轉子(zi)(zi)外圓(yuan)(yuan)(yuan)(yuan)成錐形(xing),并將端(duan)(duan)(duan)面型線方程上d 點(dian)(dian)對應的(de)那條螺旋線打(da)磨(mo)掉0.05mm。裝(zhuang)配(pei)時(shi)(shi)排(pai)氣(qi)(qi)端(duan)(duan)(duan)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)與(yu)齒(chi)(chi)(chi)(chi)(chi)根圓(yuan)(yuan)(yuan)(yuan)之間(jian)(jian)間(jian)(jian)隙(xi)(xi)取排(pai)氣(qi)(qi)端(duan)(duan)(duan)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)與(yu)齒(chi)(chi)(chi)(chi)(chi)根圓(yuan)(yuan)(yuan)(yuan)熱形(xing)變(bian)量之和,為0.28mm,此(ci)(ci)時(shi)(shi)進(jin)氣(qi)(qi)端(duan)(duan)(duan)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)與(yu)齒(chi)(chi)(chi)(chi)(chi)根圓(yuan)(yuan)(yuan)(yuan)之間(jian)(jian)間(jian)(jian)隙(xi)(xi)為0.16mm。裝(zhuang)配(pei)時(shi)(shi)排(pai)氣(qi)(qi)端(duan)(duan)(duan)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)與(yu)泵(beng)腔之間(jian)(jian)間(jian)(jian)隙(xi)(xi)取齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)進(jin)氣(qi)(qi)端(duan)(duan)(duan)徑向(xiang)熱形(xing)變(bian)量,為0.2mm, 此(ci)(ci)時(shi)(shi)進(jin)氣(qi)(qi)端(duan)(duan)(duan)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)與(yu)泵(beng)腔之間(jian)(jian)間(jian)(jian)隙(xi)(xi)為0.08mm。這樣以來裝(zhuang)配(pei)位置α、γ 處(chu)均(jun)不(bu)會(hui)發生(sheng)干涉,由于轉子(zi)(zi)cd 段(duan)和另一轉子(zi)(zi)的(de)e 點(dian)(dian)嚙(nie)合(he),de段(duan)和另一轉子(zi)(zi)的(de)d 點(dian)(dian)嚙(nie)合(he),e 點(dian)(dian)在(zai)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)上,齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)經過切削(xue)處(chu)理(li),d 點(dian)(dian)打(da)磨(mo)掉0.05mm,因(yin)此(ci)(ci)ε 處(chu)不(bu)會(hui)發生(sheng)干涉,a 點(dian)(dian)也(ye)在(zai)齒(chi)(chi)(chi)(chi)(chi)頂(ding)(ding)(ding)圓(yuan)(yuan)(yuan)(yuan)上,同(tong)理(li)β 處(chu)間(jian)(jian)隙(xi)(xi)也(ye)不(bu)會(hui)發生(sheng)干涉。確定理(li)論裝(zhuang)配(pei)間(jian)(jian)隙(xi)(xi)的(de)平均(jun)值如表3 所示。

表3 裝配(pei)間隙(xi)平(ping)均(jun)值大小對比(bi)

螺桿真空泵轉子熱形變分析及轉子優化

  由(you)文(wen)獻可知,影響螺(luo)桿真空泵(beng)返(fan)(fan)流量(liang)主要(yao)因素為(wei)齒頂圓(yuan)與泵(beng)腔的(de)間(jian)隙,其返(fan)(fan)流量(liang)計(ji)算公式(shi)為(wei):

螺桿真空泵轉子熱形變分析及轉子優化

  其(qi)中B 為縫(feng)隙長度(du);Δp 為縫(feng)隙前(qian)后壓差;δ為縫(feng)隙寬度(du)。將表3 優化(hua)前(qian)與優化(hua)后的間隙值帶入返(fan)流公式求得優化(hua)后的轉(zhuan)子可(ke)以減(jian)少52%工作狀態下(xia)齒頂圓與泵腔(qiang)之間返(fan)流量。

5、總結

  對螺桿真(zhen)空泵轉子(zi)進行(xing)溫(wen)度場和熱形(xing)變(bian)模(mo)擬計(ji)算(suan),得出轉子(zi)泵腔(qiang)內的冷(leng)配合間(jian)(jian)隙大(da)(da)小。結果(guo)顯(xian)示轉子(zi)齒(chi)(chi)(chi)頂(ding)圓(yuan)與(yu)(yu)齒(chi)(chi)(chi)根(gen)(gen)圓(yuan)之(zhi)間(jian)(jian)裝配間(jian)(jian)隙應(ying)大(da)(da)于(yu)0.28mm,齒(chi)(chi)(chi)頂(ding)圓(yuan)與(yu)(yu)泵腔(qiang)之(zhi)間(jian)(jian)裝配間(jian)(jian)隙應(ying)大(da)(da)于(yu)0.20mm。結合分(fen)析結果(guo)對轉子(zi)方程形(xing)狀(zhuang)進行(xing)優(you)(you)化設計(ji)。優(you)(you)化后齒(chi)(chi)(chi)頂(ding)圓(yuan)與(yu)(yu)齒(chi)(chi)(chi)根(gen)(gen)圓(yuan)間(jian)(jian)隙平均值減(jian)少為0.21mm,齒(chi)(chi)(chi)頂(ding)圓(yuan)與(yu)(yu)泵腔(qiang)之(zhi)間(jian)(jian)間(jian)(jian)隙平均值減(jian)少為0.14mm。利(li)用返流(liu)公式求得優(you)(you)化后的轉子(zi)可以減(jian)少52%齒(chi)(chi)(chi)頂(ding)圓(yuan)與(yu)(yu)泵腔(qiang)之(zhi)間(jian)(jian)返流(liu)量。

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