外文翻譯---液壓機(jī)械裝置振動(dòng)問題處理

1、<p><b>　　原文</b></p><p>　　Solving Vibration Problems In Hydraulic Machinery</p><p><b>　　Abstract</b></p><p>　　In the current paper, various cases of vibr

2、ation problems detected in hydraulic machinery are presented.These cases were found during several years of vibration monitoring.the problems have been classified depending on their origin.For all of them,a systematic ap

3、proach is given indicating the symptoms,the exciatation provoking them,the possibilities of amplification due to resonance and the remedies that have been applied.</p><p>　　Introduction</p><p>　

4、　Vibration problems are common in hydraulic machinery.Solving them helps to increase the machine life and to reduce maintenance costs.</p><p>　　Many cases have been found and solved during last years of moni

5、toring (Egusquiza 1998 and Egusquiza et.2000).Some of them have been due to design or mounting problems and others due to damage in machine elements.The cases presented here correspond to large machine with vertical shaf

6、t and rigid coupling.The problems found have been classified in the following types:</p><p>　　Type 1: Excessive excitations of hydraulic origin</p><p>　　Type 2: Hrust bearing problems</p>

7、<p>　　Type 3: Unbalance and misalignment</p><p>　　Type 4: Electromagnetic problem</p><p>　　A methodology to solve these types of vibration problems is proposed in the paper.The steps to fo

8、llow are indicated in Fig,1.Once the abnormal high vibration amplitudes have been detected through scheduled monitoring or machine malfunctioning.Vibration analysis has to be proformde to identify the origin of the excia

9、tion provoking them.Various techniques are available depending on the type of excitation under consideration,whether it is hydraulic,mechanic or</p><p>　　Eletromagnetion.</p><p>　　The resulting

10、high vibration levels may also be due to some type of resonace in the hydraulic system or in the mechanical compoents.Therefore, this possibility must be checed before a correct diagnostic can be made.</p><p&g

11、t;　　Finally, remedies to the probiem are proposed and their success is confirmed comparing the vibrations after the modification with theprevious ones.</p><p>　　Type 1: Excessive Hydraulic Excitation.</p&

12、gt;<p>　　Typical vibrations of hydraulic origin are generated by rotor-stator interaction (RSI) and by cacitation.</p><p>　　RSI is due to the interference between the runner blades and guide vanes.It

13、can generate pressure pulsations of high amplitude in hydraulic machines.As a result,cracks in runners and excessive vibrationlevels in machine and piping can be produced.RSI identification is normally easy with spectral

14、 analysis of vibration.The problem is to know if the vibration is high due to the excitation itself,to a high hydraulic system is high due to the excitation resonse or to a runner/motor resonance.The vibr</p><

15、p>　　Fb=n*f*zb=</p><p>　　With maximum amplitude at the lowest diametrical mode excited k according to the following equation(tanaka 1990):</p><p>　　n*zv+-k=m*zb</p><p>　　Another t

16、ypical phenomenon that can generate vibrations is cavitation.Cavitation can take several forms and can result in vibrations,losses of performance and erosion. The most common type of cavitation is part load suige. Its ne

17、gative effects are usually mitigated by means of air entrapment in draft tube. On the other hand, inlet cacitation provoking erosion of runner blades is also a concern due to its destructive effects.</p><p>

18、　　Here there are some examples for both types of hydraulic excitations.</p><p>　　High vibrations in thecasingof a multistage pump</p><p>　　A multistage pump had high vibration levels in the casi

19、ng during operation. The generated vibrations produced the burst of pipes and other elements. Initially, it was thought that the vibrations were due to wear or damage(malfunctioning). As a result, the pump was completely

20、 dismantled and repaird. Surprisingly, the vibration did not disappear.</p><p>　　A general scheme of the pump is given in fig,2.During pumping the machine delivers a flow rate of 2.8 m3/s to a head of 935 m

21、.Other machine characteristics are listed in Table 1.</p><p>　　To understand the cause of the high vibertion levels some experimental measurements and a theoretical analysis were carried out.</p><

22、p>　　From the spectral analysis it was found that the vibration amplitude occurred at 150 Hz which is fb(see Fig,5).therefore,the vibration has a fluid dynamic origin and its high amplitude might be due to several reas

23、ons such as high RSI excitation due to design,mounting,damage,or resonance. In this case,the RSI analysis gives a pressure pulsation around the impeller with a diametrical mode k=-2 rotating in the opposite direction of

24、the impeller st fb.</p><p>　　First of all, the hydraulic system response of the return channel was calculated using a transfer matrix method. No frequencies around 150Hz were found. Furthermore, the analysis

25、 of the measurements(phase and amplitude variation)at different roating speeds neither showed resonance around the excitation frequency.</p><p>　　Modal analysis from the impacts done with an insteumented ham

26、mer was carried out to check the possibility of mechuanical resonance in the casing or impeller.</p><p>　　For the casing,no resonance was found at around the frequency of 150 Hz as it can be seen in Fig,3. A

27、theoretical analysis with FEM gave similar results.</p><p>　　The frequency response functions obtained from impacts in the impeller are indicated in Fig,4. They show the presence of a mode at 472 Hz. This mo

28、de was susceptible of excitation because it corresponded to diametrical mode 2. Estimating a reduction factor of 0.45 to 0.5in order to consider the added mass and the casing boundary,the actual natural frequency would l

29、ie between 212 and 236 Hz. So, there was a low probability of resonance. In fact, no high vibration levels were present at the bearing</p><p>　　Finally, analyzing the phasing of the pressure pulsation and vi

30、bration in the casing, the diagnosis was that the high vibrations were caused by the interaction of the pressure pulsation inside the machine.</p><p>　　In this case the solution was to change the relative po

31、sition between impellers. After that, vibration was reduced considerably as it is shown in Fig,5 where RSI vibrations before and after repair are compare.</p><p>　　Vibration on runner of a pump-turbine.</

32、p><p>　　In this case, the machine was a single stage reversible pump-turbine. Its main characteristics are listed in table 2. this pump suffered form cracks in the impeller blades.</p><p>　　For the

33、 Zb and Zv combinations, the diametrical mode k=-2 occurs at 2*fb(=140 Hz) and should be the most important excitation. This is exactly what can be seen in the vibration spectrum shown in Fig, 6.</p><p>　　Af

34、ter analyzing the system response, checking the natural frequencies of runner and rotor, it was found that a rotor naturalfrequency was was close to the excitation frequency. As the system could not be changed physically

35、, the solution of the problem was devised as modifying the runner lacation where cracks appeared to reduce stresses on blades.</p><p>　　Partial load surge and inlet cavitation erosion on blades of a francis

36、turbine.</p><p>　　This unie was a vertical shaft francis turbine operating up to a maximum output power of 65 MW. The total nominal flow rate and the net head were 57.5m3/s and 122.5m. the rest of characteri

37、stics are listed in Table 3.</p><p>　　In this case two problems had been detected. The first one was excessive vibration levels in the draft tube. The second one was advanced erosion on the suction side of t

38、he blades.</p><p>　　In Fig, 7 overall vibration levels measured for the entire range of power outputs indicate that amplitudes are more important during operation at partial loads. In the Fig,8, spectral ana

39、lysis of shaft displacement using proximity probes can be observed at 20 and 55MW. When operating at 20MW, a frequency peak at 0.27*ff predominates but disappears at 55 MW. This analysis indicated the presence of a hub r

40、ope in the draft tube at partial loads.</p><p>　　Spectral analysis is enough to detect partial load surge but it is not useful for other types of cavitation. This is the case of erosive cavitation is especia

41、lly destructive.</p><p>　　Another technique to be used is to demodulate high frequency vibrations. In Fig,9, the spectra of the envelope in the frequency band form 30k to 40k Hz are plotted. Again, at 20 MW

42、 the presence of the part load surge is well detected in the top of the Fig.</p><p>　　So,the possible remedies such as optimization of air injection fins are currently being analyzed. Meanwhile, it has been

43、recommended to avoid operation at loads below 35 MW.</p><p>　　For the detection of erosive cavitation high frequency vibrations also had to be measured (Escaler et al.2002). Amplitude demodulation of high fr

44、equency bands, shown in the bottom of Fig,9, indicated the presence of a pulsating cavity in the runner at fv at 55MW. The maximum amplitude of this peak was found at 60 MW, thus indicating the maximum cavitation aggress

45、iveness. Therefore, the solution consisted in limiting the time of operation around 60MW whenever possible. A refurbishing of the runne</p><p>　　Type 2: thrust bearing problems</p><p>　　Another

46、type of problem sometimes found in vertical shaft machines is rubbing in thrust bearing which can provoke its rapid destruction. In guide bearings,radial loading is usually low and they are not so affected.</p>&l

47、t;p>　　Machines are prone to have friction during start-up and coast-down if only hydrodynamic lubrication exists. During operating, vibration can be generated especially when load on the pads is not evenly distributed

48、. A possibility for detection is to install a vertical proximity probe or an absolute vibration sensor located next to the bearing pads in axial direction. The use of joint-time frequency analysis is very adequate to ide

49、nfuty such frictions that can occur in very short periods of time.</p><p>　　At steady operation, spectral analysis helps to identify potential problems by looking at the pad passing frequency. For instance,

50、in Fig,10,this frequency disappears from the vibration signature after repairing the bearing. Although detection is easy,to quantify the level of the damage is diffcult from the vibration signature and the peak amplitude

51、. A proximity probe is convenient as well as oil analysis to complete the diagnostic.</p><p>　　In Fig, 11, another example is shown. The predominant peak at passing frequency indicates a damage in the bearin

52、g. Its amplitude decreased significantly after repair.</p><p>　　Type 3: unbalance and misalignment</p><p>　　Unbalance and especially misalignment are common problem in vertical shaft machine wit

53、h rigid coupling.</p><p>　　Unbalbance detection and solution is not diffcult except when hydraulic or magnetic forces or a resonance zre involved in it. It is important to identify the type of unbalance befo

54、re doing the repair. Vibration measurements at different loads and with the machine idle are necessary. In Fig, 12 the spectrum of a machine with unbalance produced by a blockage in runner channels can be observed. In th

55、is case, it was observed that the ff. another situation which is potentially dangerous is when a sma</p><p>　　Other cases difficilt to solve are when there is resonance with a rotor natural frequency. In Fig

56、,13，a case with misalignment can be observed. The first rotor lateral frequency is almost coincident with a times the rotating frequency. Here the machine has some degree of misalignment which is enhanced by the resonanc

57、e. In the top of the Fig,14,the 2*ff peak has an RMS amplitude around 1.2 mm/s when the machine operates at full load. Meanwhile,in the bottom of the same Fig,the same peak shows an a</p><p>　　As the natural

58、 frequency varies depending on the machine load and other paraments, the vibration amplitudes change continuosly what makes diffcult to have an accurate ternd analysis in the monitoring. In this case the solution is not

59、straightforward.</p><p>　　Rotordynamic analysis based in FEM can be used to model the motor,to identify the type of resonance and to find a remedy. Inaccuracies arise when simulating an installed machine due

60、 to the lack of exact geometrical data, bearing stiffness,and so on. Therefore simulation must be checked with some experimental data. Thisis rather complex because the natural frequency are diffcult to excite in a large

61、 machine. Joint time frequency analysis can be used during transients or after impacting tha machin</p><p>　　Type 4: electromagnetic problems</p><p>　　This type of problems are basically due to

62、eccentricity or damage in generator.</p><p>　　In Fig,15,spectra of a machine before(front) and after excessive vibration in the generatoe are shown. The predominant vibration occurs at two times the electric

63、al line frequency,in our case 100Hz. After repair of the stator, where some damage was found,the vibration amplitude at 100Hz was considerably reduced.</p><p><b>　　翻譯部分</b></p><p>　　

64、液壓機(jī)械裝置振動(dòng)問題處理</p><p><b>　　摘要：</b></p><p>　　在本篇論文中，我們將討論液壓機(jī)械裝置不同情況下的各種振動(dòng)問題。這些情況在多年的正動(dòng)監(jiān)測中發(fā)現(xiàn)的。由于引起振動(dòng)的本質(zhì)不同我們將這些情況做下歸類，對(duì)所有這些情況來說，用系統(tǒng)途徑觀察這些情況，超負(fù)荷運(yùn)行引起這些振動(dòng)。問題擴(kuò)大的原因是由于機(jī)器的共振，一些措施已經(jīng)應(yīng)用于補(bǔ)救當(dāng)中。</

65、p><p><b>　　簡介：</b></p><p>　　在液壓機(jī)械裝置中，振動(dòng)問題非常普遍。解決振動(dòng)問題可以延長機(jī)器壽命并且降低維修費(fèi)用。通過去年的監(jiān)測觀察，許多振動(dòng)問題被發(fā)現(xiàn)，并且解決了其中一部分問題。在發(fā)現(xiàn)的問題中一些是由于設(shè)計(jì)存在缺陷，一些是由于機(jī)器本身存在微小振動(dòng)并且逐年增加的結(jié)果。還有一些是由于機(jī)器內(nèi)部存在著某些零件的損壞登記。這所提到的例子大部分是有垂直通

66、道和剛性連接的大型機(jī)器。我們可以將碰到的問題歸為以下幾類：</p><p>　　類型1：液壓負(fù)荷過大</p><p><b>　　類型2：超載問題</b></p><p>　　類型3：裝置不平衡性和聯(lián)接性</p><p><b>　　類型4：電磁性問題</b></p><p>

67、;　　論文中建議用統(tǒng)計(jì)分析的方法來解決這些類型的振動(dòng)問題。圖示為統(tǒng)計(jì)分析法的具體操作步驟。當(dāng)通過定時(shí)監(jiān)測器觀察到不正常的大幅度振動(dòng)或機(jī)器的不正常運(yùn)轉(zhuǎn)。振動(dòng)分析將立即啟動(dòng)對(duì)所出現(xiàn)的問題的本質(zhì)驚醒分析。許多的技術(shù)都可以運(yùn)用到這些問題的研究中，不管機(jī)器是液壓式還是動(dòng)力機(jī)械式，或是電磁驅(qū)動(dòng)的。導(dǎo)致大幅度振動(dòng)的問題可能是液壓系統(tǒng)經(jīng)常出現(xiàn)的一些共振現(xiàn)象，或是一些機(jī)器零件的共振問題，因此這些的可能都必須再做出正確診斷前查清楚。</p>

68、<p>　　最后，問題的補(bǔ)救措施已提供出來，下一步驟是將振動(dòng)與修正前的結(jié)果進(jìn)行比較進(jìn)而得出正確的補(bǔ)救措施。</p><p>　　類型1：液壓負(fù)荷過大</p><p>　　典型的液壓振動(dòng)的產(chǎn)生是音問機(jī)器旋轉(zhuǎn)部分的相互影響，RSI是由發(fā)動(dòng)機(jī)的葉片與引風(fēng)道的相互影響產(chǎn)生。它可以在液壓裝置中產(chǎn)生大幅度的振動(dòng)。RSI通常對(duì)振動(dòng)進(jìn)行光譜分析，問題在于知道振動(dòng)是否是由于機(jī)器本身超負(fù)荷運(yùn)行產(chǎn)生，

69、對(duì)一個(gè)大型液壓裝置振動(dòng)是否是由于動(dòng)力裝置或是旋轉(zhuǎn)裝置的共振引起。振動(dòng)的頻率由下式提供：fb=n*f*zb 。最大的幅度發(fā)生在最小的管道直徑時(shí)。系數(shù)K由下列公式得到：n*zv+_k=m*zb。</p><p>　　另一個(gè)可以產(chǎn)生振動(dòng)的典型現(xiàn)象是氣蝕。氣蝕可以有多種形式出現(xiàn)。它有可能導(dǎo)致振動(dòng)的發(fā)生。機(jī)器運(yùn)轉(zhuǎn)不正常就有可能是因?yàn)榘l(fā)生了腐蝕。最通常發(fā)生的腐蝕發(fā)生在部分負(fù)荷的高峰期。它的不利影響通常是由通風(fēng)管道中空氣流動(dòng)引

70、起的。另一面由于風(fēng)道進(jìn)口通風(fēng)對(duì)動(dòng)力裝置葉片的腐蝕也是個(gè)不利的因素。下面介紹幾個(gè)液壓裝置的例子供參考：</p><p>　　多級(jí)抽水泵的高幅度振動(dòng)</p><p>　　多級(jí)抽水泵在工作時(shí)具有很大幅度的振動(dòng)，由此產(chǎn)生的大幅度振動(dòng)可能導(dǎo)致管道和其他的零件的破壞。首先，振動(dòng)被認(rèn)為是產(chǎn)生破壞或?qū)е聶C(jī)器不能正常運(yùn)轉(zhuǎn)的問題。結(jié)果把水泵全部拆開進(jìn)行修理，可是奇怪的是振動(dòng)現(xiàn)象并不能消失。</p>

71、<p>　　圖2給出了多級(jí)水泵的大體結(jié)構(gòu)。在抽水的過程中，水泵以2.8m/s的流速向935米高的地方抽水，水泵的其他性能參數(shù)在表格1中列出。</p><p>　　為了搞清楚多級(jí)水泵大幅度振動(dòng)的問題，進(jìn)行了一些實(shí)驗(yàn)測量和理論分析。從光譜分析中可以知道，振動(dòng)幅度增大發(fā)生在振動(dòng)頻率為150Hz時(shí)，因此其振動(dòng)的本質(zhì)是由一些不穩(wěn)定的流量產(chǎn)生的。多級(jí)水泵的高幅度振動(dòng)可以歸結(jié)為以下幾個(gè)原因，例如是設(shè)計(jì)時(shí)的高RSI

72、，逐漸增加的振動(dòng)頻率，零部件的損壞，共振等。在此例中，RSI分析在驅(qū)動(dòng)器旁邊測量了其振動(dòng)壓力，它是在外徑模型系數(shù)k=-2時(shí)，頻率為fb并且相反旋轉(zhuǎn)方向測得的。</p><p>　　首先，液壓系統(tǒng)回水管道的反應(yīng)是使用矩陣轉(zhuǎn)換的方法測得的，在150赫茲左右其他頻率都不可能測到。其次，對(duì)在不同轉(zhuǎn)動(dòng)速度下的測量數(shù)據(jù)進(jìn)行分析也沒有在過高負(fù)荷的頻率附近產(chǎn)生共振。從電擊錘碰撞的分析中確定機(jī)械共振的可能性。在這次實(shí)驗(yàn)分析中，頻率

73、在150赫茲附近沒有發(fā)現(xiàn)共振現(xiàn)象，我們可以從圖3中看出來。用FEM理論分析可以得到相同的結(jié)論。</p><p>　　圖4說明了在驅(qū)動(dòng)裝置中通過撞擊得到的頻率反應(yīng)函數(shù)。兩個(gè)圖顯示在472赫茲的模型。模型容易受到影響，因?yàn)樗刂睆椒较虻呐c模型2相同?？紤]到已增加的質(zhì)量和模型邊界，需要估計(jì)把導(dǎo)數(shù)降低到0.45或0.5，實(shí)際自然頻率將在212到236赫茲。所以存在共振的可能性不大，實(shí)際上在這方面根本就沒有大的振動(dòng)幅度。&

74、lt;/p><p>　　最后分析一下壓力脈動(dòng)和振動(dòng)的相位變化，診斷結(jié)果認(rèn)為大幅度振動(dòng)是由于機(jī)器內(nèi)部壓力振動(dòng)的互相作用的結(jié)果。</p><p>　　在這個(gè)例子中，溶液在兩個(gè)驅(qū)動(dòng)裝置之間改變了相對(duì)位置。隨后如圖5所示在RSI分析前后的對(duì)比當(dāng)中，振動(dòng)幅度是降低的。</p><p>　　水泵式渦輪機(jī)驅(qū)動(dòng)裝置的振動(dòng)</p><p>　　在這個(gè)例子中，機(jī)器是

75、一部單級(jí)可逆水泵式渦輪機(jī)。它的主要性能參數(shù)在表格2中列出。水泵的驅(qū)動(dòng)電動(dòng)機(jī)的葉片上發(fā)生了破裂。</p><p>　　分析完系統(tǒng)的反應(yīng)后，并檢查了電動(dòng)機(jī)和旋轉(zhuǎn)不部件的固定頻率時(shí)發(fā)現(xiàn)旋轉(zhuǎn)器的固定頻率與振動(dòng)頻率很相近。因?yàn)橄到y(tǒng)不能自動(dòng)改變它的頻率，所以問題的解決靠告便電動(dòng)機(jī)的位置，在那個(gè)位置是裂縫經(jīng)常出現(xiàn)并且減少了葉片所受的壓力。</p><p>　　這臺(tái)具有垂直通風(fēng)管道的渦輪機(jī)最大輸出功率為6

76、5MW。理論質(zhì)量流速為57.5m3/s，揚(yáng)程為122.5米。其他性能參數(shù)在表格3中列出。在這個(gè)例子中發(fā)現(xiàn)出2個(gè)問題：第一個(gè)問題是在通風(fēng)管道出現(xiàn)過大幅度的振動(dòng)，第二個(gè)問題是在葉片吸收側(cè)發(fā)生了嚴(yán)重的腐蝕。</p><p>　　圖7對(duì)各個(gè)功率輸出的整體振動(dòng)水平測量反應(yīng)出在沒有滿負(fù)荷運(yùn)轉(zhuǎn)時(shí)幅度變的更加重要。圖8在傳動(dòng)軸替代的光譜分析中，使用相近的探測其結(jié)果在20到50MW，當(dāng)在20MW運(yùn)行時(shí)，頻率高峰出現(xiàn)在0.27ff，

77、但是當(dāng)運(yùn)行在50MW的時(shí)候頻率消失。光譜分析對(duì)非滿負(fù)荷運(yùn)行足夠有效的。但是對(duì)于其他的振動(dòng)處的氣蝕分析并沒有什么價(jià)值。這是個(gè)有關(guān)氣蝕的例子，它引起的結(jié)果可以損壞一些零部件。對(duì)于進(jìn)口處尤其具有破壞性。</p><p>　　另一種技術(shù)被用于檢測大幅度振動(dòng)的技術(shù)。在圖9中在封閉的光譜分析中，頻率段定在30到40千赫之間。在20MW運(yùn)行時(shí)，部分負(fù)荷的曲線在圖中很明顯的表示出來。</p><p>　　

78、所以可能的補(bǔ)救措施象合理的安排空氣的排放，最近正在進(jìn)行的分析當(dāng)中，同時(shí)機(jī)器應(yīng)該避免在35MW以下運(yùn)行。</p><p>　　對(duì)于氣蝕的高頻率振動(dòng)也需要測量。圖9的底部給出了高頻率段振幅的強(qiáng)弱。此圖形表明了在55MW的情況下，振動(dòng)幅度的變化。最大振動(dòng)幅度峰值出現(xiàn)在60MW。因此解決的方案是在于不管任何時(shí)刻，一定要限制機(jī)器在60MW的功率上運(yùn)行的時(shí)間。一部重新組裝的電動(dòng)機(jī)（具有新穎的液壓傳動(dòng)設(shè)計(jì)）可以解決這個(gè)問題。&

79、lt;/p><p><b>　　類型2：超載問題</b></p><p>　　另一種在精確軸傳動(dòng)中經(jīng)常被發(fā)現(xiàn)的問題是在超負(fù)荷下的摩擦往往對(duì)機(jī)器的運(yùn)行速率產(chǎn)生破壞，在摩擦的導(dǎo)向，徑向軸經(jīng)常是低速的切作用影響不大。</p><p>　　在機(jī)器只有液體潤滑的情況下，開啟或者關(guān)閉機(jī)器很容易產(chǎn)生摩擦。在機(jī)器正常的運(yùn)行中，容易產(chǎn)生振動(dòng)，尤其當(dāng)機(jī)器的墊片被損壞以

80、后。一種可以用來探測的方法是插入一個(gè)近似的探測器或者一個(gè)獨(dú)立的振動(dòng)在它的軸向方向。頻率分析法在這種短時(shí)間中發(fā)生的變化中是可以使用的。</p><p>　　在穩(wěn)定的運(yùn)行中，光譜分析法可以通過獨(dú)立的分析幫助我們識(shí)別潛在的問題。例如在圖10中，在機(jī)器超載后產(chǎn)生了獨(dú)立的振動(dòng)，盡管檢查出問題是很簡單的，但是要從振動(dòng)的本質(zhì)中去解決降低破壞的程度是很難的。一個(gè)近似的探測法是對(duì)油進(jìn)行分析從而對(duì)機(jī)器的振動(dòng)進(jìn)行診斷。</p&g

81、t;<p>　　在圖11中，說明了另一種情況，在超載的時(shí)候，機(jī)器振動(dòng)產(chǎn)生了很嚴(yán)重的破壞。在進(jìn)行了檢修后，振動(dòng)幅度會(huì)明顯的降低。</p><p>　　類型3：裝置不平衡性和聯(lián)接性</p><p>　　在有剛性聯(lián)接的機(jī)器運(yùn)行時(shí)，不平衡性和聯(lián)接性是很普遍的。</p><p>　　基于FEM的離心分析法可以用于轉(zhuǎn)子模型，用來分析振動(dòng)的來源種類，并且用來尋找補(bǔ)救