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附錄1 譯 文
摘 要:錘片磨損會破壞錘片式粉碎機轉子的平衡,加劇轉子振動。該文的研究目的是基于虛擬樣機技術探討錘片磨損對轉子振動的影響規(guī)律。采用MDT和vN4D建立了SFSP112×30型錘片式粉碎機轉子的虛擬樣機模型,對不同錘片磨損情況下粉碎機轉子的振動進行了仿真。結果表明:錘片磨損后,轉子振動頻率組成變化不大,而振動幅值和強度變化較大,其中低頻段振動強度增強,高頻段振動強度降低;導致轉子質心徑向偏移的錘片磨損使轉子振動幅值和強度均變大,而導致質心軸向偏移的磨損對轉子振動影響不大;同樣由于轉子質心的徑向偏移,轉子受迫振動頻率強度增加較多。因此,為了降低子運轉時的振動,最好避免轉子質心發(fā)生徑向偏移。
關鍵詞:錘片式粉碎機；錘片；虛擬樣機(VP)；磨損；振動
簡 介
能從谷物中的營養(yǎng)提取出來的飼料粉碎機已經發(fā)展很多年了。但是因為他只能處理特殊的原料，像谷類食品和礦石，所以除了丕林島（地名）的少數(shù)人在研究飼料粉碎機外，很少人去研究他。盡管飼料粉碎機已經可以解決很多問題，比如振動、噪音、堵塞，用他特有的結構來解決問題，而且可以連續(xù)工作并達到一定的精度。
雖然一些方法，比如比較低的回轉速度，寬的轉子直徑被采用，好轉了他的性能，但是那些問題不能扯得的被解決。最近，分析了飼料粉碎機在工作狀態(tài)下轉子的轉速，旋轉的速度能被粉碎機控制在稍低或者稍高的程度。轉子的轉速在正常工作下都是不變的，除了在長時間工作摩擦后。由于錘片的排列或者是其他的因素，產生轉子的離心力不固定，所以錘片的磨損是不均衡的，因此，我們要學習掌握錘片要磨損時候的特征，為了使粉碎機振動保持穩(wěn)定。
實質上的原型技術（VP）是一個用cad加工程序代替真實的模型，為了測試這種產品的特性和特征。這就像電腦的硬件和軟件的發(fā)展，網(wǎng)絡技術通過vp技術開展起來。同時，傳統(tǒng)的模擬技術對VP的認識理解很有基礎。除了高科技種田，VP技術還適用于日益發(fā)展的農業(yè)機械設計。作者努力的將VP技術應用于工程分析技術。
對于飼料粉碎機中轉子單一的動力模型，被用來發(fā)展轉子動力學，轉子有效的運動模型被MDT和VN4D當做虛擬原型來用。VP技術模擬不同情況的磨損下，研究轉子轉動時的震動和錘片磨損的分析。
1.單一化轉子的模型
SFSP112×30的轉子的錘片被均勻的排列，它是由定子、滾球軸承、錘片、軸子組成，最大轉速為1480r/min。所以它的最大頻率應該是1480/60=24.6Hz。
圖一 SFSP112×30的轉子圖表
基于集總的單一化原則叁數(shù)方法 被單一化的模型應該有同樣的總質量，瞬間的轉動慣量有最初的質心位置決定。粉碎機的轉子被單一化的分別運行在六個圓盤里。在這系統(tǒng)里，每一個自我排列的定子，會在壓力的作用下自己運行到指定的位置，能夠計算出他們最后的位置。
2.轉子的虛擬原型
轉子的3D模型需要建立在一個MDT的三維建模軟件上，VP的技術原本是用來實現(xiàn)Vn4D的，其中包括重要的參數(shù)從轉子的發(fā)動機的功率。一些重要參數(shù)列出如下
（1）定子連接上，平鍵連接被強固連接完全代替；
（2）強固連接也被用來連接圓盤；
（3）因為軸子被用來限制錘片的位置，所以強固連接被用來限制軸子和錘片的位置；
（4）在錘片和螺釘通過強固連接，來限制彼此的旋轉動作，來完成軸的夾緊；
（5）球軸承被軸襯所代替，軸襯確定參數(shù)。
（6）電動機的限制被增加到左邊的結束，他的參數(shù)、轉力矩輸出功能被設置在平衡的感電電動機上
3.VP技術的模擬分析
為了要加速模擬速度，唯一的沒有外部的那些環(huán)境應用的負荷被模擬，同時，粉碎機需要非常短的加速時間，沒有負載的環(huán)境是不可能的。粉碎機需要加速的這段時間內，轉子跑到他的位置上。 錘片的排列的結果，在研磨中起作用的軸通常用不同種型號，錘片通過定子的排列的長短來確定。因此質心上的轉子偏離最初的位置。根據(jù)概率公差，質心的方向也就是軸運動的方向，磨損的方向是在情理之中的。此外，和磨損情形對比，錘片的磨損也是模擬的。
根據(jù)模擬的結果列出表1
磨損的圖被展現(xiàn)在圖4上，第四個錘片和軸子被標在Ⅰ和Ⅳ上，當從軸向觀察，每組的錘片，每組都標著1到8平行的定子，在圖4A磨損程度每個錘片是平等的。圖 4B條的磨損程度，每個錘片的一組是不平等的，而相應的錘片組有Ⅰ ，Ⅲ 同樣的磨損程度。至于Fig.4c和Fig.4d的磨損程度的錘片是不相同完全。圖5顯示振動加速度和動力頻譜圖的球軸承收集在這一過程中，該轉子轉過第一第二輪之后， 14號實線代表的振動響應左軸承和虛線代表是正確的。 圖4示意圖磨損形式。錘片的磨損的主體部分的振動頻率之前和之后沒有變化。 但強度在每一個頻率是完全不同的圖5振動響應每個軸承從相應的頻率，損壞轉子。在低頻階段加強和強度削弱了在高頻率的階段。特別是根據(jù)“甚至磨損”形勢的變化很大大于其他情況下。和同樣的結論可以發(fā)現(xiàn)振動擴增管轉子。通過對比Fig.5b和Fig.5c ， 可以推斷，徑向偏移嚴重破壞了平衡的轉子。這一結論也可以通過Fig.5d和 Fig.5e的對比得到。由于徑向偏移量“相鄰不均勻磨損“顯然是大于“不對稱不均勻磨損” 。強度在強迫振動頻率（24.67赫茲）增加多少更根據(jù)“甚至耐磨”和“相鄰不均勻磨損”的情況，雖然有點變化根據(jù)以上兩種情況對比。
4結論
?（1）磨損形式并不影響能使錘片的振動頻率改變的轉子。然而，它確實帶來了明顯的變化強度的頻率，其中的強度低頻率的階段，同時加強這一高頻率階段的削弱。
（2）徑向偏移現(xiàn)實出來是不穩(wěn)定的轉子相對于軸向偏移。振幅和強度大大增加時質心偏離徑向。
（3）強度的強迫振動頻率大大提高時，會出現(xiàn)無論是錘片磨損均勻或鄰近群體錘片磨損不均等方面的磨損情況。它需要較大的徑向力來抵消這兩個磨損形式，結果是不穩(wěn)定的轉子。
（4）基于以上這些結論，為了控制飼料粉碎機的轉子的振動，飼料粉碎機的轉子不應徑向偏移。因此，轉子需要很好的平衡特別是需要在達到動態(tài)平衡之前進入正常的運行。
附錄2 英文參考資料
Vibration generated by the abrasion of the hammer slicein feed-grinder based on virtual prototype technology
Abstract: The abrasion of the hammer slice can cause the rotor of the feed-grinder to lose balance and then make the grinder vibrate. A virtual prototype (VP) based on the rotor of SFSP112×30 feed-grinder was set up by using MDT and vN4D for investigating the relationship between the abrasion of the hammer slice and the vibration of the rotor. By simulating the VP with various abrasion forms, it has been found that the abrasion form does not influence the makeup of the vibration frequency but the intensity. That is, the intensity of the low-frequency stage strengthens but that of the high-frequency stage weakens when the hammer slices are worn out. The vibration amplitude and intensity both increase when the abrasion makes the centroid of the rotor offset radially. However, they do not change much when the centroid offsets axially. The intensity of the forced vibration frequency also greatly rises when the center of mass offsets radially.
Therefore, to damp the vibration of the feed-grinder the centroid of the rotor had better not offset radially.
Key words feed-grinder; hammer slice; virtual prototype (VP); abrasion; vibration
Vibration generated by the abrasion of the hammer slice in feed-grinder based on virtual prototype technology[J]. As one of the kernel equipment in feedstuff processing industry, the feed-grinder has been developed for years. But because of its special processing object, like cereal and mineral, there are few theoreti- cal studies on the feed-grinder except some experimen- tal researches. However, while the feed-grinder runs into many problems such as vibration, noise and clog- ging which mainly result from its own structure char- acteristics, running environment and fitting precision.
Although some methods such as lower rotational speed and wider rotor diameter have been adopted to im-prove its performance, those problems cannot be thor- oughly solved. Recently, et al has analyzed the vibration of the feed-grinder by calculat- ing the natural frequency of the rotor. Therefore, the rotation speed can be adjusted to be lower or high- er than the resonance speed to damp the vibration of the pulverator. But the natural frequency of the rotor is not constant, especially after long time grinding. On account of the array of the hammer slices and other factors, the hammer slices usually abrade unevenly, which causes the eccentricity of the rotor and then make the grinder vibrate[9]. Therefore, studying the characteristics when the hammer slices abrade is quite practical for taking better action to damp the vibration of the pulverator.
Virtual prototype (VP) technology is a process ofusing a CAD model, instead of a physical prototype, to test and evaluate the specific characteristics of a product or a manufacturing process[1]. The develop- ment of hardware and software of computer and network technology widely expands the application of VP. Meanwhile, traditional optimization and simula- tion techniques provide essential foundation to realize VP. Except for the hi-tech field, VP technology has also been applied to agricultural machinery design increasingly[10]. The authors attempt to apply VP technology to the engineering analysis of general machinery.
In this paper a simplified dynamic model for the rotor of the feed-grinder was developed based on rotor dynamics and the corresponding virtual prototype of the rotor was generated by using MDT and vN4D. By simulating the VP under different abrasion situations, the vibration characteristics of the rotor when the hammer slices abrade was analyzed.
1 Simplified model of the rotor
The rotor of SFSP112×30 feed-grinder with the symmetrical hammer slice array is shown in Fig.1. It consists of spindle, ball bearings, disk boards, ham-mer slices, pins and sleeves and its full-load rotational speed is 1480 r/min. So its frequency of the forced vibration should be 1480/60=24.67Hz.
Fig.1 Diagram of the rotor of SFSP112×30 feed-grinder
Based on the simplification principle of lumped parameter method[2]that the simplified model should have the same gross mass, moment of inertia and posi- tion of centroid to the original, the rotor of the pulver- ator was simplified into a one-span six-disc rotor system with two springs' support, as shown in Fig.2. The right end of the spindle and the center of each ball bearing and disk board are chosen as the positions of six disks. Fig.2 Simplified model of the rotor
The ball bearing is generally considered that it only provides stiffness because of its small damping[3]. In the system each self-aligning bearing on one side of the spindle is modeled as a spring, the stiffness of which can be calculated in the light of the following equation[4]:
2 Virtual prototype of the rotor
The 3D model of the rotor which only includes parts related to the simulation was built in MDT, a three- dimensional modeling software. The initialization of VP was fulfilled in vN4D, including importing the 3D model from MDT, modifying constraints between the parts and appending motor power[5]. Some important steps are listed below:
1) Instead of flat key joint each disk board is attached to the spindle by rigid joint which locks two bodies together absolutely.
2)Rigid jointis also used to fasten the pin with the disk board.
3) Because sleeves are used to limit the positions of the hammer slices, rigid joint is set as the constraint between the sleeve and the pin.
4) Constraint between the hammer slice and the pin is revolution joint, which is used to limit the motion of two bodies so that one body only rotates about a certain axis with respect to the other body.
5) The ball bearings are replaced by bushing constraint which can simulate the function of ball bearings. Eq. (1) is set as the stiffness function parameter of bushing constraint.
6) A motor constraint is added to the left end .
3 VP simulation and analysis
In order to accelerate the simulation speed, only those circumstances without external applied load were simulated. Meanwhile, since the pulverator needs a very short accelerating time, only the stage when the rotor runs stably is considered in this paper. As a result of the permutation of the hammer slices, the axial distribution of the material in the mill housing is often inhomogeneous and so does the wear extent of each hammer slice along the spindle. There- fore, the centroid of the rotor deviates from its original position. According to the probable deviation direction of the centroid, namely, radial, axial and both directions, four kinds of abrasion forms were specified. Furthermore, to contrast with the vibration under abrasion situations the performance with undamaged hammer slices was also simulated. The results of simulation are listed in Table 1.Table 1 VP simulation results with five abrasion forms of hammer slices
The diagrammatic sketch of the assumed abrasion forms is shown in Fig. 4. The four pin-and-sleeve groups were labeled fromⅠtoⅣclockwise when viewed from the axial direction and the hammer slices in each group are all marked from 1 to 8 parallel to the spindle. In Fig.4a the worn extent of each hammer slice is equal. In Fig. 4b the worn extent of each hammer slice in one group is unequal while the corresponding hammer slices in groupⅠandⅢhave the same worn extent. As for Fig.4c and Fig.4d the worn extent of the hammer slice is not identical entirely.
Figure 5 shows the vibration acceleration and power spectrum diagram (PSD) of the ball bearings collected in the process that the VP of the rotor ran for one second after it had wheeled for 14 s. Real line represents the vibration response of the left bearing and dashed line represents that of the right one. Fig.4 Sketch of abrasion forms.
The component of the vibration frequency changes little before and after the hammer slices are worn out. But the intensity at each frequency is quite different Fig.5 Vibration response of each bearing from the corresponding frequency of undamaged rotor.
At low-frequency stage the intensity strengthens and weakens at high-frequency stage. Especially the intensity under " even abrasion" situation changes much greater than that under other situations. And the same conclusion can be found for the vibration amplitude of the rotor. By contrasting Fig.5b and Fig.5c, it can be inferred that the radial offset of the centroid badly destroyed the balance of the rotor. This conclusion can also be acquired by contrasting Fig.5d and Fig.5e because the radial offset quantity of "adjacent uneven abrasion" is obviously larger than that of "asymmetric uneven abrasion". The intensity at the forced vibration frequency (24.67Hz) increases much more sharply under " even abrasion" and " adjacent uneven abrasion" situations while it changes a little under the other two situations.
4 Conclusions
1) The abrasion form of hammer slice does not influence the makeup of the vibration frequency of the rotor. However it really brings obvious changes to the intensity of the frequency, which exhibits that the intensity of low-frequency stage strengthens while that of high-frequency stage weakens.
2) The radial offset of the centroid can markedly disrupt the balance of the rotor compared with the axial offset. The vibration amplitude and intensity both increase greatly when the center of mass deviates radially.
3) The intensity at the forced vibration frequency is greatly raised when either the hammer slices wear evenly or the adjacent hammer slice groups wear unevenly with respect to other abrasion forms. It owes to the larger radial centroidal offset of these two abrasion forms that results in the imbalance of the rotor.
4) Based on these conclusions above, in order to damp the vibration of the feed-grinder the centroid of the rotor should not present radial offset. So the rotor needs to be well balanced especially in the dynamic balance test before going into operation.