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英文原文
Screw Compressors
2.4 Review of Most Popular Rotor Profiles
2.3 Rotor Profile Calculation
For a further analysis of the compressor geometry, several generic definitions are introduced here. The rotor gear ratio ,whereandare the numbers of lobes on the main and gate rotor. Since the screw compressor rotors are three-dimensional bodies, a helix angleis defined at the rotor radius, whilecorresponds to the pitch circle,. The helix angle defines the rotor lead h, which can be given relative to the unit angle. The rotor length L, the wrap angleand the lead are interrelated. If the rotors are unwrapped, a simple relation between the wrap and helix angles can be established,. The lead angle is the complement of the helix angle.
As shown in Fig. 2.3, the rotor displacement is the product of the rotor length and its cross section area, which is denoted by the number 1, while the overlapping areas on the main and gate rotors are denoted by the number 2.
2.4 Review of Most Popular Rotor Profiles
This section reviews a procedure to calculate various screw profiles. Initially a detailed presentation of rotor creation by the rotor generation procedure is given. The rotor profile in this case is a very simple hypothetical one. It has been applied in practice, but also been frequently used for training purposes. Furthermore, this profile may be very conveniently used as a basis for individual development of screw compressor rotors and such use is encouraged here. Based on this, other profiles are briefly derived, like the early SKBK profile, the “Sigma” profile by Kaeser, the “Hyper” profile by Hanbel and the Fu Sheng and Hitachi profiles. Also the symmetric profile and asymmetric
Fig. 2.3. Rotor cross section area and overlapping sectors
2 Screw Compressor Geometry
“A”, “D” and “G” profiles of SRM and the “Cyclon” profile by Compair are reviewed. Finally, two rack generated profiles are described namely the “N” and Rinder’s profile.
2.4.1 Demonstrator Rotor Profile (“N” Rotor Generated)
The demonstrator profile is a rotor generated “N” profile and is not to be confused with the patented rack generated “N” profile. The primary or generating lobe profile of the Demonstrator is given on the main rotor and the profile is divided into several segments. The division between the profile segments is denoted by capital letters and each segment is defined separately by its characteristic angles, as shown in the Fig. 2.4. The lobe segments of this profile are essentially parts of circles on one rotor and curves corresponding to the circles on the opposite rotor. A graphical presentation of this profile is presented in Fig. 2.5. The following summarizes the specific expressions for the x-y coordinates of the lobe profiles of the main screw rotor, with respect to the centre of the rotor. Givenare the pitch radii,andand the rotor radii r,, ,and. The external and internal radii are calculated asand,as well asandfor the main and gate rotor respectively.
In the demonstrator profile, segment A1B1 is a circle of radius on the main rotor. The angular parameter t varies between.
Fig. 2.4. Demonstrator Profile
2.4 Review of Most Popular Rotor Profiles
Fig. 2.5. Details of the Demonstrator Profile
is given, while and are calculated through the following procedure, which is presented graphically in Fig. 2.5. There the flat side of the profile is presented in the position where points F1 and F2 coincide:
Afterandare obtained from these equations,andcan be calculated as:
The other angles are:and.
On the round side of the rotors,, whereis the number of lobes in the main rotor. The radiusis now calculated from:
Other necessary angles are calculated as follows:
The segment B1C1 is on a circle of radius on the main rotor, where.
2 Screw Compressor Geometry
Profile portion A1D1 is a circle of radiuson the main rotor,.
Segment C1D1 emerges as a trochoid on the main rotor generated by the circle of radius. The trochoid is obtained from the gate rotor coordinates through the same meshing procedure. The circle C2D2 is:
Now, when all the segments of the main rotor are known, they are used as source curves. The gate rotor lobe can now be generated completely by the meshing procedure described in the previous section.
Although essentially simple, the Demonstrator profile contains all the features which characterize modern screw rotor profiles. The pressure angles on both, the flat and the round profile lobes are not zero. This is essential for successful manufacturing. The profile is generated by the curves and not by points. This further enhances its manufacturability. By changing its parameters,C, r,,,and, a variety of profiles can be generated, some with positive gate rotor torque, some suitable for low pressure ratios, and others for high pressure ratio compression. The profile is fully computerized and can be used for demonstration, teaching and development purposes.
2.4.2 SKBK Profile
Amosov’s 1977 SKBK profile is the first modern Russian profile to be published in the open literature and it is shown in Fig. 2.6. The profile has the same layout and sequence of segments as the Demonstrator profile apart from the fact that the circlesandthe substituted by cycloids and the segments AB and AF are generated by point generation. This can be readily achieved if andin the Demonstrator profile tend to zero.
Similarly to the Demonstrator profile, SKBK profile has an eccentric circle on the round lobe of the main rotor, which gives a pressure angle far different from zero in the pitch circle area. This further ensures both its ease of manufacture and the gate rotor torque stability. This characteristic of the SKBK profile was published at least five years prior the SRM “D” rotor patents which claimed the same feature. However, since the flat lobe sides on the main and gate rotors are generated by points E and A on the gate and main rotor respectively and since E is positioned on the gate rotor pitch circle, the pressure angle at the pitch circle on the flat side is zero. This does not allow manufacturing of this profile by milling or grinding unless the profile is modified.
2.4 Review of Most Popular Rotor Profiles
Fig. 2.6. SKBK Profile
Fig. 2.7. Fu Sheng Profile
2.4.3 Fu Sheng Profile
The Fu Sheng profile, as shown in Fig. 2.7, is practically the same as the Demonstrator, but has one distinguishing feature. The segment AB is an ellipse.
2.4.4 “Hyper” Profile
The “Hyper” profile is virtually the same as the Fu Sheng profile, apart from the segment AB, which is a hyperbola on the main rotor instead of the ellipse of the original Fu Sheng profile. However, despite such a small difference, the “Hyper” is a better profile giving larger screw compressor displacement, a shorter sealing line and stronger gate rotor lobes. The Hitachi profile has the same layout as the “Hyper” profile.
2 Screw Compressor Geometry
2.4.5 “Sigma” Profile
The “Sigma” is a relatively old profile. It was developed in the late nineteen seventies as a response to SRM awarding an exclusive licence to Aerzener in Germany. Other German manufacturers, such as GHH and Kaeser, therefore, needed to develop their own profiles. The “Sigma”, shown in Fig. 2.8 is a beautiful and efficient profile. However, new and better profiles are now available. The flat side of the “Sigma” lobe is the same as that of the Demonstrator profile, but the round side of the profile is generated from the flat side by an envelope of circles, which touch both the flat and the round sides, the radii of which are given in advance. This is an acceptable method of profile generation if nothing more general is known, but seriously limits the generation procedure. There are several modifications of the “Sigma” profile. One of these, which is presented here, comprises a straight line BC2 on the round side of the gate rotor. This modification significantly improves the profile, which is less limited than the original.
Fig. 2.8. Sigma Profile
2.4.6 “Cyclon” Profile
The “Cyclon” shown in Fig. 2.9 is a profile developed by Compair. The layout and sequence of profile segments are not so different from the Demonstrator, but the “Cyclon” introduces parabolae instead of circles in segments BC, GH and JH. One of the interesting features of the “Cyclon” profile is the “negative” torque on the gate rotor which results in rotor contact on the flat side of the rotors.
2.4 Review of Most Popular Rotor Profiles
Fig. 2.9. Cyclon Profile
2.4.7 Symmetric Profile
The Symmetric profile, shown in Fig. 2.10 is very simple and consists of three circles on the main rotor with centres positioned either on the rotor centre or on the pitch circle of the main rotor. Since the circles are on the main rotor with centres either at the rotor centre or on the pitch circle, they only generate circles on the gate rotor with centres either in the rotor centre, or on the rotor pitch circle. Is is therefore not surprising that this was the first screw rotor profile ever generated.
Segment D1E1 is a circle of radiuswith its centre on the rotor axis, while segment E1F1 is a circle of radius r0. Segment F1A1 is on a circle of radius r. Both, the last two segments have their centres on the rotor pitch circle. Further segments are symmetrically similar to the given ones.
Fig. 2.10. Symmetric Circular Profile
中文譯文
螺桿式壓縮機
2.4審查最流行的轉(zhuǎn)子型線
2.3轉(zhuǎn)子型線的計算
為了進一步分析的壓縮機的幾何形狀，幾個通用的定義這里介紹的。轉(zhuǎn)子的傳動比為，其中和為數(shù)字上的主，閘轉(zhuǎn)子的裂片。由于螺桿壓縮機轉(zhuǎn)子三維機構(gòu)的螺旋角被限定在轉(zhuǎn)子的半徑，而對應(yīng)的節(jié)圓，。螺旋線角度定義轉(zhuǎn)子引線h，這可以給定的相對的單位角度。在轉(zhuǎn)子的長度L，包角和引線是相互關(guān)聯(lián)的。如果轉(zhuǎn)子被解開，一個簡單的包之間的關(guān)系和螺旋角可以建立,。導(dǎo)程角為螺旋角的補。
如圖中所示2.3，轉(zhuǎn)子的位移是所述轉(zhuǎn)子的產(chǎn)品長度和其橫截面面積，這是由數(shù)字1表示，而重疊區(qū)域上的主轉(zhuǎn)子和閘轉(zhuǎn)子的由數(shù)字2表示。
2.4審查最流行的轉(zhuǎn)子型線
本節(jié)審查程序，計算各種規(guī)格型材。最初轉(zhuǎn)子由轉(zhuǎn)子產(chǎn)生過程的創(chuàng)建是一個詳細的介紹給定的。在這種情況下，轉(zhuǎn)子型線是一個非常簡單的假設(shè)性。它有在實踐中得到了應(yīng)用，但也經(jīng)常被用于訓(xùn)練目的。此外，此配置文件可以很方便地使用個人的基礎(chǔ)螺桿壓縮機轉(zhuǎn)子的發(fā)展，這種鼓勵在這里。在此基礎(chǔ)上，其他的配置文件簡單地得出， 像早期SKBK中的個人主頁上，由凱撒“西格瑪”配置文件，“超”配置文件Hanbel和傅盛和日立的配置文件。此外，對稱的輪廓不對稱。
圖.2.3.轉(zhuǎn)子的橫截面面積和重疊的扇區(qū)
2螺桿式壓縮幾何
“A”，“D”，“G”配置文件SRM的“CYCLON”配置文件康普艾綜述。最后，即兩個機架生成的配置文件中描述的“N”Rinder的個人資料。
2.4.1演示轉(zhuǎn)子型線（“N”轉(zhuǎn)子生成）
示威者個人資料的轉(zhuǎn)子產(chǎn)生的“ N”配置文件，是不是要擁有專利的機架產(chǎn)生的“N”配置文件相混淆。的主要或生成葉的主旋翼和配置文件的演示中，分成若干段。該部門的檔案分部之間用大寫字母表示，每個段分別定義其特性的角度，如在圖中所示。 2.4。葉段，這配置文件本質(zhì)上是一個轉(zhuǎn)子的圓形和曲線對應(yīng)的相反的轉(zhuǎn)子上的圓圈。在此檔案中呈現(xiàn)的圖形化表示。2.5下面總結(jié)的具體表達式的xy坐標(biāo)的波瓣的公司的的主螺桿轉(zhuǎn)子，相對于轉(zhuǎn)子的中心。特定的間距半徑，和和轉(zhuǎn)子的半徑r,，，和的。“和的內(nèi)部和外部半徑的計算公式為，以及和中的主要和閘轉(zhuǎn)子分別。在示威者配置文件中，段A1B1是一個圓的半徑主旋翼。的角度參數(shù)t的變化之間的時。
圖.2.4.演示簡介
2.4審查最流行的轉(zhuǎn)子型線
圖.2.5.詳細的演示簡介
給出，而和是通過以下步驟計算顯示于圖.2.5在那里側(cè)扁的檔案呈列點F1和F2的位置相吻合：
和后得到的這些公式，可以計算和
如：
其他的角度是：和。
圓方的轉(zhuǎn)子，，是多少在主旋翼的裂片。半徑現(xiàn)在的計算：
其他必要的角度的計算方法如下：
B1C1是一個圓的半徑的主旋翼的部分，其中。
2螺桿式壓縮機幾何
簡介部分A1D1是一個圓的半徑的主旋翼，。
段C1D1出現(xiàn)作為所產(chǎn)生的主轉(zhuǎn)子上的次擺線型閘轉(zhuǎn)子上的圓的半徑,。余擺線通過從閘轉(zhuǎn)子坐標(biāo)得到相同的嚙合過程。
圈C2D2是：
現(xiàn)在是已知的，當(dāng)所有的段的主旋翼，它們被用作源曲線。閘轉(zhuǎn)子瓣現(xiàn)在可以生成完全由嚙合在前一節(jié)中所述的方法。
雖然基本上是簡單的，演示配置文件中包含的所有功能現(xiàn)代化的螺桿轉(zhuǎn)子型線的特點。上的壓力角兩者的平的和圓形的輪廓裂片不為零。這是必不可少的成功的制造。中所產(chǎn)生的曲線，而不是由點。這進一步提高了它的制造。通過改變它的參數(shù),C，r,,,和，可以生成各種型材，一些與正閘轉(zhuǎn)子扭矩，一些合適的低的壓力比，以及其他的高壓比例壓縮。配置文件是完全電腦化，并能可用于演示，教學(xué)和發(fā)展的目的。
2.4.2SKBK簡介
Amosov “1977年SKBK”配置文件是俄羅斯第一屆現(xiàn)代個人資料予以公布在公開文獻中，并示于圖.2.6。該配置文件的段的演示配置文件除了相同的布局和順序的事實,和的圓圈的取代由擺線和段AB和AF所產(chǎn)生的點生成。這可以很容易地實現(xiàn)如果和的演示配置文件中趨于零。
同樣的演示配置文件，SKBK輪廓有一個偏心圓上的輪葉的主旋翼，它給出一個壓力角遠遠不同從零中的節(jié)距圓的面積。這進一步確保了其易于制造和所述閘轉(zhuǎn)子的轉(zhuǎn)矩穩(wěn)定。此的SKBK特性配置文件公布前至少5年的SRM“D”轉(zhuǎn)子專利要求相同的功能。然而，由于扁平瓣的側(cè)面上主轉(zhuǎn)子和閘轉(zhuǎn)子的柵極上產(chǎn)生的點E和A和主轉(zhuǎn)子分別因為E被定位在上述閘轉(zhuǎn)子的節(jié)圓，側(cè)扁的節(jié)圓上的壓力角為零。這不允許在此檔案中所制造銑削或磨削，除非配置文件修改。
2.4審查最流行的轉(zhuǎn)子型線
圖.2.6.SKBK簡介
圖.2.7.傅盛簡介
2.4.3傅盛簡介
傅盛的個人主頁上，如圖.2.7，實際上是相同的演示，但有一個顯著的特點。AB段是一個橢圓形。
2.4.4“超級”簡介
除了“超”配置文件幾乎是相同的作為傅盛配置文件,段AB,它是一個雙曲線，而不是橢圓上的主旋翼傅盛的原始輪廓。然而,盡管這樣的小的差別，“超”是一個更好的形象，增加了螺桿壓縮機的排量，更短的密封線和更強的門轉(zhuǎn)子葉片。日立的配置文件有“超”配置文件相同的布局。
2螺桿式壓縮機幾何
2.4.5“西格瑪”簡介
“西格瑪”是一個比較老的個人資料。它的開發(fā)在上世紀(jì)19作為回應(yīng)七十年代SRM授予獨家特許權(quán)， Aerzener德國。其他的德國制造商，如GHH和凱撒，因此，需要開發(fā)自己的配置文件。“西格瑪”,示于圖.2.8是一個美麗的和高效率的個人資料。然而新的和更好的配置?！拔鞲瘳敗比~的平面一側(cè)是相同的演示從平面?zhèn)扔膳渲梦募?，但生成的檔案中的圓方信封的圈子，觸摸的平坦和圓邊，半徑這是預(yù)先給定的。這是一個可以接受的方法生成的配置文件如果沒有更多的一般是已知的，但嚴重限制的產(chǎn)生過程。有幾個修改的“西格瑪”配置文件。其中之一，這里提出，包括一條直線上的圓側(cè)的BC2閘轉(zhuǎn)子。此修改大大提高了配置文件，這是少比原來的限制。
圖.2.8.西格瑪公司簡介
2.4.6“CYCLON”簡介
“CYCLON”示于圖.2.9康普艾公司開發(fā)的配置文件。布局輪廓段的順序是沒有什么不同的演示，但“CYCLON”介紹拋物線，而不是圓的線段BC，GH和JH。一個有趣的功能的“CYCLON”配置文件是在轉(zhuǎn)子接觸的門轉(zhuǎn)子，其結(jié)果在平坦的扭矩“負面”轉(zhuǎn)子側(cè)的。
2.4審查最流行的轉(zhuǎn)子型線
圖.2.9.CYCLON簡介
2.4.7對稱簡介
對稱的檔案中，示于圖.2.10是很簡單的，并且包括三個界上的主轉(zhuǎn)子和在轉(zhuǎn)子上的中心的中心定位或主轉(zhuǎn)子節(jié)圓上的。由于圓圈是在主轉(zhuǎn)子的中心在轉(zhuǎn)子中心或節(jié)圓上的，它們只產(chǎn)生閘轉(zhuǎn)子的圈上，無論是在轉(zhuǎn)子的中心的中心，或在轉(zhuǎn)子上的節(jié)圓。因此并不奇怪，這是第一次螺桿轉(zhuǎn)子型線曾經(jīng)產(chǎn)生。
段D1E1是圓的半徑，其中心在轉(zhuǎn)子上段軸，而E1F1是一個圓的半徑為。段F1A1是一個圓半徑為r。這兩個，最后兩個分部有自己的中心在轉(zhuǎn)子的螺距圈。進一步細分類似于給定的對稱。
圖.2.10.對稱圓形的輪廓