雙螺桿壓縮機的設計帶CAD圖紙兩張
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螺桿壓縮機轉子加工中刀具磨損的幾何計算方法
[摘要]：螺桿壓縮機轉子加工有磨削和銑削兩種方法，通常分兩個階段進行加工；第一階段為 粗加工，當工件被加工到它的大概尺寸即可；第二階段為精加工，當轉子被加工成它的最終尺寸時完成。材料或切削余量在精加工中被除掉，它是由磨削和銑削加工時切削刀具的設計所決定的?？紤]到螺桿壓縮機的轉子是螺旋形狀，在切削過程中，刀具上的每一點與轉子的橫向接觸線長度是不一樣的，因此，精加工時刀具的磨損速率沿著它的型線也是不一致的。包絡線的嚙合理論被用于這里來計算在切削加工過程中刀具上的每一點和轉子之間的相對運動。以一定的比例尺，在此相對運動的假設下，計算出刀具上每一點的磨損速率。通過計算結果和實驗得出的刀具的磨損速率的比較，可以看出兩者的結論是一致的。在這個基礎上，可以知道怎樣去制造一種粗加工時使半加工余料變薄的刀具，從而促使精加工時刀具的磨損速率一致。一種相似的技術正被應用于許多機器的加工過程中，而多種成型刀具也是被用于這些技術上。
[關鍵字]：螺桿壓縮機；螺旋轉子；制造刀具
1．介紹：
螺桿壓縮機屬于正排氣量的回轉式容積機器，它主要由一對嚙合的螺旋轉子組成，轉子在機殼內(nèi)做回轉運動，它的容積隨著轉子的旋轉而發(fā)生變化。今天的螺桿轉子主要被造成盤型，來用于銑削或者磨削加工。無論是哪種形式加工出來的轉子，可以用轉子的坐標系來定義它們的幾何特性，如圖1所示。 要使螺桿壓縮機運行良好，轉子必須嚙合得恰當，且在整個轉子接觸線中要保留一定的密封。這就要求有適合這種加工的刀具，且必須由合理的嚙合過程計算出來。齒輪包絡線的加工方法，如果在一個特定的相對運動中一個表面包絡另一個表面，說明這兩個表面是嚙合的。方程（1）定義了給定的表面，第二個表面由方程（2）和方程（3）給出。轉子在x,y工作表面的坐標變化函數(shù)為x(t)和y(t)。通過x(t)和y(t)就可以定義轉子的型線，圖2就是一個典型的例子。方程(4)給出了一個熟悉的嚙合表面。它們對轉子 坐標和刀具 坐標的求導就可以得到方程(5).方程(5)中的C代表轉子軸中心線之間的距離， 是轉子和刀具軸之間的角度。h和t分別指轉子和刀具的表面。這些表面的包絡線方程由方程(6)中的回轉角度以函數(shù)的形式表示出來。
因為生成的表面是由參數(shù)t來定義的，包絡線的情況可以用來計算另一個參數(shù) ，它是轉子的回轉角，是生成嚙合表面的一個因素。包絡線方程中的橫截面的生成說明線是屬于該平面的，而 是兩表面一般點的相對速度， 是刀具回轉角度。轉子的的導程 由每個轉子的回轉角度來確定；
r (t, )=[]=[xcos-ysin,xsin+ycos,p] (1)
(2)
命名
C 轉子刀具中心距 轉子回轉角度
P 轉子每弧度導程 轉子型線角度 tan=
R 刀具型線坐標 壓力角 tan=
r 轉子矢量坐標 軸角度
s 刀具磨損測量 刀具角度
t 轉子參數(shù)
x x 坐標 h 螺旋狀轉子
t y坐標 hn 轉子法面?zhèn)淞?
z z 坐標 n 轉子橫截面?zhèn)淞?
余料面積 t 刀具
圖1 轉子和刀具的坐標系
(3)
P(t, ,)=[
= (4)
(5)
(6)
(7)
方程(7)在方程(6)的基礎上得到了嚙合條件，代入具體的數(shù)據(jù)就可以求出結果。給定一個參數(shù)t,轉子橫截面的點坐標x(t)和y(t)和它們的導數(shù) 就知道拉。通過方程(1)和（2）和閥門的參數(shù) 可以計算出.
圖2 雙螺桿壓縮機轉子
改進的閥門參數(shù)可以通過方程（7）算出。這個過程一直重復進行直到兩個連續(xù)閥門之間的差異變得足夠小為止。
刀具橫截面的點坐標可以通過方程（4）算出。
（8）
嚙合條件表明，在生成螺旋表面時，精確的螺桿轉子刀具應用較廣泛且使用很方便。有關用齒輪包絡線方法生產(chǎn)直線刀具漸開線的例子在很多教材中有相關的介紹,例如Litin和Fuentes.然而Andreev[2]和xing[3]最近在他們的書中提出了用螺桿壓縮機特定形式的刀具來加工螺桿壓縮機的理論。
Stosic[4]提出了一種合適的有關螺桿旋轉轉子不平衡和不相交軸的生產(chǎn)方法。而Stosic Etal.[5]只描述了不相交軸的方法。方程（10）給出了一種逆向刀具轉子的特殊形式。它可以用來計算影響螺桿轉子制造加工設備的不足之處。
給出刀具的坐標 ，轉子型線的點坐標 通過方程（4）的逆運算可以算出。算法如下；
（9）
角度參數(shù)由下式算出：
（10）
以上式子通過方程（?。┑哪孢\算可以計算出轉子橫向坐標x和y. 如下：
（11）
這里
結果一旦計算出來， 沿著分布圖的分散性可以用來計算嚙合刀具和轉子的坐標系。同樣可以確定接觸線和轉子，轉子和刀具之間的接觸路徑。
螺桿壓縮機的密封線是由轉子附近一系列的點組成的，通常在轉子之間存在間隙，類似的，刀具和工件之間的接觸線可以被當作是轉子的接觸線，多余的備料應從轉子加工時除去。如果這些剩余原材料沒有被刀具加工掉，通常被認為是間隙忽略。在這種情況下，通過給出的余料，用間隙結果來計算出刀具的磨損量。
2．計算給定余料的坐標分布
2.1 給定余料的轉子坐標
如果把從轉子加工掉的原材料厚度 給定到轉子豎直表面的一個正常位置,粗加工時轉子法平面對應的坐標 和精加工時轉子法平面對應的坐標 的不同代表在切削加工過程中轉子和刀具的相對運動。在計算粗加工時轉子橫截面上，與方程（6）第一個有關的的r的導數(shù)，確定了轉子的法線方向。用來計算轉子法平面的坐標。它包括轉子橫截面沒有剩余備料的原材料坐標，給出的余料厚度 計算如下：
（12）
這里直徑D由下式算出
（13）
備料轉子的橫向坐標 可以通過方程（11）計算出來，角度 為粗加工時刀具的坐標，精加工時刀具的坐標由原始的轉子坐標x和y來計算。粗加工時轉子法平面對應的坐標 和精加工時轉子法平面對應的坐標 的不同代表在切削加工過程中轉子和刀具的相對運動。在計算粗加工時轉子橫截面坐標 ，精加工時橫截面坐標x,y時?？梢缘玫酵瑯拥慕Y論。該結論也可以從粗加工時轉子刀具坐標 和精加工時刀具的坐標 得出。
2.2 刀具磨損
對于開始給定的刀具，磨損程度與工件和刀具之間的相對運動速率有關。粗加工和精加工時刀具的坐標可以說明這點?；蛘咄ㄟ^粗加工時轉子和精加工時轉子法平面或橫截面的差異可以看出。以下例子是通過轉子在粗加工時橫截面坐標 和精加工時的橫截面坐標x,y的來計算橫截面的。
（14）
從方程（14）可以算出刀具的磨損量，刀具的過度磨損可以從刀具的坐標看出。坐標變化越快說明磨損速率也越快。后來用這個理論來計算由磨損刀具加工出來的轉子型線。一種使磨損具體化的可行方法是按比例逐步放大它，把它疊加到轉子或刀具型線之上，在正確的型線位置上合理地估算磨損量。
3. 實例應用
工業(yè)轉子是具有5到6個齒的相互嚙合的陰陽轉子，圖2已分別列出了它們的嚙合情況，圖中陰轉子的直徑為144mm,轉子螺旋線角度為，轉子中心距為108mm.
3.1 均勻切削的刀具磨損
由圖2給出的轉子嚙合情況可知，螺桿壓縮機轉子和它的成型刀具嚙合在既不平行也不相交的軸上。方程（7）的解可以算出轉子刀具嚙合要求。給出精加工時轉子橫截面點坐標x,y及，轉子的螺旋坐標 就可以通過方程（1）求出。用同樣的方法計算轉子粗加工時的坐標可以求得余料厚度為50。對于嚙合的陰陽轉子刀具，它們的轉子刀具中心距為180mm和200mm.粗加工和精加工刀具也是一樣的。轉子和刀具的軸線夾角為。
由均勻切削引起的刀具磨損，備料被按順序逐漸增大50次，把它疊加在刀具的坐標中，圖表3中的曲線代表了的坐標，因此刀具的磨損由刀具上的每一點引出的一定長度的線來表示。刀具的磨損沿著刀具的型線是不一致的。在轉子型線的所有點的角度，。壓力角是相等的。在這種情況下，刀具的磨損是最小的，其他任何一種情況的磨損都比它大。
3.2 利用余料切削分布圖來減少刀具的磨損
厚度變化不均勻的一定量的余料被加工掉，是我們所期望的。因為厚度變化不均勻的余料會引起刀具沿著刀具型線的方向磨損。如果余料分布被當作是均勻余料，那么引起的循環(huán)磨損可以得到一種均勻的刀具磨損。均勻的刀具磨損從經(jīng)濟上來講，應該是最佳的選擇。因為它允許刀具在整修期間或者在鋒利時能夠使用最長的時間。這種新的轉子坐標和舊轉子坐標x,y的比較在圖4中得以體現(xiàn)。轉子坐標型線上每一個特殊點引起的的一定長度的線說明轉子坐標被逐
步增大50次時，磨損結果是各不相同的。
3.3實驗驗證
通過計算出的刀具磨損型線和實際測量得到的刀具磨損型線的比較，在此基礎上生產(chǎn)的150臺雙螺桿壓縮機。圖5給出了陰陽轉子的嚙合情況。理論的未磨損型線給定的公差帶為6，它表示了一定程度的磨損。圖中實際測量的刀具磨損型線由細實線標出，計算得到的刀具磨損型線由粗實線標出。兩者的相符性說明計算結果是正確的。
圖4
圖5
4.結論
刀具磨損經(jīng)常發(fā)生在螺桿壓縮機轉子的加工過程中。從邏輯上來說，是希望厚度變化不均勻的材料從轉子加工過程中被加工掉的，否則會引起沿著刀具型線厚度不一致的磨損。如果刀具以一定尺寸逆向加工剩余材料，就會得到厚度變化均勻的材料，加工過程中刀具以一定的速率切削，會產(chǎn)生均勻的刀具磨損。齒輪包絡線理論被作為一種嚙合要求，橫向螺旋齒輪用此來計算備料的分布，它將會引起精加工時的刀具磨損。
5.致謝
作者希望感謝Lan K Smith 教授給予的鼓勵和他提供寶貴的幫助，還有Mr Jack Sauls在測量樣板時給予的幫助，感謝Mr Elvedin Mujic 在圖表制作時給予的大力支持。
6.參考文獻
[1] F.L.Litvin,A.Fuentes,齒輪幾何特性的應用理論，第二，劍橋大學學報部，劍橋大學，2004。
[2] P.A.Andreev,Vintovie kompressornie mashinii(螺桿壓縮機)SUDPROM Leninngrad,Russia,1961.
[3] Z.W.Xing,螺桿壓縮機；理論。設計和應用，中國機械報，北京，2000。
[4] N.Stosic,有關螺桿壓縮機螺旋轉子齒輪，由IMechE,機械工程報212（1998）587出版。
[5] N.Stosic,I.K.Smith,A.Kovacevic,螺桿壓縮,數(shù)學建模,運動計算，Springer,Heidelberg,2005.
Screw compressor rotor machining tool wear the geometric calculation method
[Abstract]: screw compressor rotor milling and processing a grinding two methods, usually conducted in two phases processing; first stage is rough, when the workpiece to be processed about its size to the second stage of Finished, when the rotor be processed into its final size when completed. Materials or cutting cushion in the finishing was removed, it is by milling, grinding and cutting tools determined by the design. Taking into account the screw compressor rotor is a spiral shape, in the process of cutting, cutting tool on every point of contact with the rotor of the horizontal length is not the same, therefore, finished at the rate of wear and tear tool of its type along the line is Inconsistent. Envelop the meshing theory be used here in terms of the process of cutting tool on every point and the relative motion between the rotor. To a certain scale, in this relative movement of assumptions, calculated on every point of the tool wear rate. By calculating the results and experimental tool that the rate of wear and tear, we can see that both the conclusions are the same. On this basis, can know how to create a rough time so that semi-processed materials while the thinning tool and thereby facilitate the finishing tool at the same rate of wear and tear. A similar technology is being applied to many of the machines during processing, and forming a variety of knives were also used for these technical.
Keyword: screw compressors; spiral rotor; manufacturing tool
1. Description:
? Screw compressor is a displacement of the rotary volume machines, it mainly by the meshing of a spiral rotor component, in the case, do rotor rotary movement, with its volume of the rotor spinning change. Today's main rotor was a screw-type, used for milling or grinding. In either form of processing by the rotor, rotor can be used to define the coordinates of their geometric characteristics, as shown in Figure 1. To run a good screw compressor rotor must mesh properly, and in the contact line in the rotor to retain a certain seal. This requires suitable for processing such knives, and must be a reasonable process of engagement worked out. Gear envelope of processing methods, if in a particular relative movement of a surface on another envelope, on this surface is meshing the two. Equation (1) the definition of a given surface, the second surface by equation (2) and the equation (3) is given. Rotor in x, y coordinates the work surface for the change function x (t) and y (t). Through the x (t) and y (t) can be defined the type of rotor, Figure 2 is a typical example. Equation (4) is a familiar mating surface. Rotor coordinate their knives and coordinates the derivation can be equation (5). Equation (5) in C on behalf of the rotor shaft centerline the distance between the rotor and tool is the angle between the shaft. h t mean, respectively, and the rotor and tool the surface. These surface of the envelope equation by equation (6) in the rotation angle to function in the form of that out.
Because the surface is generated by the t to define the parameters, the envelope can be used to calculate the other parameters, it is the back corner of the rotor, is generated mesh surface as a factor. Envelope equation in the cross-section of the generation that is part of the plane, but two general points on the relative speed rotary tool is the point of view. Rotor of the lead by each rotor rotary angle to determine;
r (t, )=[]=[xcos-ysin,xsin+ycos,p] (1)
Naming
C Rotor Tool center distance Rotor rotary angle
P Rotor each arc-lead Rotor-point line tan=
R Tool-line coordinate Pressure angletan=
r Vector coordinates Rot Shaft angle
s Measuring Tool Wea Tool perspective
t Rotor parameters
x x Coordinate h Rotor spiral
t y Coordinate hn Surface preparation of the rotor
z z Coordinate n Rotor cross-section preparation
Ms Liu area t Tool
Figure 1 Rotor Tool and the coordinates
(3)
P(t, ,)=[
= (4)
(5)
(6)
(7)
Equation (7) in the equation (6) on the basis of the conditions of engagement, into the specific data can be obtained results. To set a parameter t, cross-section of the rotor coordinate x (t) and y (t) and their derivative known Rafah. Through the equation (1) and (2) and the parameters of the valve can be calculated.
（8）
Meshing conditions show that the spiral in the formation surface, the screw rotor precise tool of a broader and very convenient to use. With related gear envelope production of linear cutter involute line in the example of many in the relevant materials, such as Litin and Fuentes. But Andreev [2] and xing [3] in their recent book by using screw Compressor specific forms of processing tool to screw compressor theory.
Stosic [4] propose a suitable rotation of the screw rotor imbalance and do not intersect axis production methods. And Stosic Etal. [5] not only describes the intersection axis method. Equation (10) gives a reverse tool of the special form of the rotor. It can be used to calculate the impact of screw rotor manufacturing processing equipment deficiencies.
Tool is given the coordinates, the rotor-line through the coordinates of the points equation (4) the inverse operation can be calculated. Algorithms are as follows;
（9）
Angle from the next-calculated parameters:
（10）
Shizi over by equation (!) The inverse operation can be calculated rotor horizontal coordinates x and y. are as follows:
（11）
Here
Once the results worked out along the distribution of the dispersion of meshing tool can be used to calculate the rotor and the coordinates. The same can be identified contact line and the rotor, rotor and contacts between the tool path.
Screw compressor line is sealed by a series of points near the rotor component, usually in the gap between the rotor, a similar, knives and the contact line between the workpiece can be regarded as a rotor of the contact line, redundant Preparation should be removed when the rotor machining. If these remaining tool processing of raw materials have not been out, that gap is often overlooked. In this case, presented by the more than expected, with results to calculate the gap tool wear.
2. Ms Liu calculated given the coordinates distribution
2.1 more than expected given the coordinates of the rotor
If the rotor from the processing of raw materials out of a given thickness of the rotor to the vertical surface of a normal position, rough when the rotor plane of the corresponding coordinates and finishing at the rotor plane of the corresponding coordinate the different representatives in the process of cutting the rotor and Tool of relative movement. When the rotor in the calculation of rough circumferential, and the equation (6), a related derivative of the r to determine the normal direction of the rotor. Rotor plane method used to calculate the coordinates. It does not include the rotor cross-section coordinates of the remaining preparation of raw materials, is more than the thickness of material calculated as follows:
（12）
Here diameter D calculated from the next –
（13）
Preparation of the horizontal coordinates of the rotor can equation (11) worked out at the point of cutting tools for rough coordinates, finishing tool when the coordinates from the original rotor x and y coordinates to calculate. Rough at the rotor plane of the corresponding coordinates and finishing at the rotor plane of the corresponding coordinate the different representatives in the process of cutting tool and the rotor relative movement. When the rotor in the calculation of rough cross-section coordinates, finishing at the cross-section coordinates x, y,. Can get the same conclusion. The conclusions from the rough, can also coordinate the rotor cutter knives and finishing at the coordinates of that.
2.2 tool wear
The start given the tools, wear parts and tool and the relative motion between the relevant rate. Rough and finishing tool when the coordinates can illustrate this point. Or through the rough when the rotor and finishing at the rotor plane or cross-section of the difference can be seen. The following example is through the rotor in the rough when the cross-section coordinates and finishing of the cross-section.
（14） From the equation (14) can be calculated tool wear, the cutter knives from excessive wear and tear can see the coordinates. The sooner that coordinates changes also wear faster rate. This theory was later used to wear by Cutter calculated by the rotor of the processing line. To wear a specific method is feasible in proportion to gradually enlarge it, stack it to the rotor or tool-line, the right-line position on a reasonable estimate wear.
3. Examples of applications
3. Examples of industrial application of the rotor is a 5-6 tooth meshing of the yin and yang of mutual rotor, plans were set out two of their engagement, map conversion of the diameter of 144 mm, the rotor helix angle, the rotor center distance To 108 mm.
3.1 Cutting tool wear uniform
Figure 2 is given by the rotor meshing situation tells us that screw compressor rotor and its engagement in the forming tool is neither parallel nor intersection of the axis. Equation (7) the solution can be calculated Rotor Tool meshing requirements. When the rotor is finishing cross-section point coordinates x, y and, on the rotor of the spiral can coordinate equation (1) obtained. Use the same method of calculation of rotor rough coordinates can be obtained at the thickness of material for more than 50. The meshing of the yin and yang rotor knives, their rotor knives from the Centre for 180 mm and 200 mm. Roughing and finishing tool is the same. Rotor and tool for the axis angle.
Uniform caused by the cutting tool wear, the preparation was in order gradually increased 50 times, it superimposed on the coordinates of the tool, charts, three representatives of the curve in the coordinates, the cutter knives on the wear and tear from every point leads to the To a certain length of the line said. Tool of wear and tear of the tool along the line is inconsistent. In the rotor-point line all the perspective. Pressure angle is the same. Under such circumstances, the tool is the smallest of wear and tear, no other case of wear and tear than it big.
3.2 more than expected use of cutting tool to reduce the distribution of the wear and tear
Uneven thickness over a certain amount of material was processed out, is what we expect. Because of uneven thickness of the material would cause more than cutter-type knives along the line the direction of wear. If Ms Liu is deemed to be a uniform distribution of more than expected, so the cycle of wear and tear caused can be a tool wear the uniform. Tool wear the uniform from the economic terms, should be the best option. Because it allows tool in the renovation period, or when to use sharp in the longest time. The new rotor coordinates and the old rotor coordinates x, y in comparison to be reflected in Figure 4. Rotor coordinates of a special online every point from a certain length of the line that coordinates the rotor case-by -
Step increases 50 times, wear a result, not all the same.
3.3 experimental verification
Calculated by the type of tool wear and get the actual measurement tool wear-line, on the basis of this production of the 150 twin-screw compressors. Figure 5 is rotor meshing of the yin and yang situation. Theory did not wear a given line of the tolerance zone for the 6, it said that a certain degree of wear and tear. Figure in the actual measurement tool wear-line marked by fine line, calculated type of tool wear line marked by rough line. Taken in line with the statement result of this calculation is correct.
Figure 4
Figure 5
4. Conclusion
Tool wear often occur in the screw compressor rotor machining process. Logically speaking in the hope that the uneven thickness of material from the rotor in the process of being processed out, otherwise it will cause along the tool-wear line thickness inconsistent. If a certain size tool to reverse the processing of surplus materials, will be in uniform thickness of the material, processing tool in the course of a certain rate cutting will produce a uniform tool wear. Gear envelope theory was as a meshing requirements, horizontal helical gears used this to calculate the distribution of preparation, it will cause the finishing tool wear.
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