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1、英文原文Screw CompressorsThe direction normal to the helicoids, can be used to calculate the coordinates of the rotor helicoids and from x and y to which the clearance is added as:， ， （2.19）where the denominator D is given as： （2.20） and serve to calculate new rotor end plane coordinates, x0n and y0n,wi
2、th the clearances obtained for angles = /p and respectively. These and now serve to calculate the transverse clearance 0 as the difference between them, as well as the original rotor coordinates and .If by any means, the rotors change their relative position, the clearance distribution at one end of
3、 the rotors may be reduced to zero on the flat side of the rotor lobes. In such a case, rotor contact will be prohibitively long on the flat side of the profile, where the dominant relative rotor motion is sliding, as shown in Fig. 2.29. This indicates that rotor seizure will almost certainly occur
4、in that region if the rotors come into contact with each other.Fig. 2.29. Clearance distribution between the rotors: at suction, mid rotors, and discharge with possible rotor contact at the dischargeFig. 2.30. Variable clearance distribution applied to the rotorsIt follows that the clearance distrib
5、ution should be non-uniform to avoid hard rotor contact in rotor areas where sliding motion between the rotors is dominant.In Fig. 2.30, a reduced clearance of 65 m is presented, which is now applied in rotor regions close to the rotor pitch circles, while in other regions it is kept at 85 m, as was
6、 done by Edstroem, 1992. As can be seen in Fig. 2.31, the situation regarding rotor contact is now quite different. This is maintained along the rotor contact belt close to the rotor pitch circles and fully avoided at other locations. It follows that if contact occurred, it would be of a rolling cha
7、racter rather than a combination of rolling and sliding or even pure sliding. Such contact will not generate excessive heat and could therefore be maintained for a longer period without damaging the rotors until contact ceases or the compressor is stopped.2.6 Tools for Rotor ManufactureThis section
8、describes the generation of formed tools for screw compressor hobbing, milling and grinding based on the envelope gearing procedure.2.6.1 Hobbing ToolsA screw compressor rotor and its formed hobbing tool are equivalent to a pair of meshing crossed helical gears with nonparallel and nonintersecting a
9、xes. Their general meshing condition is given in Appendix A. Apart from the gashes forming the cutter faces, the hob is simply a helical gear in which.Fig. 2.31. Clearance distribution between the rotors: at suction, mid of rotor and discharge with a possible rotor contact at the dischargeEach refer
10、red to as a thread, Colburne, 1987. Owing to their axes not being parallel, there is only point contact between them whereas there is line contact between the screw machine rotors. The need to satisfy the meshing equation given in Appendix A, leads to the rotor hob meshing requirement for the given
11、rotor transverse coordinate points and and their first derivative.The hob transverse coordinate points and can then be calculated. These are sufficient to obtain the coordinate The axial coordinate , calculated directly, and are hob axial plane coordinates which define the hob geometry.The transvers
12、e coordinates of the screw machine rotors, described in the previous section, are used as an example here to produce hob coordinates. he rotor unit leadsare 48.754mm for the main and 58.504mm for the ate rotor. Single lobe hobs are generated for unit leads :6.291mm for the main rotor and 6.291mm for
13、 the gate rotor. The corresponding hob helix angles are 85 and 95. The same rotor-to-hob centre distance C = 110mm and the shaft angle = 50 are given for both rotors. Figure 2.32 contains a view to the hob.Reverse calculation of the hob screw rotor transformation, also given in Appendix A permits th
14、e determination of the transverse rotor profile coordinates which will be obtained as a result of the manufacturing process. These ay be compared with those originally specified to determine the effect ofFig. 2.32. Rotor manufacturing: hobbing tool left, right milling toolmanufacturing errors such a
15、s imperfect tool setting or tool and rotor deformation upon the final rotor profile.For the purpose of reverse transformation, the hob longitudinal plane coordinatesand andshould be given. The axial coordinate is used to calculate , which is then used to calculate the hob transverse coordinates:， （2
16、.21）These are then used as the given coordinates to produce a meshing criterionand the transverse plane coordinates of the “manufactured” rotors.A comparison between the original rotors and the manufactured rotors is given in Fig. 2.33 with the difference between them scaled 100 times. Two types of
17、error are considered. The left gate rotor, is produced with 30um offset in the centre distance between the rotor and the tool, and the main rotor withFig. 2.33. Manufacturing imperfections0.2 offset in the tool shaft angle . Details of this particular meshing method are given by Stosic 1998.2.6.2 Mi
18、lling and Grinding ToolsFormed milling and grinding tools may also be generated by placing in the general meshing equation, given in Appendix A, and then following the procedure of this section. The resulting meshing condition now reads as: (2.22)However in this case, when one expects to obtain scre
19、w rotor coordinates from the tool coordinates, the singularity imposed does not permit the calculation of the tool transverse plane coordinates. The main meshing condition cannot therefore be applied. For this purpose another condition is derived for the reverse milling tool to rotor transformation
20、from which the meshing angle is calculated: (2.23)Once obtained, will serve to calculate the rotor coordinates after the “manufacturing” process. The obtained rotor coordinates will contain all manufacturing imperfections, like mismatch of the rotor tool centre distance, error in the rotor tool shaf
21、t angle, axial shift of the tool or tool deformation during the process as they are input to the calculation process. A full account of this useful procedure is given by Stosic 1998.2.6.3 Quantification of Manufacturing ImperfectionsThe rotor tool transformation is used here for milling tool profile
22、 generation. The reverse procedure is used to calculate the “manufactured” rotors. The rack generated 5-6 128mm rotors described by Stosic, 1997a are used as given profiles: x(t) and y(t). Then a tool rotor transformation is used to quantify the influence of manufacturing imperfections upon the qual
23、ity of the produced rotor profile. Both, linear and angular offset were considered. Figure 2.33 presents the rotors, the main manufactured with the shaft angle offset 0.5 and the gate with the centre distance offset 40 m from that of the original rotors given by the dashed line on the left. On the r
24、ight, the rotors are manufactured with imperfections, the main with a tool axial offset of 40 m and the gate with a certain tool body deformation which resulted in 0.5 offset of the relative motion angle . The original rotors are given by the dashed line.3Calculation of Screw Compressor PerformanceS
25、crew compressor performance is governed by the interactive effects of thermodynamic and fluid flow processes and the machine geometry and thus can be calculated reliably only by their simultaneous consideration. This may be chieved by mathematical modelling in one or more dimensions. For most applic
26、ations, a one dimensional model is sufficient and this is described in full. 3-D modelling is more complex and is presented here only in outline. A more detailed presentation of this will be made in a separate publication.3.1 One Dimensional Mathematical ModelThe algorithm used to describe the therm
27、odynamic and fluid flow processes in a screw compressor is based on a mathematical model. This defines the instantaneous volume of the working chamber and its change with rotational angle or time, to which the conservation equations of energy and mass continuity are applied, together with a set of a
28、lgebraic relationships used to define various phenomena related to the suction, compression and discharge of the working fluid. These form a set of simultaneous non-linear differential equations which cannot be solved in closed form.The solution of the equation set is performed numerically by means
29、of the Runge-Kutta 4th order method, with appropriate initial and boundary conditions.The model accounts for a number of “real-life” effects, which may significantly influence the performance of a real compressor. These make it suitable for a wide range of applications and include the following: The
30、 working fluid compressed can be any gas or liquid-gas mixture for which an equation of state and internal energy-enthalpy relation is known, i.e. any ideal or real gas or liquid-gas mixture of known properties. The model accounts for heat transfer between the gas and the compressor rotors or its ca
31、sing in a form, which though approximate, reproduces the overall effect to a good first order level of accuracy. The model accounts for leakage of the working medium through the clearances between the two rotors and between the rotors and the stationary parts of the compressor. The process equations
32、 and the subroutines for their solution are independent of those which define the compressor geometry. Hence, the model can be readily adapted to estimate the performance of any geometry or type of positive displacement machine. The effects of liquid injection, including that of oil, water, or refri
33、gerant can be accounted for during the suction, compression and discharge stages. A set of subroutines to estimate the thermodynamic properties and changes of state of the working fluid during the entire compressor cycle of operations completes the equation set and thereby enables it to be solved.Ce
34、rtain assumptions had to be introduced to ensure efficient computation.These do not impose any limitations on the model nor cause significant departures from the real processes and are as follows: The fluid flow in the model is assumed to be quasi one-dimensional. Kinetic energy changes of the worki
35、ng fluid within the working chamber are negligible compared to internal energy changes. Gas or gas-liquid inflow to and outflow from the compressor ports is assumed to be isentropic. Leakage flow of the fluid through the clearances is assumed to be adiabatic.3.1.1 Conservation EquationsFor Control V
36、olume and Auxiliary RelationshipsThe working chamber of a screw machine is the space within it that contains the working fluid. This is a typical example of an open thermodynamic system in which the mass flow varies with time. This, as well as the suction and discharge plenums, can be defined by a c
37、ontrol volume for which the differential equations of the conservation laws for energy and mass are written. These are derived in Appendix B, using Reynolds Transport Theorem.A feature of the model is the use of the non-steady flow energy equation to compute the thermodynamic and flow processes in a
38、 screw machine in terms of rotational angle or time and how these are affected by rotor profile modifications. Internal energy, rather than enthalpy, is then the derived variable. This is computationally more convenient than using enthalpy as the derivedVariable since, even in the case of real fluid
39、s, it may be derived, without reference to pressure. Computation is then carried out through a series of iterative cycles until the solution converges. Pressure, which is the desired output variable, can then be derived directly from it, together with the remaining required thermodynamic properties.
40、The following forms of the conservation equations have been employed in the model:中文翻译螺杆式压缩机几何的法线方向的螺旋，可以用来计算的坐标转子螺旋和的从x和y的间隙加入如：， ， (2.19)其中分母D被给定为： (2.20)，服务来计算新的转子端的平面的坐标， 和，得到的间隙角 =锌/ p和 。这些，现在的差额计算的横向间隙0在它们之间，以及原来的转子坐标和 。如果以任何方式，转子的改变它们的相对位置，该间隙的平侧面上分布在转子的一端，也可以减少到零的转子叶片。在这样的情况下，转子的接触将是令人望而却步长侧
41、扁的档案中，其中占主导地位的相对滑动转子运动，如示于图。 2.29。这表明，转子扣押几乎肯定会如果转子进入彼此接触，发生在该区域。图.29。：吸力，中间转子和转子之间的间隙分布可能转子接触放电在放电图 2.30。可变间隙分布应用到转子如下的间隙分布应该非均匀，以避免在转子转子之间的滑动运动的地方是硬转子的接触占主导地位。另外，在图2.30 ，清除率降低65微米，这是现在应用在转子靠近转子节圆的区域，而在其他区域是保持在85微米所做的那样， 1992年由Edstroem 。正如在图中可以看出的。 2.31，现在的情况，转子的接触是完全不同的。这是保持靠近转子的节圆沿转子的接触带，并完全避免在其他
42、位置。因此，如果发生接触，这将是一个滚动字符，而不是相结合的滚动和滑动，甚至是纯滑动。这样的接触不会产生过多的热量，因此可以保持一段较长时间，而不会损坏转子直到接触终止或使压缩机停止。2.6 为转子制造的工具本节描述了一代形成的工具螺杆压缩机滚齿，铣床和磨床的基础上信封资产负债程序。2.6.1 滚齿机工具螺杆压缩机转子和其形成的滚齿机工具相当于一个对相互啮合的交错轴斜齿轮与非平行不相交轴。他们的啮合条件一般除了见附录A。张裂缝形成刀具的面孔时，仅仅是一个螺旋齿轮的滚刀。图2.31。转子之间的间隙分布：在抽吸，中期的转子和可能转子接触放电在放电每个齿被称为作为一个线程， Colburne ，19
43、87 。由于其自身的轴线不平行，它们之间的唯一的点接触，而有行螺杆机转子之间的接触。需要满足的啮合在附录A中给出的公式，导致转子A “滚刀啮合要求对于给定的转子横向坐标点X01和Y01和他们的第一次衍生。滚刀横向坐标点X02和Y02计算出来的。这是足够的，以获得坐标轴向坐标z2的，直接计算，和R2是滚刀轴向平面坐标它定义滚刀的几何形状。轴向坐标z2的，直接计算，和R2是滚刀轴向平面坐标它定义滚刀的几何形状。螺杆机转子的横向坐标，描述在前面的部分，被用来作为一个例子在这里产生滚刀坐标。转子单元导致p1的有48.754毫米的主和- 58.504毫米的门转子。单叶炉产生单位领导P2 ： 6.291毫
44、米的主转子和闸转子- 6.291毫米为。相应的滚刀螺旋角分别为85 和95 。相同的转子滚刀中心距离C = 110毫米和轴角 = 50 给出了两个转子。图2.32中包含一个查看的炉灶。反向计算的炉灶 - 螺杆转子的改造，也给出了附录A，允许确定转子型线的横向坐标这将在制造过程中得到的结果。这些可能与最初指定的进行比较，以确定影响图。 2.32。转子制造业：滚齿刀具左，右铣刀制造的错误，如完美的工具设置或工具，转子变形后，最终的转子型线。如果在反向变换的目的，滚刀的纵向平面坐标R2和Z2和应给予。轴向坐标z2的使用计算 = z2/p2 ，然后将其用于计算滚刀横向的坐标：， (2.21)然后用这些
45、作为给定的坐标，以产生一个啮合判据的横向平面上的坐标的“人造”转子。原来的转子之间的比较和所制造的转子给出图。 2.33与它们之间的区别缩放100倍。二被认为是类型的错误。左边的门转子，30微米抵消在该转子与该工具，和主旋翼之间的中心距离0.2 偏移刀具轴角 。这个特殊的网格划分方法的详情给出由Stosic 1998。图。 2.33。制造缺陷2.6.2 铣削和磨削工具形成铣削和磨削工具也可以通过放置p2= 0产生啮合方程，一般在附录A中，然后按照本节的程序的。现在的啮合条件内容： (2.22)然而，在这种情况下，当一个人希望获得螺杆转子坐标从工具坐标，所施加的奇异性，不允许计算该工具的横向平面
46、坐标。主要的啮合条件不能因此其应用。为此目的，另一个条件推导了扭转铣刀到转子的变换从该啮合角计算方法是: (2.23)一旦获得，后，将用来计算转子坐标“制造”的过程。得到的转子的坐标将包含所有制造不完善的地方，如不匹配的转子 - 刀具中心的距离，在转子中的误差 - 工具轴角度，轴向移位的工具或工具变形在这个过程中，因为它们是输入到计算处理。一个完整的帐户这个有用的程序是Stosic于 1998年定义的。2.6.3 量化的制造缺陷转子 - 这里使用的工具转换生成铣削刀具轮廓。相反的步骤是用来计算“制成品”转子。机架产生的Stosic的5-6 128毫米转子的描述， 1997年a使用给定的概况：X
47、 （t）和Y（T） 。然后一个工具 - 转子的变换是用来量化后，所生成的质量的影响的制造缺陷转子型线。这两种，线性和角度偏移量进行了考虑。图2.33转子，主要制造与轴角度偏移0.5 门与中心的距离偏移量40微米原来的转子由在左边的虚线给出。在屏幕的右侧，转子制造的缺陷，主要与刀具轴向偏移为40m，具有一定的工具主体变形而导致的栅极0.5 偏移量的相对运动的角度 。原来的转子由下式给出的虚线。3螺杆压缩机性能的计算螺杆式压缩机的性能是受热力学的相互影响和流体流动过程和机器的几何形状，从而可以只能由他们同时考虑可靠地计量。这可能是实现在一个或多个维度的数学建模。对于大多数应用，一个三维模型是足够的
48、，这充分说明。3-D模型比较复杂，而且只在这里介绍的轮廓。一个更详细介绍了这个将在一个单独的出版物。3.1 一维数学模型来描述的热力学和流体的流动过程中所使用的算法的螺杆压缩机的基础上的数学模型。这个定义的瞬时工作腔的体积，其变化与旋转角或时间，能量和质量的连续性的守恒方程施加，连同一组用于定义各种代数关系的吸入，压缩和排出的工作有关的现象流体。这些形成了一套同时非线性微分方程不能得到解决封闭形式。方程组的溶液通过数值进行龙格库塔四阶的方法，用适当的初始条件和边界条件。模型考虑了一些“现实生活”的影响，这可能显著一个真正的压缩机的性能产生影响。这使得它适合一个广泛的应用范围，包括以下内容：-工作流体压缩可以是任何气体或液 - 气混合物的方程的状态和内能，焓关系是已知的，即任何理想的或真正