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英文原文
Screw Compressor
The Symmetric profile has a huge blow-hole area which excludes it from any compressor applicat -ion where a high or even moderate pressure ratio is involved. However, the symmetric profile per -forms surprisingly well in low pressure compressor applications.More details about the circular p -rofile can be found in Margolis, 1978.
2.4.8 SRM “A” Profile
The SRM “A” profile is shown in Fig. 2.11. It retains all the favourable features of the symmetric profile like its simplicity while avoiding its main disadvantage,namely, the large blow-hole area. The main goal of reducing the blow hole area was achieved by allowing the tip points of the main and gate rotors to generate their counterparts, trochoids on the gate and main rotor respectively. T -he “A” profile consists mainly of circles on the gate rotor and one line which passes through the gate rotor axis.The set of primary curves consists of: D2C2, which is a circle on the gate rotor with the centre on the gate pitch circle, and C2B2, which is a circle on the gate rotor, the centre of whi ch lies outside the pitch circle region.This was a new feature which imposed some problems in the generation of its main rotor counterpart, because the mathematics used for profile generation at tha -t time was insufficient for general gearing. This eccentricity ensured that the pressure angles on th -e rotor pitches differ from zero, resulting in its ease of manufacture. Segment BA is a circle on th -e gate rotor with its centre on the pitch circle. The flat lobe sides on the main and gate rotors were
generated as epi/hypocycloids by points G on the gate and H on the main rotor respectively. GF2 is a radial line at the gate rotor. This brought the same benefits to manufacturing as the previously mentioned circle eccentricity on
Fig. 2.11 SRM “A” Profile
2.4 Review of Most Popular Rotor Profiles 31 the opposite lobe side. F2E2 is a circle with the cent -re on the gate pitch and finally, E2D2 is a circle with the centre on the gate axis.More details on t -he “A” profile are published by Amosov et al., 1977 and by Rinder, 1979.The “A” profile is a go od example of how a good and simple idea evolved into a complicated result. Thus the “A” pro file was continuously subjected to changes which resulted in the “C” profile. This was mainly gen erated to improve the profile manufacturability. Finally, a completely new profile, the“D” profile was generated to introduce a new development in profile gearing and to increase the gate rotor tor -que.Despite the complexity of its final form the “A” profile emerged to be the most popular scre -w compressor profile, especially after its patent expired.
2.4.9 SRM “D” Profile
The SRM “D” profile, shown in Fig. 2.12, is generated exclusively by circles with the centres off the rotor pitch circles.
Similar to the Demonstrator, C2D2 is an eccentric circle of radius r3 onthe gate rotor. B1C1 is an eccentric circle of radius r1, which, together withthe small circular arc A1J1 of radius r2, is positioned on the main rotor. G2H2is a small circular arc on the gate rotor and E2F2 is a circular arc on the gaterotor. F2G2 is a relatively large circular arc on the gate rotor which produces a corresponding curve of the smallest possible curvature on the main rotor.Both circular arc, B2C2 and F2G2 ensure a large radius of curvature in the pitch circle area. This avoids high stresses in the rotor contact region.
Fig. 2.12 SRM “D” Profile
The “G” profile was introduced by SRM in the late nineteen nineties as a replacement for the “D” rotor and is shown in Fig. 2.13. Compared with the“D” rotor, the “G” rotor has the unique feature of two additional circles in the addendum area on both lobes of the main rotor, close to the pitch circle.This feature improves the rotor contact and, additionally, generates shorter sealing lines. This can be seen in Fig. 2.13, where a rotor featuring “G” profile characteristics only on its flat side through segment H1I1 is presented.
Fig. 2.13 SRM “G” Profile
2.4.11 City “N” Rack Generated Rotor Profile “N” rotors are calculated by a rack generation procedure. This distinguishes them from any others. In this case, the large blow-hole area, which is a characteristic of rack generated rotors, is overcome by generating the high pressure side of the rack by means of a rotor conjugate procedure. This undercuts the single appropriate curve on the rack. Such a rack is then used for profiling both the main and the gate rotors. The method and its extensions were used by the authors to create a number of different rotor profiles, some of them used by Stosic et al., 1986, and Hanjalic and Stosic, 1994. One of the applications of the rack generation procedure is described in Stosic, 1996.The following is a brief description of a rack generated “N” rotor profile,typical of a family of rotor profiles designed for the efficient compression of air,common refrigerants and a number of process gases. The rotors are generated by the combined rack-rotor generation procedure whose features are such that it may be readily modified further to optimize performance for any specific application.
2.4 Review of Most Popular Rotor Profiles 33
The coordinates of all primary arcs on the rack are summarized here relative to the rack coordinate system. The lobe of the rack is divided into several arcs. The divisions between the profile arcs are denoted by capital letters and each arc is defined separately, as shown in the Figs. 2.14 and 2.15 where the rack and the rotors are shown.
Fig. 2.14 Rack generated “N” Profile
Fig. 2.15 “N” rotor primary curves given on rack
34 2 Screw Compressor Geometry
All curves are given as a “general arc” expressed as: axp + byq = 1. Thus straight lines, circles, parabolae, ellipses and hyperbolae are all easily described by selecting appropriate values for parameters a, b, p and q.Segment DE is a straight line on the rack, EF is a circular arc of radius r4,
segment FG is a straight line for the upper involute, p = q = 1, while segment GH on the rack is a meshing curve generated by the circular arc G2H2 on the gate rotor. Segment HJ on the rack is a meshing curve generated by the circular arc H1J1 of radius r2 on the main rotor. Segment JA is a circular arc of radius r on the rack, AB is an arc which can be either a circle or a parabola, a hyperbola or an ellipse, segment BC is a straight line on the rack matching the involute on the rotor round lobe and CD is a circular arc on the rack, radius r3.More details of the “N” profile can be found in Stosic, 1994.
2.4.12 Characteristics of “N” Profile
Sample illustrations of the “N” profile in 2-3, 3-5, 4-5, 4-6, 5-6, 5-7 and 6-7 configurations are given in Figs. 2.16 to Fig. 2.23. It should be noted that all rotors considered were obtained automatically from a computer code by simply specifying the number of lobes in the main and gate rotors, and the lobe curves in the general form.A variety of modified profiles is possible. The “N” profile design is a compromise between full tightness, small blow-hole area, large displacement.
Fig. 2.16 “N” Rotors in 2-3 configuration
Fig. 2.17 “N” Rotors in 3-5 configuration
Fig. 2.18 “N” Rotors in 4-5 configuration
Fig. 2.19 “N” Rotors in 4-6 configuration
Fig. 2.20 “N” Rotors compared with “Sigma”, SRM “D” and “Cyclon” rotors
Fig. 2.21 “N” Rotors in 5-6 configuration
Fig. 2.22 “N” Rotors in 5-7 configuration
Fig. 2.23 “N” rotors in 6/7 configuration
sealing lines, small confined volumes, involute rotor contact and proper gate rotor torque distribution together with high rotor mechanical rigidity.The number of lobes required varies according to the designated compressor duty. The 3/5 arrangement is most suited for dry air compression, the 4/5 and 5/6 for oil flooded compressors with a moderate pressure difference
and the 6/7 for high pressure and large built-in volume ratio refrigeration applications.Although the full evaluation of a rotor profile requires more than just a geometric assessment, some of the key features of the “N” profile may be readily appreciated by comparing it with three of the most popular screw rotor profiles already described here, (a) The “Sigma” profile by Bammert,1979, (b) the SRM “D” profile by Astberg 1982, and (c) the “Cyclon” profile by Hough and Morris, 1984. All these rotors are shown in Fig. 2.20 where it can be seen that the “N” profiles have a greater throughput and a stiffer gate rotor for all cases when other characteristics such as the blow-hole area, confined volume and high pressure sealing line lengths are identical.Also, the low pressure sealing lines are shorter, but this is less important because the corresponding clearance can be kept small.The blow-hole area may be controlled by adjustment of the tip radii on both the main and gate rotors and also by making the gate outer diameter equal to or less than the pitch diameter. Also the sealing lines can be kept very short by constructing most of the rotor profile from circles whose centres are close to the pitch circle. But, any decrease in the blow-hole area will increase
the length of the sealing line on the flat rotor side. A compromise betweenthese trends is therefore required to obtain the best result.
2.4 Review of Most Popular Rotor Profiles 39
Rotor instability is often caused by the torque distribution in the gate rotor changing direction during a complete cycle. The profile generation procedure described in this paper makes it possible to control the torque on the gate rotor and thus avoid such effects. Furthermore, full involute contact between the “N” rotors enables any additional contact load to be absorbed more easily than with any other type of rotor. Two rotor pairs are shown in Fig. 2.24 the first exhibits what is described as “negative” gate rotor torque while the second shows the more usual “positive” torque.
Fig. 2.24 “N” with negative torque, left and positive torque, right
2.4.13 Blower Rotor Profile
The blower profile, shown in Fig. 2.25 is symmetrical. Therefore only one quarter of it needs to be specified in order to define the whole rotor. It consists of two segments, a very small circle on the rotor lobe tip and a straight line. The circle slides and generates cycloids, while the straight line generates involutes.
Fig. 2.25 Blower profile