Research on the Design Parameters of the Diaphragm Based on the Torsional Static-characteristics

Transcription

1 2017 5th International Conference on Mechanics and Mechatronics (ICMM 2017) ISBN: Research on the Design Parameters of the Diaphragm Based on the Torsional Static-characteristics Guo-Ping WANG 1,a, Jia-Bao WEN 1 and Shuang CHENG 1 1 The high-tech College of Xi an University of technology, Ziwu Road 35, Chang An District, Xi an, China Abstract. In view of the diaphragms of traditional diaphragm coupling in conditions of large centrifugal force, the hub or rim with prominent stress concentration, the effective size of the elastic film is small, and the tangential load distribution uneven by the bolt connection, a closed diaphragm coupling is presented, it is connected by interference fit, and eliminates the membrane disc rim, increases the effective size, improves centrifugal action. Under the static torsion loading conditions, deformation and stress distribution with the variation of membrane disc thickness, taper, double curvature and radial dimensions of the diaphragm having the linear surface, cone surface and hyperbolic surface are studied. The stress and deformation characteristics of three kinds of disc surfaces are summarized by analogy, and the design rules and selection principles of various types of diaphragm for practical application are obtained. 1 Introduction High speed metal diaphragm coupling is a coupling element of high technology of modern power equipment with multi span rotor system. It is widely used in various types of gas turbine, such as aircraft engine, ship engine and high efficiency gas turbine unit for generator. So the importance of the design and research of the diaphragm coupling is self-evident. The design of the diaphragm is key problem for diaphragm coupling, which is crucial to the overall stiffness and the misalignment compensation ability of the shaft joint. At present, the most of diaphragm couplings are in development of original Bendix s diaphragm coupling as the prototype, and designed or improved to be varied forms of single diaphragm or multi-diaphragm structure. But these couplings still remain basically the big rim, the large hub, the diaphragm between them, and the bolt connection of the rim and the flange to transfer power, as Fig.1. Figure 1. Diaphragm Coupling with Bolt Connection. a Corresponding author: diaphragmcoupling@163.com Large centrifugal stress on the diaphragm, stress concentration at the connection position between the hub/rim and the diaphragm, smaller effective diaphragm size, uneven tangential action by bolt connection are all outstanding in the mentioned structure. In recent years, research on diaphragm coupling is mainly for class Bendix diaphragm coupling, and focused on two aspects: the first one is the design problem of diaphragm coupling, including of design theory based on the strength or the fatigue strength theory [1-7]. The second aspect is for system dynamics analysis between the diaphragm coupling and the connected shafts, consisting of unbalance problem, misalignment [8-10] etc. In terms of the design problem of diaphragm coupling, diaphragm profiles design is studied by experimental or simulated method based on strength theory or fatigue strength theory; the design of connection forms for the coupling is researched a little. Interference fit is used to substitute bolt connection to achieve transmission in the article, as Fig.2, there are two hubs, two diaphragms, and a spacer shaft between them. Obviously, this coupling doesn t have rigid rim and inner hub, increases the efficient radial size of the diaphragm, improves stress distribution, and enhances the misalignment compensatory ability. Otherwise, because of its less relative subsidiary configuration and less space utilization, it can be used in micro gas turbines and has a broader market prospect. The design parameters of diaphragm profiles are researched based on torsional static characteristics in this paper, design rules and selection principles of the diaphragm profiles design parameters are presented. 15

2 3 Diaphragm Design Parameter Analyses Diaphragm design parameters include the diaphragm thickness, radial size and profile structure parameters. Here, influences on diaphragm torsional stresses and deformation are analyzed with respect to the three parameters just mentioned. Figure 2. Diaphragm Coupling with Shrink Fit. 2 Simulation Model of the Diaphragm As Figure 2, the diaphragm can be treated as a circular thin plate with torsional load or fastened end at the inner radius or outer radius. Torsional load position doesn t affect the torsional stress distribution in the diaphragm, and torsional deformation of the two diaphragms has similar rules, so just take driving end diaphragm as research object, which is fastened at inner radius and loaded torsional moment at outer radius, its parameters are shown as table 1. Especially, various diaphragm profiles are used to obtain different diaphragm characteristics for different application. In this article, solid models of linear, conical, and hyperbolic diaphragm are built by commercial software, as Figure 3(a), (b), (c). The model is established by Solid186 elements, using a free mesh or sweep grid according to the different structural shapes. Torsional moment is loaded at the outer radius of the diaphragm by node-coupling using command CERIG, shown as Figure 3(d). 3.1 Influences on Diaphragm Torsion Stress and Deformation by the Thickness Here, influences of the thickness are analyzed by solving linear diaphragm with the thickness 1mm, 1.5mm, 2mm, and 2.5mm respectively. At the outer edge of the diaphragm, the torque is applied, and the inner hole is fixed Effect of Film Thickness on Torsional Deformation As Figure 4, the torsional (circumferential) deformation increases gradually from the inside to the outside along the radial direction, and the magnitude of the torsional deformation is related to the position of the applied torque. With the increase of the thickness of the disk, the torsional resistance increases accordingly. Table 1. Diaphragm structure parameters. Inner radius Outer radius Thickness h r 1 [mm] r 2 [mm] [mm] Diaphragm (a) h=1mm (a) linear (b) conical (c)hyperbolic (d) loaded Figure 3. Simulation Model of the Linear, Conical, Hyperbolic Diaphragm Profiles and theloaded Style. (b) h=1.5mm 16

3 (c) h=2mm Figure 4. Torsional Deformation Distribution along the Radial Effect of Film Thickness on Torsional Shearing Stress (c) h=2mm Figure 5. Torsional Shearing Stress Distribution along the Radial As Figure 5, when the diaphragm is applied torque, the equivalent stress gradually decreases from inside to outside along the radial direction, independent of the load position, and the maximum torsional stress decreases with the increase of the thickness of the film disk, and the stress distribution in the film disk is at a moderate level. 3.2 Effect of Radial Film Size on Torsional Stress and Deformation The influence of the change of the outside diameter on the torsional stress and deformation of the linear diaphragm with 1mm thickness is studied. (a) h=1mm (a) h=1mm, r 2 =21mm (b) h=1.5mm 17

4 the inner diameter of the disk to reduce the maximum torsional stress and to improve the stress distribution of the disc. 3.3 Effect of Diaphragm Profiles on Torsional Stress and Deformation Conical Profiles Stress and Deformation (b) h=1mm, r 2 =22mm Figure 6. Torsional Deformation Distribution along the Radial As Figure 8 and Figure 9, with the increase of taper cone shape, torsional deformation distribution along the radial direction were decreased; the torsional resistance increases; shearing stress decreases; the minimum stress position along the membrane disc radial moving from outside to inside, and stress at the position of the minimum thickness of the membrane disc will gradually increase, then the diaphragm will probably tear. Therefore, the proper increase of taper is beneficial to the improvement of the stress and the torsional resistance of the membrane disk, but the taper of the film disk is not too large. (a) h=1mm, r 2 =21mm (a) taper=1 (b) h=1mm, r 2 =22mm Figure 7. Torsional Stress Distribution along the Radial As Figure 6 and Figure 7, with the increase of the outer diameter of the disk, the torsional deformation increases, but the maximum torsional stress on the inside of the film disk is not obvious, and its value is much more sensitive to the change of the internal radius than the outside diameter. Therefore, it is possible to increase (b) taper=1.5 18

5 (c) taper=2 Figure 8. Torsional Deformation Distribution along the Radial (c) taper=2 Figure 9. Torsional Stress Distribution along the Radial Hyperbolic Profiles (Y=K/X) Stress And Deformation As Fig.11 and Fig.12, with the increase of K value, the circumferential deformation value and shear stress in the corresponding position of the disc are gradually reduced, and the stress distribution tends to be homogenized. (a) taper=1 (a) k=5 (b) taper=1.5 (b) k=10 Figure 10. Torsional deformation distribution along the radial direction (k=5, 10). 19

6 (a) k=5 3) About conical diaphragm shape, with an increasing taper (in the allowable range) circumferential deformation and shear stress decreases at the same position of the diaphragm. the minimum stress position moves from outside to inside, stress at the minimum thickness position of the membrane disc will gradually increase and finally cause the crack of the diaphragm, so the diaphragm taper should not be too large. 4) In terms of the hyperbolic film surface, the circumferential deformation and shear stress of the same position of the diaphragm is gradually reduced and the stress distribution is gentler with the increase of the K of the scale coefficient. 5) When the diaphragm thicknesses are identical in inner diameter, by comparison of three kinds of diaphragm stress and deformation, the hyperbolic disc shows the stress distribution is the best, and has minimum stress concentration; cone shape diaphragm has better stress distribution, the larger the stress concentration; the diaphragm with equal thickness has the stress distribution of changes rapidly, the maximal concentration. For torsional deformation, the minimum is equal thickness membrane disc; the maximum is the hyperbolic cone diaphragm. Acknowledgement This work was financially supported by the Scientific Research Program of Shaanxi Provincial Education Department (Program No.17JK1022). (b) k=10 Figure 11. Torsional Stress Distribution along the Radial Direction (k=5, 10) Conclusion Based on the above analysis and comparative calculation, the following conclusions can be drawn: 1) With the increase of the thickness of the membrane disc, circumferential (Y direction) deformation along the radial direction from the inside to outside increases gradually, torsional deformation is maximum at the position of torque; equivalent stress along the radial direction from the inside to outside decreases gradually, the maximal value is in inner diameter or near the inner diameter of the diaphragm, affected a little by boundary conditions, and sensitive to the diaphragm thickness variation. 2) In the same inner radius, with the increase of film outer radius, circumferential (Y) deformation increases gradually, although the stress attenuation slowed down, the maximum equivalent stress value did not change apparently, and not sensitive to the outside diameter increases; according to further analysis, in order to improve the stress distribution the inner radius of the diaphragm should be increased appropriately. References [1] Angang Cao, Shan Chang, Chunhua Ding, Mechanical Transmission, 7, 83 (2017) (In [2] Lin Li, Yu Fan, Journal of Beihang University, 36, 1480 (2010) (In [3] Peng Yue, Yu Zhao, Xinxin Liu, Ship Science and Technology, 35, 83 (2013) (In [4] Jianmin Fang, China Aviation Institute of Youth Science and Technology Forum, 412 (2014) (In [5] Shunyu Wang, Jianmin Gong, Journal of Southeast University, 23, 136 (1993) (In [6] Peng Yue, Guanglin Deng, Lifeng Xing, Ship Science and Technology, 35, 81 (2013) (In [7] Zhaoguo Qiu, Fengpeng Zhang, Jinghui Bai, Mechanical Design and Manufacture, 7, 32 (2010) (In [8] A.K. Verma, S. Sarangi, M.H Kolekar, Journal of Failure Analysis & Prevention,14,125 (2014). [9] V.Hariharan, Middle East Journal of Scientific Research, 5,336 (2013). [10] A. Askarian, S.M.R. Hashemi, 14th International Congress on Sound and Vibration (2007). 20