本研究提出透過顆粒阻尼器(Particle Damper, PD)依工件動平衡狀況進行顆粒配置，以同時達到配重和抑制振動之雙重效果。首先透過多體動力學(Multi-Body Dynamics, MBD)建立迴轉式壓縮機模型，模型中考量循環氣體負載變化、支座與橡膠墊剛性與阻尼，並透過實驗驗證在轉動頻率下之振動之趨勢與量值，確認此模型之可靠性；未來利用此模型探討具PD之迴轉式壓縮機(新構型)之動平衡與抑振研究。
新構型模擬時需同時應用離散元素法(Discrete Element Method, DEM)和MBD進行雙向耦合得到迴轉式壓縮機之動態模擬結果；首先針對迴轉式壓縮機進行轉子系統之動平衡驗證，在此動平衡驗證中不考慮氣體負載影響；迴轉式壓縮機依據ISO 1940動平衡等級需低於G 2.5，透過PD可使轉子系統動平衡等級達到G 0.31，確認其動平衡改善成效。
然後針對新構型進行模擬並與原構型(頂配重塊)比較其抑振效果，確認新構型確實有抑振效果；也探討在不同顆粒粒徑、摩擦係數和恢復係數下，對迴轉式壓縮機系統抑振之影響；在不同顆粒半徑下皆對新構型有抑振效益，其中顆粒半徑1 mm較其他粒徑抑振效益較佳；隨顆粒摩擦係數增加，新構型系統之總動能越小，說明摩擦耗能越大，PD之抑振效果越佳；隨顆粒恢復係數增加，新構型之動能越大，說明碰撞耗能越小，PD之抑振效果越差。最後透過實驗驗證新構型之實際振動數值，徑向加速度平均可降低9.7%，切向加速度平均可降低2.46 %，確認PD之抑制振動效果。

In this study, a particle damper (PD) is proposed to configure particles according to the dynamic balance of the workpiece to achieve the dual effects of counterweight and vibration suppression at the same time. Firstly, the rotary compressor model is established through Multi-Body Dynamics (MBD), which considers the change of the circulating gas load, the stiffness, and the damping of the bearing and rubber. Experiments verify the trend and magnitude of vibration at the rotating frequency to confirm the reliability of the model. In the future, this model will be used to study the dynamic balance and vibration suppression of the rotary compressor with PD (new design).
The discrete element method (DEM) and MBD are used for two-way coupling to obtain the dynamic simulation results of the rotary compressor with PD (new design). Firstly, the dynamic balance verification of the rotor system is carried out for the rotary compressor, and the influence of gas load is not considered. According to ISO 1940, the dynamic balance level of the rotary compressor needs to be lower than G 2.5. Through PD, the dynamic balance level of the rotor system can reach G 0.31.
The new design is simulated and compared its vibration suppression effect with the original design (top weight) to confirm vibration suppression effect. The different particle sizes, friction coefficients, and restitution coefficients on the vibration suppression of rotary compressors were discussed. The new design has the vibration suppression effect under different particle radii, among which the particle radius of 1 mm is better than other particle diameters. With the increase of particle friction coefficient, the smaller the total kinetic energy of the new design, indicating that the more significant the friction energy consumption, the better the vibration suppression effect of PD. With the increase of particle restitution coefficient, the greater the kinetic energy of the new design, the smaller the collision energy consumption, and the worse the vibration suppression effect of PD. Finally, the actual vibration value of the new design is verified through experiments. The radial acceleration can be reduced by 9.7 % on average, and the tangential acceleration can be reduced by 2.46 % on average, confirming the vibration suppression effect of PD.

[1]Katare, P. K., & Kriplani, V. M. (2012). Decade Developments of Rotary Compressor. International Journal of Engineering and Technology, 2(12), 1965-1973.
[2]Aw, K. T., & Ooi, K. T. (2021). A Review on Sliding Vane and Rolling Piston Compressors. Machines, 9(6), 125.
[3]Ooi, K. T., & Wong, T. N. (1997). A computer simulation of a rotary compressor for household refrigerators. Applied thermal engineering, 17(1), 65-78.
[4]Lee, S. J., Shim, J., & Kim, K. C. (2015). Development of capacity modulation compressor based on a two stage rotary compressor–part I： Modeling and simulation of compressor performance. International Journal of Refrigeration, 54, 22-37.
[5]Park, Y. C. (2010). Transient analysis of a variable speed rotary compressor. Energy Conversion and Management, 51(2), 277-287.
[6]Wang, Z., Yu, X., Liu, F., Feng, Q., & Tan, Q. (2013). Dynamic analyses for the rotor-journal bearing system of a variable speed rotary compressor. International Journal of Refrigeration, 36(7), 1938-1950.
[7]Ba, D. C., Deng, W. J., Che, S. G., Li, Y., Guo, H. X., Li, N., & Yue, X. J. (2016). Gas dynamics analysis of a rotary compressor based on CFD. Applied Thermal Engineering, 99, 1263-1269.
[8]Agarwal, V., & Balachandran, B. (2022). Noise-assisted response steering for a rotor-stator system. Journal of Sound and Vibration, 116683.
[9]Ferraris, G., Andrianoely, M. A., Berlioz, A., & Dufour, R. (2006). Influence of cylinder pressure on the balancing of a rotary compressor. Journal of Sound and Vibration, 292(3-5), 899-910.
[10]Weaver Jr, W., Timoshenko, S. P., & Young, D. H. (1991). Vibration problems in engineering. John Wiley & Sons.
[11]Harris, C. M., Crede, C. E., & Den Hartog, J. P. (1962). Shock and Vibration Handbook, Vols. I, II, and III.
[12]Avallone, A., Eugene, B., Mark, T., (1987). Handbook for Mechanical Engineer, McGraw-Hill, New York.
[13]Van de Vegte, J., & Lake, R. T. (1978). Balancing of rotating systems during operation. Journal of Sound and Vibration, 57(2), 225-235.
[14]ISO：Balancing machines-description and evaluation, ISO 2953-1985(E), Geneva,Switzerland.
[15]Zhang, S., Gu, Z., & Zhang, Z. (2013). Dynamic balancing method for the single-threaded, fixed-pitch screw rotor. Vacuum, 90, 44-49.
[16]Zhang, H., Wu, J., Xie, F., Chen, A., & Li, Y. (2014). Dynamic behaviors of the crankshafts in single-cylinder and twin-cylinder rotary compressors. International Journal of Refrigeration, 47, 36-45.
[17]Yu, X., Mao, K., Lei, S., & Zhu, Y. (2019). A new adaptive proportional-integral control strategy for rotor active balancing systems during acceleration. Mechanism and Machine Theory, 136, 105-121.
[18]Pan, X., Lu, J., Huo, J., Gao, J., & Wu, H. (2020). A review on self-recovery regulation (SR) technique for unbalance vibration of high-end equipment. Chinese Journal of Mechanical Engineering, 33(1), 1-23.
[19]Ou, C. H., Hsu, C. H., Fan, G. J., & Chen, W. Y. (2020). Rotary machine vibration monitoring and smart balance correction. Advances in Mechanical Engineering, 12(6), 1687814020936032.
[20]Lu, Z., Masri, S. F., & Lu, X. (2020). Origination, development and applications of particle damping technology. In Particle Damping Technology Based Structural Control (pp. 21-51). Springer, Singapore.
[21]Panossian, H. (2008). Non-obstructive particle damping： new experiences and capabilities. In 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 16th AIAA/ASME/AHS Adaptive Structures Conference, 10th AIAA Non-Deterministic Approaches Conference, 9th AIAA Gossamer Spacecraft Forum, 4th AIAA Multidisciplinary Design Optimization Specialists Conference (p. 2102).
[22]Ye, H., Wang, Y., Liu, B., & Jiang, X. (2019). Experimental study on the damping effect of multi-unit particle dampers applied to bracket structure. Applied Sciences, 9(14), 2912.
[23]Fowler, B. L., Flint, E. M., & Olson, S. E. (2001, July). Design methodology for particle damping. In Smart Structures and Materials 2001： Damping and Isolation (Vol. 4331, pp. 186-197). International Society for Optics and Photonics.
[24]Lu, Z., Lu, X., & Masri, S. F. (2010). Studies of the performance of particle dampers under dynamic loads. Journal of Sound and Vibration, 329(26), 5415-5433.
[25]Lu, Z., Masri, S. F., & Lu, X. (2011). Studies of the performance of particle dampers attached to a two-degrees-of-freedom system under random excitation. Journal of Vibration and Control, 17(10), 1454-1471.
[26]Chen, J., Wang, Y., Zhao, Y., & Feng, Y. (2019). Experimental research on design parameters of basin tuned and particle damper for wind turbine tower on shaker. Structural Control and Health Monitoring, 26(11), e2440.
[27]Xu, Z., Wang, M. Y., & Chen, T. (2004). An experimental study of particle damping for beams and plates. Journal of Vibration and Acoustics, 126(1), 141-148.
[28]Lu, Z., Lu, X., Lu, W., & Masri, S. F. (2012). Experimental studies of the effects of buffered particle dampers attached to a multi-degree-of-freedom system under dynamic loads. Journal of Sound and Vibration, 331(9), 2007-2022.
[29]Lu, Z., Liao, Y., & Huang, Z. (2020). Stochastic response control of particle dampers under random seismic excitation. Journal of Sound and Vibration, 481, 115439.
[30]Moore, J. J., Palazzolo, A. B., Gadangi, R., Nale, T. A., Klusman, S. A., Brown, G. V., & Kascak, A. F. (1995). A forced response analysis and application of impact dampers to rotordynamic vibration suppression in a cryogenic environment. Journal of Vibration and Acoustics, 117(3A), 300-310.
[31] Wong, C. X., Daniel, M. C., & Rongong, J. A. (2009). Energy dissipation prediction of particle dampers. Journal of Sound and Vibration, 319(1-2), 91-118.
[32]Yao, B., & Chen, Q. (2015). Investigation on zero-gravity behavior of particle dampers. Journal of Vibration and Control, 21(1), 124-133.
[33]Ahmad, N., Ranganath, R., & Ghosal, A. (2017). Modeling and experimental study of a honeycomb beam filled with damping particles. Journal of Sound and Vibration, 391, 20-34.
[34]Xiao, W., Huang, Y., Jiang, H., Lin, H., & Li, J. (2016). Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads. Particuology, 27, 40-50.
[35]Xiao, W., Li, J., Pan, T., Zhang, X., & Huang, Y. (2017). Investigation into the influence of particles' friction coefficient on vibration suppression in gear transmission. Mechanism and Machine Theory, 108, 217-230.
[36]Cundall, P. A., & Strack, O. D. (1979). A discrete numerical model for granular assemblies. Geotechnique, 29(1), 47-65.
[37]Bolander, J. E., Eliáš, J., Cusatis, G., & Nagai, K. (2021). Discrete mechanical models of concrete fracture. Engineering Fracture Mechanics, 257, 108030.
[38]Jaggannagari, S. R., Desu, R. K., Reimann, J., Gan, Y., Moscardini, M., & Annabattula, R. K. (2021). DEM simulations of vibrated sphere packings in slender prismatic containers. Powder Technology, 393, 31-59.
[39]Corral, E., Moreno, R. G., García, M. G., & Castejón, C. (2021). Nonlinear phenomena of contact in multibody systems dynamics: a review. Nonlinear Dynamics, 1-27.
[40]Coetzee, C. J., Els, D. N. J., & Dymond, G. F. (2010). Discrete element parameter calibration and the modelling of dragline bucket filling. Journal of Terramechanics, 47(1), 33-44.
[41]Barrios, G. K., & Tavares, L. M. (2016). A preliminary model of high pressure roll grinding using the discrete element method and multi-body dynamics coupling. International Journal of Mineral Processing, 156, 32-42.
[42]Lommen, S., Lodewijks, G., & Schott, D. L. (2018). Co-simulation framework of discrete element method and multibody dynamics models. Engineering Computations. Engineering Computations, 35(3), 1481-1499.
[43]Chung, Y. C., & Wu, Y. R. (2019). Dynamic modeling of a gear transmission system containing damping particles using coupled multi-body dynamics and discrete element method. Nonlinear Dynamics, 98(1), 129-149.
[44]Tsuji, Y., Tanaka, T., & Ishida, T. (1992). Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder technology, 71(3), 239-250.
[45]Briggs, C. A., & Bearman, R. A. (1995). The assessment of rock breakage and damage in crushing machinery. In Proceedings Explore, 95, 167-172.
[46]Zhang, D., & Whiten, W. J. (1996). The calculation of contact forces between particles using spring and damping models. Powder Technology, 88(1), 59-64.
[47]Chung, Y. C., Wu, C. W., Kuo, C. Y., & Hsiau, S. S. (2019). A rapid granular chute avalanche impinging on a small fixed obstacle：DEM modeling, experimental validation and exploration of granular stress. Applied Mathematical Modelling, 74, 540-568.
[48]Wu, Y. R., Chung, Y. C., & Wang, I. C. (2021). Two-way coupled MBD–DEM modeling and experimental validation for the dynamic response of mechanisms containing damping particles. Mechanism and Machine Theory, 159, 104257.
[49]Terzioglu, F., Rongong, J. A., & Lord, C. E. (2020, September). The dissipative characteristics of oblate particles in granular dampers. In EURODYN 2020： Proceedings of the XI International Conference on Structural Dynamics (pp. 4851-4866). European Association for Structural Dynamics (EASD).
[50] Shabana, A. (2020). Dynamics of multibody systems. Cambridge university press.
[51]McConville, J.B., McGrath, J.F. (1998). Introduction to ADAMS Theory. Mechanical Dynamics Inc., Michigan.
[52]Magnus, K., & Müller, H. H. (1974). Grundlagen der technischen Mechanik (Vol. 7). Stuttgart： Teubner.
[53]Gantmacher, F. (1975). Lectures in Analytical Mechanics. Mir Publishers, Moscow.
[54]Flores, P., Ambrósio, J., Claro, J. P., & Lankarani, H. M. (2008). Kinematics and dynamics of multibody systems with imperfect joints： models and case studies (Vol. 34). Springer Science & Business Media.
[55]Frene, J., Nicolas, D., Degueurce, B., Berthe, D., & Godet, M. (1997). Hydrodynamic lubrication：bearings and thrust bearings. Elsevier.
[56]Skrinjar, L., Slavič, J., & Boltežar, M. (2018). A review of continuous contact-force models in multibody dynamics. International Journal of Mechanical Sciences, 145, 171-187.
[57]Ambrosio, J., Malça, C., & Ramalho, A. (2016). Planar roller chain drive dynamics using a cylindrical contact force model. Mechanics Based Design of Structures and Machines, 44(1-2), 109-122.
[58]Oliveri, S. M., Sequenzia, G., & Calì, M. (2009). Flexible multibody model of desmodromic timing system. Mechanics Based Design of Structures and Machines, 37(1), 15-30.
[59]Sapietová, A., Gajdoš, L., Dekýš, V., & Sapieta, M. (2016). Analysis of the influence of input function contact parameters of the impact force process in the MSC. ADAMS. In Advanced mechatronics solutions (pp. 243-253). Springer, Cham.
[60]MSC ADAMS. (2013). Help Documentation (ADAMS/Solver). MSC. Software, Cambridge.
[61]Giesbers, J. (2012). Contact mechanics in MSC Adams-A technical evaluation of the contact models in multibody dynamics software MSC Adams (Bachelor's thesis, University of Twente).
[62]Gough, J. (2009). Use of approximate calculations and finite element analysis to estimate the stiffness of rubber bushes and cylindrical mountings. Journal of Rubber Research, 12(4), 185-199.
[63]Geethamma, V. G., Asaletha, R., Kalarikkal, N., & Thomas, S. (2014). Vibration and sound damping in polymers. Resonance, 19(9), 821-833.
[64]Ashokrao Fuke, C., Anna Mahanwar, P., & Ray Chowdhury, S. (2019). Modified ethylene‐propylene‐diene elastomer (EPDM)‐contained silicone rubber/ethylene‐propylene‐diene elastomer (EPDM) blends：Effect of composition and electron beam crosslinking on mechanical, heat shrinkability, electrical, and morphological properties. Journal of Applied Polymer Science, 136(29), 47787.
[65]Wang, I. C., Wu, Y. R., & Fuh, Y. K. (2021). Vibration prediction and experimental validation of a rotary compressor based on multi-body dynamics. Mechanics Based Design of Structures and Machines, 1-13.
[66]Deresiewicz, H. (1958). Mechanics of granular matter. In Advances in applied mechanics (Vol. 5, pp. 233-306). Elsevier.