In a traditional ball balancer, the balls are usually confined in one or more plane annular runways. In fact, the balls have the ability to move across the plane and run along axial direction of the rotor, which can be used to adjust the mass-diameter moment of the system. A new cross-plane ball balancer is proposed is this paper and its capability for cross-plane vibration suppression is studied. Firstly, the vibration model of the rotor with a cross-plane ball balancer is established using Lagrange equation. Secondly, equilibrium solutions of the rotor are analyzed and stability characteristics of the steady state periodic solutions are studied using Floquet theory, influences of design parameters including the support stiffness and support damping of the rotor, and viscous damping of the balls on stability characteristics of the system are analyzed. Thirdly, stability characteristics of the rotor system and balancing capabilities of the balancer in each stable region are verified through numerical simulations. Finally, experiments are carried out to verify the effectiveness of the balancer and the correctness of the theoretical conclusions. The results show that the mass-diameter product and mass diameter moment of the rotor system can be balanced simultaneously through cross-plane motions of the balls in the complete balancing regions.
Key words
Automatic balancing /
Cross-plane ball balancer /
Stability analysis /
Floquet theory
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[1] 张西宁,刘旭,张雯雯等.注排液型砂轮平衡装置控制策略与实验研究[J].振动与冲击,2019,38(15):223-230.
Zhang X N, Liu X, Zhang W W, et al. Control strategy and tests of balancing device for liquid injection and discharge type grinding wheel[J].Journal of Vibration and Shock,2019,38(15):223-230.
[2] 运侠伦,袁世珏,梅雪松等.高速电主轴注液式一体化平衡终端优化设计与实验研究[J].振动与冲击,2021,40(15):26-33.
Yun X L, Yuan S J, Mei X S, et al. Optimization design and tests for liquid injection type integrated balancing terminal of high-speed motorized spindle[J]. Journal of Vibration and Shock, 2021,40(15):26-33.
[3] 潘鑫,彭瑞轩,何啸天等.基于径向励磁和永磁-电磁联合驱动的主动平衡执行器[J].振动与冲击,2021,40(02):23-28.
Pan X, Peng R X, He X T, Wu H Q, et al. Electromagnetic active balancing actuator based on the radial excitation and permanent magnet-electromagnetism combined driving method[J]. Journal of Vibration and Shock, 2021, 40(02):23-28.
[4] 郭文军, 张小龙, 张凯等. 双盘球式自动平衡装置动态特性分析[J]. 科学技术与工程,2020,020(011):4323-4329.
Guo W J, Zhang X L, Zhang K, et al. Dynamic characteristic analysis of double disc ball automatic balancing device[J]. Science Technology and Engineering, 2020, 020(011):4323 -4329.
[5] 王志. 大长径比柔性转子球体动平衡抑振方法研究[D]. 无锡:江南大学,2020.
Wang Z. Study on vibration suppression of large aspect ratio flexible rotors using ball balancer[D].Wuxi: Jiangnan University, 2020
[6] Ehyaei J, Moghaddam M M. Dynamic response and stability analysis of an unbalanced flexible rotating shaft equipped with n automatic ball-balancers[J]. Journal of Sound and Vibration, 2009, 321(3-5):554-571.
[7] Desmidt H A. Imbalance vibration suppression of a supercritical shaft via an automatic balancing Device[J]. Journal of Vibration and Acoustics,2009,131(4): 041001.
[8] Desmidt H A. Automatic balancing of bladed-disk/shaft system via passive autobalancer devices[J]. American Institute of Aeronautics and Astronautics Inc, 2010, 48(2):372-386.
[9] Rodrigues D J, Champneys A R, Friswell M I, et al. Two-plane automatic balancing: a symmetry breaking analysis[J]. International Journal of Non-Linear Mechanics, 2011, 46(9): 1139-1154.
[10] Tadeusz M, Dariusz S, Marco A M M. Self-balancing system of the disk on an elastic shaft [J]. Journal of Sound and Vibration, 2015, 359(2):2-20.
[11] Haidar A M, Palacios J L. A general model for passive balancing of supercritical shafts with experimental validation of friction and collision effects[J]. Journal of Sound and Vibration, 2016, 384:273-293.
[12] Chen H W,Chen Y B, Sun Z,et al. Automatic balancing of a flexible supported rotor with two disks by two ball balancers[J]. Journal of Mechanical Science and Technology, 2021, 35(7): 2781-2792.
[13] Friswell M I, Penny J, Garvey S D, et al. Dynamics of rotating machines[M]. Cambridge university press, 2010, p341.
[14] Kim W, Chung J. Performance of automatic ball balancers on optical disc drives[J]. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science, 2002, 216(11):1071-1080.
{{custom_fnGroup.title_en}}
Footnotes
{{custom_fn.content}}