In order to study the influence of the friction in a pair of disc springs on the vibration characteristics of vibration isolators, a prepressed combination disc springs vibration isolation unit was designed.A stiffness model for the combination disk springs with boundary friction was established.The correctness of the stiffness model was verified by quasi-static loading tests.And a nonlinear dynamic model for the disc spring vibration isolation unit was proposed.The average method was applied to analyze the free vibration of the disc spring vibration isolation unit, and various factors affecting the free vibration frequency of the system were investigated.Then, the forced vibration of the disk spring vibration isolation unit under base excitation was analyzed and calculated.The results show that the disc spring vibration isolation unit can be approximately equivalent to a nonlinear viscous damping system, the break-loose frequency and vibration isolation efficiency are affected by the additional support force coefficient and the cubic coefficient of stiffness under the condition of small displacement.There are abnormal jumping state and non-resonant state in the system, and the two states are correlated with the viscous damping coefficient and additional supporting force coefficient under the condition of large displacement.
惠安民1，金映丽1，张磊2，闫明1，王开平1. 边界摩擦条件下含有预紧的对合碟簧隔振单元的振动特性[J]. 振动与冲击, 2021, 40(2): 228-234.
HUI Anmin1， JIN Yingli1， ZHANG Lei2， YAN Ming1， WANG Kaiping1. Vibration characteristics of a disc spring vibration isolator with pre-tightening under boundary friction condition. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(2): 228-234.
[ 1 ] GB/T 15168-2013, Static and dynamic performance test method of vibration and impact isolator[ S ].
[ 2 ] 白鸿柏，黄协清.干摩擦振动系统响应计算方法研究综述[J].力学进展，2001，31(4):527-534.
Bai Hongbai, Huang Xieqing. A Review of Research on Response Calculation Methods of Dry Friction Vibration System [J]. Mechanical Progress, 2001,31 ( 4 ): 527 - 534.
[ 3 ] 都军民，戴双献.碟形弹簧减振器动态特性研究[J].工程机械，2009，40(11):15-18.
Du Junmin, Dai Shuangxian. Study on dynamic characteristics of disk spring damper [J]. Construction Machinery, 2009,40 (11): 15-18.
[ 4 ] Almen, J. O., and Laszlo A., The Uniform Section Disk Spring[J].ASME, 1936,58:305.
[ 5 ] Rosa, G.L., Messina, Risitano, Tangential and radial stresses of variable thickness Belleville spring[J]. Mech. Des. 1998,123(2):294–299 .
[ 6 ] Saini P K, Kumar P, Tandon P. .Design and analysis of radially tapered disc springs with parabolically varying thickness[J]. Journal of Mechanical Engineering Science, 2007,211（2）：151-158.
[ 7 ] OZAKI S,TSUDA K,TOMINAGA J.Analyses of static and dynamic behavior of coned disk springs:Effects of friction boundaries[J].Thin-Walled Structures,2012,59:132-143.
[ 8 ] PATANGTALO W,AIMMANEE S,CHUTIMA S.A unified analysis of isotropic and composite Belleville springs[J].Thin-Walled Structures,2016,109:285-295.
[ 9 ] FAWAZI N,YOON J H,OH J E,et al .Geometric design of a slotted disc spring for a prescribed load-displacement function[C]//ASME 2010 International Mechanical Engineering Congress and Exposition.American Society of Mechanical Engineers,2010:741-752.
[10] 高跃飞，杨建民.非线性缓冲隔振系统动力学分析[J].火炮发射与控制学报，2006，(1):27-30.
Gao Yuefei, Yang Jianmin. Dynamic Analysis of Nonlinear Buffer Vibration Isolation System [J]. Journal of Gun Launching and Control, 2006, ( 1 ): 27 - 30.
[11] 武锐，高建和，吴焕.基于有限元的碟簧静刚度研究[J].机械工程师，2010(8):57-59.
Wu Rui, Gao Jianhe, Wu Huan. Static Stiffness of Disc Spring Based on Finite Element Method [J]. Mechanical Engineer, 2010 ( 8 ): 57 - 59.
[12] 徐道临，周杰，周加喜，等.碟形橡胶准零刚度隔振器的设计和特性分析[J].湖南大学学报(自然科学版)，2015，42(8):22-28.
Xu Daolin, Zhou Jie, Zhou Jiaxi, et al. Design and characteristic analysis of disk rubber quasi-zero stiffness vibration isolator [J]. Journal of Hunan University ( Natural Science Edition ), 2015,42 (8): 22-28.
[13] 徐登富，张庆，吴刚.不同腐蚀介质对高锰钢摩擦学新能影响机制的研究[J]. 海军航空工程学院学报，2007，(03):398-400.
Xu Dengfu, Jasmine Zhang, Wu Gang. Study on the Influence Mechanism of Different Corrosive Media on New Tribological Energy of High Manganese Steel [J]. Journal of Naval Aeronautical Engineering College, 2007,(03):398-400.
[14] 胡广深，陆泽琦，陈立群. 非线性阻尼非线性刚度隔振系统参数识别[J]. 振动与冲击，2018，37(09):68-73.
Hu Guangshen, Lu Zeqi, Chen Liqun. Parameter Identification of Nonlinear Damping Nonlinear Stiffness Vibration Isolation System [J].Journal of vibration and shock, 2018, 37 ( 09 ): 68 - 73.
[15] K.Klotter, Non-linear Vibration problems treated by the Averaging Method of W. Rize[D].Stanford University, 1951.
[16] A.K. Mallik, Principles of Vibration Contral [M]. New Delhi:Affiliated East-West Press, 1990.
