Modeling, analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators

doi:10.1007/s10483-022-2871-6

Abstract

Abstract: Existing quasi-zero stiffness (QZS) isolators are reviewed. In terms of their advantages, a novel X-shape QZS isolator combined with the cam-roller-spring mechanism (CRSM) is proposed. Different from the existing X-shape isolators, oblique springs are used to enhance the negative stiffness of the system. Meanwhile, the CRSM is used to eliminate the gravity of the loading mass, while the X-shape structure leaves its static position. The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes. It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism. The X-shape has a strong capacity of loading mass, while the CRSM can achieve a designed restoring force at any position. The proposed isolator combines all these advantages together. Based on the harmonic balance method (HBM) and the simulation, the displacement transmissibilities of the proposed isolator, the X-shape isolators just with oblique springs, and the X-shape isolators in the traditional form are studied. The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility. However, it still has some disadvantages similar to the existing QZS isolators. This means that its parameters should be designed carefully so as to avoid becoming a bistable system, in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.

Key words: quasi-zero stiffness (QZS), cam-roller, X-shape isolator, nonlinear isolation

2010 MSC Number:

74H45

Xiaoye MAO, Mengmeng YIN, Hu DING, Xiaofeng GENG, Yongjun SHEN, Liqun CHEN. Modeling, analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators. Applied Mathematics and Mechanics (English Edition), 2022, 43(7): 1027-1044.

TrendMD

References

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[3] WOODARD, S. E. and HOUSNER, J. M. The nonlinear behavior of a passive zero-spring-rate suspension system. 29th Structures, Structural Dynamics and Materials Conference, Reston (1998)
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[23] DENG, T. C., WEN, G. L., DING, H., LU, Z. Q., and CHEN, L. Q. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mechanical Systems Signal Processing, 145, 106967(2020)
[24] XU, J. and SUN, X. T. A multi-directional vibration isolator based on quasi-zero-stiffness structure and time-delayed active control. International Journal of Mechanical Sciences, 100, 126-135(2015)[1] CARRELLA, A., BRENNAN, M. J., and WATERS, T. P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301, 678-689(2007)
[2] IKEGAMI, R. E. A. Zero-G ground test simulation methods. Proceedings of the 11th Aerospace Testing Seminar, Institute of Environmental Science, Manhattan Beach (1988)
[3] WOODARD, S. E. and HOUSNER, J. M. The nonlinear behavior of a passive zero-spring-rate suspension system. 29th Structures, Structural Dynamics and Materials Conference, Reston (1998)
[4] LACOSTE, L. LaCoste and Romberg straight-line gravity meter. Geophysics, 48, 606-610(1983)
[5] IBRAHIM, R. A. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314, 371-452(2008)
[6] GUO, L. C., WANG, X., FAN, R. L., and BI, F. R. Review on development of high-static-lowdynamic-stiffness seat cushion mattress for vibration control of seating suspension system. Applied Sciences, 10, 2887(2020)1040 Xiaoye MAO, Mengmeng YIN, Hu DING, Xiaofeng GENG, Yongjun SHEN, and Liqun CHEN
[7] NIU, F., MENG, L. S., WU, W. J., SUN, J. G., SU, W. H., MENG, G., and RAO, Z. S. Recent advances in quasi-zero-stiffness vibration isolation systems. Applied Mechanics and Materials, 397-400, 295-303(2013)
[8] ZHANG, J. Z., LI, D., CHEN, M. J., and DONG, S. An ultra-low frequency parallel connection nonlinear isolator for precision instruments. Key Engineering Materials, 257-258, 231-236(2004)
[9] CARRELLA, A., BRENNAN, M. J., KOVACIC, I., and WATERS, T. P. On the force transmissibility of a vibration isolator with quasi-zero-stiffness. Journal of Sound and Vibration, 322, 707-717(2009)
[10] CARRELLA, A., BRENNAN, M. J., WATERS, T. P., and LOPES, V., JR. Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55, 22-29(2012)
[11] TANG, B. and BRENNAN, M. J. On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 81, 207-214(2014)
[12] HAO, Z. F., CAO, Q. J., and WIERCIGROCH, M. Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses. Nonlinear Dynamics, 87, 987-1014(2017)
[13] ABOLFATHI, A., BRENNAN, M. J., WATERS, T. P., and TANG, B. On the effects of mistuning a force-excited system containing a quasi-zero-stiffness vibration isolator. Journal of Vibration and Acoustics, 137, 044502(2015)
[14] PENG, Z. K., LANG, Z. Q., ZHAO, L., BILLINGS, S. A., TOMLINSON, G. R., and GUO, P. The force transmissibility of MDOF structures with a non-linear viscous damping device. International Journal of Non-Linear Mechanics, 46, 1305-1314(2011)
[15] WANG, Y., LI, S. M., CHENG, C., and SU, Y. Q. Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. Journal of Mechanical Science and Technology, 32, 2973-2985(2018)
[16] XU, D. L., ZHANG, Y. Y., ZHOU, J. X., and LOU, J. J. On the analytical and experimental assessment of the performance of a quasi-zero-stiffness isolator. Journal of Vibration and Control, 20, 2314-2325(2014)
[17] ZHAO, F., JI, J. C., YE, K., and LUO, Q. T. Increase of quasi-zero stiffness region using two pairs of oblique springs. Mechanical Systems and Signal Processing, 144, 106975(2020)
[18] ZHAO, F., JI, J. C., LUO, Q. T., CAO, S. Q., CHEN, L. M., and DU, W. L. An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band. Nonlinear Dynamics 104, 349-365(2021)
[19] ZHAO, F., JI, J. C., YE, K., and LUO, Q. T. An innovative quasi-zero stiffness isolator with three pairs of oblique springs. International Journal of Mechanical Sciences, 192, 106093(2021)
[20] LU, Z. Q., BRENNAN, M. J., YANG, T. J., LI, X. H., and LIU, Z. G. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332, 1456-1464(2013)
[21] LU, Z. Q., YANG, T. J., BRENNAN, M. J., LI, X. H., and LIU, Z. G. On the performance of a two-stage vibration isolation system which has geometrically nonlinear stiffness. Journal of Vibration and Acoustics, 136, 064501(2014)
[22] WANG, Y., LI, S. M., NEILD, S. A., and JIANG, J. Z. Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dynamics, 88, 635-654(2017)
[23] DENG, T. C., WEN, G. L., DING, H., LU, Z. Q., and CHEN, L. Q. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mechanical Systems Signal Processing, 145, 106967(2020)
[24] XU, J. and SUN, X. T. A multi-directional vibration isolator based on quasi-zero-stiffness structure and time-delayed active control. International Journal of Mechanical Sciences, 100, 126-135(2015) Modeling, analysis, and simulation of X-shape QZS-roller vibration isolators 1041
[25] ZHU, G. N., LIU, J., CAO, Q. J., CHENG, Y. F., LU, Z. C., and ZHU, Z. B. A two degree of freedom stable quasi-zero stiffness prototype and its applications in aseismic engineering. SCIENCE CHINA Technological Sciences, 63, 496-505(2020)
[26] TOBIAS, S. A. Design of small isolator units for the suppression of low frequency vibration. Journal of Mechanical Engineering Science, 26, 280-292(1959)
[27] PLATUS, D. L. Negative-stiffness-mechanism vibration isolation systems. Optics and Metrology, 1619, 44-54(1991)
[28] LIU, X. T., HUANG, X. C., and HUA, H. X. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration, 332, 3359-3376(2013)
[29] YANG, J., XIONG, Y. P., and XING, J. T. Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism. Journal of Sound and Vibration, 332, 167-183(2013)
[30] XU, D. L., YU, Q. P., ZHOU, J. X., and BISHOP, S. R. Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 332, 3377-3389(2013)
[31] JIANG, Y. L., SONG, C. S., DING, C. M., and XU, B. H. Design of magnetic-air hybrid quasi-zero stiffness vibration isolation system. Journal of Sound and Vibration, 477, 115346(2020)
[32] LAN, C. C., YANG, S. A., and WU, Y. S. Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads. Journal of Sound and Vibration, 333, 4843-4858(2014)
[33] WANG, K., ZHOU, J. X., CHANG, Y. P., OUYANG, H. J., XU, D. L., and YANG, Y. A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dynamics, 101, 755-773(2020)
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[36] CHENG, C., LI, S. M., WANG, Y., and JIANG, X. X. Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dynamics, 87, 2267-2279(2017)
[37] CHENG, C., LI, S. M., WANG, Y., and JIANG, X. X. Resonance of a quasi-zero stiffness vibration system under base excitation with load mismatch. International Journal of Structural Stability and Dynamics, 18, 1850002(2018)
[38] WANG, Y., LI, H. X., CHENG, C., DING, H., and CHEN, L. Q. Dynamic performance analysis of a mixed-connected inerter-based quasi-zero stiffness vibration isolator. Structural Control&Health Monitoring, 27, e2604(2020)
[39] SUN, X. T., JING, X. J., XU, J., and CHENG, L. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333, 2404-2420(2014)
[40] YAN, B., WANG, Z. H., MA, H. Y., BAO, H. H., WANG, K., and WU, C. Y. A novel lever-type vibration isolator with eddy current damping. Journal of Sound and Vibration, 494, 115862(2021)
[41] LIU, C. C., JING, X. J., and LI, F. M. Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure. International Journal of Mechanical Sciences, 98, 169-177(2015)
[42] LIU, C. C., JING, X. J., and CHEN, Z. B. Band stop vibration suppression using a passive Xshape structured lever-type isolation system. Mechanical Systems and Signal Processing, 68-69, 342-353(2016)
[43] SUN, X. T. and JING, X. J. Analysis and design of a nonlinear stiffness and damping system with a scissor-like structure. Mechanical Systems and Signal Processing, 66-67, 723-742(2016)
[44] SUN, X. T. and JING, X. J. A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band. Mechanical Systems and Signal Processing, 80, 166-188(2016)[1] CARRELLA, A., BRENNAN, M. J., and WATERS, T. P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301, 678-689(2007)
[2] IKEGAMI, R. E. A. Zero-G ground test simulation methods. Proceedings of the 11th Aerospace Testing Seminar, Institute of Environmental Science, Manhattan Beach (1988)
[3] WOODARD, S. E. and HOUSNER, J. M. The nonlinear behavior of a passive zero-spring-rate suspension system. 29th Structures, Structural Dynamics and Materials Conference, Reston (1998)
[4] LACOSTE, L. LaCoste and Romberg straight-line gravity meter. Geophysics, 48, 606-610(1983)
[5] IBRAHIM, R. A. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314, 371-452(2008)
[6] GUO, L. C., WANG, X., FAN, R. L., and BI, F. R. Review on development of high-static-lowdynamic-stiffness seat cushion mattress for vibration control of seating suspension system. Applied Sciences, 10, 2887(2020)1040 Xiaoye MAO, Mengmeng YIN, Hu DING, Xiaofeng GENG, Yongjun SHEN, and Liqun CHEN
[7] NIU, F., MENG, L. S., WU, W. J., SUN, J. G., SU, W. H., MENG, G., and RAO, Z. S. Recent advances in quasi-zero-stiffness vibration isolation systems. Applied Mechanics and Materials, 397-400, 295-303(2013)
[8] ZHANG, J. Z., LI, D., CHEN, M. J., and DONG, S. An ultra-low frequency parallel connection nonlinear isolator for precision instruments. Key Engineering Materials, 257-258, 231-236(2004)
[9] CARRELLA, A., BRENNAN, M. J., KOVACIC, I., and WATERS, T. P. On the force transmissibility of a vibration isolator with quasi-zero-stiffness. Journal of Sound and Vibration, 322, 707-717(2009)
[10] CARRELLA, A., BRENNAN, M. J., WATERS, T. P., and LOPES, V., JR. Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55, 22-29(2012)
[11] TANG, B. and BRENNAN, M. J. On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 81, 207-214(2014)
[12] HAO, Z. F., CAO, Q. J., and WIERCIGROCH, M. Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses. Nonlinear Dynamics, 87, 987-1014(2017)
[13] ABOLFATHI, A., BRENNAN, M. J., WATERS, T. P., and TANG, B. On the effects of mistuning a force-excited system containing a quasi-zero-stiffness vibration isolator. Journal of Vibration and Acoustics, 137, 044502(2015)
[14] PENG, Z. K., LANG, Z. Q., ZHAO, L., BILLINGS, S. A., TOMLINSON, G. R., and GUO, P. The force transmissibility of MDOF structures with a non-linear viscous damping device. International Journal of Non-Linear Mechanics, 46, 1305-1314(2011)
[15] WANG, Y., LI, S. M., CHENG, C., and SU, Y. Q. Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. Journal of Mechanical Science and Technology, 32, 2973-2985(2018)
[16] XU, D. L., ZHANG, Y. Y., ZHOU, J. X., and LOU, J. J. On the analytical and experimental assessment of the performance of a quasi-zero-stiffness isolator. Journal of Vibration and Control, 20, 2314-2325(2014)
[17] ZHAO, F., JI, J. C., YE, K., and LUO, Q. T. Increase of quasi-zero stiffness region using two pairs of oblique springs. Mechanical Systems and Signal Processing, 144, 106975(2020)
[18] ZHAO, F., JI, J. C., LUO, Q. T., CAO, S. Q., CHEN, L. M., and DU, W. L. An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band. Nonlinear Dynamics 104, 349-365(2021)
[19] ZHAO, F., JI, J. C., YE, K., and LUO, Q. T. An innovative quasi-zero stiffness isolator with three pairs of oblique springs. International Journal of Mechanical Sciences, 192, 106093(2021)
[20] LU, Z. Q., BRENNAN, M. J., YANG, T. J., LI, X. H., and LIU, Z. G. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332, 1456-1464(2013)
[21] LU, Z. Q., YANG, T. J., BRENNAN, M. J., LI, X. H., and LIU, Z. G. On the performance of a two-stage vibration isolation system which has geometrically nonlinear stiffness. Journal of Vibration and Acoustics, 136, 064501(2014)
[22] WANG, Y., LI, S. M., NEILD, S. A., and JIANG, J. Z. Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dynamics, 88, 635-654(2017)
[23] DENG, T. C., WEN, G. L., DING, H., LU, Z. Q., and CHEN, L. Q. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mechanical Systems Signal Processing, 145, 106967(2020)
[24] XU, J. and SUN, X. T. A multi-directional vibration isolator based on quasi-zero-stiffness structure and time-delayed active control. International Journal of Mechanical Sciences, 100, 126-135(2015) Modeling, analysis, and simulation of X-shape QZS-roller vibration isolators 1041
[25] ZHU, G. N., LIU, J., CAO, Q. J., CHENG, Y. F., LU, Z. C., and ZHU, Z. B. A two degree of freedom stable quasi-zero stiffness prototype and its applications in aseismic engineering. SCIENCE CHINA Technological Sciences, 63, 496-505(2020)
[26] TOBIAS, S. A. Design of small isolator units for the suppression of low frequency vibration. Journal of Mechanical Engineering Science, 26, 280-292(1959)
[27] PLATUS, D. L. Negative-stiffness-mechanism vibration isolation systems. Optics and Metrology, 1619, 44-54(1991)
[28] LIU, X. T., HUANG, X. C., and HUA, H. X. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration, 332, 3359-3376(2013)
[29] YANG, J., XIONG, Y. P., and XING, J. T. Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism. Journal of Sound and Vibration, 332, 167-183(2013)
[30] XU, D. L., YU, Q. P., ZHOU, J. X., and BISHOP, S. R. Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 332, 3377-3389(2013)
[31] JIANG, Y. L., SONG, C. S., DING, C. M., and XU, B. H. Design of magnetic-air hybrid quasi-zero stiffness vibration isolation system. Journal of Sound and Vibration, 477, 115346(2020)
[32] LAN, C. C., YANG, S. A., and WU, Y. S. Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads. Journal of Sound and Vibration, 333, 4843-4858(2014)
[33] WANG, K., ZHOU, J. X., CHANG, Y. P., OUYANG, H. J., XU, D. L., and YANG, Y. A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dynamics, 101, 755-773(2020)
[34] AHN, H. J. Performance limit of a passive vertical isolator using a negative stiffness mechanism. Journal of Mechanical Science and Technology, 22, 2357-2364(2008)
[35] ZHANG, W. and ZHAO, J. B. Analysis on nonlinear stiffness and vibration isolation performance of scissor-like structure with full types. Nonlinear Dynamics, 86, 17-36(2016)
[36] CHENG, C., LI, S. M., WANG, Y., and JIANG, X. X. Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dynamics, 87, 2267-2279(2017)
[37] CHENG, C., LI, S. M., WANG, Y., and JIANG, X. X. Resonance of a quasi-zero stiffness vibration system under base excitation with load mismatch. International Journal of Structural Stability and Dynamics, 18, 1850002(2018)
[38] WANG, Y., LI, H. X., CHENG, C., DING, H., and CHEN, L. Q. Dynamic performance analysis of a mixed-connected inerter-based quasi-zero stiffness vibration isolator. Structural Control&Health Monitoring, 27, e2604(2020)
[39] SUN, X. T., JING, X. J., XU, J., and CHENG, L. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333, 2404-2420(2014)
[40] YAN, B., WANG, Z. H., MA, H. Y., BAO, H. H., WANG, K., and WU, C. Y. A novel lever-type vibration isolator with eddy current damping. Journal of Sound and Vibration, 494, 115862(2021)
[41] LIU, C. C., JING, X. J., and LI, F. M. Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure. International Journal of Mechanical Sciences, 98, 169-177(2015)
[42] LIU, C. C., JING, X. J., and CHEN, Z. B. Band stop vibration suppression using a passive Xshape structured lever-type isolation system. Mechanical Systems and Signal Processing, 68-69, 342-353(2016)
[43] SUN, X. T. and JING, X. J. Analysis and design of a nonlinear stiffness and damping system with a scissor-like structure. Mechanical Systems and Signal Processing, 66-67, 723-742(2016)
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