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ZHANG X, DU K. Characteristic analysis and design validation of compound rubber vibration isolator[J]. Chinese Journal of Ship Research, 2020, 15(6): 149–154 doi:  10.19693/j.issn.1673-3185.01691
Citation: ZHANG X, DU K. Characteristic analysis and design validation of compound rubber vibration isolator[J]. Chinese Journal of Ship Research, 2020, 15(6): 149–154 doi:  10.19693/j.issn.1673-3185.01691

Characteristic analysis and design validation of compound rubber vibration isolator

doi: 10.19693/j.issn.1673-3185.01691
  • Received Date: 2019-07-28
  • Rev Recd Date: 2020-03-05
  • Available Online: 2020-08-27
  • Publish Date: 2020-12-30
  •   Objectives  Due to lower weight and volume under the same working conditions, permanent magnet equipment is extensively used by many kinds of ships. However, its measured vibration at high frequencies is much higher than traditional equipment, which will affect the ship's acoustic performance, and reduce the effectiveness of using such equipment in ships. A kind of compound rubber vibration isolator is therefore designed to solve this problem.  Methods   In order to isolate the vibrations of a given piece of permanent magnet equipment, a compound rubber vibration isolator is designed by inserting middle mass into a rubber isolating system. The transmission characteristics of traditional and compound rubber vibration isolators are compared, and experimental validation for the isolating design is carried out.  Results  The results show that the proposed compound vibration isolator is feasible and can improve the vibration isolation effect of a piece of permanent magnet equipment's machine leg at high frequency. This effect can improve 20 dB compared to traditional rubber vibration isolators.  Conclusions  As a method for vibration control, the designed compound rubber vibration isolator can effectively control high frequency vibration.
  • 张晓, 杨和振. 不规则波中船舶参数横摇的概率分析[J]. 中国舰船研究, 2015, 10(3): 32–36. doi:  10.3969/j.issn.1673-3185.2015.03.006

    ZHANG X, YANG H Z. Probability analysis for ship parametric rolling in irregular waves[J]. Chinese Journal of Ship Research, 2015, 10(3): 32–36 (in Chinese). doi:  10.3969/j.issn.1673-3185.2015.03.006
    ZHANG X, YANG H Z, XIAO F. Parameter analysis of ship parametric rolling by Poincaré map[C]//Proceedings of the Eleventh ISOPE Pacific/Asia Offshore Mechanics Symposium. Shanghai,China: International Society of Offshore and Polar Engineers, 2014.
    张晓, 杨和振. 不规则波中船舶横摇参激振动敏感度分析[J]. 哈尔滨工程大学学报, 2015, 36(12): 1539–1543.

    ZHANG X, YANG H Z. Sensitivity analysis of parametric roll resonance in for ships irregular waves[J]. Journal of Harbin Engineering University, 2015, 36(12): 1539–1543 (in Chinese).
    张树生, 张克国, 宋孔杰, 等. 具有中间质量结构振动功率流的传递特性[J]. 山东大学学报(工学版), 2004, 34(1): 35–38, 43. doi:  10.3969/j.issn.1672-3961.2004.01.010

    ZHANG S S, ZHANG K G, SONG K J, et al. Dynamic characteristics of vibration power for isolation system with intermediate mass[J]. Journal of Shandong University (Engineering Science), 2004, 34(1): 35–38, 43 (in Chinese). doi:  10.3969/j.issn.1672-3961.2004.01.010
    王孚懋, 宋孔杰. 小中间质量对复杂系统隔振效果的影响及最优设计[J]. 振动工程学报, 1991, 4(3): 10–17.

    WANG F M, SONG K J. Influence of small medium mass on complicated isolation system and its optimal design[J]. Journal of Vibration Engineering, 1991, 4(3): 10–17 (in Chinese).
    张伟, 周相荣, 贺华, 等. 整体式与分布式双层隔振系统性能对比研究[J]. 噪声与振动控制, 2017, 37(4): 25–29. doi:  10.3969/j.issn.1006-1355.2017.04.006

    ZHANG W, ZHOU X R, HE H, et al. Comparative study on the vibration isolation performance between the entirety double-layer and distributed double-layer vibration isolation systems[J]. Noise and Vibration Control, 2017, 37(4): 25–29 (in Chinese). doi:  10.3969/j.issn.1006-1355.2017.04.006
    王光, 董邦宜. 小中间质量双层隔振试验研究[J]. 噪声与振动控制, 1989(4): 38–43.

    WANG G, DONG B Y. Experiment study of double-layer vibration isolation with small intermediate mass[J]. Noise and Vibration Control, 1989(4): 38–43 (in Chinese).
    ZHANG X, YANG H Z. Statistical analysis for ship parametric resonance in irregular waves[C]//Proceedings of INTER-NOISE and NOISE-CON Congress and Conference Proceedings. Chicago, IL: Institute of Noise Control Engineering, 2018: 1825-1830.
    杜冬, 禇德英, 孙中涛, 等. 多个小中间质量隔振最优设计及其性能研究[J]. 振动与冲击, 2008, 27(7): 36–41, 68. doi:  10.3969/j.issn.1000-3835.2008.07.009

    DU D, CHU D Y, SUN Z T, et al. Optimum design and performance study of multiple-small-middle-mass vibration isolation[J]. Journal of Vibration and Shock, 2008, 27(7): 36–41, 68 (in Chinese). doi:  10.3969/j.issn.1000-3835.2008.07.009
    YANG H Z, ZHANG X, XIAO F. Dynamic reliability based design optimization of offshore wind turbines considering uncertainties[C]//Proceedings of the Thirteenth ISOPE Pacific/Asia Offshore Mechanics Symposium. Jeju, Korea: International Society of Offshore and Polar Engineers, 2018.
    张克国, 王世寰, 林淑霞. 小中间质量对振动功率流的影响[J]. 噪声与振动控制, 2008, 28(2): 55–57. doi:  10.3969/j.issn.1006-1355.2008.02.016

    ZHANG K G, WANG S H, LIN S X. The effects of little intermediate mass on power flow[J]. Noise and Vibration Control, 2008, 28(2): 55–57 (in Chinese). doi:  10.3969/j.issn.1006-1355.2008.02.016
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Characteristic analysis and design validation of compound rubber vibration isolator

doi: 10.19693/j.issn.1673-3185.01691

Abstract:   Objectives  Due to lower weight and volume under the same working conditions, permanent magnet equipment is extensively used by many kinds of ships. However, its measured vibration at high frequencies is much higher than traditional equipment, which will affect the ship's acoustic performance, and reduce the effectiveness of using such equipment in ships. A kind of compound rubber vibration isolator is therefore designed to solve this problem.  Methods   In order to isolate the vibrations of a given piece of permanent magnet equipment, a compound rubber vibration isolator is designed by inserting middle mass into a rubber isolating system. The transmission characteristics of traditional and compound rubber vibration isolators are compared, and experimental validation for the isolating design is carried out.  Results  The results show that the proposed compound vibration isolator is feasible and can improve the vibration isolation effect of a piece of permanent magnet equipment's machine leg at high frequency. This effect can improve 20 dB compared to traditional rubber vibration isolators.  Conclusions  As a method for vibration control, the designed compound rubber vibration isolator can effectively control high frequency vibration.

ZHANG X, DU K. Characteristic analysis and design validation of compound rubber vibration isolator[J]. Chinese Journal of Ship Research, 2020, 15(6): 149–154 doi:  10.19693/j.issn.1673-3185.01691
Citation: ZHANG X, DU K. Characteristic analysis and design validation of compound rubber vibration isolator[J]. Chinese Journal of Ship Research, 2020, 15(6): 149–154 doi:  10.19693/j.issn.1673-3185.01691
  • 目前,在国外先进船舶中,永磁设备得到广泛应用[1]。相比传统设备,相同输出条件下的永磁设备重量更轻、体积更小,总体优势非常突出。但是,永磁设备在高频段的振动一般比传统设备高[2-3],设备机脚的振动也比传统设备的更明显,其值甚至会高出20 dB。

    传统隔振方法包括单层隔振和浮筏隔振2种[4-5]。其中:浮筏隔振虽然在高频段内效果较好,但重量大,可达十几吨,抵消了永磁设备的总体资源优势;而传统的单层隔振已无法满足永磁设备高频隔振的需求[6-8]。鉴于隔振措施在高频段的缺陷,人们开始寻求更复杂的结构来提高隔振效果,而在振源与被隔离系统之间插入中间质量则是一个简单、有效的方法[9-10]。该方法是在隔振系统中间插入附加质量以改善振动传递[11-13],提高高频隔振效果。

    本文将基于在隔振系统中间插入附加质量的设计理念,针对高频振动控制问题,提出一种用于永磁设备隔振系统的新型复合式隔振器,分析复合式隔振器的传递特性,并通过一系列试验验证设计方案的有效性。

    • 图1为传统橡胶隔振系统的受力示意图,其运动微分方程为

      $$ {{m\ddot x + C\dot x + Kx = F}}\left( {{t}} \right) $$ (1)

      式中:${{m}}$为设备重量;${{C}}$为隔振系统阻尼;${{K}}$为隔振系统刚度;${{F}}\left( {{t}} \right)$为设备激励;${{x}}$为隔振系统位移;${{\dot x}}$为位移的一阶导数;${{\ddot x}}$为位移的二阶导数。在有阻尼的情况下,传递至基座的力${{{F}}_{\rm{T}}}$由2部分组成:一部分为弹性力,幅值为${{K}} \cdot {{{x}}_0}$;另一部分为阻尼力,幅值为${{C}} \cdot \omega \cdot {{{x}}_0}$,其中,${{{x}}_{{0}}}$为激励力作用下的挠度,$\omega $为激励频率。

      Figure 1.  Load of traditional rubber isolator

      由于隔振器弹性力与位移、阻尼力与速度均成正比,所以二者相差一个90°的相角,其合力由下式表示:

      $$ \begin{split} &\quad\;\; {{{F}}_{\rm{T}}}=\sqrt{{{\left( {K}\cdot {{{x}}_{0}} \right)}^{{2}}}{+}{{\left( {C}\cdot \omega \cdot {{{x}}_{0}} \right)}^{{2}}}}{=}\\&{{{F}}_{\rm{o}}}\cdot \sqrt{\dfrac{1{+}{{\left[ 2\cdot \zeta \cdot \left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right) \right]}^{{2}}}}{{{\left[ 1-{{\left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right)}^{2}} \right]}^{{2}}}+{{\left[ 2\cdot \zeta \cdot \left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right) \right]}^{{2}}}}} \end{split} $$ (2)

      式中:${\omega _{\rm{n}}} = \sqrt {\dfrac{K}{{{m}}}}$,为系统的固有频率;ζ为阻尼比;Fo为激励力。则有

      $$ \dfrac{{{{F}}_{{\rm{T}}}}}{{{{F}}_{\rm{o}}}}{=}\sqrt{\dfrac{1{+}{{\left[ 2\cdot \zeta \cdot \left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right) \right]}^{{2}}}}{{{\left[ 1-{{\left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right)}^{2}} \right]}^{{2}}}+{{\left[ 2\cdot \zeta \cdot \left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right) \right]}^{{2}}}}} $$ (3)

      对于大多数隔振器,$2\cdot \zeta \cdot \left( \dfrac{\omega }{{{\omega }_{\rm{n}}}} \right)$远小于1,传统橡胶隔振器的传递率函数L由式(4)表示为

      $$L{{ = }}10\lg {\left(\frac{{{F_{\rm{T}}}}}{{{F_{\rm{o}}}}}\right)^2} = 10\lg {\left(\frac{{{\omega _{\rm{n}}}^2}}{{{\omega _{\rm{n}}}^2 - {\omega ^2}}}\right)^2} = 10\lg {\left(\frac{{{f_{\rm{n}}}^2}}{{{f_{\rm{n}}}^2 - {f^2}}}\right)^2}$$ (4)

      式中,$f_{\rm{n}}=\dfrac{1}{{\text{π}}}\sqrt{\dfrac{K}{m}}=\dfrac{\omega_{\rm{n}}}{2{\text{π}}}$

    • 复合式隔振器是基于在隔振系统中间插入质量的设计理念提出的,如图2所示。为分析其传递特性,建立了简化的物理模型,推导得到了如式(5)所示的传递率函数。其中,FF为基座力,${f}_{1} $为中间质量上部橡胶体的固有频率,${f}_{2} $为中间质量下部橡胶体的固有频率,$f $为激励频率,$\mu $为设备质量与中间质量的比值。

      $$ \begin{split} & \qquad\qquad\quad L= 10{\rm{lg}}{\left( {\dfrac{{{F_{\rm{F}}}}}{{{F_{\rm{o}}}}}} \right)^2} = \\& 10{\rm{lg}}{\left( {\dfrac{1}{{\dfrac{1}{{f_1^2f_2^2}}{f^4} - \left( {\dfrac{1}{{f_1^2}} + \dfrac{1}{{f_2^2}} + \mu \dfrac{1}{{f_2^2}}} \right){f^2} + 1}}} \right)^2} \end{split} $$ (5)

      Figure 2.  Sketch of compound rubber isolator

      通过式(4)与式(5)的对比可以发现,在高频段,传统橡胶隔振器的传递率$\propto 1/{f}^{2} $$\propto {f^2}$,而复合式橡胶隔振器的传递率则$\propto 1/{f}^{4} $$\propto {f^4}$,后者明显优于前者。为保证整体上复合式隔振器的刚度与传统橡胶隔振器相等,对比分析了二者的传递性能,并做出如下假设:复合式隔振器的上层刚度与下层刚度相等,且为传统橡胶隔振器刚度的2倍。同时,假设被隔振的设备重量为30 t,布置有8个隔振器。基于以上假设,对复合式隔振器与传统橡胶隔振器的传递率进行了对比,结果如图3所示。

      Figure 3.  Transfer rate comparison between compound and traditional rubber isolator

      图3可见,复合式隔振器和传统橡胶隔振器在刚度相差不大的情况下,前者的传递率明显优于后者;在较高频段,前者的传递率衰减是后者的2倍。可见,复合式隔振器有助于高频振动控制。

    • 图4所示,永磁设备与直流设备相比,机脚振动在高频段明显增加。本文以永磁设备的隔振为研究对象,基于在隔振系统中间插入中间质量的复合式隔振技术,设计了复合式橡胶隔振器。

      Figure 4.  Leg vibration comparison of permanent magnet equipment and DC equipment

      复合式隔振器设计是一个频率、承载、重量和刚度反复交互的过程,同时还需考虑隔振对象的具体要求。基于有限元方法的交互计算,得到了复合式橡胶隔振器的设计方案。图5为隔振器方案的二维图,图6为隔振器方案的三维结构。

      Figure 5.  Structure diagram of the compound rubber isolator

      Figure 6.  3D model of the compound rubber isolator

      图5(a)所示,隔振器由上板1、上橡胶层2、隔片3、中间质量4、下橡胶层5、下板6组成。插入中间质量的复合式橡胶器为部件1~部件6硫化而成的一个整体。上橡胶层2和下橡胶层5夹持中间质量4,构成含中间质量的复合隔振形式,即由上、下两层橡胶夹持中间质量的“三明治”式复合隔振器。该设计方案是基于在隔振系统中间插入质量的复合式隔振技术,即在上橡胶层隔振系统2和下橡胶层隔振系统5的中间插入质量4。设计的复合式橡胶隔振器的主要物理特性描述如下:整体结构尺寸(长×宽×高)为400 mm×400 mm×220 mm,其中上安装面尺寸为330 mm×330 mm;总质量155 kg;金属构件所用材料为Q345B钢,橡胶采用丁腈橡胶。

      采用有限元方法对复合式橡胶隔振器进行应力校核,有限元模型如图7所示。一般认为,在橡胶受压时,应力不超过10 MPa即可;在橡胶受拉时,橡胶应力不超过3~4 MPa即可;在垂向载荷作用下橡胶应力最大1.74 MPa,应力满足要求。金属结构最大应力21.3 MPa,小于材料的许用应力345 MPa。在横向载荷作用下橡胶应力最大2.37 MPa,应力满足要求。金属结构最大应力22.0 MPa,小于材料的许用应力345 MPa。设计的复合式隔振器性能参数见表1

      Figure 7.  Finite element analysis model

      垂向动刚度/(kN·mm−1)固有频率/Hz横向动刚度/(kN·mm−1)垂向−横向刚度比垂向静刚度/(kN·mm−1)总重量/kg
      17.068.56.542.619.2155

      Table 1.  Performance parameters of compound rubber isolator

    • 船舶环境主要考虑温度、耐油和盐雾。通过胶料的性能试验,可以检查复合式橡胶隔振器的环境适应性。由于丁腈橡胶属于耐油橡胶且在船用隔振器中应用广泛,所以对其耐油性将不予重点考察。

      针对橡胶材料开展相关试验,试验结果合格,具体如表2所示。

      试验项目规定值试验值适用标准
      拉伸性能拉伸强度/MPa≥1617.1GB/T 528-2009
      拉断伸长率/%≥400673
      拉断永久变形率/%≤2512
      热老化(70°,96 h)拉伸强度变化率/%−20~20−6GB /T 3512-2001
      拉断伸长变化率/%−20~20−3
      耐5%氯化钠溶液(23 ℃,72 h)质量变化率/%≤50GB/T 1690-2010
      耐3#标准油(25±5 ℃,24 h)质量变化率/%≤102GB/T 1690-2010
      脆性温度/℃≤−20−20,未破坏GB/T 1682-1994
      金属橡胶粘接强度/MPa≥3.94.76GB/T 11211-2009
      4.23
      4.34
      4.86

      Table 2.  Test results of rubber material

    • 本节验证隔振器对船舶上盐雾环境的适应性。鉴于复合式橡胶隔振器的重量较重(见表1),相当于2个成人的体重,所以采用了与隔振器相同的金属和橡胶材料进行硫化形成金属橡胶试片。按照表面处理技术规范要求对试片进行全表面的油漆处理,并按GJB 150.11A-2009《军用装备实验室环境试验方法第11部分:盐雾试验》进行试验。试验条件描述如下:盐溶液浓度(5±1)%,循环周期192 h(24 h连续喷雾和24 h干燥),循环次数4次,共192 h。

      表3所示为2个金属橡胶试片盐雾试验结果,结果显示满足技术要求。图8为试片试验前后的照片,结果显示,设计的复合式橡胶隔振器满足盐雾方面的要求。

      技术要求试验结果
      金属构件不应有明显腐蚀(金属防护层腐蚀面积占金属防护层面积的10%以下),橡胶材料表面不应有龟裂和剥落,橡胶与金属面不应有任何剥离和损坏试验192 h,两试样金属构件面约有0.4%的红锈,其他无异常

      Table 3.  Salt spray test results

      Figure 8.  Photograph of salt spray test results

    • 为了验证复合式橡胶隔振器的动态特性满足规范要求、动静刚度比在合理范围内,基于CB 1359-2002和GB/T 15168-2013开展了垂向刚度试验(图9)。根据被隔振设备重量和隔振器布置数量,分解得到隔振器载荷。

      Figure 9.  Photograph of vertical stiffness test

      试验结果表明,复合式橡胶隔振器的垂向动刚度为16.5 kN/mm,与设计值的偏差为8.3%,满足CB1359-2002要求。复合式橡胶隔振器的垂向静刚度为9.1 kN/mm,动、静刚度比为1.8,属于丁腈橡胶动静比的正常范围。

    • 在主承载方向,对试验装置上固定的复合式橡胶隔振器均匀加载,直至887 kN,隔振器变形29.8 mm。图10所示为垂向极限压缩试验过程中的载荷和位移曲线,图11为试验现场。试验结果显示,复合式橡胶隔振器未破坏、无裂纹、无脱胶等现象,满足CB1359-2002对隔振器承载的要求。

      Figure 10.  Vertical extreme compression curve

      Figure 11.  Photograph of vertical extreme compression test

    • 为开展配机试验,搭建了由基座、复合式橡胶隔振器和永磁设备组成的台架,以验证复合式橡胶隔振器的隔振效果。图12所示为试验结果。配机试验中,由于10 Hz~1 kHz频段内的背景振动较高,基座振动反而高于机脚振动。在1 ~10 kHz的高频段,被隔振设备的机脚振动明显增加,而使用复合式隔振器,保证了基座振动与一般情况下的相差不大,复合式隔振器在此频段内的设备机脚隔振效果可达41 dB,相比传统的橡胶隔振器,隔振效果提高了约20 dB。可见,复合式橡胶隔振器可明显提升高频段内设备机脚的隔振效果,有助于降低设备振动向船体的传递,提升实船应用效果。

      Figure 12.  Vibration comparison of leg and foundation of the compound rubber isolator

    • 本文基于在隔振系统中间插入质量的复合式隔振技术,提出了一种体积小、结构简单,可应用于船载永磁设备隔振的复合式橡胶隔振器设计方案,比较了传统橡胶隔振器与复合式橡胶隔振器的传递特性,并对复合式橡胶隔振器进行性能试验,验证了隔振器的动态特性、环境适应性和承载能力。结果表明,所提设计方案具有可行性,可满足规范及船用环境条件的要求,提高有限空间下设备的隔振效果,尤其是高频段内的隔振效果。本文设计的复合式橡胶隔振器可为设备隔振,特别是高频段的隔振提供途径和参考。

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