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LI Z G, ZHAO H, ZHOU N. Calculation and analysis of torsional vibration of electrical propulsion system under a short-circuit-induced impulse load[J]. Chinese Journal of Ship Research, 2020, 15(6): 60–65 doi:  10.19693/j.issn.1673-3185.01902
Citation: LI Z G, ZHAO H, ZHOU N. Calculation and analysis of torsional vibration of electrical propulsion system under a short-circuit-induced impulse load[J]. Chinese Journal of Ship Research, 2020, 15(6): 60–65 doi:  10.19693/j.issn.1673-3185.01902

Calculation and analysis of torsional vibration of electrical propulsion system under a short-circuit-induced impulse load

doi: 10.19693/j.issn.1673-3185.01902
  • Received Date: 2019-03-14
  • Rev Recd Date: 2020-06-05
  • Available Online: 2020-11-24
  • Publish Date: 2020-12-30
  •   Objectives  For an electrical propulsion system, the transient torque induced by short-circuit faults is so large that it will exert a greater impact on the safety of shipboard electric propulsion system. In order to evaluate the problem, a simulation method for analyzing the torsional vibration of a propulsion system under a short-circuit-induced torque impulse is proposed in the time domain.  Methods  Based on the torsion vibration analysis theory, a time-domain model is developed, and the system response to a transient torque impulse induced by a short-circuit is expressed. Then by using the proposed simulation model, the natural frequencies and response to the transient torque impulse for an electrical propulsion system are calculated and analyzed.  Results  The simulation results show that the dynamic characteristics of the system have a prominent role in the transmission of torque impulse, and components at frequencies above the first resonance frequency see a substantial reduction, so the torque response of the propeller is mainly based on the first resonance frequency component. If an elastic coupling is inserted into the propulsion motor and the shafting, the torque response of the system can be significantly decreased. The peak value increases with motor speed, and vibratory torque can reach several times the value of the mean torque, causing the gears to rattle and the torsion vibratory stress to grow as a result.  Conclusions  The proposed simulation modeling method is suitable for analyzing the torsional vibration response of an electrical propulsion system under a short-circuit-induced impulse load, and a numerical calculation should be carried out to check the reliability of the system during the design process.
  • 赵鹏程. 汽轮发电机组轴系扭振机理及安全性分析[D]. 北京: 华北电力大学, 2019.

    ZHAO P C. Torsional vibration mechanism and safety analysis of turbo-generator shafts[D]. Beijing: North China Electric Power University, 2019 (in Chinese).
    李晓茜. 特种工况下轴系振动特性研究[D]. 哈尔滨: 哈尔滨工程大学, 2014.

    LI X Q. Characteristics research of shaft vibration in special conditions[D]. Harbin: Harbin Engineering University, 2014 (in Chinese).
    夏凯, 孙岩桦, 张锋. 燃气轮发电机组短路故障时的机电耦合分析[J]. 应用力学学报, 2016, 33(1): 55–60.

    XIA K, SUN Y H, ZHANG F. The coupled electro-mechanical analysis for gas turbine generators during short circuit fault[J]. Chinese Journal of Applied Mechanics, 2016, 33(1): 55–60 (in Chinese).
    陈奇, 蔡龙奇, 李晓茜, 等. 短路故障时柴油发电机组隔振系统响应分析[J]. 中国舰船研究, 2013, 8(3): 66–72.

    CHEN Q, CAI L Q, LI X Q, et al. The response analysis due to short-circuit faults for the vibration isolator in a diesel generator set[J]. Chinese Journal of Ship Research, 2013, 8(3): 66–72 (in Chinese).
    TSAI J I. Design of a short-time compensation capacitor for turbine blade vibration suppression[J]. Electric Power Systems Research, 2007, 77(12): 1619–1626. doi:  10.1016/j.jpgr.2006.11.009
    OGIDI O O, BARENDSE P S, KHAN M A. Fault diagnosis and condition monitoring of axial-flux permanent magnet wind generators[J]. Electric Power Systems Research, 2016, 136: 1–7. doi:  10.1016/j.jpgr.2016.01.018
    向玲, 杨世锡, 唐贵基, 等. 汽轮发电机组轴系扭振的时频特征分析[J]. 动力工程学报, 2011, 31(9): 649–654, 671.

    XIANG L, YANG S X, TANG G J, et al. Time-frequency analysis on torsional vibration of turbo-generator shafts[J]. Journal of Chinese Society of Power Engineering, 2011, 31(9): 649–654, 671 (in Chinese).
    张会焱, 施伟峰. 船舶电力系统3相短路故障仿真[J]. 上海海事大学学报, 2013, 34(3): 43–47. doi:  10.3969/j.issn.1672-9498.2013.03.009

    ZHANG H Y, SHI W F. Simulation on 3-phase short circuit faults of ship power system[J]. Journal of Shanghai Maritime University, 2013, 34(3): 43–47 (in Chinese). doi:  10.3969/j.issn.1672-9498.2013.03.009
    陈之炎. 船舶推进轴系振动[M]. 上海: 上海交通大学出版社, 1987.

    CHEN Z Y. Propulsion shafting vibration of ship[M]. Shanghai: Shanghai Jiao Tong University Press, 1987 (in Chinese).
    COOK R D, MALKUS D S, PLESHA M E, et al. Concepts and applications of finite element analysis[M]. 4th ed. New York: John Wiley & Sons, 2002: 407-411.
    Vulkan GmbH & Co. KG . Torsional vibration calculation: Report No. 10_17_1.029[R]. Herne,Germany: Vulkan GmbH & Co. KG,2017.
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Calculation and analysis of torsional vibration of electrical propulsion system under a short-circuit-induced impulse load

doi: 10.19693/j.issn.1673-3185.01902

Abstract:   Objectives  For an electrical propulsion system, the transient torque induced by short-circuit faults is so large that it will exert a greater impact on the safety of shipboard electric propulsion system. In order to evaluate the problem, a simulation method for analyzing the torsional vibration of a propulsion system under a short-circuit-induced torque impulse is proposed in the time domain.  Methods  Based on the torsion vibration analysis theory, a time-domain model is developed, and the system response to a transient torque impulse induced by a short-circuit is expressed. Then by using the proposed simulation model, the natural frequencies and response to the transient torque impulse for an electrical propulsion system are calculated and analyzed.  Results  The simulation results show that the dynamic characteristics of the system have a prominent role in the transmission of torque impulse, and components at frequencies above the first resonance frequency see a substantial reduction, so the torque response of the propeller is mainly based on the first resonance frequency component. If an elastic coupling is inserted into the propulsion motor and the shafting, the torque response of the system can be significantly decreased. The peak value increases with motor speed, and vibratory torque can reach several times the value of the mean torque, causing the gears to rattle and the torsion vibratory stress to grow as a result.  Conclusions  The proposed simulation modeling method is suitable for analyzing the torsional vibration response of an electrical propulsion system under a short-circuit-induced impulse load, and a numerical calculation should be carried out to check the reliability of the system during the design process.

LI Z G, ZHAO H, ZHOU N. Calculation and analysis of torsional vibration of electrical propulsion system under a short-circuit-induced impulse load[J]. Chinese Journal of Ship Research, 2020, 15(6): 60–65 doi:  10.19693/j.issn.1673-3185.01902
Citation: LI Z G, ZHAO H, ZHOU N. Calculation and analysis of torsional vibration of electrical propulsion system under a short-circuit-induced impulse load[J]. Chinese Journal of Ship Research, 2020, 15(6): 60–65 doi:  10.19693/j.issn.1673-3185.01902
    • 随着电力电子技术的发展以及对绿色化、低噪声、节能减排等方面需求的增长,电力推进在船舶工程中得到了广泛应用。由于推进电机的动态扭矩激励比柴油机小很多,因此电力推进装置扭振计算及校核中通常仅考虑螺旋桨的激励特性。推进电机主要构件长期运行在温度、应力及振动等环境下,其绕组绝缘逐渐老化、变形而出现损坏,最终发生短路故障。其中,匝间短路是常见的故障之一,占故障总数的30%以上。当推进电机出现短路故障时,其瞬态扭矩激励峰值将突然增加至数倍的平均扭矩,从而使整个推进装置承受较大的冲击载荷,影响装置的运行安全。由于短路故障是破坏性的,通常不采用试验法来进行校核,因此,在船舶设计阶段,有必要对短路冲击作用下电力推进装置的安全可靠性进行计算校核。

      目前,针对短路瞬态扭矩引起的发电机组故障问题,国内外学者对机组轴系扭振特性分析及故障诊断开展了大量研究。赵鹏程[1]、李晓茜[2]、夏凯等[3]分别研究了汽轮发电机组、核电柴油应急发电机组、燃气轮机发电机组在短路故障时轴系的扭振计算方法及响应特性。陈奇等[4]计算了短路故障时柴油发电机组隔振系统的响应,指出隔振装置设计时应考虑瞬态扭矩载荷。针对汽轮发电机组单相接地故障所致瞬态电磁扭矩引起的汽轮机叶片共振损坏问题,Tsai[5]提出了在中性轴与地之间设置短时补偿电容的设计思路。为了提高发电机组运行的安全性,可通过在线测量电流及振动信号并进行频谱分析,实现短路故障监测与诊断[1, 6-7]。张会焱和施伟峰[8]利用Matlab/Simulink搭建了船舶电力系统动态数字仿真平台,分析了船舶主推进电机三相短路故障对前端柴油发电机组及电网的影响。与发电机组类似,推进电机短路故障对后端传动部件及轴系的扭振响应特性有一定影响,而相关研究工作较少。

      因此,本文将在分析冲击载荷作用下推进装置扭振计算方法的基础上,以某船的电力推进装置为对象,计算其固有特性及短路冲击作用下的扭振响应,分析系统响应特性及其影响因素。

    • 船舶推进装置的扭振特性计算中,通常将推进装置简化为图1所示的当量系统,推进电机、传动部件及轴段、推进器分别简化为等效转动惯量Jn、扭转刚度kn、相对阻尼Crn、绝对阻尼Can,由这些部件组成一个链式系统。通过受力分析,可建立系统的扭振微分方程[9],即

      $${{J\ddot \theta }} + {{C\dot \theta }} + {{K\theta }} = {{T}}(t)$$ (1)

      式中:JCK分别为N×N维的转动惯量、阻尼和刚度矩阵;TN维的激励扭矩向量,主要包括推进电机的激励扭矩和螺旋桨的激励扭矩;θN维的扭转角度向量。

      Figure 1.  Torsional vibration simulation model

      螺旋桨的激励扭矩主要为叶片次及其倍数频率,可由经验公式估算[9],此处不再赘述。而推进电机的激励扭矩主要由电磁力引起,其在正常运转工况下,激励扭矩可表示为

      $${T_{\rm{n}}}(t) = {T_{\rm{m}}}\sum\limits_{j = 1}^{{N_{\rm{n}}}} {{R_{{\rm{n}}j}}} \sin (2 {\text{π}} {f_{{\rm{n}}j}}t + {\varPhi _{{\rm{n}}j}})$$ (2)

      式中:Tm为特定转速下的平均扭矩;Rnj为扭矩系数;fnj为激励频率,等于电频率与电机极数的乘积;Φnj为相位角;下标j代表第j谐次;Nn为激励谐次总数;下标n代表正常运转工况。

      假设在t=t0时推进电机出现短路,其瞬态扭矩可表示为

      $${T_{\rm{s}}}(t) = {T_{\rm{m}}}\sum\limits_{j = 1}^{{N_{\rm{s}}}} {{R_j}} {{\rm{e}}^{{\tau _j}(t - {t_0})}}\sin [2 {\text{π}} {f_j}(t - {t_0}) + {\varPhi _j}]$$ (3)

      式中:Rj为冲击扭矩系数;τj为时间常数;fj为频率;Φj为相位角。时间常数通常为负数,故瞬态扭矩随着时间而逐渐衰减。

      在推进电机正常运转情况下,由于式(1)中激励扭矩为稳态的周期信号,通常在频率域求解方程;而对于激励为冲击型瞬态信号,通常在时间域进行求解,本文采用具有良好稳定性的Newmark算法[10]求解,利用Matlab语言编程计算。

    • 国内某科考船的电力推进装置组成如图2所示,西门子公司的三相推进电机通过复合材料短轴(表中称“复合轴”)驱动VOITH公司VSP推进器;推进器有5片桨叶,内置2级减速装置;推进电机额定功率为2 750 kW,额定转速为1 000 r/min。根据设备厂家的技术资料,电力推进装置简化为具有10个集中转动惯量的扭振当量系统,主要参数如表1所示。序号5与6、序号7与8之间为齿轮轴,直径分别为139和224 mm。

      Figure 2.  Components of electrical propulsion plant

      序号项目名称Jn
      /(kg·m2)
      kn
      /(MN·m·rad−1)
      减速比
      1电机11413.91.000 0
      2电机/复合轴连接法兰2.2744.61.000 0
      3复合轴左端3.3416.01.000 0
      4复合轴右端3.3244.61.000 0
      5复合轴/推进器连接法兰2.369.171.000 0
      6主动正齿轮2.39齿轮啮合1.000 0
      7从动正齿轮115108.00.313 4
      8主动伞齿轮10.6齿轮啮合0.070 1
      9从动伞齿轮715刚性连接0.070 1
      10VSP推进器54 2850.070 1

      Table 1.  Parameters of torsional vibration system

      根据西门子公司提供的技术资料,在三极和两极短路情况下,瞬态扭矩的主要参数如表2表3所示。在推进电机额定运转工况下,将表2表3中参数代入式(3)后得到瞬态短路冲击扭矩(图3)。可知,在三极及两极短路情况下,最大扭矩分别在短路5.6和7 ms后出现,约为稳态扭矩幅值的5.63倍和7.36倍。

      激励谐次序号Rjτjfj /HzΦj /(°)
      1−0.74−23.50090
      2−0.23−71.80090
      36.39−47.6548.94162.04

      Table 2.  Parameters of 3-pole short-circuit

      激励谐次序号Rjτjfj /HzΦj /(°)
      10.160090
      2−0.73−23.50090
      3−0.06−71.80090
      43.03−11.7550.09177.41
      51.58−35.901.1517.17
      63.21−47.6548.94160.92
      71.520.00100.60−3.87
      80.54−11.7550.5190.22
      91.59−35.9099.45−16.97

      Table 3.  Parameters of 2-pole short-circuit

      Figure 3.  Transient torque of propulsion motor

    • 1)固有振动特性。根据表1中的参数,将所有转动惯量及扭转刚度等效至推进电机端,计算得到的系统前4阶弹性扭振模态频率如表4所示,对应振型如图4所示。可见,第1阶和第3阶模态的振型节点均在转动惯量5与6之间。本文计算值与VULKAN公司扭振计算报告[11]中的结果非常接近。

      Figure 4.  Modal shapes of first four vibration modes

      模态阶数振型固有频率/Hz
      本文文献[11]
      11节点28.328.4
      22节点145.1146.1
      33节点245.4245.9
      44节点441.2441.4

      Table 4.  Natural vibration characteristics

      2)瞬态响应特性。在短路冲击扭矩作用下,推进电机轴(惯量1和2之间)和直齿轮轴(惯量5和6之间)的瞬态扭矩响应如图5所示。对其进行比较可知,对于推进电机轴,两极短路冲击下的扭矩响应大于三极短路冲击工况;但是对于直齿轮轴,则情况相反,说明系统动态特性对冲击扭矩传递有一定影响。其次,齿轮轴瞬态交变扭矩较大,至少为2倍额定扭矩以上,可引起齿轮啮合面的敲击。

      Figure 5.  Torque responses under 2-pole and 3-pole short-circuit

      图6为推进电机轴和直齿轮轴的扭矩频谱特性。在两极短路工况下,扭矩均在100.6 Hz处存在峰值,对应激励频率如表3所示,但该频率处直齿轮轴扭矩峰值比推进电机轴降低了约20 dB(图中,纵坐标扭矩幅值Ta的参考值为1 kN·m),扭矩峰值降低至与第1阶固有频率处峰值相当的程度,说明从推进电机传递到直齿轮轴的过程中出现了很大程度的衰减。在三极短路工况下,扭矩频谱峰值频率为28.2和145 Hz,对应系统的前两阶固有频率(表4),以系统第1阶模态频率成分为主,第2阶固有频率对应的峰值在传递过程中有约20 dB衰减。比较可见,对于直齿轮轴,扭矩响应均以第1阶固有频率成分为主,且三极短路时该峰值高于两极短路工况约2.4 dB,因此三极短路时扭矩时域曲线中最大值比两极短路工况大。

      Figure 6.  Torque response spectra under 2-pole and 3-pole short-circuit

      图7为推进电机不同转速出现短路时的扭矩峰值结果,图中扭矩为高速端等效值,未考虑速比影响。可见,扭矩峰值随着转速增加而增加;直齿轮轴和伞齿轮轴处扭矩低于推进电机扭矩。考虑减速比后,计算得到推进电机(1 000 r/min)三极短路工况下直齿轮轴和伞齿轮轴的最大扭转应力分别为191和152 MPa,均小于材料屈服强度400 MPa,满足要求。

      为减小VSP推进器内部件的扭转应力,考虑在推进电机与VSP推进器之间设置高弹性联轴器。假如采用VULKAN公司RATO R2410型联轴器,扭转刚度为0.594 MN·m/rad,计算得到的扭矩峰值如图8所示。可见,与扭转刚度为16 MN·m/rad的复合轴联轴器相比,扭矩峰值最大降低60%以上。

      Figure 7.  Torque peak values with speed

      Figure 8.  Effects of coupling stiffness on torque response

      图9为推进电机(1 000 r/min)三极短路工况下,分别采用复合材料轴联轴器和高弹性联轴器时推进电机轴、直齿轮轴的扭矩响应谱。可见,与复合材料轴联轴器相比,采用高弹性联轴器后扭矩响应第1个峰值(对应第1阶固有频率)降低至约11 Hz,峰值降低了约6 dB;在高于20 Hz频段,采用高弹性联轴器时传递到直齿轮轴的扭矩基本上均有所降低,说明通过高弹性联轴器降低了系统第1阶固有频率,有利于抑制推进电机处动态扭矩向传动部件及推进器端的传递。

      Figure 9.  Effects of coupling stiffness on torque response spectra

    • 本文建立了在推进电机短路故障冲击扭矩作用下的船舶推进装置扭振响应时域计算模型,以采用VSP推进器的某船电力推进装置为对象,通过数值仿真方法,分析了系统固有特性以及扭振响应特性。主要结论如下:

      1) 系统的动态特性对短路冲击扭矩的传递有重要影响,激励扭矩中高于系统第1阶弹性模态频率的成分传递至推进器端时有很大程度衰减,推进器端的动态扭矩响应以第1阶弹性模态频率成分为主。

      2) 推进器瞬态扭矩响应最大值随着推进电机转速的增加而增加,交变扭矩为平均扭矩的数倍,将引起齿轮传动装置的齿面敲击。

      3) 短路冲击扭矩引起的传动部件瞬时扭转应力较大,设计中应注意该载荷;在推进电机与传动轴−推进器之间设置高弹性联轴器,能大幅衰减冲击扭矩引起的动态响应。

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