﻿ 冰载荷下柴油机推进轴系扭振的数值方法研究
 舰船科学技术  2018, Vol. 40 Issue (8): 85-91 PDF

Research on numerical method for the torsional vibration of the diesel propulsion shafting under ice impact
WU Shuai, WU Wen-wei, XIONG Chen-xi
China Ship Scientific Research Center, Wuxi 214082, China
Abstract: A numerical method for the torsional vibration of the diesel propulsion shafting under ice impact is studied. The Newmark time-domain method of the torsional vibration of the propulsion shafting is first introduced. To the diesel propulsion shafting of a MPC Ship, using this method, the diesel transient torsional vibration in steady condition is calculated, the time-domain calculation methods and the frequency domain results is compared, the reasonability of the time-domain method is verified; considering diesel controller, the related loads are derived with rigid shafting, the shaft torsional vibration domain response is calculated in the rated speed under ice impact, the maximum response amplitude of the shafting is achieved and compared with the result of no ice impacting.
Key words: ice load     diesel     torsional vibration     rigid shafting     numerical method
0 引　言

1 轴系扭振时域计算方法Newmark理论

 ${ J}\ddot \theta + { C}\dot \theta + { K}\theta = {{ M}_{\text{主机}}}(t) + {{M}_{\text{浆}}}(t) + {{M}_{\text{冰}}}(t){\text{，}}$ (1)

Newmark $\beta$ 方法近似假设：

 ${\dot \theta _{t + \Delta t}} = {\dot \theta _t} + (1 - \delta ){\ddot \theta _t} \cdot \Delta t + \delta {\ddot \theta _{t + \Delta t}} \cdot \Delta t\text{，}$ (2)
 ${\theta _{t + \Delta t}} = {\theta _t} + {\dot \theta _t} \cdot \Delta t + (0.5 - \beta ){\ddot \theta _t} \cdot \Delta {t^2} + \beta {\ddot \theta _{t + \Delta t}} \cdot \Delta {t^2}\text{。}$ (3)

$\delta \geqslant 0.5$ $\beta = 0.25{(0.5 + \delta )^2}$ 时，此方法无条件稳定[7-8]

2 柴油机推进轴系扭振时域计算方法研究

2.1 研究对象

2.2 计算模型、激励载荷和阻尼

1）计算模型

 图 1 柴油机推进轴系扭振有限元模型 Fig. 1 The finite model of the torsional vibration of diesel propulsion shafting

2）激励载荷

 图 2 激励载荷仿真分析 Fig. 2 The simulated analysis of exciting load

3）阻尼

2.3 轴系扭振时域计算方法的可行性验证

 图 3 64 rpm时9#中间轴（左）和6#曲轴（右）的应力时程曲线 Fig. 3 The stress time course curve of inter9#(left) and crank6#(right) (64 rpm)

 图 4 64 r/min时9#中间轴（左）和6#曲轴（右）时程应力傅里叶级数分析 Fig. 4 The FFT analysis of the stress time course curve of inter9#(left) and crank6#(right) (64 r/min)

 图 5 9#中间轴和6#曲轴的6谐次扭振应力对比 Fig. 5 The comparison of the 6 order torsional vibration stress of inter9# and crank6#

3 冰载荷下柴油机推进轴系扭振的时域计算

3.1 激励载荷的计算

 $\delta n = \delta t\frac{{{M_{chai}} - ({M_{ow}} + {Q_{ice}})}}{{2\pi I}}\text{。}$ (4)

 $T(n;t) = {T_{static}}(n) + \Delta {T_{dyn}}(t)\text{，}$ (5)

$\Delta {T_{dyn}}(t)$ 是假定能够使主机维持额定扭矩 ${T_{rated}}$ 一小段短时间，可以描述为：

 $\Delta {T_{dyn}}(t) = ({T_{rated}} - {T_{static}})*(1 - t/3)\text{。}$ (6)

${T_{static}} < {T_{rated}}$ 时，t从0开始，并且3 s后结束。

 图 6 工况1柴油机均转速变化曲线 Fig. 6 The uniform speed change curve of diesel (case1)

 图 7 工况1柴油机总输出均扭矩变化曲线 Fig. 7 The total uniform torque change curve of diesel (case1)

 图 8 工况1螺旋桨均扭矩变化曲线 Fig. 8 The uniform torque change curve of propeller (case1)

 图 9 工况1冰载荷扭矩变化曲线 Fig. 9 The torque change curve of ice load (case1)

 图 10 工况1螺旋桨激励扭矩变化（考虑叶频、倍叶频） Fig. 10 The torque change curve of propeller (case1) (considering blade frequency and double blade frequency)

 图 11 工况1柴油机各气缸的输出扭矩变化曲线 Fig. 11 The torque change curve of each cylinder of diesel (case1)
3.2 轴系扭振阻尼的计算

 ${c_p} = A\frac{{{T_p}}}{{{n_p}}}\text{。}$ (7)

3.3 冰载荷下轴系扭振的时域计算

 图 12 9#中间轴在冰载荷工况1冲击下的扭振响应 Fig. 12 The response of the torsional vibration of inter9# under ice impact (case1)

 图 13 9#中间轴在冰载荷工况2冲击下的扭振响应 Fig. 13 The response of the torsional vibration of inter9# under ice impact (case2)

 图 14 9#中间轴在冰载荷工况3冲击下的扭振响应 Fig. 14 The response of the torsional vibration of inter9# under ice impact (case3)

4 结　语

1）Newmark方法可以应用于柴油机推进轴系扭振的时域仿真计算；

2）冰载荷下柴油机推进轴系的扭振计算，需要考虑调速器的影响，同时，曲轴在不同的相位角处会影响柴油机的激励扭矩，进而导致轴系产生不同的扭振响应；

3）本文提出的计算方法中，考虑到主机、桨和冰3种激励载荷由于轴转速而导致互相影响这个因素，先利用刚性轴模型，推算出各种激励载荷，然后施加在柔性有限元模型上，计算轴系扭振响应，该方法可利用通用有限元软件来进行冰载荷下轴系的扭振计算，使用范围广，可以为行业内提供参考，对提高轴系的安全性具有重要意义，同时，该种计算方式值得在其他方面进行研究和应用；

4）从有冰载荷与无冰载荷冲击下的轴系扭振应力两种结果对比来看，冰对螺旋桨冲击导致产生的轴系扭振相当严重，需要密切关注，而且对应的校核方法也需要改变。

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