船用二冲程柴油机及推进轴系的振动建模与仿真研究
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摘要
作为船舶主动力装置的大型低速二冲程柴油机,是船舶振动和噪声的一个重要的激励源,研究并控制整个柴油机的振动噪声具有非常重要的意义。本文以多体动力学、有限元法和有限差分法为基础,较为系统地研究了整个柴油机及推进轴系的振动特性。
首先,建立柔性多体动力学数学模型。基于Newton-Euler向量力学分析法和浮动坐标系,运用模态综合法(动态缩减技术),缩减各部件的自由度,建立柔性多体动力学的数学模型,并分别用Newmark、HHT、BDF法对一单缸发动机进行了数值计算,对比表明：BDF法作为计算复杂的大型船用柴油机柔性多体动力学的较佳方法。
其次,建立整机有限元模型。根据大型船用柴油机的部件及其组合结构庞大、有限元模型无法验证的特点,基于有限元法原理,对于单个部件,增加其单元数量,以其固有模态不再变化为基准,作为模型简化的参考；对于螺栓连接的组合结构,以锥度孔模型和接触理论为基础,在有限元法中用梁单元、弹簧单元模拟其连接,经螺栓连接板件的模态试验验证了该法的可靠性。在以上两步的基础上,建立了整个机体和轴系的有限元模型,并做了模态分析。
第三,基于试验台架,建立大型船用柴油机整机振动的数学模型并计算其振动响应。对大型船舶柴油机有限元模型动态缩减,各部件间的连接副均采用非线性弹簧-阻尼连接(NONL)模型,建立整机的柔性多体动力模型并用BDF法计算。结果表明：基于全柔性机体与柔性轴系的三维耦合模型能够更加全面地反映机体的振动特性。根据缩减模型的逆变换,可得到整个机体和轴系表面的位移、速度、加速度和应力分布。通过与台架试验结果对比,验证了该模型和方法的可行性。
第四,主轴承处以弹性流体动力混合润滑模型计算,对比在NONL、EHD、 TEHD三种模型下整机的振动特性。对于轴系特性,简化的NONL模型有所欠缺,在主轴承处引入了基于Reynolds方程和微凸峰接触Greenwood-Tripp模型的弹性流体动力混合润滑模型,基于质量守恒边界条件(JFO),采用有限差分与有限元法相结合的方法,分别以计入(TEHD)和不计入(EHD)温度对油膜和轴瓦的影响两种模型计算整机振动,并与非线性弹簧-阻尼连接模型一起对比,发现：计算效率依次是NONL、EHD、TEHD模型,计算精度依次是TEHD、EHD、NONL模型。因此,若仅计算机体的振动特性,NONL模型最佳；若计算整机振动特性,综合考量EHD最佳。
最后,在以上研究的基础上,以39000DWT油轮为载体,以6S50MC-C船用柴油机为研究对象,基于实船安装条件下进行整机及推进轴系振动的计算。柴油机、中间轴承座和尾轴承对应部位的双层底支撑刚度均采用动态刚度,利用经验公式得到螺旋桨在三个方向上的力／力矩激励,建立与船体耦合的整机的柔性多体动力学计算模型。先以轴系按照直线布置且无调谐轮和轴向减振器时计算。再基于三弯矩法,对轴系进行了校中计算,求出各轴承的变位,以其为基础计算轴系合理校中下整机的振动。又以单独或组合计入调谐轮、减振器、对中等因素分为5中模型进行计算对比,以及船舶双层底刚度和横向支撑刚度、轴承间隙大小改变等对整机振动特性的影响。以综合计入调谐轮、减振器、对中等因素的TW-AVD-ALN模型计算,分析整机在不同转速下的振动特性。结果表明：机体和轴系间、轴系自身的扭-纵-弯振间和整机与各边界条件间的振动是相互耦合影响的,只是相互间的耦合能量大小不一,外在表现有所差异。最后,通过实船测量的轴系扭转振动值与计算值对比,验证了模型和计算方法的准确性,为下一步整机振动的优化控制奠定基础。该法具有一定的工程价值。
The large low speed two-stroke diesel engine as the main power plant on ship is the key exciting source of ship vibration and noises. So, research and control on the vibration and noises are most significant. Based on the multi-body dynamics, finite element method and finite differenc method, vibration characteristics of the whole engine and propulsion shafting are studied systematically.
Firstly, math model on the flexible multibody dynamics is built. Based on the Newton-Euler equations and floating frame coordinates, the degree of freedoms on componets are reduced with component mode synthesis method (dynamic condensation technology). The math models on them are set up. Numerical calculation on a single-cylinder engine is done by the Newmark, HHT and BDF method respectively. The results show that BDF method is preferred to calculate the flexible multibody dynamics of the large and complex marine diesel engine.
Secondly, finite element model of the whole engine is established. According to the features of the large marine diesel engine whose components and combined structure are so big and its finite element model can not be proved, based on the finite element principle, when the natural mode of the single component doesn't change by increasing the element number any more, the model is acted as a reference to simplify the model. In view of the cone model and the contact theory, combined structre connected by the bolts is jointed by beam elements and spring elements in the finite element formulate, which is verified by the modal test. Based on the above two steps, the finite element model of the engine block and the shafting are built and their mode are analyzed.
Thirdly, the math model on the whole engine vibration of the large marine diese engine is set up and the calculation about its vibration response is done, based on the test-bench. The FEM of the large marine diesel engine is reduced with dynamic condensation technology. The components are connected by the nolinear spring-damper (NONL model). The flexible multi-body dynamics model on the whole engine is developed and its calculation is done by BDF method. It shows that3-D coupled model on the whole flexible eninge block and the flexible shafting can reveal the vibration characteristcs of the engine block more allsidely. According the inverse transformation of the condensed model, the displacement, velocity, acceleration and stress distribution of the engine block and the shafting could be got. Through comparion with the experimental results on the test frame, the possibilities of the model and the calculation method are verified.
Fouthly, the elastic-hydro-dynamic mixed lubrication model is used at the main bearings and the whole engine vibration is compared under the NONL, EHD and TEHD model. The NONL model is not enough for the shafting. The elastic-hydrodynamic fixed lubrication model is introduced to the main bearings based on the Reynolds equation and Greenwood-Tripp contact model. The whole engine vibratin is done with EHD model (without temperature effect on the oil film and the bearings) and TEHD model (with) respectively by MBD, FEM and FDM method. The comparion is also made with NONL model. It is found that the order of calculation efficiency is NONL, EHD, TEHD model in trun, the order of calculation precision is TEHD, EHD, and NONL model. Therefore, the NONL model is best if only for the engine block vibration and the EHD model is best if for the whole engine vibration.
Finally, the vibrations of the whole6S50MC-C marine diesel engine and propusion shafting are calculated, which are installed on the39000DWT oil tanker, based on above researches. Firstly, the vibration is developed under the in-line shafting without tuning wheel and axial vibration damper. Secondly, the shafting alignment is done with three-moment method and the bearing deflection is got. The vibration is studied considering the rational shafting alignment based on the bearing deflection. The vibration comparions of5models each other are finished. Also the effect of the double hull stiffness, transverse stiffness and bearing clearance on the vibration is done. With the TW-AVD-ALN model, the vibration properties of the whole engine are analysed under different speed. The results show that the vibrations are coupled each other among the engine block, the shafting and boundary conditons. At last, through comparion with the torsional vibration values measured on the ship, the model and calculation method are proved, which would lay foundation for optimization control on the whole engine vibration. The method has engineering value to some certain degree.
首先,建立柔性多体动力学数学模型。基于Newton-Euler向量力学分析法和浮动坐标系,运用模态综合法(动态缩减技术),缩减各部件的自由度,建立柔性多体动力学的数学模型,并分别用Newmark、HHT、BDF法对一单缸发动机进行了数值计算,对比表明：BDF法作为计算复杂的大型船用柴油机柔性多体动力学的较佳方法。
其次,建立整机有限元模型。根据大型船用柴油机的部件及其组合结构庞大、有限元模型无法验证的特点,基于有限元法原理,对于单个部件,增加其单元数量,以其固有模态不再变化为基准,作为模型简化的参考；对于螺栓连接的组合结构,以锥度孔模型和接触理论为基础,在有限元法中用梁单元、弹簧单元模拟其连接,经螺栓连接板件的模态试验验证了该法的可靠性。在以上两步的基础上,建立了整个机体和轴系的有限元模型,并做了模态分析。
第三,基于试验台架,建立大型船用柴油机整机振动的数学模型并计算其振动响应。对大型船舶柴油机有限元模型动态缩减,各部件间的连接副均采用非线性弹簧-阻尼连接(NONL)模型,建立整机的柔性多体动力模型并用BDF法计算。结果表明：基于全柔性机体与柔性轴系的三维耦合模型能够更加全面地反映机体的振动特性。根据缩减模型的逆变换,可得到整个机体和轴系表面的位移、速度、加速度和应力分布。通过与台架试验结果对比,验证了该模型和方法的可行性。
第四,主轴承处以弹性流体动力混合润滑模型计算,对比在NONL、EHD、 TEHD三种模型下整机的振动特性。对于轴系特性,简化的NONL模型有所欠缺,在主轴承处引入了基于Reynolds方程和微凸峰接触Greenwood-Tripp模型的弹性流体动力混合润滑模型,基于质量守恒边界条件(JFO),采用有限差分与有限元法相结合的方法,分别以计入(TEHD)和不计入(EHD)温度对油膜和轴瓦的影响两种模型计算整机振动,并与非线性弹簧-阻尼连接模型一起对比,发现：计算效率依次是NONL、EHD、TEHD模型,计算精度依次是TEHD、EHD、NONL模型。因此,若仅计算机体的振动特性,NONL模型最佳；若计算整机振动特性,综合考量EHD最佳。
最后,在以上研究的基础上,以39000DWT油轮为载体,以6S50MC-C船用柴油机为研究对象,基于实船安装条件下进行整机及推进轴系振动的计算。柴油机、中间轴承座和尾轴承对应部位的双层底支撑刚度均采用动态刚度,利用经验公式得到螺旋桨在三个方向上的力／力矩激励,建立与船体耦合的整机的柔性多体动力学计算模型。先以轴系按照直线布置且无调谐轮和轴向减振器时计算。再基于三弯矩法,对轴系进行了校中计算,求出各轴承的变位,以其为基础计算轴系合理校中下整机的振动。又以单独或组合计入调谐轮、减振器、对中等因素分为5中模型进行计算对比,以及船舶双层底刚度和横向支撑刚度、轴承间隙大小改变等对整机振动特性的影响。以综合计入调谐轮、减振器、对中等因素的TW-AVD-ALN模型计算,分析整机在不同转速下的振动特性。结果表明：机体和轴系间、轴系自身的扭-纵-弯振间和整机与各边界条件间的振动是相互耦合影响的,只是相互间的耦合能量大小不一,外在表现有所差异。最后,通过实船测量的轴系扭转振动值与计算值对比,验证了模型和计算方法的准确性,为下一步整机振动的优化控制奠定基础。该法具有一定的工程价值。
The large low speed two-stroke diesel engine as the main power plant on ship is the key exciting source of ship vibration and noises. So, research and control on the vibration and noises are most significant. Based on the multi-body dynamics, finite element method and finite differenc method, vibration characteristics of the whole engine and propulsion shafting are studied systematically.
Firstly, math model on the flexible multibody dynamics is built. Based on the Newton-Euler equations and floating frame coordinates, the degree of freedoms on componets are reduced with component mode synthesis method (dynamic condensation technology). The math models on them are set up. Numerical calculation on a single-cylinder engine is done by the Newmark, HHT and BDF method respectively. The results show that BDF method is preferred to calculate the flexible multibody dynamics of the large and complex marine diesel engine.
Secondly, finite element model of the whole engine is established. According to the features of the large marine diesel engine whose components and combined structure are so big and its finite element model can not be proved, based on the finite element principle, when the natural mode of the single component doesn't change by increasing the element number any more, the model is acted as a reference to simplify the model. In view of the cone model and the contact theory, combined structre connected by the bolts is jointed by beam elements and spring elements in the finite element formulate, which is verified by the modal test. Based on the above two steps, the finite element model of the engine block and the shafting are built and their mode are analyzed.
Thirdly, the math model on the whole engine vibration of the large marine diese engine is set up and the calculation about its vibration response is done, based on the test-bench. The FEM of the large marine diesel engine is reduced with dynamic condensation technology. The components are connected by the nolinear spring-damper (NONL model). The flexible multi-body dynamics model on the whole engine is developed and its calculation is done by BDF method. It shows that3-D coupled model on the whole flexible eninge block and the flexible shafting can reveal the vibration characteristcs of the engine block more allsidely. According the inverse transformation of the condensed model, the displacement, velocity, acceleration and stress distribution of the engine block and the shafting could be got. Through comparion with the experimental results on the test frame, the possibilities of the model and the calculation method are verified.
Fouthly, the elastic-hydro-dynamic mixed lubrication model is used at the main bearings and the whole engine vibration is compared under the NONL, EHD and TEHD model. The NONL model is not enough for the shafting. The elastic-hydrodynamic fixed lubrication model is introduced to the main bearings based on the Reynolds equation and Greenwood-Tripp contact model. The whole engine vibratin is done with EHD model (without temperature effect on the oil film and the bearings) and TEHD model (with) respectively by MBD, FEM and FDM method. The comparion is also made with NONL model. It is found that the order of calculation efficiency is NONL, EHD, TEHD model in trun, the order of calculation precision is TEHD, EHD, and NONL model. Therefore, the NONL model is best if only for the engine block vibration and the EHD model is best if for the whole engine vibration.
Finally, the vibrations of the whole6S50MC-C marine diesel engine and propusion shafting are calculated, which are installed on the39000DWT oil tanker, based on above researches. Firstly, the vibration is developed under the in-line shafting without tuning wheel and axial vibration damper. Secondly, the shafting alignment is done with three-moment method and the bearing deflection is got. The vibration is studied considering the rational shafting alignment based on the bearing deflection. The vibration comparions of5models each other are finished. Also the effect of the double hull stiffness, transverse stiffness and bearing clearance on the vibration is done. With the TW-AVD-ALN model, the vibration properties of the whole engine are analysed under different speed. The results show that the vibrations are coupled each other among the engine block, the shafting and boundary conditons. At last, through comparion with the torsional vibration values measured on the ship, the model and calculation method are proved, which would lay foundation for optimization control on the whole engine vibration. The method has engineering value to some certain degree.
引文
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