Study on Forced Torsional Vibration of CFRP Drive-Line System with Internal Damping

The use of CFRP transmission shaft has positive effect on the weight and flexural vibration reduction of drive-line system. However, the application of CFRP transmission shaft will greatly reduce the torsional stiffness of the drive-line, and may cause strong transient torsional vibration. Which will seriously affect the performance of CFRP drive-line. In this study, the forced torsional vibration of the CFRP drive-line system is carried out using the lumped parameter model. In addition, the effect of rotary inertia, internal damping, coupling due to the composite laminate, and excitation torque are incorporated in the modified transfer matrix model (TMM). Then, the modified TMM is used to predict the torsional frequency and forced torsional vibration of a CFRP drive-line with three-segment drive shafts. The results of modified TMM shown that the rotational speed difference of the CFRP transmission shaft segment is much larger than metal transmission shaft segment under excitation torque. And compared the results from finite element simulation, modified TMM and torsional vibration experiment respectively, and it has shown that the modified TMM can accurately predict forced torsional vibration behaviors of the CFRP drive-line system.     

Torsional vibration of a shaft with a circumferential crack

The influence of a circumferential crack upon the torsional dynamic behavior of a shaft is studied. Introduction of such a crack results in lower torsional natural frequencies due to the added flexibility.

The strain energy release function is related to the compliance of the cracked shaft, that is to the local flexibility due to the introduction of the crack. This function is related to the stress intensity factor which for torsion of a shaft with a circumferential crack has a known expression. As a result, the local flexibility of the shaft due to the presence of the crack has been computed. This result can be further utilized to yield the dynamic response of a shaft with complex geometry.

The torsional natural frequency is expected to decrease with increasing crack depth. To establish such function, a continuous shaft with a circumferential crack was analyzed. The fundamental natural frequency showed strong dependence on the crack depth. This dependence is smaller as the order of the frequency increases. Experimental results are in close agreement with analysis.

The results show that the change in dynamic response due to the crack is high enough to allow the detection of the crack and estimation of its location or magnitude.     

Detecting natural crack initiation and growth in slow speed shafts with the Acoustic Emission technology

This paper presents results of an experimental investigation to assess the potential of the Acoustic Emission (AE) technology for detecting natural cracks in operational slow speed shafts. A special purpose built test rig was employed for generating natural degradation on a shaft. It was concluded that AE technology successfully detected natural cracks induced on slow speed shafts.     

Effect of stacking sequence on the torsional stiffness of the composite drive shaft

Torsional stiffness is an important parameter judging the performance of composite drive shaft. In this paper, a new mechanical analytical solution of torsional stiffness for the composite drive shaft with balance laminate is derived based on classical lamination theory and mechanical analysis. Finite element analysis (FEA) has been used to calculate the torsional stiffness of carbon fiber-reinforced plastic (CFRP) drive shaft. A torsion test platform has also been constructed to measure the torsional stiffness of CFRP drive shaft specimens. Results of the mechanical analytical solution, FEA, and experiments show that the composite tube with the location of ±45° layers near to the outer surface is larger than the ones with the location of ±45° layers near to the inner surface. The effect of stacking sequence on torsional stiffness is larger in the thick-walled than that in the thin-walled composite drive shaft. The mechanical analytical solution can complement classical lamination theory which cannot reflect the effect of stacking sequence in calculating the torsional stiffness.     

Experimental and dynamic system simulation and optimization of a centrifugal pump-coupling-engine system. Part 2: System design

A comprehensive theoretical non-linear torsional dynamic model of a pump-coupling-engine assembly has been constructed, with some of the system characteristics evaluated through the finite element method. Coupling elements have non-constant stiffness, which makes the dynamic system non-linear. The resulting model provided information on the torsional vibration response of the system and therefore allowed analysis of the effect of different designs on the torsional system dynamics. Model outputs have been compared to experimental test rig results where system rotational inertia and four different couplings have been studied. The main aim of the work was to improve system design in order to guarantee reliable operation. The model facilitated a dynamic characterization of the system and has been used as predictive tool for subsequent design.     

拉杆疲劳裂纹导致的组合转子性能退化研究

 组合转子作为燃气轮机等的核心部件,其性能退化机理并不明确,揭示其性能退化机理并有效地进行性能退化评估对燃气轮机等长期安全运行具有重要意义.为此,从结构损伤导致性能退化的角度出发,分析拉杆裂纹引起的组合转子性能退化特性.分别建立了组合转子有限元模型和弯曲、扭转刚度模型,利用有限元模型对拉杆上含初始裂纹的组合转子进行裂纹扩展分析,得到拉杆裂纹扩展速率;利用弯曲和扭转刚度模型分析了不同深度的裂纹对组合转子振动的影响,得到组合转子固有频率随裂纹尺寸的变化规律;并提出了衡量由微裂纹导致的组合转子性能退化的度量指标,实现了拉杆裂纹引起的组合转子性能退化的定量评估.研究表明：随着拉杆裂纹尺寸的增大,裂纹的扩展速率变快;拉杆裂纹的存在对组合转子的弯振影响较大,对扭振影响相对较小.     

The spur planetary gear torsional stiffness and its crack sensitivity under quasi-static conditions

The sun–planet and ring–planet tooth mesh stiffness variations and the resulting transmission errors are the main internal vibration generation mechanisms for planetary gear systems. This paper presents the results of torsional stiffness analysis of involute spur planetary gear systems in mesh using finite element methods. A planetary gear model with three planet gears and fixed ring gear and its subsystem models have been developed to study the subsystem and overall torsional stiffnesses. Based on the analysis of torsional mesh stiffness, predictive models for single branch sun–planet–ring and overall planetary gear torsional stiffnesses have been proposed. A crack coefficient was introduced to the sun–planet and ring–planet meshes to predict the effect and sensitivity of changes to the overall torsional mesh stiffness. The resulting mesh stiffness crack sensitivity of the overall gear system was analysed under quasi-static conditions. It was found that the carrier arm stiffness has great influence on the crack sensitivity while the overall stiffness was most sensitive to the crack on the sun–planet mesh.     

An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack

When a tooth crack failure occurs, the vibration response characteristics caused by the change of time-varying mesh stiffness play an important role in crack fault diagnosis. In this paper, an improved time-varying mesh stiffness algorithm is presented. A coupled lateral and torsional vibration dynamic model is used to simulate the vibration response of gear-rotor system with tooth crack. The effects of geometric transmission error (GTE), bearing stiffness, and gear mesh stiffness on the dynamic model are analyzed. The simulation results show that the gear dynamic response is periodic impulses due to the periodic sudden change of time varying mesh stiffness. When the cracked tooth comes in contact, the impulse amplitude will increase as a result of reductions of mesh stiffness. Amplitude modulation phenomenon caused by GTE can be found in the simulation signal. The lateral–torsional coupling frequency increases greatly within certain limits and thereafter reaches a constant while the lateral natural frequency nearly remains constant as the gear mesh stiffness increases. Finally, an experiment was conducted on a test bench with 2 mm root crack fault. The results of experiment agree well with those obtained by simulation. The proposed method improves the accuracy of using potential energy method to calculate the time-varying mesh stiffness and expounds the vibration mechanism of gear-rotor system with tooth crack failure.     

Evaluation of the increased stiffness for the elastic coupling under the dynamic loading conditions in a ship

Torsional vibration is restricted during design because it can cause fatigue fractures of the shaft due to repetitive vibratory torque and should be verified by analytical calculations as well as experiments. Torsional vibration is a characteristic of propulsion systems and is strongly related to their natural frequency; differences between measured and analytically predicted torsional vibration could be caused by variation of parameters related to natural frequency such as stiffness, damping, and components' inertial masses. In this investigation, extreme torsional vibration caused by increased coupling stiffness is expected to be the main root cause of fracture. The variation of coupling stiffness is investigated in a laboratory excitation test in order to determine the root cause of increased stiffness. Torsional vibration analysis error is identified as the main cause, where calculated values are quite different from measured results. It is shown that this difference is caused by torsional stiffness differences between the cases of the analytic model and the real ship.     

双跨柔性转子--轴承系统动力学理论与实验研究

建立了一个双跨转子实验台,转轴两端均由滑动轴承支撑并由柔性联轴节相连。一跨转轴附带质量相等的两个圆盘,另一跨转轴附带质量不相等的两个圆盘。首先针对该实验模型建立了非稳态运动力学模型并进行数值计算;其后分别在单跨(双轴承支撑)和双跨(四轴承支撑)转子系统上进行了对比实验研究,揭示升速过程中的油膜失稳现象。计算和实验发现,柔性联结后的两跨转子,其失稳运动存在强烈的相互影响,实验发现了以前未见文献报道的双低频现象。     

The effect of helicoidal cracks on the behaviour of rotating shafts

Fatigue cracks can develop in rotating shafts: their propagation is mainly in planes perpendicular to the axis of rotation, but also slant or helicoidal cracks could appear in industrial machine shafts. In this paper the static elastic behaviour of a shaft affected by a slightly helicoidal crack has been analysed by means of 3D finite element non-linear models, calculating deflections in different load conditions. Differences with respect to shafts affected by planar cracks of same depth and extension are emphasized. In order to simulate the dynamic behaviour of rotating shafts, a simplified model of the elastic behaviour of the cracked shaft has been developed, validated and substituted to the cumbersome 3D model. This model has then been introduced in the model of a power plant turbogroup shaft line in order to analyse its behaviour. The results show the additional vibrations caused by the crack which could be measured in different operating conditions of the group.     

多轴系耦合作用下齿轮系统转子裂纹故障的振动特性研究

为了探究多轴系耦合齿轮系统中的转子裂纹故障与单轴系转子裂纹故障振动响应特性的异同点,基于Jones轴承建模理论,建立滚动轴承的拟静力学模型;利用Timoshenko梁单元建立传动轴的有限元模型;考虑时变啮合刚度、齿轮传递误差、陀螺效应等因素,利用集中参数法建立齿轮副的动力学模型。将轴承、传动轴与齿轮副模型进行集成,建立齿轮系统非线性动力学模型;利用能量释放率理论与应力强度因子为零法分析裂纹转子单元的呼吸效应,利用Newmark-?数值积分法对转子裂纹故障进行动力学仿真,研究转子裂纹故障的振动响应特征。结果表明：与单轴系转子裂纹故障不同,当齿轮系统发生转子裂纹故障时,由于齿轮啮合的引起的耦合效应及转子裂纹引起的呼吸效应,时域响应表现出明显的幅值调制现象,频域中转频及其2倍频幅值增加明显,在啮合频率处伴有明显的边频带。研究结果为齿轮系统转子裂纹故障的监测与诊断提供了理论基础。     

碳纤维复合材料传动轴承扭性能优化设计

利用数值模拟分析的方法研究了铺层角度、厚度、顺序以及对称性对碳纤维复合材料传动轴抗扭性能的影响规律。研究发现结构抗扭截面系数在单向铺层方向为接近0°、45°及接近90°时较高,且随着铺层厚度增加而增大;扭转刚度则在40°～70°较好。在接近0°和接近90°铺层间铺设45°铺层能提高零件抗扭性能;与反对称铺层方案相比对称铺层方案更有利于零件承受扭矩。将优化铺层方案应用在某型号风机传动轴的设计中,试验证明能够满足使用要求并达到节约原材料的目的。     

Parametric study to identify the cause of high torsional vibration of the propulsion shaft in the ship

Since torsional vibration can lead to fatigue failure of the propulsion shaft in a ship, it should be restricted from the first step of the design through calculation and verified at the sea trial test step through measurement. Considering that the torsional vibration of the shaft is a system characteristic, it is strongly related to the vibration modes at the natural frequencies of the shaft. Therefore, the actual torsional vibration problem can occur due to the variation of parameters such as those of the vibration system, including mass of inertia, damping, and stiffness, which differ from the design.In this research, the root cause analysis of the high torsional vibration which occurred in the actual ship is described through a parametric study performed using numerical analysis. Parameters that can increase the torsional vibration of the propulsion shaft are selected, including coupling stiffness, shaft stiffness, coupling damping, and shaft damping. Through the torsional vibration calculations with variations of these parameters, the extent of the effect of these parameters on the torsional vibration of the propulsion shaft is investigated and the cause of the increased torsional vibration is identified.     

Condition Monitoring of Slow‐Speed Shafts and Bearings with Acoustic Emission

Abstract: For various rotating machinery applications, condition monitoring using high‐frequency Acoustic emission (AE) technology has remained a subject of intense study since the late 1960s. This paper demonstrates the results of an investigation for detecting and monitoring natural crack initiation and propagation in slow‐speed rotating machinery with the AE technology. In addition to highlighting previous work published by the authors [ 1 - 3 ] on condition monitoring of slow‐speed rotating machinery, this paper presents experimental results on accelerated bearing fatigue under starved lubricating conditions. For these investigations, purpose‐built test rigs were employed for generating natural degradation on both a bearing and a shaft. It is concluded that crack initiation and propagation on slow‐speed bearings and shafts can be detected with the AE technology.     

U型波纹管的扭转振动固有频率的计算

采用等效的薄壁圆管模型来分析U型波纹管的扭转振动固有频率,为此要确定U型波纹管的等效半径和扭转刚度。等效半径采用两种计算方法。扭转刚度的计算即采用了钱伟长关于旋转壳的扭转刚度积分公式,也采用了等效的圆管模型方法,由此得到的相应的U型波纹管扭转固有频率的计算方法分别称为积分法和简化法。没有关于波纹管扭转固有频率的实验见诸文献。采用有限元法来验证上述计算方法,取得了很好的一致。积分法更为精确,简化法更适于工程计算。     

挠曲轴系横向振动计算及分析

根据某近海拖轮的推进系统,将其轴系进行分析和简化,利用有限元软件ANSYS分别建立正常轴系和挠曲轴系横向振动的计算模型,对轴系的固有频率变化进行分析。通过数值模拟,研究轴系发生弯曲的情况下,轴系的弯曲变形对固有频率的影响。发现挠曲轴系固有频率的大小比正常轴系的固有频率要小,而且随着振动阶数的上升而明显减小。对于其他边界条件的轴来说,也具有相同的性质。这对船舶设计以及航行的安全性具有一定的指导意义。     

An investigation into hybrid carbon/glass fiber reinforced epoxy composite automotive drive shaft

This paper examines the effect of fiber orientation angles and stacking sequence on the torsional stiffness, natural frequency, buckling strength, fatigue life and failure modes of composite tubes. Finite element analysis (FEA) has been used to predict the fatigue life of composite drive shaft (CDS) using linear dynamic analysis for different stacking sequence. Experimental program on scaled woven fabric composite models was carried out to investigate the torsional stiffness. FEA results showed that the natural frequency increases with decreasing fiber orientation angles. The CDS has a reduction equal to 54.3% of its frequency when the orientation angle of carbon fibers at one layer, among other three glass ones, transformed from 0° to 90°. On the other hand, the critical buckling torque has a peak value at 90° and lowest at a range of 20–40° when the angle of one or two layers in a hybrid or all layers in non-hybrid changed similarly. Experimentally, composite tubes of fiber orientation angles of ±45° experience higher load carrying capacity and higher torsional stiffness. Specimens of carbon/epoxy or glass/epoxy composites with fiber orientation angles of ±45° show catastrophic failure mode. In a hybrid of both materials, [±45°] configuration influenced the failure mode.     

Thrust bearing design for high-speed composite air spindles

The air spindles whose shafts are made of carbon fiber composite are appropriate for high-speed and high-precision machining such as small hole drilling of printed circuit board (PCB) or wafer cutting for manufacturing semiconductors because the carbon fiber composite shaft has low rotational inertia, high damping ratio and high fundamental natural frequency.

The axial load capability and stiffness of air spindles for drilling operation are dependent on thrust bearings that are composed of air supply part mounted on the housing and rotating part mounted on the rotating shaft of spindle.

Since the stresses induced in the rotating part of thrust bearing by centrifugal force are very high at high-speed rotation, the axial stiffness and load capability of an air spindle should be designed considering the stresses induced by the centrifugal force as well as the natural frequency of rotating shaft to avoid the resonant whip vibration of the spindle.

In this work, the air supply part of a thrust air bearing for a high-speed composite air spindle was designed considering its axial stiffness and load capability. The rotating part of the thin thrust bearing was designed through finite element analysis considering the static and dynamic characteristics under axial load and the centrifugal force during high-speed rotation.     

传动轴的扭振测试结果的分析

从扭振测试系统的构成、扭振角信号的采集及扭振测试系统的实现做了详细的介绍,在对某器件的传动轴进行测试后,通过分析转速和扭振角的关系、加速度和扭振角的关系,从而对测试结果做了有针对性的分析。