Shaft System Research Articles

Vibration damping capacity of a rotating shaft heat treated by various procedures

Abstract Many of today’s rotating shaft systems require the superior stability characteristics of a rotating shaft to prevent system instability. Rotating shaft material properties play a crucial role in the vibration behavior of rotating shaft systems. It is important to control vibrations in the systems because excessive vibration amplitudes can cause inefficiency and system failure. The objective of this study is to investigate the vibration damping capacity of a rotating shaft treated by various procedures (deep cryogenic treatment, induction hardening, hot forging, and conventional heat treatment) in order to see the effects of the treatment procedures. An AISI 4140 steel material for the rotating shaft was selected because it is the most widely used material in industry. The rotating shaft is supported on oil lubricated journal bearings rather than rolling element bearings as used in prior studies by the authors. The results showed that rotating shaft material damping capacity due to treatment processes plays a major role for the rotating shaft systems stability. It is observed that the vibration damping ability of the rotating shaft with induction hardening to dissipate mechanical vibration was superior to deep cryogenic treatment, especially to hot forging and conventional heat treatment processes. Also, the results indicate that the dynamics characteristics of the rotating shafts supported by oil lubricated journal bearings are different to those supported by rolling element bearings.

Temperature evolution on infinite/finite-length cylindrical solids subjected to reciprocating motion heat source

This work presents a physics-based predictive model for temperature rise in cylindrical solids heated by constant-strength, periodic-motion heat source. The heat source motion path, heat transfer boundary conditions and solid dimension are considered in the theoretical model. Analytical solutions to both the infinite or finite length cylinders are constructed with respect to convection and corresponding boundary conditions. Dimensionless controlling parameters are discussed to reveal temperature field evolution. The predicted results in the temperature rise agreed well with the measured data for a Z-direction feeding drive screw shaft system. The proposed model provides an efficient and accurate design tool for engineering calculation and process-parameter planning through inverse analysis.

Coupling dynamic behavior of aero-engine rotor system caused by rolling, pitching and yawing maneuver loads

It is an important embodiment of fighter's comprehensive ability to have high maneuverability. Therefore, it is necessary to study the coupling dynamic behavior of rotor system in typical maneuvering flight. Based on the finite element method, a 6-node rotor-bearing-disk system model with three kinds of maneuvering loads, nonlinear contact force of rolling bearing, eccentric unbalanced force of disk and gravity field is established in this paper, and the dynamic responses of the system under rolling, pitching and yawing maneuvering is analyzed in detail. The Newmark-β method is used to solve the system model. The system responses under different rotation speeds and two given rotation speeds are mainly analyzed. The system responses under three kinds of maneuvering loads are compared and analyzed. Finally, the 7-node stepped shaft system model is used to verify the universality of the analysis results in this paper. It is found that, under the same maneuvering load value, the possibility of rub-impact and frequency division components caused by different flight modes are different. The research in this paper can provide a cognitive basis for the mechanism of system rubbing fault under different maneuvers.

Shafting Torsional Vibration Analysis of 1000 MW Unit under Electrical Short-Circuit Fault

Taking a 1000 MW turbine generator as the research object, the short-circuit fault in electrical disturbance is analyzed. Since it is very difficult to carry out fault analysis experiments and research on actual systems, simulation analysis is one of the more effective means of electrical fault diagnosis; the simulation’s results approach the actual behavior of the system and are ideal tools for power system analysis, and can provide an empirical basis for practical applications. The short-circuit fault model of the SIMULINK power system is built to analyze the two types of faults of generator terminals short-circuit and power grid short-circuit. The impact load spectrum, fault current and speed fluctuation between low-voltage rotors were extracted and analyzed. The conclusion is that the impact value of electromagnetic torque at the generator terminal is greater than that on the power grid side. The impact value of a two-phase short-circuit at the generator terminal is the largest, and that of a three-phase short-circuit on the power grid side is the smallest. The transient impulse current of a three-phase short-circuit at any fault point is greater than that of a two-phase short-circuit; the impulse current of the grid side short-circuit is much greater than that of the generator terminal short-circuit; the speed fluctuation and fluctuation difference caused by the three-phase short-circuit in the grid side are the largest. The alternating frequency of the transient electromagnetic force of the four kinds of faults avoids the natural frequency of the torsional vibration of the shaft system, and the torsional resonance of the shaft system in the time domain of the short-circuit fault will not appear. However, after the fault is removed, the residual small fluctuation torque in the system has a potential impact on the rotor system. This research shows an analysis of the structural integrity and safe operation of turbine generator units after a short-circuit fault, which can not only be applied to engineering practice, but also provide a theoretical basis for subsequent research.

Analysis of Deformations and Von-Misses Stresses of the Main Shaft System in a Load Break Switch

Abstract This paper presents the study of deformations and Von-Misses stresses of the main shaft system during opening and closing operations of a rotary SF6 load break switch (LBS). The shaft consists of three axially connected parts made of steel where components are on ground potential and of plastic material, which is on high potential. The insulating shaft carries three rotating knife-blade contacts for the three phases. Static deformation of the insulating shaft is calculated by applying a defined torque between the two ends of the shaft. The results allow deducing the dynamic deformation. Maximum values of Von-Misses stresses are located at the geared connection between the plastic and the steel shaft. The rotation of the shaft system is measured synchronously by two optical rotary encoders in the front and rear sides of the LBS. The results confirm the twisting of the shaft system and provide its elastic deformation values. Travel curves obtained on both side of the LBS show different courses with respect to overtravel and rebound. Discrepancies can be explained by the deformation of the main shaft due to the acting forces, whereas manufacturing tolerances resulting in loose have a certain contribution.

Modelling and Dynamic Analysis of an Unbalanced and Cracked Cardan Shaft for Vehicle Propeller Shaft Systems

The vibrational behaviour of misaligned rotating machinery is described and analysed in this paper. The model, constructed based on the equations of vehicle dynamics, considered the dynamic excitation of a single Hooke’s joint. The system adopted the breathing functions from a recent publication to approximate the actual breathing mechanism of a cracked driveshaft. The study aimed to understand the transmission of a nonlinear signal from the unbalanced and cracked driveshaft to an unbalanced driven shaft via a Hooke’s joint. The governing equation of the system was established based on the energy principle and the Lagrangian approach. The instantaneous frequency (IF) identification of the cracked driveshaft was extracted based on the synchrosqueezing wavelet technique. To correlate the results, the nonlinear synchrosqueezing wavelet transforms combined with the classical waves techniques were experimentally used in various scenarios for dynamic analysis of the Cardan shaft system. The variations in the dynamic response in the form of a rising trend of higher harmonics of rotational frequency and increased level of sub-harmonic peaks in both shafts were presented as significant crack indicators. The synchrosqueezing response showed breathing crack excitation played a crucial role in the mixed faults response and caused divergence of the vibration amplitudes in the rotor’s deflections. The simulation and test results demonstrated that the driveshaft damage features impacted the transfer motion to the driven shaft and the Hooke’s joint coupling was the principal source of instability in the system. The proposed model offers new perspectives on vibration monitoring and enhancement analysis to cover complex Cardan shaft systems.

Blade damage monitoring method base on frequency domain statistical index of shaft’s random vibration

The shaft vibration based blade damage monitoring method has become another research focus in addition to tip timing technology because of its simple testing system. However, how to extract the accurate and effective blade damage information from the vibration response of the shaft is the key to the implementation of this method. In this paper, a blade damage monitoring method based on the frequency domain statistical index of shaft’s random vibration is proposed. Firstly, a continuum dynamic model of blade disk shaft system is established and verified for the statistical feature analysis of rotor system with blade damages, in which the coupling among shaft’s bending, torsion and blade’s bending is considered. Then, base on the vibration response from the dynamic model, a blade damage monitoring method is constructed, in which the harmonic components of forced vibrations are removed, the random vibration component is retained, and the mean frequency and bandwidth index in the resonance frequency band of the random torsional vibration is adopted as the blade damage monitoring index. After that, a blade-disk-rotor system test bed is designed and the vibration measurement system is constructed. The experimental results verify the effectiveness of the proposed methods and indicators. To sum up, the verified dynamic model can provide abundant simulation data under various working conditions and various fault parameters for the research of diagnosis index and methods. The random excitation is inherent in the running rotor system, so the random vibration based blade damage monitoring method is easy to implement. The statistical index based method is a simple and effective way to extract the damage information of blade in random vibration. Therefore, the research results of this paper can provide important supplements to the blade damage monitoring.

Active vibration control of a time-varying shafting system using an adaptive algorithm with online auxiliary filter estimation

An active vibration control method is proposed to attenuate the longitudinal vibration of a time-varying propulsion shafting system excited by the propeller force. In this method, two inertial actuators are mounted symmetrically on the thrust bearing base to suppress the longitudinal vibration, and an adaptive algorithm with online auxiliary filter estimation is applied to consider the time-varying characteristics induced by the longitudinal stiffness of the thrust bearing. The dynamic model of a shaft-foundation coupled system is established to evaluate the active control method, in which the variable longitudinal stiffness of the thrust bearing is expressed explicitly. The proposed adaptive control algorithm is compared to the conventional Fx-LMS method. Numerical and experimental results have demonstrated that the active control method is able to suppress the longitudinal vibration transmission of the foundation of the coupled system with variable characteristics, and compared to the conventional Fx-LMS method, the proposed adaptive control method is effective even in the case of a considerable variation in the control channel as the shaft speed changes continuously.

Method to Evaluate the Impact of Integration of PMSG on Stability of Synchronous Generator Shaft Under Weak Grid Connection

With the continuous growth in the amount of wind power accessed by the AC grid, the impact of the grid connection of wind-power generators with the power system has gradually increased. In this study, the subsynchronous oscillation of a synchronous generator (SG) shaft caused by the integration of direct-drive permanent-magnet synchronous generators (PMSGs) was investigated. The mechanism governing the effect of the connection strength between the PMSG and AC power system on the stability of the generator shaft system was analyzed based on the complex torque coefficient method. When the connection strength between the PMSG and AC power system weakens, the same voltage variation that occurs at the point of common coupling of the PMSG stimulates more intense power fluctuations in the PMSG, and the electrical damping injected by the PMSG into the SG increases considerably. This may cause the oscillation mode dominated by the generator shaft system to move to the right half of the complex plane, thereby reducing the stability of the generator shaft system. In addition, the evaluation process of the influence of the PMSG on the SG shaft system was summarized, and the proposed method can determine the stability of the AC power system after the integration of the PMSG. Finally, the effectiveness of the proposed method was validated via study cases, and conclusions were drawn. This method is expected to serve as a useful tool for the risk assessment of subsynchronous oscillations in wind farms.

Shaft system profile reconstruction method based on L-shaped axial four-probe method

The inability to extract spatial axis and radial multi-error coupling phenomenon exists in the process of axial profile reconstruction, which is essentially a first harmonic suppression problem as well as a multi-error decoupling problem. In this paper, a four-probe system is constructed based on an L-shaped arrangement in two adjacent planes. First, the mathematical model of the first harmonic suppression problem of the shaft system is established in the first plane, and the first harmonic component of roundness error is used as the axial reference for reconstructing the profile, and the value of the first-order harmonic component is solved by theoretical derivation, and the spatial axis of the reconstructed shaft system profile is fitted with it, which proves the correctness of the established mathematical model by the data simulation. Then, the radial mixed error detection is carried out in two adjacent planes in the axial direction, and the results measured at the two measurement positions are analyzed theoretically to obtain the tilt error decoupling formula. It breaks through the limitation that the error separation online detection cannot be performed in the standard ball measurement method. The experiment verifies that the accuracy of the spatial axis is improved by up to 0.5 μm after decoupling the tilt error, and the accuracy of the reconstructed circularity profile of a single section is improved by up to 2.657 mm. In the comparison experiment with the standard ball measurement method, the difference of the measured roundness error between the two methods does not exceed 1.2 μm, which proves that the online inspection method proposed in this paper can guarantee the accuracy of the reconstructing circularity profile.

Study of Effective Parameters in Stability and Vibration of Marine Propulsion Shafting Systems

The marine propulsion system is a system that a ship depends on in travelling and maneuvering in the existence of different types of waves, which reduce the efficiency of the system. In this work, different types of vibration such as torsional, lateral and longitudinal and their effect on ship and propulsion system are studied. Vibration seriously threatens the reliability and safety of the ship. The finite element method is established to study vibration at different rotational speeds. In this work vibration, analysis and modeling with simulation for cases of lateral and torsional vibration are performed by using MatLab software. In addition, ANSYS 2019 R3 is used to study some cases of marine propulsion system. In this work, effective parameters that play important role in vibration reduction such as the diameter, stiffness, couple unbalance and mass unbalance are discussed. The results of that analysis provided can help to predict the problems. In general, to achieve better stability and safety, all the conditions of the propulsion system must be taken into account to diagnose the problem. Hence, the data which are provided in diagrams and tables can be used as a guide in the design stage or maintenance stage to treat system problem and then take the proper action.

Investigation of dynamic behavior of Hollow Rotor Shaft System through FEM

Generally, there is two kinds of rotor system used for transforming the power from one source to another, one is solid rotor system, and another is the hollow rotor shaft system. In comparison to solid shaft, the hollow shaft is of less weight, for a given diameter and length. In addition, the hollow shaft has a larger Strength to weight ratio and has a greater polar moment of inertia. Thus, they can transmit more torque compared to solid shafts. The main purpose of this paper is to analyze the dynamic behavior of hollow shafts with a particular interest in estimation of damping. This study also evaluate the dynamic response of different rotor thicknesses at various speeds where hollow shafts and solid shafts modelled through ANSYS 16. The proposed analysis performed in both frequencies as well as time domains, in which the Campbell diagram, the critical speed, and the orbits are numerically determined. Further, this study also illustrates the convenience of the hollow shafts at different inner diameters for rotor dynamics applications. The analytical results (ANSYS 16) were validated through the experimental results.

Test and simulation for the airtightness of backdraft dampers in residential cooking exhaust shaft systems

PM2.5 emissions from cooking are harmful to human health, and kitchen ventilation is an effective method to reduce the PM2.5 concentration. Cooking exhaust shaft system is a ventilation system widely used in kitchens of residential buildings. However, there is a reverse flow of cooking emissions and odor migration in cooking exhaust shaft system because of the air leakage of backdraft dampers. The aim of this paper is to quantify the airtightness of backdraft dampers and their effect on air quality. There are two types of backdraft dampers widely used in residential cooking exhaust shaft system in China. The blade of one type of damper has two bearing points on the frame and the other type of damper has one bearing point. A total of 40 backdraft dampers (20 Two Bearing Points and 20 One Bearing Point dampers) were selected to test airtightness. Test results show that the airtightness of the 40 backdraft dampers varies greatly, with the air leakage ranging from 7 m3/(h·m2) to 846 m3/(h·m2) at a static pressure difference of 250 Pa. Of the 40 dampers, only 18 One Bearing Point dampers have air leakage lower than 366 m3/(h·m2) specified in ASHRAE Standard 90.1–2016. It is recommended that the One Bearing Point dampers should be utilized in the residential cooking exhaust shaft system. Using the poor, medium, and good One Bearing Point dampers in residential cooking exhaust shaft system for different floors, the air leakage of the closed backdraft dampers is simulated, and the result is 0.6 m3/h ~8.0 m3/h with different rates of simultaneous use. These air leakages may cause the PM2.5 concentration in non-cooking kitchens to exceed the WHO Interim Target-1 of 35 μg/m3. It is suggested a stricter airtightness standard of backdraft damper should be formulated, and the air leakage of backdraft damper should not be greater than 1/5 of the ASHRAE standard specified value.

A novel geometric model of breathing crack and its influence on rotor dynamics

The present research focuses on performing the dynamic study of a cracked, internally damped, composite rotating shaft system with journal bearing end supports. A novel mathematical formulation is proposed to introduce a time-varying stiffness matrix for simulating the breathing behaviour of the crack. The random search algorithm is used as one of the metaheuristic processes to carry out the optimization and generate time-dependent geometric parameters of the cracked surface for one full rotation. The derived stiffness matrix is used in the composite shaft’s higher order motion equation obtained through equivalent modulus theory, whose internal damping properties are incorporated using operator-based viscoelastic model. Eigenanalysis is carried out to perform a thorough study of dynamic characteristics of cracked shaft considering the crack depth and crack position as two important parameters. The effect of crack on stacking sequence as well as mode shapes of the heterogeneous laminated shaft is also studied.

Application of Deep Reinforcement Learning to Predict Shaft Deformation Considering Hull Deformation of Medium-Sized Oil/Chemical Tanker

The enlargement of ships has increased the relative hull deformation owing to draft changes. Moreover, design changes such as an increased propeller diameter and pitch changes have occurred to compensate for the reduction in the engine revolution and consequent ship speed. In terms of propulsion shaft alignment, as the load of the stern tube support bearing increases, an uneven load distribution occurs between the shaft support bearings, leading to stern accidents. To prevent such accidents and to ensure shaft system stability, a shaft system design technique is required in which the shaft deformation resulting from the hull deformation is considered. Based on the measurement data of a medium-sized oil/chemical tanker, this study presents a novel approach to predicting the shaft deformation following stern hull deformation through inverse analysis using deep reinforcement learning, as opposed to traditional prediction techniques. The main bearing reaction force, which was difficult to reflect in previous studies, was predicted with high accuracy by comparing it with the measured value, and reasonable shaft deformation could be derived according to the hull deformation. The deep reinforcement learning technique in this study is expected to be expandable for predicting the dynamic behavior of the shaft of an operating vessel.

Kinematic Analysis and Performance Test of a 6-DOF Parallel Platform with Dense Ball Shafting as a Revolute Joint

To meet the special requirements of the third mirror adjustment system for an optical telescope, a 6-P-RR-R-RR parallel platform using offset RR-joints is designed with high precision, a large load-to-size ratio and high stiffness. In order to improve the adjustment accuracy and the stiffness of the whole mechanism, each rotating joint in the subchain is designed as a zero-gap bead shaft system. When compared with a traditional Hooke joint, the offset RR joint has certain characteristics, including large carrying capacity and easy processing and adjustment, that effectively reduce the risk of interference with the joint during rotation and increase the working space of the entire machine. Because of the additional variables introduced by the offset joints, the kinematics problem becomes much more complicated. Regarding the P-RRRRR series subchain, the kinematics model is established using the Denavit–Hartenberg parameter method and then solved by the numerical iteration method. The stiffness of the parallel platform is analyzed and tested, including static and fundamental frequency. Motion performance testing of the parallel platform is performed.

Vibro-acoustic characteristics of a coupled pump-jet – Shafting system – SUBOFF model under distributed unsteady hydrodynamics by a pump-jet

This study presents the unsteady hydrodynamics of the excitations from a pump-jet running in the wake of a SUBOFF model and the vibro-acoustic characteristics of a coupled pump-jet – shafting system – SUBOFF model under unsteady excitations. The excitations of the pump-jet are obtained by CFD and the vibro-acoustic responses are predicted by coupled FEM/BEM. A mapping method based on radial basis function is established between CFD and structural mesh to apply the distributed pulsation forces on the wet surface of the pump-jet. The effect of the method used to apply the excitation forces on vibro-acoustic responses is investigated by applying distributed or equivalent pulsation forces at different areas of the pump-jet. Modal shapes, transmitted forces, sound radiation power, radiation directivity pattern and panel contributions are reported to illustrate the characteristics of the vibro-acoustic responses and the influence of the method used to apply the excitation forces on the responses. It is seen that the shaft frequency and the longitudinal mode resonant frequency of the shafting system are the typical characteristic frequencies with large magnitude in vibro-acoustic responses of the coupled system. Compared with applying concentrated forces applied at hub or 0.7 R, the responses produced by applying distributed forces on the whole pump-jet present modes and excitation characteristics with more reasonable magnitudes, illustrating the importance of applying distribute forces instead of concentrated forces. Besides, the contribution of the distributed forces on rotor is dominant since the responses of applying distributed forces on the pump-jet and applying distributed forces on rotor are similar.

Optimization of vibration performance of range extender based on structural parameters

In this paper, the simulation model of the range extender system is established to calculate the torsional vibration performance of the shafting system, and the calculation results of the speed nonuniformity and torsional vibration amplitude are obtained. After analyzing the influence of shafting structural parameters on vibration results, the design parameters of torsional damper, flywheel, generator rotor and coupling are optimized through grouping calculation and neural network model based on optimization, so as to improve the vibration performance of shafting.

Estimation of longitudinal excitation of propeller using a novel hybrid method

Due to the limitation of working environment and structure conditions, it is difficult to directly measure the propeller excitation of ship propulsion shafting system. A method based on waveguide function and modal method combining with shafting vibration response measurement was proposed to estimate the propeller longitudinal excitation indirectly. Firstly, a waveguide transfer model for the general structure of the propulsion shafting is proposed that is suitable for estimating propeller excitation from shafting vibration response. Secondly, the longitudinal excitation of the propeller is calculated by measuring the waveguide coefficients of any shaft sections via the proposed hybrid method. Finally, the scheme is verified by a concrete example. The simulation results prove its feasibility and effectiveness for estimating propeller excitation by measuring the shafting vibration response, which provides a novel scheme for accurately grasping the propeller excitation and effectively controlling the vibration and noise of hull structure.

An efficient method for vibration equations with time varying coefficients and nonlinearities

An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.