Shaft System Research Articles

Dynamic analysis of a quasi-zero stiffness vibration isolator in propulsion shaft system

The propulsion shaft system is a vital component of underwater vehicles. The longitudinal vibration transferred from the propulsion shaft to the bearing housing affects the reliability of underwater vehicles and the sensitivity of detection equipment. The quasi-zero stiffness (QZS) vibration isolator has extremely excellent isolation performance, but it has not been applied in propulsion shaft systems yet. This work establishes a propulsion shaft system dynamic model with QZS vibration isolator and proposes a QZS vibration isolator with a wider QZS zone. The accuracy of the proposed vibration isolator force-displacement characteristic calculation model is confirmed by comparing with the ADAMS results. Moreover, the vibrations of the bearing outer raceway and housing are considered in the dynamic model. The dynamic model in this work is verified by an experiment. The bearing housing accelerations and displacements with and without a QZS vibration isolator are compared to show the isolation performance and application possibilities. In addition, a transverse vibrations analysis and a run-up analysis are conducted. This work provides an effective way to isolate longitudinal vibration transferred from the propulsion shaft to housing.

Torsional damper design for diesel engine: theory and application

Abstract Torsional vibration is the primary cause of engine crankshaft failure. Consequently, the reduction of engine vibration is of paramount importance for the enhancement of automotive safety and comfort. However, the lack of comprehensive insight into the damping mechanism of the torsional damper has impeded the effective control of engine torsional vibration. In order to gain insight into the vibration characteristics of the shaft system in an inline six-cylinder diesel engine, an analysis of the system’s behaviour during both free and forced vibration was conducted. A mathematical relationship was deduced between the dimensions, material, operational temperature and damping properties of the silicone oil damper. The objective was to determine the optimal damping and moment of inertia of the damper, with the aim of minimizing the torsional amplitude of the sixth harmonic. The results demonstrate a reduction in the six-harmonic torsional amplitude from 0.32° to 0.14° following the installation of the damper. The mean and relative deviations between the calculated and experimental results are 0.0018° and 0.83%, respectively. To facilitate the design of the silicone oil damper, a software program, Vibsim, was developed based on Visual Studio for the design and torsional vibration analysis of the silicone oil damper. This software is reliable in calculating results and is user-friendly.

Dynamics and stability analysis of unbalance responses in mid‐positioned electrically assisted turbocharger rotor

AbstractElectrically assisted turbochargers (EAT) improve intake efficiency by motor‐assisted compressor impeller rotation, enhancing the system's transient response. However, the addition of motor rotor components has increased the number of unbalanced positions in the shaft system, leading to problems such as excessive compressor end vibration and complex changes in oil film stability. To evaluate the effects of unbalance in the motor rotor, along with the parameters of floating ring bearings (FRB), on the dynamic response of EAT, a finite element model of an EAT rotor supported by nonlinear FRB is developed, and the vibration response of the compressor end bearing is obtained by numerical integration. The results indicate: (1) In contrast to the effect of compressor and turbine unbalance, proper motor rotor unbalance is more effective in suppressing oil whirl instability in the high‐speed operating range. However, a new inner oil film whirl “instability interval” is also induced in the low‐speed operating range, leading to an increase in the Y1 compressor‐end amplitude at low and medium speeds, and this “instability interval” increases with the amount of unbalance. (2) When an oil whirl occurs in the oil film, the maximum eccentricity of the bearing surges and is greater than 0.3, which can be used as an effective threshold for determining whether the oil film is unstable in engineering applications. (3) A suitable outer oil‐film clearance range should be , otherwise, a wide range of outer oil‐film whirl instability occurs. Controlling the amount of unbalance and oil‐film clearance to suppress the sub‐synchronous vibration of the EAT, provides a theoretical basis for the design of the dynamics of the nonlinear rotor bearing system and improves the stability of the turbocharger's operation.

Study on the Effect of Cracks in Diaphragm Couplings on the Dynamic Characteristics of Shaft System

Diaphragm couplings are prone to developing diaphragm cracks under prolonged high-speed operating conditions, which can lead to degradation in the performance of the transmission system and affect the dynamics of the shafting system. To investigate the effects of diaphragm cracks on the dynamics of couplings and the shafting system, a finite element model of a diaphragm coupling with a crack failure is established using ANSYS finite element software to analyze the time-varying characteristics of the diaphragm coupling’s angular and radial stiffness. A shaft dynamics model of the diaphragm coupling with a crack is developed using Timoshenko beam elements to analyze the impact of different crack lengths and locations on the dynamics of the shafting system. The validity of the dynamic model for a diaphragm coupling with a crack is verified through a constant speed experiment conducted on a rotor test bench. The results indicate that diaphragm crack failure causes a change in the periodicity of the time-varying stiffness of the diaphragm coupling, leading to a distinct 2× component appearing in the frequency domain of the transmission shaft system.

Optimizing the bearing vertical offset of a marine propeller shaft system

Optimizing the bearing vertical offset of a marine propeller shaft system

Vibration characteristics of a pretwisted multi-blade-shaft system with blade stiffness mismatch

The substructure mode synthesis method is employed to establish a mathematical model in this paper. The main body is represented by shaft, while the branching components are represented by blades. By solving this model, accurate frequency results of the rotating blade-shaft system are obtained at a high computational speed that meets engineering requirements. The resulting mode diagram aligns with that of the finite element model. Utilizing this model, the stiffness detuning of the rotating blade shaft system is investigated through a combination of surrogate modeling and ant colony algorithm, leading to several significant findings. It is observed that an increase in the standard deviation of stiffness detuning amplifies the length of frequency interval while minimally affecting the frequency mean value. Moreover, an increase in average stiffness expands the interval length for system frequencies. Additionally, higher rotational speeds reduce the interval length for blade-dominant vibrations but extend it for shaft-dominant vibrations.

A novel multi-excitation transient vibration framework for coupling three- and one-dimensional pumped storage hydropower shafting systems

In vibration models of shafting systems, the hydraulic excitation is difficult to characterize due to the complex and changeable hydraulic factors. Thus, hydropower units are not well understood in terms of their dynamics and stability control under transient processes. A hydraulic–mechanical–electric multi-excitation transient vibration calculation framework is developed for analyzing the relationship between shafting vibration and internal flow regimes. First, the boundary data from penstocks, tailraces, and hydro-turbine are interacted with using one-dimensional and three-dimensional (1D–3D) coupling; Second, user-defined function secondary development is applied to achieve two-stage guide vane closure and the runner's variable speed rotation; Third, based on the computational fluid dynamics results, a multi-excitation vibration model is established to analyze shafting system characteristics. There is less than 1.2% error between the algorithm and the field test in terms of speed peak values. Under braking or reverse pumping modes, various vortice clusters are generated in the blade channel as well as the cascade, blocking the flow passage and leading to the runner's unbalanced force. Three sudden increases in vibration amplitudes of the shafting system have occurred in the radial direction under load rejection, each corresponded to the runner's stall rotations. The change trend in axial vibration amplitudes, however, is closely related to the change in axial hydraulic thrust. Furthermore, in braking and reverse pumping conditions, the axis trajectory is more complex under the action of multiple coupling factors than when only hydraulic factors are considered.

Torsional vibration analysis and fuzzy adaptive PID control optimization of underwater vector propulsion shaft systems

To examine the torsional vibration of vector propulsion shaft system (VPSS), a four-degree-of-freedom vibration model of the VPSS is established by concentrated mass approach, and the torsional vibration differential equation of the VPSS is deduced based on the Lagrange approach. The vibration differential equations is addressed numerically applying the Runge-Kutta algorithm to investigate the effect of various working shaft angles β on the free and forced vibration of the VPSS under the excitation conditions. To further reduce the torsional vibration amplitude and avoid fatigue damage of the system, and considering the nonlinear relationship within the system, this study develops a fuzzy adaptive PID approach to control the VPSS. The results show that the maximum torsional vibration amplitude of the VPSS is reduced by more than 70% and the transient response time is shortened by more than 90% with this control approach, which effectively reduces the torsional vibration amplitude of the VPSS and thereby significantly improves the safety performance of the underwater vehicle. This may provide technical references for the vibration control theory of the VPSS as well as engineering applications.

Dynamic characteristics analysis and vibration control of coupled bending-torsional system for axial flow hydraulic generating set

Aiming at the vibration problems of shaft system for axial flow hydraulic generating sets caused by complex excitations, the coupled bending-torsional dynamic equations of rotor-runner system are established considering multi-effect including hydraulic, mechanical, electrical and other external vibration sources. Whether taking the torsional degree of freedom into account, the stability and disparate destabilization laws of system periodic solutions are analyzed using the shooting method combined with Floquet theory. On this basis, the influence of coupling bending-torsional effect on system dynamic behaviors is discussed through bifurcation diagrams, Poincaré maps, trajectories, time domains and frequency spectrums. Furthermore, in order to alleviate the unsteady vibration of rotor as well as runner, the magnetorheological fluid damper is introduced into the shaft system, and numerical simulations are performed on models of coupled bending-torsional systems with or without the magnetorheological fluid damper. The analyses indicate that the interaction between bending and torsional vibration of the shaft system will expand the chaotic sustained range for rotor. Meanwhile, the amplitude of the rotor-runner system is magnified owing to the torsional vibration, which leads to local rubbing faults of the system under specific operating conditions, while the intervention of the magnetorheological fluid damper can significantly suppress the nonlinear motion of rotor and runner, reduce the amplitude of system vibration, so as to avoid the occurrence of friction defects effectively. The above research results can provide conducive references for fault diagnosis, optimized design, and vibration control of axial flow hydraulic generating sets.

A novel 4-DOF marine stern bearing support model considering discrete distribution effects

To address the issue of the traditional support model's inability to accurately describe the non-uniform dynamics behavior inside the bearing, this study proposes a novel 4-degree-of-freedom (DOF) bearing support model that incorporates the discrete distribution effects induced by the bi-directional misalignment and bending deformation of the journal. Additionally, a coupling algorithm is designed to study the interaction behaviors between the marine stern bearing lubrication performance and the shaft dynamics. Moreover, a full-size marine shaft alignment test rig for measuring dynamic bearing loads is designed to verify the validity of the present model. On this basis, the effects of different bearing models, rotational speeds, external loads, and bush elastic modulus on the shaft dynamic alignment and the static and dynamic characteristics of the stern bearing are investigated. The experimental results indicate that the 4-DOF model, which takes into account discrete distribution, exhibits a more precise prediction of the alignment characteristics of the shaft system, with a forecast error for the stern bearing load of 1.32%. Heavy loads or low rotational speeds significantly deteriorate the edge-loading effect and increase the stiffness and damping coefficient of the bearings. The bearing lubrication performance directly affects the alignment performance of the shaft system, particularly in low-speed conditions. A softer bush material can increase the minimum oil film thickness, carrying region, and damping coefficient, mitigate the phenomenon of edge-loading, and facilitate the vibration control of the shaft. Research results have made a great contribution to marine shaft alignment optimization and structure design.

Research on the transient dynamic characteristics of the low-density polyethylene compressors shaft system with operating pressure exceeding 180 MPa

The safe and stable function of hyper-compressors with operating pressures exceeding 180 MPa is a guarantee for the low-density polyethylene production process, and the transient dynamics of the compressor shaft system under stable operating conditions are an important concern for the design, maintenance, and fault detection of such compressors. Therefore, this paper presents a finite-element model of the hyper-compressor shaft system and analyzes the dynamic stress and fatigue life of the crankshaft, the connecting rod, the crosshead, and the plunger. In order to verify the accuracy of the model, all stages of the compressor's plunger stress and the torque of the crankshaft–motor connection end were tested in the field. The dynamic gas pressure of each stage cylinder was obtained by the tested stress of the corresponding plunger, then it was set as the load input of the finite-element model. The results show that: the average errors of the simulated plunger stress at two stages are 0.14% and 0.21%, respectively; the mean, peak, valley, and range errors of the torque at the crankshaft–motor connection end are 3.80%, 12.37%, and 3.49%, respectively; the simulated first-order torsional natural frequency of the shaft system is 78 Hz with an error of 8.3%. In the occurrence of the first-order torsional resonance, the maximum torsional stress appears at the crankshaft–motor connection end. The maximum dynamic stress alternating amplitude of the hyper-compressor shaft system under stable operating conditions is 103.7 MPa with a minimum life of 3.309 × 109, which occurs at the crankshaft–motor connection end and is converted into 31.48 years. The finite-element model, test, and simulation data presented in this paper can provide a reference for the fault detection and optimization design of hyper-compressors.

Effect of AVL-based time-domain analysis on torsional vibration of engine shafting

The torsional vibration of the shaft system in hybrid car engines has a significant impact on the overall performance of the vehicle, and it is more complex in hybrid cars compared to traditional cars. Traditional methods for torsional vibration analysis of shaft systems have significant limitations and cannot handle nonlinear and transient problems. To explore the torsional vibration characteristics of hybrid vehicle shaft systems, a simplified engine shaft system torsional vibration equivalent model is innovatively constructed. In addition, a method for quickly determining the confidence level of the torsional vibration equivalent model is proposed. Additionally, the transient dynamic characteristics of a multi-body dynamics model containing a dual mass flywheel are analyzed in depth using the time-domain solver of AVL-exact PU. The results demonstrated that the simulation of 4th and 6th harmonics resonated at critical speeds of 4,195 rpm and 2,771 rpm, respectively, with angular displacement amplitudes of 0.141 deg and 0.047 deg. In fact, resonance was measured at 4,250 rpm and 3,040 rpm, with amplitudes of 0.14 deg and 0.052 deg. These two were basically consistent in key parameters. When the shaft model was started under operating conditions, the amplitudes of harmonics 1, 2, and 4 were basically consistent below 750 rpm, and there were slight differences after 750 rpm. Therefore, the AVL-based engine torsional vibration simulation model constructed has high credibility.

Research on the Dynamic Response Characteristics of the Propulsion Shaft System with an On-Shaft Generator in Ships

Research on the Dynamic Response Characteristics of the Propulsion Shaft System with an On-Shaft Generator in Ships

Torsional behaviors of motor rotor of permanent magnet semi-direct drive system for aerial passenger device

Considering the influence of motor shaft torsional damping, the torsional dynamics equations of a permanent magnet semi-direct drive rotor system in an aerial passenger device are derived. The derivation relies on the coupling between the mathematical model and the gear dynamics model of the permanent magnet motor, and the Lagrange–Maxwell equations are used for streamlined analysis. To protect the motor under extreme working conditions, the influence of supercritical Hopf bifurcation caused by different torsional dampings of the motor shaft on the torsional vibration of the motor rotor is investigated. Based on the Hurwitz criterion, the influence of the linear control gain and nonlinear gain of the washout filter on the system bifurcation point and the limit cycle amplitude of the system is analyzed. Then, from the perspective of the system instability and oscillation caused by friction damping change of the drive motor and the complex electromechanical coupling behavior in the permanent magnet semi-direct drive cutting drive system of the aerial passenger device, the system stability domain is defined. The results can be applied to effectively suppress the torsional vibration of the shaft system in the permanent magnet semi-direct drive system of the aerial passenger device, providing a theoretical guidance for stable operation of the system.

Optimal transient power sharing method for shipboard MVDC System based on segmented variable step dynamic programming

Supplying power for large pulsed power load with shipboard medium voltage direct current integrated power system has continued to be a challenge. The energy storage device configured in the system can effectively mitigate the power impact on grid and gas turbine gensets, but it also complicates the system operation, requiring advanced power sharing and control strategies for support. In this paper, the control framework of system configured with hybrid energy storage is presented, the objective function to quantify transient power disturbance on gas turbine genset is established, and the segmented variable step dynamic programming method for system transient power sharing is innovatively proposed and employed to derive the optimal transient power-sharing scheme for the rectangular and triangular large pulsed power load conditions. Compared with the conventional approach through MATLAB/Simulink simulation, the scheme derived from segmented variable step dynamic programming demonstrates enhanced utilization of the transient power compensation capability of hybrid energy storage, and leads to a reduction in the power regulation pressure on gas turbine gensets. In the assumption of two typical operating processes, as the results of the power impacts，the transient regulation rate of the genset rotor is reduced from 10.4 % to 9.9 % and from 13.7 % to 8.6 %, respectively, the fatigue damage of shaft system is decreased by 53 % and 94.4 %, respectively, and the maximum inlet relative temperature of gas generator turbine is reduced by 0.015 and 0.139, respectively.

Impact of Installation Deviations on the Dynamic Characteristics of the Shaft System for 1 Gigawatt Hydro-Generator Unit

The shaft system, transferring the kinetic energy of water flow into electrical energy, is the most critical component in hydropower plants. Installation deviations of the shaft system for a giant hydro-generator unit can have significant impacts on its dynamic characteristics and overall performance. In this investigation, a three-dimensional geometry of the shaft system of an operating hydro-generator unit prototype with a rated power of 1 GW is established. Then, the calculation model of the shaft system is generated accordingly with tetrahedral and hexahedral elements. By applying different boundary conditions, the finite-element method is used to analyze the influences of installation deviations, including shaft radial misalignment and angular misalignment, on the dynamic characteristics of the shaft system. The calculation results reveal that the installation deviations change the natural frequencies, critical speeds, and mode shapes of the shaft system to a certain degree. The natural frequencies of the backward precession motion with installation deviations are reduced by 23% and 38% for the rated speed and the maximum runaway speed. Furthermore, for the forward precession motion, they increased by 30% and 48%, respectively. The critical speeds for the shaft system with radial and angular deviations are 3.2% and 3% larger than the critical speed of the shaft system without any mounting deviations. The radial and angular installation deviations below the maximum permissible values will not result in the structural performance degradation of the 1 GW hydro-generator shaft system. The conclusion drawn in this research can be used as a valuable reference for installing other rotating machinery.

Technological Advancements in Oscillation Reduction for Propulsion Shaft Systems

Technological Advancements in Oscillation Reduction for Propulsion Shaft Systems

Vibration analysis of the propulsion shaft system considering dynamic misalignment in the outer ring

Propulsion shaft systems play a crucial role in marine applications, particularly in ships and underwater vehicles. However, existing research often overlooks the dynamics involved in the transmission of vibrations from the bearing to the housing and subsequently to the hull, which affects vibration control in marine equipment. Therefore, this study introduces an enhanced dynamic model for a propulsion shaft system, incorporating the dynamics of the bearing outer ring and housing. The proposed model deduces the deformation relationships between the ball and the inner/outer ring, considering the outer ring translation and swing. The contact force between the outer ring and bearing housing is calculated using conformal contact theory. Timoshenko beam theory is used to develop the shaft dynamic model, while the propeller, bearing components, and bearing housing are represented through the lumped parameter method. To validate the proposed model, an experiment is conducted, demonstrating its accuracy. The study provides analysis of the bearing contact force, shaft dynamics, and bearing housing dynamics. Additionally, the influence of bearing clearances on the shaft and bearing housing dynamics is investigated. The results show that controlling bearing #2 clearance to below 20 μm helps reduce the system vibrations.

Water entry of a sphere moving along a circular path at a constant speed

When a marine propeller rotates in partially submerged conditions, air is entrained from above the undisturbed free-surface, which is called the reference surface, and the ventilated air surrounds the propeller blades, causing thrust loss and excessive vibration, all of which seriously damage the durability of the propeller shaft system of a ship. In the present study, the entry of a propeller blade is simplified by the water entry problem of a sphere moving along a circular path at a constant speed. A high-speed camera was employed to capture the rapidly changing flow structures in detail. Above the reference surface, we focused on the free-surface disturbances, including splash and dome formation. Beneath the reference surface, the development and collapse of ventilated cavities, followed by the line-vortex cavity and cavity undulation, were observed. The ventilated cavity of the present study appears to be more elongated than those of the free-falling sphere's water entry experiments. Two parallel vortical structures appeared after the cavity pinch-off, and bubbles were entrained into these structures to form the line-vortex cavity. The sphere's drag was directly measured via the torque meter attached to the sphere's rotating axis. The relation between the measured drag and the flow around the sphere was identified.

Optimized design of silicone oil torsional damper for diesel generator

Abstract Due to the high cylinder pressure and high-performance requirements, the silicone oil damper of an inline six-cylinder diesel generator needs to be optimized to reduce the crankshaft stress. The centralized mass method was used to simplify the crankshaft system. A multi-body dynamic model was established, and the crankshaft stress and torsional vibration amplitude were simulated. The results show that the excessive shear stress at generator crank pin 5 is due to the resonance between the first-order intrinsic frequency of the shaft system and the 3rd harmonic torsional vibration. The shear stress was analyzed for different damper thicknesses and stiffnesses, and it was found that the shear stress at crank pin 5 was minimized when the damper thickness was 60 mm and the torsional stiffness was 250,000 N·m/rad. The torsional amplitudes at different speeds and frequencies were measured in the bench test, and the results were consistent with the calculations. The designed silicone oil torsional damper meets the requirements of the 2000-hour bench test.