Stability Of Shaft Research Articles

Impact of excavation footage on vertical shaft lining deformation and surrounding rock stress in Xiyu conglomerate

The Xiyu conglomerate, which is extensively distributed in Xinjiang, China, presents challenges for vertical shaft construction owing to its poor cementation and low strength. The selection of an appropriate footage length is paramount for ensuring safe construction. Based on the shaft pipeline construction project of the Xinlongkou Hydropower Station on the Kuitun River, this study investigated the impact of footage length on the stability of vertical shafts within the Xiyu conglomerate strata using finite element simulation and measurement data to analyze the lining displacement and change in stress in the surrounding rock. The results show that the excavation footage has little effect on the lining’s horizontal displacement during vertical shaft excavation. A mathematical model was developed to describe how the vertical displacement of the lining varies with the excavation footage and vertical shaft depth. Below a critical threshold, the stress in the surrounding rock cannot be effectively alleviated, leading to a concentration of stress; above that critical threshold, an excessively large excavation increases the load on the surrounding rock. Based on the simulation results and factors such as economic benefits, construction speed, and safety, an excavation footage of 4 m is judged to be appropriate.

Vibration and stability analysis of a spinning shaft with arbitrary boundaries subjected to partial load

This paper deals with the flexural vibration and dynamic stability of a spinning shaft subjected to partial load. Based on the theorem of moment of momentum and the theorem of motion of center of mass, the governing equation of motion for the spinning shaft system is obtained. Four kinds of boundary conditions including pinned-pinned, clamped-clamped, free-free, and elastic supports are considered. The exact whirl frequency equation is derived analytically for different boundary conditions. The obtained model is confirmed by comparing with the results reported in the available literature, and excellent agreement is presented. A numerical investigation is carried out to examine the effects of support stiffness, mass ratio, eccentric distance, and slenderness ratio on the whirl characteristics and stability of the system in terms of the obtained model. The results show that the whirl frequency and critical spinning speed of the system are dependent on these parameters, and the stability is mainly governed by the mass ratio and eccentric distance.

Numerical Analysis on the Unsteady Radial Load on the Shaft of a Large-Scale Dredge Pump Unit

Vibration and fatigue damage of pump shafts has become a prominent engineering problem, indicating the need for higher-quality reliability analysis of the pump unit in the design stage. In this study, the unsteady flow field in a large centrifugal dredge pump was numerically simulated via the unsteady Reynolds-averaged Navier-Stokes (URANS) method with the SST k-ω model. An experiment was carried out to verify the numerical method. The hydraulic radial force on the impeller and the total radial load were calculated based on computational fluid dynamics. The flow field with a double volute was simulated, analyzed, and compared to the flow field with a single volute. The stress of the pump shaft caused by the radial load was also calculated and discussed. The results show that the impeller gravity determines the time-averaged value and fluctuation frequency of the total radial load on the shaft, which must be considered in the shaft stability analysis. The total radial load fluctuating in asymmetric cycle results in stress cycles with different features at different circumferential locations. The application of a double volute effectively reduces the radial load on the pump shaft, which decreases the time-averaged hydraulic radial force by 38% and its fluctuation amplitude by 3%, decreases the time-averaged total radial load by 20% and its fluctuation amplitude by 28% in the design condition, and decreases the local stress at the narrowest shaft section by 44%. A double volute can be applied to weaken vibration and fatigue damage for a pump shaft if it is acceptable for the pump efficiency to be lowered.

A study on the shaft stability and prediction of electromagnetic and NVH characteristics of permanent magnet synchronous machine according to the different pole/slot combination

In this study, electromagnetic noise sources of permanent magnet synchronous motors with 8-pole 9-slot and 12-slot fractional slot concentrated windings were analyzed through finite element analysis, and the radiated noise/vibration levels were compared through structural-acoustic analysis. In addition, the stability of the rotational shaft generated vibration was analyzed. Electromagnetic noise sources are classified into cogging torque, torque ripple, and unbalanced magnetic force. The effect of electromagnetic noise sources on vibration/noise was analyzed in the frequency domain through the electromagnetic-mechanical coupling analysis. The noise level was compared to the electromagnetic noise source characteristics for each frequency using the waterfall diagram, and additional vibration due to mechanical resonance was analyzed using critical speed analysis while taking the rotor's bearing stiffness into account.

Numerical Estimation of Shaft Stability and Surface Deformation Induced by Underground Mining Transferred from Open-Pit Mining in Jinfeng Gold Mine

In this study, a three-dimensional finite difference numerical model of the Jinfeng Gold Mine, including surface topography, ore body, shafts, and main faults, was built to estimate the shaft stability and surface deformation induced by underground mining transferred from open-pit mining. Satellite monitoring data of surface displacement at several points was used to calibrate the numerical model. The sequence of excavation and filling in the simulation was determined according to the mining schemes with appropriate simplification. The distribution of large deformations in simulation is consistent with the cracking areas on the slopes and surface. Besides, shaft deformation in the simulation is small, which is consistent with the reality that there are no large deformations of shafts in the underground mining activities above 30 m level. After the completion of simulated underground mining, the deformations of shafts and surface are generally far less than the critical deformation. Hence, we concluded that the shafts and surface of the Jinfeng Gold Mine can remain stable in the underground mining stage. Overall, the method in the study provides references for the estimation of shaft stability and surface deformation in the underground mining stage of mine transfer from open pit.

Analyzing Support Stability of Deep Shaft Based on Plastic Softening and Dilatancy of Hard Rock Mass

To explore the stability analyses and control methods for surrounding rocks in deep hard rock shafts, this paper is based on field engineering geological surveys and laboratory rock mechanics tests and relies on the main shaft being constructed in the Shaling Gold Mine of China as the engineering background. The quality of the rock mass is evaluated by the Q system, rock mass rating (RMR) and geological strength index (GSI). The mechanical parameters of the surrounding rock mass of the shaft are calculated by using the generalized Hoek–Brown failure criterion, and the main support system is determined based on the rock mass classification system. Based on the finite element method, a two-dimensional plane strain model is constructed to analyze and evaluate the deformation and plastic region range of surrounding rocks for different support systems. On this basis, considering the dilatancy and plastic softening characteristics of hard rock masses, an analytical solution of the stress, strain and plastic region radius of hard rock around shafts in homogeneous media is proposed. Finally, the plastic region of the surrounding rock is measured by the P-wave velocity test method. The results show that after considering the dilatancy and plastic softening characteristics of the rock mass, the numerical simulation, theoretical analytical solution and measured results are basically consistent, and the proposed support system can effectively ensure the stability of the shaft.

Parametric resonance and bifurcation analysis of thin-walled asymmetric gyroscopic composite shafts: An asymptotic study

Nonlinear geometries and cross-sectional asymmetry can be among the most critical contributing factors affecting the performance and stability of composite shafts. The influence of these factors, which should be devoted to particular attention in the design of these systems and have not been investigated yet, are evaluated analytically in this study. The shaft is simply supported, made of orthotropic multi-layers, and spinning at a constant speed. To express the nonlinear system’s behavior, which is due to the large amplitude of the vibrations, it is assumed that the shaft is under the stretching assumption. Moreover, a rectangular cross-section is used to model the asymmetry that results in parametric excitation in the system. To accurately investigate the behavior of composite material, an optimal lay-up is employed. The gyroscopic coupling is included because of Rayleigh beam theory, and Euler’s angles are employed to achieve the angular velocities. The analytical study of the parametrically excited system, obtained by the method of multiple scales, is performed in two categories of resonant and nonresonant cases. In the nonresonant case, the analytical investigation suggests that the asymmetric shaft behaves like a symmetric one therefore, the parametric excitations do not have a significant impact. This claim is confirmed by numerical results. Also, the presence of the gyroscopic coupling and hollowness of the shaft causes the beating phenomenon in the system. However, in the resonant case, the presence of parametric excitation plays a pivotal role. The results also show that under certain conditions and despite the presence of damping, asymmetric balanced rotors can have a nontrivial stable amplitude. This response exists as long as the parametric excitation effects dominate the damping effects. Although damping reduces the vibrations’ amplitude, it can improve the stability of the system and eliminates unstable responses. Furthermore, the time response and frequency response curve of the system is carefully evaluated for various geometric design parameters and operation speed. Depending on the operating speed, the system can experience supercritical or subcritical pitchfork bifurcation. In addition, a detailed description of the system’s Campbell’s diagram, damping effect, and bifurcation is provided. Furthermore, it is proved that internal resonance cannot occur in the system. The accuracy of the analytical responses of the resonant case is compared with numerical ones. Stability of trivial and nontrivial responses is discussed in the time response and phase portrait of the system simultaneously. Finally, in the undamped system, multi-frequency responses are appeared as homoclinic and heteroclinic closed orbits.

Analysis of Point Contact Isothermal Elastohydrodynamic Lubrication Characteristics of a New Type of Trigeminal Universal Coupling for Automobile

This thesis designed a new type of trigeminal universal coupling structure that changes the original surface contact sliding friction into point contact rolling friction. We analyzed the characteristics of isothermal elastohydrodynamic lubrication to ensure new construction on the drive shaft stability, reliability, and durability. First, we established a contact model of the improved new structure and analyzed the isothermal elastohydrodynamic characteristics of the point contact. Then we studied the input shaft frequency, load, deflection angle, and lubrication characteristics. Research indicated that the other being equal, the faster the input shaft frequency could lead to a thicker oil film, a higher oil film pressure, and a higher secondary pressure peak. The higher load could cause the thinner oil film thickness, the lower oil film pressure, the later position where the pressure begins to increase, and the less obvious second pressure peak. The greater deflection angle could bring about the thicker oil film thickness, the higher oil film pressure, the earlier position where the pressure began to increase, and the earlier position at which the secondary pressure peak was located. This phenomenon was more pronounced in the contact center area.

Investigation on operational stability of main shaft of a prototype reversible pump turbine in generating mode based on ensemble empirical mode decomposition and permutation entropy

Investigation on operational stability of main shaft of a prototype reversible pump turbine in generating mode based on ensemble empirical mode decomposition and permutation entropy

Critical Instability Criterion of Large-Diameter Shafts in Deep Topsoil Based on Ultimate Strain Analysis

Shaft stability plays an important role in mine safety. Most of the previous studies focused on the stress analysis of shafts using monitoring data. Since the shaft wall state in the deep topsoil stratum is still not clear, the ultimate analysis method is adopted to study the bearing capacity and the strain of a large-diameter shaft wall in Yanzhou coal mine. First, the bearing capacity of the shaft wall is discovered. The value of the auxiliary shaft, main shaft and ventilating shaft is 22.22 MPa, 22.07 MPa and 21.73 MPa, respectively. Then, the ultimate strain of the shaft wall is obtained; the designed ultimate strain corresponding to those shafts is 1.468‰, 1.458‰ and 1.435‰, while the working ultimate strain is 2.078‰, 1.800‰ and 2.638‰, respectively. Since the working values are greater than the design values, the shaft walls need to be reinforced, which is consistent with the field situation. Finally, numerical analysis based on the finite difference method (FDM) is performed to investigate the evolution process of ultimate strain on the shaft wall. The results show the ultimate strain could provide a theoretical basis for safe service and management of a large-diameter shaft in a deep topsoil area.

Destruction Characteristics and Control Countermeasure of Shaft Surrounding Rock Mass in Complex Geological Environment

Increasing construction depth, changeable failure formations, and redistributed stress conditions inevitably make the mechanical response of mining shaft rock mass complicated. The design method and construction technology of deep shaft need to be perfected urgently. We studied the stability and control method of a main shaft from −930 m located in a deep gold mine. It is concluded that the surrounding rock of the shaft faces conditions including non-high-stressed, high-stressed, and possible instabilities. The failure types include structural plane-controlled failure, deep stress induced failure, rock burst, low confining pressure shear failure, spalling, and frequent conversion of multiple failure. The damages of the surrounding rock mass at −930~−1500 m displayed “ear-shaped” damage, with damage ranges of less than 2.5 m. The shaft temporary reinforcement adopted bolt mResh beam support, in which the length of the bolt was 2.5~3 m, and the row spacing was 1.5 m. The steel type and diameter were determined by the on-site bolt pull test. This temporary support countermeasure plays an important role in preventing shaft deformation and is worth promoting in similar mines.

해외 목조건축물 사례분석을 통한 생활SOC의 목재 적용방안 고찰

Purpose: This study aims to comprehensively analyze the effects of wood, structural problem solving method, carbon reduction, etc. used through overseas wooden construction precedents and use them as basic data to apply Living SOC wood in the future. Method: First of all, the theoretical consideration of the necessity of applying wood or wood structure to Living SOC was conducted. To this end, we reviewed the basic matters on the current status of Living SOC and the use of wood through previous studies. Next, we analyzed the case of overseas wooden buildings that were already completed to actively use wooden codes and wood in the future. Finally, based on the analyzed results, the possibility of wood use and wood painting for Living SOC was verified, and through this, a plan to apply wood for Living SOC in the future was presented. Result: In this study, the possibility of wood use and application to domestic Living SOC projects was verified through the structural possibility of overseas wooden buildings and carbon-neutral characteristics analysis. In most buildings in Korea, structures were mainly used as modern building materials instead of wood, and wood use is still insignificant. However, in developed countries, high -rise wooden buildings are already appearing, which proves structural stability and carbon neutral effects of wooden shafts. Therefore, in the case of Korea, it is necessary to actively revitalize the use of wood and the wooden architecture, focusing on public buildings including Living SOCs, with reference to these advanced cases.

Deterministic and probabilistic basal heave stability analysis of circular shafts against hydraulic uplift

Circular shafts are commonly required for urban development. Their construction often encounters underground water, which can make shafts more prone to hydraulic heave and to soil uplifts which may cause serious accidents. Therefore, the basal heave stability analysis of shafts subjected to a hydraulic uplift is essential to ensure their safety. In this study, deterministic and probabilistic analyses of supported circular shafts in clayey soils subjected to hydraulic uplifts are presented. The effects of the permeability anisotropy coefficient (rk), the soil-wall interface strength coefficient (ri) and the soil tension cut-off coefficient (rt) are discussed. The basal heave safety factor is evaluated by a Finite Element Limit Analysis (FELA). A Stochastic Finite Element Limit Analysis (SFELA) is introduced to perform the probabilistic analyses by coupling the FELA, an adaptive Polynomial Chaos Kriging (PCK), the Monte-Carlo Simulations (MCS), the First Order Reliability Method (FORM) and the Global Sensitivity Analysis (GSA). It is then carried out to get valuable probabilistic results. Several academic cases are considered: (1) effects of rk on the flow vectors, seepage pressures and water head distributions; (2) effects of rk, ri and rt on the shaft stability considering by safety factor and failure probability; (3) importance rank of rk, ri, soil cohesion and friction angle. The results indicate that the permeability anisotropy coefficient, the soil-wall interface strength and the tension cut-off have a remarkable influence on the circular shaft stability when a hydraulic uplift is considered.

A Primary Support Design for Deep Shaft Construction Based on the Mechanism of Advanced Sequential Geopressure Release

The construction of 1500 m depth shaft in Xincheng Gold Mine, China, faces complex stress conditions such as high geostress (>50 MPa), high ground temperature (>50 °C), high water-pressure (>9 MPa), and highly corrosive. Traditional deep shafts excavated by the sinking and lining method cannot adapt to high geostress problems, such as rock bursts and large deformations, etc., in the deep shaft construction process. To avoid and adjust the high geostress induced the rockburst and large deformations, the mechanism of the advanced sequential geopressure release (ASGR) has been proposed for the ground control in deep shaft construction. In this paper, the safe distance between the concrete lining and the shaft excavation face is determined based on the ASGR mechanism, which can provide the space for geopressure release, and primary support based on rock mass quality and numerical simulation was employed to control the geopressure and deformation. A new support scheme for the deep shaft is proposed, using long bolts to restrain severe deformations, metal mesh, and a double reinforcement bar to improve the induced stress distribution. According to the results, the construction scheme of deep shaft has been improved, and the safe support distance of the proposed scheme is determined to be 12 m, with an interval of three excavation cycles. Compared to the original scheme of shaft lining after excavation, the proposed scheme based on the ASGR mechanism can effectively improve the geopressure release and benefit from controlling the rockburst and large deformation of deep shaft induced by high geostress conditions. The stress distribution in the lining is more uniform, and safety factor of the lining is increased to 2.0, which is benefit the long-term stability of deep shaft.

Numerical Modeling on Blasting Stress Wave in Interbedding Rheological Rockmass for the Stability of the Main Shaft of Mine

High rheological property and strong mining disturbance are prominent conditions in deep rock projects, and often present a coupled process to induce rockbursts, collapse and land subsidence. This paper aims to investigate the effect of surrounding rheological rockmass on the main shaft of mine with interbedding structure under coupled blasting stress wave condition. Based on elastic damage theory and the constitutive equation of rheological rockmass, considering the total strain rate in tensor form, a double-rock model was established. The model was then validated by comparing the numerical simulations with the test results. Matlab was used to develop the COMSOL software, allowing numerical simulation of the failure of shaft rock sequentially subjected to this complex loading path. The results from the rheology-impact numerical simulations show that the double-rock rheology was greatly affected by the dynamic disturbance. Under high creep stress and constant impact stress wave, the last failure of the double-rock with higher creep stress is more severe than that of double-rock with lower creep stress. The numerical simulation of the shaft in situ stress was used to predict the collapse of the rheological rockmass with interbedding structure. The preliminary results suggest that one contribution to this phenomenon is likely related to irreversible damage in the rock during the creep-disturbance process. Dynamic disturbance also promoted the failure of the rock near the interbedding structure, but also increased the strain and stress. This may reflect the initial compaction and elastic phase the rock near the interbedding structure related to the large compressive strength of the hard rock during the dynamic disturbance. The numerical results indicate that a circle-shaped spalling damage zone is prone to develop around the shaft with increased time. We discuss the reason for the decreased stress on point A2 near the interbedding structure of the shaft by visco-elastic theory. The results clearly showed insufficient stability of surrounding rockmass, thus the initial design of shaft is not reasonable. This study has important referential significance for main shaft design for similar mines.

Changes in Propeller Shaft Behavior by Fluctuating Propeller Forces during Ship Turning

It is known that a ship’s shafting system can be adversely affected by hull deformation, variations in the engine power, the propeller load, and eccentric propeller thrusts, thereby increasingly affecting the behavior of the shaft’s movement. A deformed shafting system may also lead to a potential risk of bearing damage by causing a change in the local load of the rear part of the after-stern tube bearing of the propeller shaft. With this concern, a series of previous studies were focused on optimizing the effects of hull deformation by securing a proper level of propulsion shaft stability and optimizing the relative inclination angle and oil film retention based on a quasi-static state, that is, Rules for the Classification of Steel Ships and experiences of shipyards. However, despite our efforts to resolve this issue, marine accidents involving stern tube bearing damage have continued to occur under relatively unattended ship motions in a transient state, that is, a quasi-static state that can possibly cause sudden stern flow field changes. Therefore, to improve the stability of the propulsion shaft, it is necessary to understand ship motions and the conditions of shafting systems in a dynamic state and a transient state when the system is designed. From this point of view, this study investigated the effect of changes in eccentric propeller forces on the motion of the propeller shaft in a representative transient state of a 50,000 deadweight tonnage tanker by means of the strain gauge method and a displacement sensor. The research findings demonstrate that propeller thrust fluctuations have a direct effect on the shaft stability by significant changes in the shaft motion that can lead to unbalanced supporting loads on the stern tube bearing. These results clearly reproduce the cause of damage to the ship in which the accident occurred at a reliable level and will be a reference for establishing pragmatic guidelines for preventing damage to similar ships in the future.

Stability of Hydrogen Turbopump Rotor Shaft Axially Self-Balanced

Abstract Controlling the vibration levels of turbopump rotor shafts is a key feature for the reliability of space engines. Turbopump components are exposed to high static and dynamic stress levels, and therefore are particularly sensitive to high-cycle fatigues. Among the numerous dynamic excitations that affect the turbopump, self-induced instabilities are the most critical ones because of the exponential growth rate of vibration levels. These flutter-like phenomena may account for rotor shaft instabilities of turbopumps designed with an axial balancing system (ABS). Such a system is necessary to avoid heavy static loads on bearings and is commonly used in high power turbopumps in the space industry. It consists of a fluid cavity located in the back of a centrifugal compressor. Instabilities induced by the ABS have been studied within the framework of a research and technology program using a reduced scale hydrogen turbopump demonstrator called TPtech. This paper focuses on experimental and numerical analysis of rotor instabilities induced by the ABS. A coupled dynamic model of the rotor shaft and the ABS cavity is presented. It shows instabilities of the rigid rotor axial mode, but also of an axisymmetric rotor mode. This result is consistent with the data acquired during TPtech test campaign. The instability mechanism is complex as it involves the rotor modes, the flow in the ABS cavity, and its acoustic modes. Therefore, TPtech tests performed in representative conditions are valuable. They have permitted tool validation and have provided design rules to prevent occurrence of such phenomena.

A novel evaluation model of shaft stability based on combination weighting method and PROMETHEE II decision-making algorithm

A novel evaluation model of shaft stability based on combination weighting method and PROMETHEE II decision-making algorithm

Effect of Nanoparticle on the Performance of Water Lubricated Journal Bearing

Journal bearings have widespread use in machinery with rotating shafts. Hydrodynamic journal bearings have lubricating fluid present between shaft and bearing to reduce friction and allow smooth operation. The lubricating fluid develops pressure when bearing is in operation and this pressure is used to carry load on the shaft. The commonly used lubricants in the industry are petroleum based synthetic oils. To do away with the disposal issues and toxicity regarding synthetic oils, water is used as the lubricating fluid for this study. The effect of adding nanoparticles to water is studied and a program in MATLAB is developed to determine the characteristics of bearing, namely load carrying capacity, coefficients of stiffness and coefficients of damping for shaft speeds 500 rpm, 1000 rpm and 1500 rpm. It is observed that addition of nanoparticles results in increased magnitude of load carrying capacity and the bearing exhibits high value of damping and stiffness coefficients indicating stability of shaft for every speed.

Sequential stress control and delayed support in deep shaft construction

In constructing hard rock mine deep shafts, the failure caused by high stress is a significant problem. A construction section extending from the -930 m to -1271 m level of a 1527 m deep shaft was selected as a case study. Q, RMR, and GSI rock mass quality classifications of the surrounding rock were obtained to determine the shaft’s maximum unsupported sinking cycle height in different construction sections. The potential failure mode, failure zone shape, and failure depth of the surrounding rock shaft under high stress were then analyzed theoretically, empirically, and by numerical simulation, sequential stress control and delayed support technology was proposed according to the results. The temporary and permanent support timing parameters were calculated and verified by the empirical chart, numerical simulation, convergence-confinement theory, and theoretical formula. Results show that the surrounding rock in all the construction sections from -930 m to -1271 m belongs to the mild or severely pressure squeezed strata. The potential failure mode is stress-controlled, and the failure zone of the surrounding rock is “ear” shaped. Temporary support strengthens the rock mass, improves the shear capacity of surrounding rock, and prevents the broken rock from falling but does not release stress. Permanent support, conversely, cannot bear the stress of surrounding rock. The stress and elastic strain energy in rock mass should be released to the greatest extent possible before installing permanent support; it is not advisable to install it too early. The time and cycle height of delayed permanent shaft support were comprehensively determined to be four days and 16 m, respectively. The numerical simulation and safety factor proof show that the sequential stress control process effectively minimizes stress in surrounding rock and ensures long-term shaft stability.