Stability Of Shaft Research Articles

Simultaneous resonance and stability analysis of unbalanced asymmetric thin-walled composite shafts

The combined effects of asymmetry and geometrical nonlinearity have a serious effect on the stability of composite shafts. These effects, that should be given special attention in the designing of these structure, are revealed in this study. The asymmetry of the shaft is modeled with a rectangular cross-section that makes the shaft transverse stiffness in one plane to differ from the other. This in effect, manifests itself as a parametric excitation of the system. Moreover, the analysis also considers the large lateral amplitude that can produce geometric nonlinearity and stretching of the system. Parametrically excited equations of the motion are obtained by considering the Euler's angles, the anisotropic properties of the constituent material, and employing the extended Hamilton's principle. Non-classical effects such as gyroscopic moment, rotary inertia, and nonlinear couplings due to stretching are also taken into account. However, because of the thin-walled features of the system, the shear deformations and warping effects are ignored. After discretizing the resulting equations, they are solved by employing the method of multiple scales (MMS). To justify/evaluate the proposed model's accuracy, several comparisons are made with various authentic results in the literature. In addition, to verify the results of the MMS solutions, numerical analyses are used based on the Runge-Kutta method. The effects of damping, eccentricity, and asymmetry were examined on the stability of the system. The illustrated results indicated the occurrence of hardening nonlinearity in the system. It was proved that when the rotational speed was in the neighborhood of forward frequency, despite the presence of nonlinear couplings in the equations, axial and torsional vibrations would not be excited. Furthermore, although the asymmetry affected the amplitude and phase of the system, it did not change the frequency of the vibrations and the type of bifurcation. With a fairly good balance, the unstable response of the asymmetric shaft could be easily eliminated, while even an accurate balance could not eliminate the unstable response of the asymmetric one.

Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based on the Applicability Analysis of Leakage Models Using Bulk-Flow Method

Abstract Labyrinth seals are widely applied in the turbomachinery to control the leakage flow through the clearance between stationary and rotating components. The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial to the analysis of the fluid excitation rotordynamics of labyrinth seals. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of seventy-two leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

The stability of shafts under the action of periodic axial loads

The paper presents the investigation results of the harmonic periodic axial loads’ influence on the stability of shaft. Such loads can be appeared during the running of the vessel passing the turbulence zones from the side of the propeller to the shafting. In shafting, the influence of oscillatory motion performed in adjacent part, which is transmitted through the coupling due to longitudinal movements, can be periodic, too. Therefore, the question of the stability of such shafts during rotation is relevant. In this way, the task of such drill-rod study stability has actuality. In this case, the various modes of vibration and stability loss are possible. In this regard, the study was done by developed software, in which a technique of computer simulation of the oscillating motion of considerable length rotating rods under the action of axial periodic loads is implemented. Such software gives the possibility to model the oscillatory motion of rotating rods and determine the parameters by witch the dynamic stability loss of the studying system can occur. Using this software the diagrams with regions of stable and unstable motion of the rotating shaft were drawn for various parameters of the considered system. The process of oscillation is considered in space with account of inertia forces and geometric nonlinearity of the rod. It is shown, that on certain rotational speeds and frequencies of vibro-impact load there are ranges of unstable motion where the run of equipment can inevitably lead to destruction. The obtained results are analyzed. The conclusion about the possibility of running the equipment in certain frequency ranges is made.

Probabilistic basal heave stability analyses of supported circular shafts in non-homogeneous clayey soils

Circular shafts are commonly used to construct accesses to facilitate tunnel boring machine works and can be used as ventilation systems, subway stations or emergency exits. This study presents a probabilistic analysis of supported circular shafts in undrained and non-homogeneous clayey soils to reflect the uncertainty influences of the soil undrained shear strength at the ground surface, non-homogeneity coefficient, unit weight and soil-wall adhesion factor. The basal heave safety factor is evaluated by an axisymmetric lower bound Finite Element Limit Analysis and a probabilistic analysis is discussed using the adaptive Polynomial Chaos Kriging technique-based Monte-Carlo Simulation and a Global Sensitivity Analysis (GSA). After deterministic and probabilistic comparisons, academic cases are performed to get some insights for the following problems: (1) importance of the uncertainty’s consideration; (2) effect of the soil-wall interface; (3) influence of non-homogeneous soils on the circular shaft’s stability. Besides, some sensitivity analyses are conducted to discuss the input random variables importance. Obtained results show that the coefficient of variation, soil-wall adhesion factor and soil non-homogeneity coefficients have a remarkable influence on the circular shaft stability.

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.

Evaluation of vertical shaft stability in underground mines: comparison of three weight methods with uncertainty theory

Evaluation of vertical shaft stability in underground mines: comparison of three weight methods with uncertainty theory

Numerical Modelling of a Void Behind Shaft Lining using FDM with a Concrete Spalling Algorithm

Purpose The aim of the research presented in this paper was to determine the impact of voids behind the lining on shaft stability. Methods This paper presents an example of extending the FLAC3D with the possibility of the simulation of concrete detachment and separation under specific conditions by means of a developed FISH routine. Results The appearance of voids and cavities behind the lining has been repeatedly observed in active shafts in Polish coal mines and can lead to the emergence of tensile forces in the lining. The study included 366 models of shafts using the rock mass properties of typical shale stone, coal, and sandstone found in the Upper Silesian Coal. Practical implications he presented concrete spalling algorithm may be used, especially, for the stability evaluation of locally damaged shaft lining or when there is a suspicion of void behind the lining. Originality/value An important limitation of all continuous methods is the inability (except when using some additional tools) to simulate the rotations of predefined elements (blocks) and their separation from the rest of the object. The concrete spalling algorithm presented extends the capabilities of FLAC3D with the possibility of simulating the detachment and separation of destroyed lining fragments.

Sinkhole Hazard Caused by Inactive Mining Shafts as Illustrated by a Selected Example

Loss of stability of shafts liquidated in the past is a frequent cause of sinkhole creation on the surface. This manuscript presents such a case study. The sinkhole was created shortly after intense rainfall, so it can be assumed that displacement of the rock material in the shaft took place, i.e. the phenomenon of suffusion. One of the research aims was to confirm the assumption about the displacement of rock material filling the shaft on the basis of selected methods of sinking forecasting. Ex post forecast sinkhole creation was conducted using two methods (Bell and finite element method). It was assumed that the material filling the shaft lowered itself to a height determined on the basis of the sinkhole and shaft dimensions. Both methods gave the same results, consistent with the literature . The manuscript also presents a short overview of technologies used for decommissioning shafts and assesses their effectiveness in terms of preventing sinkhole creation. These methods have been used since the nineteenth century until present times. Considering the suffusion phenomenon, the paper proposes a way to drain rainwater from the shaft area, which was another purpose of the work. The necessity to find and verify the ways to secure decommissioned shafts from water is indicated as an important future direction of research.

Geometric stability of stepped shafts by ribbing its surface

The article discusses the technology of manufacturing low-stiff long multistage shafts made of stainless steels. A feature of this technology is the cutting of annular cooling fins on the entire surface of the shaft blank during machining and their use in thermal operations and further to finishing turning. To implement the technology, self-centering steady rests with double rollers were used during machining.

Micro Hierarchical Structure and Mechanical Property of Sparrow Hawk (Accipiter nisus) Feather Shaf

In this study, the real 3D model of the feather shaft that is composed of medulla and cortex is characterized by X-ray computer tomography, and the structural features are quantitatively analyzed. Compression and tensile tests are conducted to evaluate the mechanical performance of the feather shaft and cortex at different regions. The analysis of the 3D model shows that the medulla accounts for ∼70% of the shaft volume and exhibits a closed-cell foam-like structure, with a porosity of 59%. The cells in the medulla show dodecahedron and decahedron morphology and have an equivalent diameter of ∼30 μm. In axial compression, the presence of medulla enhances the shaft stability. Especially, the combined effect of the medulla and cortex increases the buckling strength of the middle and distal shaft by 77% and 141%, respectively, compared to the calculated value of the shaft using linear mixed rule. The tensile properties of the cortex along the shaft axis are anisotropic because of the different fiber structures. As the fiber orientation gradually becomes uniform in the axial direction, the Young’s modulus and tensile strength of the cortex on the dorsal gradually increase from calamus to the distal shaft, and the fracture mode changes from tortuous fracture to V-shaped fracture. The cortex on the lateral shows the opposite trend, that is the distal shaft becomes weaker due to fiber tangles.

Analysis of Cusp Catastrophic Model for Vertical Stability of Drilling Shaft Lining

The vertical stability analysis of the drilling shaft lining has long been a technical problem in the construction of underground space development projects. And the critical depth of vertical stability was a key parameter to judge its stability. To determine this parameter, a simple and practical computational method would be helpful. In this paper, a new vertical stability analysis model of shaft lining structure based on catastrophe theory was proposed. In accordance with the mechanical analysis, the catastrophic instability mechanics was analyzed and a new critical depth of drilling shaft lining was deduced. Further, the rationality and feasibility of the catastrophic calculation model was proved by the numerical simulation results in a case. And the sensitivity of the influencing parameters was also analyzed, which provided theoretic reference for optimization design and guiding security construction. The results implied that catastrophic calculation model, as an alternative method for shaft stability analysis, could be applied to theoretical analysis and guiding engineering practice in the study of drilling shaft lining’s vertical stability.

Comparison of semicircular and bent tips regarding regional differences in oscillation amplitude under various torsional power settings.

To analyze the difference between the behavior of semicircular (balanced) and bent (mini) tips at 20 incremental torsional power settings. Tsukazaki Hospital, Himeji, Japan. Experimental study. Using an ultra-high-speed video camera HPV-X2, the 2 tips during torsional oscillation were recorded, comparing tip behavior at power settings from 5% to 100% by tracking points 1 to 5 (tip end and at 1325, 2650, 3975, and 5035 μm from the tip end). Both tips increased their amplitude widths, drawing an S-curve at all points as the torsional power setting was increased, reaching their upper limits from 70% to 90% torsional power. At all 20 power settings, both tips showed significantly different amplitudes (all P < .01), and the difference of the amplitude increased as the power setting increased. Although, at points 1 and 3, the balanced tip amplitude was nearly 1.5 times larger than the mini tip amplitude, the amplitude difference was 10 μm or less at points 2 and 4. At point 5, the mini tip amplitude was at least 3 times more than the balanced tip amplitude. The amplitude does not increase proportionally and varies markedly with the tip shape on reaching the upper limit, suggesting that a higher power setting might not contribute greatly to nuclear fragmentation. The balanced tip might cause greater damage to surrounding tissues if it is inserted at approximately 3 mm from the wound site. To obtain maximum shaft stability using the balanced tip, it is important to insert at least 5 mm.

Research on the Pump Shaft Stability Analysis of Multistage Centrifugal Pump During Closed-Valve Start-Up Process

In order to analyze the pump shaft stability of multistage centrifugal pump during the closed-valve start-up process, the transient internal fluid field and structural field during the closed-valve start-up process of the TDM 35-140×13 segmental multistage centrifugal pump are solved by transient fluid-solid coupling. The transient deformation and vibration velocity of the pump shaft are analyzed. It is found that the maximum deformation amount of the third stage impeller and the pump shaft cylindrical contact surface (N=7 node area) during the whole closed-valve transition start-up process is the largest. The maximum deformation in the region where the nodes 1≤N≤10 are significantly greater than that in other regions. In the 11≤N≤19 node, with the node position coordinate value N increasing, the maximum deformation amount is continuously decreasing. During the entire closed-valve transition start-up process, the vibration speed of the pump shaft fluctuates drastically. In the node of 1≤N≤19, with the node position coordinate value N increasing, the maximum vibration velocity first increases and then decreases. The maximum vibration speed at N=11 nodes is higher than that of all other nodes.

Stability Analysis of Composite Shafts Considering Internal Damping and Coupling Effect

A mathematical model is proposed to analyze the stability of composite shafts, considering the internal damping, transverse shear deformation and Poisson’s coupling effect at the same time. The strain–displacement relations are described using the Timoshenko beam theory, and the strain energy and kinetic energy are expressed using the weak form quadrature element method (QEM), for which each nodal point has 4 degrees of freedom. Then, the motion equation of the system is established using the Lagrange equation. The instability thresholds of the composite shaft are determined using the proposed model. The results were compared with those calculated by the equivalent modulus beam theory (EMBT), equivalent single layer theory (ESLT) and simplified homogenized beam theory (SHBT). Good agreement has been achieved. Therefore, the proposed model can be effectively used for the dynamic analysis of composite shafts.

Analysis of belt bridge mode and blasting vibration response spectrum in a mine

With the wide application of blasting technology, people pay more and more attention to the impact of blasting vibration on the surrounding environment and buildings. To blasting vibration analysis and evaluation of the effect on the stability of the skip shaft, belt bridge based on the large finite element analysis software ANSYS Workbench entity unit model, the belt of the bridge structure modal frequency and applying 2 cm/s numerical simulation of blasting vibration load was the response of the study. The calculation results show that the maximum stress value is 0.0063 MPa, belt bridge in belt bridge at the top of the column, in the concrete design tensile strength of 1.43 MPa. The maximum strain of the belt bridge is 5.05×10-8, which is within the allowable elastic deformation range of the building, and is far less than the ultimate tensile strain of C40 concrete 1×10-4. The skip well is in a stable state.

Deformation Failure Mechanism of Deep Vertical Shaft in Jinchuan Mining Area

Vertical shafts play an important role in the safe operation of mines. The stability of vertical shafts has always been a difficult problem in mining engineering, especially with the increasing of mining depth. In order to keep the engineering works stable, it is necessary to make the deformation failure mechanism of vertical shafts clear. This paper describes a case study of the deformation and failure mechanisms of the vertical shaft in Jinchuan No. 2 mining area in Gansu Province, China. Long-term deformation trends and characteristics of the vertical shaft are analyzed through ground movement and GPS monitoring of ground fissures. Then, based on previous research experience and a detailed field investigation, the modes, influencing factors, and mechanisms of deformation failure in the vertical shaft are studied. To further investigate the mechanism of shaft deformation failure and damage process under mining, the Universal Discrete Element Code (UDEC) software with Trigon approach is employed to build the numerical model of the vertical shaft. Through displacement, stress, and damage analysis, the time, location, and cause of vertical shaft failure during mining are explicitly illustrated. The results suggest that the upper and lower parts of the fault are activated in different ways. The damage to the vertical shaft is still developing at a very high rate under mining with filling method. All our results throw light on the nature of deformation and failure of vertical shafts, and several suggestions for the engineering of deep vertical shafts are finally put forward, providing a reference for other engineering.

Investigation of stress field parameters at deep horizons of the Gayskoye field**

The extraction of solid minerals is associated with the penetration of man into the subsoil by creating either relatively simple or extremely complex structures. All mining operations can be safely and efficiently carried out only on the basis of calculating the stability of these structures, which is based on knowledge of the physical and mechanical properties, the stress state of the rock mass and the patterns of their redistribution and formation in mountain structures. The presented studies confirmed the regularities of the formation of natural stresses in the rock mass, which is the sum of gravitational, static tectonic and variable components, which are formed as a result of uniform periodic volumetric expansion and contraction of the Earth. The problem of shaft stability is due to the need to solve problems to determine the level of stress-strain state and strength properties in concrete lining. The parameters of stresses in the shaft lining and monitoring of their changes were determined using the method of measuring unloading deformations. When analyzing the stresses obtained experimentally by analytical means in the concrete lining of mine shafts, a connection was established with the results of measurements in the rock mass on the basis of 50 meters. Based on the experiment, it was confirmed that theoretical and experimental studies prove that a hierarchically blocky massif of magmatic and metamorphic rocks behaves as an elastic and isotropic medium and changes in natural stresses in the massif Δ on the basis of 5-7 ranks of geoblocks, on the contour of the trunk based on 2 –3 ranks of geoblocks and in the concrete lining of mine shafts Δσb obey this law.

Evaluation on the Stability of Vertical Mine Shafts below Thick Loose Strata Based on the Comprehensive Weight Method and a Fuzzy Matter-Element Analysis Model

Damage to mine shafts located below thick loose aquifers, caused by coal seam mining, can seriously affect the operational safety of mines. In view of such a problem, the comprehensive weight method and the fuzzy matter-element analysis method were used to analyze and evaluate the stability of mine shafts below thick, loose aquifers. Based on data relating to shaft structure parameters collected from fifteen damaged shafts in coal mines in East China, a comprehensive analysis was performed. The results showed that (1) the two indexes of surface subsidence velocity and water level drop value at the bottom of a loose aquifer have a large influence on the stability of shafts below thick loose aquifers, and (2) the predicted results of thirteen sets of samples were the same as the results measured during actual production; the accuracy of the model was 86.67%. The comprehensive weight method and the fuzzy matter-element analysis model both show good reliability for evaluating the stability of mine shafts below thick loose aquifers and can provide a scientific reference for the analysis of the stability of mine shafts in areas with thick loose strata, as well as for the design of comprehensive control plans that could subsequently be implemented.

Double-rotator and valve plate distribution radial piston pump

PurposeThe drive shaft and the distribution shaft of a traditional radial piston pump are in a cantilever state. To solve this problem, this paper aims to present a radial piston pump with through shaft driving and valve plate distribution.Design/methodology/approachThe working principle of the pump is discussed in detail. In this radial piston pump, valve plate distribution parts are designed to distribute oil to the piston chambers, and the distribution shaft is replaced. A bearing is installed between the stator and rotator to reduce the friction. The transmission shaft is supported by two bearings to ensure smooth operation. The support force of the transmission shaft is optimized. In addition, the flow pulsation principle is presented. To accomplish the change, the displacement of the radial piston pump, the proportional control system is designed.FindingsAfter completing the machining and assembly of the pump, an experimental study was carried out. The results show that the output flow of the pump is basically the same as the theoretical flow.Originality/valueThe friction between the slipping shoes and the stator is greatly reduced due to the function of rolling bearings. The higher stability of the driveshaft is obtained for the reason of double-sided support. The radial piston pump has a novel structural design in reducing the friction between the shoes and the stator and improving the stability of the transmission shaft.

Safe zone for lateral pin placement for external fixation of the distal humerus

External fixation is a common, efficient technique used for humeral shaft stabilization and elbow fractures. There are reports of radial nerve injuries associated with this procedure. In this study, we investigated the course and variability of the radial nerve along the lateral humerus in relation to the elbow joint to determine a relatively safe zone for lateral pin placement in external fixation. Twenty upper extremities from 10 cadavers were studied. The nerve branches and course of the radial nerve along the lateral humerus were carefully dissected. Straight lines (a, b, and c) were made connecting three landmarks (the acromion, coracoid process, and anterior wall of the axilla) in the proximal upper extremity to the lateral condyle (LC) of the humerus; their intersections with the radial nerve (A, B, and C) were marked. We analyzed whether the intersection positions were correlated with the connecting line lengths. The mean lengths of the connecting lines were (a) 27.24 ± 2.57, (b) 26.18 ± 2.79, and (c) 20.95 ± 1.44 cm; the distance between the intersection points and the LC of the humerus were (Aa) 7.56 ± 1.31, (Bb) 6.90 ± 2.27, and (Cc) 5.01 ± 0.83 cm; and the measured intersection points of the radial nerve in the lateral aspect of the humerus were (A) 18.48%-34.82%, (B) 13.48%-40.00%, and (C) 19.27%-28.05% of the lengths of lines a, b, and c, respectively. Our data provide a more reliable reference to predict the course of the radial nerve on the lateral humerus and define a safe zone for pin placement. Clin. Anat., 33:637-642, 2020. © 2019 Wiley Periodicals, Inc.