Eigen value analysis of composite hollow shafts using modified EMBT formulation considering the shear deformation along the thickness direction

Composite hollow shafts are used in power transmission applications due to their high specific stiffness and high specific strength.The dynamic characteristics of these shafts are important for transmission applications.Dynamic modelling of these shafts is generally carried out using Equivalent Modulus Beam Theory(EMBT)and Layerwise Beam Theory(LBT)formulations.The EMBT formulation is modified by considering stacking sequence,shear normal coupling,bending twisting coupling and bending stretching coupling.It is observed that modified EMBT formulation is underestimating the shafts stiffness at lower length/mean diameter(l/dm)ratios.In the present work,a new formulation is developed by adding shear deformation along the thickness direction to the existing modified EMBT formulation.The variation of shear deformation along the thickness direction is found using different shear deformation theories,i.e.,first-order shear deformation theory(FSDBT),parabolic shear deformation theory(PSDBT),trigonometric shear deformation theory(TSDBT),and hyperbolic shear deformation theory(HSDBT).The analysis is performed at l/d_(m) ratios of 5,10,15,20,25,30,35,and 40 for carbon/epoxy composites,E-glass/epoxy composites,and boron/epoxy composite shafts.The results show that new formulation has improved the bending natural frequency of the composite shafts for l/d_(m)<15 in comparison with modified EMBT.The effect of new formulation is more significant for the second and third bending modes of natural frequencies.

Parameter Study on a Composite Sound-Absorbing Structure Liner in Elevator Shafts

With the growing global environmental awareness,the development of renewable and green materials has gained increased worldwide interest to substitute conventional materials and are favorable for sustainable economic development.This paper proposed a novel eco-friendly sound absorbing structure(NSAS)liner for noise reduction in elevator shafts.The base layer integrated with the shaft walls is a damping gypsum mortarboard,and a rock wool board and a perforated cement mortarboard are used to compose the NSAS.Based on the acoustic impedance theory of porous materials and perforated panels,the sound absorption theory of the NSAS was proposed;the parameter effects of the rock wool board(flow resistivity,porosity,structure factor)and perforated panel(perforated rates,thickness,density,perforated diameter)on NSAS absorption were discussed theoretically for absorption improvement,and experiments were also conducted.Numerical results showed that the perforation rate,the thickness of the perforated plate,and the porosity,flow resistance,and volume density of the rock wool board played a key issue in the absorption performances of the NSAS.Experiments verified the accuracy of the proposed theoretical model.Wideband sound absorption performance of the NSAS at frequencies between 500–1600 Hz was achieved in both numerical analysis and experiments,and the sound absorption coefficient was improved to 0.72 around 1000 Hz after parameter adjustments.The NSAS proposed in this paper can also be made of other renewable materials with preferable structure strength and still has the potential to broaden the absorption bandwidth.It can provide a reference for controlling the elevator shaft noise.

Development of a spring analogue approach for the study of pillars and shafts

In civil and mining operations that involve ground excavation and support, the loads are distributed between the ground and support depending on their relative stiffness. This paper presents the development of conceptual single-degree-of-freedom models, which are used to derive equations for estimating displacements and stresses for ground-support interaction problems encountered in pillars in room-andpillar mining(natural support system), and liners for circular vertical shafts(artificial support systems).For pillar assessment, mine-pillar interaction curves can be constructed using a double spring analogy.Additionally, the effectiveness of different support systems can be evaluated depending on their effect upon the mine-pillar system. For shaft design, an initial estimation of the required lining strength and thickness can be readily made based on a double ring analogue. For both problems, the results from the proposed approach compare well with those obtained by finite element numerical simulations.

Scanning Based Induction Heating for AISI 4340 Steel Spline Shafts-3D Simulation and Experimental Validation

This paper presents an investigation of non-stationary induction heating process applied to AISI 4340 steel spline shafts based on 3D simulation and experimental validation. The study is based on the knowledge, concerning the form of correlations between various induction heating parameters and the final hardness profile, developed in the case of stationary induction heating. The proposed approach focuses on analyzing the effects of variation of frequency, power and especially scanning speed through an extensive 3D finite element method simulation, comprehensive sensitivity study and structured experimental efforts. Based on coupled electromagnetic and thermal fields analysis, the developed 3D model is used to estimate the temperature distribution and the hardness profile. Experimentations conducted on a commercial dual-frequency induction machine for AISI 4340 steel splines confirm the feasibility and the validity of the proposed modelling procedure. The 3D model validation reveals a great concordance between simulated and measured results, confirms that the model can effectively be used as framework for understanding the process and for assessing the effects of various parameters on the hardening process quality and performance and consequently leads to the most relevant variables to use in an eventual hardness profile prediction model.

Importance of Geotechnical Investigation for Design and Construction of Shafts over 1000 m Deep

In most cases, copper ore deposits occur at great depths, so the optimization of excavation costs is of utmost importance to identify the most cost effective and productive mining methods, such as block caving or similar methods specifically developed for these deposits. To be able to apply such methods, it is necessary to have a detailed knowledge of the rock mass in terms of its geomechanical, engineering geological and hydrogeological characteristics. This research aims to reduce geological and geotechnical unknowns, analyze in detail the geological environment, and predict geotechnical conditions for the construction of the shaft. This paper uses the example of Borska Reka Copper Deposit, located in Serbia to illustrate the importance of geotechnical investigation to enable best practice in design and construction of shafts that are over 1000 m deep.

EXPERIMENTAL STUDY ON OPEN－DIE COLD EXTRUSION FORMING TECHNIQUE FOR INVOLUTESPLINE SHAFTS

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A methodology for lining design of circular mine shafts in different rock masses

In this study, the finite element numerical modelling of 2D shaft sections in a Hoek–Brown medium are carried out in a non-hydrostatic stress state in an attempt to predict pressures developing around mine shafts. An iterative process of applying support pressure until observing no failure zone around the shaft is used to simulate the required lining support pressure for different shaft models. Later, regression analysis is carried out to find a generic shaft pressure equation representing the rock mass and the stress state. Finally, the developed pressure equation which shows a good agreement with a case study is used in elastic ‘‘thick-walled cylinder" equation to calculate the lining thickness required to prevent the development of a failure zone around the shaft. At the end of the study, a user-friendly object-oriented computer program ‘‘Shaft 2D" is developed to simplify the rigorous shaft lining thickness calculation process.

ON THE REPEATED NATURAL FREQUENCIES FOR TORSIONAL VIBRATION OF SHAFTS

To investigate the repeated frequency condition (RFC) for torsional vibration of shafts’ system, the transfer matrix method was adopted. Firstly, the transfer relationship from the boundary to engaging disks of double shafts’ system(DSS) was constructed. Secondly, the RFC of DSS was deduced out and the methods to select mode shape were presented. Finally, the relationship was extended to multilevel transmission system (MTS), and the RFC of this system was explored. The conclusions is this: 1) the necessary RFC requires the existence of joint engaging couple (JEC); 2) for DSS, the sufficient is the number of boundary transfer factors (f B) larger than 2; 3) the whole system can be split into independent groups, the total multiplicity is the sum of independent solution number of every group, the latter is the number of independent f B=0 inside the group minus 1.

Theoretical analysis of nonlinear vibration characteristics of gear pair with shafts

The circumferential vibration of a gear pair is a parametric excitation caused by nonlinear tooth stiffness,which fluctuates with meshing.In addition,the vibration characteristics of the gear pair become complicated owing to the tooth profile error and backlash.It is considered that the circumferential vibration of the gear pair is affected by the torsional vibration of the shafts.It is important to understand quantitatively the vibration characteristics of the gear system considering the shafts.Therefore,the purpose of this research was to clarify the nonlinear vibration characteristics of a gear pair considering the influence of the shafts using theoretical methods.To achieve this objective,calculations were performed using equations of motion in which the circumferential vibration of the gear pair and the torsional vibration of the shafts were coupled.The nonlinear tooth stiffness was represented by a sine wave.The influence of tooth separation was considered by defining a nonlinear function using backlash and the tooth profile error.For the numerical calculations,both stable and unstable periodic solutions were obtained by using the shooting method.The effect of the shafts on the gear system vibration were clarified by comparing the results in the cases in which the shaft was not considered,one shaft was considered,and both shafts were considered.

Curve Veering in Torsional Systems with Stepped Shafts

In this study, the influence of geometrical parameters on the curve veering phenomenon in a tor-sional system with stepped shaft is investigated. Three approximate solutions including finite el-ement, Rayleigh-Ritz and discretization methods, along with an exact solution are employed to obtain the natural frequencies of the structure. The study reveals that, under specific circumstances, the results obtained by approximate methods are very close to the exact solution. The curve veering behavior is manifested irrespective of the method employed. It is concluded that for the structure studied the curve veering behavior is not because of the approximate techniques used to compute the natural frequencies, and is an inherent behavior of the structure.

Ground Subsidence Following Groundwater Drawdown by Excavating of 500 m Deep Investigation Shafts in Granite Body in Mizunami, Central Japan in 2004-2012

Two 500 m deep investigation shafts were excavating in the granite body in Mizunami, central Japan by JAEA (Japan Nuclear Cycle Development Institute) in 2004-2012. Groundwater with volume of 700 m3 was generally pumping a day to prevent the shafts from submerging in 2012 following the excavating. As a result of pumping the groundwater, the ground water level lowered to 60 m in the borehole with the distance of 200 m from the excavating shafts in 2012. Leveling network extending 2 km × 2 km around the shafts was established to detect the vertical deformation around the shafts in 2004, and precise leveling was done every year. An 18 mm ground subsidence was detected in the benchmark close to the shafts for 8 years in 2004-2012, and time series of subsidence at benchmark was consistent with the groundwater drawdown. The groundwater drawdown and ground subsidence were caused by the pumping ground water in excavating shafts.

On the Bump Tests of Cracked Shafts Using Acoustic Emission Techniques

An investigation about the application of Acoustic Emission (AE) techniques to analyze the dynamic response of different cracked shafts rendered in bump tests is presented in this work. The experimental apparatus devised for this work complies of six shafts with different transverse crack sizes and a high-frequency data acquisition system. The AE signals generated in the bump tests performed on the different cracked shafts are captured by a wideband AE transducer. Those signals are treated by using statistical moments, wavelet transforms, and frequency- and time-domain procedures. A transverse crack of predetermined depth is etched into each shaft. The experimental results show that the values of kurtosis and skewness estimated for the AE signals can be used to identify the crack size.

A Multiscale Reliability-Based Design Optimization Method for Carbon-Fiber-Reinforced Composite Drive Shafts

Carbon fiber composites,characterized by their high specific strength and low weight,are becoming increasingly crucial in automotive lightweighting.However,current research primarily emphasizes layer count and orientation,often neglecting the potential of microstructural design,constraints in the layup process,and performance reliability.This study,therefore,introduces a multiscale reliability-based design optimization method for carbon fiber-reinforced plastic(CFRP)drive shafts.Initially,parametric modeling of the microscale cell was performed,and its elastic performance parameters were predicted using two homogenization methods,examining the impact of fluctuations in microscale cell parameters on composite material performance.A finite element model of the CFRP drive shaft was then constructed,achieving parameter transfer between microscale and macroscale through Python programming.This enabled an investigation into the influence of both micro and macro design parameters on the CFRP drive shaft’s performance.The Multi-Objective Particle Swarm Optimization(MOPSO)algorithm was enhanced for particle generation and updating strategies,facilitating the resolution of multi-objective reliability optimization problems,including composite material layup process constraints.Case studies demonstrated that this approach leads to over 30%weight reduction in CFRP drive shafts compared to metallic counterparts while satisfying reliability requirements and offering insights for the lightweight design of other vehicle components.

Analysis of the Cross-Wedge Rolling Process of Toothed Shafts Made from 2618 Aluminium Alloy

The paper presents the results of a thermo-mechanical analysis of the rolling two stepped shafts.One of the shafts has a toothed step with skew teeth,while the other has a worm winding in the shape of a trapezoidal screw.The shape of the rolling tools resembles that of the tools used in the Roto-Flo rolling method;yet unlike in Roto-Flo,the shafts are hot-rolled and no centres are used to stabilize the position of the workpiece during the forming process.For the calculations made with use of the DEFORM-3D process simulation system it has been assumed that the rolled shafts are made from 2618 aluminium alloy.As a result of the calculations made,it has been found that the toothed stepped shafts can be formed in one pass by means of the cross rolling process.Additionally,the temperature and strain distribution in the rolled product have been determined as well as some data concerning the forces which are necessary for the rolling process have been obtained.

Evaluation of excavation damaged zones(EDZs)in Horonobe Underground Research Laboratory(URL)

Excavation of underground caverns,such as mountain tunnels and energy-storage caverns,may cause the damages to the surrounding rock as a result of the stress redistribution.In this influenced zone,new cracks and discontinuities are created or propagate in the rock mass.Therefore,it is effective to measure and evaluate the acoustic emission(AE)events generated by the rocks,which is a small elastic vibration,and permeability change.The authors have developed a long-term measurement device that incorporates an optical AE(O-AE)sensor,an optical pore pressure sensor,and an optical temperature sensor in a single multi-optical measurement probe(MOP).Japan Atomic Energy Agency has been conducting R&D activities to enhance the reliability of high-level radioactive waste(HLW)deep geological disposal technology.In a high-level radioactive disposal project,one of the challenges is the development of methods for long-term monitoring of rock mass behavior.Therefore,in January 2014,the long-term measurements of the hydro-mechanical behavior of the rock mass were launched using the developed MOP in the vicinity of 350 m below the surface at the Horonobe Underground Research Center.The measurement results show that AEs occur frequently up to 1.5 m from the wall during excavation.In addition,hydraulic conductivity increased by 2e4 orders of magnitude.Elastoplastic analysis revealed that the hydraulic behavior of the rock mass affected the pore pressure fluctuations and caused micro-fractures.Based on this,a conceptual model is developed to represent the excavation damaged zone(EDZ),which contributes to the safe geological disposal of radioactive waste.

Early Treatment Outcome of Humeral Shaft Fracture Non-Union in Adults: Comparative Study of Plating versus Interlocking Nailing

Background: Fractures of humeral shaft in adults are common injuries. Humeral shafts non-union either from late presentation after initial treatment by traditional bone setters or failed non-operative orthodox care is a major problem in this part of the world. This non-union is a major treatment challenge with increased cost of care and morbidity in this part of the world. Humeral shaft non-union can be treated with locked intra-medullary nailing (LIMN) or dynamic compression plating (DCP). Study on comparison of these methods of fixation in this part of the world is scarce in literature search, hence the reason for this study. Objective: The objectives of this study are: (1) to compare early clinical outcome following fixation of humeral shaft fracture nonunion with DCP versus LIMN;(2) to compare the time of radiologic fracture union of DCP with LIMN;(3) to compare complications following fixation of humeral shaft fracture nonunion with DCP versus LIMN. Patients and Methods: This was a randomized control study done for 2 years in which fifty adult patients with humeral shaft non-union were recruited. The patients were grouped into 2 (P = DCP & N = LIMN). Forty five of the patients completed the follow up periods of the study and then analyzed. The P group had ORIF with DCP while the N group had ORIF with LIMN. Both groups had grafting with cancellous bones. Each patient was followed up for a period of 6 months at the time which radiographic union is expected. Any patient without clinical and/or radiographic evidence of union after six months of surgery was diagnosed as having recurrent non-union. The data generated was analyzed using SPSS Version 23. The results were presented in charts and tables. The paired t-test was used while considering p value Result: Forty five patients completed follow up. There was a male preponderance (4:1), right humerus predominated (3:2). Motor vehicular accidents were the commonest cause of the fractures (62%). Most non-union fractures occurred at the level of the middle 3rd of the humeral shaft (60%). Failed TBS treatment was the commonest indication for the osteosynthesis (71%). More patients had plating (53%) compared to 47% who had LIMN. Most patients (93.4%) had union between 3 to 6 months irrespective of fixation type with no significant statistical difference between the union rate of DCP and LIMN (p value 0.06) with similar functional outcome and complication rates irrespective of the type of fixation. Conclusion: This study showed that the success rates in term of fracture union, outcome functional grades and complication rates were not directly dependent on the types of the fixation: plating or locked intra-medullary nailing.

Functional Outcomes of Adult Tibia Shaft Fractures Treated with Solid Intramedullary Nails versus Hollow Nails: A Systematic Review

Introduction: The management of fractures of the tibia shaft is an important aspect of orthopaedic care, and the selection of the surgical method for fixation can substantially impact patient outcomes. The current review aims to compare the outcomes of adult tibia fractures treated with solid nails to those treated with hollow nails. Methods: A search on Scopus, PubMed, and Cochrane Library, using three keywords (Outcome, Tibia shaft fractures, Nail) was conducted in April 2023. Results were compiled and two independent reviewers screened and selected eligible articles After removing duplicates, titles and abstracts were read to exclude ineligible studies. Full-text articles of the remaining papers were read to select eligible studies which were further critically appraised to ascertain their methodological quality. The data extracted from the selected papers were synthesized using a combination of pooling of results, tests of statistical difference (t-test and chi-square) and narrative synthesis methods. Results: A total of 2295 articles were obtained from the databases and citation searching. A total of 9 papers were identified as eligible and included in the review. Findings revealed that there is no statistical difference in the outcomes of tibia fractures treated with either solid or hollow nail groups such as duration of surgery (p = 0.541), rate of delayed and non-union (p = 0.342), and rate of surgical site infections (p = 0.395). Conclusion: Intramedullary nailing of tibia shaft fractures with either solid or hollow nails have similar functional outcomes.

Balancing of flexible shafts: minimizing the maximum residual vibrations in the sense of D-metric

Based on introducing the concept of the metric induced by a set of vectors, as well as minimizing the maximum amplitude of residual vibrations in the sense of this metric, an approach for determining the balance correction for flexible shafts is presented. The advantages of the proposed method are two-fold. Firstly, the approach is available when upper bound con-

Analysis of Transmission Power and Efficiency of Side-Mounted Inductive Power Supply System for Metal Rotary Shafts

The online detection of metal shaft parameters,such as torque,power and deformation,is widely applied in engineering projects.The power supply of metal shafts is the key to the detection reliability and practicality.However,traditional slip ring and battery power supply are limited in reliability and service life.In this paper,a side-mounted inductive power supply system for the rotating metal shaft is designed by using a Utype core.The equivalent reluctance and circuit models of the system are analyzed,and the methods of improving the coupling coefficient and transmission efficiency are proposed from theoretical analysis.Through the finite element simulation analysis of the system,the general relationships between the transmission power and efficiency of the system and the number of coil turns,the working frequency and the load are analyzed.The accuracy of theoretical analysis and simulation analysis is verified by the practical power transmission experiments.This paper provides a novel and reliable power supply method for inductive power supply of rotating equipment,and enriches the solutions of rotating power supply.

Small-diameter vertical shafts constructed in the shallow space of steep mountainous areas

Japan is a mountainous country comprising several islands,in which mountains occupy 70%of the entire land.Therefore,numerous transmission line towers have been constructed in the shallow space of steep mountainous areas.In such construction,monorails and/or cableways are generally used to transport materials and equipment to the construction site instead of using a construction road,as the former method is more economically viable.However,with this method,drill rigs or vertical shaft sinking machines cannot be transported to the site.Four small-diameter vertical shafts of 2.5 or 3.0 m as the foundation for high-voltage transmission line towers in mountainous areas are traditionally constructed manually in Japan.Over the past two decades,however,dangerous and poor environmental conditions for workers regarding the manual construction of these small-diameter vertical shafts have become a major problem.Meanwhile,owing to the poor environmental conditions of small-diameter vertical shafts to be constructed in the shallow space of steep mountainous areas,a decrease has occurred in the number of young workers entering these projects.Namely,the construction of transmission line towers with using the manually traditional small-diameter vertical shafts is becoming difficult in Japan from abovementioned problems.Hence development of a new technology to solve the problems is necessary for Japan’s economic growth.With this knowledge,the authors have developed a new small-diameter vertical shaft construction system,in which workers do not have to enter the vertical shaft during construction,as machines are used instead.The applicability of the proposed system was confirmed by means of the construction of three actual vertical shafts at two construction sites,as well as in factory and field tests.The applicability and details of the final proposed system are summarized in this paper.