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.

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.

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.

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.

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.

Properties of New Mullite-SiC Bricks for CDQ Shafts

Currently the service life of CDQ shafts in China is mainly restricted by the properties of the inclined flue bricks.In this work,based on the systematic analysis of the damage mechanism of inclined flue refractories,high performance mullite-SiC bricks were developed.The bricks were produced by corundum,andalusite,SiC and other high purity raw materials.Metal silicon and alumina ultra micropowder were added to form dispersion multi-phase structure,fortifying the matrix and improving the microstructure.The products have excellent properties such as low porosity,high density,good wear resistance,high refractoriness under load,and good thermal shock resistance.The products can replace the ordinary mullite-SiC bricks and obtain a good service life.

Analysis of unlined pressure shafts and tunnels of selected Norwegian hydropower projects

Norwegian hydropower industry has more than 100 years of experiences in constructing more than4000 km-long unlined pressure shafts and tunnels with maximum static head of 1047 m（equivalent to almost 10.5 MPa） reached at unlined pressure tunnel of Nye Tyin project. Experiences gained from construction and operation of these unlined pressure shafts and tunnels were the foundation to develop design criteria and principles applied in Norway and some other countries. In addition to the confinement criteria, Norwegian state-of-the-art design principle for unlined pressure shaft and tunnel is that the minor principal stress at the location of unlined pressure shaft or tunnel should be more than the water pressure in the shaft or tunnel. This condition of the minor principal stress is prerequisite for the hydraulic jacking/splitting not to occur through joints and fractures in rock mass. Another common problem in unlined pressure shafts and tunnels is water leakage through hydraulically splitted joints or pre-existing open joints. This article reviews some of the first attempts of the use of unlined pressure shaft and tunnel concepts in Norway, highlights major failure cases and two successful cases of significance, applies Norwegian criteria to the cases and reviews and evaluates triggering factors for failure.This article further evaluates detailed engineering geology of failure cases and also assesses common geological features that could have aggravated the failure. The minor principal stress is investigated and quantified along unlined shaft and tunnel alignment of six selected project cases by using threedimensional numerical model. Furthermore, conditions of failure through pre-existing open joints by hydraulic jacking and leakage are assessed by using two-dimensional fluid flow analysis. Finally, both favorable and unfavorable ground conditions required for the applicability of Norwegian confinement criteria in locating the unlined pressure shafts and tunnels for geotectonic environment different from that of Norway are highlighted.

FATIGUE LIVES FOR INDUCTION HARDENED SHAFTS MATERIALS ACCORDING TO THE ENVIRONMENTAL TEMPERATURES

Rotary bending fatigue tests were carried out with two kinds of materials, S43C and S50C, using the front engine and front drive shaft （FF shaft） of vehicle. The specimens were induction hardened about 1.0mm depth from the specimen surface, and the hardness value on the surface was about HRC56-60. The tested environment temperatures were -30, 25 and 80℃ in order to look over effect of the induction hardening and the environmental temperatures on the fatigue characteristics. The fatigue limit of induction hardened specimens increased more about 45% than non-hardened specimens showing that the endurances of S43C and S50C were 98.1 and 107.9MPa in non-hardened samples, 147.1 and 156.9MPa in hardened samplesrespectably. The maximum tensile and compressive stress on the small circular defect was about ＋250 and -450MPa respectively when circular defect is situated on top and bottom. The fatigue life increased 80, 25 and -30℃ in order regardless of hardening. In comparison of the fatigue lives on the basis of tested result at 25℃, the fatigue lives of non-hardened specimens decreased about 35%, but that of hardened specimens decreased about only 5% at 80℃ more than at 25℃. And fatigue life of non-hardened and hardened specimens were about 110% and 120% higher at -30℃ than that of 25℃. Based on the result of stress distribution near the defect, the tensile and compressive stress repeatedly generated by load direction were the largest on the small circular defect due to the stress concentration.

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 whale 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.

Dynamic Formulations and Beating Phenomena of Rotating Euler-Bernoulli Flexible Shafts

In this paper, the intrinsic behavior of rotating Euler Benoulli flexible shafts was studied due to coupled bending and torsional vibrations. The equations of motion of the shaft with unbalanced eccentricity and viscous material damping were derived by the Hamilton principle. The numerical solution was obtained using the perturbation approach and mode assuming method. The influences of the coupled vibrations between the bending and torsion, the rotating speed, material damping and the slenderness ratio of the shaft were analyzed. It is clearly shown that the beating phenomena can occur when the interaction of torsion and flexure is considered.

Quick determination of gas pressure before uncovering coal in cross-cuts and shafts

The determination of gas pressure before uncovering coal in cross-cuts and in shafts is one of the important steps in pre- dicting coal and gas outbursts. However, the time spent for testing gas pressure is, at present, very long, seriously affecting the ap- plication of outburst prediction techniques in opening coal seams in cross-cuts and shafts. In order to reduce the time needed in gas pressure tests and to improve the accuracy of tests, we analyzed the process of gas pressure tests and examined the effect of the length of boreholes in coal seams in tests. The result shows that 1) the shorter the borehole, the easier the real pressure value of gas can be obtained and 2) the main factors affecting the time spent in gas pressure tests are the length of the borehole in coal seams, the gas emission time after the borehole has been formed and the quality of the borehole-sealing. The longer the length of the bore- hole, the longer the gas emission time and the larger the pressure-relief circle formed around the borehole, the longer the time needed for pressure tests. By controlling the length of the borehole in a test case in the Huainan mining area, and adopting a quick sealing technique using a sticky liquid method, the sealing quality was clearly improved and the gas emission time as well as the amount of gas discharged greatly decreased. Before the method described, the time required for the gas pressure to increase during the pressure test process, was more than 10 days. With our new method the required time is only 5 hours. In addition, the accuracy of the gas pressure test is greatly improved.

CFD simulation of hydrodynamics and mixing performance in dual shaft eccentric mixers

This work aims to systematically study hydrodynamics and mixing characteristics of non-Newtonian fluid(carboxyl methyl cellulose,CMC)in dual shaft eccentric mixer.Fluid rheology was described by the power law rheological model.Computational fluid dynamics was employed to simulate the velocity field and shear rate inside the stirred tank.The influence mechanism of the rotational modes,height difference between impellers,impeller eccentricities,and impeller types on the flow field have been well investigated.We studied the performance of different dual-shaft eccentric mixers at the constant power input with its fluid velocity profiles,average shear strain rate,mixing time and mixing energy.The counter-rotation mode shows better mixing performance than co-rotation mode,and greater eccentricity can shorten mixing time on the basis of same stirred condition.To intensify the hydrodynamic interaction between impellers and enhance the overall mixing performance of the dual shaft eccentric mixers,it is critical to have a reasonable combination of impellers and an appropriate spatial position of impellers.

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.

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.

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.

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.

TORSIONAL OSCILLATION CHARACTERISTICS OF ROTARY SHAFTS BASED ON TORSION AND BENDING COUPLED VIBRATION

弯曲和扭转上的扭力的摆动特征联合了旋转的柄系统的颤动用 elasto 动态的理论和另外的数学方法被调查，例如差别途径， Fourier 变换，和小浪变换。集体怪癖和另外的令人激动的形式影响弯曲，这被结束，扭转联合了旋转的柄的颤动。扭力的颤动由与把颤动弄弯的振幅的变化一起把颤动特征线性弄弯引起了。同时，精力光谱与小浪分析专注于高频率区域。