Nonlinear Dynamic Modeling for a Diesel Engine Propeller Shafting Used in Large Marines

Longitudinal vibration,torsional vibration and their coupled vibration are the main vibration modes of the crankshaft-sliding bearing system.However,these vibrations of the propeller-crankshaft-sliding bearing system generated by the fluid exciting force on the propeller are much more complex.Currently,the torsional and longitudinal vibrations have been studied separately while the research on their coupled vibration is few,and the influence of the propeller structure to dynamic characteristics of a crankshaft has not been studied yet.In order to describe the dynamic properties of a crankshaft accurately,a nonlinear dynamic model is proposed taking the effect of torsional-longitudinal coupling and the variable inertia of propeller,connecting rod and piston into account.Numerical simulation cases are carried out to calculate the response data of the system in time and frequency domains under the working speed and over-speed,respectively.Results of vibration analysis of the propeller and crankshaft system coupled in torsional and longitudinal direction indicate that the system dynamic behaviors are relatively complicated especially in the components of the frequency response.For example,the 4 times of an exciting frequency acting on the propeller by fluid appears at 130 r/min,while not yield at 105 r/min.While the possible abnormal vibration at over-speed just needs to be vigilant.So when designing the propeller shafting used in marine diesel engines,strength calculation and vibration analysis based only on linear model may cause great errors and the proposed research provides some references to design diesel engine propeller shafting used in large marines.

Transient Model for Shafting Vibration of Hydro Turbine Generating Sets

The shafting vibration is closely related to the rotational angular speed.The angular speed of hydro turbine generating sets(HTGS)is rapidly change in fault transient,it maybe reduce the shafting damage.By means of energy analysis,the differential equation of shafting vibration for the HTGS is derived,in which include the equation of generator rotor and hydro turbine runner,it can be applied to transient analysis.Shafting model is transformed into first order differential equation groups,and is combined with the motion equation of HTGS to build integrated model.Various additional forces of shafting are taken as input inspire in proposed model,the generality of model is good.At last,the shafting vibration in emergency stop transient is simulated.

Experimental study on integral axial squeeze film damper to suppress longitudinal vibration of propulsion shafting

This paper aims at investigating the effectiveness of squeeze oil film in suppressing the longitudinal vibration of propulsion shaft systems through a novel integral axial squeeze film damper(IASFD).After designing the IASFD,a propulsion shafting test rig for the longitudinal vibration control is built.Longitudinal vibration control experiments of the propulsion shafting are carried out under different magnitude and frequency of the excitation force.The results show that both IASFD elastic support and IASFD elastic damping support have excellent vibration attenuation characteristics,and can effectively suppress the longitudinal vibration of the shaft system in a wide frequency range.However,IASFD elastic damping support has a more significant vibration reduction effect than the other supports,and increasing the damping of the system has obvious effect on reducing the shafting vibration.For an excitation force of 45 N,the maximum reduction of the vibration amplitude is 89.16%.Also,the vibration generated by the resonance phenomenon is also significantly reduced.

Shafting Coupled Vibration Research Based on Wave Approach

Because of propeller hydrodynamic influence, the shafting vibration is a coupled vibration which includes torsional, longitudinal and whirling vibrations. It is unsuitable to analyze different vibrations of propulsive shafting systems with development of shipbuilding technologies. To overcome the shortages of traditional marine standards, we establish a new numerical model of the shafting coupled vibration. And we put forward shafting coupled vibration calculation to ensure better reliability of main propulsion system. The shafting system is modeled into two sub-systems, a continuous one and a discrete one. Wave approach and transit matrix method are used to investigate displacement and stress fields in continuous and discrete sub-systems, respectively. And vibrations of different modes in both sub-systems are coupled by using dynamic equilibrium and continuity condition to deduce the global equations governing the motion of shafting. The coupling calculation is then used to research the reason of a very large crude carrier(VLCC) stern hull vibration. It is shown by the comparison of the results from both coupling and dependent vibration calculations that vibration in deferent directions will cause deformation in the same mode, which leads to extra stress and displacements on shafting, especially as the resonant frequencies of different vibration modes match each other. This is helpful to prevent ship stern vibration due to poor shafting vibration calculation.

Shafting Alignment Based on Hydrodynamics Simulation Under Larger Rudder Corner Conditions

With the rudder angles getting larger and larger,the moment and force on propeller shafts,which are caused by complex flowing field,become more and more.They influence the shafting alignment greatly.Stress analysis of propeller shafts has been done under increasing rudder corner conditions with complex hydrodynamics simulation for a great domestic liquified natural gas(LNG) vessel,which is with dual propulsion systems.The improved three-moment equation is adopted in the process of dual propulsive shafting alignment.The calculated results show that the propeller hydrodynamic characteristics,which affect dual propulsive shafting alignment greatly,must be considered under large rudder angle conditions.Shafting accidents of Korean LNG vessels are interpreted reasonably.At the same time,salutary lessons and references are afforded to the marine multi-propulsion shafting alignment in the future.

A strategy for strengthening chaotic mixing of dual shaft eccentric mixers by changing non-Newtonian fluids kinetic energy distribution

Efficiently modulating the velocity distribution and flow pattern of non-Newtonian fluids is a critical challenge in the context of dual shaft eccentric mixers for process intensification,posing a significant barrier for the existing technologies.Accordingly,this work reports a convenient strategy that changes the kinetic energy to controllably regulate the flow patterns from radial flow to axial flow.Results showed that the desired velocity distribution and flow patterns could be effectively obtained by varying the number and structure of baffles to change kinetic energy,and a more uniform velocity distribution,which could not be reached normally in standard baffle dual shaft mixers,was easily obtained.Furthermore,a comparative analysis of velocity and shear rate distributions is employed to elucidate the mechanism behind the generation of flow patterns in various dual-shaft eccentric mixers.Importantly,there is little difference in the power number of the laminar flow at the same Reynolds number,meaning that the baffle type has no effect on the power consumption,while the power number of both unbaffle and U-shaped baffle mixing systems decreases compared with the standard baffle mixing system in the transition flow.Finally,at the same rotational condition,the dimensionless mixing time of the U-shaped baffle mixing system is 15.3%and 7.9%shorter than that of the standard baffle and the unbaffle mixing system,respectively,which shows the advantage of the U-shaped baffle in stirring rate.

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.

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.

Beyond p-y method:A review of artificial intelligence approaches for predicting lateral capacity of drilled shafts in clayey soils

In 2023,pivotal advancements in artificial intelligence(AI)have significantly experienced.With that in mind,traditional methodologies,notably the p-y approach,have struggled to accurately model the complex,nonlinear soil-structure interactions of laterally loaded large-diameter drilled shafts.This study undertakes a rigorous evaluation of machine learning(ML)and deep learning(DL)techniques,offering a comprehensive review of their application in addressing this geotechnical challenge.A thorough review and comparative analysis have been carried out to investigate various AI models such as artificial neural networks(ANNs),relevance vector machines(RVMs),and least squares support vector machines(LSSVMs).It was found that despite ML approaches outperforming classic methods in predicting the lateral behavior of piles,their‘black box'nature and reliance only on a data-driven approach made their results showcase statistical robustness rather than clear geotechnical insights,a fact underscored by the mathematical equations derived from these studies.Furthermore,the research identified a gap in the availability of drilled shaft datasets,limiting the extendibility of current findings to large-diameter piles.An extensive dataset,compiled from a series of lateral loading tests on free-head drilled shaft with varying properties and geometries,was introduced to bridge this gap.The paper concluded with a direction for future research,proposes the integration of physics-informed neural networks(PINNs),combining data-driven models with fundamental geotechnical principles to improve both the interpretability and predictive accuracy of AI applications in geotechnical engineering,marking a novel contribution to the field.

Clinical effect of operative vs nonoperative treatment on humeral shaft fractures:Systematic review and meta-analysis of clinical trials

BACKGROUND Whether operation is superior to non-operation for humeral shaft fracture remains debatable.We hypothesized that operation could decrease the nonunion and reintervention rates and increase the functional outcomes.AIM To compare the clinical efficacy between operative and nonoperative approaches for humeral shaft fractures.METHODS We searched the PubMed,Web of Science,ScienceDirect,and Cochrane databases from 1990 to December 2023 for clinical trials and cohort studies comparing the effects of operative and conservative methods on humeral shaft fractures.Two investigators independently extracted data from the eligible studies,and the other two assessed the methodological quality of each study.The quality of the included studies was assessed using the Cochrane risk bias or Newcastle-Ottawa Scale.The nonunion,reintervention and the overall complications and functional scores were pooled and analyzed using Review Manager software(version 5.3).RESULTS A total of four randomized control trials and 13 cohort studies were included,with 1285 and 1346 patients in the operative and nonoperative groups,respectively.Patients in the operative group were treated with a plate or nail,whereas those in the conservative group were managed with splint or functional bracing.Four studies were assessed as having a high risk of bias,and the other 13 were of a low risk of bias according to the Newcastle-Ottawa Scale or Cochrane risk bias tool.The operative group had a significantly decreased rate of nonunion[odds ratio(OR)0.30;95%CI:0.23 to 0.40,reintervention(OR:0.33;95%CI:0.24 to 0.47),and overall complications(OR:0.62;95%CI:0.49 to 0.78)].The pooled effect of the Disabilities of Arm,Shoulder,and Hand score showed a significant difference at 3[mean difference(MD)-8.26;95%CI:-13.60 to-2.92],6(MD:-6.72;95%CI:-11.34 to-2.10),and 12 months(MD:-2.55;95%CI:-4.36 to-0.74).The pooled effect of Visual Analog Scale scores and the Constant-Murley score did not significantly differ between the two groups.CONCLUSION This systematic review and meta-analysis revealed a trend of rapid functional recovery and decreased rates of nonunion and reintervention after operation for humeral shaft fracture compared to conservative treatment.

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.

Coupling Mathematical Model of Marine Propulsion Shafting in Steady Operating State

According to the analysis of the problems about the operation of marine propulsion shafting in steady state,the geometric and mechanical coupling relationships between marine propulsion shafting and oil film of bearings in two-dimensional space are established,and a coupling mathematical model of the marine propulsion shafting in steady operating state is proposed.Then the simulation of a real ship is carried out,and the variation laws of some special parameters such as bearing load and deflection are obtained.Finally,the results of simulation are verified by experimental data of a real ship,which can provide the mathematical model and analysis method for the research on the characteristics of ship propulsion shafting condition in steady state.

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.

Crack Fault Diagnosis and Location Method for a Dual-Disk Hollow Shaft Rotor System Based on the Radial Basis Function Network and Pattern Recognition Neural Network

The crack fault is one of the most common faults in the rotor system,and researchers have paid close attention to its fault diagnosis.However,most studies focus on discussing the dynamic response characteristics caused by the crack rather than estimating the crack depth and position based on the obtained vibration signals.In this paper,a novel crack fault diagnosis and location method for a dual-disk hollow shaft rotor system based on the Radial basis function(RBF)network and Pattern recognition neural network(PRNN)is presented.Firstly,a rotor system model with a breathing crack suitable for a short-thick hollow shaft rotor is established based on the finite element method,where the crack's periodic opening and closing pattern and different degrees of crack depth are considered.Then,the dynamic response is obtained by the harmonic balance method.By adjusting the crack parameters,the dynamic characteristics related to the crack depth and position are analyzed through the amplitude-frequency responses and waterfall plots.The analysis results show that the first critical speed,first subcritical speed,first critical speed amplitude,and super-harmonic resonance peak at the first subcritical speed can be utilized for the crack fault diagnosis.Based on this,the RBF network and PRNN are adopted to determine the depth and approximate location of the crack respectively by taking the above dynamic characteristics as input.Test results show that the proposed method has high fault diagnosis accuracy.This research proposes a crack detection method adequate for the hollow shaft rotor system,where the crack depth and position are both unknown.

An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

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.

Optimal Structural Parameters for a Plastic Centrifugal Pump Inducer

The aim of the study is to determine the optimal structural parameters for a plastic centrifugal pump inducer within the framework of an orthogonal experimental method.For this purpose,a numerical study of the related flow field is performed using CFX.The shaft power and the head of the pump are taken as the evaluation indicators.Accordingly,the examined variables are the thickness(S),the blade cascade degree(t),the blade rim angle(β1),the blade hub angle(β2)and the hub length(L).The impact of each structural parameter on each evaluation index is examined and special attention is paid to the following combinations:S2 mm,t 2,β1235°,β2360°and L 140 mm(corresponding to a maximum head of 98.15 m);S 5 mm,t 1.6,β1252°,β2350°and L 140 mm(corresponding to a minimum shaft power of 63.06 KW).Moreover,using least squares and fish swarm algorithms,the pump shaft power and head are further optimized,yielding the following optimal combination:S 5 mm,t 1.9,β1252°,β2360°and L 145 mm(corresponding to the maximum head of 91.90 m,and a minimum shaft power of 64.83 KW).

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.

Delayed dislocation of the radial head associated with malunion of distal radial fracture: A case report

BACKGROUND Traumatic radial head dislocation(RHD)is a well-described injury in the pediatric population.It is usually associated with an injury to the ulna in Monteggia fracture-dislocation,although it can occur as an isolated injury.Traumatic RHD with ipsilateral radial shaft fracture has rarely been reported.Delayed RHD secondary to the malunion of an isolated radial shaft fracture is extremely rare.CASE SUMMARY We report a 9-year-old boy with limited pronation of the right elbow.The patient was diagnosed with delayed RHD associated with the malunion of a distal radial fracture.Since the annular ligament was disrupted with forearm rotation causing subluxation of the radial head,a modified double-strip Bell Tawse procedure was performed to reconstruct the annular ligament without corrective osteotomy for the malunited site.Four years after surgery,the angulation deformity of the distal radius was corrected with the restoration of the normal curvature of the radius.There was no recurrence of RHD.CONCLUSION Annular ligament reconstruction without corrective osteotomy could reduce RHD and restore the normal curve of the radial shaft in children with delayed dislocation of the radial head associated with malunion of the radial shaft.Annular reconstruction using double triceps tendon strips might be useful for maintaining a more stable reduction by augmenting anterolateral parts.