Torsional Deformation Research Articles

An explicit nonlinear model for large spatial deflections of symmetric slender beams

Flexible slender beams are commonly used in compliant mechanisms and continuum robots. However, the modeling of these beams can be complicated due to the geometric nonlinearity becoming significant at large elastic deflections. This paper presents an explicit nonlinear model for large spatial deflections of a slender beam with uniform, symmetrical sections subjected to general end-loading. The elongation, bending, torsion, and shear deformations of the beams are modeled based on Timoshenko’s assumptions and Cosserat rod theory. Subsequently, the nonlinear governing differential equations for the beam are derived from the quaternion representation of the rotation matrix. The explicit load–displacement relations of the beam are obtained using the improved Adomian decomposition method. This method is superior to the classical Adomian decomposition method in terms of convergence rate and domain. The convergence and superiority of the method are also rigorously demonstrated. Simulations are provided to verify the one-, two-, and three-dimensional deflections of beams. Real-world experiments have also been performed to validate our method’s effectiveness with two different beam configurations. The results indicate that the proposed method accurately estimates large spatial deflections of flexible beams.

Lower limb maltorsion and acetabular deformity in children and adolescents with X-linked hypophosphatemia.

X-linked hypophosphatemia (XLH) is a rare monogenetic skeletal disorder. Lower limb deformities contribute substantially to impaired gait quality and burden of disease in patients with XLH. Standardized data regarding onset and severity of lower limb maltorsion are unavailable. This study aimed to evaluate lower limb maltorsion using rotational magnetic resonance imaging (MRI) and computed tomography (CT). Rotational MRI and CT of children and adolescents with verified XLH were evaluated retrospectively. Femoral and tibial torsion, acetabular anteversion, and axial acetabular coverage were measured and compared with published age-adapted radiographic, clinical measurements and MRI data, respectively. Fifteen patients (mean age, 10.7 years) were included in the study. Decreased femoral torsion was observed in 47% (14/30 femora) and femoral retrotorsion in 17% (5/30 femora). Ten of 13 hips with coxa vara deformity presented with decreased femoral antetorsion. Reduced external tibial torsion manifested in 64% (18/28 tibiae). Abnormal axial femoral head coverage was present in 67% (20/30 hips), whereas 53% (16/30 hips) showed increased acetabular anteversion. Femoral and tibial torsional pathologies were found in children and adolescents with XLH. The occurrence of severe femoral retrotorsion in a 2-year-old child prior to ambulation raises questions regarding the biomechanical impact of gait on the development of torsional deformities in XLH.

A novel method for predicting carburizing and quenching deformation of the gear with the mandrel based on carburizing expansion strain and dynamic thermal boundary conditions of quenching

During the carburizing quenching process, the interaction of multiple physical fields leads to significant nonlinearity in the mechanical properties and physical characteristics of the material, making prediction of carburizing quenching deformation particularly challenging. Based on the phase transformation thermo-elastic-plastic constitutive equation, this paper innovatively incorporated the deformation of interstitial solid solution induced by carburization, and integrated experimental data on material properties for 8620RH, a multi-field model for carburizing quenching was constructed. The accuracy of the proposed deformation prediction model was validated through experiments on cylindrical samples and the calculation results from specialized heat treatment software Dante. Based on the deformation prediction model, considering the flow effect of quenching medium in gear quenching process, and introducing dynamic heat boundary conditions during quenching, a finite element model for predicting carburizing and quenching deformation of the gear with the mandrel was constructed to study the deformation distribution of the gear. The accuracy of the deformation prediction model was verified through the carburizing quenching experiment of the gear with the mandrel. The results show that compared with the classical model which does not consider the carburizing expansion strain and the dynamic thermal boundary conditions, the proposed model demonstrates higher predictive accuracy in torsional deformation and expansion deformation. The research work provides a novel model and method for improving the accuracy of predicting carburizing and quenching deformation in gears.

Aerodynamics of a three-dimensionally deformed rigid wing

A flexible wing with a large aspect ratio emerges in many modern engineering applications (e.g. solar planes and super large wind turbine blades) and its interaction with incident flow differs markedly from conventional fluid–structure interactions (FSI), exhibiting frequently a large three-dimensional (3D) deformation. Yet, there is little information on how such deformation may change wing aerodynamics. This work investigates the aerodynamic performance of deformed and cantilever-supported NACA0012 rigid wings with an aspect ratio of 9, using ANSYS Fluent with the SST-κ-ω turbulence model at a chord-length-based Reynolds number Rec of 1.5 × 105. Numerical simulation is validated experimentally. The wing tip bending displacement is up to 4.14c, and the maximum twisted angle is up to 7°. The angle α of attack varies from 0° to 20° at mid span of the wing. It has been found that the torsional deformation can significantly advance the local flow separation, reattachment, bubble length, and transition from laminar to turbulence, resulting in a drop in the critical angle αcr of attack, at which the separation bubble size reaches the maximum. Accordingly, the lift and drag coefficients increase, as well as the bending and pitching-up moments, though the stall is advanced due to a change in local α. The tip vortex is also enhanced, inducing strong downwash postponing the separation bubble on the wing and resulting in redistributed force near the wing tip that increases markedly the local bending moment but decrease the local pitching-up moment. On the other hand, the bending deformation tends to produce an effect opposite to the torsion on the flow structure and causing little change in the lift coefficient, though reducing the induced drag and moments appreciably. With both deformations in place, the torsion overwhelms the bending in general in terms of its impact upon aerodynamics and flow structures, the latter acting to cancel at least partially the effect of the former.

Hybrid modelling of dynamic softening using modified Avrami kinetics under Gaussian processes

This paper presents a new method of modelling that combines several approaches to anticipate the softening of nickel-niobium alloys during dynamic recrystallization (DRX). The study employs an extensive dataset obtained from hot torsion deformation tests conducted on high-purity nickel and six nickel-niobium alloys. The niobium concentration in these alloys varies from 0.01 to 10 wt % (Matougui et al., 2013). The hybrid technique integrates the Avrami model to provide early predictions about the kinetics of recrystallization and then uses mechanistic modelling to assess the progression of softening caused by dynamic recrystallization (DRX). The integrated technique is improved by using Gaussian process regression analysis, which investigates the softening properties and offers useful insights into the effects of niobium additions on dynamic softening behaviour. This unique hybrid framework combines multiple modelling tools to reveal intricate connections impacted by solute addition, therefore enhancing our comprehension of the physical events that take place during the hot deformation of superalloys. The use of empirical, mechanistic, and machine learning methods in this hybrid model provides a more thorough and detailed investigation of DRX processes in these alloys.

Investigation into the shear effect of torsion extrusion process

Torsion extrusion (TE) is a severe plastic deformation (SPD) technique with the potential to be used for the preparation of large bulk materials with enhanced mechanical properties. Shear deformation is the key factor for SPD to enhance the materials properties. However, it is not clear by far that what shear strains are dominant in torsion extrusion process and how they distribute in the extruded materials. These issues are crucial to the working parameters design of the torsion extrusion process for maximizing the shear effect. To this end, a plasticine billet with two colors was applied as experimental material, and the material flow pattern was revealed by measuring the twisted bicolor interfaces. The torsion extrusion was implemented using a die with a wavy cross-sectional bearing segment (W-TE), which is able to prevent the circumferential sliding of the materials against the die. Flow velocities were re-built according to the bicolor interfaces at each section in a cylindrical system. Strain rates and shear strains induced by torsion deformation along the radius of the material were formulated based on the velocity field and Eulerian variable derivatives, from which the dominant shear strain can be recognized. A shear effect index (SEI) was proposed to evaluate the contribution of the shear strains induced by torsion, and the distribution of SEI was analyzed. Furthermore, the W-TE experiments on the as-cast TiB2/2026 Al composite were carried out to demonstrate the positive correlation between the shear effect and the microstructural improvement, and finite element simulation for such experiments showed the consistency of the simulated deformation patterns with the plasticine measured ones. The evaluation method and the experimental results deepened the understanding to the shear effect of torsion extrusion process.

Shaking table test of TLD/TLCD vibration control for offshore wind turbine support structure

In this research, a scale-model with a similarity-ratio of 1:15 is specifically designed for shaking table test based on a 6.45MW OWT (Offshore wind turbine). The scale-model is equipped with a TLD (Tuned liquid damper) at the top and a TLCD (Tuned liquid column damper) at 2/3 of its height. Various external excitations with distinct spectral characteristics are applied to analyze the vibration characteristics of the OWT and the damping performance of the TLD/TLCD. The results indicate that the dynamic characteristics satisfy the similarity-ratio between the prototype-model and scale-model. The acceleration response of the OWT is significantly influenced by the external excitation spectrum, whereas the displacement response is primarily governed by the model 1st-order natural-frequency. With the mass eccentricity applied at the tower top and bidirectional excitation input, torsional deformation occurs in the tower, resulting in a ‘beat vibration’ phenomenon. Upon the incorporation of TLD/TLCD, the vibration response attenuation-ratio can reach up to 70 % under harmonic excitation, up to 25 % under seismic excitation and up to 50 % under equivalent base acceleration. After the implementation of vibration attenuation, there is a significant reduction in the time-domain response, and the rate of reduction is accelerated. In the frequency-domain response, the spectral peak at the natural-frequency disappears.

Failure analysis and structural optimization of unequal-parameter metal bellows in resistance to bending and torsional composite deformation

In practical engineering applications, metal bellows are subjected to complex environmental conditions, and they usually deform under the combined effects of tension, bending and torsion. In this paper, the bending and torsion composite deformation of unequal parameter metal bellows arranged alternately by large wave and wavelet is studied. Firstly, the finite element model of metal bellows is constructed, and the finite element simulation analysis of its mechanical properties is carried out. Taking the simulation results as samples, the multi-objective structural optimization of unequal parameter metal bellows under the condition of bending and torsion composite deformation is carried out. Combined with the bending-torsion composite deformation test and fracture microscopic characterization, the bending-torsion composite deformation characteristics and fracture failure mechanism of equal-parameter metal bellows (EPMB) and unequal-parameter metal bellows (Un-EPMB) were compared and analyzed. The results show that under the same deformation conditions, compared with the EPMB, the elastic limit bending line displacement and elastic limit torsion angle displacement of Un-EPMB are increased by 52.94 %, and the bending and torsional stiffness are greatly improved, moreover, the alternating waveform arrangement led to relatively gradual stress transfer through the Un-EPMB during the bending-torsion composite deformation process, thereby reducing stress concentration. Thus, the Un-EPMB exhibited more favorable mechanical properties. Unlike in the EPMB, which underwent fracture along the grain boundary, the cracks in the Un-EPMB appeared in the middle layer and propagated to both sides in a wavelike pattern. The dimples were distributed in the middle layer of the fracture, which indicates ductile behavior.

Cluster analysis to identify the most prominent gait patterns in children with torsional deformities

Cluster analysis to identify the most prominent gait patterns in children with torsional deformities

Surface roughness prediction model and surface topography analysis of 2.5D-Cf/SiC in two-dimensional ultrasonic assisted grinding based on GA-BP neural network

Because of the anisotropy and non-uniformity, the grinding surface quality of Cf/SiC composites is difficult to be accurately predicted. The quality of the surface directly determines the assembly accuracy. To better predict the surface quality of 2.5D-Cf/SiC composites, the BP neural network was optimized by genetic algorithm (GA), and the surface roughness prediction model of fiber orientation, ultrasonic amplitude, and machining parameters was established. The empirical formula prediction model of surface roughness was established by the method of multiple linear regression analysis. The results show that the prediction accuracy of GA optimized BP neural network is the best, followed by the empirical formula, and the prediction effect of the BP neural network is the worst. The average absolute percentage error of these three models is 10.045%, 16.912% and 26.6245% respectively. The kinematic models of conventional and two-dimensional ultrasonic-assisted grinding of single particles were established respectively. Based on the kinematic model, the reasons for the reduction of surface roughness by 2D ultrasonic-assisted grinding are explained. According to the orthogonal test results, the surface roughness decreases the most when vs is 0.66m/s, vw is 100mm/min, ap is 150μm along the fiber orientation of 0°, and the maximum percentage of reduction is 53.18%. Increasing the linear speed, reducing the feed speed, reducing the grinding depth, and applying ultrasound can reduce the extrusion pressure along the axis of 0° fiber, and then reduce the length and depth of cracks and thus reduce the surface defects. The axial shear force of the 90° oriented abrasive particles on the fiber is reduced, thus reducing the surface damage caused by torsional deformation. Reduce 3D surface profile and improve surface quality. The maximum percentage reduction of each parameter index is as follows: root mean square height decreased by 28.8%, skew decreased by 88.61%, kurtosis decreased by 48.97%, maximum crest height decreased by 48.55%, maximum sag height decreased by 40.09%, maximum height decreased by 43.93%, and arithmetic mean height decreased by 26.06%.

Angular and torsional malalignments of the paediatric knee joint

Abnormal angular and torsional alignment of the lower extremities during growth are acommon reason for consultation of apaediatrician or orthopaedist. There is often uncertainty about the pathological value of these abnormalities and the need for treatment, even among specialists. In the course of physiological growth and development processes, the axial and torsional alignment of the legs sometimes change considerably and in characteristic patterns. The ability to assess whether abnormal angular or torsional alignments of the lower limb in the course of growth should still be regarded as normal or already as pathological, depending on age and gender, is essential for the treating physician and requires precise knowledge of the physiological development processes and the tolerable limits in all three spatial dimensions. After careful explanation to the frequently concerned parents, arestrictive approach with observation of the spontaneous course of correction on the basis of regular clinical check-ups makes sense in the majority of cases. Pathological deviations from the physiological conditions are rare overall, can be idiopathic or of secondary origin and should be further clarified diagnostically using imaging procedures. As conservative measures are ineffective, pronounced angular and/or torsional deformities of the legs requiring treatment can only be corrected by surgical intervention, even in children and adolescents. The surgical treatment modalities available are varied and differ in terms of their invasiveness and complication profile, depending on the localization, type and severity of the deformity, as well as the age and possible concomitant diseases of the affected child or adolescent.

Atomic scale investigation of the phase transformation path from HCP to FCC in high-purity hafnium during torsion deformation

Although the hexagonal close-packed (HCP) to face centered cubic (FCC) martensitic phase transformation has been frequently observed and discussed in many HCP metals and alloys, the detailed phase transformation path has been disputed. Here, we studied the potential phase transformation path from HCP to FCC phase in high-purity hafnium (Hf) under torsional deformation condition. Results indicated that the HCP to FCC phase transformation was not accomplished directly by the glide of a/3[11¯00] Shockley partial dislocations on every other {0001} planes, but progressively transitions to the FCC lattice through multiple intermediate states. The complete phase transformation process can be further refined as: HCP → body-centered tetragonal (BCT)-like structure → 12R long-period stacking-ordered (LPSO) structure → FCC, and each step was accommodated by basal stacking faults. This work is instructive on the phase transformation from HCP to FCC not only in Hf but also in other HCP metals.

In-Depth Study on the Application of a Graphene Platelet-reinforced Composite to Wind Turbine Blades.

Graphene platelets (GPLs) are gaining popularity across various sectors for enhancing the strength and reducing the weight of structures, thanks to their outstanding mechanical characteristics and low manufacturing cost. Among many engineering structures, wind turbine blades are a prime candidate for the integration of such advanced nanofillers, offering potential improvements in the efficiency of energy generation and reductions in the construction costs of support structures. This study aims to explore the potential of GPLs for use in wind turbine blades by evaluating their impact on material costs as well as mechanical performance. A series of finite element analyses (FEAs) were conducted to examine the variations of mechanical performances-specifically, free vibration, bending, torsional deformation, and weight reductions relative to conventional fiberglass-based blades. Details of computational modeling techniques are presented in this paper. Based on the outcomes of these analyses, the mechanical performances of GPL-reinforced wind turbine blades are reviewed along with a cost-benefit analysis, exemplified through a 5MW-class wind turbine blade. The findings affirm the practicality and benefits of employing GPLs in the design and fabrication of wind turbine blades.

Cyclic loading test on hysteresis performance of replaceable link with slit web

The paper introduces a novel design for replaceable links, which incorporates strategically placed slits in the web to reduce the bearing capacity of the link. This design innovation ensures localized plastic deformation within the link, facilitating disassembly and replacement after earthquake. Two types of steel materials, Q235 steel, and LYP160 steel, are employed in constructing the replaceable links. Three replaceable links with slit web were designed according to the material properties of the steel and the number of slits and were subjected to cyclic loading tests. The test results show that the primary failure modes of the link include web failure between slits, torsional deformation of the web between slits, slight buckling of flanges and stiffeners, and web tearing. The material overstrength coefficients of the three specimens range from 0.83 – 1.41, and the overstrength coefficients due to strain hardening range from 1.08 – 2.49, with a maximum plastic rotation reaching up to 0.16 rad.

Mechanical behavior and seismic control performance of a metallic torsional damper for flexible structures

The use of metallic dampers is an effective way to reduce seismic responses and dissipate excessive vibration energy for civil structures. Conventional metallic dampers employed energy dissipation by plastic deformation under bending or shear modes are hard to design, and may cause uniform distribution of stress in the metallic components. In this paper, employing the high plastic deformation capacity of aluminum materials, a metallic torsional damper using a gear and rack device (MTDGRD) is proposed to enhance the control effectiveness for the structural response reduction under earthquakes. The static mechanical behavior and energy dissipation of aluminum metallic components under torsional deformation are experimentally studied. Moreover, the configuration and working principle of the proposed damper are introduced. The dynamic behavior of the proposed damper is experimentally studied. For precise modeling in simulations, the elastic-plastic theory of torsional deformation is used to derive the mechanical model of the proposed damper and the model accuracy is validated by experimental data. Finally, numerical simulations under different seismic ground motions controlled by a proposed MTDGRD are compared to that controlled by a conventional tuned mass damper (TMD) for a 10-floor flexible structure. The results show that aluminum 6061# of the energy dissipation capacity is higher than aluminum 1060#. The dynamical tests show that the loading frequency and operational cycles have very limited effect on mechanical behavior and energy consumption capacity of the MTDGRD. The proposed dynamic mechanical model of the MTDGRD has considerable accuracy in numerical simulations and seismic control simulations show the better performance of the proposed damper in reducing structural displacement responses than the conventional TMD with a mass ratio of 0.5 %.

Enhanced torsional strength and plasticity synergy of multi-component alloy via multi-level gradient structures

This study investigates an approach to enhance the strength and torsional angle, as well as analyze the microstructure and mechanical properties of a multi-component Cu-based alloy. A unique gradient-structured alloy is successfully synthesized by subjecting CuAl10Fe5Ni4Mn0.23 to high-frequency large torsional deformation. The results showed that the multi-level gradient structure due to high-frequency deformation significantly enhances the torsional strength of CuAl10Fe5Ni4Mn0.23 alloy. With a torsional rate of 120°/min and a maximum torsional angle achieved at 40°, after 200 cycles, compared to non-torsional samples, the torsional strength increased by 75.69 % and the torsion angle also increased by 38.36 %. The combination of the alloy primary structures along with gradient structures forms a new microband structure that synergistically improves the mechanical properties of multi-component alloys. The proposed large torsion deformation alters the structure of multi-component alloys, resulting in a gradient structure that simultaneously enhances both strength and plasticity, resolving current reciprocal dilemmas between these two factors.

Comprehensive Analysis of Laser Peening Forming Effects on 5083 Aluminum Alloy.

In order to investigate the laws of the laser peening forming process and the effects of laser peening on the surface quality and tensile properties of 5083 aluminum alloy, experiments were conducted utilizing various laser peening paths, energies, and plate thicknesses. Subsequently, laser peening forming experiments were performed on S-shaped and different shapes of aluminum alloy substrates. The impact of different laser peening durations on surface morphology and tensile properties was then analyzed. Results indicated that the largest bending deformation perpendicular to the laser peening path reached 12.5 mm. In cases where the laser peening path was inclined relative to the horizontal direction, torsional deformations were observed in the aluminum alloy plate. For laser energy levels of 5 J, 6 J, and 7 J, deformation amounts were 3.8 mm, 4.9 mm, and 5.4 mm, respectively. Plates with thicknesses of 4 mm exhibited convex deformation, while those with 2 mm thickness showed concave deformation. Furthermore, following one and two laser peening cycles, the residual stresses in the alloy plates were -80 MPa and -107 MPa, the surface hardness increased by 16 HV and 31 HV, the roughness increased by 2.495 μm and 3.615 μm, and the tensile strength increased by 9.5 MPa and 18.5 MPa, respectively.

Study on Mechanism of Stick–Slip Vibration Based on Torque Characteristics of PDC Bit

Stick–slip vibration (SV) of drill string systems is the main cause of fatigue failure of PDC bits under complex drilling conditions. Exploring its mechanism is helpful for identifying the causes of bit failure and developing preventive measures to prolong bit service life. In this study, the influence of various factors on torque characteristics is tested by drilling rock breaking with various PDC bits and the variations in torsion variables and torsion speed of drill string systems under different torque loading conditions of drill bits are ascertained. Through a finite element simulation of the drill string–bit system, the influence of the PDC bit on the torsional deformation with variable torque is determined, and the influence mechanisms of bit size, tooth structure, invasion depth, rock strength, and other factors on the SV induced by a PDC bit are established. The results show that the change in the reaction resistance moment of the formation rock leads to variation in the driving speed of the drill string system, which is one of the main reasons for the SV. Even if the torque change in the bit is minor, SV will occur if the drill string is too long.

The formation mechanism of the nano-equiaxed (α+β) duplex phases structure during aging process after high pressure torsion deformation

The aim of this study was to investigate the effects of the nano equiaxed (α+β) duplex phases (NEDP) structure on the mechanical properties of metastable β type titanium alloy. To achieve this, the Ti-3.5Al-5Mo-4 V (Ti-B20) alloy was subjected to high pressure torsion (HPT) deformation and aging treatment. The results demonstrated that the NEDP (α+β) structure exhibited high thermal stability even after prolonged aging. Through systematic transmission electron microscopy (TEM) characterization, it was confirmed that the formation of the NEDP structure was attributed to the generation of crystal defects such as dislocation cells and dislocation pile-ups during HPT deformation. In addition, it was found that the orientation relationship between the α and β phases was [21̅1̅0]α//[111]β after prolonged aging, and the interlocked of coherent interface between the α and β phases allowed the NEDP (α+β) structure to maintain its thermal stability during long-term aging. Therefore, this paper provides valuable guidance for the fabrication of nano-equiaxed dual-phase structures.

Effects of Graphene Reinforcement on Static Bending, Free Vibration, and Torsion of Wind Turbine Blades.

Renewable energy markets, particularly wind energy, have experienced remarkable growth, predominantly driven by the urgent need for decarbonization in the face of accelerating global warming. As the wind energy sector expands and turbines increase in size, there is a growing demand for advanced composite materials that offer both high strength and low density. Among these materials, graphene stands out for its excellent mechanical properties and low density. Incorporating graphene reinforcement into wind turbine blades has the potential to enhance generation efficiency and reduce the construction costs of foundation structures. As a pilot study of graphene reinforcement on wind turbine blades, this study aims to investigate the variations of mechanical characteristics and weights between traditional fiberglass-based blades and those reinforced with graphene platelets (GPLs). A finite element model of the SNL 61.5 m horizontal wind turbine blade is used and validated by comparing the analysis results with those presented in the existing literature. Case studies are conducted to explore the effects of graphene reinforcement on wind turbine blades in terms of mechanical characteristics, such as free vibration, bending, and torsional deformation. Furthermore, the masses and fabrication costs are compared among fiberglass, CNTRC, and GPLRC-based wind turbine blades. Finally, the results obtained from this study demonstrate the effectiveness of graphene reinforcement on wind turbine blades in terms of both their mechanical performance and weight reduction.