Torsional Analysis Research Articles

Nonlinear modeling and torsional vibration analysis of heavy-duty vehicle powertrain system during acceleration

Nonlinear modeling and torsional vibration analysis of heavy-duty vehicle powertrain system during acceleration

Evaluating the safety of the redesigned shafting system following the propeller redesign aimed at enhancing CII and EEXI

In July 2023, the International Maritime Organization (IMO) set a target to achieve net-zero greenhouse gas emissions by 2050, introducing key measures such as the Energy Efficiency Design Index (EEDI), the Energy Efficiency Existing Ship Index (EEXI), and the Carbon Intensity Indicator (CII). The maritime industry explored adaptations, including engine de-rating, energy-efficient technologies, and propeller modifications, and beyond. This study assessed the safety implication of a redesigned shafting system, resulting in a propeller redesign to enhance the CII and EEXI on a 6500 TEU container ship built in 2006. Through an analysis of annual output per TEU from 2000 to 2015, the study focused on container ships built from 2005 to 2007 with high-output engines (9.4–9.5 kW/TEU). After selecting a sample ship, the study determined engine power limits according to the EEXI regulations and assessed their impact on the CII. Subsequently, the study redesigned the shafting system, performing torsional vibration calculations and shaft alignment analyses to ensure the safety of the modified system. While an enhanced CII rating was predicted, the tightening CII regulations imply this benefit may be short-lived, lasting approximately two years. Thus, additional measures are essential to prolong the improved CII rating.

Melting and crystallization temperatures, foaming, and fluid-induced crystallization of poly (ε-caprolactone) in compressed CO2 and N2

Melting and crystallization temperatures of poly(ε-caprolactone)(PCL) exposed to CO2 and N2 have been evaluated at pressures up to 125 bar using High Pressure Torsional Braid Analysis. It is shown that in contrast to CO2, exposure to high pressure N2 does not lead to a significant depression of Tm or Tc. Instead, these transition temperatures tend to increase in nitrogen, reflecting more of a hydrostatic pressure rather than a solvent effect. Another factor that may play a role is the fluid-induced crystallization which tends to increase the melting temperature. By conducting foaming at properly selected temperatures along the rigidity reduction paths which are scaled with respect to the melting temperatures in CO2 or N2, foams with low bulk foam densities of about 0.2 g/cm3 could be generated in CO2 at 100 bar and in N2 at 200 bar.

Numerical method for the primary torsional capacity of arbitrary steel cross sections considering nonlinear plastic behaviour

In structural design, plastic capacities of cross sections are of great importance for evaluating the capacity of steel members. Moreover, when it comes to problems of member stability, states of partial plasticisation are of interest as well. Depending on the cross section geometry and the material law to be considered, the determination can be challenging. This particularly applies to load conditions characterised by shear stress states, as for instance in the case of primary torsion (St. Venant's torsion). Simplifications are therefore often made with regard to the cross section geometry and engineering models are applied if the plastic limit moment of primary torsion Mpl,xp is to be determined. However, numerical methods allow a precise determination of properties and stress distributions of arbitrary cross section. In the present study, corresponding finite element formulations are combined with a plasticity algorithm for torsional analysis considering effects of nonlinear isotropic hardening. The approach approximates the nonlinear material law by a multilinear curve, which is stepwise evaluated based on linear hardening formulations. It allows determining states of partial cross section plasticisation for any strain or deformation state as well as the identification of the plastic limit capacity of the cross section. Results of the implemented algorithm are presented and verified for different common steel profiles showing excellent agreement to comparative studies.

Torsional vibration analysis and active anti-disturbance decoupling control of duplex trident universal joints

Torsional vibration analysis and active anti-disturbance decoupling control of duplex trident universal joints

Torsional and lateral vibration analysis of wind turbine generator bearing outer ring fault considering unbalanced magnetic pull

Rolling bearings play a critical role in wind turbine generators, operating continuously in an electromagnetic excitation environment. Their fault vibration characteristics are affected by unbalanced magnetic pull (UMP), which has received little attention in previous studies. Moreover, torsional vibration can provide advantages in bearing fault diagnosis, since it has a good signal-to-noise ratio (SNR) and it can be easily measured by the encoder. However, torsional vibration is rarely considered in the existing model of wind turbine generator. Accordingly, this paper proposes a dynamic model with 8 degrees of freedom to analyze the bearing outer ring fault characteristics of wind turbine generator under the influence of UMP, while also taking into account the torsional vibration in the model. The validity of the model is verified through experiments conducted on a test rig. The results displays modulation of the ball pass frequency outer (BPFO) harmonics with both UMP frequency and rotation frequency in lateral vibration, and this phenomenon can also be observed in instantaneous angular speed (IAS) and instantaneous angular acceleration (IAA) signals that represent torsional vibration. Besides, the lateral vibration spectrum reveals two distinct resonance bands, and simulation analysis suggested that the rotor and bearings give rise to low-frequency and high-frequency resonance, respectively. This study provides a reference for bearing faults diagnosis in wind turbine generator.

Research on modified lumped parameter method in torsional vibration analysis of reciprocating compressor shaft

Abnormal vibrations often occur during the operation of reciprocating compressors under different load conditions. To efficiently and accurately calculate the torsional vibration response of the shafting under various working conditions, a modified lumped parameter method (MLPM) based on finite element mode modification is proposed. MLPM is derived from the lumped parameter method (LPM) and incorporates corrections to the stiffness matrix based on the multi-degree-of-freedom modal calculation using a finite element model. This allows MLPM to combine the high accuracy of finite element method (FEM) with the fast computing speed of LPM. To demonstrate the effectiveness of MLPM, an abnormal vibration compressor equipped with a stepless capacity control system is considered. MLPM is utilized to calculate the torsional natural frequency (TNF) and torsional torque response of the compressor’s shafting. The computed 1st-order TNF error between MLPM and FEM is only 0.20%. In the time domain, the torque response error of MLPM is less than 3.07%, while in the frequency domain, it is less than 0.57%. Moreover, MLPM exhibits a significantly increased calculation speed of more than 95% compared to FEM. By comparing MLPM results with torsional vibration test data, the 1st-order TNF error is found to be less than 0.50%, and the frequency-domain torque response error is no more than 8.91%. Furthermore, MLPM is effectively applied to solve the abnormal vibration problem of the compressor. It proposes a modification plan for the shafting, which successfully avoids torsional resonance and reduces the peak value of the torque response by 54.77%. These results demonstrate that MLPM is highly suitable for practical engineering applications due to its combination of high accuracy and fast computing speed.

Analysis of torsional vibration characteristics for wind turbine drivetrain under external excitation

This work studies the torsional vibration characteristics analysis of the wind turbine drivetrain with the variation of internal parameter and external excitation. The electromechanically coupled torsional vibration model for wind turbine drivetrain is first established by taking into account the torsional vibration angle of the PMSG. Then, frequency response analysis of main parametric resonance is illustrated by multiple scale method, and the influences of the system parameters involving power factor angle, number of pole pairs, torsional stiffness, and wind speed excitation on the torsional vibration characteristics of wind turbine drivetrain are investigated. Moreover, the critical condition for homoclinic chaos in terms of the system parameters is derived by means of Melnikov’s method. The function relationship and the boundary curve of chaos threshold are obtained. Meanwhile, the effects of excitation amplitude and damping factor on the system transition to chaos are studied in detail. The analytical predictions including phase portrait, bifurcation diagram and Lyapunov exponent are investigated. The research results can offer a theoretical basis for further the parameter design and control of wind turbine drivetrain.

Evaluation the relationship between myocardial fibrosis and left ventricular torsion measured by cardiac magnetic resonance feature-tracking in hypertrophic cardiomyopathy patients with preserved ejection fraction.

The relationship between left ventricular (LV) torsion and myocardial fibrosis (MF) in hypertrophic cardiomyopathy (HCM) patients with preserved ejection fraction was still not well understood. New developments in cardiac magnetic resonance (CMR) enable a much fuller assessment of cardiac characteristics. This study sought to assess the impact of HCM on myocardial function as assessed by LV torsion and its relationship with MF. HCM (n = 79) and healthy controls (n = 40) underwent CMR. According to whether there was late gadolinium enhancement (LGE), patients were divided into LGE+ group and LGE- group. LV torsion and torsion rate were measured by CMR feature-tracking (CMR-FT). MF was quantitatively evaluated through LGE imaging. LGE was present in 44 patients (56%). Compared with healthy controls, torsion increased in the LGE- group (P < 0.001). Compared with LGE+ group, torsion was higher in the LGE- group (P < 0.001). There was no significant difference in torsion between LGE+ group and healthy controls. Correlation analysis showed that torsion was correlated with LGE% (r= -0.443) and LGE mass (r= -0.435) respectively. On multivariable logistic regression analysis, LV torsion was the only feature that was independently associated with the presence of LGE (OR 0.130; 95% CI 0.040 to 0.420, P = 0.01). The best torsion value associated with MF was 1.91 (sensitivity 60.0%, specificity 77.3%, AUC = 0.733). In HCM patients with preserved ejection fraction, CMR-FT derivedLV torsion analysis holds promise for myocardial fibrosis detection.

Galerkin-Kantorovich variational method for solving saint venant torsion problems of rectangular bars

The unrestrained torsional analysis of bars is an important theme in elasticity theory, first solved by Saint-Venant using semi-inverse methods. It has been considered and solved by several others using analytical methods and numerical procedures due to the importance in the design of machine parts under torsional moments. In this paper, the Saint Venant torsion problem is solved for rectangular prismatic bars using Galerkin-Kantorovich variational method (GKVM). The work presents a detailed theoretical framework of the problem, deriving using first principles considerations the stress compatibility equation in terms of the Prandtl stress function ϕ(x,y). The derived domain equation which is required to be satisfied over the rectangular cross-sectional domain is a partial differential equation of the Poisson type. GKVM is adopted as the solution method for finding the solution to the domain equation. The unknown Prandtl stress function ϕ(x,y) is assumed, following Kantorovich method to be a product of an unknown function for fx sought to minimize the Galerkin-Kantorovich variational functional (integral) (GKVF) and a known function (y2-b2) which satisfies the boundary conditions at all boundary points in the y-direction, that is, at y=±b. The resulting GKVF is a simplified functional whose integral is a second order inhomogeneous ordinary differential equation (ODE) in fx. The integrand is solved to find fx leading in a full determination of the Prandtl stress function. The expression for stresses, torsional moments and torsional parameters are then found and they satisfy the boundary conditions and the domain equation. The results for the torsional moments and torsional parameters are identical to previous results obtained using double finite sine transform method (DFSTM), and analytical methods. The merit of GKVM is that it has led to the exact solution of the unrestrained torsion problems.

Scale-dependent torsional frequency analysis of right triangle anisotropic advanced composite microscale rods

Despite several theoretical investigations on the torsional dynamic behavior of non-circular micro/nanorods, the torsional behavior of right triangle cross-section is still unevaluated. Therefore, Timoshenko-Gere theory in conjunction with nonlocal strain gradient theory is developed for modeling the scale-dependent torsional dynamic of right triangle microscale rods. Various anisotropic materials, i.e. hexagonal, trigonal, triclinic, and monoclinic materials are regarded as the constituent material of microscale rods. The shear stress function is developed for right triangle shape and according to the calculated shear stress function, the warping function of right triangle shape is obtained. The nonlocal governing equation of the torsional dynamic of anisotropic microrods is obtained with the help of the energy approach and solved using an analytical method by regarding two different boundary conditions. The accuracy of the proposed model is validated with recent similar investigations. Because of the lack of mechanical research on right triangle microrods, the proposed methodology was validated with equilateral triangle nanowire reported in the literature. Eventually, the various remarkable variants’ effects on change of scale-dependent torsional frequency are assessed comprehensively. It is found that hexagonal and triclinic materials have the largest and smallest values of frequency. Also, nonlocal parameter, b/h ratio play a decreasing role and length scale parameters and mode number plays an increasing role.

Clinical and hematological analysis of testicular torsion in children.

Analyze the clinical manifestations, laboratory tests, and imaging data of testicular torsion to provide clinical insights for timely and accurate diagnosis and treatment of testicular torsion. A retrospective analysis was conducted on the clinical data of 67 pediatric patients suspected of testicular torsion, admitted and subjected to surgical exploration from June 2018 to June 2023. Based on whether the torsed testicle was excised during surgery, the patients were divided into orchiectomy group (40 cases) and orchidopexy group (27 cases). Combining clinical symptoms, signs, ultrasound examinations, and laboratory tests, the study aimed to summarize the influencing factors on the onset, diagnosis, and treatment of testicular torsion. The clinical manifestations of all 67 pediatric patients were generally typical. Color Doppler Flow Imaging (CDFI) and surgical exploration were performed for all cases, and the results were consistent. Testicular color doppler ultrasound suggested reduced or absent blood flow, leading to surgical treatment in all cases. All patients had unilateral testicular torsion, with 46 cases (68.66%) on the left side and 21 cases (31.34%) on the right side. Intrafunicular torsion occurred in 60 cases (89.55%), while extrafunicular torsion occurred in 7 cases (10.45%). The onset distribution was as follows: 20 cases in spring, 16 cases in summer, 16 cases in autumn, and 15 cases in winter. Univariate analysis indicated significant statistical differences in age, degree of testicular torsion, duration of symptoms, NEUT, NLR, and occurrence of tunica fluid between the two groups of patients. Multivariate logistic regression analysis showed that the duration of symptoms and the occurrence of hydrocele were independent risk factors for determining testicular viability. Testicular torsion is more common in children and adolescents, with clinical manifestations including scrotal pain, scrotal redness and swelling, abdominal pain, nausea, and vomiting. In the early stages of testicular torsion, inflammatory markers in the blood increase, and preoperative ultrasound indicates hydrocele. This suggests that the testicle is in an early twisted state, with good viability and potential for preservation.

Linear Longitudinal Strength Analysis of a Multipurpose Cargo Ship under Combined Bending and Torsional Load

Cargo ships with wide hatches usually have thin walls and limited torsional rigidity. Consequently, conducting a comprehensive torsional analysis is important because these loads can exert a significant impact. In this paper, the structural response of a multipurpose cargo ship to combined bending and torsional loads is studied using finite element analysis. The bending and torsional moments are calculated following the rules and standard regulations followed by the classification society. The ship’s 3D finite element model was verified using beam theory and direct calculations. In contrast, the accuracy of torsional stress was confirmed by comparing thin wall girder theory with direct calculation results. This study thoroughly examined the impacts of the still water bending moment, the vertical wave bending moment, and the wave-induced torsional moment on the structural response of ships. Furthermore, it scrutinised the impact of torsion on both open-deck and closed-deck ships. Hull girder normal stresses at midship due to still water and the vertical wave bending moment are shown to contribute to almost 70% of total stress in an inclined condition; stresses resulting from the horizontal wave bending moment contribute nearly 10%, while warping stresses contribute approximately 20% in open-deck ships. It is also shown that torsion has little impact on closed-deck ships. Finally, a buckling analysis was conducted to assess the ship’s buckling criteria, confirming that the linear buckling criteria were satisfied.

Rigid body qualified curved beam approach for lateral torsional buckling of arches

The curved beam finite element approach based on the potential energy formulation is widely recognized as a versatile tool for lateral torsional buckling analysis of arches. However, there exist a variety of potentials, which were developed with distinct assumptions. The diversity of energy-based curved beam theories introduces confusions in practical applications. This paper aims to examine various potential energy formulations as to whether or not they obey the rigid body rule which is a prerequisite for valid second-order analysis. The induced moments at the ends of curved beam element that have been neglected from and/or the distributed moments that should be removed from available potentials are identified to help them become rigid body qualified. Based on the revised potential functional, a curved beam finite element formulation has been developed to effectively predict yet with less effort the out-of-plane critical load for circular and parabolic arches subject to various loading and constraint conditions. The results of numerical examples demonstrate that a potential energy formulation eligible for describing the out-of-plane behavior of curved beam is required to be rigid body qualified by fulfilling two aspects: (i) the neglected end moments that are imperative for satisfying the rigid body rule must be considered unless the virtual work done by them vanishes, and (ii) undesirable distributed moments that may be induced when undergoing the rigid body motion should be removed by considering all essential potential components.

Application and Experimental Validation of Seven-Degree-of-Freedom Beam Element for Girder Bridges during Deck Construction

During bridge deck construction, the deck finishing machine and the fresh concrete often produce large vertical loads and torsional moments acting on the bridge girder system. In some cases, these loads can cause excessive vertical deflection and transverse rotation in the bridge girders, leading to many maintenance and safety problems, such as changes in deck thickness and local and global instabilities during construction. To minimize the potential problems caused by deck construction, the AASHOTO LRFD Bridge Design Specification requires consideration of these torsional moments during the design procedure, and a detailed three-dimensional finite element analysis may be conducted. However, for bridge girders with open-section thin-walled sections, only the solid or shell element can be used to recognize the warping of the girder since the torsional warping effect is not included in the classical beam element. In this research, a warping degree of freedom was added to a beam element, and a three-dimensional beam element with seven degrees of freedom (7-DOF) at each node was derived as an alternative method for analyzing girder bridges during deck construction. A computer program based on the 7-DOF beam element was also developed in MATLAB. To assess the 7-DOF beam element, one bridge was selected to measure the transverse rotation, vertical deflection, and stress of the exterior girder and the first interior girder during deck construction. Also, three full-scale numerical models using solid elements, classical three-dimensional beam elements, and 7-DOF beam elements were created based on the geometries and loads of the experimental bridge. A comparative study was conducted by comparing the results from the numerical models and experimental monitoring data to evaluate the 7-DOF beam element. The results showed that the 7-DOF beam element had excellent behavior in analyzing the girder bridges under construction load, especially in the torsional analysis of bridge girders. Also, unlike the solid element model, which also provided reasonable results, the 7-DOF beam element model can compute the internal forces of the cross-sections along the bridge, which allows the 7-DOF beam element to be an alternative approach for design and research requiring less modeling effort and computational complexity.

Analysis of the noise mechanism and interactions of torsional decoupling devices in the belt driven 48V mild hybrid powertrain

This paper analyzed the mechanism of rattle noise from a decoupling damper pulley in a 48V belt driven mild hybrid powertrain with a three-cylinder turbo engine. To decouple the 48V belt drive from the high engine torque fluctuation of the engine, a decoupling device at the front end of engine is employed, which interacts with the rear end decoupling device and results in the rattling issue. In this study as opposed to the conventional engine torsional vibration studies which neglect the low inertia belt drive, the effective inertia of 48V belt drive is considered in 1D, 3D torsional vibration analyses of the entire powertrain as it easily reaches up to 20% of the whole torsional inertia. In this way, the impact inside the crank torque fluctuation decoupler was identified as the source of the rattle noise, which verified in the experiments. The interaction of the front end belt drive and the various types of rear end flywheel is also analyzed through parametric studies.

Torsional Buckling Analysis of Composite Anisogrid Conical Shells: Theoretical Approach and Numerical Validation

Torsional buckling analysis of composite anisogrid conical shells, with equiangular helical ribs, was investigated based on an equivalent variable stiffness continuum model. The buckling analysis is complicated by the variable geometry and stiffness of the lattice conical shell along the meridian. The smearing approach and the gradual function of the lattice cells were used to build the corresponding continuum model with varying stiffnesses. Recurrence relations were constructed from linearized buckling equations of the equivalent conical shell using the power series method and Fourier decomposition. The excellent precision and tremendous efficiency of the analytical solution was validated compared with numerical results through many design parameters of the lattice conical shell, such as the thickness of the ribs, the radius at the small end, and the height of the cone. Finally, a parametric analysis was used to discuss the influence of parameters on the critical buckling torsional moment. It is found that increasing rib thickness, end radius, the height of the cone, and strengthening boundary constraints can improve the critical buckling torsional moment.

Torsional Dynamics of Axially Graded Viscoelastic Carbon Nanotubes

Torsional vibration analysis of the axially functionally graded carbon nanotubes has been carried out. Nonlocal stress gradient elasticity theory has been used in continuum mechanics model of the carbon nanotube. Variation of the material properties of the axially graded nanostructure has been assumed in exponential form. Differently from the majority of literature works, viscous damping and nonlocal parameters have been assumed in grading form. Energy functional for the carbon nanotube has been achieved with minimum potential energy principle and weak form solution has been obtained with the Ritz Method. Effects of material grading, nonlocality and viscoelasticity to the torsional dynamics of axially graded carbon nanotube have been investigated. Results of the present work could be useful in modeling and production of axially functionally graded nanostructures.

Torsional vibration characteristics analysis and adaptive fixed‐time control of wind turbine drivetrain

AbstractThe drivetrain has an important impact on the stability and reliability of wind turbines operating in complex conditions, which belongs to the electromechanical coupling system. This work studies the two domains of research on drivetrain vibration analysis and control method in detail. The electromechanically coupled torsional vibration model is first established by considering the air gap magnetic field energy of the PMSG. Preliminary analysis in terms of Hamiltonian energy indicates that there is sufficient energy to sustain the exciting oscillation behaviors. Moreover, to reduce the vibration amplitude caused by wind speed or torsional stiffness, a novel adaptive fixed‐time control method is proposed to solve the issue of wind turbine drivetrain chaotic oscillation with uncertainties and disturbances. Furthermore, the proposed method not only can prevent the jumping and bifurcation of torsional vibration from happening, but also there are the advantages of the control scheme with high accuracy, fast convergence rate and strong robustness. For the fair comparison, three different control methods have been used to demonstrate the superiority of the control scheme by the simulation results. The research results can provide a theoretical basis for the parameter design and control of wind turbine drivetrain.

Torsional vibration analysis of grid-forming PMSG wind turbine

Torsional vibration analysis of grid-forming PMSG wind turbine