Torsion Beam Research Articles

Failure mode analysis of torsion beam rear suspension under service conditions

The failure mode of torsion beam rear suspension under service conditions was investigated, which refers to the identification of the failure position and failure critical loads because the failure of automobile structures was mainly caused by fatigue. Service loading histories, in the form of wheel loads (forces and moments) and strains of critical regions were measured on a test track of a proving ground. Failure position was determined by comparing the damage values of the critical regions calculated with linear damage rule, while critical loads were determined by the correlation analysis between wheel loads and strain of failure position. The results of damage comparison and correlation analysis indicate that fatigue failure occurs on the torsion beam near the welding seam between it and reinforcing part and could be attributable to vertical forces on the wheel, especially the difference between left and right wheel which introduced an additional torque on the beam. The correctness of the deduced failure mode was demonstrated by conducting fatigue tests on MTS 6DOF road load simulator under all wheel loads and only vertical forces. The conclusion could be helpful for the design and developing load spectrum for accelerated durability test of this kind rear suspension.

Reliabilty-based Torsional Design of Reinforced Concrete Beams Strengthened with CFRP Laminate

The structural reliability of torsional concrete beams strengthened with full and strip wrapping of carbon fiber reinforced polymer (CFRP) laminate is investigated. The first order-second moment reliability method has been applied to make a reliability assessment on the torsional capacity designed by technical guideline in Iran. The code No.345 published by the Management and Planning Organization of Iran (MPO 345-2006) is the first technical code in Iran for design of concrete members strengthened with CFRP laminate. In this work, the average reliability indexes for unstrengthened, strengthened with full wrap and strengthened with strip wrap beams have been found. The results indicate that the MPO design guideline are some unconservative. A reliability strengthening ratio is introduced for assessment of the variation in average reliability index before and after strengthening with different resistance factors. A parametric study on this factor reveals that if the reliability level of the strengthened reinforced concrete beams is kept to be consistent with their similar unstrengthened beams, a value of 0.89 and 0.81 for strengthened with full wrap and strengthened with strip wrap, should be applied, respectively.

Double Laplace Transform Computing Dynamic Response of the Large Thickness to Span Ratio Beam

In this paper, use double Laplace transform, in the image space deep beam deflection and corner of analytic is obtained,Then use the numerical inversion of Laplace transform ,time domain dynamic response curve is calculated. Also apply to the combined effects of sandwich beam bending and torsion beam dynamic response calculation.

Improved hot-stamping analysis of tubular boron steel with direct measurement of heat convection coefficient

There are two types of hot-stamping processes, direct and indirect, depending on the sequence of the heating, forming, and quenching steps and the method used for each step. In this study, an indirect hot-stamping process consisting of forming at room temperature, heating, and water quenching was applied to develop a coupled torsion beam axle. The analysis results indicated that the application of the heat convection coefficient is critical in the simulations and must take into account the temperature and specific location in the model to ensure the accuracy of the heating and quenching analysis. The heat convection coefficients used in the analysis were directly measured at various positions of the tube (e.g., outside, inside, and bending region) using thermocouples, and the final values were determined through correlation between the actual tests and numerical analysis. The experimental and simulated final deformed shape and temperature distribution were in good agreement.

Determination Analysis of the Torsion Beam Suspension FEA Model and Fatigue Strain Based on Road Test

Accurate FEA model of torsion beam suspension and its strain histories are keys to precisely predicting its fatigue life. A strain analysis method is presented, integrating FEA and neural network analysis. The displacement and force histories of the wheel center and strain histories of multiple measurement points on the suspension are measured from road durability test. Apply transient response analysis to determine the FEA model and obtain strain histories of the measurement points. Use a neural network method to obtain accurate additional load. By comparing analysis results and test data, the accurate strain response of torsion beam suspension can be gained

A structural gradient theory of torsion, the effects of pretwist, and the tension of pre-twisted DNA

A structural gradient theory of torsion of thin-walled beams is developed. A non-local estimate of the mean value of the angle of twist of the beam leads to a shear gradient that is energetically consistent with a bi-moment, in the spirit of the averaging theory of Vardoulakis and Giannakopoulos (2006). The geometric details of the cross section play the role of the microstructure of the beam, introducing a size effect in the torsion problem. The appropriate boundary conditions are derived from the variational formulation of the problem. The proposed gradient elasticity theory is identical to Vlasov’s torsion theory of thin walled elastic beams. The tension of pre-twisted DNA is analyzed at high axial loads, where enthalpic elasticity prevails. A size effect is naturally introduced, indicating that shorter DNA lengths lead to stiffer response in torsion. It is shown also that the complete unwinding of DNA triggers the debonding of its strands.

Probabilistic assessment of torsion in concrete beams externally strengthened with CFRP composites

This paper illustrates an analytical probabilistic study of concrete beams subjected to torsion that are strengthened with carbon fiber reinforced polymer (CFRP). Hii and Al-Mahaidi’s method is one of the best analytical models for evaluating the torsional capacity of CFRP strengthened reinforced concrete beams. The first-order reliability method is carried out to probabilistically assess the capacity of CFRP-strengthened beams. For this aim, the statistical characteristics of design variables and model errors have been considered, followed by the determination of the average reliability indexes of the strengthened beams. The effect of each design variable on the average reliability is also determined. The assessment shows that the Hii and Al-Mahaidi’s analytical model is unconservative. In order to correct the situation, a more relaxed set of resistance factors for use in a load and resistance factor design format are needed. These are then determined for two target reliability levels of \( \beta_{\text T} \) = 3.0 and \( \beta_{\text T} \) = 3.5. It is found that factors of 0.9200 and 0.8225 are needed for target reliability levels, \( \beta_{\text T} \) = 3.0 and \( \beta_{\text T} \) = 3.5, respectively. Values of 0.9 and 0.8 are suggested for use in real practice depending on the target reliability sought.

Calculation of Bridge Transverse Load Distribution Coefficient Based on Generalized Rigid Cross-Beam Method

Rigid cross-beam method is one of the most widely used calculation strategy for bridge transverse load distribution coefficient, which is based on grillage theory. However, the shear deformation of the main girder and the difference of transverse load distribution in longitudinal direction are ignored in the calculation process. In this paper, a generalized rigid cross-beam method are proposed based on the displacement beam theory and torsion theory of thin-walled bars, which can take account of the influence of shearing deformation, the difference of the transverse load distribution in longitudinal direction, and torsional behavior of the beam. Numerical simulation demonstrated that the proposed method possesses favorable accuracy and applicability.

Experimental and theoretical investigation on torsional behaviour of CFRP strengthened square hollow steel section

Carbon fibre reinforced polymer (CFRP) has been used to strengthen steel members in bending and compression. There is a lack of understanding on behaviour of CFRP strengthened steel beams subject to torsion. This paper presents an experimental study on the behaviour of CFRP strengthened square hollow section (SHS) beams in pure torsion. A set of tests on CFRP strengthened steel specimens under torsion was carried out in which several different strengthening configurations were used. CFRP sheet wrapping consisted of different configurations including vertical, spiral, and reverse-spiral wrapping were used. The results showed that using CFRP could improve the elastic and plastic torsional strength of CFRP strengthened steel beam specimens. The number of layers of CFRP and the strengthening configurations were important factors for the improvement. Based on the measured values of the torsional moment at yielding and at ultimate, the corresponding twists, the torsional behavioural curves and the failure modes of the strengthened beam specimens, useful concluding remarks are presented.

A coupled bending-torsion model for electrostatically actuated torsional nano/micro-actuators with considering influence of van der Waals force

In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton’s second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of the bending stiffness to the torsion stiffness of the supporting torsion beams is relatively low, the dominant instability mode of the actuator would be the bending mode and otherwise the dominant instability mode would be the torsion mode. It is also observed that the presence of the vdW force can significantly reduce the pull-in angle and pull-in deflection of the nano/micro-actuator. The presented results also show that the vdW force can lead to considerable reduction in the pull-in voltage of the actuator. The equilibrium behavior of the actuator is studied, and it is observed that the vdW force and also bending of the supporting torsion beams greatly reduce the maximum allowable voltage which can be applied to the actuator. Results of this paper can be used for successful design of electrostatically actuated torsional nano/micro-actuators where the size of the actuator is sufficiently small, and as a result, the vdW force plays a major role in the system.

열간성형공법으로 제작된 현가부품의 피로특성 연구

Hot forming using boron steel is currently used for manufacturing low-weight automobile body parts, and a high tensile strength of about 1,500 MPa is obtained after hot forming. However, a high fatigue life is a more important factor than high strength when it is used for automobile suspension parts. A tubular torsion beam axle (TTBA) is one of these suspension parts, and this research deals with the fatigue characteristic of TTBA using hot forming. The low cyclic fatigue life of boron steel is investigated according to the cooling method. In addition, a structural and fatigue analysis of TTBA is performed to predict the fatigue life. The stress concentration that occurs in the tubular torsion beam is found, and the longest fatigue life occurs when rapid cooling is utilized in the TTBA fabrication.

Numerical Simulation of the Kinematic Behavior of a Twist Beam Suspension Using Finite Element Method

The use of numerical simu lations in the design of automotive components has contributed to reducing the design time, decreasing the prototypes costs and increasing reliability of the final product. In addition, the search for solutions of lo w cost and satisfactory performance is essential for the success of the product in the world market. Twist-beam suspensions are an examp le of this co mpetit ive environ ment. This solution presents a very satisfactory performance when applied to light vehicles and has an excellent relationship between cost / benefit in the automotive market. It is estimated that more than 90% of light vehicles manufactured in emergent countries use this type of suspension at the rear. Despite its acceptance in the automotive market there are few studies related to the twist -beam suspension, perhaps because of its simplicity and low cost design and ease of manufa cturing. Un like other types of suspension, the twist-beam has a flexib le torsion beam connecting the swing arms. The evaluation of the deformation of this flexib le element becomes essential to understand their kinemat ic behavior. Thus, the use of software based only on the rigid body dynamics is not suitable to analy ze this type of suspension. The main objective of this work was to evaluate through numerical simu lation based on finite element method, the influence of the torsion beam on the kinematic behavior of a twist-beam suspension. It was evaluated the influence of both the position and orientation of the torsion beam on the suspension, under symmetric and asymmetric loadings.

Computation Method for Fatigue Strain in a Long-span Steel Bridge Asphalt Pavement by Using the Three-hierarchy Structure

To derive the strain formulas of fatigue design for a steel bridge asphalt pavement, the three-hierarchy structure, which includes simplified models of plane bending strain for a full bridge, transverse flexural-tensile strain attributed to steel box beam torsion, and continuous laminated beam bending strain of the asphalt pavement of a partial bridge, was analyzed. Based on the model for a multi-span, elastic-supported continuous beam, the elastic foundation beam model and the main calculation parameters, namely, the equivalent support stiffness of the bracing cable, bending stiffness of the main beam, torsion stiffness of the steel box beam section, the equivalent support stiffness of bridge deck stiffener, the worst load locations for full bridge, as well as eccentric and partial loads, were analyzed. The method for calculating the flexural-tensile strain at steel deck surface was obtained by using the three-hierarchy structure model. According to the bridge deck stiffener model, the transverse flexural-tensile strain at the pavement surface exceeded 80%. On the other hand, the plane bending model of the main girder found that the strain is no more than 15% with full bridge loading. The main girder torsion model determined that the strain exceeded 15%.

Fractographic Observation of Various Loading Modes of Fibre Reinforced Laminates

One of the major disadvantages of laminated composites is their tendency to delaminate. Unidirectional glass/epoxy laminates have been tested under static conditions by the use of fracture mechanics. Mode I, mode II, mixed mode I-II, mode III and mixed mode II-III tests were performed. Double cantilever beam (DCB), end-notched flexure (ENF), mixed-mode bending (MMB) and edge crack torsion (ECT) specimens were used. Scanning electron microscopy technique was used to identify distinguishing fractographic features and to establish the differences between the various modes of fracture after specimens testing. The propagated orientation of the delamination could be specified from the patterns of fracture surface. Scanning electron micrographs of fractured surfaces showed that the most predominant fractographic features in mode I and mode II are the large amount of fibre pull-out and the cusps markings respectively. In the MMB specimen the fracture surfaces are characterized by fibre breakage under shearing with fractures localized in the resin with cusps having an orientation of 90º (mode II) and also fractures localized in the resin and along the resin/fibre interface (mode I). Mode III characterization concluded that some limited mixed mode II-III seems to be present for ECT specimen on delamination initiation and growth, but a large majority of mode III delamination is present.

A high-quality factor of 267 000 micromechanical silicon resonator utilizing TED-free torsional vibration mode

In industrial applications of a micromechanical silicon resonator as a physical sensor, a high-quality factor Q and a low-temperature coefficient of Q (TCQ) are required for high sensitivity in a wide temperature range. Although the newly developed thin film encapsulation technique enables a beam to operate with low viscous damping in a vacuum cavity, the Q of a flexural vibration mode is limited by thermo-elastic damping (TED). We proposed a torsional beam resonator which features both a high Q and a low TCQ because theoretically the torsional vibration mode does not suffer from TED. From experiments, Q of 267 000 and TCQ of 1.4 for the 20 MHz torsional vibration mode were observed which were superior to those of the flexural mode. The pressure of the residual gas in the cavity of only 20 pl volume, which is one of the energy loss factors limiting the Q, was successfully estimated to be 1–14 Pa. Finally, the possibilities of improving the Q and the difference of the measured TCQ from a theoretical value were discussed.

Application of Rigid-Flexible Coupling in Stiffness Calculation of Double Wishbone Suspension

Based on multi-body Dynamics theory, the 1/4 multi-rigid model of double wishbone suspension of automobile in ADAMS/View is created, and use ANSYS software to analyze torsion beam flexibility. Furthermore, the rigid-flexibility model has been created and the rigid change of suspension line along with the tire dynamics change is simulated. The result shows that the rigid-flexible coupling model is more accuracy than the multi-rigid one and fits the practical situation even better. This paper proposes an efficient method for analyzing the rigid of double-wishbone suspension vertical line.

An analytical approach for design and performance evaluation of torsion beam rear suspension

Torsion beam rear suspension systems have been widely used in small passenger cars owing to their compactness, light weight, and cost efficiency. To study the roll behavior of torsion beam suspension systems, analytical equations to obtain roll center height, roll steer, and roll camber have been developed in terms of geometry points through the kinematic consideration of the system on the assumption of rigid body motion. In most cases, commercial software for finite element methods or experimental equations for individual parts are utilized for the design and evaluation of the suspension systems. This paper, however, proposes an analytical method to calculate the torsional stiffness of a torsion beam for various loading conditions based on the assumption that a torsion beam is in the range of linear torsional angles with a constant cross section. The proposed method is useful for exploring suspension system design, especially in the early stage of vehicle system development in which detail design parameters such as layout, cross sections, and materials are not yet determined. It is shown that the torsional stiffness and roll stiffness predicted using the proposed method has sufficient precision with around four percent difference from the results of finite element analysis and bench tests.

Analytical modeling of bending effect on the torsional response of electrostatically actuated micromirrors

This paper presents analytical solutions for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. First the energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. These equations are then solved using Homotopy Perturbation Method (HPM) for the especial case of α=0 where α is a small nondimensional geometrical parameter defining the starting point of the underneath electrodes. Then straight forward perturbation method is applied for finding the pull-in angle and pull-in displacement of the micromirror for the general case of α≠0. The presented results which were in excellent agreement with numerical simulations show that neglecting the bending effect in electrostatic torsion micro actuators can lead to several hundred percent of overestimation of the stability limits of the device. In order to study the voltage-angle and voltage-displacement behavior of the micromirror, equilibrium equations are solved using HPM. Presented results are in good agreement with numerical simulations and also with experimental findings.

CTBA 지오메트리 보상 시스템 개발

CTBA(Coupled Torsion Beam Axle) has been adapted as the rear suspension of a compact car. Because that has the advantage of cost and weight in comparison with multi-link type. But CTBA has the disadvantage in vehicle stability to become oversteer occurring toe-out of the rear wheel when cornering and braking. In this study, we suggested CTBA Geometry Compensation System to overcome the disadvantage of CTBA. We predicted braking and cornering vehicle performance from proposed equation and numerical simulation. And also, the results were compared to objective and subjective evaluation in vehicle.

Nonlinear free vibrations of thin-walled beams in torsion

Nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warpings are investigated. The coupled nonlinear torsional–axial equations of motion are considered. Ignoring the axial inertia term leads to a differential equation of motion in terms of angle of twist. Two sets of torsional boundary conditions, that is, clamped–clamped and clamped-free boundary conditions are considered. The governing partial differential equation of motion is discretized and transformed into a set of ordinary differential equations of motion using Galerkin’s method. Then, the method of multiple scales is used to solve the time domain equations and derive the equations governing the modulation of the amplitudes and phases of the vibration modes. The obtained results are compared with the available results in the literature that are obtained from boundary element and finite element methods, which reveals an excellent agreement between different solution methodologies. Finally, the internal resonance and the stability of coupled and uncoupled nonlinear modes are investigated. This study can be a preliminary step in the understanding of complex dynamics of such systems in internal resonance excited by external resonant excitations.