Objective In order to solve the TBS (torsion bar shaft) torsional stiffness and strength for the outer support anti-rolling device in railway vehicles, an analytical method of introducing the TBS ...deformation coordination conditions is proposed. Method Taking 1/2 TBS for the outer support anti-rolling device as an example, based on its stress state and load distribution, the structural symmetry and the characteristics of bearing anti-symmetric working loads are used to introduce structural deformation coordination conditions for solving the unknown forces and moments of a primary statically indeterminate system, obtaining the shear force and bending moment distribution of the TBS, and deriving calculation formulas for the torsional stiffness and strength of the anti-rolling torsion bar device. Using the outer support anti-rolling torsion bar device made of 52CrMoV4 spring steel as an example, a comparative analysis is conducted between the analytical solution calculation results and the finite element model ca
This paper examines the use of various materials for the force limiter torsion bar found in an automotive seat belt assembly. We have selected the following materials: carbon steel, cast stainless ...steel, cast low alloy steel and cast aluminium alloy. The primary method used for this study is finite element analysis (FEA) and the use of the named materials on a 3D model of the torsion bar, constructed using the dimensions of a standard part. The 3D models were created with a 3D CAD program and the FEA analysis was carried out with special software. For the input values, the torsion bar was fixed at one corner and a 360 degree rotation shift at the other corner. A fine mesh of 1.5 mm/element was also set to get a more accurate analysis. The results of this study are in the form of stress, strain, safety factor and displacement plots generated by the FEA analysis software showing the difference between the materials. The main outcome of the study is to determine the best overall material to manufacture the part in terms of performance and cost.
In this paper, a simple but effective trailing edge flap system was proposed. This preliminary concept uses a more practical and stable actuation system which consists of a motor-driven worm gear ...drive and flexible torsion bar. The flexible torsion bar is designed to be easily twisted while keeping bending rigidity as a sup-port and the worm gear drive not only provides a high torque to overcome aero-dynamic forces on the flap area and the torsional rigidity of the support bar, but also acts as a brake to avoid instability due to the high torsional flexibility of sup-port bar. A preliminary level design study was performed to show the applicability of the new trailing edge flap system for wind turbine rotor blade or helicopter blade.
•A novel Tension-Torsion Hopkinson bar was developed.•The dynamic tensile-shear failure envelope of commercially pure copper is studied.•The high-rate loading paths show proportional direct and shear ...strain.•The Drucker-Prager criterion approximates the failure stress envelope.•The failure stress locus indicates rate dependence from low to high strain rates.
In this paper, we present the dynamic response of commercially pure copper subjected to combined tension-torsion loads representative of real case impact scenarios. Experiments were conducted both quasi statically, at a strain rate equal to 10−3 s−1, and dynamically at strain rates in the region between 500 s−1 and 1000 s−1. All high rate experiments were conducted using a novel Split Hopkinson Tension-Torsion Bar instrumented with high-speed photographic equipment. The dynamic combined loading experiments demonstrate the capability of the apparatus to generate longitudinal and torsional stress waves which are synchronised upon loading of the specimen. The presented data show that dynamic equilibrium conditions and nearly steady strain rates were achieved during the experiments. Additionally, the analyses of the loading paths show that nearly proportional strain loading was attained during testing.
The measured experimental results illustrate, for the first time, the failure stress locus of the material over a wide range of stress states including pure torsion, shear-dominated combined tension-shear, tension-dominated combined tension-shear and plain tension. The quasi-static and dynamic failure envelopes are herein presented in the normal stress vs shear stress space to motivate the development of accurate and effective constitutive models. To conclude, the Drucker-Prager criterion was employed to approximate the failure loci and to assess the rate sensitivity of the material. A moderate asymmetry of the uniaxial ultimate stresses in tension and compression is predicted both at quasi-static and dynamic strain rates.
Display omitted
•A novel tension-torsion Hopkinson bar was developed.•The dynamic tensile-shear failure envelope of commercially pure titanium is studied.•The high-rate loading paths show proportional direct and ...shear strain.•The Drucker-Prager criterion approximates the failure stress envelope.•The failure stress locus indicates rate dependence from low to high strain rates.
The mechanical response and failure mechanism of commercially pure titanium subjected to combined tension-torsion loading are studied experimentally at strain rates ranging from 10−3s−1 to 103s−1. A novel tension-torsion split Hopkinson bar (TTHB) equipped with a high speed camera was utilised during high-rate experiments, while quasi-static tests were conducted using a universal screw-driven machine. The multiaxial dynamic experiments demonstrate the ability of the developed TTHB apparatus to achieve synchronisation of longitudinal and torsional waves upon loading the specimen, to satisfy the dynamic equilibrium of the specimen and to attain constant strain rate loading. The failure envelope of commercially pure titanium was analysed over a wide range of stress states including pure torsion, shear-dominated combined tension-shear, tension-dominated combined tension-shear, and plain tension. The analyses of the loading paths show that these were nearly proportional in terms of strain. The multiaxial failure stress locus was constructed in the normal versus shear stress space from experiments conducted at low and high rates of strain.
The Drucker-Prager criterion was employed to approximate the failure envelope and to assess its rate sensitivity. The failure stress locus of commercially pure titanium and its rate dependence are reported for the first time. The TTHB apparatus developed allows the definition of the failure stress locus of aerospace materials directly from experiments and, therefore, the evaluation of the existing failure/yielding criteria.
The boundary value problems and closed form solutions for the strain localization in a softening bar under pure torsion with the continuum damage and the embedded discontinuity formulations are ...developed. In this formulation, quasi-brittle materials such as concrete or mortar are considered. The boundary value problem is developed from a variational formulation and the corresponding Euler-Lagrange differential equation. These formulations include not only the continuum damage model, in which the twist angle jump and the angular strain concentration are smeared into the volume of the bar, but also the embedded discontinuity model, in which the twist angle jump and the angular strain localization are lumped into a zero thickness localization zone. The non-linear behaviour of the materials is described by a continuous constitutive model for the continuum damage model and by a discrete constitutive model for the embedded discontinuity model; both constitutive relationships include linear or exponential softening. Solutions to overcome the problem of crack bandwidth dependency when modelling strain localization with continuous models are developed, these solutions are based on a rational analysis of the kinematics of the strain model and on the fracture energy per unit area. To validate the developed closed form solutions for the strain localization problem in a softening bar under torsion, three examples of concrete cylindrical specimens under torsion are presented. The relationship between the total area under the twisting moment-twist angle curves and the fracture energy of the material guarantees the correctness of the developed closed form solutions.
•Closed solutions for localization in a pure torsion softening bar are developed.•Relationship between fracture energy under tension and under torsion is developed.•Average strain and embedded discontinuity kinematics are compared.•Solutions to overcome the mesh dependency when modelling localization are proposed.
The deformation performance of maraging steel samples fabricated using the laser powder bed fusion technique was evaluated using the split Hopkinson torsion bar (SHTB) test. Thin-walled tubular ...maraging steel samples were deformed under dynamic torsional loading at strain rates of 260 s−1 to 720 s−1 using twist angles varying from 3 to 12°. Microstructural and textural investigations were carried out on deformed samples using the electron backscatter diffraction technique and scanning electron microscopy. Results showed that maraging steel samples fractured when deformed using an angle of twist of 12° and strain rate of 650 s−1. As a result of deformation localization at high strain rates, adiabatic shear bands are developed in some thin-walled tubular torsion specimens deformed using the 12-degree angle of twist, leading to fracture. Textural studies showed that texture weakening occurred with an increment in strain rate ascribable to grain fragmentation. In this study, two models (empirically and semi-empirically) were employed for describing maraging steel performance during high strain-rate torsional loading. Simulation results based on Kobayashi-Odd and Nemat-Nasser models agreed well with the experimental data.
•Maraging steel parts were produced by the laser powder bed fusion technique.•High strain rate torsion test was conducted on maraging steel samples.•Angle of twist 3, 6, 9, and 12° was applied in this study.•Fracture happened in the angle of twist 12° for maraging steel.•Kobayashi–odd and Nemat-Nasser constitutive models were used for dynamic shear stress-strain response.
In this paper, the torsion problem is analyzed by boundary element method (BEM). After applying a new error estimation technique in the BEM, we can derive the numerical error of BEM. We extend the ...research of previous literature by the authors Chen and Chen 1, to the real engineering problem. This paper estimates the discretizing error caused by using BEM for solving the torsion problem with inclusions. The main characteristic of this technique is that the exact solution is not known in prior. In the technique, we need to create an auxiliary problem that the government equation, domain shape, and boundary condition type are the same as the given real problem. Besides, it has an analytical solution that satisfies the governing equation. We can derive the suitable number of elements by solving the auxiliary problem. Subsequently, by using the suitable number of elements in the BEM, we can obtain the appropriate solution for the real problem. Finally, several cases in the literature are given to illustrate the validity of the novel approach applied in the BEM to solve the real problem.
Military vehicles are required to negotiate drastic ride environments. Therefore, the vibration magnitudes which are transmitted to the vehicle chassis through the suspension system due to dynamic ...vehicle-terrain interactions, are usually large. Hence, it is necessary to study the vibrations that are transmitted to the sprung mass as it negotiates different types of terrain at different speeds. The present study is focused on the development of sprung mass non-linear pitch dynamics mathematical model of a military vehicle with a trailing arm torsion bar suspension system. The trailing arm kinematics and dynamics are incorporated into the non-linear governing equations of motion of the sprung and unsprung masses which consider the effects of sprung mass large pitch angular motions. The model is solved by coding in Matlab. The sprung mass non-linear pitch dynamics mathematical model is validated with an equivalent multi-body dynamics model which is developed by using MSC.ADAMS. This mathematical model would play a key role to fine-tune the vehicle and suspension parameters as well as comparatively evaluate the performance of the hydro-gas suspension system. The model can further be extended to include the military vehicle weapon recoil effects which can cause considerable magnitudes of vehicle pitch. Apart from simulating ride dynamics of the entire vehicle, the influence of movement with crane payload on the military recovery vehicle pitch dynamics can also be brought out as a useful extension of this mathematical model.
PDF
