Extrusion of axi-symmetric bi-metallic tubes from solid circular billets: application of a generalised upper bound analysis and some experiments

The generalised upper bound technique previously applied to the determination of working pressures in extrusion–piercing of solid billets (Chitkara NR, Aleem A. Int J Mech Sci 2001;43:1685–709.) to form hollow monometallic tubes is extended to analyse the problem of bi-metallic tube extrusions through profile shaped dies and mandrel combinations. Theoretical results of mean extrusion pressures obtained from the generalised upper bound analysis are compared with those obtained earlier by the generalised slab method of analysis (Chitkara NR, Aleem A. Int J Mech Sci 2001;43:2857–82.) and some experiments. A few salient observations made during the experimental investigations carried out into forward extrusion of bi-metallic tubes made of h.c. copper and c.p. aluminium are also given and the results commented upon.     

Forging and heading of hollow spur gear forms: an analysis and some experiments

To analyse the process of incremental forging and heading of hollow spur gear forms from initially ring-type specimens, the two types of theoretical approaches followed were an adaptation of the upper bound technique, applied previously to the solution of solid spur gear form forging (Chitkara NR, Bhutta MA. International Journal of Mechanical Sciences 1996;38(8–9):891–916) and the modification of the slab method of analysis given earlier for the case of spline forging and adapting it to the tapered teeth representing the actual profile teeth of the spur gear with the pressure angle of 14 °, (Chitkara NR, Bhutta MA. International Journal of Mechanical Sciences 1996;38(8–9):871–89). In each case, the theoretical results estimated were compared with those obtained experimentally during quasi-static forging and heading of hollow spur gear forms using the model material, tellurium lead. The characteristic deformation modes and some salient observations made on working pressures are given and the results commented upon.     

Extrusion of axi-symmetric tubes from hollow and solid circular billets: : a generalised slab method of analysis and some experiments

To analyse the mechanics of extrusion of an axi-symmetric tube starting from either a hollow or a solid circular billet, a generalised analytical approach based on the slab method of analysis is developed for a somewhat general case of tube extrusion through a general profile-shaped die and over a general profile-shaped mandrel. The results of mean extrusion pressures obtained from the theoretical analysis for the various die–mandrel combinations are compared with the experimental investigation carried out on a model material and with the work of other authors. These show reasonably good agreements.     

Extrusion of axi-symmetric bi-metallic tubes: some experiments using hollow billets and the application of a generalised slab method of analysis

A generalised slab method of analysis is developed for the extrusion of axi-symmetric bi-metallic tubes through profiled shaped dies and over profile shaped mandrels. It is applied to different combinations of die shapes and mandrels. An experimental investigation into forward extrusion of bi-metallic tubes made of cp aluminium and hc copper was also carried out and the resultant non-dimensionalised extrusion pressures, flow patterns and characteristic deformation modes observed are given and the results commented upon. The theoretical results of extrusion pressures obtained from the analysis are compared with the experimental as well as those of other authors. These show reasonably good agreement.     

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

This article studies tubular hydroforming of high strength low alloy (HSLA) and dual phase (DP600) straight tubes under the action of end feeding loads. Experiments demonstrate that higher end feed loads enhance the formability of the tubes and increase the internal fluid pressure for onset of necking and bursting. Because of the action of the internal pressure and the axial compressive load, the onset of localization (necking) is due to a complex three-dimensional state of stress. Using free expansion experiments, approximate upper and lower bound strain-based forming limit curves are determined for the tube materials. These limit curves, in turn, are used to derive upper and lower bound extended stress-based forming limit curves [Simha et al., Prediction of necking in tubular hydroforming using an extended stress-based FLC. Transactions of the ASME Journal of Engineering Materials and Technology 2007;129(1): 36-47]. In conjunction with finite element computations that use solid elements to model the tube, these stress-based limit curves are used to predict upper and lower bound necking pressures under the action of end feed loading. These predictions of necking pressures, when an appropriate coefficient of tube-die friction is used, are found to bracket the experimentally measured necking pressures. Computations using plane stress shell elements to model the tubes are shown to give erroneous results, since the plane stress approximation is not valid when tubes are hydroformed in a die.     

Generation of Gas Discharge Plasma by an Arc Source with a Cold Hollow Cathode

The results from a study of an arc plasma source with a cold hollow cathode are presented. The source generates plasma with a density of ∼10¹⁰ cm⁻³ in a volume of ∼0.2 m³ at discharge currents of up to 150 A, an arc discharge operating voltage of 30–40 V, and a low pressure of 0.1–1 Pa. The motion of the cathode spot in the crossed electric and magnetic fields inside the hollow cathode and the cathode’s special design make it possible to eliminate almost completely the penetration of the sputtered cathode material into the working vacuum chamber.__________Translated from Pribory i Tekhnika Eksperimenta, No. 3, 2005, pp. 62–66.Original Russian Text Copyright © 2005 by Schanin, Koval, Akhmadeev.     

Near net shape spline forging: An experimental investigation and a simple upper bound analysis

A simple analysis based on an upper bound elemental technique is presented for the incremental forging of a near-net shaped splined rotor shaft-type component formed using a cylindrical rod-type specimen. The results of an experimental investigation made into the working pressures and deformation modes observed during progressive forging of tellurium-lead specimens of different aspect (length to diameter) ratios into spline shaped components are compared with those predicted theoretically. The agreement was found to be reasonable and encouraging.     

A Plasma-Cathode Electron Source for Ribbon-Beam Generation at Forevacuum Pressures

A plasma electron source producing a ribbon beam at pressures of up to 60 mTorr is described. The discharge with an extended rectangular-section hollow cathode is used as a plasma generator. Electrons are extracted through the emission slit in the anode covered by a metal mesh. The maximum electron-beam current is 1 A, and the energy is 2–6 keV. The beam characteristics are presented, and the conditions for attaining the maximum operating pressure are analyzed.     

On the collapse of dented cylinders under external pressure

In this paper the reduction in the collapse pressure of long cylinders which have local dents is evaluated through a combination of experiment and analysis. A number of stainless steel tubes, with diameter-to-thickness ratios of approximately 33,24 and 19, were indented to various degrees with spherical indentors of two diameters. The geometry of each dent was recorded using an imperfection scanning system and the cylinders were subsequently collapsed under external pressure. Denting reduces the local collapse resistance of the cylinder. For larger dents the collapse pressure was found to approach the propagation pressure of the tube. Collapse was found to be relatively insensitive to the detailed geometry of a dent but to be critically dependent on the maximum ovalization of its most deformed cross section (Δ_0d). The collapse pressures of tubes with dents produced by indentors of different diameters could be well correlated through this measure of the dent geometry.The denting and collapse processes were simulated numerically using appropriately nonlinear elastoplastic shell analyses. Both steps of such simulations were shown to be in good agreement with experimental results for a broad variation of the parameters of the problem. The key role of the geometric parameter Δ_0d was exploited in order to generate a Universal Collapse Resistance Curve for dented cylinders. It was possible to show that the post-limit load response (P — Δ) of a cylinder, with a small but axially uniform initial ovality, provides a very good lower bound to the collapse pressures of the dented cylinders plotted against the dent parameter Δ_0d. The significance of this curve is that it can be used to estimate the reduction in the collapse pressure of a cylinder with any dent geometry from only one relatively simple measurement of the geometry of the dented section.     

An upper bound analysis for the reshaping of thick tubes with experimental verification

Reshaping process based on the cold roll forming technology is a process in which noncircular pipes can be produced from circular pipes. A generalized upper bound solution for the deformation of thick tubes between four flat rolls has been formulated. The deforming zone has been divided into two areas namely the “contact region” and the “free region”. Owing to the different physical character of these deforming zones two different kinds of admissible velocity fields have been obtained for each of the deforming zones. To formulate the stream lines and stream surfaces in the deforming zones use has been made of the Bezier curves which have been utilized to define stream lines in such a way that could be manipulated easily to obtain the optimum shape for the upper bound solution to be optimized. This new formulation was used to predict the upper bound on power. Using the theory presented here, the influence of process parameters such as radius of rolls, initial pipe dimensions; amount of roll gap reduction and the roll speed on the final rolled product were investigated. In order to verify the theoretical results, an experimental rolling rig was designed and built which comprised of four flat rolls. Using this rig Al 6101 round pipes were rolled and the variations in the above-mentioned parameters were investigated. Quantities such as energy, wall thickness, and corner radius of the tube were observed and measured. Comparison of theoretical and experimental results showed good agreement and hence demonstrated the capabilities of the new formulation presented here.     

Nosing of thin-walled PVC tubes into hollow spheres using a die

In a recent work, the authors presented a new single-stage nosing process for manufacturing metallic hollow spheres from thin-walled tubes that is capable of extending the formability limits of conventional nosing (Alves and Martins in J Strain Anal Eng Des 43:205–216, 2008). The fundamentals of the process were investigated by means of standard finite element analysis and its technological viability was evaluated by means of experimentation on industrial AA6060 aluminium alloy tubes. This paper is aimed on extending the scope of single-stage nosing so as to include the production of polymer hollow spheres. The investigation draws from the development of an innovative extension of the flow formulation that is capable of modeling cold plastic deformation of pressure-sensitive yield surfaces under a nonassociated flow rule to the identification and analysis of the major process parameters that influence formability and quality of the polymer hollow spheres. The overall performance of the process is assessed by means of a combined theoretical and experimental investigation made with industrial polyvinyl chloride (PVC) tubes. Results show that the innovative extension of the finite element flow formulation is capable of successfully modeling cold forming of polymers and that single-stage cold nosing of thin-walled PVC tubes can be successfully utilized for manufacturing sound hollow spheres.     

A gas-ion source with a grid-stabilized plasma cathode

A two-stage source of a broad beam of gas ions is described. The source contains a grid-stabilized plasma cathode and an anode stage with a multicusp magnetic field. The emission current of the plasma cathode (which is based on a glow discharge with a hollow cathode) is controlled between 0.1 and 1 A. The voltage that is applied to a bipolar diode between its cathode grid and anode plasma and determines the energy of fast electrons ranges from 50 to 200 V. The operating pressure of the argon in the anode stage is 4 × 10^–3–1 × 10^–1 Pa. A beam of argon ions having an energy of up to 5 keV and a current of >100 mA is formed by a two-electrode ion-optical system with a working area of 50 cm².__________Translated from Pribory i Tekhnika Eksperimenta, No. 2, 2005, pp. 107–111.Original Russian Text Copyright © 2005 by Gavrilov, Kamenetskikh.     

Frequencies and mode shapes for thick truncated hollow cones

The finite element method of analysis is employed to study the vibration of truncated thick hollow cones. The three-dimensional strain–displacement equations are used to formulate the finite element in the conical coordinate system. Axial symmetry is assumed and the formulation is reduced to two dimensions while maintaining the three-dimensional character of the analysis. The accuracy of the analysis is established by comparing results for free–free boundary conditions with existing solutions. The effects of different boundary conditions, including fixed–free and fixed–fixed, are studied to determine their effects on the frequency of vibration. Frequency results are given for an additional boundary condition corresponding to a layer attached to the exterior of a rigid cone. Nondimensional results for an isotropic material with Poisson's ratio of 0.3 are presented in terms of tables, plots of frequency versus cone apex angle and plots of selected mode shapes.     

An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming

In this paper, a combined experimental and numerical investigation of free hydroforming of aluminium alloy tubes is conducted. The tubes are subjected to different loading histories involving axial compression and internal pressure. The circumferential and axial strains experienced by the tubes are continuously recorded along with the pressure and axial load. The numerical simulations are carried out using both 2D axisymmetric and 3D finite-element formulations by applying the experimentally recorded axial load and internal pressure. In the latter, a geometric imperfection is introduced in the form of wall thickness reduction at the tube mid-length in order to trigger necking which happens after significant bulging and beyond the stage of peak pressure. The strain histories and peak pressures obtained from the simulations agree well with those determined from the experiments. Further, the forming limit curve predicted by the simulations as well as from a M–K analysis incorporating the computed strain paths corroborate well with the experimental data. The role of nonproportional straining on the mechanics of failure of the tubes due to bulging and necking is studied in detail.     

Theoretical method for estimation of mean pressure on contact area between rolling tools and workpiece in cross wedge rolling processes

The paper gives a new method no determine the mean unit contact pressures on a material—tool contact surface in cross wedge rolling processes (CWR). The dependencies worked out on the basis of the energy and the upper bound methods permits rolling forces to be determined which are comparable to experimentally measured ones. The analysis provides equations which relate the mean contact pressure q_m to the basic process parameters, namely the forming angle α, the spreading angle β, the relative reduction of a portion δ and the shear friction factors m and m_k.     

An accurate de-lamination model for weakly bonded laminates subjected to different sets of edge boundary conditions

This paper extends the applicability of a new method (Soldatos and Watson. Acta Mechanica 1997;123 (3): 163–86; Soldatos and Watson. International Journal of Solids and Structures 1997;34 (22):2857–85; Soldatos and Watson. Mathematics and Mechanics of Solids 1997;2(4):459–89; Shu and Soldatos. International Journal of Solids and Structures 2000;37:4289–307) towards the accurate stress analysis of weakly bonded laminates. The main advantage of the method stems from the fact that it is based on a suitable version of a generalised two-dimensional plate theory that makes use of a small number of degrees of freedom, which is not dependent on the number of the layers involved. Hence, although the method can accommodate with relative ease any set of boundary conditions imposed at the plate edges, it avoids the computationally expensive consequences of corresponding two-dimensional layer-wise plate models or relevant three-dimensional finite element considerations.     

Fuzzy sliding mode controlled slider–crank mechanism using a PM synchronous servo motor drive

The dynamic response of a sliding mode controlled slider–crank mechanism, which is driven by a permanent magnet (PM) synchronous servo motor, is studied in this paper. The rod and crank are assumed to be rigid. The Hamilton’s principle and Lagrange multiplier method are applied to formulate the equation of motion. Reducing the differential-algebraic equations and employing the Runge–Kutta numerical method, the state variable representation is obtained. Moreover, based on the principles of the sliding mode control, a position controller is developed. Then, a simple fuzzy inference mechanism is utilized to estimate the upper bound of uncertainties for the sliding mode controller. Numerical results show that the dynamic behavior of the proposed controller–motor–mechanism system is robust to parametric variation and external disturbance.     

On the transverse vibrations of non-uniform beams with axial loads and elastically restrained ends

The dynamic behaviour of slender tapered beams is examined, in the presence of conservative axial loads, and lower and upper bounds on the free vibration frequencies are obtained. Two different approaches are employed, in order to obtain a narrow range to which the frequencies belong. In the first case a Rayleigh–Ritz method is used, with displacement trial functions given by linearly independent orthogonal polynomials. In the latter case the structure is reduced to rigid bars, connected together by means of elastic hinges, and lower bound to the true frequencies is obtained. It is well known that the Rayleigh–Ritz approach leads to upper bounds, and therefore a (narrow) range is obtained for the exact frequencies.The paper ends with some numerical examples which confirm the usefulness of the proposed methods, and are in good agreement with some previously known results.     

Shape heading of splines and solid spur gear forms:: an analysis and some experiments

To analyse the process of near-net shape heading of splines and solid spur gear forms with the 15 actual involute teeth, each with a pressure angle of , where in each case these were to be forged integral with the shaft and one end of the initial deforming cylindrical specimen was considered as constrained. Two types of theoretical approaches, i.e. the upper-bound technique (Chitkara and Bhutta. Proceedings of 28 MT DR Conference, 1990. p. 431–42; Chitkara and Bhutta. International Journal of Mechanical Sciences 1995;37(12):1247–68; 1996;38(8–9):891–916) and the slab method of analysis (Chitkara and Bhutta. International Journal of Mechanical Sciences 1996;38(8–9):871–89) employed earlier for simple forging of the product were suitably modified to account for the constraint, were applied. In each case, the estimated theoretical results for the die loads at increasing die movements were compared with those observed experimentally during the quasi-static incremental heading of splines and solid spur gears using tellurium lead as the model material for the specimens. The characteristic deformation modes and some salient observations made on the working pressures during the heading process vis-à-vis simple forging of these products are given and the results are commented upon.     

On the propagation pressure of long cylindrical shells under external pressure

Local imperfections induced in long tubes subjected to high external pressures can lead to local collapse, from which a propagating buckle can be initiated. This can result in catastrophic collapse of large sections of the structure. The propagation pressure is the lowest pressure at which such a buckle will propagate. For common structural metal tubes with diameter-to-thickness ratios of less than 100, the propagation pressure is typically half an order of magnitude lower than the collapse pressure of the intact tubes. As a result, the design of several tubular structures with external pressure loading requires that the collapse and propagation pressures be accurately known. This paper deals with the experimental and analytical challenges of establishing the propagation pressure. A special purpose three-dimensional analysis, in combination with experimental observations and results, is used to demonstrate a mechanism of initiation of propagating buckles in long tubes, to study the parametric dependence of the propagation pressure and to illustrate the effect of axial tension on the propagation pressure. Propagation pressures predicted with this analysis are used to evaluate the strengths and weaknesses of simpler models developed in the past.