Springback analysis of channel cross-sectioned bar of work-hardening materials under torsional loading

2016 ◽  
Vol 33 (7) ◽  
pp. 1899-1928 ◽  
Author(s):  
Radha Krishna Lal ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
V.P. Singh
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Work Hardening ◽  
Finite Difference Approximation ◽  
Channel Cross Section ◽  
Difference Approximation ◽  
Plastic Behavior ◽  
Torsional Loading ◽  
Hardening Material ◽  
Content Type

Purpose The purpose of this paper is to deal with the springback problems of channel cross-section bars of linear and non-linear work-hardening materials under torsional loading. Using the deformation theory of plasticity, a numerical scheme based on the finite difference approximation has been proposed. The growth of the elastic-plastic boundary and the resulting stresses while loading, and the springback and the residual stresses after unloading are calculated. Design/methodology/approach The numerical method which has been described in this paper for obtaining the solution of elasto-plastic solution can also be used for other sections. The only care that needs to be taken is to decrease the mesh size near points of stress concentration. The advantage of this technique is that it automatically takes care of all plastic zones developing over the section at different loads and gives a solution satisfying the elastic and plastic torsion equations in their respective regions. Findings As expected, elastic recovery is found to be more with decreasing values of n and λ. The difference in springback becomes more and more with increasing values of angle of twist. The material will approach an elastic ideally plastic behavior with increasing values of λ and n. Originality/value It seems that no attempt has been made to study residual stresses in elasto-plastic torsion of a work-hardening material for a channel cross-section.

Springback Analysis of Rectangular Sectioned Bar of Non Linear Work-Hardening Materials under Torsional Loading

2013 ◽  
Vol 393 ◽  
pp. 422-434 ◽  
Author(s):  
Radha Krishna Lal ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
V.P. Singh ◽  
Sandeep Kumar
Keyword(s):  
Work Hardening ◽  
Deformation Theory ◽  
Rectangular Cross Section ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Torsional Loading ◽  
Rectangular Section ◽  
Steel Bars ◽  
Non Linear ◽  
Theoretical Results

This paper deals with the springback problems of rectangular section bars of non-linear work-hardening materials under the torsional loading. Using the deformation theory of plasticity, a numerical scheme based on the finite difference approximation has been proposed. The growth of the elastic-plastic boundary and the resulting stresses while loading, and the springback and the residual stresses after unloading are calculated. The results are verified experimentally with mild steel bars having a rectangular cross-section and the experimental results have been found to agree well with the theoretical results obtained numerically.

Elastic–plastic deformation and residual stresses in helical springs

2019 ◽  
Vol 16 (3) ◽  
pp. 448-475
Author(s):  
Vladimir Kobelev
Keyword(s):  
Residual Stresses ◽  
Closed Form ◽  
Cross Section ◽  
Circular Cross Section ◽  
Content Type ◽  
Closed Form Solutions ◽  
Helical Springs ◽  
First Case ◽  
Setting Process ◽  
The Wire

Purpose The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs. Design/methodology/approach For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis. Findings For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws. Research limitations/implications The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses. Practical implications The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions. Social implications The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs. Originality/value Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

Analysis on the steady state performance of a multi pad externally adjustable fluid film bearing

2019 ◽  
Vol 71 (6) ◽  
pp. 803-809 ◽  
Author(s):  
Girish Hariharan ◽  
Raghuvir Pai
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Fluid Film ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Content Type ◽  
Bearing Load ◽  
Performance Capability ◽  
Film Profile

Purpose This study aims to investigate the performance characteristics of an externally adjustable bearing with multiple pads in steady state conditions. The proposed adjustable bearing geometry can effectively control the hydrodynamic operation in bearing clearances by adjusting the pads in radial and tilt directions. These pad adjustments have a significant role in improving the bearing characteristics such as load capacity, attitude angle, side leakage, friction variable and Sommerfeld number, which will be analysed in this paper. Design/methodology/approach The adjustable bearing is designed with circumferentially spaced four bearing pads subjected to similar radial and tilt adjustments. Tilt angles are applied along the leading edges of bearing pads. A modified film thickness equation is used to incorporate the pad adjustments and accurately predict the variation in film profile. Finite difference approximation is adopted to solve the Reynolds equation and discretize the fluid film domain. Findings For negative radial and tilt adjustments, higher hydrodynamic pressures are generated in bearing clearances, which increases the bearing load capacity at different eccentricity ratios. From comparative analysis for different pad adjustments, superior bearing performance is observed for bearing pads under negative radial and negative tilt adjustments. Originality/value This research presents a detailed theoretical approach to analyse the performance capability of a four pad adjustable bearing geometry, which is not available in literatures. Improved bearing performances with negative pad adjustments can attract bearing designers to implement the proposed adjustability-bearing concept in rotating machineries.

Shock waves analysis of planar and non planar nonlinear Burgers’ equation using Scale-2 Haar wavelets

2017 ◽  
Vol 27 (8) ◽  
pp. 1814-1850 ◽  
Author(s):  
Sapna Pandit ◽  
Manoj Kumar ◽  
R.N. Mohapatra ◽  
Ali Saleh Alshomrani
Keyword(s):  
Nonlinear Term ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Finite Difference Approximation ◽  
Haar Wavelets ◽  
Difference Approximation ◽  
Content Type ◽  
Gauss Elimination ◽  
Gauss Elimination Method ◽  
Better Than

Purpose This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave. Design/methodology/approach First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method. Findings Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions. Originality/value The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.

Generalized Algorithms for Interactive Warping Analysis of Porous Cross Sections

1999 ◽  
Author(s):  
Y. C. Pao ◽  
Erik L. Ritman
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Image Data ◽  
Ct Scanning ◽  
Iterative Solution ◽  
Coefficient Matrix ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Cross Sectional ◽  
The Cross

Abstract Algorithms have been developed for warping analysis and calculation of the shearing stresses in a general porous cross section of a long rod when it is subjected to twisting torques at its ends. The shape and dimensions of the cross section full of holes are defined from the binary segmented image data with by a micro-CT scanning technique. Finite difference approximation of the Laplace equation governing the cross-sectional warping leading to the matrix solution by a Gauss-Seidel process is discussed. Method of pointer matrix which keeps the locations of the nonzero elements of the coefficient matrix, is employed to expedite the iterative solution. Computer programs are coded in QuickBASIC language to facilitate plotting of the computed distributions of warping and shearing stresses. The classical torsional problem of square and thin-walled cross sections are used to reexamine the accuracy of the developed algorithms and results are found to be in very good agreement.

Optimizing production while reducing machinery lockout/tagout circumvention possibilities

2016 ◽  
Vol 22 (2) ◽  
pp. 188-201 ◽  
Author(s):  
Abdoulaye Badiane ◽  
Sylvie Nadeau ◽  
Jean-Pierre Kenné ◽  
Vladimir Polotski
Keyword(s):  
Production Planning ◽  
Manufacturing System ◽  
Production Costs ◽  
Worker Safety ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Inventory Level ◽  
Maintenance Policy ◽  
Content Type ◽  
Bellman Equations

Purpose – The optimization of production imposes a review of facility maintenance policies. Accidents during maintenance activities are frequent, sometimes fatal and often associated with deficient or absent machinery lockout/tagout. Lockout/tagout is often circumvented in order to avoid what may be viewed as unnecessary delays and increased production costs. To reduce the dangers inherent in such practice, the purpose of this paper is to propose a production strategy that provides for machinery lockout/tagout while maximizing manufacturing system availability and minimizing costs. Design/methodology/approach – The joint optimization problem of production planning, maintenance and safety planning is formulated and studied using a stochastic optimal control methodology. Hamilton-Jacobi-Bellman equations are developed and studied numerically using the Kushner approach based on finite difference approximation and an iterative policy improvement technique. Findings – The analysis leads to a solution that suggests increasing the “comfortable” inventory level in order to provide the time required for lockout/tagout activities. It is also demonstrated that the optimization of lockout/tagout procedures is particularly important when the equipment is relatively new and the inventory level is minimal. Research limitations/implications – This paper demonstrates that it is possible to integrate production, maintenance and lockout/tagout procedures into production planning while keeping manufacturing system cost objectives attainable as well as ensuring worker safety. Originality/value – This integrated production and maintenance policy is unique and complements existing procedures by explicitly accounting for safety measures.

Laser shock processing with two different laser sources on 2050‐T8 aluminum alloy

2011 ◽  
Vol 2 (1) ◽  
pp. 87-100 ◽  
Author(s):  
Patrice Peyre ◽  
Neila Hfaiedh ◽  
Hongbin Song ◽  
Vincent Ji ◽  
Vincent Vignal ◽  
...  
Keyword(s):  
Aluminum Alloy ◽  
Residual Stresses ◽  
Work Hardening ◽  
Material Behavior ◽  
Al Alloy ◽  
Numerical Comparison ◽  
Laser Shock ◽  
Content Type ◽  
Surface Deformations ◽  
Laser Sources

PurposeThe purpose of this paper is to conduct a comparative study of the surface modifications induced by two different lasers on a 2050‐T8 aluminum alloy, with a specific consideration of residual stress and work‐hardening levels.Design/methodology/approachTwo lasers have been used for Laser shock peening (LSP) treatment in water‐confined regime: a Continuum Powerlite Plus laser, operating at 0.532 mm with 9 ns laser pulses, and near 1.5mm spot diameters; a new generation Gaia‐R Thales laser delivering 10 J‐10 ns impacts, with 4‐6mm homogeneous laser spots at 1.06 mm. Surface deformation, work‐hardening levels and residual stresses were analyzed for both LSP conditions. Residual stresses were compared with numerical simulations using a 3D finite element (FE) model, starting with the validation of surface deformations induced by a single laser impact.FindingsSimilar surface deformations and work‐hardening levels, but relatively lower residual stresses were obtained with the new large 4‐6 mm impact configuration. This was attributed to a reduced number of local cyclic loadings (2) compared with the small impact configuration (4). Additionally, more anisotropic stresses were obtained with small impacts. FE simulations using Johnson‐Cook's material' behavior were shown to simulate accurately surface deformations, but to overestimate maximum stress levels.Research limitations/implicationsThis work should provide LSP workers a better understanding of the possible benefits from the different LSP configurations currently co‐existing: using small (<2 mm) impacts at high‐cadency rates or large ones (>4‐5 mm). Moreover, experimental results and simulated data had never been presented on 2050‐T8 Al alloy.Originality/valueAn experimental (and numerical) comparison using two distinct laser sources for LSP, has never been presented before. This preliminary work should help LSP workers to choose adequate sources.

Stochastic design optimization accounting for structural and distributional design variables

2018 ◽  
Vol 35 (8) ◽  
pp. 2654-2695 ◽  
Author(s):  
Xuchun Ren ◽  
Sharif Rahman
Keyword(s):  
Finite Difference ◽  
Design Optimization ◽  
Failure Probability ◽  
Structural Design ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Mixed Design ◽  
Content Type ◽  
Design Variables ◽  
Mixed Design Variables

Purpose This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables. Design/methodology/approach The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms. Findings New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability. Originality/value In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.

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