The use of dual-stream functions in the analysis of three-dimensional metal forming processes

1991 ◽  
Vol 33 (4) ◽  
pp. 313-323 ◽  
Author(s):  
Manuel J.M. Barata Marques ◽  
Paulo A.F. Martins
Keyword(s):  
Metal Forming ◽  
Three Dimensional ◽  
Stream Functions

On the Solution of Three-Dimensional Metal-Forming Processes

1977 ◽  
Vol 99 (3) ◽  
pp. 624-629 ◽  
Author(s):  
V. Nagpal
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Rectangular Shape ◽  
Admissible Velocity ◽  
Die Forging ◽  
Stream Functions ◽  
Open Die Forging

The use of “dual-stream functions” in analyzing some three-dimensional metal-forming processes is demonstrated in this paper. The problems discussed are open-die forging of blocks, rolling of a rectangular bar with spread, piercing by elliptic and rectangular punches, and extrusion of a rectangular shape. For these forming processes, kinematically admissible velocity fields are selected using characteristics of the two stream functions. Approximate upper-bound solutions of the forming processes can be obtained from the proposed velocity fields.

Metal Forming With Laser Origami: Parameter Analysis and Optimization

2020 ◽  
Author(s):  
Peiwen J. Ma ◽  
Yue Hao ◽  
Jyh-Ming Lien ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
Metal Forming ◽  
Search Algorithm ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Parameter Analysis ◽  
Forming Process ◽  
Polygonal Mesh ◽  
Target Shape ◽  
Material Usage ◽  
Metal Forming Process

Abstract Laser origami is a metal forming process where an initially planar sheet is transformed into a target three-dimensional (3D) form through cutting and folding operations executed by a laser beam. A key challenge in laser origami is to determine the locations of the cuts and folds required to transform the planar sheet into the 3D target shape. The region of the planar sheet that can be transformed into the target shape through these cuts and folds is denoted as the net. This paper presents a method to determine optimal net(s) for laser origami based on criteria including minimum energy usage, minimum fabrication time, minimum error in the fold angles, and minimum material usage. The 3D target shape is given as a polygonal mesh. To generate a net, each edge in the mesh must be classified as a cut or a fold. The energy, time, and other parameters associated with cutting or folding each edge are determined using experimentally calibrated formulas. A search algorithm is subsequently implemented to find combinations of cut and folded edges that provide an optimal set of nets for the given 3D target shape based on a cost function. Nets that are disconnected or have overlapping regions are discarded since they are invalid for laser origami. The method is demonstrated by applying it to different target shapes and cost functions.

NESTED INVARIANT 3-TORI EMBEDDED IN A SEA OF CHAOS IN A QUASIPERIODIC FLUID FLOW

2009 ◽  
Vol 19 (07) ◽  
pp. 2181-2191 ◽  
Author(s):  
HOPE L. WEISS ◽  
ANDREW J. SZERI
Keyword(s):  
Fixed Point ◽  
Fluid Flow ◽  
Cross Sections ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Elliptic Type ◽  
Two Phase ◽  
Dimensional Phase Space ◽  
Hyperbolic Fixed Point ◽  
Stream Functions

Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincaré sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincaré cross-section. This framework has applications to tidal and other mixing problems of geophysical interest.

scholarly journals An Alternate Method to Springback Compensation for Sheet Metal Forming

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Waluyo Adi Siswanto ◽  
Agus Dwi Anggono ◽  
Badrul Omar ◽  
Kamaruzaman Jusoff
Keyword(s):  
Hybrid Method ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Tolerance Range ◽  
Compensation Process ◽  
Dimensional Deviation ◽  
Three Dimensional Models ◽  
Cold Stamping

The aim of this work is to improve the accuracy of cold stamping product by accommodating springback. This is a numerical approach to improve the accuracy of springback analysis and die compensation process combining the displacement adjustment (DA) method and the spring forward (SF) algorithm. This alternate hybrid method (HM) is conducted by firstly employing DA method followed by the SF method instead of either DA or SF method individually. The springback shape and the target part are used to optimize the die surfaces compensating springback. The hybrid method (HM) algorithm has been coded in Fortran and tested in two- and three-dimensional models. By implementing the HM, the springback error can be decreased and the dimensional deviation falls in the predefined tolerance range.

Prediction and Optimization of Deformations in Coupling Mechanism Based Laser Forming of Sheet Metals

2019 ◽  
Vol 969 ◽  
pp. 552-557
Author(s):  
Kuntal Maji
Keyword(s):  
Process Parameters ◽  
Metal Forming ◽  
Three Dimensional ◽  
Laser Forming ◽  
Coupling Mechanism ◽  
Sheet Metals ◽  
Forming Process ◽  
Out Of Plane ◽  
Metal Forming Process ◽  
Plane Deformations

Fabricating three dimensional shaped surfaces from flat sheet metals by laser forming, both out-of-plane and in-plane deformations are required. This article presents the modeling of coupling mechanism activated laser forming of sheet metals based on experimental data for prediction and optimization of bending and thickening deformations. Experiments were performed based on a central composite design of experiments on coupling mechanism based laser metal forming process considering the input process parameters like laser power, scan speed and spot diameter, bending and thickening were taken as the outputs. Neural network and neuro-fuzzy system-based models were developed to carry out both forward and inverse modeling of the laser metal forming process under the coupling mechanism. Multi-objective optimization based on the non-dominated sorting genetic algorithm was used to obtain multiple optimal solutions to achieve different amounts of out-of-plane and in-plane deformations. The proposed method could guide for a suitable selection of the process parameters to produce three-dimensional shapes utilizing coupling mechanism-based laser forming using multiple laser line heating.

A Numerical and Experimental Study of Sheet Metal Bending by Pulsed Nd:Yag Laser with DOE Method

2009 ◽  
Vol 83-86 ◽  
pp. 1076-1083 ◽  
Author(s):  
M. Hosseinpour Gollo ◽  
Hassan Moslemi Naeini ◽  
G.H. Liaghat ◽  
S. Jelvani ◽  
M.J. Torkamany
Keyword(s):  
Experimental Study ◽  
Sheet Metal ◽  
Nd:Yag Laser ◽  
Metal Forming ◽  
Flexible Manufacturing ◽  
Three Dimensional ◽  
Laser Source ◽  
Laser Forming ◽  
Beam Diameter ◽  
Doubly Curved

Metal forming by a laser source is an efficient and economical method for forming sheet metal into straight bend and doubly curved shape. It can be most useful in the automation of sheet metal forming. This paper presents an FEM model for three dimensional thermo-mechanical simulation of the laser forming. The aim of this simulation and experimental study is to identify the response related to deformation and characterize the effects of process parameters such as laser power, beam diameter, scans velocity and pulse duration, in terms of bending angle for a square sheet part. Extensive experimentation, including a design of experiments, is performed to address the above-mentioned aims. From these experiments it has been determined that laser forming using Nd:YAG laser is a flexible manufacturing process for steel sheet bending.

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