scholarly journals The inverse task solution for the calculation of sweeps of sheet parts by integral geometry

2021 ◽  
Author(s):  
Vladimir Mironenko ◽  
Denis Elovenko ◽  
Alexander Graf ◽  
Verena Kräusel ◽  
Catherine Ledovskikh
Keyword(s):  
Integral Geometry ◽  
3D Model ◽  
Mathematical Problem ◽  
Sheet Thickness ◽  
Integral Form ◽  
Cad Model ◽  
Dynamic Calculation ◽  
Forming Process ◽  
The Given ◽  
Rational Shape

Abstract This article deals with the search for a rational semi-finished product for parts of the integral form. Here a variant of the solution of the given problem is described based on the inverse solution of the mathematical problem. The reasons and the nature of the problem occurring in standard approaches to the calculation of the semi-finished product are shown using the example of two parts with aerodynamic curvature. The material and sheet thickness of the components are selected to suit the application. The forming process is also the same as the initial situation. The rational shape of the part can be found using the optimization solution based on the discrepancy of the contours with respect to the sweeps of the dynamic calculation and the CAD model. The new shape of the blank makes it possible to realize the forming process of the parts with minimal deviations from the contour of the 3D model.

Dieless Water Jet Incremental Micro-Forming

2018 ◽  
Author(s):  
Yi Shi ◽  
Jian Cao ◽  
Kornel F. Ehmann
Keyword(s):  
Process Parameters ◽  
Thin Shell ◽  
High Speed ◽  
Single Point ◽  
Sheet Thickness ◽  
Water Jet ◽  
Micro Forming ◽  
Forming Process ◽  
Thin Foils ◽  
High Pressure Water Jet

Compared to the conventional single-point incremental forming (SPIF) processes, water jet incremental micro-forming (WJIMF) utilizes a high-speed and high-pressure water jet as a tool instead of a rigid round-tipped tool to fabricate thin shell micro objects. Thin foils were incrementally formed with micro-scale water jets on a specially designed testbed. In this paper, the effects on the water jet incremental micro-forming process with respect to several key process parameters, including water jet pressure, relative water jet diameter, sheet thickness, and feed rate, were experimentally studied using stainless steel foils. Experimental results indicate that feature geometry, especially depth, can be controlled by adjusting the processes parameters. The presented results and conclusions provide a foundation for future modeling work and the selection of process parameters to achieve high quality thin shell micro products.

BENDING BEHAVIOR OF SIMPLY SUPPOTED METALLIC SANDWICH PLATES WITH DIMPLED CORES

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6179-6184 ◽  
Author(s):  
DAE-YONG SEONG ◽  
CHANG GYUN JUNG ◽  
DONG-YOL YANG ◽  
DONG GYU AHN
Keyword(s):  
High Precision ◽  
Sandwich Plate ◽  
Sheet Thickness ◽  
Radius Of Curvature ◽  
Sandwich Plates ◽  
Collapse Load ◽  
Forming Process ◽  
Simply Supported ◽  
Bending Behavior ◽  
Sandwich Core

Metallic sandwich plates are lightweight structural materials with load-bearing and multi-functional characteristics. Previous analytic studies have shown that the bendability of these plates increases as the thickness decreases. Due to difficulty in the manufacture of thin sandwich plates, dimpled cores (structures called egg-box cores) are employed as a sandwich core. High-precision dimpled cores are easily fabricated in a sectional forming process. The cores are then bonded with skin sheets by multi-point resistance welding. The bending characteristics of simply supported plates were observed by the defining measure, including the radius ratio of the small dimple, the thickness of a sandwich plate, and the pattern angle (0°/90°, 45°). Experimental results revealed that sandwich plates with a thickness of 2.2 mm and a pattern angle of 0°/90° showed good bendability as the punch stroke under a collapse load was longer than other cases. In addition, the gap between attachment points was found to be an important parameter for the improvement of the bendability. Finally, sandwich plates with dimpled cores were bent with a radius of curvature of 330 mm for the sheet thickness of 2.2 mm using an incremental bending apparatus.

scholarly journals DEFRAGMENTATION THINKING STRUCTURE TO OVERCOME ERRORS IN ADDRESSING MATHEMATICAL PROBLEM

2021 ◽  
Vol 10 (1) ◽  
pp. 339
Author(s):  
Siti Puri Andriani ◽  
Triyanto Triyanto ◽  
Farida Nurhasanah
Keyword(s):  
High School ◽  
Problem Solving ◽  
Random Sampling ◽  
Mathematical Problem ◽  
Islamic State ◽  
Algebraic Functions ◽  
Process Error ◽  
Procedural Error ◽  
The Subject ◽  
The Given

This research is intended to describe students' procedural errors in solving problems derivative of algebraic functions and efforts to overcome these errors by using the defragmentation process. Error analysis is carried out based on the procedural error theory based on Elbrink which includes the following aspects of errors: 1) Mis-identification; 2) Mis-generalization; 3) Repair Theory; and 4) Overspecialization. The subjects in this study are students of class XII MIPA Islamic State Senior High School (MAN) 3 Tulungagung taken from snowball random sampling. In taking the subject, the researchers select one of the students who make procedural errors by considering the completeness of the students when solving the given problems based on the problem-solving phase according to Polya. Based on the results of this study, it is found that the procedural errors made by the students are repair theory errors and overspecialization.  The defragmenting process to correct these errors is intended to provide dis-equilibration and scaffolding. The results after the defragmenting process are the students can correct their mistakes and the structure of their thinking.Keywords: Defragmenting structure thinking; derivative algebraic functions; problem solving; procedural errors. AbstrakPenelitian ini bertujuan untuk menggambarkan kesalahan prosedural siswa dalam menyelesaikan masalah turunan fungsi aljabar dan upaya untuk mengatasi kesalahan tersebut dengan menggunakan proses defragmenting. Analisis kesalahan dilakukan berdasarkan konsep teori kesalahan prosedural menurut Elbrink yang mencakup aspek kesalahan sebagai berikut: Mis-identificstion; 2) Mis-generalization; 3) Repair Theory; dan 4) Overspecialization. Subjek dalam penelitian ini adalah siswa kelas XII MIPA MAN 3 Tulungagung yang diambil secara snowball  random sampling. Dalam pengambilan subjek dipilih salah satu siswa yang melakukan kesalahan prosedural dengan mempertimbangkan kelengkapan siswa ketika menyelesaikan masalah yang diberikan berdasarkan tahap pemecahan masalah menurut Polya. Dari hasil penelitian ini ditemukan bahwa kesalahan prosedural yang dilakukan siswa ialah kesalahan repair theory dan overspecialization. Proses defragmenting yang dilakukan untuk memperbaiki kesalahan tersebut ialah dengan memberikan dissequillibrasi dan scaffolding. Hasil yang diperoleh setelah proses defragmenting dilakukan ialah siswa mampu memperbaiki kesalahannya dan struktur berpikirnya.Kata kunci: Defragmenting struktur berpikir, kesalahan prosedural, pemecahan masalah, turunan fungsi aljabar.

Analytic program derivation in type theory

1998 ◽  
Author(s):  
Petri Mäenpää
Keyword(s):  
Mathematical Method ◽  
Problem Solving ◽  
Type Theory ◽  
Mathematical Problem ◽  
Geometric Analysis ◽  
Algebraic Method ◽  
Point Of View ◽  
Program Derivation ◽  
Mathematical Problems ◽  
The Given

This work proposes a new method of deriving programs from their specifications in constructive type theory: the method of analysis-synthesis. It is new as a mathematical method only in the area of programming methodology, as it is modelled upon the most successful and widespread method in the history of exact sciences. The method of analysis-synthesis, also known as the method of analysis, was devised by Ancient Greek mathematicians for solving geometric construction problems with ruler and compass. Its most important subsequent elaboration is Descartes’s algebraic method of analysis, which pervades all exact sciences today. The present work expands this method further into one that aims at systematizing program derivation in a heuristically useful way, analogously to the way Descartes’s method systematized the solution of geometric and arithmetical problems. To illustrate the method, we derive the Boyer-Moore algorithm for finding an element that has a majority of occurrences in a given list. It turns out that solving programming problems need not be too different from solving mathematical problems in general. This point of view has been emphasized in particular by Martin-Löf (1982) and Dijkstra (1986). The idea of a logic of problem solving originates in Kolmogorov (1932). We aim to refine the analogy between programming and mathematical problem solving by investigating the mathematical method of analysis in the context of programming. The central idea of the analytic method, in modern terms, is to analyze the functional dependencies between the constituents of a geometric configuration. The aim is to determine how the sought constituents depend on the given ones. A Greek analysis starts by drawing a diagram with the sought constructions drawn on the given ones, in the relation required by the problem specification. Then the sought constituents of the configuration are determined in terms of the given ones. Analysis was the Greeks’ method of discovering solutions to problems. Their method of justification was synthesis, which cast analysis into standard deductive form. First it constructed the sought objects from the given ones, and then demonstrated that they relate as required to the given ones. In his Geometry, Descartes developed Greek geometric analysis-synthesis into the modern algebraic method of analysis.

scholarly journals Investigation of a partial, inductive short-time heat treatment of thin metal sheets integrated into the forming process

2018 ◽  
Vol 190 ◽  
pp. 12008
Author(s):  
Benjamin Clausius ◽  
Petra Maier
Keyword(s):  
Heat Treatment ◽  
Strain Hardening ◽  
Sheet Thickness ◽  
Local Strain ◽  
Single Step ◽  
Thin Metal ◽  
Recrystallization Annealing ◽  
Forming Process ◽  
Metal Sheets ◽  
Short Time

Flanging is a widespread method in the sheet metal working industry to connect same or different materials by forming. Especially the sealing technology makes high demands on the flanging process: a low sheet thickness of the inner eyelet is necessary for proper sealing. The outer edges of the neck rings are mostly manufactured by shear cutting. The quality of the cut surface and the level of the local strain hardening influence decisively the limit of the flanging process by possible cracking. This paper is focused on the dependencies of these factors regarding thin metal sheets of different materials with a thickness down to 100 μm. It could be shown that strain hardening has a stronger effect on the process limits compared to the notch effect of the sheet edges when using standard values for the clearance of the shear cutting tool. Furthermore, a process is investigated with a partial inductive short-time heat treatment of the most deformed edge area. Due to the low thickness of the material and low heat capacities related thereto, it is possible to integrate a recrystallization annealing as single step into the forming process. As a result, the strain hardening can be removed from the affected zone directly between two forming steps to increase the process limits.

scholarly journals Material properties and structure of natural graphite sheet

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Martin Cermak ◽  
Nicolas Perez ◽  
Michael Collins ◽  
Majid Bahrami
Keyword(s):  
Material Properties ◽  
Coefficient Of Thermal Expansion ◽  
Electrical Contact ◽  
Sheet Thickness ◽  
Electronics Cooling ◽  
Forming Process ◽  
Electrical Contact Resistance ◽  
Natural Graphite ◽  
Graphite Sheet ◽  
Thermally Conductive

Abstract Natural graphite sheet (NGS) is compressible, porous, electrically and thermally conductive material that shows a potential to be used in fuel cells, flow batteries, electronics cooling systems, supercapacitors, adsorption air conditioning, and heat exchangers. We report the results of an extensive material characterization study that focuses on thermal conductivity, thermal diffusivity, electrical conductivity, coefficient of thermal expansion (CTE), compression strain, and emissivity. All the properties are density-dependent and highly anisotropic. Increasing the compression from 100 to 1080 kPa causes the through-plane thermal and electrical conductivities to increase by up to 116% and 263%, respectively. The properties are independent of the sheet thickness. Thermal and electrical contact resistance between stacked NGS is negligible at pressures 100 to 1080 kPa. In the in-plane direction, NGS follows the Wiedemann-Franz law with Lorenz number 6.6 $$\times $$ × 10$$^{-6}$$ - 6 W $$\Omega $$ Ω K$$^{-2}$$ - 2 . The in-plane CTE is low and negative (shrinkage with increasing temperature), while the through-plane CTE is high, increases with density, and reaches 33 $$\times $$ × 10$$^{-6}$$ - 6 K$$^{-1}$$ - 1 . Microscope images are used to study the structure and relate it to material properties. An easy-to-use graphical summary of the forming process and NGS properties are provided in Appendices A and B.

Improved Sheet Bulk Metal Forming Processes by Local Adjustment of Tribological Properties

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
H. Hetzner ◽  
J. Koch ◽  
S. Tremmel ◽  
S. Wartzack ◽  
M. Merklein
Keyword(s):  
Contact Pressure ◽  
Metal Forming ◽  
Material Flow ◽  
System Analysis ◽  
Sheet Thickness ◽  
Fe Model ◽  
Forming Process ◽  
Bulk Metal ◽  
Bulk Metal Forming ◽  
Functional Features

This paper is focused on a combined deep drawing and extrusion process dedicated to the new process class of sheet bulk metal forming (SBMF). Exemplified by the forming of gearings, combined sheet and bulk forming operations are applied to sheet metal in order to form local functional features through an intended and controlled change of the sheet thickness. For investigations on the form filling and the identification of significant influencing factors on the material flow, a FE simulation model has been built. The FE model is validated by the results of manufacturing experiments using DC04 with a thickness of 2.0 mm as blank material. Due to the fact that the workpiece is in extensive contact to the tool surface and that the pressure reaches locally up to 2500 MPa, the tribological conditions are a determining factor of the process. Thus, their influence is discussed in detail in this paper. In the first instance, different frictional zones having a distinct effect on the resulting material flow are identified and their effect on improved form filling is demonstrated. Subsequently, a more comprehensive methodology is developed to define tribological zones of forming tools. For this, a system analysis of the digital mock-up of the forming process is performed. Besides friction, other relevant aspects of forming tool tribology like contact pressure, sliding velocity, and surface magnification are considered. The gathered information is employed to partition the tools into tribological zones. This is done by systematically intersecting and re-merging zones identified for each of the criterion. The so-called load-scanning test allows the investigation of the friction coefficient in dependence of the contact pressure and possible loading limits of tribological pairings. It provides an appropriate tribological model test to evaluate tribological measures like coatings, surface textures and lubricants with respect to their targeted application in particular zones. The obtained results can be employed in the layout of further forming processes to reach the desired process behavior. This can be, for example, an improved form filling, less abrasive wear and adhesive damage or lower forming forces, respectively tool load for an improved durability of the die.

Research on the Finite Element Simulation of the Laser Shock Forming of TC4 Titanium Alloy

2016 ◽  
Vol 693 ◽  
pp. 1121-1128 ◽  
Author(s):  
Guo He Li ◽  
David Mbukwa ◽  
Wei Zhao
Keyword(s):  
Finite Element ◽  
Sheet Metal ◽  
Laser Energy ◽  
Sheet Thickness ◽  
High Amplitude ◽  
Laser Spot ◽  
Laser Shock ◽  
Forming Process ◽  
Element Analysis ◽  
Laser Shock Forming

laser shock forming, which combines the metal forming and material modification, is a non-mode, flexible forming new technology using laser-induced force effect of high amplitude shock waves to obtain the plastic deformation of sheet metal. in this paper, the simulation of laser shock forming process of tc4 sheet metal was carried out through the commercial finite element analysis software abaqus. the influence of the sheet thickness, laser energy, constraints aperture and laser spot spacing on the sheet metal deformation are investigated. the results show that: with the increase of sheet thickness, the deformation range of sheet decreases, and the amplitude of deformation decreases firstly and then increases. the deformation increases linearly with the increase of laser energy. the larger boundary constraint aperture leads to the larger deformation of sheet metal. there are no obvious influence on the forming accuracy when an opposite laser spot spacing is adopted. therefore, under the condition of meeting the accuracy requirement, for improving the efficiency, adopting a certain laser spot spacing to finish the forming should be considered.

scholarly journals Study on Thickness Thinning Ratio of the Forming Parts in Single Point Incremental Forming Process

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mingshun Yang ◽  
Zimeng Yao ◽  
Yan Li ◽  
Pengyang Li ◽  
Fengkui Cui ◽  
...  
Keyword(s):  
Deformation Zone ◽  
Incremental Forming ◽  
Single Point ◽  
Sheet Thickness ◽  
Single Point Incremental Forming ◽  
Forming Process ◽  
Feeding Speed ◽  
Forming Angle ◽  
Tool Diameter ◽  
Thinning Rate

An excessive thickness-reducing ratio of the deformation zone in single point incremental forming of the metal sheet process has an important influence on the forming limit. Prediction of the deformation zone thickness is an important approach to control the thinning ratio. Taking the 1060 aluminum as the research object, the principle of thickness deformation in the single point incremental forming process was analyzed; the finite element model was established using ABAQUS. A formula with high accuracy to predict the deformation zone thickness was fitted with the simulation results, and the influences of process parameters, such as tool diameter, step down, feeding speed, sheet thickness, and forming angle, on thinning ratio were analyzed. The accuracy of the finite element simulation was verified by experiment. A method to control the thinning rate by changing the forming trajectory was proposed. The results showed that the obtained value by using the fitted formula is closer to the experimental results than that obtained by the sine theorem. The thinning rate of the deformation zone increases with the increase of tool diameter, forming angle, and sheet thickness and decreases with the increase of step down, while the feeding speed had no significant effect on the thinning ratio. The most important factor of the thinning ratio is the forming angle, and the thinning ratio can be effectively reduced by using the forming trajectory with a uniformly distributed pressing point.

Dual-Phase Materials Extrusion Process for Rapid Fabrication of Ceramic Dental Crown

2010 ◽  
Vol 97-101 ◽  
pp. 4050-4053 ◽  
Author(s):  
Dong Bin Zhu ◽  
An Ping Xu
Keyword(s):  
3D Model ◽  
Solid Freeform Fabrication ◽  
Extrusion Process ◽  
Human Tooth ◽  
Dual Phase ◽  
Positioning System ◽  
Forming Process ◽  
Freeform Fabrication ◽  
Rapid Fabrication ◽  
Dental Crown

A novel ceramic forming process, dual-phase materials extrusion process based on solid freeform fabrication (also known as rapid prototyping), has been developed. It is a kind of selective slurry extrusion (SSE) technique previously proposed in our group. The dual-phase materials extrusion machine was constructed with micro-extrusion system and 3-axial positioning system. To demonstrate the usability of this machine, a functionalized dental crown was directly fabricated with support material and dental material from 3D model (STL format) of a human tooth. The fabrication time is usually in 20-50 min.

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