Gary L. Kinzel

Mathematical modeling of plane-strain bending of sheet and plate

Abstract Plane-strain (or straight-line) bending is a major sheet-forming operation. Precise prediction of springback is a key to designing bending dies, to controlling the process and the press, and to assessing the accuracy of part geometry. In this paper, a complete theory and reliable mathematical models for plane-strain sheet bending have been established to predict springback, bendability or the minimum bending ratio ( R/t ), strain and stress distributions, and the maximum loads on the punch and the die. The elastoplastic bending model incorporates the true (non-linear) strain distribution across the sheet thickness. Swifts strain-hardening law, Hills (1979) non-quadratic yield criterion for normal and planar anisotropic materials, and the plane-strain deformation mode. A computer code called “BEND” has been developed to simulate the air bending and die bending processes with a U-die, a V-die, and a wiping-die. Simulation results were compared to experimental data, good agreement being observed. Air bending simulations show that the springback angle is proportional to the bending moment and the bent arc length between the punch and the die. The bending moment is greater for materials with higher strength, strain hardening and normal anisotropy, which increase the springback. For such materials, decreasing the bent arc length by reducing the die opening or die clearance is an effective way to reduce the springback. In air bending, springback can be compensated for by overbending through a deeper punch stroke and the necessary stroke can be preset in the press controller using the predicted curve of springback vs. stroke.

A new model for springback prediction in which the Bauschinger effect is considered

Springback prediction is an important issue for the sheet metal forming industry. Most sheet metal elements undergo a complicated cyclical deformation history during the forming process. For an accurate prediction of springback, the Bauschinger effect must be considered to determine accurately the internal stress distribution within the sheet metal after deformation. Based on the foundations for isotropic hardening and kinematic hardening, Mroz multiple surface model, plane strain assumptions, and experimental observations, a new incremental method and hardening model is proposed in this paper. This new model compares well with the experimental results for aluminum sheet metal undergoing multiple-bending processes. As is well known, aluminum is one of the most difficult sheet metals to simulate. The new hardening model proposed in this paper is not only a generic model for springback prediction but also a hardening model for sheet metal forming process simulation.

Simulation of roll forming process with the 3-D FEM code PAM-STAMP

Abstract Roll forming is a well known process used to manufacture long sheet metal products with constant cross section. Despite the long history of the process, the design procedure for the roll formed products, forming rolls, and roll pass sequences still remains more an art than a science. Thus, to avoid forming defects and to reduce the process development efforts, finite element analysis can be used to predict strain distributions and sheet geometry during and after the process. This paper summarizes the results of roll forming simulations made with a commercial FEM code. Deformed geometry and strain distributions predicted by simulations are compared with the results from previously conducted experiments. This study provided considerable experience how and when it is best to apply a commercial 3-D FEM code to the design of a roll forming process.

Deep drawing of round cups from tailor-welded blanks

Recent developments in the welding technology and the considerations regarding material cost, dimensional accuracy and weight, force automakers and appliance manufacturers to use tailor-welded blanks in their stamping operations. The welding of blanks with different thicknesses, materials and/or surface conditions introduces many challenging formability problems for process development and tool design. In cooperation with industrial partners, projects are being conducted at the ERC for Net Shape Manufacturing to study the formability of tailor-welded blanks and develop guidelines for tool design. This paper gives a summary of the preliminary work done on the deep drawing of round cups from tailor-welded blanks.

Computer-aided design of a leg for an energy efficient walking machine

Abstract Vehicles with legs instead of wheels have been studied for a number of years. One of the reasons for interest in such vehicles is that animals use only 10% as much energy as wheeled or tracked vehicles when traveling over rough terrain. The leg geometry is the most crucial aspect of the design since it strongly influences the efficiency of the vehicle. The legs should be simple in structure, and when the motion of the body is on a horizontal straight line, only one actuator per leg should be active in order to have good energy efficiency. The design of an energy efficient walking machine leg is described in this paper. In the design procedure, the motion of the leg is considered first, and a very simple leg developed from a 4-bar linkage and designed using a computer-aided interactive program is described. Second, the forces on this leg during a typical motion cycle are discussed. The leg is driven by a primary actuator for straight line walking and two secondary actuators which vary working height and change direction. A prototype of the leg is being built in The Department of Mechanical Engineering at The Ohio State University.

Wrinkling criterion for an anisotropic shell with compound curvatures in sheet forming

Abstract Wrinkling criteria are proposed for an elastic isotropic and plastic anisotropic shell with compound curvatures in the noncontact region of a sheet subjected to internal forming stresses. A quasi-shallow shell is modeled by Donnell-Mushtari-Vlasov (DMV) shell theory. A bifurcation functional from Hills general theory of uniqueness and bifurcation in elastic-plastic solids is used to model the local wrinkling phenomenon. Both strain hardening and transverse anisotropy are taken into consideration. This wrinkling criterion is especially useful as a failure criterion in three dimensional finite element modeling (FEM) of sheet forming. Given the principal stresses or strains and the geometry provided at each incremental deformation step, the criterion can be used to predict wrinkles in the elements in the unsupported region.

Process and die design for multi-step forming of round parts from sheet metal

Abstract Designing process sequences for deep drawing of round cups has traditionally been a trial and error process. This paper describes a Computer Aided Engineering (CAE) system for designing process sequences and the corresponding tooling that is currently being developed at the Engineering Research Center for Net Shape Manufacturing (ERC/NSM). This system will help designers in developing and evaluating process sequences and in predicting possible problems before the manufacturing of tools and the production of parts. This will lead to substantial savings in time and costs. The CAE system consists of a rule-based design module to generate the process sequences and an analysis module based on the Finite Element Method (FEM) to predict potential problems by simulating the forming processes. This paper discusses the implementation of the rules to design process sequences as well as some aspects of the numerical simulation of the forming processes.

Improvement of hem quality by optimizing flanging and pre-hemming operations using computer aided die design

Abstract Flanging and hemming of straight edge-flat surface (plane strain) aluminum killed-draw quality steel was investigated restricting the study to the radius flat hem with an inner sheet. The major process parameters in straight edge hemming were determined and relations between them and some forming defects were established. Among these parameters were flanging die corner radius, pre-hem path, pre-hem stroke and final hemming force. Possible process and tool design modifications, which may lead to quality improvements in hemming were tested experimentally and using FEM. The commercial finite element program DEFORM was used to simulate the flanging and hemming operations including springback, and the predictions were compared with limited experimental results. Results of the experiments and simulations were summarized in the form of trend-lines for the use of process and die designers.

Bending, flanging, and hemming of aluminum sheet—an experimental study

Abstract Hemming is often used as the last stage of stamping operations. It is used either to improve appearance (to create a smooth edge rather than a razor edge with burrs) or to attach one sheet metal part to another. Hemming is defined as folding of bent or flanged sheet 180° or more. However, the deformation mechanism, and hence the process, is different and more complex than simple bending and flanging process. Therefore, very little information is available in research literature, and most of the hemming dies are designed based on trial and error. This paper gives the results obtained from the hemming experiments that were conducted at the Engineering Research Center for Net Shape Manufacturing (ERC/NSM) by using Aluminum Alloy 1050.

Blank holder force (BHF) control in viscous pressure forming (VPF) of sheet metal

Abstract An eight-point BHF control system with a flexible blank holder is designed and built as part of an experimental viscous pressure forming (VPF) machine. This paper describes results of VPF experiments, and addresses several blank holding issues specific to the VPF process. FEM simulations of hydroforming with a multi-point BHF control and an elastic blank holder are conducted to fine-tune the control system as well as to predict the forming loads. The FEM results are compared with experimental VPF results. The viscous medium “blow through” phenomenon between the blank holder and the sheet during VPF is described and quantified.