A hydromechanical deep drawing process (which replaces the conventional rigid blank-holder tool with a hydrostatic fluid pressure) is utilized to study the roles played by die curvature, interfacial friction, material hardening, etc. in deep drawing performance. The analytical study is based on limit analysis in plasticity (applying both the upper and the lower bounds simultaneously) with a special emphasis on the geometry of the die profile. The resulting relationships between the various parameters obtained through the bounds are backed by an independent numerical solution using Woo's finite difference scheme. The associated experiments, with which the limit analysis is compared, were conducted with aluminium blanks at various die radii and with various holding fluid pressures. The relatively close proximity of the above solutions, in describing the observed behaviour of the process, enables one to draw a few general conclusions about the strength of the limit analysis in describing realistic deep drawing processes. Also potential improvements concerning the choice of die radius of curvature and the blank holding force are indicated.

This paper is Part II of a three part series on the design, analysis and construction of a flexible press with a double knuckle linkage drive. In Part I, this drive was shown to have the desirable characteristics of large force (mechanical advantage) over the ram stroke and controllability (constant ram velocity in the working stroke). In this paper, this linkage design is further optimized by kinematic simulation using programs CATIA and KINLYN, and an enumeration search procedure. This optimization results in increased echanical advantage in the working part of the stroke and reduced cycle times. Mechanical advanatage and ram velocity curves for the optimal design are compared with several design variants. This design with constant force and velocity in the working storke is espcially suited to applications in precision forming especially cold extrusion and sheet metal-forming processes.

Mechanical presses are widely used in the metal-forming industry because they are inexpensive, easy to automate, need low maintenance and offer high production rates. This paper is Part I of a three part series on the development of a flexible computer controlled precision press with double-toggle linkage driven by a servo-motor. It discusses techniques for simulating the load-stroke characteristics of mechanical linkage drives and presents results of comparison of a newly developed double-toggle linkage drive with four example drives from commercial metal-forming presses. The paper concludes that though this new design has lower mechanical advantage than some of these commercial drives, its ability to deliver constant load over most of the stroke makes it a strong competitor to hydraulic presses in the extrusion and sheet metalforming applications. In addition the drive, developed in this study, is found to be efficient in terms of space requirements.

This paper is the last part of a three part series on the design, analysis and construction of a flexible electric servo-motor controlled mechanical press for precision forming. In Part I, characteristics of the available mechanical drives for presses were compared and a double knuckle drive selected for this press application. This drive was shown to have the desirable characteristics of a large mechanical advantage and a constant ram velocity over the working stroke. Part II presented an enumeration search procedure for optimization of the link design for maximizing the mechanical advantage at the working stroke, with the constraint of a constant working velocity. This procedure was applied to the double knuckle linkage drive and the optimized dimensions selected. This paper presents the application of the above procedures to the development of a 30 ton double action press. Focus of this paper is on the scaling of the optimized desing, force and torque analysis and the selection of press specifications.

The feasibility of replacing the rigid blankholder in the conventional deep drawing process with a 'soft' hydrostatic fluid pressure is examined. The recommended fluid pressure range (the 'working zone') which guarantees a sound product in different circumstances is presented. The locus curve for possible failure by wrinkling of the flange and the locus curve for possible ductile rupture along the wall provide the lower and the upper limits respectively of the 'working zone'. These loci are found by a systematic series of deep drawing tests with different constant fluid pressure blankholders for three kinds of materials (copper, aluminium and stainless steel) at various thicknesses and friction conditions. The influence of the friction coefficient, the drawing ratio and the workpiece wall thickness on the blankholder fluid pressure needed to suppress flange wrinkling becomes evident experimentally.

In the current study, a system for computer control of the variable blank-holder force (BHF) was implemented for a deep-drawing process, using a multi-action, computer-controlled press. The press was developed at the Engineering Research Center for Net Shape Manufacturing for simulation research in the cold forming of complex parts and for sheet-metal forming. The controlled blank-holder forces (BHF) system was programmed and tested. It was found that the system has a quick response and enables the user to preset the desired BHF path over the entire punch stroke. An acceptable BHF range was predicted experimentally by performing a series of deep-drawing tests with different constant BHF. The acceptable BHF range obtained is bounded by two critical loci, the rupture locus and the wrinkling locus. Various experiments were performed with different constant BHFs located within an acceptable zone. Higher punch forces were recorded and a thinner product was obtained for the higher BHF test. From the experimental results, it is expected that the minimum acceptable BHF locus (slightly above the wrinkling locus) is the optimal path of BHF variation during the drawing stroke.

The goal of the current study is to adapt a servo-motor driven multi-action press for forming of sheet metal parts under precise velocity control and variable blankholding force. The Engineering Research Center for Net Shape Manufacturing [ERC/NSM] has developed a computer controlled multi-action press with two independently driven punches for research in cold forming of complex parts, using physical modeling techniques. Recently, the same press was modified and upgraded for use in sheet metal forming. As a result of its special design and construction, this press is highly controllable and can perform a wide range of sheet metal forming processes. Tests were conducted in order to obtain the actual press characteristics. Axisymmetric deep drawing experiments were performed with 1100-O annealed aluminum material using all three actions of the press. In these preliminary experiments, the crucial role of blankholding force control on final product quality and drawability was established.

In the hydroforming process the punch deforms the blank to its final shape by moving against a controllable fluid-pressure in a pre-determined path. The present work exhibits the fact that the final geometry of the product (mainly the wall thickness variations) depends on the overall history by which the fluid pressure-path is operated during the drawing process. In addition, other phenomena akin to hydroforming processes have been observed, e.g. the shift in the location of the rupture site (if it occurs) from near the bottom of the product to near its lip and the (slight) variation in the final length of the product. In order to explain these occurrences a detailed numerical stress analysis is offered, featured by an ad-hoc “finite difference” scheme. It differs from previous solutions by admitting changes in the thickness of the blank and still accounting for the blank/tool interfacial friction and the out-of-plane curvature of the product. The material behavior of the blank includes exponential strain hardening, normal anisotropy and initial strain. The experiments shown here were carried out on aluminum sheets with a specially built hydroforming machine.

The concept of Maximum Drawing Ratio (MDR), supplementary to the well-known Limit Drawing Ratio (LDR), is defined, examined, and illustrated by experiments. In essence the MDR is reached when the two basic failure modes, namely: rupture (due to tensile instability) and wrinkling (due to buckling instability) are delayed till they occur simultaneously. Thus the process is beneficially utilized for higher drawing ratio by postponing earlier interception of either one of the above failures alone. The ability to suppress (up to a certain extent) the appearance of these failure modes depends heavily on the fluid-pressure path which controls the hydroforming process. The effect of the material properties, like the strain hardening exponent, the normal anisotropy of the blank, etc., as well as the geometrical properties (i.e., the thickness of the blank, the radius of curvature at the lip, etc.) on the MDR, are considered here in some detail. The nature of the solutions by which MDR is reached is discussed.

AbstractIn Part I, a simple mathematical model was proposed, based on dimensional similarity parameters, to describe the characteristics of flexible plastic foams under impact conditions. The model assumes that the foam is a rate‐dependent material. In the present part we extended the similarity model, by including the density of the foam parameter (for the same material and technological process). The density parameter is significant for systems cushioning with regard to weight and cost constraints. The behavior of flexible foams was studied with density as the variable parameter in a range of 100–240 kg/m3, with constant geometrical dimensions, for a wide range of drop heights and masses. We used the similarity parameters approach to predict the characteristics of the foams for various foam densities. The results show that for particular tested cases, the maximum deformation, the maximum deceleration, and the time pulse‐period decrease as the foam density increases.

The geometrical and material constraints which limit the quality of hydroforming products in regard to failure by wrinkling (buckling) and/or rupture (tensile instability) are investigated in a unified framework. The analysis is based on limit theorems of plasticity (with a power-law hardening and Mises-Hill normal anisotropy) and resulted in distinct bounds for the permissible operating fluid pressure path. The parameteric study which follows includes a wide range of physical variables, some of which (not considered hitherto) show substantial effects on anticipated failure. Experiments with copper, aluminum, steel, and stainless steel agree very well with the supposition that premature failure (up to certain situations) is avoidable if the fluid pressure path is restricted to travel only within the suggested bounds.

AbstractA simple mathematical model is proposed, based on dimensional similarity parameters, to describe the characteristics of flexible plastic foams under impact conditions. The model assumes that the foam is rate‐dependent material, when the dynamic stress is a function of the strain and the strain rate. The similarity parameters include the geometric dimension of the foam, the mass of the absorbing body, and the drop height. By using this model, one can predict the maximum deformation, the maximum decelerations, and the time‐pulse period for a wide range of drop heights and masses, by conducting several drop tests. We verified the efficacy of this model by performing free‐fall drop tests with flexible polyurethane foam having a uniform density of 240 kg/m3.

The critical fluid-pressure locus above which rupture by tensile instability may occur in the hydroforming deep-drawing process, is formulated and tested. The formulation is based on the classical theory of plasticity (with simple power-law hardening and Mises-Hill normal anisotropic yielding) assuming plane strain tensile failure. Further simplifications, such as assuming constant blank thickness and a constant Coulomb friction coefficient, enable one to account for the coupling effect between the self-adjusted blank curvature and the governing material parameters on rupture. Experiments with copper blanks are aimed to demonstrate that under certain conditions, failure by rupture may be prevented if the path of the working fluid pressure nowhere exceeds the predicted critical-pressure locus path. On the other hand, it is shown that the working fluid pressure should nowhere be lower than a predetermined minimum pressure locus to prevent wrinkles at the rim. Thus a distinct operating zone, lying between the upper and the lower pressure loci, is identified and recommended for practical use.

An instability analysis of flange buckling against lateral fluid pressure in deep drawing is considered. It is intended to explain the experimental fact that relatively low fluid pressure when applied to the flange area can suppress buckling. The analysis is based on the approximate ‘energy method’ with the inclusion of the work against the fluid. The attention is focused on the initiation of the deep drawing process, where buckling (of non-hardening material) is most susceptible. A special apparatus which enables the replacement of a rigid blank-holder by a lateral fluid-pressure was used for testing. A general solution to the critical pressure, above which the deep drawing can be terminated without buckling, is provided. The prediction of the critical pressure and the number of the associated buckling ‘waves’ (wrinkles) agree very well with the experiments. The pertinent geometrical and material variables (as blank thickness, drawing ratio, Young modulus, yield strength, etc.) are grouped in nondimensional form and plotted for various parameters to provide an engineering-type solution for potential users.

Critical lateral fluid pressure for suppression of plastic buckling of annular plates during deep drawing by hydroforming process is examined. The theoretical prediction, utilizing the energy method, is accompanied by experiments. The outcome enables to program a fluid pressure path (with respect to the punch travel) which may prevent, to some extent, premature buckling at the flange area of the product. The governing geometrical and material parameters (as plate thickness, drawing ratio, strain hardening exponent, buckling modulus, flange-cup transition curvature, etc.) are all viewed through their effects on the critical fluid pressure at buckling. Hydroforming experiments with blanks made of copper, aluminum, steel and stainless steel with various geometries validate the analysis and demonstrate the technological usefulness of the results.

It has been shown elsewhere that according to the magnitude of the removal rate, three distinct grinding mechanisms can be observed when austenitic stainless steel is ground by alumina wheels. Using a previously obtained expression relating the CLA roughness to grinding parameters, the observed variation in the surface finish with grinding time, with the effective wheel depth of cut, d, and with wheel parameters is explained qualitatively for each of the grinding mechanisms. When wheel loading occurs (i.e. at the high removal rates) it is found that the relation between the CLA roughness and the effective depth of cut is of the predicted form viz., a power function but the index is greater than 0.3, the value to be expected from the empirically observed relation between the Peak-to-Valley roughness, Rt, and the CLA roughness, Ra. In fact, with loaded wheels it is found that Ra = d0.78 which, remarkably, is exactly the relation obtained elsewhere when data obtained during high speed grinding was analysed.

The forms of wheel wear occurring during each of the three grinding mechanisms which can occur when materials exhibiting high adhesion are ground by alumina wheels are examined and it is shown that at very low removal rates, when the grains wear attritiously, the wear occurs via a thermally controlled wear mechanism. At higher removal rates, when workpiece material adheres locally to the grains, the wear occurs via combined thermally and mechanically controlled mechanisms, while at the highest removal rates, when wheel loading occurs, wear is essentially mechanically controlled. It is shown that in this latter form of grinding, the primary source of wheel wear is grain loss from the wheel which occurs when the adherent material becomes detached from the wheel surface. The adherent material is shown to be made up of individual grinding chips which first adhere to the “rake” face of the grains and then to each other to form a compacted mass which, after going through its life cycle, becomes detached from the wheel. The dependence of the longevity of the adherent blocks on grinding conditions is deduced and from this the influence of the factors affecting wheel wear when loading occurs is explained.

Three distinct grinding mechanisms have been found to occur when 304 L stainless steel is ground by alumina wheels. The first results in the grits becoming worn by attritious wear and occurs when temperatures in the grinding zone are relatively high, the second occurs at lower grinding temperatures and results in isolated, tiny areas of workpiece material adhering to grits while the third becomes manifest at relatively low grinding temperatures and results in areas of the wheel, large in comparison to the size of a grit, being covered by adherent workpiece material. Previous proposals advanced to explain metal build-up on the grinding wheel are shown to be inadequate and the phenomenon of large-scale metal transfer to the grinding wheel is shown to be related to the ductility of the workpiece along with the degree of protection conferred by the oxide of the workpiece material. This explanation is confirmed by grinding experiments performed on a series of oxide-resistant workpieces ground in air and, in particular, by the grinding of mild steel in an argon atmosphere under which conditions large-scale transfer of workpiece material to the wheel occurred.

Equations expressing the dependence of the force components on grinding parameters and on the fraction of the wheel surface area over which workpiece material adheres during the grinding of workpiece materials which exhibit high adhesion are derived. These are shown to express the experimentally observed relations between the force components for each of the three grinding mechanisms which occur when this class of workpiece is ground. When large scale adhesion of workpiece material to the wheel surface occurs and more than five percent of the wheel surface is occupied by transferred material, the force components arise in large measure as a result of the forces generated through this metal/metal contact.