Altair's Student Guides - CAE for Simulation of Metal Forming

CAE for Simulation of Metal Forming

Contents

Contents Introduction ......................................................................................................2 About This Series ...........................................................................................2 About This Book .............................................................................................2 Supporting Material ........................................................................................3 Product Design vs. Tool Design ..........................................................................4 Design Principles ............................................................................................4 Conflicting Demands.......................................................................................5 Tool Design - Analysis, Design and Optimization ..............................................7 Summary .......................................................................................................8 Metal Forming – An Overview.............................................................................9 Metals – Cradle To Grave................................................................................9 Sheet Metal.................................................................................................. 10 Drawing The Fuller Picture ............................................................................ 12 Critical Data - Material Properties .................................................................. 19 Its (Almost) All About Steel ........................................................................... 22 Numerical Analysis – An Introduction ................................................................ 24 Numerical Models ......................................................................................... 24 Important Terms .......................................................................................... 28 Summing Up ................................................................................................ 32 Finite Element Methods and Forming ................................................................ 33 A Retrospective ............................................................................................ 33 The Tool Designer and The Analyst ............................................................... 35 The Product Designer and The Analyst .......................................................... 37 Incremental Analysis - Numerical Aspects ...................................................... 38 Summary ..................................................................................................... 42 Putting It All Together: HyperForm ................................................................... 43 Process-Centric Modeling .............................................................................. 43 Forming Simulation – What and How............................................................. 44 Summary of Steps Involved .......................................................................... 49 Advanced Topics ............................................................................................. 51 Commercial Terms ....................................................................................... 51 Data Files – What Goes Where ...................................................................... 52 Glossary And References.................................................................................. 54 References................................................................................................... 59 Other Resources........................................................................................... 59 Sample Material Properties............................................................................ 59

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Introduction

CAE for Simulation of Metal Forming

Introduction About This Series To make the most of this series you should be an engineering student, in your third or final year of Mechanical Engineering. You should have access to licenses of HyperWorks, to the Altair website, and to an instructor who can guide you through your chosen projects or assignments. Each book in this series is completely self-contained. References to other volumes are only for your interest and further reading. You need not be familiar with the Finite Element Method, with 3D Modeling or with Finite Element Modeling. Depending on the volumes you choose to read, however, you do need to be familiar with one or more of the relevant engineering subjects: Design of Machine Elements, Strength of Materials, Kinematics of Machinery, Dynamics of Machinery, Probability and Statistics, Manufacturing Technology and Introduction to Programming. A course on Operations Research or Linear Programming is useful but not essential.

About This Book Of all the books in this series, this is by far the easiest for a mechanical engineer to understand. The subject is far less abstract than those covered in the other books, and the immediate relevance of the methods discussed is remarkable. Like the other books in this series, it is self-contained. Access to a press-shop, of course, will not only be extremely useful, it’s almost indispensable. While a knowledge of FEA won’t hurt, it is not essential. As we will see, the techniques used are at the very cutting edge of numerical analysis, but these are so closely aligned with physically meaningful manufacturing processes that an understanding of manufacturing technology is more than enough to appreciate, to learn, and to bring this power to bear. The various references cited in the book will probably be most useful after you have worked through your project and are looking for ways to increase the depth of the simulation techniques you have learned.

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CAE for Simulation of Metal Forming

Introduction

Supporting Material Your instructor will have the Instructor’s Manual that accompanies these volumes – it should certainly be made use of. Further reading and references are indicated both in this book and in the Instructor’s Manual. If you find the material interesting, you should also look up the HyperWorks On-line Help System. The Altair website, www.altair.com, is also likely to be of interest to you, both for an insight into the evolving technology and to help you present your project better.

You have your way. I have my way. As for the right way, the correct way, and the only way, it does not exist. Friedrich Nietzsche

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Product Design vs. Tool Design

CAE for Simulation of Metal Forming

Product Design vs. Tool Design Depending on the relative importance of the different stages of the product’s lifecycle, designers often emphasize one or more approaches to product design. One approach that’s familiar to anyone who has worked with a hierarchical solid-modeler is Design for Manufacture. In this approach, the designer is urged to pay attention to how the product will finally be manufactured – how the material will be cut, molded, pressed, cast, welded, and so on.

Common Design Philosophies Design for …

The tools that are used to manufacture the product must, of course, themselves be designed. This discipline is assigned to the tool designer, and the practice is often assigned to the tool room. This distinction between tooldesign and product-design has one unfortunate aspect to it. The tools themselves are the critical but underappreciated lesser cousins!

… … … … … … … … … … … …

assembly disassembly ease of use installation maintenance manufacture quality reliability reuse speed cost environment

As a result, the words “product design” are readily comprehensible to almost any engineer. They may mean different things to different engineers, but all these meanings are pretty much always correct since different products require different design methods. The words “tool design” are a little fuzzier. Even engineers who find the phrase familiar are prone to misunderstand it.

Design Principles Our interest lies not in the differences between tool design and product design. Our approach is from an entirely different direction: we want to study how the principles of product design can be applied to tool design. This is not as radical as it may sound, since the tool itself is a product, of course: it is the product that’s designed by the tool engineer or tool designer. From our perspective, the tool that’s being designed is a product like any other product, except that it may itself be used to manufacture other products. This means that the requirements that the tool-designer faces should be similar to those faced by the (to use the term in its traditional meaning) 4

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Product Design vs. Tool Design

product designer. The familiar trinity – time – cost - quality - apply here too. Tool designers too have to grapple with the problems of designing the tool faster, making the tool itself cheaper, and improving the quality of the tool. There are important differences of course, as we’ll shortly see, but from a simulation perspective, tool designers stand to derive similar benefits from a successful application of CAE1. Unfortunately, not all manufacturing processes are amenable to simulation: we just don’t know enough of mechanics to be able to reliably simulate the performance of several manufacturing processes using mainstream CAE techniques. There are other ways to model these processes, of course. For instance, some are modeled empirically, some use abstracted models, etc. HyperWorks itself offers methods to simulate several manufacturing processes - forging, friction stir welding, extrusion, molding and forming. Metal forming is itself a vast subject – as we’ll summarize in the next chapter – but there is one process in particular that has shown itself to be amenable to FEA and gained widespread adoption in the recent past. That’s the focus of this book. Apart from the fact that metal forming is well suited for CAE, it’s also a huge business worldwide. For instance, in the automotive industry a typical vehicle program averages US$ 500,000 per toolset. Automotive dies worldwide are a 25 Billion USD business!

Conflicting Demands Unlike the traditional product designer, the tool designer, like Damocles, has to contend with a peculiar problem. Remember that time – cost – quality are the most fundamental objectives of any design. Unfortunately for the tooldesigner, the design of the tool has an impact not just on the cost of the tool itself, but of the products that are manufactured using this tool. This is because product-marketing companies recover the price of the tool from the price of the products. The mathematics is not always simple. The direct contribution of the tool cost to the cost of each product is easy: it’s the cost of the tool divided by the number of products manufactured using this tool.

1

Short for Computer Aided Engineering, usually taken to mean Finite Element Methods. 5

Product Design vs. Tool Design

CAE for Simulation of Metal Forming

But there are several indirect costs that are harder to account for. For instance, since the tool is bound to wear, the denominator in the previous equation depends on the design, which determines the tool life. Further, the amount of raw material that’s required for each product also depends on the efficiency of the tool itself. If there’s a high wastage, the contribution of material-cost to the cost of the final product will rise. The tool-designer’s misfortune is not complete yet. Many times by the time the tool-designer gets involved in the product-design cycle, the product specifications in terms appearance, function, etc. are already frozen. This means the tool-designer has to live with constraints that make a difficult job even harder to deal with. And since the clock is already ticking – the project is already underway! – the tool designer’s brow is understandably furrowed. The cost of the tool, the cost of personnel, etc. are often insignificant compared to the cost of delay for the OEM. What all this boils down to is the fact that even though the design principles are similar for product design and tool design, tool-designers and productdesigners are often at loggerheads. All the aspects that product designers drive for – aesthetically pleasing appearance, reduced weight, tightly controlled dimensions, … - seem perversely chosen to make the tool designer’s job that much harder. One solution is to push for a closer integration between the manufacturing shop-floor and the product-design department. Involving experienced machinists in the design cycle as early as possible makes sense, but is not always possible. This is particularly true in the layered-procedure that OEMS deploy to work with long supply-chains. As a rule, the automotive industry, the aircraft industry and the consumer electronics industry divide the productlifecycle among the various levels of the supplychain. Design For Manufacture is intended to make this 6

“When I first entered the automotive business in 1980, there were approximately 30 original equipment manufacturers (OEMs) globally. While the exact numbers will vary a bit depending upon the source used, in that same year, there were approximately 35,000 automotive suppliers worldwide. Fast forward to 2006, and we have 13 OEMs and somewhere between 6,000 and 8,000 suppliers globally. North American OEMs concluded that by tiering their supply base, there would be greater product innovation, better manufacturing efficiencies, and faster time to market. The Tier Ones would maintain their relationship with the OEM and all of the other suppliers would organize underneath them. Tier Twos would focus on components or sub modules, Tier Threes would focus on processes, and Tier Fours would primarily be material producers.” From The New Supply Chain by Kim Korth Automotive Design and Production

CAE for Simulation of Metal Forming

Product Design vs. Tool Design

easier, but relying on feature-based modeling doesn’t always work adequately. Given the pressures of product design, too many product designers end up making unreasonable demands of the tool-designer. Obviously since both the designers – tool and product – are working towards the same goal, this is not a happy situation at all. What, if anything, can simulation do to help? Quite a bit, it turns out.

Tool Design - Analysis, Design and Optimization The techniques discussed in the other books in this series cover the use of analysis and optimization in product design, but pay little attention to manufacturability of the product. It is readily apparent, from the discussion above, that this is an aspect that needs to be addressed: since careful part design can help, it makes sense to provide the product designer with techniques that can help estimate the manufacturability of the product. Since we don’t expect the product designer to be an expert with all aspects of manufacture, the simulation-method needs to be easy to use and suitable for an order-of-magnitude estimate. Further, since product designers are involved in the early part of the design cycle, the simulation tool should be quick. The tool designer, as opposed to the product designer, is certainly expected to be an expert on manufacturing techniques. This means the simulation techniques must provide the tool-designer with enough coverage to match the level of expertise. And since the tool designer gets called into the design process after the product specifications are largely decided, the simulation technique must be powerful enough to provide the tool designer to investigate, in intricate detail, the impact of product-design changes on the cost and performance of the tool. Finally, even if product-design changes are ruled out, the simulation technique must give the tool designer ways to drive for a first-time-right tool design. Analysis of a design is easier than the design itself. An analyst starts with a well-defined problem and searches for the solution. In contrast the designer is faced with a problem that is rarely clearly defined, and that almost always has more than one acceptable solution. If CAE is used to verify a design, it’s often too late in the design cycle to implement any changes that the analyst recommends, unless the analyst predicts failure. Wouldn’t it be great if the designer had a method that 7

Product Design vs. Tool Design

CAE for Simulation of Metal Forming

could help suggest designs that are least likely to get rejected by subsequent CAE? In other words, we would like to put forward our definition of a “satisfactory” design, and have the software suggest to us a tool-design that is most likely to pass the subsequent analyst’s verification.

Summary This discussion, then, leads us to a few unarguable points: •

CAE is used more widely for product design than tool design

•

tool-design can and should use similar CAE methods

•

product designers need a quick and relatively approximate method to estimate manufacturability

•

tool designers need detailed and accurate methods to simulate the performance of design alternatives

We’ll spend the rest of this book investigating how to convert these wishes to fact.

If I had eight hours to chop down a tree, I'd spend six hours sharpening my ax. Abraham Lincoln

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CAE for Simulation of Metal Forming

Metal Forming – An Overview

Metal Forming – An Overview Many design methods can be reduced to formulae – concise and convenient, if not always easy to work with. Manufacturing topics, by nature, tend to be much more difficult to encapsulate. Both the width and depth can be intimidating, and even a cursory summary will take more time and space than we can afford. Since there are several books that do the job admirably, we won’t attempt to reproduce the material here. Our goal in this chapter is to summarize the metalworking processes that are relevant to our simulation goal.

Metals – Cradle To Grave Of the 88 elements in the periodic table2, 61 are metals, from Lithium to Bismuth. Few of these occur widely enough to be affordable, and even fewer provide the strength that structural design demands. Almost invariably, mechanical engineers rely on either Steel or Aluminum. In either case, the journey from the ore to the pure metal is not of any interest to us. What is important to remember is that neither iron nor aluminum is usable in its purest form. Almost invariably, they are alloyed to provide desirable characteristics. While the methods we will study in this book can be applied to Aluminum too, our focus will be restricted to steel, which is more widely used than Aluminum for structural purposes3.

In (the) search for lighter cars, the automotive industry shows a considerable interest in the application of aluminum for car body panels. The basic requirement for those sheets is to have a high formability, so the panels can be stamped, while retaining or preferably increasing their strength when the part is painted and baked. The formability and strength are still inferior compared to steel.

A Comparative Study of Two Al-Mg-Si Alloys for Automotive Applications Scripta Materialia VOL. 35 ISSUE: 8 15 Oct 1996

When tool-designers talk of the raw material, then, they mean the physical form in which it is received for further processing.

2

Excluding the Lanthanides and Actinides Aluminum is widely used in the aircraft industry, where it is being seriously challenged by composites.

3

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Metal Forming – An Overview

CAE for Simulation of Metal Forming

Metalworking starts where the furnace leaves off. Steel is either cast in ingots and rolled to a more manageable size, or continuous casting delivers billets or blooms directly from the furnace. Rolling, apart from reducing the size, also work-hardens the material. Properties of the metal, of course, can be manipulated by one or more of several heat-treatment processes – annealing, quenching, tempering, and so on – as well as by surface treatment processes such as nitriding or carborising. Aluminum is frequently extruded, unlike steel. Both metals can be cast, using either gravity diecasting or pressure die-casting, following which machining provides the necessary finish and dimensional control. From a tool-design perspective, all the operations above involve the design of a tool – whether it’s the cutting tool used for machining, the die for casting, or the rolls for rolling. The raw material doesn’t have to be purchased as billets, blooms or rods: sheets are usually sold as coils. A sheet of thickness more than 4 mm is normally referred to as a plate. The word sheet is used if the thickness is between 0.5mm and 4mm – any thinner, and it is called a foil.

Sheet Metal Sheet metal is not only inexpensive and lightweight, it can be worked quite easily. As a result, it’s used pretty much everywhere – from computer cabinets to roofing sheets. Sheet metal is sometimes specified by its gauge4, which is not always easy to interpret since the gauge refers to the weight of the sheet, not it’s thickness. As a result, a sheet of one alloy can have a different thickness than the same gauge sheet of another alloy. Sheets are produced by either hot or cold rolling. The latter is more difficult, but produces stronger steel since it’s work-hardened. Cold-rolled steel is usually annealed to improve its ductility. Methods of converting the raw material to finished component involve one or more operations like bending, forming, stamping, drawing, deep drawing, punching, piercing, lancing, blanking, trimming, flanging, embossing and coining. For instance the commonly used beverage cans are first blanked, deep drawn, redrawn, ironed, domed, necked and seamed! It’s not always easy to distinguish between stamping, forming, embossing and drawing. The differentiating factor is usually the depth of deformation – that is, how much the metal is deformed from its raw state. From another 4

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Sometimes spelt gage

CAE for Simulation of Metal Forming

Metal Forming – An Overview

point of view, drawing involves a flow of the material while the others do not. Piercing, punching, lancing, trimming and coining involve fracture of the metal, while the other processes only involve plastic flow. From a stress-analysis perspective, this means that the metal is deformed beyond the yield point, so that plastic deformation occurs. While elastic deformation vanishes when the applied forces are removed, plastic deformation is permanent. This is significant. In courses on the Strength of Materials or the Design of Machine Elements, we usually seek to ensure that the stresses are below the elastic limit of the metal. In our sheet-metal working process, we want to design the process such that the stresses are above the yield point. The mechanics of fracture is not fully understood. Neither, for that matter, is the plastic deformation of steel, but there are several theories that serve adequately well from an engineering-design point of view. As a result, simulation of sheet metal forming is today largely restricted to the processes that involve plastic flow. Traditionally sheet metal processes assume that the raw material has uniform properties. This is reasonable when working with coils, which are produced in bulk5. In some cases, however, the standard-sized blanks are welded together to provide a non-standard size to the metalworker. Called tailor welded blanks, these pose a slightly more complicated design problem since the properties of the blank in the neighborhood of the weld are different from the properties in the rest of the material.

The development of the automotive body represents a major challenge for all manufacturers as they continuously work to reduce the time and cost of bringing a new vehicle to market. Using practices such as concurrent engineering, rapid prototyping and computer simulation, manufacturers have reduced their development costs and lead-time by integrating process engineering and manufacturing into the design phase or "front end" of body development. This integration has been far less common from the product and process design phases forward into the manufacturing validation phases. Changing a part dimension typically requires physical rework to the dies. This rework may involve several iterations making it an expensive and time-consuming process. Moreover, the effects of excessive die rework are not limited to additional construction and tryout costs. Several manufacturers maintain that numerous rework iterations for a set of component dies also impacts the reliability of the tooling. Constant grinding and welding of dies increases the likelihood of subsequent tooling failure.

An Integrated Approach to Body Development Auto-Steel Partnership www.a-sp.org

5

Studies do show variation within strips, but these are often within the acceptable range. 11

Metal Forming – An Overview

CAE for Simulation of Metal Forming

This complication, of course, is the main reason the designer turns to them – because it allows you to tailor the properties of the blank by choosing which part of the blank should have which properties. In any case, the tool designer’s goal is to design both the tool and the process so as to ensure that after the metalworking is done, the finished product meets specifications. Specifications themselves can vary widely. In some cases, notably the outer panels of car bodies, the finish must be good enough that the product need be subjected to no more work, except painting. In other cases, dimensional accuracy is critical. Some product designers demand a thickness that’s close to uniform. The last is often specified as a permissible thinning percentage. And in addition to meeting these specifications, the tool designer must also ensure that the tool-life is adequate, the tool cost is kept as low as possible, and the process requirements are within the capability of the available press shops! If, for instance, the tool designer chooses a blank that is too thick, the press itself may get damaged.

Drawing The Fuller Picture Bending (using a press brake) is well documented, and easy to design for mainly because the deformation is along a straight line. The designer’s prime interest is in understanding the stretch that the bending process induces. Hand calculations are usually enough to provide engineering accuracy. Many CAD packages also allow the calculation of the unfolded or developed shape, given the final product. It’s when the deformation is along a more complex path that CAE is indispensable. This “complex path” is the characteristic of the three “forming” processes: stamping, drawing and deep-drawing. (The principal modes of deformation that characterize forming are stretching and bending.) In all of these, a press deforms the raw material or blank. The blank is held by a blank-holder or binder, between the punch and die. When the punch and die are forced together by the press’ ram, the metal deforms.

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CAE for Simulation of Metal Forming

Metal Forming – An Overview

In some cases the punch is above the blank – the working principle is the same. Presses are principally of two types – mechanical and hydraulic. The latter, as the name suggests, uses fluid pressure to generate the forming force, like the Bramah Press that’s used in high-school physics classes to explain hydrostatics. The press was invented by Joseph Bramah and patented in 1795. It’s interesting to note that Bramah was principally a lock-maker: the fact that locks require high-precision components motivated him to develop tools to assist in the manufacturing process. There are several differences between mechanical and hydraulic presses, but the only ones that are important to our study are the speed of the press and the forming force, as we will see when discussing simulation. Hydraulic presses are easier to control, which means the designer can choose a forcevs.-time variation. With mechanical presses, the designer doesn’t have this option. Presses are also categorized as single acting, double acting or triple acting. A double acting die, for instance, has two slides. In addition to the ram the ejector also moves. Further methods of categorization exist – based on the bed size, the shut height, and so on - but are not listed here as they are not important for our study. A closer look at the press itself, focusing on the die and punch, shows us the parameters that are important to the die designer. If the deformation is plastic, the metal remains in this deformed shape. If the deformation is elastic, the metal regains its original shape – it springs back to the undeformed shape when released from the die. In many cases the deformation is largely plastic, leaving some pockets of elastic deformation. This leads to springback. 13

Metal Forming – An Overview

CAE for Simulation of Metal Forming

Remember that after bending, residual compressive stresses remain on the inside of the bend, while residual tensile stresses are present on the outside radius of the bend. When the bending force is removed, the metal springs back until the residual stresses are balanced by the metals ability to resist deformation. Materials like steel that have a high Modulus of Elasticity (as compared to tensile strength) spring back less than materials with a lower modulus. One way to account for springback is to provide a compensation – bend the material beyond the required angle, so that after springback it is in the required shape. Of the several questions the tool designer has to answer, one of the most vexing is how many stages are required to form the component. Components that have a low draw-depth (relative to the major transverse dimension – for example, the radius of a cup) can be formed in one stage, while deeper draw depths require a multi-stage process. That is, the blank is worked in different dies to reach the final shape.

The goal is to reduce the number of stages as far as possible, since both cost and time-required are directly proportional to the number of stages. For instance, the component shown above can be completed in a single stage if a double-acting press is used, even if the depth demands two stages with a single-acting press. Sometimes a transfer die is used to automatically move the component from one stage to the next, reducing material handling costs. Regardless of the number of stages, the cost of the press and dies often means that OEMs adopt a hub-and-spoke approach. In this approach, a single press-shop feeds several assembly shops. If the gap between the time of manufacture and the time of assembly is large, the component may deform under its own weight. Remember that we are dealing with sheetmetal which is thin, and is often quite long and wide, as with a car bonnet. This is a product-design problem, not something the die-designers have to worry about.

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Metal Forming – An Overview

But components like these pose another problem for the die-designer. If the formed component is thin enough that it will sag under its own weight, the blank will be, if anything, even more flexible. This means that when the blank is placed on the binder, the designer needs to account for the gravityrelated deformation that takes place before the punch makes contact with the blank. This gravity-effect can significantly change the behavior of the tool, so should not be ignored6. In some cases the binder is curved, in which case the bending of the blank when the binder is clamped shut, before the punch contacts the blank, is called binderwrap. Like the gravity-effect, this too can significantly change the behavior of the tool.

Hydroforming Hydroforming is a technique that is less widespread, but not only is it often commercially viable, it is sometimes essential. It is often used to form tubes, with operations like bending, flaring, beading and bulging. The press, of course, is hydraulic, but the critical difference with the more “traditional” hydraulic press is the method of application of force on the blank. For tube hydroforming, for instance, fluid at a high pressure is forced into the tube. This pressure makes it deform. Apart from the fact that a liquid can enter areas that a solid punch or die cannot, the advantage is that the pressure is uniform all across the component7. Hydroforming is slower since the fluid pressure has to be ramped up, and hydroforming presses are more expensive to construct. The effect they have on the strength of the finished component is sometimes so useful that the increased cost and slower production rate is acceptable as illustrated by the table8, in which the “baseline” costs are for a “traditional” forming press:

6

See CAE And Design Optimization – Basics for methods used to stiffen sheet-metal components after assembly. 7 As Pascal’s Law tells us it should. 8 See Lightweight SUV Frame – Design Development, May 2003, on the Altair website. 15

Metal Forming – An Overview

CAE for Simulation of Metal Forming

Baseline

Hydroformed

Annual Sales – 220,000 units

$58,400,000

$72,200.000

Tooling

$19,400,000

$17,500,000

Capital

$1,800,000

$2,600,000

$265.65

$328.18

Component Cost per vehicle

Process Parameters Now that we are familiar with the general machine and tool related aspects, let’s take a closer look at the process of forming itself. We know that the tool-designer’s job starts from where the product-designer left off. Decisions or choices made by the part-designer will obviously have a significant impact on the tool-designer, of course, but there are some aspects that can be decided entirely by the tool designer. These aspects, specific to the manufacturing process, are what we call the process parameters. From what we have studied so far, we know that the tool designer’s goals are •

to reduce the tool cost

•

estimate the blank shape and size

•

decide the number of stages

•

calculate the required press tonnage

•

to maintain the specified thickness of the formed sheet

•

to achieve the required finish – wrinkles and tears must be avoided

The tool designer has to choose a combination of process parameters that will yield a component that matches these specifications. And this is where simulation shows its power! 16

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Metal Forming – An Overview

Sheet metal behavior during actual press production is difficult to define and measure. Production involves the interaction of many variables, which means that the impact of one variable on the process outcome can be difficult to even observe, let alone measure9! Current research10 holds that there are about 30 parameters that must be specified to define the forming process. This is bad enough from a manufacturing perspective, since it means that all these factors should be controlled if the manufacturing process must be repeatable. From a tool designer’s perspective, it is even worse! Even if the 30 parameters had the simplest possible binary form, that is if each is restricted to being either “on” or “off”, this leaves the designer with designer with 230 possible combinations – that’s 1,073,741,824 combinations. In reality, of course, most of the parameters can vary continuously, making an already difficult problem almost impossible to tackle. Fortunately, research has shown that the parameters are, like most other things in the world, subject to the Pareto Principle. That is, there are a vital few parameters that have the most effect on the outcome of the process. The same work cited above classifies these into seven categories: blank condition, blank lubrication, stamping press variables, metal properties, die condition, miscellaneous, and interactive variables. For our purpose, the process variables that are important are: •

“Stamping processes have so many input variables affecting variation, with some estimates at well over 100, that even world-class stamping operations routinely operate outside of statistical control, with non-stable process means between die sets, especially on larger flimsy parts. Manufacturers experience difficulties estimating mean part dimensions, relative to nominal and process variation because these attributes are product and process co-dependent. Potential attributes affecting variation include material properties (steel variations in gauge, grade, and coatings), part geometry (size and shape), die engineering and construction, and stamping press variables. The infinite number of design and process possibilities make it nearly impossible to accumulate sufficient historical knowledge for a designer to accurately assign tolerances that consistently meet future process capability.” from Automotive Sheet Steel –

Stamping Process Variation The Auto-Steel Partnership, 2000 http://www.a-sp.org

velocity of the tool – direction of

9

See CAE and Design Optimization – Advanced for a discussion on the Design Of Experiments (DOE) to study such affects. 10 Siekirk,J., Process Variable Effects on Sheet Metal Quality, Journal of Applied Metalworking, American Society for Metals, July 1986 17

Metal Forming – An Overview

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motion and variation with time •

properties of the material

•

thickness of the sheet

•

lubrication

•

binder force

•

punch and die radii

•

clearance between the punch and die

This helps reduce the problem to a more tractable level, and allows remarkably accurate simulation of the complex process, as we will see in the subsequent chapters. Before we go on, though, it’s important to note that in some cases the product design specifies the material to be used, while on other cases the tool designer has some room to maneuver. This is a mixed blessing since not all parameters of steel improve in tandem. For instance, as hardness rises toughness (or shock resistance) usually falls. Either way, the tool designer needs to estimate the formability of the material – that is, how is it likely to flow within the die under a given set of process parameters.

Lubricants Of all the process parameters, lubrication is one that merits a special discussion. In the first place, friction is poorly understood even today. The “laws” of frictions should really be called “theories”. In the second place, the lubricants are not easily quantified. What is a lubricant? In general, it’s a substance that is interposed between two surfaces in relative motion. The purpose is to reduce friction between the surfaces, and thereby reduce wear. In the context of sheet metal forming, lubricants have multiple origins and multiple effects. In several cases, a coating is applied to the sheet at the steel mill to inhibit rusting. This often remains on the sheet, and can be used 18

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Metal Forming – An Overview

to aid forming. In other cases, a lubricant is applied in the press shop after the blank has been cut from the coil or sheet. Alternately, a lubricant may be applied selectively to assist flow in critical areas of the die. Lubricants should be cleanable, compatible with all subsequent treatments the component will undergo such as the application of an adhesive or a surface coat, cost effective, storable, weldable, non-toxic, and so on. From an impact-on- formability perspective, the lubricant principally affects the coefficient of friction between the tool surfaces and the blank. A low coefficient of friction encourages flow, while a high coefficient of friction retards flow. The lubricant also helps by preventing accumulation of metal on the tool - called galling. If galling occurs, scoring, the plowing of the metal, will follow.

Critical Data - Material Properties Steel is a material that engineers have worked with for long years now, so its elastic properties are familiar to every undergraduate engineer – the density, Poisson’s Ratio and Young’s Modulus or Modulus of Elasticity. Forming, as we have seen, involves plastic flow, so we must expand our lexicon a little. The yield stress and tensile strength of the material are easily obtained from the stress-strain curve. If the stress exceeds the tensile limit, the material will fracture, which means our sheet-metal will tear. Between the yield point and fracture, the material undergoes plastic deformation. There are several theories of plasticity, but one has been found to work well for the simulation of sheet-metal forming – power-law hardening. Under this theory, the stress strain dependence is of the form

σ = K ∗ (ε 0 + ε ) n where K is the strength coefficient, ε0 is the pre-strain coefficient and n is the strain-hardening exponent.

n is given by

19

Metal Forming – An Overview

n= where

(d [ln σ T ]) d [ln ε ]

CAE for Simulation of Metal Forming

ε is the strain

K can be calculated using the equation

K=

σ u ∗ en nn

where σu is the tensile strength, e is 2.718 (the base for natural logarithms) and n is the strain-hardening exponent. Once we have K, we can use the equation

σ  ε 0 =  y  K 

1 n

to calculate ε0. Some materials exhibit strain-rate sensitivity. That is, the stress-strain relationship is given by

σ = kε n • ε& m In this case, we calculate m using the equation

m= where

ε& is the strain rate,

(d [ln σ T ]) d [ln ε& ]

dε , and σT is the true stress dt

(Recall the difference between engineering stress / strain and true stress / strain: the former uses the original dimension while the latter uses the instantaneous dimension.). 20

CAE for Simulation of Metal Forming

Metal Forming – An Overview

Finally, we commonly assume that steel is isotropic, which is reasonable below the elastic limit. Sheet metal forming, however, needs to account for a form of anisotropy because of the way the sheet is manufactured – the rolling process results in a different “flow-ability” in-plane and out-of-plane. The Lankford coefficient11, also called the anisotropy ratio, is defined as the ratio of the width-plastic-strain to the through-thickness plastic strain. The higher the value, the easier it is to draw the material. The value of r is direction dependent, so often we calculate r - the average of the r in the 0, 45 and 90 degrees directions and ∆r using the equations

r=

(r o +2r45 + r90 )

∆r =

A high value of

4

(r o −2r45 + r90 ) 4

r and a low ∆r indicate better formability.

In effect, therefore, we can characterize the plastic-behavior of the steel by specifying the strain-hardening coefficient n. To sum up, the data we require is

11

•

the Poisson’s Ratio – typically 0.3

•

the Modulus of Elasticity – typically 2.07E11 N/m2

•

the density – typically 7,830 kg/m3

•

yield stress – for example, 390 MPa for a High Strength Steel

•

tensile strength – for example, 469 MPa for a High Strength Steel

•

strain-hardening coefficient n – for example, between 0.2 and 0.3 for steels with a yield stress < 345 MPa

Named for Lankford W.T. Published with Snyder SC and Bausher JA, Trans. ASM

1950; 42:1197 21

Metal Forming – An Overview

•

CAE for Simulation of Metal Forming

anisotropy ratio r – for example, 1.0 to 1.4 for cold rolled rimmed steel

All this is from a theoretical perspective, but it doesn’t tell the complete story. The tool-designer has to actually get these values! One option is to measure it, while the other – and more reasonable – option is to get it from the supplier of the steel and verify it by testing a sample. It is important to pay attention to quantifiable parameters, as opposed to descriptive terms. For example, the terms “stronger” and “harder” are not as useful as the yield-stress and Rockwell hardness respectively.

Its (Almost) All About Steel It would be foolish to claim that sheet metal is only about steel: applications that demand good electrical conductivity, for instance, use copper or brass. Specialty applications or areas where the cost of production is not the most critical factor – such as aerospace – work with more exotic metals, often in the form of sheets. Metal itself, of course, is often challenged by composite materials. In this book, however, we will restrict our attention to steel, as we have already noted. This is not just because steel is still very widely used. It’s also because, despite the steady inflow of worthy challengers, the champion isn’t done just yet. As a recent review12 observed:

"In North America legislative pressure to reduce fuel consumption has sparked the search for a lighter car. Aluminum and plastics can indeed produce vehicles that are lighter than current steel models. And these lighter vehicles also have other benefits, such as fewer parts, by using space frame construction though steel could also do this. An aluminum panel weighs about half as much as a steel panel of equivalent strength, and using more aluminum could, it is claimed, also meet other criteria, although the past 15 years have seen considerable savings (albeit offset by luxury fittings and safety features) achieved

12

22

AZoM.com: http://www.azom.com/details.asp?ArticleID=534

CAE for Simulation of Metal Forming

Metal Forming – An Overview

through rationalization of car body structures and the use of lighter gauge, higher strength steels. At present, alternative materials are most competitive in low volume production where tooling, rather than materials, most affects unit cost. Aluminum could reduce body weight by up to 40%, but new steel technologies promise reductions of up to 35%, leaving aluminum only just ahead."

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. E.T.Bell

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Numerical Analysis – An Introduction

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Numerical Analysis – An Introduction The simulation technique we will study is based on the Finite Element method. But just as you do not need to know thermodynamics to use an internal-combustion engine, our study of Finite Elements will be restricted to specific items only. We will study enough that we can use the method, rather than the underlying theory in depth. Read this chapter and the next with this in mind. In this chapter, we outline the basics of FEA as relevant to our application – the modeling and simulation of sheet-metal dies, punches, and the blank. We will complete our study of the FE method in the next chapter13.

Numerical Models As a designer, you need to anticipate the behavior of the product you’re designing. You will need to guess at the conditions it is likely to be exposed to, and then to predict how it will respond to these conditions. In some situations, the behavior is independent of time – these are called

steady state problems. In others, the solution varies with time – these are called transient problems. In some situations, the response of the body to stimuli is linear. That is, there is a linear correlation between input and output. Such a model is, obviously, called a linear problem. Other situations are non-linear because there’s no linear dependence between stimulus and response. It’s important to remember that the product you’re analyzing does not know whether it is “linear” or not. You, as the analyst, can choose to model it as linear or as non-linear, depending on which is more likely to give you useful results. Since we are designers, not mathematicians, we are not interested in results that are “exactly correct”. We are willing to settle for “approximately correct” provided we get the results in time and at a cost we can afford. As you know from your courses on Linear Algebra and Differential Equations, linear equations are far easier to solve than non-linear equations. Therefore, 13

A Designer’s Guide to Finite Element Analysis, a part of this series, covers FEA in

more detail, and from a more general perspective. 24

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Numerical Analysis – An Introduction

we very often choose to model behaviors as linear even if a non-linear model is more precise. We tend to choose non-linear models only if there’s no linear model that’s even reasonably accurate. Non-linear models are of several types – the materials used, the geometry involved, or conditions on the boundary can cause the “non-linear” nature. Examples of material non-linearity are plastic deformation, melting and solidification – the stiffness of the body changes as the material properties change. Other problems involve geometric non-linearities - the stiffness changes as the body deforms even if the material’s properties do not change – take for example the reduced rigidity of a plastic bottle as it is crushed. An example of boundary non-linearities is contact, because the stiffness of the part or assembly changes as sections come into contact with each other. Some models, such as those required to simulate metal-forming, involve several of these types of “non-linearities”.

What is FEA Finite Element Analysis (FEA) simulates a physical part or assembly’s behavior by dividing the geometry of the part into a number of elements of standard shapes, applying loads and constraints, then calculating variables of interest – deflections, stresses, temperatures, pressures, etc. The behavior of an individual element is usually described by a relatively simple set of equations. Just as the set of elements would be joined together to build the whole structure, the equations describing the behaviors of the individual elements are joined into a set of equations that describe the behavior of the whole structure. One way of looking at it is to recall the approach you studied in Engineering Mechanics14. There, you drew free body diagrams of each member in the structure, wrote equations that related the unknown forces in each member, then wrote equations that had to be satisfied for the forces between members if equilibrium is to be satisfied. Solving these equations gave you the forces in each member. Elements themselves are defined by specifying the nodes, which are the vertices of the element. Just as 4 corners define a rectangle, the nodes define the shape of an element.

14

A more complete discussion is presented in A Designer’s Guide To Finite Element

Analysis. 25

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When you choose an element to represent a part of the product, you are also specifying the parameters that define the behavior across the element. For instance, in a stress analysis, if you know the 6 components of deformation15 at any point, you can calculate the strain from this by taking the first spatial derivative. And once you know the strain, you can use the material properties to calculate the stress. For the Finite Element Method, every node has these parameters associated with it, just as in a trussstructure every member has forces associated with its end-points. From the values at the nodes, you can interpolate for the values between the nodes. Suppose you were asked to digitize a surface, using a Coordinate Measuring Machine. Unless your surface were absolutely flat, you would not space the measurement points evenly. Since you have to interpolate between measured values, you would naturally choose to have more measurement points at areas where the surface curves sharply. In mathematical terms these areas have a high derivative, or rate-of-change. In a similar fashion, for an FE analysis you would create smaller elements (which means more nodes) at areas where you expect the stress to be high16. The choice of the sizes of elements depends on many things - the anticipated stress levels of a certain area, the detail wanted in the results, the stability of a solution algorithm, the available computational power, and so on. A Finite Element program takes the elements you have defined, lists the equations for each unknown value, puts them together as a matrix equation, then solves all these for the values of the unknown parameters. The equilibrium equation is of the form

[K ]{u} = { f } Since it’s analogous to the equations of spring-deflection, K is often called the Stiffness Matrix, u is called the deformation vector, and f is called the load vector. K is a square matrix, with one row (and column) for each 15

The 6 components are the translations along the 3 axes, and rotations about the 3 axes 16 A high stress means a high strain, from Hooke’s Law. Strain is the first derivative of deformation. Hence a high stress area is one where the deformation has a high derivative. And this, of course, means the rate-of-change of deformation is high in areas of high stress. 26

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Numerical Analysis – An Introduction

unknown variable in the problem-definition. If, for instance, you have used 100 nodes in your model, and each node has 6 unknowns17, your stiffness matrix would be 600 x 600. u and f are each column-matrices. In our example, each has 1 column and 600 rows. A computer is required because of the large number of calculations needed to analyze a part or assembly. It is not uncommon for a model to have more than 1,00,000 unknowns (called degrees of freedom). The power and low cost of modern computers has made Finite Element Analysis available to many disciplines and companies.

What are Finite Difference Methods? The Finite Element method is applicable to spatial-variations – that is, it can be used to calculate the variation of our quantities of interest over space. What if the quantities vary with time too? Such problems are called dynamic, and require transient analysis as opposed to static or steady-state analysis. For a problem in dynamics, the matrix equation above turns out to be

[M ]{u&&} + [C ]{u&} + [K ]{u} = { f } For transient problems, the Finite Difference method is usually used. In this method, derivatives are represented as differentials. For instance, the equation

u& = v =

du dt

is approximated by the familiar difference equation

v=

ut + ∆t − ut ∆t

While the approach is logical and simple, there are some subtleties to this. In a transient analysis, we must know the initial conditions. In this example, then, we must know ut and vt. From this, we can use the difference equation to calculate 17

The 6 components of deformation are the translations along 3 axes and the rotations about the 3 axes 27

Numerical Analysis – An Introduction

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ut + ∆t = vt • ∆t + ut Since we have ut and ut+∆t, can we estimate vt+∆t? If we can, we can apply the equation above to estimate ut+∆t. And by stepping forward in time, we can calculate the solution at any required instant of time. But estimating the value of vt+∆t is ambiguous. As shown in the figure, it is not clear to us whether the tangent (which is what v is) that we can calculate using the equation

u t + ∆t − u t ∆t

is more correct at time = t, or time = t+∆t or somewhere in between. Clearly, unless the time variation is linear, our calculated derivative is likely to be wrong at any point. Which should we choose? Without going into the detail, we will simply note that the choice leads to different finite difference methods – the backward difference method, the forward difference method, the central difference method, and so on.

&& . Similar logic is applied to the calculation of the acceleration, u

Important Terms As with any technical subject, Numerical Analysis has a wide range of terms that have very specific meanings given the context. Here, we’ll review those that are particularly relevant to our task.

Elements An element is a shape for which the Finite Element program can write out the equations relating the unknown and known quantities. An element is defined by its nodes – the unknowns at each node are called the degrees of freedom. Shapes that are accepted in most finite element programs are triangles, quadrilaterals, lines, tetrahedra, pentahedra and hexahedra. The sizes of and the number of elements usually have a bearing on the accuracy of the solution. As problems become more complex (advancing in complexity from linear-statics to nonlinear-dynamics), the requirements on shapes and sizes of elements become increasingly stringent. These 28

CAE for Simulation of Metal Forming

Numerical Analysis – An Introduction

requirements are often referred to as mesh-specifications, and these are usually strongly analysis-program dependent. In most analyses, the more the number of elements, the better the results. However, the computer time and disk-space required to solve the equations also goes up. Most analysts have to settle for a quality of results that they can afford, given the available computer resources.

Element Types Choosing the element type is an important part of any Finite Element analysis. Elements are categorized based on their shape or topology, the number of nodes needed to define them, and the mechanics or behavior they represent. Element types are usually solver dependent – they vary based on the solver used. The elements listed below are specific to OptiStruct, but are available in almost every commercially available analysis package. Categorization based on Mechanics Beams and Bars (or rods or trusses) are represented by one-dimensional elements – lines or curves – but can lie in 3D space. Plain Strain, Plane Stress and Axi-symmetric elements are two-dimensional shapes that can be used only if the entire model lies in one plane only. Plates and Shells represent surfaces that are two-dimensional in the sense that they have no volume, but lie in 3D space. Solid Elements represent volumes. Categorization based on Topology Standard 2D Elements (plane strain, plane stress, axi-symmetric, plate and shell) are either triangular or quadrilateral. Standard 3D elements are either tetrahedral, pentahedral, or hexahedral. A pyramid with a rectangular base is a pentahedron, as is a wedge. However the two are different element types: the pyramid has 5 nodes while the wedge has 6. Not all solvers support pentahedral elements, and some support only one of the two pentahedra. In most stress-analysis problems, quadrilateral and hexahedral elements are preferred over triangular and tetrahedral elements. For reasons that you can find in the references listed at the end of this volume, they give much better results: more accurate and less CPU intensive.

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Numerical Analysis – An Introduction

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1D elements are all (topologically) curves – either straight lines or arcs, depending on the number of nodes. Typical applications are as beams, bars, rods, pipes, springs, cold- or hot-runners, and axi-symmetric shells. Categorization based on Order The variation of the unknown quantity between nodes is assumed (by the analysis code) to be linear, or quadratic, or cubic, etc. Linear and parabolic elements are the most common. Linear elements have two nodes along each edge, while parabolic elements have three nodes along each edge. Further refinements do exist – for instance, parabolic quadrilateral elements can have either 8 or 9 nodes.

Geometry Preparation While it is possible to build a model directly using elements and nodes, this is not often done today. The geometry that defines the area to be analyzed (also called the “domain”) is usually created first using a CAD program, and elements are created to encompass that boundary or represent the volume. CAD designers create models for manufacture. As many details are included as possible. For a numerical analysis, we often choose to ignore aspects that we think will not significantly affect the solution. For instance, a single hole of 1 mm radius in a plate that is 2 meters wide can probably be ignored safely when calculating the deformation of the plate. Therefore the first task that most analysts are faced with is that of preparing the geometry for analysis. This involves tasks like removal of features, extraction of mid-surfaces, extrapolation of surfaces, etc. Further, the CAD world has an abundance of data exchange formats, since most CAD applications use proprietary data storage formats. A transfer of data from the CAD package to the FE preprocessor sometimes results in a loss of accuracy – gaps are introduced during the import process, for example. Also, CAD assembly models are sometimes made up of parts that were created in different CAD applications. Therefore a cleaning-up of the geometry is often required. This involves filling gaps, eliminating small edges or surfaces that will mislead the automatic-mesh-generation routines, eliminating dangling faces, and so on.

30

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Numerical Analysis – An Introduction

Mesh Creation Once the geometry is more or less ready for discretization, you then start to subdivide the geometry into elements or grid points. The collection of elements is usually referred to as a mesh. Meshes that consist of triangular or quadrilateral elements can often be generated automatically, while tetrahedral or hexahedral meshes usually require considerable manual intervention.

Mesh Editing Once a mesh has been created, the analyst checks if it meets the specifications – several measures of quality are checked, depending on the analysis requirements. Usually, some editing of the mesh is required. Depending on the complexity of the mesh, this can be done either semiautomatically or manually.

Preparing for Analysis Once the mesh is ready, additional data is specified – the properties of the materials used, the thickness or cross-sectional properties of shell or beam elements, the conditions on the boundaries (restraints, loads or excitations), initial conditions, data for the specific solution algorithm to be employed, kind of output required for text and graphics records, and so on. Once this is done, the data is turned over to the solution program for the next phase – solving. Data is often written out in the form of a text file, which is referred to as a deck. Each line of text in the deck is commonly referred to as a card. A card image is the format followed by the analysis program to interpret the text on the line. The procedure of building the Finite Element Model is sometimes referred to as FEM – short for Finite Element Modeling. Some books, however, use FEM to refer to the Finite Element Method.

Solving The model created in the earlier steps is now taken up for solution – the computer program reads the data, calculates matrix entries, solves the matrix equations and writes data out for interpretation.

31

Numerical Analysis – An Introduction

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This task is CPU-intensive, and is often called processing18. Most of the time, very little interaction from the user is required. In some cases, the analyst periodically monitors results to check that they are indeed on the right track. If the solution seems to be evolving in an unexpected direction, the analyst can stop the solver and modify the model, thereby saving valuable time.

Post-Processing After the program has evaluated the results, the analyst examines and interprets the data – looking for errors or improvements in design. As with pre-processing, this calls for substantial interaction from the analyst.

Guidelines on Element Choice Learning which element to choose is a little like learning driving. Guidelines exist, but can’t be applied blindly. You need to adapt them to specific situations. In the specific context of sheet-metal, we most often use shell or plate elements. In other words, our finite element modeling task is much simpler than the problem the general finite element model has to contend with.

Summing Up This last aspect is comforting, since model preparation usually takes up to 80% of many analysis tasks. Unfortunately for us, there are no free lunches: our challenge lies in the complexity of the solution. Remember that the simulation of sheet metal forming is not only a transient problem, it involves all three types of non-linearities – material, geometric and boundary. In the next chapter we’ll look at the strictures imposed on us by methods used by today’s analysis techniques, and how to deal with them effectively.

I don't think knowledge should be an obstacle to understanding. Maurice Biot

18

Hence the term pre-processing for the preceding steps, and post-processing for the subsequent steps. 32

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Finite Element Methods And Forming

Finite Element Methods and Forming Forming is a complex process, and the Finite Element method is often difficult to apply correctly. It’s logical, then, to conclude that the application of finite element methods to sheet metal forming will be even more complicated. Somewhat surprisingly, this is not the case. First, we have seen that a relatively small subset of the forming process parameters is adequate – this simplifies the first part. Next, the finite element method’s strength comes from its generality. It is applicable to a wide range of problems. Our focus, however, is very narrow – this helps cut out a lot of the complexity in the second part of the package. If even this reduction in complexity is not enough motivation, a review of the historical methods of design brings home the fact that CAE is indispensable!

A Retrospective Since metal forming is a lot older than computers or the Finite Element method, it’s logical to ask how designers managed before the advent of numerical simulation. That’s a little like asking how people handled transportation before the advent of the automobile: they managed, but it wasn’t elegant and it wasn’t efficient. Arguments between designers and engineers were all too frequent. “The

engineers may say the design is too difficult to execute; it's going to add weight or cost. They ask if they can move something an inch.” said automotive legend Bob Lutz in an interview19, “We say, No, the whole vehicle concept depends on the integrity of the design. Try to work with it, without watering it down." Die design was based on heuristics to estimate the die-face. This was followed by tryout, which meant the die and punch had to be manufactured and experimented with. The experimentation almost always led to considerable rework. Worse, the time taken to arrive at an acceptable design and suitable process parameters could rarely be forecast. 19

See the Corporate Design Foundation - http://www.cdf.org/issue_journal/6.html 33

Finite Element Methods And Forming

CAE for Simulation of Metal Forming

Estimation of the blank shape and size was another source of concern. In the first place, procedures to estimate the blank size were reliable only for single-stage draws. Further, such estimates were less accurate than desired (remember that wasted material adds to material cost) since graphical methods were used in the main. These methods are roughly similar to the development-of-surfaces methods covered in basic engineering drawing courses. They take into account the shape of the object, but do not allow for the flow of the material. This explains why these methods are not suitable for deep-drawing: as the flow of material increases, the method’s accuracy falls. Tool and Die making was, in the good old days, largely an art. Simulation has helped turn it into a science. The pressure exerted by consumer demand has helped drive the push towards more reliable and accurate forms of design. The changes in the shape of cars is an excellent example – in the interview cited above, Bob Lutz explains

“In the teens, cars looked like horseless carriages. In the late '20s and '30s, they became very boxy, and in the mid-'30s, they became boxes with rounded corners. Toward the end of the '30s, streamlining came in. In the '50s, we got into the "pontoon" shape where the fenders disappeared. Then we moved more and more toward pure aerodynamic shapes.” The conclusion is clear: pre-CAE methods of tool-design left a lot to be desired. But history is not all bunk. Two methods that tool designers have long relied on are instructive: circle-grid analysis and the Forming Limit Diagram20 (FLD). Circle-grid analysis involves electrochemically etching small circles onto the surface of the blank. After the tryout, the deformation of the circles is examined. Since a deformed circle is an ellipse, the direction of the major and minor axes of the resulting ellipses indicates the direction of maximum and minimum deformation. Further, the percentage stretch can be measured, which in turn indicates the engineering strain.

20

34

Also called the Keeler-Goodwin diagram.

CAE for Simulation of Metal Forming

Finite Element Methods And Forming

A high stretch of the circle indicates forming problems, but we can do even better than this. Each material has a particular failure-strain ratio under a given set of process parameters – the limit depends mainly on the sheet thickness, the strain-hardening exponent, and so on. That is, if the ratio of major and minor strains exceeds this value – the forming limit - the metal will tear. To use this measure of failure, we first plot the forming limit curve on a graph, with the minor-strain on the x-axis and the major-strain on the yaxis. Now using the values measured from the circle-grid analysis, we check whether the various points on the blank are under or over the forming limit curve. If all circles are under the FLD, the forming process is safe. Note that this method does not remove the need to tryout. Instead, it improves the utility of the tryout by providing a quantitative measure of the results of the tryout. Remember that the FLC itself has to be determined experimentally. If the specimen has local defects (tearing, thinning, etc.), the FLC is obtained by measuring the major and minor strains in areas that have defects and neighboring areas that are defect free. This boundary is plotted as a solid line on the FLD.

The Tool Designer and The Analyst Now advances in computing capabilities have been faster than advances in basic mechanics. Accordingly, simulation techniques today tend to use the FLD to estimate formability: the mechanics is the same, but the tryout can be done numerically. Instead of physically building and testing under various combinations of process parameters, we run the simulations on the computer. What this means is that the analyst today cannot dispense with the tooldesigner. The tool-design experience and insight guides the combinations of parameters to simulate. In the absence of such guidance, the analyst is faced with literally infinite combinations! Optimization techniques can help address this issue, but these are beyond the scope of our discussion21. One of the main reasons for this dependence on tool-design experience is that metal-forming is very much a manufacturing process. Industry practices and local conditions must be accounted for. There is little use in specifying a process that is not achievable by the available press-shop! 21

See CAE and Design Optimization - Advanced 35

Finite Element Methods And Forming

CAE for Simulation of Metal Forming

Consider, for example, the choice of the addendum. As shown in the figure (the exploded view is shown on the right), this is the region between the undeformed blank and the finished component – it’s trimmed off after the forming is complete.

The product designer specifies the final component, which is what you get after trimming. Assuming the blank is a flat sheet (as it will be for the first stage of any drawing operation), what should the shape of the addendum be? Obviously this is a decision related to the die-face itself. One way to construct the addendum is to use blends, fillets and other CAD operations to fill the area between the trim-line and the flat sheet. However, the addendum design itself can critically impact the flow of material. Proper addendum design ensures uniform panel stretch, since it affects the balance of material movement. On a related note, consider the design of the blank-holder. If a material does not flow evenly, it will either wrinkle (because the material is flowing in too fast) or it will thin, and perhaps tear (because it isn’t flowing in fast enough). The blank holder pressure can be adjusted to ensure looser or tighter gripping of the component. But what if the component is not uniform? In the first figure on the left, since the section A is the same as section B, the effect of blank holder pressure is the same on both. But in the second figure, the two sections are unequal. If the same blank holder force is used, side A will wrinkle or the other side will tear. Controlling blank holder pressure locally is not always possible. To deal with the situation shown, the designer has to slow down the flow of material on one side – this is done using a draw bead. Just as a speed-bump on a road forces vehicles to slow down, the bead retards flow of material in the blank. The designer has to specify the location of the bead, its radius and height,

36

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Finite Element Methods And Forming

after which the analyst can check the performance of the die in a given press.

The Product Designer and The Analyst The discussion above is relevant to the tool-designer, but what of the product designer? If analysis shows that the part as-designed is hard to manufacture, chances are the part design itself may need to be modified. Early in the product life cycle, many parameters are still open to change. As the design cycle progresses, it becomes harder and harder to implement changes, since other disciplines are involved. An early-warning system that can help identify extremely-hard-tomanufacture products will certainly be useful. Several CAD packages offer some checks for this – one such check is the search for an undercut, the presence of which can complicate the die-design considerably. If the partdesigner can avoid an undercut, the subsequent tool-design becomes easier. Several such guidelines are available for the product designer: avoid unequal draw-wall depths, avoid drastic shape changes, minimize the depth of the draw, design for trimming in one direction, provide reliefs at the flanges, and so on. Most of these guidelines are qualitative, not quantitative. The tool-designer must work with the actual values, while the product designer only seeks to follow a general approach. Applying the same logic, the tool-designer needs a quantitative measure of the formability, while the product designer can benefit from a qualitative measure, provided it is quick and convenient. Using Finite Element models to carry out a non-linear finite element analysis allows a detailed simulation of the draw process. This approach is called incremental analysis, since the analysis program steps-forward in small increments of time, and is ideal for the tool-designer. An inverse-method, similar to the manual blank-size calculation method is better suited for the product designer. Not only is it extremely fast, it also provides order-of-magnitude estimates of the various parameters of interest – the blank size and shape, the FLD and so on. As with the manualcalculation method, the inverse method is reasonably accurate for singlestage draws, but loses accuracy and relevance rapidly as the number of stages rises. 37

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Incremental Analysis - Numerical Aspects The forming process is quite rapid, often finishing in a few milliseconds22. The duration, in fact, is of the same order as the duration for which car crash-tests are conducted. It’s not surprising, then, that the numerical techniques used for the simulation of sheet-metal forming have drawn heavily on the methods perfected by vehicle-safety analysis software. Events of such a short duration are inherently hard to simulate – both the numerical methods and the theories of mechanics are not as general as desired. As a result, several FE modeling decisions are governed by a combination of theory and practice. In this section, we will review the modeling approaches used specifically for the simulation of sheet-metal forming. These are not applicable to FE analysis in more general circumstances. This has one very useful side-effect: the availability of these guidelines makes it easier for the analyst to simulate forming even without an in-depth understanding of the mechanics and the mathematics! This is a remarkably useful aspect. Metal-forming is one of the most challenging problems in solid mechanics. It involves all three types of nonlinearity (geometric by virtue of the large deformations and strains involved, material by virtue of the plastic deformation, and boundary since contact is involved). Since the guidelines address the most critical aspect of simulation – modeling – even this challenging task can be carried out with a high degree of confidence.

Choice of Elements Finite element modeling involves two important choices at the meshpreparation stage. The first is the type of elements to use, and the second is the size of the elements. Since the blank is a sheet, shell or plate elements are appropriate. Automatic mesh-generation for shell elements is quite advanced, which this makes this stage quite easy. The punch and die must also be modeled, of course. But our interest lies in the force they exert on the blank, not in the deformation they themselves undergo. Accordingly, we can model the punch or die using shells too and 22

The velocity of the ram of a mechanical press is of the order of meters / second, while the draw depth is of the order of millimeters or centimeters. 38

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Finite Element Methods And Forming

then tell the analysis program that they are to be treated as infinitely rigid elements. This avoids one of the more time consuming aspects of general FE modeling – the construction of hexahedral elements. In either case one guideline is to ensure that there are no fewer than 6 elements for each quadrant of a circular arc.

Explicit vs. Implicit Time-integration methods are categorized as implicit or explicit methods. Without going into the mathematics, we will simply state the relevant characteristics: •

it is faster to calculate the solution for each step using an explicit method

•

explicit methods are conditionally stable – that is, the time limit must not exceed a specific value. As a result, explicit methods require more time steps than implicit methods for the simulation to reach the same elapsed-time.

We know that the forming itself is fast, of the order of milliseconds. Accordingly, we invariably use an explicit time integration method to simulate this. Springback and gravity-analysis are slower – so we use an implicit method for these parts of the simulation.

Time Step Size: The CFL Criterion But what is the maximum permissible time-step size for an explicit integration method? The step-size is limited by the Courant-Frederick-Levy criterion. This imposes a theoretical limit on the maximum time-step, based on the time it takes for a stress-wave to propagate across the element. For a shell element, the maximum time step time is given by

∆te =

Ls c

39

Finite Element Methods And Forming

CAE for Simulation of Metal Forming

where c is the speed of sound in the material and Ls is the characteristic length of the element23. We can calculate c for any material using the Elasticity Modulus E, density ρ and Poisson’s Ration ν and the formula

c=

E ρ (1 − υ 2 )

For a given mesh, the time step is limited by the smallest element in the mesh. In other words, the finer the mesh, the smaller the time step. A finer mesh size will give more accurate results, but the time for analysis will go up not just because the number of elements has increased but because the number of steps will also rise – because the time step size reduces as the element size reduces. This doesn’t seem very helpful, in itself, particularly when we remember that forming involves large deformation. That is, the element shape itself will change considerably as the analysis progresses. One option is to start with elements that are small enough that the deformation will not change the element’s shape appreciably, but this is hard to decide before carrying out the analysis. And the analysis cannot be carried out until the elements are chosen. The answer to this impasse lies in the use of adaptive refinement.

Adaptive Refinement One remarkable facet of the finite element method is that the error in the analysis can be estimated from the approximate solution itself. Programmers can use this characteristic to adapt the mesh based on the estimated error. This is of enormous help, since it frees the analyst from the burden of choosing the “right” element size. You can specify a reasonable size and let the program itself correct the mesh as the analysis proceeds. There are several different ways in which the mesh can adapt – the elements can be reduced in size (h-adaptive), the order of interpolation can 23

The characteristic length can be calculated in several ways, as explained in the online documentation. One option is to use the altitude of the element as the characteristic length.

40

CAE for Simulation of Metal Forming

Finite Element Methods And Forming

rise (p-adaptive), nodes can be relocated (r-adaptive), or a combination of these (hp-adaptive, for instance). If the program uses adaptive refinement, it must also check and change the time-step size as the analysis proceeds, of course, using the CFL criterion as a limit. At each time step, the program checks the maximum time step permissible, as decided by the smallest element in the mesh. The smallest element, then, works as a bottleneck – it limits the time step size. What if there are only a few elements that are so small? Mass-scaling provides a way out.

Energy Balance Non-linear analysis, particularly when it involves friction (which is a nonconservative force) is more of an engineering tool than a numerical science. In a precise calculation, energy is always conserved. In many explicit analyses, we tolerate some imbalance in energy in return for a reduced analysis time. Depending on the problem, some level of loss of energy from the system is usually tolerated. The actual tolerable level depends on how much time and effort you can afford, but 10% is often deemed acceptable.

Mass Scaling In a similar vein, we are often willing to artificially boost the mass of elements in order to increase the time step size. The justification for using it lies in the fact that we may be unwilling to let a small section of the model penalize the rest. Accordingly, we may tell the program to increase the density of elements by a particular factor, provided the mass of the whole model does not rise by more than (for instance) 10%. Mass scaling helps since the mass of the element appears in the numerator of the CFL criterion, so an increase in mass increases the time step. Of course, this increase in mass is physically meaningless, and does degrade the accuracy of the analysis.

Contact As the punch approaches the die, the program must check whether or not contact has taken place. It must then track the deformation of the blank and the movement of the punch, using the die face as the limit. Depending on the lubricant used, the coefficient of friction determines the friction forces and consequent energy loss. Implementing this search-and-solve process is computationally expensive, and difficult. 41

Finite Element Methods And Forming

CAE for Simulation of Metal Forming

Contact algorithms today are much more robust than they were even a few years ago, and by and large are fairly reliable.

Summary Simulation of forming requires powerful computing resources, a working knowledge of the finite element method, access to process and material data, and an excellent understanding of the manufacturing processes themselves. It is challenging, there’s no doubt about that, but is remarkably accurate when applied right. With these techniques, verification of designs for forming, stamping, drawing and deep-drawing can be modeled reliably and accurately, taking into account binderwrap and gravity-deformation. Further, springback can be calculated so that compensation can be provided at the design stage if necessary. Operations that involve fracture (like trimming and piercing) cannot be simulated in themselves, but can be included in the simulation flow. For instance, we can predict how holes will change shape as the metal is formed, and whether the component will change shape after trimming as residual stresses are released. Implicit in all this, of course, is the fact that the simulation is only as good as the data: if the material data is unreliable or if the process parameters are incorrectly specified, it is foolish to expect the results to be realistic! Several other aspects like design of the die face, optimization of the die, and estimation of the affect of residual stresses on the strength of the part are also possible using current simulation techniques, but are beyond the scope of this book.

If the facts don't fit the theory, change the facts. Albert Einstein

42

CAE for Simulation of Metal Forming

Putting It All Together - HyperForm

Putting It All Together: HyperForm After all the discussion of how careful we must be to get the process parameters right, to get the material data right, and to setup the numerical analysis right, HyperForm can seem like an anticlimax. It is entirely possible for a beginner to setup, run and present the results of an analysis in a fraction of the time it takes to conduct a more general finite element simulation. This is not because our earlier discussions were off track: it is indeed true that simulation of metal-forming is indeed difficult to conduct and it’s all too easy to generate wrong results. It is HyperForm’s modeling approach, coupled with the relatively focused demands of the task, that make it so easy to get going. In this chapter we •

summarize the tasks HyperForm can be used for

•

review the data required for complete definition of the problem

•

how to review results

Process-Centric Modeling Many design-and-modeling tools are hard to learn because they provide a combination of depth and breadth. HyperMesh and HyperView, for instance, can be (and are!) used for an extremely wide variety of very demanding applications. Our goal is much less general: we are restricting our attention to one specific type of product (sheet-metal) and one specific process (forming). Accordingly, we do not need a modeling application that can be used for general requirements; we need an application that talks the language of metal forming. Further, we expect the application to be used either by tool designers or by product designers. As we have seen, there are some common approaches and some differences between the approaches that tool and product designers take. HyperForm addresses exactly this process: starting from the designed product, it provides options for the product-designer and the tool-designer. And it is this aspect, this tailor-made application for the specific product and process, that makes it so easy to setup and perform the analysis. 43

Putting It All Together - HyperForm

CAE for Simulation of Metal Forming

But don’t let this ease of use lull you into feeling secure. While it’s easy to use HyperForm, and results can be remarkable accurate, it is also extremely easy to generate results that are off-track. After getting comfortable with HyperForm, in fact, it’s a good idea to go back and review the earlier chapters to recall the areas that are absolutely critical! An extract from a recent article24 serves well to drive home the limitations and strengths of simulation, and to stress the importance of design knowhow:

Initial claims for forming simulation were probably exaggerated: (the) reality is that running simulation will generally add time to the development program – the time and cost savings result from avoiding problems later which can throw the intended program off track. It is clear that applying simulation effectively has the potential to avoid major problems and save huge amounts of time and money. There is (an) issue to resolve regarding who is responsible for the die design. If the (product designers) uses Die Face Engineering to create a full tooling model they can examine formability of their own designs. However the simulation results will only be valid for this die face – if the product is then sent to an external tooling engineer there is no guarantee that the same process will be adopted. On the other hand, is the (product designers) issue their tooling process to the tooling engineer they will potentially be taking responsibility for the tool design, with major implications if the process does not, after all, make an acceptable part. Remember this difference in roles – tool designer and product designer since it is central to the approach HyperForm takes.

Forming Simulation – What and How The product designer’s goals are to check whether the tool is formable. This is quite a hard task, since early in the design stage the material itself may not have been frozen. Further, a design that is hard to manufacture in a single stage may be eminently manufacturable if multiple stages can be used. So the product-designer’s analysis is not so much to identify the process parameters that are best suited for a design proposal: instead, the 24

Dutton, T., Review of Sheet Metal Forming and Simulation – Progress to Date, Future Developments, 8th International LS-Dyna User’s Conference

44

CAE for Simulation of Metal Forming

Putting It All Together - HyperForm

product designer’s requirements will be met if the simulation shows that the product is easy to manufacture in a single stage. Such a product, it is reasonable to expect, will pose few problems for the tool designer later in the design cycle. Tool designers, of course, need to run what-if-analyses to check the various alternatives available to them. This analysis must be accurate, even if demanding. But there’s another problem tool-designers have to deal with that’s less technically demanding but no less important for the impact it has on cost. Remember that the tool designer is often requested to commit to a cost-ofmanufacture for a given product. That is, the tool designer not only has to design the tool, but also has to estimate the cost-per-manufactured-part, and agree to supply the parts at that price if the order is awarded. The tool designer cannot be sure that the order will be won, so cannot afford to invest heavily in simulation. The time for that will come after the order has been won. At the same time, the tool designer must respond rapidly, since the enquiring customer is shopping for a reliable and reasonable price. How can the tool designer deal with this? Remember that there are two costs: the cost of design and the cost of manufacture. The former is a one-time activity. The latter is a running cost. It is directly proportional to the number of parts produced, since costs like labor and raw-material cost are incurred for every part that’s produced. Errors in the estimation of the raw material required, that is the blank, can be expensive indeed! The need of the hour, obviously, is to get an estimate on the size of the blank. Going one step further, the blank itself is cut from a coil or strip of sheet metal. The problem is to choose an arrangement of blanks on a given width of coil so as to minimize wasted material. The two products shown clearly show that one necessitates a higher wastage than the other. It makes sense, then, to introduce discuss HyperForm separately for each of the three tasks: one-step inverse simulation, incremental analysis, and blank calculation. In any case, HyperForm starts where CAD leaves off – data from a CAD package is essential to get started with simulation. The product itself is 45

Putting It All Together - HyperForm

CAE for Simulation of Metal Forming

essential, and depending on the role played by the analyst, additional data may be required too, as we will see.

One-Step Simulation The only data we require is the CAD model of the product itself. If the component has holes, we can investigate both alternatives – one where the holes are made prior to forming, and the other where the holes are made after forming. To simulate the latter, we just fill the holes up before carrying out the analyses. The component is first checked for undercuts – that is, whether it can be ejected properly from the die. To check this, we need to set the draw direction (the axis of relative travel of the punch and die). The convention in HyperForm is that the tool travels along the “Z” axis. If an undercut is detected, in some cases it can be fixed by altering the orientation of the product relative to the draw direction. This is called tipping. Once the product has been oriented correctly, we generate a finite element mesh. The elements only need to be fine enough to satisfy the requirements of the “inverse” method (described earlier) that’s used to estimate the blank shape. Automatic mesh generation is usually adequate. Then we specify the material used and the thickness of the sheet. This can be selected from a library of data that comes with HyperForm or, if accurate data is available, can be entered explicitly. That’s it – the model is ready for analysis. Given this data, HyperForm calculates the blank shape and the FLD diagram. The latter serves to check whether the product is likely to wrinkle, tear, or exceed the maximum permissible variation in thickness. The approach above is reliable for parts that can be formed using a single stage, and that do not require post-forming trimming. If the part requires trimming, the flange that is to be trimmed off can be added to the mesh before simulation, of course. This method requires a little more caution, since the size of the flange can affect the formability. It does offer the advantage that the impact of drawbeads can be investigated: you can run the simulation with and without drawbeads to determine whether t his impacts the results.

46

CAE for Simulation of Metal Forming

Putting It All Together - HyperForm

Since the analysis is not very detailed, the normal approach is to use analytical drawbeads. That is, instead of actually modeling the bead itself, a line or curve that represents the center of the draw bead is specified, and the analysis carried out.

Blank-size estimation and Nesting Once the blank size has been calculated, how do you calculate how to lay it out on a specified strip? HyperNest, a part of HyperForm, is the module you would use for this. Our focus in this book is on the simulation of formability, so we will not discuss this here – look up the on-line documentation for details.

Incremental Analysis Setting up a problem for a more detailed analysis – using the incremental solver instead of the one-step solver – is similar, except that there are a few more parts to be modeled, and a few more process parameters. Once you understand the principle, the same approach can be followed regardless of how complex the forming sequence is. So we’ll first segregate the processes, then look at the steps. •

Gravity analysis, binder-wrap analysis and springback analysis are all similar in that they can be treated as static events. That is, the time-variation of deformation or forces is insignificant: all we want to calculate is the shape of the product and the stressdistribution when it reaches steady-state. Accordingly, we use an implicit time integration scheme for these steps. Since we do not expect large stress variations in these steps, we can also use a relatively coarse mesh for the analyses.

•

Actual forming – when the blank undergoes plastic deformation under the effect of the punch and die – is very definitely a transient analysis. Here, we use an explicit time integration scheme given the short duration of the calculations. Since the component deforms quite dramatically, we must either start with a mesh that’s fine enough to capture the worst state, or use adaptive refinement. While a fine mesh is undoubtedly better, practical considerations mean that adaptive refinement is normally used.

•

The last step that is important for our simulation is trimming. This is an operation that involves metal fracture, not flow, and 47

Putting It All Together - HyperForm

CAE for Simulation of Metal Forming

we have already said that this is hard for us to simulate since the mechanics is poorly understood. But trimming releases residual stresses, so if we are to carry out springback analysis, we have to include trimming if the analysis is to be realistic. The approach we use is a workable compromise. We don’t simulate the cutting process itself. Instead, before springback analysis we remove the elements that represent the regions that are trimmed off. Since the remaining element free boundaries are stress free, this allows us to allow for the release of residual stresses. From a logical perspective, we can view each of these 3 steps as independent analyses. This allows us to build complex processes by simply performing them in the sequence that a particular process may require, regardless of how many stages are involved, how many times the component is trimmed, and so on. And this is exactly what HyperForm does, except that it takes care of the book-keeping and administrative work involved in transferring data from one step to the other. Unlike the one-step analysis, however, incremental analysis can be exceedingly computationally intensive. Analysis times of several hours are not uncommon!

Data Required HyperForm makes it easy for us to setup the analysis, but the reliability of the results depends strongly on the quality of the data. Data required is of 4 principal types: •

Material properties – Elasticity Modulus, Poisson’s Ratio, Tensile Strength, n, r, Density

•

Geometry of the blank, punch and die

•

Process specifications – lubrication, blank holding force, tool kinematics (velocity) and drawbeads

Material data is best obtained either from the steel-suppliers, or from actual tests. The geometry of the blank, punch and die are best obtained as CAD data from the die designer – remember that the addendum, for example, can significantly affect the performance. It’s up to the analyst to ensure that the mesh is fine enough, as discussed earlier. 48

CAE for Simulation of Metal Forming

Putting It All Together - HyperForm

Experience has taught us that some process specifications allow us a little more liberty. The friction coefficient, for example, can rarely be estimated reliably, so order-of-magnitude assumptions from previous successful simulations are usually adequate. The punch velocity is almost always scaled up to reduce simulation time. Many presses do not allow for accurate control of the blankholding force which means we cannot estimate the actual forces reliably. So even if we know that the force is not uniform across the blank, we often assume it is.

Summary of Steps Involved For one-step analysis: •

import the CAD model of the final component

•

fill holes if they are to be created after the forming

•

generate a shell mesh of the component

•

orient the component so the draw direction is along the z-axis

•

check for undercuts and tip the component if necessary

•

specify the material properties – indicative values are adequate

•

specify the thickness of the component

•

identify areas that are to be trimmed, if any, so that the solver can take these into account when estimating the blank size

•

specify analytical drawbeads, if any

•

run the analysis

•

inspect the results – thinning, formability and press tonnage. Thinning percentage is best viewed as a contour, while formability is best viewed as the FLD

For incremental analysis:

49

Putting It All Together - HyperForm

CAE for Simulation of Metal Forming

•

import the CAD model of the punch and die, if available, else derive it from the component model25

•

orient the components so the draw direction is along the z-axis

•

mesh the blank, punch, die, binder (and ejector, if present) with shell elements. The mesh should be created at the mid-surface of the blank, and the clearance between the punch and die should be captured accurately. Drawbeads are best modeled explicitly, instead of using analytical definitions.

•

specify material properties for the blank – this should be as accurate as possible

•

specify material properties for the tool – punch, die, binder and ejector. Since we treat these as rigid (undeformable components) the values are not critical

•

specify the tool motion by assigning the velocity and maximum travel to the punch

•

specify the blankholding force

•

use the multi-stage manager in case multiple steps (gravity, springback, multiple-stages, etc.0 are involved

•

run the analysis

•

inspect the results – thinning, wrinkling, tool motion and the FLD. Thinning is often viewed as an animated contour.

Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense Buddha

25

Remember that this is convenient, but not recommended since it means the analyst is making assumptions that are best left to the die designer 50

CAE for Simulation of Metal Forming

Advanced Topics

Advanced Topics The simulation of metal forming is a little like car-racing: extremely satisfying when it works, but it can easily go off the rails. Few of the items listed in this chapter are essential – they can be ignored unless you are faced with a problem that requires that little extra.

Commercial Terms Several steel alloys are designed specifically for their forming characteristics. Steel’s properties are strongly dependent on the phase-composition – martensite, bainite, austenite, pearlite, etc. Alloying elements affect the properties too, as has been long recognized. Micro-alloyed steels increase the hardness of the steel because of the presence of carbides of micro alloy elements such as Titanium and Vanadium. Phosphorous-alloyed steel also has increased hardness. Nitrogen and Carbon are used in Bake Hardened steels. Aluminum, Silicon or Manganese are added to molten steel (in the furnace, before it solidifies) to reduce the oxygen content. Called killed steels because the metal is less chemically active when cast, these have more uniform properties than rimmed steels. Rimmed steels, which usually have a carbon content below 0.15% (as against killed steels which have a content > 0.25%) are formed because incomplete deoxidation allows the formation of bottom and side rims that are purer than the rest of the ingot. Steels are further classified as •

HSLA – High Strength Low Alloy

•

HSS – High Strength Steel, with a yield strength from 210 to 550 MPa

•

UHSS – Ultra High Strength Steels, with a yield strength > 550 MPa

•

AHSS – Advanced High Strength Steel

•

DP Alloy – Dual Phase Alloy steels that contain mainly ferrite and martensite 51

Advanced Topics

CAE for Simulation of Metal Forming

•

TRIP Steel – Transformation Induced Plasticity Steels that are mainly austenite and martensite

•

DQ – Draw Quality steel

•

CQ – Commercial Quality steel

•

DDQ and EDDQ – Deep Draw Quality and Extra Deep Draw Quality steel

•

AKDQ – Aluminum Killed Draw Quality steel

•

CRDQ – Cold Rolled Draw Quality steel

•

IF – Intersitial Free steel

HSS, AHSS and UHSS are more formable, as evident from the low ratio of the yield strength to the ultimate strength.

Data Files – What Goes Where Since HyperForm can take care of the data management for multi-stage analyses, you’ll probably need to read this section only if you plan on manually setting up the different stages. The model you create using HyperForm is stored in a binary file with the extension “.hf”. If the one-step solver is used, no other files are involved or needed. The incremental solver, though, is “external” to HyperForm. This makes sense if you consider that since incremental analyses can take hours to run, in some cases it is more useful to submit the analysis to the solver and exit from HyperForm. In these cases, the data in the HypeForm file is written out to a plain-text file that’s sometimes called a “data deck” since each line in the text file is the equivalent of the computer cards that were used to submit data to the computer in the early days of computing26. The incremental solver in turn

26

52

See, for example, http://en.wikipedia.org/wiki/Unit_record_equipment

CAE for Simulation of Metal Forming

Advanced Topics

writes a set of files which you should load for post-processing – to view the results. .parm

HyperForm input deck.

.out

Model and run information.

.dat

Input data summary.

.err

Error file.

.res

Results files.

_thk.nas

NASTRAN deck with stamped thickness distribution.

opt.dat

Input deck for optimization runs

I didn't fail the test, I just found 100 ways to do it wrong. Benjamin Franklin

53

Glossary and References

CAE for Simulation of Metal Forming

Glossary And References

54

Bed

The main foundation and supporting structure upon which the operating parts of the machine are mounted and guided.

Bending

The shaping of sheet metal by straining the metal around a straight axis. A bending operation compresses the interior side of the bend and stretches the exterior side.

Binder Bounce

On initial contact, the blank holder can bounce. As a result, the material flows faster for this brief period – it’s not being held as designed. Faster flow can lead to wrinkles.

Binder

The upper and lower holding surfaces (part of the draw die) which press the metal-sheet against the draw ring to control metal flow.

Blank

A flat, precut metal shape ready for subsequent press operation. The piece of sheet metal, produced in cutting dies, that is to be subjected to further press operations. A blank may have a specific shape developed to facilitate forming or to eliminate a trimming operation subsequent to forming.

Blank Development

The process of determining the optimum size and shape of a blank for a specific part; the resultant flat pattern.

Blank Holder

Same as binder.

Blanking

A shearing operation that creates a hole in sheet metal by separating an interior section. The removed piece of metal is the desired section.

Bolster plate

A plate that is designed to hold in place the lower die shoe. The bolster plate is attached to the top surface of the press bed.

Clearance

The amount of space between the outer edge of the punch and the inner edge of the die cavity. A proper amount of clearance is necessary for an effective shearing operation.

Combination Die

A die that performs more than one operation (e.g. blanking and piercing) for each stroke of the press.

Compound Die

See Combination Die

Deep drawing

The drawing of deeply recessed parts from sheet material through plastic flow of the material when the depth of the recess equals or exceeds the minimum part width. A drawing operation where a part

CAE for Simulation of Metal Forming

Glossary and References

exceeds the minimum part width. A drawing operation where a part is produced from a blank by the action of a punch in which the sheet is pulled into a die cavity and the flange of the blank is compressed in the circumferential direction. The area directly under the punch remains undeformed.

Die

A complete tool consisting of a pair or combination of pairs of mating members for producing work in presses, including all supporting and actuating parts of the tool. The upper member or members are attached to the slide or slides of the press and the lower member is clamped or bolted to the bed or bolster with the die members being shaped to cut or form the material placed between them when the press makes a stroke. The main tool is typically attached to the lower portion of the die set. The die contains a recess that provides space for the shaping or shearing of sheet metal.

Die Holder

Another term used for the lower die shoe.

Die Retainer

A hardened steel block containing machined impressions or cavities that shape the metal as the punch descends from above. The die retainer also holds the die button.

Die Set

The collective assembly of upper and lower die shoes, guide pins and bushings, and punch and die retainers.

DQSK steel

Drawing Quality Special Killed Steel, a highly formable grade of mild steel usually aluminum deoxidized and sometimes referred to as DQAK (Drawing Quality Aluminum Killed).

Drawbead

A ridge constructed around a portion of a die cavity to control metal flow. A groove in the mating blank holder allows die closing.

Drawing

A sheet metal deformation process in which plastic flow results in a positive strain in one direction in the plane of the sheet surface and a negative strain at 90 degrees. The process of cold forming a flat precut metal blank into a hollow vessel without excessive wrinkling, thinning, or fracturing. For sheet metal, a forming operation that transforms a flat disc of stock into a hollow cup with an enclosed bottom. Drawing operations can also create boxes and more intricate shapes as well.

Elastic limit

The maximum stress to which a material may be subjected, and yet return to its original shape and dimensions on removal of the stress.

Elongation

The amount of permanent extension in a tensile test specimen.

55

Glossary and References

56

CAE for Simulation of Metal Forming

Engineering strain

The unit elongation given by the change in length divided by the original length. Preferably called nominal strain.

Engineering stress

The unit force obtained when the applied load is divided by the original cross-sectional area. Preferably called nominal stress.

Forming Limit Diagram (FLD)

An empirical curve showing the biaxial strain levels beyond which failure may occur in sheet metal forming. The strains are given in terms of major and minor strains measured from deformed circles, previously printed onto the undeformed sheet.

Guide Post

A hardened rod positioned in the lower die shoe that fits into a bushing in the upper die shoe to guide the punch during operation.

Guide Post Bushing

A hardened steel tube that slides over the guide post and directs the upper die shoe during operation.

Hardness

The ability of a material to resist permanent penetration by a much harder body.

High strength steel (HSS)

By Auto/Steel partnership definition, any sheet steel product whose initial yield strength is specified 30 KSI or higher. These include bake hardenable steels.

Lock beads

Draw beads designed to allow no metal flow.

Lower Die Shoe

The lower plate of a die set that supports the die retainer and die button.

Lubricant

Any substance interposed between two surfaces in relative motion for the purpose of reducing friction and/or wear between them. Any surface which has the specific property of reducing friction between two surfaces in contact.

Major strain

Largest principal strain in the sheet surface. Often measured from the major axis of the ellipse resulting from the deformation of a circular grid.

Metal clearance

Depending on the stock thickness being used to make the part in the die, it is the running clearance on the bottom of the press stroke between flange steels or male and female form steels.

Minor Strain

The principal strain in the sheet surface in the direction perpendicular to the major strain. Often measured from the minor axis of the ellipse resulting from deformation of a circular grid.

n value

The work-hardening exponent derived from the relationship between true stress and true strain. It is a measure of stretchability. Often called the work-strengthening exponent.

CAE for Simulation of Metal Forming

Glossary and References

called the work-strengthening exponent.

Necking

Localized thinning that occurs during sheet metal forming prior to fracture. The onset of localized necking is dependent upon the stress state which is affected by geometric factors.

Pilot

A long, slender punch with a rounded tip used to position the metal sheet by entering a previously formed hole. Pilots are longer so that they enter the sheet before other tools form the metal.

Plain-carbon Steel

A basic grade of steel, which contains less than 3 percent of elements other than iron and carbon.

Plastic strain ratio (r value)

A measure of the normal plastic anisotropy as defined by the ratio of the true width strain to the true thickness strain in a tensile test. The average plastic strain ratio ( r ) is determined from tensile samples taken in at least three directions from the sheet rolling direction, usually at 0, 45 and 90 degrees. It is a measure of deep drawability.

Press Brake

A type of press with an open frame and very wide bed. Press brakes are often used for bending operations, and they are typically manually operated.

Brake Press

See Press Brake

Progressive Die

A die containing a series of stations that perform one press operation after another in series. A progressive die gradually forms a part as it moves through the die, and the last operation separates the part.

Punch

The tool typically attached to the upper portion of the die set that shapes or penetrates the sheet metal.

Punch holder

Another term for the upper die shoe.

Punch press

A machine with a stationary base and an upper ram that moves along a vertical axis to shear, bend, or form sheet metal.

Punch retainer

The device used to mount the punch on the upper die shoe.

Punching

A shearing operation that creates an open hole in sheet metal by separating an interior section. The removed metal section is discarded scrap.

Ram

The main upper portion of the press that slides up and down within the press frame. The upper die shoe is attached to the ram.

57

Glossary and References

Slug

The discarded section of scrap produced by a punching operation.

Station

A position within a progressive die where a punch and die perform a single metalworking operation. Progressive dies consist of a series of stations.

Stripper

A plate designed to remove sheet metal stock from the punch as it pulls away from the die during the operation.

Stroke

The distance marked by the farthest ends of reciprocating vertical movement of the press ram.

Tensile strength

The maximum stress that a material is capable of withstanding without breaking under a gradually and uniformly applied load. The strength calculated at the maximum load, in a tensile test, by dividing the maximum load by the original cross-sectional area. The ultimate strength of a material, measured in pounds per square inch in tension on the original cross section tested, which, if exceeded, causes sectional deformation leading to ultimate rupture.

Thickness strain

Thickness strain is the change in thickness of the material due to forming. Thickness strain or metal thin-out can be measured using an ultrasonic thickness gauge. It is necessary to do some circle grid analysis to determine the location of the thickness strain on the forming limit diagram, but then this technique can be used as a quick non-destructive test. Since this variable can be most closely linked to breakage it will provide the primary comparison to setting the level of critical process variables.

Tool Steel

A type of steel designed for excellent wear resistance, toughness, and strength. Tool steels are typically variations of high-carbon steels.

Toughness

The ability of a metal to absorb energy without breaking or fracturing.

Upper Die Shoe

The upper plate of a die set that secures the punch retainer.

V-bending

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CAE for Simulation of Metal Forming

A bending operation performed by compressing the sheet metal between a V-shaped punch and die.

Wiping die

The tool used in an edge bending operation that provides the corner over which the extended portion of sheet metal is bent.

Work-hardening

An increase in hardness and strength caused by plastic deformation.

Yield strength

The stress at which a steel exhibits a specified deviation from the proportionality of stress to strain. Generally, the yield strength is the measure of the stress at which a steel sample will begin to

CAE for Simulation of Metal Forming

Glossary and References

measure of the stress at which a steel sample will begin to permanently deform under a tensile stress.

Yield stress

A stress at which a steel exhibits the first measurable permanent plastic deformation.

References Eary, D.F. & Reed, E.A. (1997). Techniques of Pressworking Sheet Metal: An Engineering Approach to Die Design Ostergaard, D.E. (2000). Advanced Diemaking http://www.autosteel.org From the American iron and Steel Institute – wealth of information about steel. http://www.metalformingmagazine.com From the American iron and Steel Institute – wealth of information about steel.

Other Resources www.altair-india.com/edu, which is periodically updated, contains case studies of actual usage. It also carries tips on software usage.

Sample Material Properties Be careful when using these properties. Some properties vary widely with alloying elements or processing parameters, so treat these as indicative. It’s probably safe to use them in exploratory design efforts, but not in designs that will be manufactured. For those, you should look for values from the material supplier.

Material

Grade

Yield Strength (MPa)

Tensile Strength (MPa)

n value

r value

HR

DQSK

234.42

330.95

0.20

1.1

HR

DQ

246.14

338.5

0.19

1.1

HR

CQ

268.2

386.1

0.19

NA

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Glossary and References

CAE for Simulation of Metal Forming

CR

EDDQ

137.9

303.34

0.26

1.9

CR

DQSK

182.7

310.2

0.23

1.8

CR

DQ

186.16

315.78

0.22

1.6

CR

CQ

208.22

324.05

0.20

1.3

Also remember to check the units in your model – they must be consistent! The recommended units for incremental analyses are:

60




Length

mm




Stress

MPa




Blankholder force

N




Drawbead force

N/mm




Density

mg/mm




Time

s




Velocity

mm/s