Finite Element simulations of the manufacturing of a sheet metal part

Transcription

1 Finite Element simulations of the manufacturing of a sheet metal part Mikael Schill

2 Finite Element simulations of the manufacturing of a sheet metal part Summary This Report presents a summary on how Simulation Based Design (SBD) using Finite Element (FE) simulations can be used by sheet part manufacturing industries. It includes a discussion on the possible benefits and also the challenges. Further, the tool design process is divided into four different stages and a description on which type of simulation tools that is suitable for each phase is done. The output from each simulation tool is presented as well as the required input. This Report was developed during the previous FRC+ project, implemented in the central Häme region between 1 February 2011 and 31 August Key funding bodies of FRC+ were European Social Fund, the Häme Centre for Economic Development, Transport and the Environment, and the HAMK University of Applied Sciences. Simulation- project partners were Dynamore Nordic AB and Sako Finland Oy. 1

3 Contents 1 Introduction 2 Simulation Based Design (SBD) 3 Using SBD in the design process 4 Quote phase 4.1 Onestep solvers 5 Evaluation phase 5.2 Incremental solvers 5.2 Incremental solver input Tool geometry Blank geometry Blank material Forming process 5.3 Incremental solver output 6 Decision phase 6.1 Optimization 6.2 Blank and trimming geometries 6.3 Springback compensation 7 Robustness phase 7.1 Monte carlo analysis 7.2 Scrap handling 7.3 Tool stresses 2

4 1 Introduction Today, the sheet metal part manufacturing industry is facing many challenges. One of the main issues is the increasing competition from low cost countries. The effect of this is that there is a limited amount of available business opportunities and the importance of every opportunity becomes crucial to the company. Another challenge for the manufacturing industry is the increasing complexity of the parts. The complexity can for instance arise from a demand on cost or design. But one of the most common issues is the increased use of high strength steels that has lower formability and an increased springback which can force the part out of tolerance. These demands have to be met by the industry or the increased competition will force the companies out of business. In order to deal with the new demands, the manufacturing industry needs to evolve beyond its common knowledge. This could mean investing in new equipment and offering business opportunities outside its field of expertise. Of course, this is could be a huge risk for the company. It is a well known fact that changes to the design or manufacturing process should be made as early as possible in the design process. In fact, the cost for every modification increases dramatically with the number of decisions that has been made in the project. The crucial point is to base these decisions on the best possible knowledge. If the company has vast experience in the process and material, the decisions are usually based on solid knowledge and the number of prototypes can be kept at a minimum. However, if the company has limited experience, the knowledge has to be gained during the design process which means using a lot of prototypes which is both expensive and time consuming. One way of decreasing the number of costly prototypes and decrease the time to market is to use Finite Element modeling of the manufacturing process. By doing this, the knowledge of the part problems in both design and manufacturing are moved backwards in the design process meaning that the early crucial decisions can be based on the best possible knowledge. Further, it reduces the risk for costly design changes and the need for prototypes which dramatically reduces the design process cost. Basing the decisions on simulation results is commonly known as Simulation Based Design (SBD). 2 Simulation Based Design (SBD) Simulation Based Design means using simulations in the design process instead of physical prototypes and basing decisions on the results from simulations instead of testing. These are the decisions that moves the design process forwards. In practice, a virtual model of e.g. the part is created using Finite Elements (FE). The virtual model is treated as a physical product. That means that it is manufactured, tested and used as a physical product. Also, all changes that are made to the product design, manufacturing process etc are carried out in the virtual world. In an extreme case, this means that the first serial product that is produced is the first prototype. This is actually the case for many products e.g. in the automotive industry that has used Simulation Based Design for many years. The benefits of using SBD are many. Using prototypes is very expensive since it involves manufacturing and design of tooling. Also, it is very time consuming since the tooling has to be milled and this has to be fitted into the workshop schedule. Often, the 3

5 prototype will not behave as the finished product anyway which renders the prototype and testing useless. However, the possibly biggest benefit is the increased innovation that comes with using SBD. It is possible to do changes and evaluate ideas that would never be possible in a physical world. The user has the possibility to e.g. try out different materials and process setups in a fraction of the time it would take using prototypes. Also, if the simulations are connected in an optimization loop, the part or manufacturing can be optimized to e.g. minimize the risk for fracture or minimize the scrap. Of course, there are some challenges with using SBD. If a company decides to use virtual models, it means a completely new design process. This involves e.g. educating or hiring personnel, investing in software and computer hardware. As with all changes, this cannot be carried out too fast so it has to rely on a long term commitment. 3 Using SBD in the design process For a typical sheet metal part manufacturing company the FE simulation can be divided into 4 parts in the design process, see Figure 1. Figure 1: FE simulation phases in a process design chain Quote: In this phase, time is very important. The person doing the quote needs a tool which can identify the problem areas and roughly decide if and how the part can be manufactured. Also, in this phase it is possible to give the customer input on how the part can be changed to increase the manufacturability. Further, a simulation tool is needed that can give a very quick estimate on the amount of material and the corresponding part cost and material utilization. 4

6 Evaluation: In the evaluation phase, the decision is made on how the part will be manufactured e.g. the number of process stages, drawbeads and tool forces. The simulation tools used in this phase need to be moderately accurate since most of the simulations are done in this phase. Decision: When the process design is done in the evaluation phase it is time to verify the hard tooling. This could for instance include optimizing the blank geometry to decide the trimming dies. If the part suffers from severe springback a decision has to made if the geometry of the tooling should be compensated for the springback deformation. Also, if drawbeads are used, this is where the drawbead geometry is determined. Robustness: In the robustness phase, the process is subjected to variations which can occur in the manufacturing process. This could be due to varying material properties but also due to thickness variations or differences in friction. Simulations can identify the crucial parameter in order to minimize the scrap which can then be targeted at an early stage as a requirement for e.g. the material supplier. 4 Quote phase A high number of quotes increase the chance of receiving an order. Of course, the quote has to be accurate as well. In order to minimize the simulation effort and time, a tool which is easy to use and very fast is necessary. Such a tool is the onestep solver. 4.1 Onestep solvers Onestep solvers, or inverse solvers, are based on total plasticity. This means that an assumption is made that the blank deforms from flat to part shape during proportional loading, see Figure 2. One benefit of this is that the solver is very fast since it only simulates the final state. Also, no tooling is needed and the simulation can performed using only the part geometry. The simulation can give a rough estimate on the formability (wrinkling fracture, thickness etc.) and the required initial blank shape. It is often combined with a nesting program which distributes the blank on to a coil and optimizes the position to maximize the material utilization. Some solvers can also handle different amounts of blankholder forces, drawbeads and tailor welded blanks. The programs are often very easy to use. Thus, it does not require any experience in FE simulations. 5

7 Figure 2: Onestep/inverse solver functionality One drawbacks of this method is that since the tooling is not modeled, the solution can not include this effect. Thus, if the tooling has a large influence on the forming result, the method will not be that accurate. Also, if the deformation is not proportional, the assumption of total plasticity will not be valid. This makes the simulation tool unsuitable for parts which are produced using several process stages. Also, a part with a high amount of material draw in typically also violates the proportional strain path assumption. Nevertheless, onestep solvers are an invaluable tool for many forming tool companies. 5 Evaluation phase In this phase the number of process stages, blankholder force and the possible use of drawbeads need to be decided. The effect of the tooling is thus important. It is therefore recommended to switch to an incremental solver for this phase. 5.1 Incremental solvers The name incremental solvers come from the fact that the solution is determined with time increments apart. Thus, the simulation starts with a flat blank and then the tooling is closed and the part is deformed. At subsequent time increments the solution is determined as the solution steps through the complete process. Given that the necessary number of timesteps is calculated, this generates a very high level of accuracy. Basically, two types if incremental solvers exist, implicit and explicit. Implicit solvers: The implicit solvers use unknown information when determining the solution at the next timestep. The timestep starts with an assumption and the solver checks if this assumption is correct by looking at the force equilibrium. If the assump- 6

8 tion is correct then the solver moves on to the next timestep. Otherwise it modifies its assumption and recalculates the timestep. The main characteristics of an implicit solver are: - The timestep can be arbitrary as long as the solver finds equilibrium. - It uses a lot of internal memory which in reality reduces the number of elements in the FE model which could influence the accuracy. Explicit solvers: This type of solver only uses known information. Thus, the velocity, accelerations and forces at the current timestep is used to calculate the deformation at the next timestep. This makes the solution very fast. However, if the timestep is too large, the solution will diverge. The main characteristics of an explicit solver are: - The timestep size is limited due to convergence. However, each timestep is very fast. - The method is very memory efficient. In reality, the necessary timestep size is not arbitrary in the implicit case. A minimum number of timesteps are needed in order to get a solution which does not depend on the number of timesteps. This is generally not a problem in the explicit case since a very high number of timesteps are calculated. 5.2 Incremental solver input Tool geometry The incremental solver input is generated in a pre-processor that sometimes is part of the solver package and the procedure of creating the virtual model is usually denoted pre-processing. As stated earlier, the tool geometry is needed. However, only the surfaces that are in contact with the blank are used. In order to reduce the time spent in the CAD software many software companies offer pre-processor which has a semi- automated interface for generating the necessary tool surfaces. This is called Die Face Engineering (DFE) or Die Design, see Figure 3. If the tool design is made elsewhere, it is typically imported in the pre- processor using the IGES or STEP format. The tooling is assumed to be rigid. Thus, it does not deform during the forming process. 7

9 Figure 3: Die face engineering/die design Blank geometry The intial blank geometry is needed and is either generated inside the pre-processor or imported using the IGES or STEP format. The geometry is divided into finite elements, which is often referred to as meshing. The size of the elements is very important. A higher accuracy is generally acquired with smaller element size. But, the simulation time increases with the number of elements. Since a majority of the simulations are done in this phase and the results are more general in nature, the accuracy can be kept at a reasonable level in favor of the simulation time Blank material The blank material is a very important input. Depending on the choice of material, the part can fail or be successfully produced. The pre- processors often come with a built in material library which can be used as a starting point. However, it is recommended for accuracy reasons that the user should acquire this information from either material testing or the material supplier. The absolute minimum of information needed is the material hardening behavior that can be gained from a simple tensile test, see Figure 4. It describes how the stress varies in the material as a function of the strain. 8

10 Figure 4: FE model of a tensile test If the material is produced through rolling or has a material texture, the material behavior can be different depending on the coil direction. This is denoted as anisotropy. Tensile tests in different material directions (rolling, 45 degrees and transverse directions) can determine the amount of anisotropy which is characterized by the Lankford or R- values Forming process The forming process needs to be defined and input to the pre-processor. This includes moving the tooling to initial positioning and defining the corresponding movements during the process. Typically, prescribed motion is defined on the moving tool. However, if the binder is subjected to a binder force, i.e. using gas springs, this is applied in the simulation as well. If simulation time is critical then analytical modeling of drawbeads is often used. This means that the actual geometry of the drawbead is not modeled. Instead, it is defined by a curve on the tooling and if the blank is moving perpendicular to the line, a restraining force is applied, see Figure 5. The benefit of this is that the simulation is a lot faster since it requires a lot less elements. Also, since the drawbead is defined as a contact that applies an opposing force, the level of the restraining is very easily adjusted. This is very time efficient in the evaluation phase. The drawback is of course that the accuracy is not as high as it would have been with the actual bead geometry. Figure 5 : Analytical drawbead modeling 9

11 If the forming process contains multiple stages, then all the stages are modeled. The simulations are then run in consecutive order, and the simulation results are transferred from each forming stage to the other, see Figure 6. Figure 6: Multistage forming analysis 5.3 Incremental solver output The output from the simulation is viewed in a post-processor. The user can view the forming of the part as a movie or at separate timesteps. On top of the deformation, specific results such as e.g. part thickness can be viewed in a fringe plot, see Figure 7. 10

12 Figure 7: Fringe plot of part thickness The output from an incremental forming simulation includes a lot of information, e.g. wrinkling, material draw-in, tool forces and final part shape, see Figure 8. Apart from the forming results, the final part can be exported to another simulation, e.g. crash or fatigue analysis, where the results from the forming simulation are of importance. Figure 8: Part wrinkling during material draw in 11

13 The Forming Limit Diagram (FLD) is a forming specific post processing tool which is often used to evaluate formability. The FLD contains the major and minor principal strain state of each element. The principal strain states are compared to a limit curve, and if all of the elements are below the curve then the forming is considered to be without fractures, see Figure 9. However, elements that are positioned above the limit curve are considered to be fractured. The curve is often denoted Forming Limit Curve (FLC) and it can either be experimentally or analytically determined. Figure 9: FLD and Formability key The FLD is often used to evaluate other formability criteria as well. For instance, if an area of elements is compressed in one direction (negative minor principal strain) without being stretched in the other, then it is suspected that this area is prone for wrinkling. Also, if the elements are close to the FLC within a safety margin, it is assumed to at risk for failure. However, it should be noted that the only criteria that have an experimental and analytical basis is the failure criteria and thinning criteria. All the other criteria are just interpretations of the principal strain state. 6 Decision phase When the forming process stages are determined with satisfactory results and a acceptable safety level for fracture and wrinkling it is time to move into more detail regarding the tool design. The simulation tool that is used for this stage is still the incremental solver. However, the level of accuracy is increased by reducing the element size and introducing physical drawbeads. 6.1 Optimization Before making the final decisions on the tool design it is possible to fine tune the parameters in order to get an optimized result. For instance, the basic level of a drawbead restraining force was determined in the evaluation phase. If the simulation software is coupled to an optimization routine it is possible to iteratively modify the restraining forces to minimize the risk for failure while keeping the part wrinkle free. Also, if ana- 12

14 lytical drawbeads were used, the drawbead geometry that generates the corresponding restraining force has to be determined. This can also be done using optimization. For some forming processes, the final trim is done before the first forming stage. The reasons for this are several. First of all it reduces scrap and tooling which thus reduces cost. Also, this is often done for press-hardened parts which are difficult to cut due to the high strength. The challenge is then to determine the trimming geometry which yields the correct final part shape. A first estimate can be done using a onestep solver. However, if the forming process contains several forming steps, the trim geometry might not be that accurate and needs modifications. Most simulation software has the possibility to compare the received part geometry with the nominal part geometry and adjust the trimming curve accordingly. When the trimming geometry is determined it can be evaluated for cutting angles and problem areas where a cam might be necessary to receive a good cut, see Figure 10. Figure 10: Trimming curve evaluation 6.3 Springback compensation Springback deformation is gaining increased focus in the sheet metal forming community. This is partly due to an increased research in numerical methods and material modeling that significantly has increased the springback prediction accuracy. Since the software users are getting consistent results, they are more prone to use the results in the design process. One major reason for springback prediction is of course due to the increased use of high strength steels. The traditional methods for reducing springback, e.g. increased stretch, might not be applicable for high strength steels due to reduced formability. Also, blankholding increases the amount of scrap which is a disadvantage. One solution to reduce the springback is to compensate for the deformation in the forming tools. The software compares the received part geometry with the nominal part and 13

15 calculates the deviation. This deviation is then transferred to the tool geometry which is modified accordingly. Typically, a scale factor is used on the deviation in order to control the compensation. Since this method to reduce springback modifies the geometry, the software should check for undercut which could occur. This is in general a nonlinear problem which means that several iterations might be necessary in order to receive a part within tolerance, see Figure 11. Figure 11: Springback compensation procedure 7 Robustness phase In the decision phase, the final tool geometry and process was decided and possibly optimized. In the robustness phase it is possible to assure that the production of the part is smooth and that any variation that can occur does not result in increased scrap. 7.1 Monte carlo analysis The forming process has many parameter variations which can affect the final part. These variations include e.g. blank thickness, material hardening, friction or blankholding due to tool deformation. A Monte Carlo analysis can be done by assigning a distribution to variables in the forming simulation. The result of such a study is to decide the probability of part failure. If the part fails, where does it fail and which is the governing parameter. By this, it is possible to target the parameters that are important for minimizing scrap and make the proper steps to avoid the problem. 14

16 7.2 Scrap handling One of the major causes for press line interruptions is that sheet metal scrap gets stuck in the scrap removing channels inside the trimming tooling. If this is not simulated, the problem will not be identified until the tooling is finished. By performing scrap shedding/removal analysis it is possible to see how the scrap falls through the scrap exits and identify if there is risk for congestion, see Figure 12. Figure 12: Scrap shedding/removal simulation 7.3 Tool stresses As mentioned in Section 5.2.1, the tooling is assumed to be rigid. This is done for mainly two reasons. Firstly, the model size would be too large to use in an iterative simulation sequence. Secondly, the complete tool geometry is not known until the decision phase is finished. However, it is a well known fact that the tooling is far from rigid and the deformation of the tooling can influence the forming result, see Figure 13. When the CAD geometry of the tooling is finished, an FE simulation can be carried out to calculate the deformations. If the deformations are too large, it could affect the blankholding. Also, the simulation could be coupled to a topology optimizer which adds stiffeners wherever needed to minimize the deformation while e.g. minimizing the weight of tool for handling. Further, the stresses can be used in a fatigue analysis to evaluate the risk for cracks. 15

17 Figure 13: Tool deformation (Courtesy of Volvo Cars) 16