The taguchi method for the optimum design

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Abstract:

The most frequent defects generated by cold plastic forming in the parts made from metal sheets are caused by the springback phenomenon. The springback effects mainly determine the decrease of accuracy of the drawn part by changing its shape and dimensions after the tool removing. The present paper analyses the results obtained from the application of the Taguchi method in the designing phase of the drawing processes in order to increase the accuracy of the parts made from metal sheets by reducing or eliminating the springback effects. The optimization system based on the above mentioned method performs the reduction of the springback intensity by an optimum design of the drawing tools geometry and process parameters.

1. Introduction

The most frequent defects generated by the cold plastic forming in the case of parts made from metal sheets are caused by the springback phenomenon. The springback effects are contrary to the effects of the forming load application and it determines the following modifications on the part and its material after the tools removing: the alteration of the part form and dimensions and the change of the state of stresses and strains in the deformed material. The studies related to the determination of the causes and factors that influence the springback intensity were generally devoted for the analysis of parts having simple configuration (U or CI shapes). The main factors of influence of the springback are as follows: the material and forming parameters, the part and tool geometry, the forming conditions etc. The methods adopted for the reduction or elimination of the springback effects are as follows:

• the calculation of springback parameters by using some mathematical models and the utilization of the results in the designing phase of tools. But the created models for the springback calculation are generally based on different simplifying hypotheses relative to different factors of influence and were generally elaborated for parts having simple configuration (especially for U or Q - bent parts). For example, the first models used to calculate the springback parameters were constructed by assimilating the springback with a bending process. The increase of the parts complexity and the utilization of high strength materials have conducted to the need to elaborate new models for the determination of springback parameters, models that take into consideration the influence of new factors. Thus, the recent elaborated models are based on the determination of springback parameters using theoretical estimations of different factors of influence. So, Morestin and Boivin created a model for the calculation of springback parameters based on the determination of the residual stress distribution using the Prandtl and Reuss plasticity equations associated with a hardening cinematic model Lemaitre -Chaboche. The deficiency of the model is represented by the fact that its application can be only made for some materials whose elasticity varies according to the deformation phase (for example, in the case of some aluminium alloys, the Young module doesn't vary according to plastic deformation). Joannic and Gelin created a model based on the assumption that the springback is the effect of a contact force and of a heterogeneous redistribution of efforts on the sheet thickness; the model was used for the simulation of the deep-drawing in the case of the U and S-shape parts. But, between the values determined using the above mentioned models and the results obtained from experimental investigation significant differences have been resulted.
• the application of the following technical solutions in the designing of forming tools or process: the correction of tools geometry with the value of springback angle, the supplemental deformation of the material, the utilization of stiffeners, the utilization of punches with coining strips, the utilization of an arched counterpunch that induces supplemental deformations for the compensation of springback, the utilization of variable blank holder force etc. The application of such technical solutions leads to the reduction of springback intensity but, on the other side, it leads to the increase of the tools complexity and costs.

Based on the above presented aspects, it can be concluded that the development of designing methods that must permit the reduction or elimination of the springback effects just from the designing stage of the forming tools and process is needed. An optimal solution that can be applied to solve this problem consists in the elaboration of a design system based on different methods of optimization and the establishment on its basis of an optimum geometry of tools and of optimum process parameters in order to increase the drawing accuracy. The present paper analyses the conditions and steps needed and the results obtained from the application of the Taguchi method for the optimization of the drawing tools geometry and processes parameters. The optimization based on the above mentioned method has as main purpose the reduction or elimination of springback effects and hence the determination of optimum parameters of the drawing tools and processes.

2. Basic Data And Conditions Of Application Of The Optimization Method

The above presented method was applied in the case of a hemispherical part having the theoretical geometry and made from E220 steel sheets. The initial configuration of tool used to obtain the part did not consider springback effects. ,

analyzed part

The part obtained using such tool is shown in Fig. 3 where significant deviations from the theoretical shape can be remarked. The geometric parameters of the part that must be considered in optimization are shown in Fig. 4; these parameters are as follows: the part radius (Rp), the flange connection radius (Rf), the radius of flange connection circle (p) and the angle of the flange with the horizontal axis (a).

initial tools be considered in optimization

The drawing process has been simulated using the ABAQUS-Explicit software. The simulation was performed along and normal to the loading direction. A three dimensional model used for simulation was created in order to ensure the simulation of a quasi-static problem and to obtain the state of equilibrium after the forming operation.

The geometry of the model is shown in Fig. 5; in simulations was only used a quarter of part that has two symmetry conditions: symmetry of yz plane (A) and symmetry of xy plane (B). The part was considered as deformable with a planar shell base. The integration method was Gaussian with 5 integration points for every node, equal distributed through the thickness of the shell. The elements used for the blank mesh were of S4R type. The blank-holder, punch and die were modelled as rigid surfaces. The contact interactions between the blank and the tools were modelled using the penalty method. In order to describe the plastic behaviour of the used material, 10 points were chosen from the stress - strain diagram. The material was considered elastic-plastic with an isotropic hardening. The sheet thickness was equal to 0.8 mm and the blank radius was equal to 105 mm. The materials elastic properties used for simulation were as follows: Young's modulus 2.1x10 MPa, Poisson's ratio 0.3, density 7800 kg/m3. The coefficient of friction used for the contact between blank, punch, die and blankholder was |i = 0.4. The process parameters were as follows: drawing depth =61.8 mm, drawing speed = 54 mm/s. A symbolic mass of 1 kg was attached to the blankholder and punch and an initially concentrated load of 30kN was applied to the reference node of the blankholder. The fields of variation of the parameters used in optimization were as follows: punch radius rp = 54...56mm, die radius rm = 5...7mm and blankholder forceBHF = 20.. .70kN.

Description Of The Method

In order to study the entire field of variation of the parameters that influence springback by applying a small number of experiments; the Taguchi method uses a special design of orthogonal arrays. The method is developed in the following main steps: Step 1: Formulation of the problem, the success of each experiment being dependent on the correct understanding of the nature of problem. Step 2: Identification of the output parameters of performance that are most relevant for the problem. Step 3: Identification of control factors, noise factors and signal factors. The control factors are those that can be controlled in the conditions of normal production. The noise factors are those that are either too difficult or too expensive to control in the conditions of normal production. Signal factors are those that affect the mean performance of the process. Step 4 Selection of the factor levels, possible interactions and interaction effects. Step 5 Design of an appropriate orthogonal array (OA). Step 6 Preparation of the experiments/simulations. Step 7 Running of the experiment with appropriate data collection. Step 8 Statistical analysis and interpretation of experimental results. Step 9 Undertaking a confirmatory run of the experiment. The output parameters of performance are materialized by the geometric parameters of the part (Rp, Rf, a and p). The control factors are as follows: the geometrical factors of the tools: punch radius (rp), die radius (rm) and the main technological factor of the drawing process: blankholder force (BHF); the above mentioned factors are represented.

The optimization has been developed in order to obtain an efficient design of the drawing tool and process. The conventional optimum is determined without considering noise factors. The method is applied in the case of problems with discrete variables. The orthogonal array based on the Taguchi concept is used to arrange the discrete variables. Four influence factors on three levels of variation were chosen in order to select the factor levels, the possible interactions and the interaction effects. The controllable factors that are used and their levels of variation are presented.