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Control system of a mini hydraulic press for evaluating springback in sheet metal forming
Journal of Materials Processing Technology 176 (2006) 55–61
Control system of a mini hydraulic press for evaluating springback in sheet metal forming P. Sun, J.J. Gr´acio ∗ , J.A. Ferreira Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Received 13 April 2005; received in revised form 8 February 2006; accepted 8 February 2006
Abstract The paper proposes a method of evaluating springback that occurs after unloading during sheet metal forming of a control system. A linear displacement occurring by springback of the components formed is used as the reference value of springback to evaluate actual springback, and displayed on the control interface in real time. The proposed method is based on measurements performed during closed loop controlled stamping operations. To perform the close-loop control of the hydraulic press two pressure sensors are installed in the cylinder chambers and a position sensor (optical scale with a resolution of 1 m) is installed on slip rod of punch. Both control and monitoring software run on a real-time hardware board that is directly programmed through the Matlab/Simulink environment. The data of the hydraulic force and punch position, as also the springback effects, can be shown on the control/monitoring interface in real time during stamping process. For the work, an experimental example is used to build and test the control system on a mini-press (I), and a linear model was provided to test the strategy to control the punch position and/or force. Hardware-in-the-loop simulation techniques are also used in experiments to verify the control of overall system. System models possess the characteristics of less computing power and adjusting parameters easily. The punch position can be controlled with high precision in a moving travel of 200 mm. The purpose of the work is to offer an effective way for evaluating springback in real time during sheet metal forming. © 2006 Elsevier B.V. All rights reserved. Keywords: Springback; Sheet metal forming; Evaluation; Control system
1. Introduction Springback is a common phenomenon in sheet metal forming, caused by the elastic recovery of the internal residual stresses during unloading. Although fundamental theoretical analyses have been developed to quantify the springback behaviour, their application to sheet metal forming processes is limited since discrepancies are often observed when the theoretical predictions are compared with the measured data. This has led to the development of various empirical equations, suited to the particular forming process examined. The lack of agreement between the theories and practical observations arises mainly from the variation of the material properties, and the complexity and peculiarity of the individual forming process, which lead to an uncertainty of the forming parameters (such as the tension induced during forming and die conformity) [1]. At present, there have been much effort to evaluate or decrease springback. Work of applying finite element method to ∗
Corresponding author. Tel.: +351 34 370 827; fax: +351 34 370 953. E-mail address: [email protected] (J.J. Gr´acio).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.02.009
analyze sheet stamping processes, carried out by Wang, Budiansky (cited in reference Key et al. [2]). Morestin et al. [3] predicted springback in deep drawing processes taking account of the nonlinear kinematic hardening of the material. Along with the rapid progress of computing environments, a range of numerical methods for predicting springback in sheet metal forming has recently developed [4]. Most finite element simulation of sheet metal forming have focused on the prediction of the part springback during sheet metal forming processes, and such efforts typically involve the use of 2D models [5,6]. However, in the literature, few papers deal with evaluating the springback during stamping processes in real time. Therefore, it is necessary that study of evaluating the actual springback during stamping in real time. In the present research, is a real-time control method proposed for the springback that occurs after unloading during sheet metal forming. A linear displacement occurring by springback of the formed workpieces is used as the reference value of springback to evaluate actual springback. The reference value of springback is calculated by knowing the thickness of the workpiece and the position change of punch (hs ), and displayed on the control interface in real time. The results from the real-time
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P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
feedback control of the force or velocity/position of the tools are attached to the hydraulic press. The method is a practical method of evaluating springback in stamping process. To perform close-loop control of the hydraulic press, two pressure sensors are installed in the cylinder chambers and a position sensor (optical scale with a resolution of 1 m) is installed on slip of punch rod. The control and monitoring software run on a realtime hardware board that is directly programmed through the Matlab/Simulink environment. The hydraulic force and punch position data, as also the springback effects, can be shown on control/monitoring interface in real time during stamping process. For the work, an experimental example is use to test the control system on a mini-press (I), and a linear model was developed, and a linear model was provided to test the strategy of position and force control of draw punch. The models of the cylinder and control valve as well as the springback mechanism in the device were described. The technique of hardware-inthe-loop simulation based on MATLAB® /Simulink® is used in experiments to verify the control process of overall system. System models possess the characteristics of less computing power and adjusting parameters easily. The position can be controlled with high precision in a moving travel of 200 mm. Results of closed loop model simulation are compared to real test data. 2. Springback behaviour Industrial applications like deep drawing, blanking processes, and bending are all characterized by localized plastic deformations. But elastic recovery that, occurs after unloading, always exists in stamping process. Springback occurs with all types of forming by bending, when bending in presses, folding, roll forming, and roll bending. As a result of springback, the bending die angle α1 does not correspond precisely to the angle desired at the workpeice α2 (Fig. 1). The angle ratio is so-called springback factor κR , which depends on the material characteristics and the ratio between the bending radius and sheet metal thickness: κR =
α2 r1 + 0.5t = α1 r2 + 0.5t
Fig. 2. Springback phenomenon in productions.
inside radius at the die [mm], r2 the inside radius at the workpiece [mm], and t is sheet metal thickness [mm] [7]. Factors that affect springback include variations in both material and process parameters [8], such as material properties, sheet thickness, friction condition, binder force, tooling geometry, and lubricant condition. In addition, element type, mesh density, and material model in FEM simulation could have significant influence on springback prediction. Fig. 2 is springback phenomenon in actual production. Analysis has indicated that, springback in sheet metal forming can be reduced by changing clamping condition and material properties, but cannot be completely eliminated due to the existence of residual stresses generated in forming. Then, how accurately calculating, controlling and showing the springback of the formed workpieces has become one of focus problems to designers and manufacturers in sheet forming field. 3. The method of evaluating springback 3.1. Control method description
(1)
where α1 is angle at the die (required bending angle) [◦ ], α2 the desired angle at the workpiece (after sprigback) [◦ ], r1 the
Fig. 1. Elastic recovery after bending. t, sheet metal thickness; α1 , required bending angle; α2 , desired angle; r1 , inside radius of die; r2 , inside radius of workpiece.
The method is a practical one for evaluating springback in stamping process, and results from the real-time feedback control of the force or velocity/position of the tools attached to the hydraulic press. To perform close-loop control of the hydraulic press two pressure sensors are installed in the cylinder chambers and a position sensor (optical scale with a resolution of 1 m) is installed on slip rod of punch. The control and monitoring software run on a real-time hardware board that is directly programmed through the Matlab/Simulink environment. The hydraulic force and punch position data, as also the springback effects, can be shown on control/monitoring interface in real time during stamping process. A linear displacement occurring by springback of the formed workpieces is used as the reference value of springback (δ) (see Fig. 3). The reference value of springback is calculated, by knowing the thickness of the workpiece and the position change of punch (hs ) under the action of the springback force, and displayed on the control interface in real time.
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
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Fig. 3. Schematic diagram of a stamping process.
A schematic diagram of a stamping process is shown in Fig. 3, where δ is a linear displacement occurring by springback and is defined as the reference value of springback, t the thickness of workpiece, and hs displayed on the control interface in real time is a position change of punch. After punch finishes drawing, adjusting the hydraulic pressure (P1 and P2 ) of cylinder chambers makes the punch move up slowly until the formed workpiece finishes elastic recovery. In that case, the formed workpiece will generate a displacement, and position change of punch, hs , can be considered as a change occurring under only the action of the springback force FS (Figs. 6 and 7). The hs can accurately be measured through the experimental interface of control system, as shown in Fig. 4. The reference value of springback (δ) can be estimate according as relation of hs on control interface. The real-time measurement of the springback can lead to enhance the control strategies by adapting the controller parameters and improving the reference trajectories for the punch position or force. These data (controller parameters and optimal reference trajectories) can be used as a database for duly regulating the size of the die. 3.2. Principle analysis In stamping, the process of sheet forming starts with the loading then the drawing and ends with the unloading operation (Fig. 5). Springback angle of the formed workpiece will lead to
Fig. 6. Diagram of punch position in sheet metal drawing.
a dimension error (a linear displacement) along drawing direction after unloading. Therefore, the dimension error can also reflect the change grade of springback size. The hydraulic press will be equipped with a set of sensors to measure the system pressures and piston position. The actuation force is measured indirectly through two pressure sensors installed on the cylinder chambers. The work cylinder rod position is acquired with an optical scale with 1 m of resolution. The velocity was obtained by differentiation of the position signal. All inputs of the sensors and the electrical valves are connected to a low cost DSP based real-time card (model DS1102) from dSPACE® , in such a way that real-time control and acquisition can be performed. During stamping process the hydraulic force and punch from sensors can be shown on control interface in real time. The process can be divided in three steps: the first step (see Fig. 6) is the drawing phase and punch position is h0 (equal to the sheet thickness, t). In the second step, adjusting the hydraulic pressure (P1 and P2 ) of cylinder chambers makes the punch move up slowly until the formed workpiece finishes elastic recovery. In that case, the formed workpiece will generate a displacement,
Fig. 4. (a and b) The display component of punch position in two kinds of control interface.
Fig. 5. Process of sheet metal forming.
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and position change of punch, hs , can be considered as a change occurring under only the action of the springback force FS (see Fig. 7). And the punch position will be accurately measured in real time. According to these measurements (and also the chamber pressure data), the springback force FS can be estimated, if the dynamic behaviour of the cylinder and proportional valve is known. Relationship between FP and P1 is FP = P1 A1 − P2 A2
(2)
When FP = Fg + Ff − FS
(3)
Punch position is given by hs = t + δ
(4)
Fig. 8. Diagram of punch position after unloading.
The reference value of springback (δ) is expressed as δ = hs − h0
(5)
where P1 , P2 are the pressure inside the cylinder chambers; A1 , A2 , the cylinder chambers areas; t, the sheet thickness; h0 and hs , punch position. Fg , Ff are gravitation of punch and friction of cylinder seal (which can calculate through total mass of punch and friction coefficient of seal). The pressure P1 value can operate on control interface expediently. The third step is adequately unloading process, as shown in Fig. 8. FP > Fg + Ff , punch departs from workpiece and move to h position. The third step does not have relations withspringback. In actual operation, setting an allowable reference value of springback (ε) to compare with actual reference value of springback (δ). When δ < ε, i.e., hs < ε + t
(6)
Springback of formed workpieces suffices precision requirement. When hs > ε + t
(7)
springback is out of tolerance, die size need to be adjust.
Fig. 7. Punch position with springback force.
Thus, the method proposed can inspect springback grade during sheet metal forming in real time. Note that loading and unloading of blank holder (force FN ) is operated independently. 4. Experimental device and experiments 4.1. Experimental device First a hydraulic mini-press (I) with a 200 mm working travel for the punch was built (see Fig. 9). The correct and convenient control system was built in order to test precision of punch position during stamping process. The mini-press (I) is actuated by a hydraulic servo-cylinder driven by a high performance servo-solenoid valve (Fig. 10). The hydraulic force is indirectly measured through two pressure sensors installed in the cylinder chambers. The piston position is measured through an optical scale with a resolution of 1 m and its acceleration is monitored with an accelerometer. The mini-press (I) allows compression, tensile or both types of solicitation. The compression capacity is useful to simulate the approach and work tasks, and the tensile capacity to simulate the backward movement (Table 1). To evaluate the control performance, springback mechanism is replaced by a shock absorber in the experimental device in order to represent the springback behaviour of formed workpieces in stamping. This is an initial approach to represent the elastic recover of material in a typical stamping task. Hydraulic circuit and control system of experiment prototype can be addressed by Fig. 11. A variable volume axial piston pump coupled to a pressure accumulator with a 5 l capacity provide the hydraulic power at a constant pressure. To reduce the development time hardware-in-the-loop simulation experiments were performed with a linear model of the press, in order to test and optimize the control algorithms to control punch position and/or force.
Fig. 9. Schematics of the hydraulic mini-press (I).
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
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Fig. 11. Hydraulic circuit and control system diagram of experiment prototype.
where ap = dvp /dt is the piston acceleration and M is the total mass in motion (load, piston, rod). The absorber characteristics measured in [9] are:
Fig. 10. The hydraulic mini-press (I) in experiment.
K = 1.75 N m−1 ,
4.2. Experiment and simulation
B = 400 N s m−1
The other values used in the linear model for simulation purposes are:
4.2.1. Modelling To test the force and position control, a hydraulic servo system (proportional valve, linear actuator) is modelled. Fig. 12 shows the diagram of the control valve and hydraulic cylinder as well as the springback mechanism used in the tests. The linear model was used to perform hardware-in-the-loop simulation experiments as a base to test different control strategies without the associated dangerous when testing a controller directly on real hydraulic hardware. The overall performance of the linear model was satisfactory for the test bed of set-up. The dynamic behaviour of the linear model, being satisfactory for the test platform, needs to be upgraded with some non-linear effects, like the friction in the cylinder seals or the non-linear valve behaviour, to be used in the evaluation of different control algorithms. The model of the hydraulic cylinder was created by an engineering analysis of the actual hydraulic cylinder and valve. The piston velocity is vp = dxp /dt, and the cylinder dynamics is defined as: M · ap = P1 A1 − P2 A2 − K · xp − B · vp
V1 = 1.05 × 10−4 m3 , A2 = 8.765 × 10−4 m2 ,
V2 = 1.72 × 10−4 m3 , M = 5 kg,
A1 = 1.257 × 10−3 m2 ,
β = 8.5 × 108 Pa.
(8)
Table 1 Components of hydraulic mini-press (I) Nome
Type
Servo-cylinder Servo-valve Pressure sensor Optical scale Real time card Acceleration sensor Computer
KBSDG4V-3 P15RVA1 Resolution of 1 m DS1102 FA201 Fig. 12. Work state diagram of the mini-press (I) and dynamic model of springback mechanism.
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P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
Fig. 14. Comparison between real and simulation results.
Fig. 13. Diagram for the hardware-in-the-loop simulation experiments. The linearized valve and cylinder equations is defined as:
⎡
⎤
⎡
⎢ ⎢ ⎢ p˙ 2 ⎥ ⎢ ⎢ ⎥=⎢ ⎣ v˙ p ⎦ ⎢ ⎢ ⎣ x˙ p p˙ 1
−
βe Kc V1 0 A1 M 0
βe A1 V1 βe A2 V2 B − M 1
−
0 βe − Kc V2 A2 − M 0
⎡ βe ⎤ Kq 0 ⎢ V1 ⎥ ⎢ βe ⎥ xs − K 0 ⎢ ⎥· +⎢ V q ⎥ g 2 ⎣ 0 1⎦ 0
⎡
⎤
⎤
⎡ ⎤ ⎥ p1 ⎥ ⎢ ⎥ 0 ⎥ ⎥ · ⎢ p2 ⎥ ⎥ ⎣ vp ⎦ K ⎥ − ⎦ xp M 0
Fig. 15. Results of controlling the piston position with a PD controller both in real and HILS experiments.
0
(9)
0
⎡
⎤
⎡
p1
A ControlDesk application was developed in order to change the parameters of the controllers. The ControlDesk software tool is provided by dSPACE to build experimental interfaces. It is well suited for data acquisition, and set-up of Graphical User Interface (GUI) is intuitive and simple. It is also possible, to change of the reference signals in real time. The experimental data can be stored for post-processing in Matlab® framework.
⎤
p1 1 0 0 0 ⎢ ⎥ ⎣ p2 ⎦ = ⎣ 0 1 0 0 ⎦ · ⎢ p2 ⎥ ⎣ ⎦ xp
0
0
0
1
vp
xp
The measured valve parameters for a work pressure of 70 × 105 Pa were [10] Kq = 4.8 × 10−4 m3 s−1 and Kc = 4 × 10−12 m3 s−1 Pa−1 . 4.2.2. Experiment and results The control and simulation platform is based on two real-time hardware cards (model DS1102) from dSPACE® . The base cards of the DSP are programmed by the Matlab® and Simulink® platforms. The position/force hybrid structure for the controller is implemented in one card, the force gain (Gf ) and the position gain (Gp ) will allow the definition of the contribution in the position and force controllers for the control signal applied to the proportional valve. The control of position, velocity and force is based on a proportional and derivative controller (PD). Fig. 13 shows the platform used to perform hardware-in-the-loop simulation experiments with the linear model of the mini-press. Hardware-in-the-loop simulation [11] refers to a technology where some of the components of a pure simulation are replaced with actual hardware.
Fig. 16. (a and b) Experiment device (II) and stamping tools.
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61 To evaluate the linear model performance, a sequence of experiments was performed with different reference signals (shape, amplitude, and frequency). Figs. 14 and 15 present the results of controlling the real-time simulation and the control of the real mini-press (I) [12]. The reference position signal is a square wave, both systems were controlled by a proportional plus derivative controller with the proportional constant equal to 25 and with a unitary derivative gain. The experimental results for control of real mini-press (I) show good agreement with the simulation (Fig. 15). Hydraulic mini-press (II), second experiment device is designed (see Fig. 16(a and b)). It is similar to an actual hydraulic press, and will is used to carry out forming experiment for testing and analyzing the reference value of springback.
5. Conclusions The method of evaluating springback in sheet metal forming in real time on a hydraulic press was proposed in the present work. Springback behaviour of the formed workpiece after unloading during stamping is described. A real prototype and a linear model of the mini-press (I) were developed. The linear model was used to perform hardware-in-the-loop simulation (HILS) experiments as a base to test different control strategies without the associated dangerous when testing controllers directly on real hydraulic hardware. The method proposed can become a useful way for improving efficiency and quality of production in sheet metal forming through next technologic integrity. The new press system will be instrumented and used to perform the final experimental work. Acknowledgement The authors gratefully acknowledge that the Portuguese Foundation of Science and Technology (FCT) give grand support to this study.
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References [1] W.Y.D. Yuen, Springback in the stretch-bending of sheet metal with non-unifom deformation, J. Mater. Proc. Technol. 22 (1990) 1– 20. [2] S.W. Key, R.D. Kring, K.J. Bathe, On the application of finite element method to metal forming processes, Comp. Mech. Appl. Mech. Eng. 17/18 (1979) 579–608. [3] F. Morestin, M. Boivin, C. Silva, Elasto plastic formulation using a kinematic hardening model for springback analysis in sheet matal forming, J. Mater. Proc. Technol. 56 (1996) 619–630. [4] Makinouchi, Sheet metal forming simulation in industry, J. Mater. Proc. Technol. 60 (1996) 19–26. [5] A. Makinouchi, E. Nakamichi, E. Onate, R.H. Wagoner, Prediction of spring-back and side-wall curl in 2-D draw bending, J. Mater. Proc. Technol. 20 (1995) 361–374. [6] W. Klingberg, U.P. Singh, W. Urquhart, A finite element simulation of free bending, in: Proceedings of International Conference on Sheet Metal, University of Ulster, 1994, pp. 201–211. [7] Taylan Alten, Metal Forming Handbook, Press, G¨oppingen, Germany, 1998. [8] Y. Hu, G.N. Walters, A Few Issues on Accuracy of Springback Simulation of Automobile Parts, SAE Paper No. 1999-01-1000, SAE SP-1435. [9] P. Talaia, A. Rocha, J.A. Ferreira, Suspension Analysing Equipment Based on a Hydraulic Servo-Cylinder, in: Proceedings of CONTROLO 2002—Fifth Portuguese Conference on Automatic Control, University of Aveiro, Portugal, 2002, pp. 297–301. [10] J.A. Ferreira, F.G. Almeida, M.R. Quintas, Semi-empirical model for a servo solenoid valve, J. Syst. Control Eng. 216 (13) (2002) 237– 248. [11] H. Hanselmann, Hardware-in-the-loop simulation testing and its integration into a CACSD toolset, in: Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, Dearborn, Michigan, USA, 1996, pp. 152–156. [12] P. Sun, P.M. Talaia, J.J. Gr´acio, J.A. Ferreira, The study and analysis of a real-time control method for springback in sheet metal forming, in: Proceedings of the Sixth International ESAFORM Conference on Materrial Forming, Salerno, Italy, 2003, pp. 263–266.
Control system of a mini hydraulic press for evaluating springback in sheet metal forming P. Sun, J.J. Gr´acio ∗ , J.A. Ferreira Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Received 13 April 2005; received in revised form 8 February 2006; accepted 8 February 2006
Abstract The paper proposes a method of evaluating springback that occurs after unloading during sheet metal forming of a control system. A linear displacement occurring by springback of the components formed is used as the reference value of springback to evaluate actual springback, and displayed on the control interface in real time. The proposed method is based on measurements performed during closed loop controlled stamping operations. To perform the close-loop control of the hydraulic press two pressure sensors are installed in the cylinder chambers and a position sensor (optical scale with a resolution of 1 m) is installed on slip rod of punch. Both control and monitoring software run on a real-time hardware board that is directly programmed through the Matlab/Simulink environment. The data of the hydraulic force and punch position, as also the springback effects, can be shown on the control/monitoring interface in real time during stamping process. For the work, an experimental example is used to build and test the control system on a mini-press (I), and a linear model was provided to test the strategy to control the punch position and/or force. Hardware-in-the-loop simulation techniques are also used in experiments to verify the control of overall system. System models possess the characteristics of less computing power and adjusting parameters easily. The punch position can be controlled with high precision in a moving travel of 200 mm. The purpose of the work is to offer an effective way for evaluating springback in real time during sheet metal forming. © 2006 Elsevier B.V. All rights reserved. Keywords: Springback; Sheet metal forming; Evaluation; Control system
1. Introduction Springback is a common phenomenon in sheet metal forming, caused by the elastic recovery of the internal residual stresses during unloading. Although fundamental theoretical analyses have been developed to quantify the springback behaviour, their application to sheet metal forming processes is limited since discrepancies are often observed when the theoretical predictions are compared with the measured data. This has led to the development of various empirical equations, suited to the particular forming process examined. The lack of agreement between the theories and practical observations arises mainly from the variation of the material properties, and the complexity and peculiarity of the individual forming process, which lead to an uncertainty of the forming parameters (such as the tension induced during forming and die conformity) [1]. At present, there have been much effort to evaluate or decrease springback. Work of applying finite element method to ∗
Corresponding author. Tel.: +351 34 370 827; fax: +351 34 370 953. E-mail address: [email protected] (J.J. Gr´acio).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.02.009
analyze sheet stamping processes, carried out by Wang, Budiansky (cited in reference Key et al. [2]). Morestin et al. [3] predicted springback in deep drawing processes taking account of the nonlinear kinematic hardening of the material. Along with the rapid progress of computing environments, a range of numerical methods for predicting springback in sheet metal forming has recently developed [4]. Most finite element simulation of sheet metal forming have focused on the prediction of the part springback during sheet metal forming processes, and such efforts typically involve the use of 2D models [5,6]. However, in the literature, few papers deal with evaluating the springback during stamping processes in real time. Therefore, it is necessary that study of evaluating the actual springback during stamping in real time. In the present research, is a real-time control method proposed for the springback that occurs after unloading during sheet metal forming. A linear displacement occurring by springback of the formed workpieces is used as the reference value of springback to evaluate actual springback. The reference value of springback is calculated by knowing the thickness of the workpiece and the position change of punch (hs ), and displayed on the control interface in real time. The results from the real-time
56
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
feedback control of the force or velocity/position of the tools are attached to the hydraulic press. The method is a practical method of evaluating springback in stamping process. To perform close-loop control of the hydraulic press, two pressure sensors are installed in the cylinder chambers and a position sensor (optical scale with a resolution of 1 m) is installed on slip of punch rod. The control and monitoring software run on a realtime hardware board that is directly programmed through the Matlab/Simulink environment. The hydraulic force and punch position data, as also the springback effects, can be shown on control/monitoring interface in real time during stamping process. For the work, an experimental example is use to test the control system on a mini-press (I), and a linear model was developed, and a linear model was provided to test the strategy of position and force control of draw punch. The models of the cylinder and control valve as well as the springback mechanism in the device were described. The technique of hardware-inthe-loop simulation based on MATLAB® /Simulink® is used in experiments to verify the control process of overall system. System models possess the characteristics of less computing power and adjusting parameters easily. The position can be controlled with high precision in a moving travel of 200 mm. Results of closed loop model simulation are compared to real test data. 2. Springback behaviour Industrial applications like deep drawing, blanking processes, and bending are all characterized by localized plastic deformations. But elastic recovery that, occurs after unloading, always exists in stamping process. Springback occurs with all types of forming by bending, when bending in presses, folding, roll forming, and roll bending. As a result of springback, the bending die angle α1 does not correspond precisely to the angle desired at the workpeice α2 (Fig. 1). The angle ratio is so-called springback factor κR , which depends on the material characteristics and the ratio between the bending radius and sheet metal thickness: κR =
α2 r1 + 0.5t = α1 r2 + 0.5t
Fig. 2. Springback phenomenon in productions.
inside radius at the die [mm], r2 the inside radius at the workpiece [mm], and t is sheet metal thickness [mm] [7]. Factors that affect springback include variations in both material and process parameters [8], such as material properties, sheet thickness, friction condition, binder force, tooling geometry, and lubricant condition. In addition, element type, mesh density, and material model in FEM simulation could have significant influence on springback prediction. Fig. 2 is springback phenomenon in actual production. Analysis has indicated that, springback in sheet metal forming can be reduced by changing clamping condition and material properties, but cannot be completely eliminated due to the existence of residual stresses generated in forming. Then, how accurately calculating, controlling and showing the springback of the formed workpieces has become one of focus problems to designers and manufacturers in sheet forming field. 3. The method of evaluating springback 3.1. Control method description
(1)
where α1 is angle at the die (required bending angle) [◦ ], α2 the desired angle at the workpiece (after sprigback) [◦ ], r1 the
Fig. 1. Elastic recovery after bending. t, sheet metal thickness; α1 , required bending angle; α2 , desired angle; r1 , inside radius of die; r2 , inside radius of workpiece.
The method is a practical one for evaluating springback in stamping process, and results from the real-time feedback control of the force or velocity/position of the tools attached to the hydraulic press. To perform close-loop control of the hydraulic press two pressure sensors are installed in the cylinder chambers and a position sensor (optical scale with a resolution of 1 m) is installed on slip rod of punch. The control and monitoring software run on a real-time hardware board that is directly programmed through the Matlab/Simulink environment. The hydraulic force and punch position data, as also the springback effects, can be shown on control/monitoring interface in real time during stamping process. A linear displacement occurring by springback of the formed workpieces is used as the reference value of springback (δ) (see Fig. 3). The reference value of springback is calculated, by knowing the thickness of the workpiece and the position change of punch (hs ) under the action of the springback force, and displayed on the control interface in real time.
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
57
Fig. 3. Schematic diagram of a stamping process.
A schematic diagram of a stamping process is shown in Fig. 3, where δ is a linear displacement occurring by springback and is defined as the reference value of springback, t the thickness of workpiece, and hs displayed on the control interface in real time is a position change of punch. After punch finishes drawing, adjusting the hydraulic pressure (P1 and P2 ) of cylinder chambers makes the punch move up slowly until the formed workpiece finishes elastic recovery. In that case, the formed workpiece will generate a displacement, and position change of punch, hs , can be considered as a change occurring under only the action of the springback force FS (Figs. 6 and 7). The hs can accurately be measured through the experimental interface of control system, as shown in Fig. 4. The reference value of springback (δ) can be estimate according as relation of hs on control interface. The real-time measurement of the springback can lead to enhance the control strategies by adapting the controller parameters and improving the reference trajectories for the punch position or force. These data (controller parameters and optimal reference trajectories) can be used as a database for duly regulating the size of the die. 3.2. Principle analysis In stamping, the process of sheet forming starts with the loading then the drawing and ends with the unloading operation (Fig. 5). Springback angle of the formed workpiece will lead to
Fig. 6. Diagram of punch position in sheet metal drawing.
a dimension error (a linear displacement) along drawing direction after unloading. Therefore, the dimension error can also reflect the change grade of springback size. The hydraulic press will be equipped with a set of sensors to measure the system pressures and piston position. The actuation force is measured indirectly through two pressure sensors installed on the cylinder chambers. The work cylinder rod position is acquired with an optical scale with 1 m of resolution. The velocity was obtained by differentiation of the position signal. All inputs of the sensors and the electrical valves are connected to a low cost DSP based real-time card (model DS1102) from dSPACE® , in such a way that real-time control and acquisition can be performed. During stamping process the hydraulic force and punch from sensors can be shown on control interface in real time. The process can be divided in three steps: the first step (see Fig. 6) is the drawing phase and punch position is h0 (equal to the sheet thickness, t). In the second step, adjusting the hydraulic pressure (P1 and P2 ) of cylinder chambers makes the punch move up slowly until the formed workpiece finishes elastic recovery. In that case, the formed workpiece will generate a displacement,
Fig. 4. (a and b) The display component of punch position in two kinds of control interface.
Fig. 5. Process of sheet metal forming.
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and position change of punch, hs , can be considered as a change occurring under only the action of the springback force FS (see Fig. 7). And the punch position will be accurately measured in real time. According to these measurements (and also the chamber pressure data), the springback force FS can be estimated, if the dynamic behaviour of the cylinder and proportional valve is known. Relationship between FP and P1 is FP = P1 A1 − P2 A2
(2)
When FP = Fg + Ff − FS
(3)
Punch position is given by hs = t + δ
(4)
Fig. 8. Diagram of punch position after unloading.
The reference value of springback (δ) is expressed as δ = hs − h0
(5)
where P1 , P2 are the pressure inside the cylinder chambers; A1 , A2 , the cylinder chambers areas; t, the sheet thickness; h0 and hs , punch position. Fg , Ff are gravitation of punch and friction of cylinder seal (which can calculate through total mass of punch and friction coefficient of seal). The pressure P1 value can operate on control interface expediently. The third step is adequately unloading process, as shown in Fig. 8. FP > Fg + Ff , punch departs from workpiece and move to h position. The third step does not have relations withspringback. In actual operation, setting an allowable reference value of springback (ε) to compare with actual reference value of springback (δ). When δ < ε, i.e., hs < ε + t
(6)
Springback of formed workpieces suffices precision requirement. When hs > ε + t
(7)
springback is out of tolerance, die size need to be adjust.
Fig. 7. Punch position with springback force.
Thus, the method proposed can inspect springback grade during sheet metal forming in real time. Note that loading and unloading of blank holder (force FN ) is operated independently. 4. Experimental device and experiments 4.1. Experimental device First a hydraulic mini-press (I) with a 200 mm working travel for the punch was built (see Fig. 9). The correct and convenient control system was built in order to test precision of punch position during stamping process. The mini-press (I) is actuated by a hydraulic servo-cylinder driven by a high performance servo-solenoid valve (Fig. 10). The hydraulic force is indirectly measured through two pressure sensors installed in the cylinder chambers. The piston position is measured through an optical scale with a resolution of 1 m and its acceleration is monitored with an accelerometer. The mini-press (I) allows compression, tensile or both types of solicitation. The compression capacity is useful to simulate the approach and work tasks, and the tensile capacity to simulate the backward movement (Table 1). To evaluate the control performance, springback mechanism is replaced by a shock absorber in the experimental device in order to represent the springback behaviour of formed workpieces in stamping. This is an initial approach to represent the elastic recover of material in a typical stamping task. Hydraulic circuit and control system of experiment prototype can be addressed by Fig. 11. A variable volume axial piston pump coupled to a pressure accumulator with a 5 l capacity provide the hydraulic power at a constant pressure. To reduce the development time hardware-in-the-loop simulation experiments were performed with a linear model of the press, in order to test and optimize the control algorithms to control punch position and/or force.
Fig. 9. Schematics of the hydraulic mini-press (I).
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
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Fig. 11. Hydraulic circuit and control system diagram of experiment prototype.
where ap = dvp /dt is the piston acceleration and M is the total mass in motion (load, piston, rod). The absorber characteristics measured in [9] are:
Fig. 10. The hydraulic mini-press (I) in experiment.
K = 1.75 N m−1 ,
4.2. Experiment and simulation
B = 400 N s m−1
The other values used in the linear model for simulation purposes are:
4.2.1. Modelling To test the force and position control, a hydraulic servo system (proportional valve, linear actuator) is modelled. Fig. 12 shows the diagram of the control valve and hydraulic cylinder as well as the springback mechanism used in the tests. The linear model was used to perform hardware-in-the-loop simulation experiments as a base to test different control strategies without the associated dangerous when testing a controller directly on real hydraulic hardware. The overall performance of the linear model was satisfactory for the test bed of set-up. The dynamic behaviour of the linear model, being satisfactory for the test platform, needs to be upgraded with some non-linear effects, like the friction in the cylinder seals or the non-linear valve behaviour, to be used in the evaluation of different control algorithms. The model of the hydraulic cylinder was created by an engineering analysis of the actual hydraulic cylinder and valve. The piston velocity is vp = dxp /dt, and the cylinder dynamics is defined as: M · ap = P1 A1 − P2 A2 − K · xp − B · vp
V1 = 1.05 × 10−4 m3 , A2 = 8.765 × 10−4 m2 ,
V2 = 1.72 × 10−4 m3 , M = 5 kg,
A1 = 1.257 × 10−3 m2 ,
β = 8.5 × 108 Pa.
(8)
Table 1 Components of hydraulic mini-press (I) Nome
Type
Servo-cylinder Servo-valve Pressure sensor Optical scale Real time card Acceleration sensor Computer
KBSDG4V-3 P15RVA1 Resolution of 1 m DS1102 FA201 Fig. 12. Work state diagram of the mini-press (I) and dynamic model of springback mechanism.
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P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61
Fig. 14. Comparison between real and simulation results.
Fig. 13. Diagram for the hardware-in-the-loop simulation experiments. The linearized valve and cylinder equations is defined as:
⎡
⎤
⎡
⎢ ⎢ ⎢ p˙ 2 ⎥ ⎢ ⎢ ⎥=⎢ ⎣ v˙ p ⎦ ⎢ ⎢ ⎣ x˙ p p˙ 1
−
βe Kc V1 0 A1 M 0
βe A1 V1 βe A2 V2 B − M 1
−
0 βe − Kc V2 A2 − M 0
⎡ βe ⎤ Kq 0 ⎢ V1 ⎥ ⎢ βe ⎥ xs − K 0 ⎢ ⎥· +⎢ V q ⎥ g 2 ⎣ 0 1⎦ 0
⎡
⎤
⎤
⎡ ⎤ ⎥ p1 ⎥ ⎢ ⎥ 0 ⎥ ⎥ · ⎢ p2 ⎥ ⎥ ⎣ vp ⎦ K ⎥ − ⎦ xp M 0
Fig. 15. Results of controlling the piston position with a PD controller both in real and HILS experiments.
0
(9)
0
⎡
⎤
⎡
p1
A ControlDesk application was developed in order to change the parameters of the controllers. The ControlDesk software tool is provided by dSPACE to build experimental interfaces. It is well suited for data acquisition, and set-up of Graphical User Interface (GUI) is intuitive and simple. It is also possible, to change of the reference signals in real time. The experimental data can be stored for post-processing in Matlab® framework.
⎤
p1 1 0 0 0 ⎢ ⎥ ⎣ p2 ⎦ = ⎣ 0 1 0 0 ⎦ · ⎢ p2 ⎥ ⎣ ⎦ xp
0
0
0
1
vp
xp
The measured valve parameters for a work pressure of 70 × 105 Pa were [10] Kq = 4.8 × 10−4 m3 s−1 and Kc = 4 × 10−12 m3 s−1 Pa−1 . 4.2.2. Experiment and results The control and simulation platform is based on two real-time hardware cards (model DS1102) from dSPACE® . The base cards of the DSP are programmed by the Matlab® and Simulink® platforms. The position/force hybrid structure for the controller is implemented in one card, the force gain (Gf ) and the position gain (Gp ) will allow the definition of the contribution in the position and force controllers for the control signal applied to the proportional valve. The control of position, velocity and force is based on a proportional and derivative controller (PD). Fig. 13 shows the platform used to perform hardware-in-the-loop simulation experiments with the linear model of the mini-press. Hardware-in-the-loop simulation [11] refers to a technology where some of the components of a pure simulation are replaced with actual hardware.
Fig. 16. (a and b) Experiment device (II) and stamping tools.
P. Sun et al. / Journal of Materials Processing Technology 176 (2006) 55–61 To evaluate the linear model performance, a sequence of experiments was performed with different reference signals (shape, amplitude, and frequency). Figs. 14 and 15 present the results of controlling the real-time simulation and the control of the real mini-press (I) [12]. The reference position signal is a square wave, both systems were controlled by a proportional plus derivative controller with the proportional constant equal to 25 and with a unitary derivative gain. The experimental results for control of real mini-press (I) show good agreement with the simulation (Fig. 15). Hydraulic mini-press (II), second experiment device is designed (see Fig. 16(a and b)). It is similar to an actual hydraulic press, and will is used to carry out forming experiment for testing and analyzing the reference value of springback.
5. Conclusions The method of evaluating springback in sheet metal forming in real time on a hydraulic press was proposed in the present work. Springback behaviour of the formed workpiece after unloading during stamping is described. A real prototype and a linear model of the mini-press (I) were developed. The linear model was used to perform hardware-in-the-loop simulation (HILS) experiments as a base to test different control strategies without the associated dangerous when testing controllers directly on real hydraulic hardware. The method proposed can become a useful way for improving efficiency and quality of production in sheet metal forming through next technologic integrity. The new press system will be instrumented and used to perform the final experimental work. Acknowledgement The authors gratefully acknowledge that the Portuguese Foundation of Science and Technology (FCT) give grand support to this study.
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