On-Line Thinning Measurement in the Deep Drawing Process

Transcription

1 Moshe Berger Eyal Zussman* Department of Mechanical Engineering, Technion Israel Institute of Technology Haifa 3000, Israel On-Line Thinning Measurement in the Deep Drawing Process The conventional deep drawing process is limited to a certain Limit Drawing Ratio (LDR), beyond which localized wall thinning and rupture occur. One way to increase the LDR is to try to capture the onset of necking and to adjust process parameters in order to delay or avoid necking. This paper describes a method for monitoring the wall thickness of a cup during the deep drawing process. Measurement utilizes a noncontact ultrasound gauge that is located orthogonally to the drawn cup s wall and is immersed in oil to create an acoustic coupling. Monitoring is based upon a deep drawing process model using a thin blank with a round cross-section. Thickness distribution along a longitudinal axis is predicted and is used as a trajectory to track in-process thinning variations that may lead to tearing. The robustness of the measurement system is examined by applying the technique in different experiments. Results show that in-process measurements correlate well with grid strain analysis of a formed sheet metal part. DOI: / Introduction *To whom all correspondence should be addressed. Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received Aug. 000; Revised July 001. Associate Editor: R. Smelser. The conventional deep drawing process is limited to a certain Limit Drawing Ratio LDR, beyond which rupture occurs. Consistent prediction of the LDR is difficult because of variations in forming conditions such as variations in material properties, tooling conditions, lubrication methods and blank dimensions. These variations alter the regions of tearing and buckling and affect operational process parameters, thereby leading to complex control problems 1. The current industrial practice for any given final part depth and forming conditions is to define a range of safe control parameters that avoids part failure. For example, when a force control approach is adopted, a safe blank-holder force range is defined in order to avoid tearing or wrinkling. Ideally, the safe range of forces can be shrunken by dynamically adapting the force bounds to product conditions during process execution. Nevertheless, the problem remains How to obtain in-vivo information regarding product conditions. More practically, the problem boils down to What can be measured? and How can it be measured? so that we can establish the correct operational parameters. The goal of this research is to construct a method that continuously adjusts the operational parameters during the forming cycle in order to eliminate part failure arising from sheet instability. Specifically, in this paper we suggest performing direct measurement of the strains along the drawn part s wall in order to avoid the eventual occurrence of plastic instability as may be demonstrated by localized wall thinning and rupture. There are several ways to monitor plastic flow in the deep drawing process they can be classified as being either direct or indirect measurements of incipient failure. Siegert et al. and Ahmetoglu et al. 3 proposed measuring the blank holder force trajectory, or the punch force trajectory. Siegert et al. and Lo and Jeng 4 proposed measuring the blank displacement. Direct force measurement along the die radius was suggested by Kernosky et al. 5, who developed a special die shoulder force transducer. Fenn and Hardt 6 developed a buckling transducer for the forming process that provides information directly from the unsupported region. The sensor relies on deflection of a ring located on the circumference of the cup and an arrangement of photocells and illuminators which together serve to provide a measurement for global buckling. In this paper, we propose a specially designed, direct measurement technique to quickly and accurately detect incipient failure. The proposed measurement is based on an ultrasonic transducer located below the die that can provide in-vivo measurement of cup thickness. The objectives of this paper are as follows: To derive a model to determine the drawn cup wall thickness trajectory To describe the ultrasonic-based procedure to measure the cup wall thickness during process execution To demonstrate the accuracy of the above process by means of measurement simulations and experiments. Background In a typical deep drawing operation Fig. 1, a thin circular blank of initial radius R 0 and thickness t 0 is held between a blank holder and a die. When a cylindrical punch moves down at velocity U 0, the material under the blank holder is drawn, and deformed into a cup shape with radius R d. The deep drawing process is limited to a certain LDR which marks the maximum allowable drawing ratio R 0 /R d before rupture. Rupture is usually manifested by strain localization followed by disintegration 7. A closer look at the evolution of the drawn cup reveals two major phases: embossing and drawing. Once the embossing phase has been completed the drawing process begins in which the blank is bent and compressed over the die radius, then straightened and pulled down to form a vertical cylinder. For purposes of predicting strain distribution and deformation regimes in the drawing process, we have adopted an upper bound analysis which provides us with an analytic solution 8. Numerical solutions of the strain distribution in the drawing process have been reported by Harpell et al. 9 and by Cao and Boyce 10. In order to fulfill the upper bound conditions, namely an admissible and continuous velocity field, the workpiece is divided into five geometrical zones surrounding the punch and along the die see Fig.. In the first zone Zone I the thickness t(r) is assumed to be a function of the initial position (r 0 ) of a point in the blank see Appendix I. tr ln r 0 r C t 1t 0 (1) where: r 0 R 0 R c r is the initial location of a point in the material. 40 Õ Vol. 14, MAY 00 Copyright 00 by ASME Transactions of the ASME

2 Fig. 1 Schematic of sheet metal deep drawing Fig. 4 The measurement configuration R c h R 0 x d x p x d d t 0 x p p t 1/ 0 R p R d h Hence, a material element with maximal thickness is the one that starts the process at position rr 0 and reaches its maximal thickness at the end of Zone I, where rx d. In Zone II, the workpiece thickness does not change since there is no velocity along the thickness direction. Nevertheless, thickness changes in Zone I are taken into account. Therefore, the thickness of the workpiece at the end of Zone II, t, is a function of the punch position, h, and t(x d ); tx d d t tx d d () x d d The regions of the cup wrapped around the punch face and fillet, Zones III, IV and V, respectively, are subject to tensile stresses under resisting frictional forces. Once the flow stress is exceeded, these zones are stretched, and the region around the punch fillet slides over it to cause a thinning of Zone III. Hence, in the compressed zone Zone I, the blank tends to thicken, as the zones in the tensile regime Zone III, IV, and V tend to thin. Therefore, in monitoring the wall in order to avoid eventual plastic instability, Fig. The admissible wall thickness from which the admissible velocity field was driven one should check those zones that are most prone to thinning as well as those that are non-work-hardened, especially above the punch fillet. The in-plane strains in this region determine the height at failure and are closely related to the thickness strain of the material when incompressibility is assumed. An experimental observation of a manufactured cup s thickness is shown in Fig. 3 to demonstrate thickness distribution within the different cup zones. It is observed that the critical strain where the material is thinnest is above the punch fillet. Starting at this point, the thickness changes linearly all along Zone III positions Assuming that the thickness above the punch fillet at the end of Zone III is t 0, and the thickness along Zone III changes linearly, the expected thickness in Zone III is: t III tx d H tx dt 0 (3) H p d This function is subsequently used as a predictive model in monitoring the thickness distribution along the cup wall. 3 Measuring Approach The proposed measuring approach utilizes an ultrasonic sensor positioned against the cup wall see Fig. 4. Pulsed ultrasonic waves are generated at a repetition rate up to 5 MHz, and the reflected waves are continuously measured and processed. An oil layer is situated between the sensor and the sheet metal and used as an acoustic coupling medium. Transmitted longitudinal waves travel through the oil and impinge upon the sheet metal. Part of the sound energy is reflected and the rest is transmitted. The transmitted part travels through the sheet metal and impinges upon the interface of the sheet metal and the punch. At this point, part of it is again reflected and the rest is transmitted, where the ratio between the reflected and transmitted parts is determined by surface rigidity. The time difference between the first and second echoes can be correlated with cup thickness. As a one-dimensional problem see Fig. 5, ultrasonic wave propagation can be described by a reduced wave equation: u t c u x (4) Fig. 3 Experimental results of the thickness distribution along a longitudinal axis of a drawn cup, drawing ratioä. The blank is made of copper t 0 Ä0.5 mm, CÄ430 kgõmm, nä0.31. Journal of Manufacturing Science and Engineering MAY 00, Vol. 14 Õ 41

3 Fig. 5 Areas of the measurement configuration Boundary conditions in this case can be described for the sensor, the sheet metal and the punch. For the sensor during the 0 : ua 0 level of signal Assuming that the sensor behaves as a rigid body compared to the oil, whenever there is no transmission, the acoustic displacement on the 0 : u0 The acoustical pressure on the punch interface at the far side of the sheet metal, is zero, assuming that acoustical resistance is maximal due to a minimal air gap a resilient interface. Hence, the respective boundary condition du metal dx metal 0, where metal E du metal dx metal In the interface between the sheet metal and the oil, stresses and displacements are equal. Hence, the boundary condition K du Oil dx Oil E du metal dx u Oil u metal where Oil K du Oil dx Oil Given Eq. 4 and the respective boundary conditions, wave displacement was simulated by using a finite difference scheme see Fig. 6. It should be noted that on crossing an interface from a material with acoustic impedance z 1 to a material with acoustic impedance z, the transmitted wave maintains its displacement direction and the reflected wave maintains its displacement direction if z z 1, but changes its direction if z z When the propagated wave reaches a resilient media, similar to an air layer, the wave is totally reflected along the x-axis The elapsed time between the transmission and reception of the sound wave is directly proportional to the distance traveled. If the speed of the sound in the oil, c 0, is known, the distance of the sheet metal from the sensor can be found; dc 0 timeofflight (5) In case that viscosity effects are considered then the speed of sound in the oil, c 0, should be represented by a complex sound velocity 1. Upon moving from measuring the first echo to measuring the second echo, and using this to measure wall thickness, several considerations relating to signal quality and potential resolution arise. In particular, when a thin wall is measured the thickness of a thin wall is considered to be approximately 500 m and thickness deviations are in the range of 50 m, a high frequency sensor or a small wave number (c/ f ) must be used in order to avoid interference of the first and second echoes. As can be seen in Fig. 6, lowering the sensor pulse frequency will shrink the gap between the echoes and will create interference between them. For example, when copper or magnesium AZ31 based materials are drawn, the desired sensors used to measure the wall thickness should have a pulse frequency greater than 15 MHz in order to achieve a reasonable resolution. However, even though a higher Fig. 6 Wave displacement along the time axis. The sensor is located in xä0, wave displacement is observed at a distance of sä3 mm 100 time unit from the sensor, oil layer length is 3 "d, where d is the wall thickness. C-S: wave propagates from the cup to the sensor. S-C: wave propagates from the sensor to the cup. frequency would allow a more accurate measurement to be made, higher frequencies are attenuated dramatically 1. Since our goal is to measure the thickness variation with good resolution, it can be shown that the thickness can be correlated to the echo amplitude. In the event there is interference from several echoes, the thickness can be correlated to the amplitude of the envelope obtained. Recalling that the pressure of the ultrasonic of the transmitted and received waves, P 1, and P at the oil and the sheet metal respectively are see Fig. 7; P 1 A 1 e jtk 1 x B 1 e jtk 1 x ; P A e jtk x B e jtk x ; The wave velocity can be derived from the complex pressure by differentiation 1: V i j P i k i i c i x Then, the respective velocity can be determined, Fig. 7 Wave characterization in the measurement setup (6) 4 Õ Vol. 14, MAY 00 Transactions of the ASME

4 V i 1 A i c i e jtk 1 x B i e jtk 1 x (7) i The respective boundary conditions P P 1 P, V 1 V Substituting the boundary condition results in the reflected amplitude, i.e., the pressure amplitude that the sensor receives, we get; R 1 A 1 Z 11Z 1 (8) B 1 Z 1Z 1 1 Where: e jk d Z i i c i k c const Hence, the reflection amplitude depends on the sheet metal width, d, R 1 R 1 (d), a feature that can be used to measure thickness. Practically, in real time application, the maximum signal level can be extracted relatively quickly by comparing it to a threshold related to the thickness. This technique is applied below. The calibration process will first be is described, and then experiments results will be presented. 4 Experimental Results In all of the work presented here, a simple axisymmetric conical cup was used. To perform the experiments described below, a press with variable blank holder displacement was used see Fig. 8. The press is equipped with an LVDT to measure the punch displacement. An ultrasonic sensor is located below the die lip and immersed in an oil chamber. The pressure in the oil chamber is regulated throughout the drawing process by a unidirectional valve. Drawing speed was around U 0 1 mm/sec. The material used was copper C430 kg/mm, n0.31, where the initial blank thickness was t mm, with a radius of R 0 7 mm. The punch radius was R p 36 mm, the radius of the punch nose p 5 mm, and the radius of the die lip, d 5.5 mm. Low friction was achieved by using a lubricant type SAE 0. The ultrasonic sensor was connected to a general purpose pulser/receiver card which was PC-embedded. The card functions are integrated into the PC-based press controller and enabled one to close a control loop with a 0 Hz sampling rate. Before the experiments for in-process measurements were begun, a calibration process was carried out. Calibration tests were conducted using flat copper sheet which was immersed in an oil Fig. 9 Envelope of the reflected signal for different sample thicknesses copper t 0 Ä0.38, 0.44, 0.5, 0.53 mm chamber located in a special jig orthogonal to the sensor. The surface roughness of the samples was in the range of R a m. The oil temperature was 5 C degrees. The sample thickness was measured first by a micrometer and then by an ultrasonic sensor with a frequency of MHz. The envelope positive value of the reflected signal, including the transmitted signal echoes, is presented in Fig. 9. The thickness of the sample can be characterized either by the amplitude level of the reflected signal or by the time of arrival. However, the most repeatable and easily recognized feature is the level of the reflected signal. Given the set of maximum levels of the reflected signals, a calibration graph can be generated which correlates the thickness with the maximal signal level see Fig. 10. The graph shows a linear relationship between the thickness and the reflected signal. An additional set of measurements was recorded with an ultrasonic sensor with frequency of 5 MHz. Again, a linear relation was obtained between the signal level and the sample thickness. In the first set of experiments, pre-formed drawing ratio drawn cups were measured. Given a drawn cup attached to the punch, the punch was moved backward and forward while its thickness was continuously measured along a longitudinal curve of the cup in Zone III. Later, the cup was removed and measured by strain grid analysis grid dimension 1.7 mm and also by a micrometer. All measurements were carried out along the same longitudinal curve. The correlation between the measurements was high, and the maximum difference of 1.5 percent was repeatedly obtained. The measurement results are displayed in Fig. 11. The in-process experimental results are shown in Fig. 1. The curves present thickness as a function of punch displacement, which is sensed on-line by a stationary sensor. In addition, a trajectory of the thickness based on Eq. 3 is depicted. In general, the trend of the measured thickness trajectory is towards thinning at the beginning of the motion followed by thickening. This trend confirms the predictive model, and indeed deviations from the Fig. 8 Deep drawing experimental setup Fig. 10 Calibration graph relating the maximum level of the reflected signal with the sample thickness copper. The graph presents the combined data using two sensors set at and 5 MHz frequencies. Journal of Manufacturing Science and Engineering MAY 00, Vol. 14 Õ 43

5 5 Summary The development effort described in this paper has yielded a novel measurement technique for the inspection and control of drawn cup wall thickness during process execution. The measurement technique employs a noncontact ultrasonic-based gauge. Repeat studies show that the measurement accuracy already meets accepted standards. The thickness trajectory of the drawn cup wall has been determined based on an upper bound analysis. The study demonstrates that the calculated thickness trajectories conform well to experimental results. The accuracy of the proposed measurement system demonstrates its potential use as a feedback mechanism in a control system that can adapt operational parameters to product conditions. In principle, whenever the onset of necking is detected, process parameters can be adapted to product conditions in order to enlarge the critical strain 13. Further research is attempting to develop a multi-probe measurement system that will be located on the circumference of the drawn cup wall, or swept across the critical region of a sheet during deep drawing. This will also be appropriate solution for complex geometries. Fig. 11 Thickness trajectory of a manufactured part. Three measurement methods are compared: an ultrasonic sensor based on maximum amplitude, a micrometer, and a strain grid analysis. Fig. 1 Thickness trajectory of the predicted model CtÄ0.1 and in-process measurements of two groups of results labeled as Cup#1, and Cup#, Drawing ratioä. predicted model are at most 6 percent at the end of the stroke. It is believed that this difference can be attributed to the fact that the model i.e., Eq. 1 provides an upper bound on the forces of the process. Nevertheless, there is a single degree of freedom in the model, which in this case was selected as Ct0.1. Further investigation of how to select the optimal coefficient in the model would be of value. Measurement error analysis results show that the main source of inaccuracy in the proposed ultrasonic measurements is due to geometrical and dimensional tolerances in the press, assuming that all disturbances are stationary. Worst-case results illustrate that concentricity of the die and the punch is the most critical tolerance. In the worst case, based on the actual dimensions of the press copper blank, the reflected energy would be reduced by 7 percent. Such a reduction in reflected energy would cause the thickness to deviate by 5 nm. However, this deviation in thickness does not exceed the desired resolution. Acknowledgment This research was partially supported by the Israel Ministry of Science. The authors are indebted to Dr. J. Passi from Sonotron Ltd. for his ongoing support of the project. The authors also wish to thank Dr. L. Rubinski for her skillful contribution and assistance throughout the experimental phase. Nomenclature H current traveling distance of the punch R p punch radius R 0 outer radius of the blank R c instantaneous outer radius of the flange R d outer radius of the cup x d position of the center of the curvature of the flange/ cup transition Zone II d radius of the curvature of the flange/cup transition Zone II x p position of the center of the punch tip p radius of the punch tip h current distance between punch tip center and Zone II center r polar coordinates C t constant t 0 initial blank thickness u(x,t) ultrasonic wave displacement c wave velocity E Young s modulus C material strength coefficient P acoustic pressure effective stress U 0 punch velocity t(x) thickness of the sheet metal t sheet metal thickness in the end of Zone II toruidal angle K bulk modulus Z acoustic impedance Appendix I Assumptions: Constant90 degrees 0 degrees at the beginning of zone II 90 degrees at the end of zone II t(r) the thickness in Zone I; t(r)ln(r 0 /r)c t 1t 0 where: r 0 R 0 R c r the initial location of a point in the material. C t constant tt(x d ) the thickness at the end of Zone I. Radius of the blank rim 8: R c h R 0 x d x p x d d t 0 x p p t 1/ 0 R p R d h Radial velocity in Zone I; u ri U x d /rt(x d )/t(r) where U u II 0 44 Õ Vol. 14, MAY 00 Transactions of the ASME

6 In Zone II, the workpiece thickness doesn t changed no velocity along the thickness direction, nevertheless, the thickness change in Zone I is taken into account. u II U 0 sin x d sin x d sin t t d t The velocity at the end of Zone I beginning of Zone II: U u II 0;90 U 0 x d t x d t d t let t 0 t(x d ) then, and U u II 0;90 U 0 x d x d t tx d d tx d, u rirxd U x d r tx d tr U The velocity at the end of Zone II beginning of Zone III: Since t t then, u II 90;90 U 0 t t d t u II 90;90 U 0 d t Considering constant mass rate flow in Zone II then, u II 90;90 t u II 0;90 tx d U 0 d t t U 0 x d t tx d d tx d tx d Let d then, References x d 1 d t x d 1 d tx d x d t tx d tx d d x d t tx d d tx d d x d d 1 Siegert, K., Haussermann, M., Losch, B., and Rieger, R., 000, Recent Developments in Hydroforming Technology, J. Mater. Process. Technol., 98, pp Siegert, K., Dannenmann, E., Wagner, S., and Galaiko, A., 1995, Closed Loop Control System for Blank Holder Forces in Deep Drawing, CIRP Ann., 44, pp Ahmetoglu, M. A., Kinzel, G., and Altan, T., 1997, Forming of Aluminum Alloys-Application of Computer Simulations and Blank Holding Force Control, J. Mater. Process. Technol., 71, pp Lo, S-W, and Jeng, G-M, 1999, Monitoring the Displacement of a Blank in a Deep Drawing Process by Using a New Embedded-Type Sensor, Int. J. Adv. Manuf. Technol, 15, pp Kernosky, S. K., Weinmann, K. J., Michler, J. R., and Kashani, A. R., 1998, Development of a Die Shoulder Force Transducer for Sheet Metal Forming Research, ASME J. Manuf. Sci. Eng., 10, pp Fenn, R. C., and Hardt, D. E., 1993, Real Time Control of Sheet Stability During Forming, ASME J. Eng. Ind. 115, pp Tirosh, J., and Sayir, M., 1987, High Speed Deep Drawing of Hardening and Rate Sensitive Solids with Small Interfacial Friction, J. Mech. Phys. Solids, 35, pp Dejmal, I., Tirosh, J., and Shizizly, A., 00, On the Optimal Die Curvature in Deep Drawing Processes, International Journal of Mechanical Sciences in press. 9 Harpell, E. T., Worswick, M. J., Finn, M., Jain, M., and Martin, F., 000, Numerical Prediction of the Limiting Draw Ratio for Aluminum Alloy Sheet, J. Mater. Process. Technol., 100, pp Cao, J., and Boyce, M. C., 1997, A Predictive Tool for Delaying Wrinkling and Tearing Failures in Sheet Metal Forming, ASME J. Eng. Mater. Technol., 119, pp Graff, K. F., 1975, Wave Propagation in Elastic Solids, Clarendon, Oxford. 1 Skudrzyk, E., 1971, The Foundations of Acoustics Basic Mathematics and Basic Acoustics, Springer Verlag, Berlin. 13 Zussman, E., 000, Influence of Temperature and Strain Rate on Plastic Instability during Deep Drawing, Transactions of the North American Research Institution of SME, XXVIII, pp Journal of Manufacturing Science and Engineering MAY 00, Vol. 14 Õ 45