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Research Papers

Multi-Input Multi-Output (MIMO) Modeling and Control for Stamping

[+] Author and Article Information
Yongseob Lim1

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125limys@umich.edu

Ravinder Venugopal

 Intellicass Inc., 1804 rue Tupper, Suite 4, Montréal, QC H3H 1N4, Canada

A. Galip Ulsoy

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(4), 041004 (Jun 16, 2010) (12 pages) doi:10.1115/1.4001332 History: Received December 17, 2008; Revised February 12, 2010; Published June 16, 2010; Online June 16, 2010

The binder force in sheet metal forming controls the material flow into the die cavity. Maintaining precise material flow characteristics is crucial for producing a high-quality stamped part. Process control can be used to adjust the binder force based on tracking of a reference punch force trajectory to improve part quality and consistency. The purpose of this paper is to present a systematic approach to the design and implementation of a suitable multi-input multi-output (MIMO) process controller. An appropriate process model structure for the purpose of controller design for the sheet metal forming process is presented and the parameter estimation for this model is accomplished using system identification methods. This paper is based on original experiments performed with a new variable blank holder force (or variable binder force) system that includes 12 hydraulic actuators to control the binder force. Experimental results from a complex-geometry part show that the MIMO process controller designed through simulation is effective.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of a sheet metal forming process

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Figure 2

Problems of part quality in the sheet metal forming process: (a) wrinkling, (b) tearing, and (c) spring-back

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Figure 3

Process control of sheet metal forming

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Figure 4

Experimental system: (a) test die with actuators and sensors, (b) a stamped part showing locations of process variables, or top-view of (a)

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Figure 5

Commanded blank holder force trajectories (i.e., Fb1) for a hydraulic actuator shown Fig. 4

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Figure 6

Experimental punch force trajectories based on three different types of blank holder force at four locations: (a) Fp1, (b) Fp2, (c) Fp3, and (d) Fp4

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Figure 7

Model for a simple stamping process: (a) schematic and (b) lumped models

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Figure 8

Qualitative validation of the control-design model structure through experiments via comparison to Eq. 6 of a change in binder force and the resulting punch force response

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Figure 9

Schematic diagram of process model for estimation (Ts=0.002 s).

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Figure 10

Estimated MC models obtained by N4SID and Least-squares algorithm: (a) Fb7, (b) Fb8, (c) Fb9, and (d) estimated MC models

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Figure 11

Estimated fourth order perturbation model based on experimental data: (a) δFp1, (b) δFp2, (c) δFp3, and (d) δFp4

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Figure 12

Validation results with estimated fourth order perturbation model based on experimental data: (a) δFp1, (b) δFp2, (c) δFp3, and (d) δFp4

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Figure 13

The punch force differences between lubricated and nonlubricated conditions with the same binder forces

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Figure 14

Block diagram of SIMO PI control system (e.g., Kp∊R3×1, Ki∊R3×1, and Gp∊R1×3) at each corner of the press/die

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Figure 15

Frequency response analysis based on the PI control gains for the punch force (i.e., Fp1)

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Figure 16

Simulation results with step input for the punch force 1 (i.e., Fp1): (a) output 1, (b) input 1, (c) input 2, and (d) input 3

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Figure 17

Simulation results of punch force as output tracking reference punch force: (a) Fp1, (b) Fp2, (c) Fp3, and (d) Fp4

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Figure 18

Comparison of three binder forces for the punch force (i.e., Fp1 shown in Fig. 1) between experiment and simulation

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Figure 19

Experimental results of punch force tracking reference punch force with initially commanded high constant binder force (i.e., 16 tons): (a) Fp1, (b) Fp2, (c) Fp3, and (d) Fp4

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Figure 20

Improved part quality comparisons: (a) wrinkling problem with constant 8 ton binder force, without PC; (b) tearing problem with constant 16 ton binder force, without PC; and (c) improved part, with PC for complex part geometry (i.e., double-door panel)

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