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TECHNICAL PAPERS

Model-Based Machining Force Control

[+] Author and Article Information
Robert G. Landers, A. Galip Ulsoy

  Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125

J. Dyn. Sys., Meas., Control 122(3), 521-527 (Oct 20, 1999) (7 pages) doi:10.1115/1.1286821 History: Received October 20, 1999
Copyright © 2000 by ASME
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Figures

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Block diagram of model-based machining force control system
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Stability borderline for machining force control system for static force process. Analysis (line) from Eq. (12) and simulations (circles). Parameters: FR=0.2 kN,f(0)=0.2 mm,α=0.5,θ=0.8705,b0=−0.9048,fmin=10−10 mm, and fmax=1.0 mm.
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Marginally stable force responses. In region α<α*<2α (top thick line with circles): FR=0.6 kN,f(0)=0.4 mm,α=0.5,θ=0.8705,b0=−0.9048,fmin =10−10 mm,fmax =1.0 mm,α*=0.5, and θ/θ*=21.02. Outside region α<α*<2α (bottom thin line with squares): FR=0.2 kN,f(0)=0.2 mm,α=0.5,θ=0.8705,b0=−0.9048,fmin=10−10 mm,fmax=1.0 mm,α*=0.3, and θ/θ*=22.73.
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Stability borderline for machining force control system for static force process. Analysis (line) from Eq. (12) outside of Region I and from Eq. (19) inside Region I. Simulations (circles). Parameters are given in Fig. 2.
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Stability borderline generated by linearization analysis (surface) and verified via simulations (spheres). Simulation parameters: FR=0.4 kN,f0=0.1 mm,α=0.7,θ=2.0,a=−0.8206,bl=−1.562, and b0=0.6413. The parameter A*=−0.6377.
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Stability borderline (linearization analysis-line, simulations-circles) for α*=0.6 and simulation parameters given in Fig. 5. The parameter A*=−0.6377.
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Schematic of experimental machining system and workpiece
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Force (circles) and feed (thick line) responses to step change in commanded feed (thin line) for static system. Force sample period is 0.08 s and feed sample period is 0.01 s.
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Force response (thick line) for static model-based force controller. Parameters: FR=0.285 kN (thin line), α*=0.63,θ*=1.0,f(0)=0.1 mm,fmin=10−4 mm,fmax=0.4 mm, and τc=0.4 s(b0=−8187).
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Stability borderline of model-based machining force control system for a static force process. Analysis (thick line), simulations (circles), and experiments (squares) for τc=0.8 s(b0=−0.9048). Analysis (thin line), simulations (triangles), and experiments (diamonds) for τc=1.6 s(b0=−0.9512). Experimental parameters: FR=0.285 kN,f(0)=0.2 mm,α=0.63,θ=0.76,fmin=10−4 mm, and fmax=0.4 mm.
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Force (circles) and feed (thick line) responses to step change in commanded feed (thin line) for first-order system. Force sample period is 0.08 s and feed sample period is 0.01 s.
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Force response (thick line) for first-order model-based force controller. Parameters: FR=0.285 kN (thin line), a*=−0.85,α*=0.63,θ*=1.0,f0=0.4 mm,fmin=10−4 mm,fmax=0.6 mm, and ωc=π rad/s and ζc=0.7071 (b1=−1.6480 and b0=0.7009).
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Stability borderline of model-based machining force control system for a first-order force process. Analysis (thick line), simulations (empty squares), and experiments (solid squares) for ωc=π rad/s. Analysis (medium line), simulations (empty circles), and experiments (solid circles) for ωc=2π rad/s. Analysis (thin line), simulations (empty triangles), and experiments (solid triangles) for ωc=4π rad/s. Experimental parameters: FR=0.285 kN,f0=0.2 mm,α=0.63,a=−0.85,θ=0.76,fmin=10−4 mm,fmax=0.6 mm, and ζc=0.7071.

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