Modeling and Analysis of Fixturing Dynamic Stability in Machining

Transcription

1 Modeling and Analysis of Fixturing Dynamic Stability in Machining Haiyan Deng, Ph.D. Candidate Precision Machining Research Consortium (PMRC) George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia, USA Advisor: Prof. Shreyes N. Melkote PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

2 Introduction Machining Fixture: Establish and maintain required position and orientation of a workpiece Directly affects operational safety and part quality Limitations of Previous Work: (Carr Lane Mfg Co., 1995) Majority ignores system dynamics, e.g., inertia, damping, material al removal effect No information available on experimental investigation of fixture- workpiece dynamics during machining No information available on optimization of fixture-workpiece dynamics PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

3 Objectives Establish a mathematical procedure to analyze dynamic stability of a fixtured workpiece in machining Model and investigate material removal effect on system dynamic behavior Optimize fixture design to achieve fixturing dynamic stability Quantify and synthesize dynamics-induced induced part quality errors Run machining experiments to validate and refine models PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

4 Stability Analysis Criteria Stable Unstable PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

5 Stability Analysis Procedure PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

6 Stability Modeling Minimize P, Q i P xi ( Q i i j, Q ) yi Subject to : + ( Q ( π a Π ) C ) ( P, F =, M = = F xi P P S y cj 2 2 i yi 2 i i µ P S i Q xi, Q yi ) Clamping Statics [ M ] q & v + [ M& ] q& + [ K] q = Q( t) Machining Dynamics Lift-off Fixturing Stability Macro-slip max{ t zi ( t)} ( t) = d ( t) ji max { [ k 2 2 i PMRC Industrial Advisory Board Meeting, Georgia xi xi Tech yi yi March S zi 14 & zi t 15, 26 ji ( t)] δ + [ k ji ( t)] µ [ k ( t) ]}

7 Simulation Example (1) Original Workpiece Final Part PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

8 Simulation Example (2) Force (N) Cutting Forces 2 Fz -2 Fy -4 Fx Tool position ( ) Displacements (µm or µrad) First Pass Last Pass Workpiece Motion vs. Spindle Speed β 1 γ z Spindle Speed (RPM) PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

9 Translational Displacement (µm) Translational Displacement (µm) 5 Simulation Example (3) First Pass Workpiece Translations Last.15 Pass time (sec) x y z x y z Last.15 Pass time (sec) β -3 γ PMRC Industrial Advisory Board Meeting, Georgia 1357 Tech March 14 & 15, time (sec) time (sec) Rotational Displacement (µrad) Rotational Displacement (µrad) First Pass Workpiece Rotations α β γ α

10 Simulation Example (4) Local Normal Displacement (µm) First Pass: Lift-off Check Lift-off Check (First Pass) First Pass: Contact Macro-slip Index Check Local Normal Displacement (µm) Last Pass: Lift-off Check Lift-off Check (Last Pass) Last Pass: Contact Macro-slip Index Check Excessive Friction Force (N) Macro-slip Check (First Pass) Contact Index FC 26 = [5261.3, PMRC Industrial , Contact Advisory Index 331.1] Board Meeting, (N) Georgia FC = Tech [1713.1, , March ] 14 & (N) 15, 26 Excessive Friction Force (N) Macro-slip Check (Last Pass)

11 Experimental Validation (1) Setup Schematic Z Y x PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

12 Experimental Validation (2) 6 4 Three Cutting Forces Fx Fy Fz 2 Z Y x Force (N) Measured Sec PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

13 Experimental Validation (3) Sampling Rate = 3 pts/sec 3 2 Simulated vs. Experimental Dynamic Motion 4 3 Sim Exp Simulated vs. Experimental Dynamic Motion Sim Exp Displacement (µm) 1-1 Displacement (µm) Second Second Dynamic displacement of a surface point measured by eddy current sensor PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

14 1 5 Acceleration Data De-noising Sampling Rate = 5 pts/sec Ax: original Experimental Validation (4) -5 CG: Simulated vs. Experimental Power Power Ax: de-noised with low-pass filtering Frequency (Hz) Power Spectral Density: Experimental Power Spectral Density: Simulated a x (m/s 2 ) a x (m/s 2 ) Simulated Acceleration at CG - Ax Sec Experimental Acceleration at CG - Ax Sec PMRC Industrial 1 15 Advisory 2Board 25 Meeting, Georgia Tech March 14 & 15, 26 Frequency (Hz)

15 Conclusions A fixture-workpiece system presents significant dynamics during machining. Proper fixture design requires dynamic modeling. Material removal affects fixture-workpiece dynamics significantly. Dynamic motions of simulated and physical fixtureworkpiece systems present similar frequency content. Experimental workpiece motion is larger than simulated workpiece motion because actual system is more flexible PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26

16 Acknowledgment This research was supported by a grant from the National Science Foundation (DMII ) PMRC Industrial Advisory Board Meeting, Georgia Tech March 14 & 15, 26