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Research Papers

Frequency Optimal Feed Motion Planning in Computer Numerical Controlled Machine Tools for Vibration Avoidance

[+] Author and Article Information
Burak Sencer

Assistant Professor
Department of Mechanical, Manufacturing and
Industrial Engineering,
Oregon State University,
Corvallis, OR 97331
e-mail: Burak.sencer@oregonstate.edu

Shingo Tajima

Department of Mechanical,
Manufacturing and Industrial Engineering,
Oregon State University,
Corvallis, OR 97331
e-mail: tajimas@oregonstate.edu

1Corresponding author.

Manuscript received March 26, 2016; final manuscript received June 23, 2016; published online August 9, 2016. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 139(1), 011006 (Aug 09, 2016) (13 pages) Paper No: MANU-16-1183; doi: 10.1115/1.4034140 History: Received March 26, 2016; Revised June 23, 2016

This paper presents a novel trajectory generation technique, which has the capability to avoid excitation of inertial vibrations in precision manufacturing equipment. A major source of vibrations in fast moving precision manufacturing equipment is the inertial vibrations that are excited due to frequency content of reference motion commands (trajectory). In general practice, those inertial vibrations are avoided within the controller architecture through notch filtering. Or, input-shaping methods are utilized to attenuate critical frequency components of the reference trajectory so that lightly damped vibration modes of the structure are not excited. Instead of employing those postfiltering techniques that add unwanted delay to the coordinated motion, this paper introduces a direct trajectory generation technique with a shaped frequency content to suppress inertial vibrations. The time-stamped acceleration profile of the feed profile is defined as a ninth-order polynomial. Polynomial coefficients are solved through an optimization procedure where the objective function penalizes total frequency energy in a desired frequency band. As a result, generated reference acceleration commands do not contain any excitation near the vibration modes of the system and hence excitation of inertial vibrations is avoided. The proposed frequency optimal feed profiling (FOFP) system can be utilized to generate high-speed accurate point-to-point (P2P) trajectories as well as to interpolate continuous multi-axis coordinated motion. Effectiveness of the proposed FOFP scheme is evaluated through rigorous comparison against the well-known minimum jerk feed profiles (MJFP) technique through simulations and experiments. Experimental validation is performed on an in-house controlled machine tool with flexible structure.

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Figures

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Fig. 1

Polynomial motion profiles

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Fig. 2

P2P feed motion planning: (a) P2P toolpath, (b) frequency optimal trajectory, and (c) interpolation to axes

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Fig. 3

Frequency optimal feed motion planning strategy with kinematic constraints: (a) FOFP for P2P trajectories and (b) flowchart of FOFP generation

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Fig. 4

Continuous FOFP generation strategy: (a) continuous part with blended corners, (b) deceleration/cornering/acceleration phases, and (c) axis interpolation

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Fig. 5

FOFPs generated with different frequency bands: (a) tangential feedrate, (b) tangential acceleration, (c) frequency spectrum of acceleration/deceleration, (d) tangential federate, (e) tangential acceleration, (f) frequency spectrum of acceleration/deceleration (g) tangential federate, (h) tangential acceleration, and (i) frequency spectrum of acceleration/deceleration

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Fig. 6

Experimental setup with structural flexibilities

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Fig. 7

P2P feed profile kinematics: (a) displacement profiles, (b) velocity profiles, (c) acceleration profiles, and (d) frequency spectrum of acceleration

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Fig. 8

Experimentally recorded vibration of the beams during P2P motion: (a) x-axis beam acceleration, (b) DFT of acceleration signal (x-axis), (c) y- axis beam acceleration, and (d) DFT of acceleration signal (y-axis)

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Fig. 9

Continuously interpolated tool-path and blended corner kinematics: (a) toolpath, (b) x–y axis velocities along corner blend, and (c) x–y axis acceleration along corner blend

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Fig. 10

Continuous motion profiles generated by FOFP and MJFP: (a) tangential velocity, (b) axis velocities, (c) axis accelerations, and (d) DFT of accelerations during cornering phases

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Fig. 11

Experimentally recorded vibration of beams during continuous path interpolation: (a) beam acceleration (x-axis) and (b) beam acceleration (y-axis)

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