0
Research Papers

Surface Location Error and Surface Roughness for Period-N Milling Bifurcations

[+] Author and Article Information
Andrew Honeycutt

Department of Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
9201 University City Boulevard,
Charlotte, NC 28223
e-mail: ahoney15@uncc.edu

Tony L. Schmitz

Mem. ASME
Department of Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
9201 University City Boulevard,
Charlotte, NC 28223
e-mail: tony.schmitz@uncc.edu

1Corresponding author.

Manuscript received September 7, 2016; final manuscript received November 28, 2016; published online January 30, 2017. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 139(6), 061010 (Jan 30, 2017) (8 pages) Paper No: MANU-16-1490; doi: 10.1115/1.4035371 History: Received September 07, 2016; Revised November 28, 2016

This paper provides time domain simulation and experimental results for surface location error (SLE) and surface roughness when machining under both stable (forced vibration) and unstable (period-2 bifurcation) conditions. It is shown that the surface location error follows similar trends observed for forced vibration, so zero or low error conditions may be selected even for period-2 bifurcation behavior. The surface roughness for the period-2 instability is larger than for stable conditions because the surface is defined by every other tooth passage and the apparent feed per tooth is increased. Good agreement is observed between simulation and experiment for stability, surface location error, and surface roughness results.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Cutting force geometry. The normal and tangential direction cutting forces, Fn and Ft, are displayed. The fixed x (feed) and y directions, as well as the rotating normal direction, n, are also shown. The angle ϕ defines the tooth angle. The tool feed is to the right for the clockwise tool rotation and the axial depth is in the z direction.

Grahic Jump Location
Fig. 2

(Left) Feed direction (x) vibration versus time with once-per-tooth sampled points (circles) for b= 0.5 mm. (Right) Poincaré map with once-per-tooth sampled points. Because the cut is stable, all sampled points appear at the same location.

Grahic Jump Location
Fig. 3

(Left) Feed direction (x) vibration versus time with once-per-tooth sampled points (circles) for b= 2.5 mm. (Right) Poincaré map with once-per-tooth sampled points. The period-2 bifurcation behavior shows two sampled point locations. Because the solution alternates between two values, this is referred to as a flip bifurcation.

Grahic Jump Location
Fig. 4

(Left) Feed direction (x) vibration versus time with once-per-tooth sampled points (circles) for b= 5 mm. (Right) Poincaré map with once-per-tooth sampled points. The secondary Hopf instability yields an elliptical distribution of sampled points.

Grahic Jump Location
Fig. 5

(Left) Spatial trajectory of the cutter tooth for b= 2.5 mm. (Right) Magnified view of upper surface of tooth trajectory. The machined surface is defined by the points at the top of the trajectory for the up milling cut. The period-2 behavior gives upper and lower tooth paths. The upper path defines the final surface, although material is removed for each tooth passage.

Grahic Jump Location
Fig. 6

Flexure-based experimental setup with laser vibrometer (LV), laser tachometer (LT), and capacitance probe (CP). The feed direction and the flexible direction for the single degree-of-freedom flexure are also identified. The setup was located on a Haas TM-1 CNC milling machine.

Grahic Jump Location
Fig. 7

The workpiece included four ribs that were initially machined to the same dimensions. The {5 mm axial depth, 2 mm radial depth} cuts were then performed on one edge at a different spindle speed for each rib. The SLE was calculated as the difference between the commanded, C, and measured, M, rib widths. The flexible direction for the flexure is identified.

Grahic Jump Location
Fig. 8

Predicted (left) and measured (right) Poincaré maps for 3180 rpm. Period-2 behavior is seen. Note that x indicates the flexible direction for the flexure. The feed direction was y for these experiments.

Grahic Jump Location
Fig. 9

Predicted (left) and measured (right) Poincaré maps for 3300 rpm. Stable behavior is seen.

Grahic Jump Location
Fig. 10

Predicted (left) and measured (right) Poincaré maps for 3600 rpm. Stable behavior is seen with increased amplitude relative to 3300 rpm (Fig. 9).

Grahic Jump Location
Fig. 11

SLE prediction from time domain simulation (line) and experimental results from rib cutting tests (circles). The four period-2 bifurcation tests are identified.

Grahic Jump Location
Fig. 12

Commanded surface (dashed line), CMM scan (solid line), and simulation result (circles) for 3180 rpm (period-2). These results correspond to Fig. 8.

Grahic Jump Location
Fig. 13

Commanded surface (dashed line), CMM scan (solid line), and simulation result (circles) for 3300 rpm (stable). These results correspond to Fig. 9.

Grahic Jump Location
Fig. 14

Commanded surface (dashed line), CMM scan (solid line), and simulation result (circles) for 3600 rpm (stable). These results correspond to Fig. 10.

Grahic Jump Location
Fig. 15

Scanning white light interferometer line scan (line) and simulation results (circles) for 3180 rpm (period-2)

Grahic Jump Location
Fig. 16

Scanning white light interferometer line scan (line) and simulation results (circles) for 3300 rpm (stable)

Grahic Jump Location
Fig. 17

Scanning white light interferometer line scan (line) and simulation results (circles) for 3600 rpm (stable)

Grahic Jump Location
Fig. 18

Combined stability and SLE map for rib cutting process dynamics. The secondary Hopf instability is represented by the dark zone, the period-2 behavior is identified by the dotted zone, and the SLE is given by the contours (i.e., lines of constant SLE).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In