This document investigates the effects of different tool paths on material removal during polishing. It analyzes scanning, bi-scanning, Hilbert, and Peano paths through simulations and experiments. The key findings are: (1) Material removal maps show distinct patterns depending on the path, with peaks and valleys forming along the paths. (2) Hilbert paths produce the highest unevenness in material removal, while Peano paths produce the most uniform removal without edge effects. (3) Experiments confirm simulations, with Peano paths demonstrating smooth removal both along and across the tool path direction. In conclusion, Peano and Hilbert paths are best suited for uniform polishing due to their balanced and well-distributed tool path directions.

1. An Investigation of the Effects of
Tool Path in the Removal of
Material in Polishing
Submitted By: Govind Krishnan G R
ME 8
Roll No:23

2. Introduction
 Polishing is done to remove machine
lines and reduce surface roughness
 Done to better appearance and to
obtain a smooth surface
 Conventional polishing uses fixed,
adhered or loose abrasives
 Required skilled workers and
specialized tools

3. Automation in Polishing
 Automation is required in polishing to
attain more uniformity, quality
precision and finish
 Tool paths are required for polishing
such that they cover the entire
surface

4. Topics Covered
 Introduction to 4 commonly used tool
paths in polishing
 Effects of these paths in removal of
material

5. Terms Used
 Pitch(p): is the distance between
adjacent path segments.
 Material Removal Map:2D map that
indicates the depth of material
removed by tool following a certain
path
 Peak to Valley height(hpv)
 Path Density: inverse of path pitch

6. Tool Paths
 a. Scanning Path:
Commonly used for
polishing and
machining
 b. Bi-Scanning Path:
Scanning in 2
orthogonal directions
 c. Hilbert Path:
Surface filling path
 d. Peano Path: Surface
filling path

7. Polishing Effects From Adjacent
Path Lines
 Path lines are evenly spaced lines
 Contact is assumed to be ellipsoidal
 Material removal map is standardized
by taking average depth of removal
as unity
 Normalised hpv vs Pitch is plotted

8. hpv vs Pitch
 Noticeable change
is that hpv
decreases with
decrease in pitch
 Considering locally,
hpv increases with
decrease in pitch

9. Material Removal Map
 Material removal
map const along
path line
 Undulates along
orthogonal
direction
 Undulation due to
overlapping of
removal profile

10. Material Removal Map Along
Orthogonal Direction
 Primary peak: top of
removal profile of
individual path lines
 Secondary peak:
formed due to
overlapping of
adjacent path lines
 a).70<p<1: as shown
in fig
 b).50<p<.70 here
secondary is higher
 c)p=.5 here primary is
not visible

11. Polishing with different Path
Patterns
 Effect of path patterns in the uniformity of
material removal
 Removals of
1. Inner surface
2. Edges
are examined
 Assume tool contact to be circular
 For circular contact shape of removal
profile is parabolic

12. Inner surface
 Scanning Paths
1. Evenly spaced
troughs and
alternate crests
2. hpv decreases with
increase in path
density
3. Increase in path
density leads to
increase in
overlapping and
more uniformity

13. Inner Surface (contd..)
 Bi-Scanning Path
1. Scanning along
two orthogonal
directions
2. Contain isolated
peaks and valleys
3. Peaks are at
intersection of
crests and valleys
at intersection of
troughs
4. Hpv same as in
scanning path

14. Inner Surface (contd..)
 Peano Path:
1. Grids produced by
Peano and bi
scanning paths are
similar
2. Orientation of grid
is at 45˚
3. Contains
rectangular grid of
peaks and valleys
4. hpv similar to
scanning path

15. Inner Surface (contd..)
 Hilbert Path:
1. Highest hpv among
all
2. Irregular ridges
along path line
direction
3. High points are at
intersection of
ridges and lowest
between ridges

16. Near Edges
 Scanning Path:
 Line of peaks of
alternating heights
present at the edge.
 Present at the end of 2
crest lines
 Due to short path
segments
 Bi-Scanning Path:
 High edge peaks are
present
 Average edge peak
height less compared to
scanning due to two
component scans
 Higher corner peaks due
to edge effects by scans
from both directions

17. Circular Contact: Near Edges(contd)
 Peano Path
 No edge effects are
present
 Similar to pattern
obtained from bi-
scanning but edge
peaks are absent
 Hilbert Path
 No edge effects
 Peaks of irregular
heights dispersed
throughout the
surface

18. Polishing Experiments
 To investigate how tool path affects
uniformity of removal
 Specimens of Aluminum plates of surface
flatness between 2-3μm
 Tools contain alumina mixed in a binding
material of synthetic rubber
 Specimen fixed
 Tool movement using a NC motion platform
 Tool orientation and polishing force was set
constant during the expt
 Removal Map and Line Profiles are plotted

19. Polishing Experiment on Scanning
Path
 Path Pitch set at 1mm
 Tool movement in North-South
direction
 From (a)Removal Map
 Uniform removal in inner
surface
 Discoloration in north and
south edges indicate edge
effect
 From(b)East West Profile
 Less uniform due to
overlapping
 From(c)North South Profile
 More uniform
 Edge peaks are present
 Extra removal near edges

20. Polishing Experiment on Peano Path
 Path Pitch set at
0.5mm
 From (a)Removal Map
 Uniform inner surface
except a few isolated
regions
 From(b)East West Profile
 Rough as it is across
tool sliding direction
 From(c)North South
Profile
 Smooth, along tool
sliding direction
 Absence of Edge effects

21. Discussions and Summary
 Removal map contains crests and troughs for
sacnning path and grids of peak and valleys for bi-
scanning and peano
 hpv of Hilbert path is gretest
 Short path segments form edge peaks
 Edge effect absent for Hilbert and Peano
 Extra removal of material from edges in scanning
paths attributed to accumulation of debris
 For uniform removal tool path direction should be well
distributed and path lines should be well balanced
 Hence Peano and Hilbert Paths are most suited

22. Thank You