J. Eur. Opt. Society-Rapid Publ. 21, 37( 2025) 71
Fig. 7.( a) Simulated and experimental footprints and( b) 2D section profile across the influence footprint.
3 Results and discussion
Shape adaptive grinding with the newly developed wheel type tooling was adopted to correct the form and surface finish on the channel. Feed moderation strategy was adopted for form correction of the surface. Feed moderation works on the principle of controlling the material removal locally by varying the feed rate along the tool path. In order to enable feed moderation, removal characteristics of the tool has to be obtained in terms of influence function. The influence function of the wheel tool was modeled based on Preston’ s equation of material removal rate [ 15 ]. The idealized contact between the wheel tool and the workpiece is shown in Figure 6.
Contact force between tool and workpiece is given as: �
F n ¼ K T a S b ð1Þ
where, F n is the normal force, T is the wheel offset and S is the shore hardness of the rubber. Coefficients K, a and b are taken as 5.77 10 �2, 1.49 and 1.45, respectively [ 15, 16 ]. Maximum pressure P max in the contact area can be obtained as
P max ¼ F n
A c
: ð2Þ
A c is the contact area which can be estimated as A c = l b, where b is the width of contact and l is the contact length. Width of contact b is equal to the width of a pellet; refer Figure 5, as a single line pellet strip is wrapped around the wheel for finishing. Length of contact l is determined from triangle DOAB. Contact pressure between an elastic tool and workpiece follows gaussian distribution where the pressure is maximum at center and diminishes towards the edges [ 17 ]. Pressure at any point( x i, y i) in the contact region can be estimated as:
P s ¼ P max exp � x
i 2 2 c
þ y i ð3Þ
2r 2
where, r is the standard deviation, and c is the modification coefficient. Tool influence function( TIF) for the wheel tool can be estimated as [ 18 ]:
Fig. 8. Error map for form correction.
Table 2. Form error results for various corrective runs. Run
Process time
Target correction
Achieved P-V( lm)
1 |
2 h 07 min |
25 % |
18.3 |
2 |
49 min |
33 % |
14.6 |
3 |
55 min |
50 % |
13.9 |
4 |
1 h 07 min |
33 % |
7.8 |