| US 7,507,267 B2 | ||
| Abrasive tools made with a self-avoiding abrasive grain array | ||
| Richard W. J. Hall, Southborough, Mass. (US); Jens M. Molter, Hamburg (Germany); and Charles A. Bateman, Rutland, Mass. (US) | ||
| Assigned to Saint-Gobain Abrasives Technology Company, Worcester, Mass. (US) | ||
| Filed on Sep. 16, 2005, as Appl. No. 11/229,408. | ||
| Application 11/229408 is a continuation of application No. 10/683486, filed on Oct. 10, 2003, abandoned. | ||
| Prior Publication US 2006/0010780 A1, Jan. 19, 2006 | ||
| Int. Cl. B24D 3/00 (2006.01); B24D 11/00 (2006.01); B24D 3/02 (2006.01); C09K 3/14 (2006.01) | ||
| U.S. Cl. 51—293 [51/308; 51/309] | 20 Claims |
| 1. A method for manufacturing abrasive tools having individual abrasive grains placed in a controlled, random spatial array
such that the individual grains are non-contiguous, comprising the steps of:
(a) selecting a two-dimensional planar area having a defined size and shape;
(b) selecting a desired abrasive grain grit size and concentration for the planar area;
(c) selecting a series of coordinate value pairs (x1, y1) such that the coordinate values along at least one axis are restricted to a numerical sequence wherein each value differs
from the next value by a constant amount;
(d) decoupling each selected coordinate value pair (x1, y1) to yield a set of selected x values and a set of selected y values;
(e) randomly selecting from the sets of x and y values a series of random coordinate value pairs (x, y), each pair having
coordinate values differing from coordinate values of any neighboring coordinate value pair by a minimum value (k);
(f) generating an array of the randomly selected coordinate value pairs having sufficient pairs, plotted as points on a graph,
to yield the desired abrasive grain concentration for the selected two dimensional planar area and the selected abrasive grain
grit size; and
(g) centering an abrasive grain at each point on the array.
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