Coated abrasive article based on a sunflower pattern

Abstract

An abrasive article having a plurality of abrasive areas arranged in a non-uniform distribution pattern, wherein the pattern is spiral or phyllotactic, such as a spiral lattice, and in particular those patterns described by the Vogel model, such as a sunflower pattern.

What is claimed is: 
     
         1 . An abrasive article comprising:
 a coated abrasive having a plurality of abrasive areas arranged in a pattern,   wherein the pattern has a controlled non-uniform distribution, and   wherein the pattern is at least one of a radial pattern, a spiral pattern, a phyllotactic pattern, an asymmetric pattern, or combinations thereof.   
     
     
         2 . The abrasive article of  claim 1 , wherein the pattern is a spiral pattern. 
     
     
         3 . The abrasive article of  claim 2 , wherein the spiral pattern is one of an Archimedean spiral, a Euler spiral, a Fermat's spiral, a hyperbolic spiral, a lituus, a logarithmic spiral, a Fibonacci spiral, a golden spiral, or combinations thereof. 
     
     
         4 . The abrasive article of  claim 3 , wherein the pattern has a controlled asymmetry. 
     
     
         5 . The abrasive article of  claim 4 , wherein the controlled asymmetry is an at least partial rotational asymmetry about the center of the pattern. 
     
     
         6 . The abrasive article of  claim 5 , wherein the rotational asymmetry extends to at least 51% of the abrasive areas of the pattern. 
     
     
         7 . (canceled) 
     
     
         8 . (canceled) 
     
     
         9 . The abrasive article of  claim 1 , wherein the pattern is a phyllotactic pattern. 
     
     
         10 . The abrasive article of  claim 9 , wherein the pattern is a spiral phyllotactic pattern. 
     
     
         11 . The abrasive article of  claim 10 , wherein the pattern has a number of clockwise spirals and a number of counter-clock wise spirals, wherein the number of clockwise spirals and the number of counterclockwise spirals are Fibonacci numbers or multiples of Fibonacci numbers. 
     
     
         12 . (canceled) 
     
     
         13 . The abrasive article of  claim 11 , wherein the number of clockwise spirals and the number of counterclockwise spirals are in a ratio that converges on the golden ratio. 
     
     
         14 . The abrasive article of  claim 10 , wherein the spiral phyllotactic pattern has a controlled asymmetry. 
     
     
         15 . The abrasive article of  claim 10 , wherein the spiral phyllotactic pattern is a sunflower pattern. 
     
     
         16 . The abrasive article of  claim 11 , wherein the pattern is described in polar co-ordinates by the following equation:
   φ= n*α,r=c√n   (Eq. 1)
   where:   n is the ordering number of an abrasive area, counting outward from the center of the pattern;   φ is the angle between a reference direction and a position vector of the n th  abrasive area in a polar coordinate system originating at the center of the pattern, such that the divergence angle between the position vectors of any two successive abrasive areas is a constant angle α;   r is the distance from the center of the pattern to the center of the n th  abrasive area; and   c is a constant scaling factor.   
     
     
         17 . The abrasive article of  claim 16 , wherein at least about 51% of the abrasive areas conform to Eq.1. 
     
     
         18 . The abrasive article of  claim 16 , wherein the pattern has a divergence angle in polar co-ordinates that ranges from about 100° to about 170°. 
     
     
         19 . The abrasive article of  claim 16 , wherein the pattern has a divergence angle that is 137.508°. 
     
     
         20 . (canceled) 
     
     
         21 . (canceled) 
     
     
         22 . (canceled) 
     
     
         23 . (canceled) 
     
     
         24 . (canceled) 
     
     
         25 . (canceled) 
     
     
         26 . (canceled) 
     
     
         27 . The abrasive article of  claim 16 , wherein the pattern has a total open area of about 15% to about 99.5% of the surface potential surface area of the abrasive article. 
     
     
         28 . The abrasive article of  claim 16 , having a total abrasive surface area that ranges from about 4.5% to about 85% of the total potential surface area. 
     
     
         29 . (canceled) 
     
     
         30 . (canceled) 
     
     
         31 . A coated abrasive article comprising:
 a backing layer having a first major side and a second major side; and   an abrasive layer disposed on the first major side of the backing layer,   wherein the abrasive layer comprises a plurality of abrasive areas arranged in a pattern having a controlled non-uniform distribution, and the pattern is a phyllotactic pattern.   
     
     
         32 . A method of making an abrasive article comprising:
 disposing an abrasive layer on a backing;   wherein the abrasive layer comprises a plurality of abrasive areas arranged in a pattern having a controlled non-uniform distribution that is at least one of a radial pattern, a spiral pattern, a phyllotactic pattern, an asymmetric pattern, or combinations thereof.   
     
     
         33 . (canceled) 
     
     
         34 . (canceled) 
     
     
         35 . (canceled) 
     
     
         36 . (canceled) 
     
     
         37 . (canceled) 
     
     
         38 . (canceled) 
     
     
         39 . (canceled) 
     
     
         40 . (canceled) 
     
     
         41 . (canceled) 
     
     
         42 . (canceled) 
     
     
         43 . (canceled) 
     
     
         44 . (canceled) 
     
     
         45 . (canceled)