Patent ID: 7398938

Claim:
A refining cone having a working surface, a radially inner end and a radially outer end, the working surface including a plurality of bars having inner and outer ends, laterally spaced by intervening grooves and extending generally outwardly toward said outer end across said conical surface, said plurality of bars being curved with the shape of a logarithmic type spiral from the inner to the outer ends of the bars, wherein the shape of said bars conforms within manufacturing tolerances to the mathematical expression in polar coordinates in an original x-y plane orthogonal to the cone axis: r=a·e k·φ where k=cot α and k=0→circle this curve projected onto the working surface has a shape change according to the following formulae: α := a ⁢ ⁢ tan ⁡ ( tan ⁡ ( α ⁢ ⁢ cone · π 180 ) sin ⁡ ( 20 · π 180 ) ) · 180 π bw := bw ⁢ cone sin ⁡ [ ( 90 - α ⁢ ⁢ cone ) · π 180 ] 2 + cos ⁡ [ ( 90 - α ⁢ ⁢ cone ) · π 180 ] 2 sin ⁡ ( 20 · π 180 ) 2 gw ⁢ ⁢ 1 := gw ⁢ ⁢ 1 ⁢ cone sin ⁡ [ ( 90 - α ⁢ ⁢ cone ) · π 180 ] 2 + cos ⁡ [ ( 90 - α ⁢ ⁢ cone ) · π 180 ] 2 sin ⁡ ( 20 · π 180 ) 2 where “r” is the radial position along the centerline of the bar, “a” is a scale parameter for r and αis the intersecting angle between any tangent to the curve and the generatrix of the coordinate system, Gw 1 cone and bwcone are bar and groove width on the cone, gw and bw the bars and grooves width in the original x-y plane, the angle acone denominates the angle of the logarithmic type spiral curve on the working surface between a tangent to the curve and the generatrix of the cone, and, a is the angle of the logarithmic spiral in the x-y-plane.