Patent ID: 7077026

Claim:
A gear system comprising: a pinion having a pinion tooth number (N 1 ), a pinion pitch circle radius (R p1 ), and a first plurality of teeth, each tooth having a first-tooth profile; and a mating gear having a mating-gear tooth number (N 2 ), a mating-gear pitch circle radius (R p2 ), and a second plurality of teeth, each tooth having a second-tooth profile, wherein the pinion and the mating gear form a gear pair having a gear ratio (m G ) equal to N 2 /N 1 , a face width (F w ) and a face-width factor (f w ) equal to (2·R p2 )/F w , and wherein the relative curvature of the first-tooth profile and the second-tooth profile is a multiple of a reference relative curvature (K ref ), the multiple defined by the expression K m ·K ref , where K ref = 1 sin ⁡ ( 20 ) · ( 1 R p1 + 1 R p2 ) and K m is a relative curvature multiplier that is more than a i,j −δ and less than a i,j +2δ, where δ is between 0 and 0.15 and a i,j is defined by a predetermined relationship between the gear ratio (m G ) and the face-width factor (f w ), the predetermined relationship corresponding to at least one relative curvature multiplier value in a relative curvature multiplier value table having the following properties: Face Width Factor (f w ) Gear Ratio (m G ) 4.0 5.0 6.0 1.0 0.41 0.40 0.39 1.5 0.43 0.41 0.40 2.0 0.43 0.43 0.41 2.5 0.48 0.45 0.41 3.0 0.48 0.48 0.44 4.0 0.48 0.48 0.48 6.0 0.46 0.46 0.46 16.0 0.43 0.43 0.43.