A lean flank design methodology for spiral bevel gears by modification of conjugate flank was proposed for the predesigned higher-order transmission errors and contact pattern. The conjugate flank of gear was used as reference flank to construct the pinion flank. The reference flank was modified according to the predesigned higher-order transmission errors

and then it was modified secondly according to the predesigned contact pattern

so the topology of the pinion flank also could be controlled precisely to meet the need of the precise control of higher-order transmission errors and contact pattern. The developed approach was illustrated with numerical example and the result showed that the transmission error was 6-order function with the magnitude 3.1"

and contact path orientation was nearly 25° from root cone. The digital rolling test was employed for tooth contact analysis

and the results showed that the shape and magnitude of transmission errors

contact path orientation and contact ellipse could be precisely controlled. This proposed flank methodology basing on modification of conjugate flank can also serve as a basis for developing a general technique of flank design for other gear types.