We can make sure that the tooth/ teeth precision is higher than the JIS O standard by flank grinding the numerous teeth of the small module of the high-speed cylindrical gear with a gear grinder. The cylindrical grinding gear is being used in compressors, generators, etc, which require large amounts of high-speed revolutions, because it can achieve a peripheral speed of more than 100m/s while running smoothly with a quiet connection. When a helical gear of different torsions is placed on the same axis a double helical gear is formed. This cylindrical grinding gear is advantageous in design and is useful because it can be used by rotary devices that require high-speed revolutions, it can offset the thrust power generated from the right/ left torsion on the same axis and the flank can be grinded with a gear grinder.