Gear transmission system

A gear transmission system (20) comprising:

• at least a first cylindrical gear (21), a second cylindrical gear (22), and a third cylindrical gear (33);
• each of the first, the second and the third cylindrical gears (21, 22) comprising a plurality of teeth (23, 26), and
• the teeth (23) of the first cylindrical gear (21) having a first tooth flank (24) for contacting a first tooth flank (27) of the teeth (26) of the second cylindrical gear (22) according to a predefined first contact line (30), and the teeth (34) of the third cylindrical gear (33) have a first tooth flank (35) for contacting a second tooth flank (25) of the teeth (23) of the first cylindrical gear (21) according to a predefined second contact line (30);
• wherein the first tooth flanks (24, 27) of the teeth (23, 26) of each of the first and second cylindrical gears (21, 22) have a tooth shape and tooth properties determined by the predefined first contact line (30);
• the first tooth flank (35) of the teeth (32) of the third cylindrical gear (33) and the second tooth flank (25) of the teeth (23) of the first cylindrical gear (21) have a tooth shape and tooth properties determined by the second contact line (30);
• and
• the properties comprising at least one of:
• tooth root stress,
• contact pressure,
• transmission error,
• tooth gear mesh stiffness or
• hydrodynamic oil film build-up.