Bi-helical toothed wheel with variable helix angle and non-encapsulated profile for a hydraulic gear apparatus

A hydraulic gear apparatus, comprising:

• a pair of identical meshing bi-helical toothed wheels being bound to support shafts and each toothed wheel of said pair of identical meshing bi-helical toothed wheels including:
• a plurality of teeth;
• a crest of a tooth of the plurality of teeth of one of said identical meshing bi-helical toothed wheels having engaged contact to a tooth bottom disposed between respective tooth crests of two adjacent teeth of the plurality of teeth of the other of said identical meshing bi-helical toothed wheels so that fluid is prevented from being encapsulated between a profile of the tooth crest of the one of said identical meshing bi-helical toothed wheels and a profile of the tooth bottom of the other of said identical meshing bi-helical toothed wheels during rotation of said pair of identical meshing bi-helical toothed wheels;
• wherein each tooth of the plurality of teeth:
• has a variable helix angle with continuous function in a longitudinal direction parallel with a rotation axis of one of the support shafts that corresponds to a respective toothed wheel of said pair of identical meshing bi-helical toothed wheels:
• begins with a right-handed helix at an end of the respective toothed wheel and ends with at left-handed helix at an opposite end of the respective toothed wheel of said pair of identical meshing bi-helical toothed wheels;
• includes a transition point between the right-handed helix and the left-handed helix in which the variable helix angle is 0° and right and left derivatives of a helix angle function are finite and equal at the transition point.