Worm gear unit and method of producing same

A method of producing a worm wheel that is meshed with a worm shaft, the worm shaft having a helical tooth ridge that has at each side a roundly concave outer surface, the method comprising:

• preparing a circular plate blank;
• and
• cutting a cylindrical peripheral portion of the circular plate blank to produce thereabout equally spaced teeth each of which has at each side a roundly convex outer surface, the roundly convex outer surface being shaped to be intimately engaged with the roundly concave outer surface of the helical tooth ridge of the worm shaft upon proper coupling between the worm shaft and the worm wheel,
• wherein a radius of curvature of a curved bottom of each groove defined by two neighboring teeth of the worm wheel is larger than a radius of curvature of the helical tooth ridge of the worm shaft,
• wherein a meshed engagement between each tooth of the worm wheel and the helical tooth ridge of the worm shaft is represented by a first characteristic line that shows a relation between an allowable error of maximum meshing position of the worm shaft in an axial direction relative to the worm wheel and a radius ratio between the first radius of curvature and the second radius of curvature,
• wherein a meshed engagement between each tooth of a reference worm wheel and a helical tooth ridge of a reference worm shaft is represented by a second characteristic line, each tooth of the reference worm wheel having at each side a flat outer surface and the helical tooth ridge of the reference worm shaft having at each side a flat outer surface;
• wherein the first characteristic line and the second characteristic line intersect at a given point;
• and
• wherein the meshed engagement between each tooth of the worm wheel and the helical tooth ridge of the worm shaft is satisfied by the first characteristic line, where the radius ratio is equal to or greater than a value that indicates the intersecting given point of the first and second characteristic lines.