Toothing system of a gearwheel having involute roller toothing
In the toothing system ( 1 ) of a gearwheel having a plurality of teeth ( 2, 3; 19 ) whose tooth flanks ( 4, 5, 6; 22 ) have involute form above a tooth-root region ( 7, 8, 9; 23 ) of the tooth flanks ( 4, 5, 6; 22 ), the tooth-root region ( 7, 8, 9; 23 ) of the tooth flanks ( 4, 5, 6; 22 ) that, as viewed in normal section, extends between a root useful point ( 15, 16, 17; 23 ) and a root point (F) has elliptical shape, tangentially adjoins the involute region of the tooth flank ( 4, 5, 6; 22 ) at the root useful point ( 15, 16, 17; 24 ) and tangentially contacts the root circle (FKS) at the root point (F). In its tooth-root region ( 7, 8, 9; 23 ), the tooth flank ( 4, 5, 6; 22 ), as viewed in normal section, substantially follows a partial section (B) of an ellipse ( 10, 11, 12 ; E) whose semiaxes (a, b) have different lengths, one semiaxis (a, b) of the ellipse ( 10, 11, 12 ; E) being inclined at an ellipse tilting angle alpha larger than 0° and smaller than 90° relative to a radial (R) through the root point (F). Furthermore, the tooth flanks ( 4, 5, 6; 22 ) of the teeth ( 2, 3; 19 ) of the toothing are symmetric to one another across a symmetry plane (A) that divides the respective tooth ( 2, 3; 19 ) in axial direction.
1. A toothing system ( 1 ) of a gearwheel having a plurality of teeth ( 2 , 3 ; 19 ) whose tooth flanks ( 4 , 5 , 6 ; 22 ) have involute form above a tooth-root region ( 7 , 8 , 9 ; 23 ) of the tooth flanks ( 4 , 5 , 6 ; 22 ),
wherein the tooth-root region ( 7 , 8 , 9 ; 23 ) of the tooth flanks ( 4 , 5 , 6 ; 22 ) that, as viewed in normal section, extends between a root useful point ( 15 , 16 , 17 ; 24 ) and a root point (F) has elliptical shape, tangentially adjoins the involute region of the tooth flank ( 4 , 5 , 6 ; 22 ) at the root useful point ( 15 , 16 , 17 ; 24 ) and tangentially contacts the root circle (FKS) at the root point (F),
characterized in that,
in its tooth-root region ( 7 , 8 , 9 ; 23 ), the tooth flank ( 4 , 5 , 6 ; 22 ), as viewed in a transverse cross-section, substantially follows a partial section (B) of an ellipse ( 10 , 11 , 12 ; E) whose semiaxes (a, b) have different lengths, one semiaxis (a, b) of the ellipse ( 10 , 11 , 12 ; E) being inclined at an ellipse tilting angle alpha larger than 0° and smaller than 90° relative to a radial (R) through the root point (F), and in that the tooth flanks ( 4 , 5 , 6 ; 22 ) of the teeth ( 2 , 3 ; 19 ) of the toothing are symmetric to one another across a symmetry plane (A) that divides the respective tooth ( 2 , 3 ; 19 ) in axial direction.
2. A toothing system according to claim 1 , characterized in that the major semiaxis (a) of the two semiaxes (a, b) of the ellipse ( 10 , 11 , 12 ; E) is inclined at the ellipse tilting angle alpha, with 0° <alpha<90° , from the radial (R) through the root point (F) toward the tooth flank ( 4 , 5 , 6 ; 22 ).
3. A toothing system according to claim 1 , characterized in that the semiaxes (a, b) of the ellipse ( 10 , 11 , 12 ; E) as well as the ellipse tilting angle alpha are chosen in such a way that the maximum stress in the root region of the tooth is minimal for a predesignated force acting perpendicular to the tooth flank ( 4 , 5 , 6 ; 22 ) in the tooth-root region.
4. A toothing system according to claim 1 , characterized in that the mutually facing tooth flanks ( 5 , 6 ) of two neighboring teeth ( 2 , 3 ) merge tangentially into one another without any intermediate space.
5. A gearwheel with a toothing system according to claim 1 , characterized in that the gearwheel is a cylindrical gear.
6. A gearwheel pair comprising two gearwheels according to claim 5 .
7. A gearwheel according to claim 5 , characterized in that the cylindrical gear is straight-toothed.
8. A gearwheel with a toothing system according to- claim 1 , characterized in that the gearwheel is a bevel gear ( 18 ).
9. A gearwheel according to claim 8 , characterized in that the bevel gear is straight-toothed.
10. A gearwheel according to claim 8 , characterized in that the length of the semiaxes a and b of the ellipse (E) and/or the ellipse tilting angle alpha vary over the pitch-cone distance.
11. A gearwheel according to claim 8 , characterized in that the ellipse tilting angle alpha and the semiaxis ratio a/b are constant at least over part of the length of the toothing.