Patent ID: 6324931
Filing Date: 2001-12-04
Classification: B23F,F16H,Y10T

Abstract:
A gear having a plurality of teeth, each tooth having a working surface contacting a working surface of a tooth of a meshing gear, said working surface of each tooth of the gear being between a top land and a bottom land defining a tooth height, and wherein the working surface has a root profile geometry of which is determined in accordance with the following equation:r.sup.(K) =F.sub.1.multidot.r.sup.(A) +F.sub.2.multidot.r.sup.(B) +F.sub.3.multidot.4.multidot..delta..multidot.(r.sup.(C) -r.sup.(A))+F.sub.4.multidot.4.multidot..delta..multidot.(r.sup.(B) -r.sup.(C)),wherer.sup.(K) --a position vector of any point K on a tooth surface located in a gear tooth root area;r.sup.(A) --a position vector of a predetermined point A on the tooth surface in the gear tooth root area other than the gear tooth root cone, known;r.sup.(B) --a position vector of a predetermined point B on the tooth surface in the gear tooth root area other than the gear tooth root cone, known;F.sub.1 =2u.sup.3 -3u.sup.2 +1;F.sub.2 =-2u.sup.3 +3u.sup.2 ;F.sub.3 =u.sup.3 -2u.sup.2 +u;F.sub.4 =u.sup.3 -u.sup.2 ;u is a real number, 0.ltoreq.u.ltoreq.1;.delta.--a coefficient determined from the following equation:.delta.=(r.sup.(E) -r.sup.(A) -AC.multidot.t.sub.1 +h.multidot.t.sub.3)/(h.multidot.t.sub.3),wherer.sup.(E) --a position vector of a predetermined point E on a tooth surface located in a gear tooth root cone, known;AC--distance between the points A and C;t.sub.1 --a unit tangent vector of the point A;t.sub.2 --a unit tangent vector of the point B;r.sup.(C) --a position vector of a point C being an intersection point of said unit vectors t.sub.1 and t.sub.2, known;t.sub.3 --a unit vector along a line ME,where a point M is a middle of the line AB.