Method for determination of longitudinal and profile modification of tool gear tooth surface

A method for determination of longitudinal and profile modification of a tool gear tooth (1) which linearly meshes with a gear to be machined comprising rotating a gear blank and the tool gear in synchronism, while the parameters of longitudinal and profile modification of a machining surface (5) of the tool gear tooth (1) are determined in a plurality of contact points (6 to 14) arranged on said machining surface symmetrically with respect to a longitudinal axis (15) and a profile axis (16), in accordance with the following relationship;

• ##EQU10## where:
• .delta.--the amount of modification of the tool gear tooth (1) in a direction perpendicular to a radius r identifying the location of a contact point on the machining surface (5) relative to a center (0) of rotation of the tool gear measured in radians;
• .DELTA.p--the requisite change in the normal component of the cutting force measured in Newtons;
• G--the rigidity, where the torsional rigidity is the torque applied to the shaft divided by the turning angle of the driveshaft as a result of the twisting of all shafts of the kinematic train, of an arrangement providing for synchronous rotation of the gear blank and the tool gear as reduced to the tool gear axis measured in Newton meters/radians;
• whereas:
• .DELTA.p is obtained from the following equation:
• ##EQU11## where:
• p--the normal component of the cutting force measured in Newtons;
• V.sub.s --the velocity of relative sliding motion between the machining surface (5) and a surface (3) being machined measured in meters/second;
• V.sub.r --the velocity of movement of the contact point along the surface (3) being machined measured in meters/second.