Gear Flank Deviations

Profile Deviations: Are the deviations normal to the transverse involute profiles, i.e. in the plane tangent to the base cylinder, measured within the profile evaluation range L_a. They are referred to the transverse section. Unless otherwise specified, the following rules according to ISO 1328, part 1, shall apply: The length of the evaluation range L_a is 92% of the active length L_AE, extending from point E. Point E is the end point of the effective contact with the mating gear or, if this is unknown, with a rack having standard rack tooth proportions. In the remaining 8% of L_AE, for the total profile deviation F_a and the profile form deviation f_fa, excess material (plus deviation) which increases the amount of deviation must be taken into account, whereas for minus metal deviation the tolerance shall be three times the tolerance specified for the evaluation range L_a.
Total profile deviation FA: The distance between two design profiles which enclose the actual profile over the evaluation range L_a, subject to provisions of the above.
Profile slope deviation f_Ha: The distance between two design profiles which intersect the mean profile at the end points of the evaluation range L_a. The profile slope deviation F_Ha is positive when the mean profile rises from the design profile towards the nonmaterial side at the tooth tip; it is negative when the mean profile drops towards the material side at the tooth tip. The mean profile slope deviation f_Ham is the algebraic mean of the profile slope deviations of a number of flanks distributed uniformly around the circumference.	diagram to follow
Profile form deviation f_fa: The distance between two profiles parallel to the mean profile which enclose the actual profile over the evaluation range L_a.	diagram to follow
Base diameter deviation f_db and Pressure angle deviation FA Both the base diameter deviation f_db and the pressure angle deviation FA are directly related to the profile slope deviation f_Ha and can be calculated with the following equations: f_db = f_Ha · (d_b/L_a) d_beff = dB(1+(f_Ham/L_a)) If f_Ha is given in µm and dB and L_a in mm, f_db is obtained in µm and FA in mrad (1 mrad = 206.26 arc seconds). In practice, e.g. for correction of machine tool settings, calculations are mainly made on the basis of arithmetic mean values f_Ham, f_dbm, and f_am. For example: f_dbm = f_Ham · (dB/L_a) d_beff = dB(1+(f_Ham/L_a)) A positive base diameter deviation corresponds to a negative pressure angle deviation, and vice versa.	diagram to follow
Profile undulation f_wa A profile deviation which recurs periodically throughout the angle of generation or the generating path, is termed profile undulation f_wa when it is recognised by a series of several waves of almost constant amplitude f_wa and a constant wavelength l_a. A profile diagram might contain a number of different undulations superimposed one on the other.	Diagram to follow

Helix Deviations: A helix is the intersection of the tooth flank with a cylinder concentric about the gear axis, usually with the reference cylinder of the gear. Helix deviations are measured in the direction of transverse base tangents over the helix evaluation range L_b. Unless agreed otherwise, the evaluation range L_b according to ISO 1328, part 1, is applied: It is equal to the 'length of diagram' (facewidth excluding tooth end chamfers), shortened at each end by the smaller of the two values - 5% of facewidth or by the length equal to one module. In the '5% end zones', for the total helix deviation F_b and the helix form deviation f_fb, excess material (plus deviation) which increases the amount of deviation must be taken into account, whereas for minus metal deviation the tolerance shall be three times the tolerance specified for the evaluation range L_b.
Total helix deviation F_b the distance between two design helices which enclose the actual helix over the evaluation range L_b.	diagram to follow
Helix slope deviation f_Hb The distance between two design helices which intersect the mean helix at the extremities of the evaluation range L_b. The helix slope deviation is positive when it increases the absolute value of the helix angle, and negative when it reduces it. In the case of spur gears, deviations are always positive. Their direction is identified by an index 'r' (in the sense of a right-hand thread), or 'l' (in the sense of a left-hand thread). The mean helix slope deviation f_Hbm is the algebraic mean of the helix slope deviations of a number of flanks distributed uniformly around the circumference.	Diagram to follow
Helix form deviation f_fb The distance between the two design helices parallel to the mean helix which enclose the actual helix over the evaluation range L_b.	diagram to follow
Helix angle deviation f_b The difference between the actual helix angle corresponding to the mean helix angle and the specified helix angle. It can be calculated from the helix slope deviation fhb, where approximately: f_b = (fhb/LB) · cos²b If fhb is in µm and LB is in mm, f_b is supplied in mrad; multiplication by 206.26 further supplies f_b in angular seconds.
Helix undulation f_wb A helix form deviation which recurs periodically across the facewidth is termed helix undulation f_wb when it is recognised by a series of several waves of almost constant amplitude f_wb and a constant wavelength l_b. A number of different undulations might also occur, mutually superimposed.	Diagram to follow

Generator Deviations: A generator is the line of intersection between the tooth flank and a plane tangent to the base cylinder. It is a straight line, and its inclination agrees with the base helix angle of the gear teeth, i.e. with the helix angle on the base cylinder, since the tangent plane can be regarded as the development of the base cylinder surface. On spur gears the generator is identical with the helix.

Measurement of the deviation of the generator from its desired shape - if undertaken at all - is taken in the transverse section and tangential to the base cylinder.

Diagram to follow