Machinery's Handbook, 31st Edition
Spur Gearing 2237 As in the previous sections, φ is the pressure angle of the gear; n is the number of teeth in the pinion; b is the dedendum constant; r c is the rack or hob tip radius constant; P is the gear diametral pitch and d TIF is the true involute form diameter. Similarly, for the mating gear:
b r
r
N 4
− +
2 2 c φ
c
(20) (21)
tan tan E
c
m
φ = −
sin
cos
φ
cos cos D P E N TIF φ =
where N is number of teeth in this mating gear and D TIF is the true involute form diameter. Profile Checker Settings.— The actual tooth profile tolerance will need to be determined on high performance gears that operate either at high unit loads or at high pitch-line veloc ity. This is done on an involute checker, a machine which requires two settings, the gear base radius and the roll angle in degrees to significant points on the involute. From the smallest diameter outward these significant points are: TIF, Contact Diameter, LPSTC, Pitch Diameter, HPSTC, and Outside Diameter. The base radius is: (22) The roll angle, in degrees, at any point is equal to the tangent of the pressure angle at that point multiplied by 57.2958. The following table shows the tangents to be used at each significant diameter. cos R P N 2 b φ =
Significant Point on Tooth Profile
Pinion tan e tan b tan c
Gear tan E tan B tan C tan φ tan D tan A
For Computation
TIF
(See Formulas (18) & (20) ) (See Formulas (2) & (5) ) (See Formulas (8) & (10) ) ( φ = Pressure angle) (See Formulas (14) & (16) )
Contact Dia. LPSTC Pitch Dia. HPSTC Outside Dia.
tan φ tan d tan a
(See Formulas (4) & (1) ) Example: F ind the significant diameters, contact ratio and hob tip radius for a 10-diame tral pitch, 23-tooth, 20-degree pressure angle pinion of 2.5-inch outside diameter if it is to mesh with a 31-tooth gear of 3.3-inch outside diameter. Thus: n = 23 d O = 2.5
P = 10 N = 31 D O = 3.3 φ = 20 °
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