Machinery's Handbook, 31st Edition
WORM GEARING
2271
Table 1. Formulas for Proportions of American Standard Fine-pitch Worms and Wormgears ANSI B6.9-1977 LETTER SYMBOLS P = Circular pitch of wormgear P = Axial pitch of the worm, P x , in the central plane P x = Axial pitch of worm P n = Normal circular pitch of worm and wormgear = P x cos λ = P cos ψ λ = Lead angle of worm d o d C Worm
Radius or Chamfer
ψ = Helix angle of wormgear n = Number of threads in worm N = Number of teeth in wormgear N = nm G m G = Ratio of gearing = N ÷ n
D
D o
Wormgear
0.0556 F G
F G min 0.8888 F G
Item
Formula
Item
Formula
WORMGEAR DIMENSIONS a
WORM DIMENSIONS
l nP x =
Lead
Pitch Diameter Outside Diameter
D = NP ÷ π = NP x ÷ π
Pitch Diameter
tan d l ' π λ = ^ h
D o = 2 C − d + 2 a
. F 1125 min G # =
d d a 2 o = +
Outside Diameter
Face Width
c d a 2 4 o 2 − − h ^
2
d
h
^
o +
Safe Minimum Length of Threaded Portion of Worm b
F D D W o 2 2 = − DIMENSIONS FOR BOTH WORM AND WORMGEAR
Addendum
a = 0.3183 P n
Tooth thickness
t n = 0.5 P n
Whole Depth Working Depth
h t = 0.7003 P n + 0.002 Approximate normal pressure angle c φ n = 20 degrees
h k = 0.6366 P n
Clearance
Center distance
C = 0.5 ( d + D )
c = h t − h k
All dimensions in inches unless otherwise indicated. a Current practice for fine-pitch worm gearing does not require the use of throated blanks. This results in the much simpler blank shown in the diagram which is quite similar to that for a spur or helical gear. The slight loss in contact resulting from the use of non-throated blanks has little effect on the load-carrying capacity of fine-pitch worm gears. It is sometimes desirable to use topping hobs for producing wormgears in which the size relation between the outside and pitch diameters must be closely controlled. In such cases the blank is made slightly larger than D o by an amount (usually from 0.010 to 0.020) depending on the pitch. Topped wormgears will appear to have a small throat which is the result of the hobbing operation. For all intents and purposes, the throating is negligible and a blank so made is not to be considered as being a throated blank. b This formula allows a sufficient length for fine-pitch worms. c As stated in the text on page 2270 , the actual pressure angle will be slightly greater due to the manufacturing process. Although the pressure angle of the cutter or grinding wheel used to produce the worm is 20 degrees, the normal pressure angle produced in the worm will actually be slightly greater, and will vary with the worm diameter, lead angle, and diameter of cutter or grind ing wheel. A method for calculating the pressure angle change is given under the heading Effect of Production Method on Worm Profile and Pressure Angle . Pitch Diameter Range of Worms: The minimum recommended worm pitch diameter is 0.250 inch and the maximum is 2.000 inches.
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