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Omni Gear and Machine Corporation
90 Bissel Street
Joliet, Illinois 60432
Toll Free: (800) 876-7216
Fax: (815) 723-9207
Hours: Mon.-Fri. 7:00AM-4:30PM
Sat. 7:00AM-noon

Technical Gear Information

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Wire
Measurements
EXTERNAL HELICAL GEARS

Determining Tooth
Thickness of External
Helical Gear with
Dimension over Pins
or Balls

TO GET HAVING RULE FORMULA
N Number of teeth Given 31
DP Normal diametral pitch 11
  Normal pressure angle 25
h Pitch helix angle 45
d Pin diameter 0.15709
DE Dimension over pins even # of teeth  
DO Dimension over pins odd # of teeth 4.07900
αd Transverse pressure angle TAN(αn)=TAN(αn)/COS(h) 33.40320
H Base helix angle TAN (H)= TAN (h) •COSαd 39.85571
dD Transverse pin diameter d/COS(H) 0.20463
PD Pitch diameter N/[DP•COS(h)] 3.98551
BD Base diameter PD•COS(αd) 3.32717
CE Twice the center distance of pin and gear even # of teeth DE-d ***********
CO Twice the center distance of pin and gear odd # of teeth (DO-d)/COS(90/N) 3.92695
β Pressure angle to pin center COS(β)=BD/CE or CO 32.08442
INVβ Involute function of b TAN(β)-[β(π/180)] 0.06694
INVαd Involute function of ad TAN(αd)-[αd(π/180)] 0.07646
E   π/N 0.10134
D   dD/BD 0.06150
td Transverse arc tooth thickness PD•(E+INVβ-INVαd-D) 0.12082
tn Normal arc tooth thickness td/COS(h) 0.08544

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Reprinted from Ash Gear & Supply

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