Project ForgeMachine Design
Design Against Static Load
GATE 2008
Hard
One tooth of a gear having 4 module and 32 teeth is shown, with the gear tooth and its corresponding tooth space making equal intercepts on the pitch circumference. The chordal tooth thickness 'a' and chordal addendum 'b', respectively, are closest to
- A6.08 mm, 4 mm
- B6.48 mm, 4.2 mm
- C6.28 mm, 4.3 mm
- 6.28 mm, 4.1 mm
Explanation
Pitch radius R=mT/2=4×32/2=64mm. Circular tooth thickness (arc, tooth=space) t=πm/2=6.283mm, subtending angle φ=t/R=0.0982 rad. Chordal thickness a=D·sin(φ/2)=128×sin(2.8125°)≈6.28mm. Chordal addendum b=addendum+(D/2)(1-cos(φ/2))=4+64(1-cos2.8125°)≈4+0.077≈4.1mm.
Source: GATE ME 2008 (2008)
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