Solution_tutorial_9_2011_gears

# Solution_tutorial_9_2011_gears - Solution tutorial 9 gears...

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Solution – tutorial 9 – gears 1. Pitch diameter 2. mm (US units uses pitch not module) 3. The angle between the normal force and the tangential force – this is always 90 0 4. The average number of teeth in contact 5. Centre distance if mounted correctly is ½ (20 + 50) x 10 = 350 mm Actually, 355 mm = ½( D p + (50/20) D p ), giving D p = 202.857 mm compared to 20 x 10 = 200 mm ie 3 mm more. 6. 20000 = T ϖ = T (1900/60) x 2 π Hence T = 100.519 Nm F t = T /(½ D p ) = 100.519 x 1000/(20 x 12/2) = 837.66 N Total force = F t /cos(20 0 ) = 891.4 N 7. False – undercutting is only needed if the number of teeth is less than 18. 8. Input speed n a = 800 rpm. Adding relative velocities. Planet-sun contact: as radius is proportional to the number of teeth, arm radius is proportional to N s + N p n a ( N s + N p ) – n p N p = n s N s Planet-ring gear contact n a ( N o + N p ) + n p N p = 0 hence, eliminating n p n s = 2 n a ( N s + N p )/ N s = 2 x 800 (25+20)/25 = 2880 RPM ccw (+ve) Check using angular velocities relative to the arm, which are related by conventional

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Solution_tutorial_9_2011_gears - Solution tutorial 9 gears...

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