Find Number of Teeth for Gear and Angular Velocity Ratio

PROBLEM

For the gearbox shown, we know the number of teeth for the following gears: Z1 = 20, Z2 = 34, and Z3 = 18. Shafts 0, B, and Z are coaxial.

The gear sets have modules m12 = 4 mm and m34 = 3 mm.

a) Determine the number of teeth for gear 4 (Z4).

b) Determine the ratio ωZ/ωB, i.e., from shaft Z to shaft B, when ω0=0.

c) Determine the ratio ωZ/ω0, i.e., from shaft Z to shaft 0, when ωB=ω0/2.

N.B. – All gears are cut with a standard rack (α = 200 , ha = m , c = 0.25m), with no displacement.

SOLUTION

Dynamic loads

W1 = 3kN = 3 × 10N

W2 = 2kN = 2 × 10N

W3 = 1kN = 1 × 10N

Number of revolutions

n= 0.1n

n= 0.2n

n= 0.3n

n= [1- (0.1+0.2+0.3)]n = 0.4n

Life of the bearing corresponding to reliability of 95% L90 =  20 × 10rev

Life of the bearing corresponding to reliability of 90% L90 = ?

b = 1.17

Since we know L95 value,

Equivalent dynamic loads

So, the dynamic load rating,