**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

W_{1} = 3kN = 3 × 10^{3 }N

W_{2} = 2kN = 2 × 10^{3 }N

W_{3} = 1kN = 1 × 10^{3 }N

Number of revolutions

n_{1 }= 0.1n

n_{2 }= 0.2n

n_{3 }= 0.3n

n_{4 }= [1- (0.1+0.2+0.3)]n = 0.4n

Life of the bearing corresponding to reliability of 95% L_{90 }= 20 × 10^{6 }rev

Life of the bearing corresponding to reliability of 90% L_{90 }= ?

b = 1.17

Equivalent dynamic loads

So, the dynamic load rating,