Question

A gear having a diameter of 40 cm transmits 10 kW at 250 r.p.m. If the pressure angle is 20°, the force on the tooth of the gear is:
1. 2075 N
2. 2100 N
3. 1935 N
4. 2030 N

Answer 1

Correct Answer - Option 4 : 2030 N

Concept:

Spur gear:

• Spur gears are those gears in which teeth are straight and parallel to the axis of the shaft.
• These types of gear are noisy, more fatigue and have less life.
• Spur gears are used for very low power transmission.

Force analysis in Spur gear:

• Total force (F) acts on the common normal of the mating gears.
• Total force can be divided into two components.

1.Tangential component (Ft) = Fcosϕ

2. Radial component (Fr) = Fsinϕ

   where ϕ is pressure angle

• Ft is used to produce the power required and Fr provides thrust.
• Torque produced can be calculated as:

          T = Ft × R    (where R is pitch radius)

• The power produced can be calculated as:

           P = T × ω   (where ω is the angular velocity of gear)

Calculation:

Given:

N = 250 rpm, D = 0.4 m, P = 10 kW, ϕ = 20°

Power, P = Fcosϕ × R × ω

\(P=Fcos \phi \times R\times \frac{2\pi N}{60}\)

\(10 \times10^4 ​​=Fcos 20 \times 0.2\times \frac{2\pi \times 250}{60}\)

The total force on tooth is, F = 2030 N