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
-
Ftis 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:
ω = 200 rad/s,
\(D = 50{\rm{}}mm = 0.05{\rm{}}m \Rightarrow R = \frac{D}{2} = 0.025m\)
P = 3 kW = 3000 W
ϕ = 20°
\(\begin{array}{l} P = Tw \Rightarrow T = \frac{P}{w} = \frac{{3000}}{{200}} = 15N.m\\ T = {F_t} \times R \Rightarrow {F_t} = \frac{T}{R} = \frac{{15}}{{0.025}} = 600N\\ F = \frac{{{F_t}}}{{\cos \phi }} = \frac{{600}}{{\cos 20^\circ }} = 638.5N \end{array}\)