GATE Past Year Questions: Gears | Theory of Machines (TOM) - Mechanical Engineering PDF Download

Since higher pair has a line or point contact and lower pair has a surface of Area contact. Hence both are true. i.e., spur gear has line contact (Higher pair) and Revolute joint has surface contact (lower pair).

Lewis equation is given as

⇒ nearest stress in gear tooth taking in account some F.O.S., σ = 58

P = Tω
∴ 20 × 10³ =T.2π × 30
⇒ T =106. 1 Nm
Now, T = F_t. r

∴ Resultant force,

We know

where, Np = speed of pinion, NG = speed of gear wheel TG = number of teeth of gear, Tp = number of teeth of pinion

or N_G = 400 r.p.m.
Since power transmitted by both gear will be equal
i.e. T_pω_p = T_Gω_G
where,
Tp = torque transmited by pinion
TG = torque transmitted by gear wheel

∴ Torque transmitted by gear, T_G = 60 N-m.

⇒ b = addendum + PR
The addendum = module for standard addendum


∴ OP= 64 cos ϕ = 63.9
⇒ b = m + PR
= 4 + (64 - 63.9) = 4.1 mm

Z_min = Minimum number of teeth on pinion to avoid interference.

Worm gearing isused for reduction ratios greater than 20.

Velocity reduction = 36/1440 = 1/40
For this kind of reduction, worm gear arrangement is most suitable.