Answer to Question #223562 in Mechanical Engineering for Lesego Luka

Question

The request for this project is to design the diameter of the output shaft of a single reduction gearbox with a 20⁰ pressure angle involute spur gear set. The gearbox consists of two (2) shafts, four (4) bearings, two (2) spur gears, and gearbox steel casing, as shown in Figure 1 below. The gearbox is powered by a 3 kW Power, 50 Hz AC electric motor with a speed of 1440 rpm. The main goal of the gearbox is to reduce the speed to 575 rpm. The gearbox had to abide by the following: 1. The weight of the motor and gears do not add to the bending or shear stresses of the system and will be ignored when doing calculations. 2. The entire system is bolted to a horizontal bedplate and will only be accessible from the top surface. 3. The machine components, including bolts, shafts, and bearings, must all be designed with a factor of safety (ns) as 2.5. 

Answer 1

F_t = Transmitted Force

F_n = Normal Force or Separating Force

F_r = Transmitted Force

$\theta =$ pressure angle =20

$T = \frac{63000\times 3}{1440} =$ 13.125 kN

Gear Ratio $= \frac{N_B}{N_A} = \frac{1440}{575} =2.5$