a simple gear system consisting of a gearwheel A and pinion B of which the centre distance is approximately 700 mm. If the circular pitch of the gears is 40 mm and the gears have a velocity ratio of 4:1, calculate: 5.1 The number of teeth on pinion B.
To calculate the number of teeth on pinion B, we first need to determine the number of teeth on gearwheel A.
Given that the velocity ratio is 4:1, it means that the gearwheel A has 4 times more teeth than pinion B.
Let x be the number of teeth on gearwheel A and y be the number of teeth on pinion B.
x = 4y
Next, we can calculate the pitch diameter of gearwheel A:
Pitch diameter of gearwheel A = Number of teeth on gearwheel A * Circular pitch
= x * 40 mm
= 4y * 40 mm
= 160y mm
Since the center distance is approximately 700 mm, we can express this as:
Pitch diameter of gearwheel A + Pitch diameter of pinion B = Center distance
160y + (40y) = 700
200y = 700
y = 3.5
Therefore, the number of teeth on pinion B is 3.5. However, since the number of teeth must be a whole number, we can round this up to the nearest whole number which is 4.
Therefore, the number of teeth on pinion B is 4.