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 exact centre distance
To calculate the exact center distance between gearwheel A and pinion B, we first need to determine the number of teeth on each gear.
Given that the circular pitch is 40 mm and the velocity ratio is 4:1, we can set up the following equations:
For gearwheel A:
Number of teeth on gearwheel A = (π * Pitch Diameter of gearwheel A) / Circular Pitch
= (π * 40) / 40
= π
For Pinion B:
Number of teeth on pinion B = (π * Pitch Diameter of pinion B) / Circular Pitch
= (π * 40) / 40 * (4/1)
= 4π
Now, we can calculate the pitch diameter of each gear:
Pitch Diameter of gearwheel A = Number of teeth on gearwheel A / π
= π / π
= 1
Pitch Diameter of Pinion B = Number of teeth on pinion B / π
= 4π / π
= 4
The center distance between the two gears can be found using the formula:
Center distance = Pitch Diameter of gearwheel A + Pitch Diameter of Pinion B
= 1 + 4
= 5 mm
Therefore, the exact center distance between gearwheel A and pinion B is 5 mm.