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 gearwheel A
First, let's determine the pitch diameter of the gears:
Pitch Diameter of gearwheel A = Number of teeth on gearwheel A x Circular pitch
Pitch Diameter of pinion B = Number of teeth on pinion B x Circular pitch
Given that the velocity ratio is 4:1, we can write:
Number of teeth on gearwheel A / Number of teeth on pinion B = 4
Let x be the number of teeth on gearwheel A, then the number of teeth on pinion B is x/4.
Now, let's calculate the pitch diameters:
Pitch Diameter of gearwheel A = x x 40 mm = 40x mm
Pitch Diameter of pinion B = (x/4) x 40 mm = 10x mm
Next, we need to find the centre distance between the gears:
Centre Distance = Pitch Diameter of gearwheel A + Pitch Diameter of pinion B = 700 mm
Substitute the pitch diameters we calculated:
40x + 10x = 700
50x = 700
x = 14
Therefore, the number of teeth on gearwheel A is 14.