how to solve 9

Question

5. a taper of 1-in-5 on the diameter that must be tested for correctness by using 18mm diameter rollers. The centre distance between the top and bottom rollers is 55mm. The taper is 80mm long. The top diameter of the taper is 50mm. Calculate from a neat construction the distance across the top and bottom rollers.

Answer 1

The Taper is 1 in 5 on the diameter.

Diameter of the rollers = 18 mm

Centre distance between roller is 55 mm

Top diameter of the taper is 50 mm

Let us construct a taper with two roller on each side

First let us find the angle of the Taper

tanα = 1/5

α = tan^-1(1/5)

α = 11.30°

Now consider triangle XYZ then tanα = YZ / XY

Centre Distance XY = 55

YZ = XY * tanα

YZ = 55 * tan(11.30)

YZ = 10.99

Therefore the distance across the top and bottom rollers is 10.99 mm.