Answer to Question #304162 in Mechanical Engineering for Jhonny

Question

Two shafts, having axes in the same plate intersecting at an angle of 45°, turn in opposite senses at 30 rpm and 90 rpm. Draw a pair of cone to be located on these shafts and turn in pure rolling contact. Diameter of base of smaller cone is 1 in. Calculate the cone angles.

Answer 1

Solution;

From the diagram;

$\frac{r_1}{sin(45-\gamma_2)}=\frac{r_2}{sin\gamma _2}$

To find r,we can use the relation;

$\frac{N_2}{N_1}=\frac{r_1}{r_2}$

$r_2=\frac{90}{30}×1$ =3inch

Hence;

$\frac{3}{45-\gamma_2}=\frac{1}{sin\gamma _2}$

Hence;

$\gamma _2=10.79°$

$\gamma _1=45-10.79=34.21°$