While turning taper using turning attachment, the setting was done for $4^{\circ},$ but the tool is set 2.5 mm below the centre. If the workpiece diameter at the small end is 35 mm. Possible error in taper angle will be _______min.

1.81

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Solution

The correct option is A 1.81
1.81

Taper angle, $α = 4^{\circ}$

Tool is set below the centre OE = h = 2.5 mm

First find the radius of big end,

$O C^{2} = O E^{2} + C E^{2}$
$= O E^{2} + O B^{2}$
$= O E^{2} + (A B + O A)^{2}$

$= O E^{2} + {(A B + \sqrt{(O D^{2} - A D^{2})})}^{2}$

$= h^{2} + {(A B + \sqrt{r^{2} - h^{2}})}^{2}$

AB = CD

Taper angle, $t a n α = \frac{R - r}{l} = \frac{A B}{l}$
$A B = l t a n α$

$O C^{2} = h^{2} + {(l t a n α + \sqrt{r^{2} - h^{2}})}^{2}$

$= (2.5)^{2} {(90 t a n 4^{\circ} + \sqrt{(17.5)^{2} - (2.5)^{2}})}^{2}$

OC = 23.7458 mm

Produced taper angle is,
$α = t a n^{- 1 [\frac{23.7458 - 17.5}{90}]} = {3.96989}^{\circ}$

Error in taper angle $= 4^{\circ} - {3.96989}^{\circ} = {0.03011}^{\circ}$

= 1.81 (min)

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While turning taper using turning attachment, the setting was done for 4∘, but the tool is set 2.5 mm below the centre. If the workpiece diameter at the small end is 35 mm. Possible error in taper angle will be _______min. 1.81

While turning taper using turning attachment, the setting was done for $4^{\circ},$ but the tool is set 2.5 mm below the centre. If the workpiece diameter at the small end is 35 mm. Possible error in taper angle will be _______min.

1.81