Answered: Figure and table given below shows the…

Precision Machining Technology (MindTap Course List)

2nd Edition

ISBN:9781285444543

Author:Peter J. Hoffman, Eric S. Hopewell, Brian Janes

Publisher:Peter J. Hoffman, Eric S. Hopewell, Brian Janes

Chapter4: Drill Press

Section4.3: Drill Press Operations

Problem 3RQ: What unit of measure is used to define cutting speeds?

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Question

Figure and table given below shows the design details of a taper turning operation with a cutting speed of 22 m/ minute, feed 0.2 mm/ revolution; Depth of cut of 0.5 mm. Using the given data find the following. (a) Diameter "D" in mm . (b) Spindle speed in rpm. (c) Time for n passes to complete taper turning in minutes.

d
q°
L1
SI.
Parameter in
Dimension in
No: Drawing
mm
1
d
35
2
L1
28
|Cutting speed (Cs) in m/
minute
3
22
Taper angle "a" in degrees
4
14

Expert Solution

Step 1

$G i v e n d a t a C u t t i n g s p e e d V_{c} = 22 m / m i n F e e d f = 0.2 m m / r e v o l u t i o n D e p t h o f c u t d = 0.5 m m T a p e r a n g l e α = 4^{0} S m a l l d i a m e t e r d = 35 m m L e n g t h o f c u t L_{1} = 28 m m T o d e t e r m i n e 1] D i a m e t e r D = ? (m m) 2] S p i n d l e s p e e d N = ? (r p m) 3] T i m e f o r n p a s s e s t o c o m p l e t e t a p e r t u r n i n g .$

Step 2

$C a l c u l a t i o n d i a m e t e r o f t h e s h a f t w i t h t h e h e l p o f t a p e r a n l g e t a n (\frac{α}{2}) = \frac{D - d}{2 L} D - d = \tan (\frac{α}{2}) \times 2 L D = t a n (\frac{α}{2}) \times 2 L + d D = t a n (\frac{4}{2}) \times 2 (28) + 35 D = t a n (2) \times (56) + 35 D = 36.9555 m m = 37 m m (A p p r o x)$

Step 3

$C a l c u l a t i o n o f s p i n d l e s p e e d N (r p m) C u t t i n g v e l o c i t y V_{c} = \frac{π D N}{1000} S p i n d l e s p e e d N = \frac{V_{c} \times 1000}{π D} D = 37 m m V_{c} = 22 m / m i n N = \frac{V_{c} \times 1000}{π D} N = \frac{22 \times 1000}{π \times 37} N = 189.26 (r p m)$

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