Question:
A lathe has to have five spindle speeds. It is to cater for work ranging from 25mm to 200mm in diameter. Allowing for a cutting speed of 25m/min, find the spindle speeds using:
a) Arithmetic Progression
b) Geometric Progression
Answer:
a) Firstly utilise the formula for Feed Rate:
Calculate spindle speed for the 1st and 5th term in the series as we have the diameters for these terms:
1st term: Diameter = 200mm,
5th term: Diameter = 25mm,
The formula for Arithmetic Progression is as follows. Use Arithmetic formula and re-arrange to find the common difference (d):
Where,
a = First term
d = Common difference
n = nth term
Now use formula to find remaining spindle speeds:
Therefore according to Arithmetic Progression the 1st to 5th spindle speeds are
[40, 110, 179, 249, 318 rev/min].
b) We know from answer (a) that the 1st and 5th spindle speeds are:
The formula for Geometric Progression is as follows.
Where,
a = First term
r = Common ratio
n = nth term
Use Geometric formula and re-arrange the 5th term to find the common ratio (r):
Now use Geometric formula to find the remaining spindle speeds:
Therefore according to Geometric Progression the 1st to 5th spindle speeds are
[40, 67, 113, 189, 318 rev/min].
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