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Formulas for Turning

¨Cutting speed (vc)

* Divide by 1,000 is to change to m from mm. vc (m/min): Cutting speed Dm (mm): Workpiece diameter p (3.14): Circle ratio n (min-1) :Spindle speed Check the item you want to calculate, input values in the two boxes, and then press the Calculate button. n (min-1) Dm (mm) vc (m/min)
	(Example) What is the cutting speed when n= 700 min-1, and the external diameter is ø50?
	(Answer) Substituting p=3.14, Dm=50 and n=700 into the formula vc=(p×Dm×n)÷1000=(3.14×50×700)÷1000 =110 (m/min) Cutting speed is 110 m/min.

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¨Feed (f)

f (mm/rev.): Feed per revolution l (mm/min): Cutting length per min n (min-1): Spindle speed Check the item you want to calculate, input values in the two boxes, and then press the Calculate button. l (mm/min) n (min-1) f (mm/rev)
	(Example) What is the feed per revolution when n=500 min-1, and the cutting length per minute is 120 mm/min.
	(Answer) Substitute n=500 and l=120 into the formula f=l÷n=120÷500=0.24 (mm/rev) The answer is 0.24 mm/rev.

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¨Cutting time (Tc)

Tc (min.): Cutting time lm (mm): Workpiece length l (mm/min): Cutting length per minute Input the values lm (mm) l (mm/min) Tc (min) second (s)

(Example) What is the cutting time when 100mm workpiece is machined at 1,000min-1, with feed=0.2mm/rev?

(Answer) First, calculate the cutting length per minute from the feed and the spindle speed. l=f×n=0.2×1000=200(mm/min) Substitute the answer above into the formula. Tc=lm÷l=100÷200=0.5(min) 0.5×60=30(sec) The answer is 30 seconds.

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¨Theoretical finished surface roughness (h)

h (µ): Finished surface roughness f (mm/rev.): Feed per revolution R (mm): Insert corner radius Input the values f (mm/rev) R (mm) h (µm)
	(Example) What is the theoretical finished surface roughness when the insert corner radius is 0.8 mm and feed=0.2mm/rev?
	(Answer) Substituting f=0.2 mm/rev, R=0.8 mm into the formula. h=f2÷(8×R)×1000=0.22÷(8×0.8)×1000=6.25µm The theoretical finished surface roughness is 6 µm.