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§ 17

Cutting force and power requirement in turning

How many kW does the cut require, and can the machine handle it?

Answer: Before heavy rough cutting you should know whether lathe spindle motor can handle it. Power depends on cutting speed cutting depth feed and material's specific cutting force kc. kc is looked up as kc1 (at 1 mm chip thickness) in tool supplier's material table and corrected for actual chip thickness which at cutting angle 90° equals feed. Calculator gives cutting force net power and power motor must deliver.

Formula

kc = kc1 · hm^(−mc), hvor hm ≈ f ved en indstillingsvinkel på 90°

Fc = ap · f · kc (N)

Pc = vc · ap · f · kc ÷ 60.000 (kW, med vc i m/min)

Motoreffekt = Pc ÷ virkningsgrad

Symbols and units in the formula
SymbolMeaningUnit
vcCutting speed (vc)m/min
apDepth of cut (ap)mm
fTension (f)mm/omdr
kc1Material (kc1 at 1 mm chip thickness, Sandvik)N/mm²
mcChip thickness exponent (mc)
etaMachine's efficiency%
=Power the motor must deliverkW
=Cutting power at cut (Pc)kW
=Cutting force (Fc)N
=Specific cutting force at this clamping (kc)N/mm²

Validity and source

Source
Sandvik Coromant, formler for drejning (kc = kc1 · hm^−mc)

Does not apply when

  • kc1 and mc are material table values (Sandvik Coromant: unalloyed steel kc1 1,500 N/mm², mc 0.25; austenitic stainless 2,150 and 0.21; grey cast iron 1,150 and 0.28). Lower clearance angle and negative rake angle increase force. Use the figure to choose a cut, not as a guarantee.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Cutting speed (vc)200 m/min
  • Depth of cut (ap)2 mm
  • Tension (f)0.25 mm/omdr
  • Material (kc1 at 1 mm chip thickness, Sandvik)1,500 N/mm²
  • Chip thickness exponent (mc)0.25
  • Machine's efficiency80 %

Giver

  • Power the motor must deliver4.42 kW
  • Cutting power at cut (Pc)3.54 kW
  • Cutting force (Fc)1,061 N
  • Specific cutting force at this clamping (kc)2,121 N/mm²

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Sådan bruger du den

Før du tager et tungt skrubsnit, skal du vide, om drejebænkens motor kan trække det. Er effekten for høj, går maskinen i stå, eller skæret brækker. Beregneren giver skærekraften og den effekt, motoren skal levere.

Step by step

  1. Vælg skæredata: Vc, snitdybde og tilspænding.
  2. Vælg materialet, så kc1 kommer fra Sandviks materialetabel, og indtast mc (typisk 0,2-0,28).
  3. Indtast maskinens virkningsgrad, typisk 70-85 %.
  4. Sammenlign motoreffekten med spindelmotorens effekt på typeskiltet.

Typical errors

  • At bruge kc1 direkte uden at rette for spåntykkelsen. Ved små tilspændinger er kc højere.
  • At glemme maskinens virkningsgrad.
  • At sammenligne med motorens topeffekt. Den kontinuerlige effekt er lavere.

Examples from everyday life

Skrub i ulegeret stål

Du skrubdrejer en aksel i C45 med Vc 200 m/min, 2 mm snitdybde og 0,25 mm/omdr. Maskinen har en virkningsgrad på 80 %.

Cutting speed (vc)
200 m/min
Depth of cut (ap)
2 mm
Tension (f)
0.25 mm/omdr
Material (kc1 at 1 mm chip thickness, Sandvik)
Ulegeret stål, ca. 0,45 % C (kc1 ≈ 1.500)
Chip thickness exponent (mc)
0.25
Machine's efficiency
80 %

It means: kc ved denne tilspænding er 2,121 N/mm², og skærekraften 1,061 N. Snittet kræver 3.54 kW ved skæret, og motoren skal yde 4.42 kW.

Tungt snit i rustfrit

I austenitisk rustfrit tager du 4 mm snitdybde med 0,35 mm/omdr og Vc 160 m/min. mc er 0,21. Maskinens spindelmotor er på 11 kW.

Cutting speed (vc)
160 m/min
Depth of cut (ap)
4 mm
Tension (f)
0.35 mm/omdr
Material (kc1 at 1 mm chip thickness, Sandvik)
Rustfrit, austenitisk (kc1 ≈ 2.150)
Chip thickness exponent (mc)
0.21
Machine's efficiency
80 %

It means: Snittet kræver 12.51 kW af motoren. Det er mere end de 11 kW, så tag en mindre snitdybde eller sænk Vc.

Rule of thumb

Pc i kW ≈ Vc × ap × f × kc ÷ 60.000. Dobbelt snitdybde giver dobbelt effekt.

How to check the answer

Skærekraften × Vc ÷ 60.000 skal give skæreeffekten i kW.