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Analysis of rotational speed variations on cutting force coefficients in high-speed ball end milling


In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool deflection, tool failure, machine tool chatter and vibration, etc. Thus, an accurate prediction of cutting forces prior to actual machining is very much essential for a good insight into the process to produce good quality machined parts. In ball end milling, the cutting forces are proportional to the chip cross-sectional area and constant of proportionalities are referred as cutting force coefficients and they depend on many factors, like cutter geometry, cutting conditions, tool material and workpiece material properties. However, determining these specific cutting force coefficients in ball end milling process is not at all straightforward; rather it is fairly complex. Machining with higher cutting speed affects the chip formation mechanisms and finally causes a significant change in the cutting force coefficients. In the present study, the effect of rotational speeds has been investigated on the cutting force coefficients. A series of experiments have been performed at higher rotational speed. It has been found that the cutting force coefficients are influenced by rotational speed significantly. The results are also verified using experiments.

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a p :

Axial depth of cut (mm)

a e :

Radial depth of cut(mm)

f z :

Feed per tooth (mm/tooth)

N :

Rotational speed (rpm)

R :

Cutter radius (mm)

R z :

Local radius of cutter (mm)

R zi :

Local radius of ith cutting edge element on cutter (mm)

R(δ i ):

Local radius of cutter considering local lag angle (mm)

β :

Radial immersion angle (radian)

κ :

Axial immersion angle (°)

β ij :

Radial immersion angle of i th element of j th cutting edge (radian)

δ i :

Local lag angle (°)

δ i (z):

Local lag angle at axial position z (°)

δo :

Maximum lag angle (°)

θ :

Cutter rotation angle (radian)

ϕ p :

Pitch angle (radian)

ψ :

Helix angle (°)

ψ i :

Local helix angle (°)

\( \bar{F}_{x,y,z} \) :

Average force in x-, y- and z-directions (N)


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The experimental work was carried out using Vertical Milling Center in Manufacturing Technology Laboratory, CSIR-CMERI, Durgapur, India. The authors acknowledge the support extended by Mr. S. Y. Pujar for his assistance in conducting experiments.

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Correspondence to Mithilesh K. Dikshit.

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Technical Editor: Márcio Bacci da Silva.

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Dikshit, M.K., Puri, A.B. & Maity, A. Analysis of rotational speed variations on cutting force coefficients in high-speed ball end milling. J Braz. Soc. Mech. Sci. Eng. 39, 3529–3539 (2017).

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  • Average force
  • Ball end milling
  • Coefficients mechanistic model