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Cutting force and surface roughness depend on the tool path used in side milling: an experimental investigation


This paper proposes a method, based on the driven and self-propelled rotary tool cutting processes, using tool path strategies on side milling with a solid end mill to change the process kinematics. The main objective of this work is to evaluate the path’s influence on the cutting forces and surface roughness, and simultaneously the impact of milling parameters (cutting speed—v c , feed—f, and path period—T). A randomized experiment and a Taguchi Method were applied, and as a result of the experiments, the sinusoidal and triangular paths imply lower net forces (45–70%) and can improve surface quality with similar cutting times to the linear path method, as demonstrated by simulations. Mainly, the triangular and sinusoidal paths could increase the effective feed in the perpendicular direction of the programed feed; however, the maximum material thickness removed remains constant. Thus, this increase in feed causes a specific cutting force reduction, and consequently, forces become smaller than those on the linear path. It is possible to improve the surface roughness in comparison to the linear path, a 20–30% reduction, using the alternative paths (sinusoidal and triangular). Minimal cutting forces and surface roughness can be achieved with triangular path (also easier to program), path period T = 60 mm, cutting speed v c  = 120 m/min, and feed f = 0.1 mm/rev.

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The authors gratefully acknowledge professor I. S. Jawahir for advice during our period at the University of Kentucky. Also, the Brazilian research funding agencies Fundação Araucária [13/2014 - 4697.452.46755.29082014], CNPq (National Council for Scientific and Technological Development), CAPES (Federal Agency for the Support and Improvement of Higher Education), and FAPESP (São Paulo Research Foundation) for their financial support of this work. We would like to thank SENAI at Mogi Guaçu, represented by Ricardo Henrique Inácio for preparing the workpieces and making some equipment available and finally to Espaço da Escrita (Unicamp) that provided the English review.


a p axial depth of cut (mm)

a e radial depth of cut (mm)

CAM computer-aided manufacturing

HSS high-speed steel

LN linear path

SIN sinusoidal path

TRIA triangular path

DST descending sawtooth path

AST ascending sawtooth path

RMS root mean square

F x direction “x” force

F y direction “y” force

F z direction “z” force

F net net force

Ra average of roughness profile (μm) v c – cutting speed (m/min)

f feed (mm/rev)

fz feed per tooth (mm/tooth)

p path

T period (mm)

ANOVA analysis of variance

S/N ratio signal to noise ratio

k s specific cutting force

θ helix angle

b undeformed chip width

l fz feed length per tooth

h undeformed cutting thickness

r e tool edge radius

SPRT self-propelled rotary tool

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Correspondence to Rodrigo Henriques Lopes da Silva.

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Lopes da Silva, R.H., Hassui, A. Cutting force and surface roughness depend on the tool path used in side milling: an experimental investigation. Int J Adv Manuf Technol 96, 1445–1455 (2018).

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  • Surface roughness
  • Size effect
  • Plowing
  • Cutting force
  • Design of experiment
  • Taguchi method