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Optimization of simplified grinding wheel geometry for the accurate generation of end-mill cutters using the five-axis CNC grinding process

  • Muhammad WasifEmail author
  • Syed Amir Iqbal
  • Aqeel Ahmed
  • Muhammad Tufail
  • Mahmoud Rababah
ORIGINAL ARTICLE
  • 38 Downloads

Abstract

A simple geometric and optimal method is adopted for the five-axis CNC grinding of the end-mill cutters. In this research, initially a simplified parametric profile of the grinding wheel is constructed using line segments and circular arcs. The equation of the wheel swept-surface in five-axis grinding is derived. Then subjected to the flute profile design, the profile parameters of the grinding wheel, its relative location, and orientation with respect to the end-mill cutter are optimized, ensuring a specified normal rake angle. Finally, validation of the newly developed method has been performed using the CAD simulation; two virtually ground flutes are measured and compared with the given specifications. The normal rake angle is related with the radial rake angle by a relationship established in this work. This innovative approach can determine the non-standard grinding wheel that can be economically produced or dressed to accurately grind the end-mill cutters using the five-axis CNC grinding process.

Keywords

Five-axis grinding End-mill cutter Optimal CNC programming The inverse method 

Nomenclature

AM

Angular displacements of the mill-cutter about its axis

BM

Angular displacements about the carriage assembly rotation axis

Cr

Crossover probability

D

Constant of differentiation

DE

Differential evolution

F(l)

Designed flute profile

Fm

Ground flute profile

I

Tangent vector of the side-cutting edge at point PC

J

Vector along the rake face

K

Cross product of I and J

M

A plane perpendicular to the end-mill axis

PC

Point on helical side cutting edge C(θ) on the end-mill cutter

S

Line formed by intersection between planes Γand Π

T1

Length of line segment oGP1

T2

Length of line segment P1P2

T3

Length of line segment P4P5

PW

Point with parameter \( \left({u}_{{\mathbf{P}}_{\mathbf{W}}},{v}_{{\mathbf{P}}_{\mathbf{W}}}\right) \) in G coordinate system

R1

Radius of circular arc P2P3

R2

Radius of circular arc P3P4

SV(u, v, t)

Flute surface

WL(xWL, yWL, zWL)

Grinding-wheel location

f0f1

Line segment

f1f2

Circular arc

f2f3

Circular arc

f3f4

Line segment

l

Flute profile parameter

\( {l}_{{\mathbf{f}}_1} \)

Length of f0f1

\( {l}_{{\mathbf{f}}_2} \)

Length of curve f1f2

\( {l}_{{\mathbf{f}}_3} \)

Length of curve f2f3

\( {l}_{{\mathbf{f}}_4{\mathbf{f}}_5} \)

Length of segment f3f4

\( {l}_{{\mathbf{f}}_5} \)

Length of segment f4f5

pop

Main population

rnd

Random number

r1

Radius of f1f2

r2

Radius of f2f3

t

Specified rake angle

u

Parameter of grinding-wheel along its width

v

Angular parameter of the wheel

vR

A unit vector passing through the point PC

(xWL. yWL,zWL)

Grinding-wheel location

αn

Normal rake angle

αR

Radial rake angle

β1

Angle of line segment P1P2

γS

Secondary relief angle

γP

Primary relief angle

ψ

Helix angle

θ

Rotation angle about zT-axis

μ

Grinding-wheel rotation about xG-axis

η

Grinding-wheel rotation about zG-axis

T ≕ (oTxTyTzT)

Tool coordinate system

G(oGxGyGzG)

Grinding-wheel coordinate system

M(oMxMyMzM)

Machine coordinate system

Γ

Plane passing through point PC and normal to the cutting edge

Π

Plane normal to the cutting velocity

Notes

Authors’ contributions

All the authors have taken equal part in performing the research and are sequenced their names in consent with each other. In this research,

• A simplified parametric profile of the grinding-wheel is constructed using line segments and circular arcs. The equation of the wheel swept-surface in five-axis grinding is derived.

• Subjected to the flute profile design, the profile parameters of the grinding wheel, its relative location, and orientation with respect to the end-mill cutter are optimized, ensuring a specified normal rake angle.

• Validation of the newly developed method has been performed using the CAD simulation, two virtually ground flutes are measured and compared with the given specifications.

Grinding of end-mill cutter flutes are often achieved through the inverse method, in which a free-form grinding wheel is first determined and manufactured, the grinding wheel is then used to accurately generate the flutes; however, such free-form grinding wheels are very difficult and expensive to manufacture. Moreover, this method neither generates the rake face with the defined normal rake angle accurately nor generates the precise side-cutting edges on the end-mill cutters. To solve this issue, a simple geometric optimization approach is adopted for the multi-axis CNC grinding of the end-mill flutes.

This new approach can determine the non-standard grinding wheel that can be economically produced or dressed to accurately grind the end-mill cutters using the five-axis CNC grinding process.

Compliance with ethical standards

Conflict of interest

All the authors jointly worked together and contributed in the research and there is no conflict of interest applicable to this research or publication of it.

Availability of data and material

Authors of this publication confirm that the data supporting the findings of this study are available as its supplementary materials.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial and Manufacturing Engineering (IMD)NED University of Engineering and TechnologyKarachiPakistan
  2. 2.Mechanical Engineering DepartmentHashemite UniversityZarqaJordan

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