Investigation of tool deflection during milling of thread in Cr-Co dental implant

  • Anna Carla AraujoEmail author
  • Guillaume Fromentin


Milling is a good option for manufacturing internal threads in hard-to-cut dental components due to lower cutting forces. In the case of a very small drilled diameter, the tool cannot be large enough to reduce tool deflection nor sufficiently small to avoid the influence of the tool penetration. As a consequence, both situations need to be considered and no other research study dealt with this aspect for the modeling of thread milling forces. This article deals with the analysis of forces, deflection, and undercutting during machining of one typical internal thread geometry used for implants in a chrome-cobalt dental alloy. The geometry is analyzed considering the influence of tool penetration and it is presented new equations to identify the regions where it occurs. Machining experiments are conducted acquiring cutting forces and tool axis position in order to calculate the tool radial forces and estimate tool deflection. Manufactured threads geometry is measured to evaluate dimension quality. It can be claimed that the tool trajectory should consider one extra revolution around the drilled hole in order to machine the undercut material due to tool deflection for this small tool diameter.


Thread milling Dental alloy Thread accuracy Chrome-cobalt Tool deflection 



Nominal thread diameter (mm)


Drilled diameter and Internal thread diameter - ISO 68-1 (mm)


Tool envelop diameter described by the front cutting edge (mm)


Diameter of the tool axis trajectory during full machining (mm)


Thread pitch (mm)


Number of machined threads at the same time


Maximum number of machined threads


Axial depth of cut (mm)


Maximum axial depth of cut (mm)


Number of tool flutes


Angle between flutes


Tool helix angle


Tooth working Angle


Cutting continuity


Spindle speed (rpm)


Cutting speed (m/min)


feed per tooth (mm/th)


feed per tooth projected in xy plane


feed per tooth projected in z direction


Maximum uncut chip thickness in front cutting edge (mm)

t, t1, t2

time (s)


Radial penetration during full machining (mm)


Radial depth of cut (mm)


Fixed Reference Frame in O and CNC tool axis coordinates: \((\hat {x(t)},\hat {y(t)},\hat {z(t)})\)

F0 = [Fx, Fy, Fz]

Force components in R0


Drilled hole position, R0 Referential Frame Origin


Moving reference Frame centered in O and tangential to workpiece surface

F1 = [Frad, Ftan, Fz]

Force components in R1


Moving reference frame centered in tool axis and fixed in one point of the cutting flute

F2 = [Fr, Ft, Fz]

Force components in R2


Angle of Tool Axis Position, angle between R1 and R0


Tool Revolution Angle, angle between R2 and R0 (rad/s)

Q, A, A1, B:

Special location points on tool axis trajectory

P1, P2, P3:

Points in hole surface


Angle between \(\overline {OP_{2}}\) and \(\overline {OA}\)


Pitch height in tool, located in the i thread (mm)


Pitch height in workpiece, located in the i thread (mm)


Difference between thread height and radial penetration located in i thread(mm)


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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical Engineering Department - Poli/COPPEUniversidade Federal do Rio de Janeiro (UFRJ)Rio de JaneiroBrazil
  2. 2.LaBoMaP, Arts et Metiers ParisTechClunyFrance

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