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Frictionally damped tool holder for long projection cutting tools

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Abstract

The machining of complex geometries and deep cavities requires the use of long projecting tool holders. However, due to their high length-to-diameter ratio, these tool holders have a high degree of static and dynamic compliance. High dynamic compliance reduces process stability and thus productivity. A new approach to lessen this is to increase the damping of long projecting tool holders by using friction dampers integrated into the tool holder shaft. The mathematical description and experimental testing of large friction-damped tool holders are the subject of this paper. With the aid of experimental modal analysis and cutting tests, the dynamic compliance and maximal cutting depth were determined. Due to the integration of friction segments in the tool holder shaft, the maximal depth of cut could be increased about 75% compared to a reference tool holder with the same diameter and length configuration.

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Abbreviations

ae :

Width of cut

ap :

Depth of cut

ap,max :

Maximal depth of cut

Aseg,i,j :

Cross section area of segment i, j

B:

Bending stiffness

D:

Damping ratio

\({\text{D}}_{{{\uppsi }_{{\text{k}}} ,{\text{m}} + }}\) :

Damping ratio of the m-th design point for high configuration of parameter k

\({{\text{D}}_{{{{{\uppsi}}}_{\text{k}}},{\text{m}} - }}\) :

Damping ratio of the m-th design point for low configuration of parameter k

dco :

Diameter of the core

dsh,i :

Inner diameter of the shaft

dsh,o :

Outer diameter of the shaft

dt :

Tool diameter

Eco :

Young's modulus of the core

Eseg,i,j :

Young's modulus of segment i, j

Esh :

Young's modulus of the shaft

fres :

Resonance frequency of the tool holder

fz :

Feed per tooth

F′i,j :

Friction force per length in the contact zone i, j between adjacent segments

F′seg,co,j :

Friction force per length in the contact zone between core and j-th segment for i = 1

F′seg,sh,j :

Friction force per length in the contact zone between shaft and j-th segment for i = Nsegr + 1

hseg :

Wall thickness of the segments

i:

Index for number of segment in r-direction

Ico :

Moment of inertia of area of the core

Iseg,i,j :

Moment of inertia of area of the segment i, j

Ish :

Moment of inertia of area of the shaft

j:

Index for number of segment in φ-direction

Lseg :

Length of the segments

Lsh :

Length of the shaft

n:

Rotational speed

Ncon :

Number of friction contact zones

Ndp :

Number of design points

Npar :

Number of parameters

Nsegφ :

Total number of segments in φ-direction

Nsegr :

Total number of segments in r-direction

pi,j :

Pressure in the friction contact zone i, j

pi,j,opt :

Optimal pressure in the contact zone i, j

qi,j :

Ratio of cross section between adjacent segments i, j and i + 1, j

s:

Standard deviation

\({{\text{u}}_{\text{e}}}\) :

Elastic deformation in Z-direction

\({{\text{u}}_{{\text{e,i,j}}}}\) :

Elastic deformation of the segment i, j in Z-direction

\({{\text{u}}_{{\text{e,seg,co,j}}}}\) :

Elastic relative deformation of the:segments with i = 1 and the core in Z-direction

\({{\text{u}}_{{\text{e,seg,i,j}}}}\) :

Elastic relative deformation of adjacent segments in Z-direction

\({{\text{u}}_{{\text{e,seg,sh,j}}}}\) :

Elastic relative deformation of the:segments with i = Nsegr and the shaft in Z-direction

\({{\text{u}}_{{\text{e,sh}}}}\) :

Elastic deformation of the shaft in Z-direction

\({{\text{u}}_{{\text{e,co}}}}\) :

Elastic deformation of the core in Z-direction

\({{\text{u}}_{\text{k}}}\) :

Kinematic displacement in Z-direction

\({{\text{u}}_{{\text{k,i,j}}}}\) :

Kinematic displacement of the segment i, j in Z-direction

\({\tilde {\text{u}}_{{\text{k,i,j}}}}\) :

Kinematic displacement of alternatingly arranged segment i, j in Z-direction

\({u_{{\text{k,sc,i,j}}}}\) :

Kinematic displacements of the shaft and core in Z-direction

\({u_{{\text{k,seg,co,j}}}}\) :

Kinematic relative displacement of the segments with i = 1 and the core in Z-direction

\({{\text{u}}_{{\text{k,seg,i,j}}}}\) :

Kinematic relative displacement of adjacent segments in Z-direction

\({{\text{u}}_{{\text{k,seg,sh,j}}}}\) :

Kinematic relative deformation of the segments with i = Nsegr and the shaft in Z-direction

w:

Bending deformation in Y-direction

w0 :

Bending deformation at the tip

\({\text{W}_{\text{D}}}\) :

Dissipation energy

\({W_{{\text{D,seg}}}}\) :

Dissipation energy based on the friction work between the segments

\({{\text{W}}_{{\text{D,seg,co}}}}\) :

Dissipation energy based on the friction work between the segments with i = 1 and the core

\({{\text{W}}_{{\text{D,seg,sh}}}}\) :

Dissipation energy based on the friction work between the segments with i = Nsegr and the shaft

\({{\text{W}}_{{\text{pot,max}}}}\) :

Maximal potential energy of the tool holder

X:

X coordinate

Y:

Normal distance from the neutral fibre of the shaft

Yc,i,j :

Normal distance from the neutral fibre of the shaft to contact zone i, j

Ys,i,j :

Normal distance from the neutral fibre of the segment i, j to contact zone i, j

ΔY:

Resolution of eddy current sensor

z:

Number of teeth

Z:

Length coordinate

γ2 :

Coherence

\({\updelta _{{\text{res}}}}\) :

Compliance of tool holder in Y-direction at the tip at resonance excitation

Δφseg :

Angular width of the segments

φ:

Angular coordinate

µ:

Coefficient of sliding friction

\({\uppsi _k}\) :

Normalized effect of parameter k on the damping ratio D

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Acknowledgements

The IGF-project 18559 N/1 (“Development of frictionally damped tool holder for long projecting rotating tools”) supported by the AiF within the programme for the promotion of industrial research (IGF) from the Federal Ministry of Economy and Energy due to a decision of the German Bundestag. The authors would like to thank Sandvik for providing the cutting tools.

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Authors and Affiliations

  1. Institute of Production Engineering and Machine Tools, Leibniz Universität Hannover, Hannover, Germany

    Berend Denkena, Benjamin Bergmann & Christian Teige

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  1. Berend Denkena
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  2. Benjamin Bergmann
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  3. Christian Teige
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Correspondence to Christian Teige.

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Denkena, B., Bergmann, B. & Teige, C. Frictionally damped tool holder for long projection cutting tools. Prod. Eng. Res. Devel. 12, 715–722 (2018). https://doi.org/10.1007/s11740-018-0847-7

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