An Analytical Model for Grinding Force Prediction in Ultra-Precision Machining of WC with PCD Micro Grinding Tool

Abstract

Micro grinding with a poly crystalline diamond (PCD) tool is one of the promising approaches for fabricating a micro mold on difficult-to-cut materials. As the process can also achieve good surface integrity without additional finishing processes, it could shorten total processing time and reduce total energy and resource impact. Modeling of micro grinding is necessary to understand the key design factors of the PCD tool which influence the grinding force inducing geometric errors in micromachining. This research proposes a model to describe the micro grinding of the difficult-to-cut material and predict the grinding force. The model for calculating the grinding force has been established considering contact area, grit size and distribution, tool shape, cutting depth, and cutting speed. Micromachining experiments with a PCD micro grinding tool fabricated by wire electro discharge machining have been conducted in tungsten carbide and provided the validation of the proposed model.

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Abbreviations

A c :

Cutting area (m2)

A p :

Plowing area (m2)

A s :

Contact area of the tool (m2)

d g :

Grit size (m)

d t :

Tool diameter (m)

dg,max, dg,min :

Maximum or minimum grit size (m)

d g,mean :

Mean grit size (m)

Et, Ew :

Elastic modulus of the tool and workpiece (N/m2)

F, Fn, Ft :

Grinding force, normal grinding force, and tangential grinding force (N)

Fn,r, Fn,p, Fn,c :

Normal force in rubbing, plowing, and cutting (N)

Ft,r, Ft,p, Ft,c :

Tangential force in rubbing, plowing, and cutting (N)

hc, hp :

Critical cutting depth and critical plowing depth (m)

\( h_{t}^{i} \) :

Uncut chip thickness of i grit at t moment (m)

H, Hs, Hv :

Hardness, scratch hardness, and Vickers hardness, of the workpiece (N/m2)

kd,t, kl,t :

Stiffness of the tool in lateral and depth direction (N/µm)

kd,w, kl,w :

Stiffness of the workpiece in lateral and depth direction (N/µm)

kx,m, ky,m, kz,m :

Stiffness of the machine tool in x-, y-, and z-axis direction (N/µm)

kx,total, ky,total, kz,total :

Stiffness of the total system in x-, y-, and z-axis direction (N/µm)

L :

Tool length (m)

N :

The number of grits (–)

P :

Static load (N)

r i :

Distance of i grit from center of the tool (m)

S :

Spindle speed (RPM)

t :

Time (s)

V :

Tool speed in grinding direction (m/s)

Vx, Vy, Vz :

Tool speed in x-, y-, and z-axis direction (m/s)

xc, yc, zc :

Grit center coordinate (m)

\( x_{ran}^{i} \), \( y_{ran}^{i} \), \( z_{ran}^{i} \) :

Random vector of i grit (m)

\( x_{d}^{i} , y_{d}^{i} , z_{d}^{i} \) :

Grit position in grinding in depth direction (m)

\( x_{l}^{i} , y_{l}^{i} , z_{l}^{i} \) :

Grit position in grinding in depth direction (m)

α :

Half included angle of the tip (°)

β work :

The diamond grain rate of the raw PCD (%)

δ :

Elastic deformation of the tool and the machine tool (m)

σ :

Standard deviation of grit size (m)

\( \upsilon_{t} , \upsilon_{w} \) :

Poisson’s ratio of the tool and workpiece (–)

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Acknowledgements

Authors gratefully acknowledge the financial support and the donation of the ROBONANO α-0iB, one of the latest ultra-precision machine tool, to MIN LAB at UW-Madison from the FANUC Corporation, Japan.

Funding

This study was funded by FANUC Corporation.

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Correspondence to Sangkee Min.

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Dr. Sangkee Min has received research grant from FANUC Corporation. Other authors have no conflict of interest.

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Maeng, S., Lee, P.A., Kim, B.H. et al. An Analytical Model for Grinding Force Prediction in Ultra-Precision Machining of WC with PCD Micro Grinding Tool. Int. J. of Precis. Eng. and Manuf.-Green Tech. 7, 1031–1045 (2020). https://doi.org/10.1007/s40684-020-00199-2

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Keywords

  • Micro-grinding
  • Wire electro discharge machining (WEDM)
  • Poly crystalline diamond tool
  • Difficult-to-cut material