Table 1 Heat flux models in drilling
From: Recent Advances in Drilling Tool Temperature: A State-of-the-Art Review
Authors and year | Model | Divide into ECTs | Inverse heat conduction | Plowing effect | The materials’ property |
|---|---|---|---|---|---|
Agapiou et al. 1994 [7] | \(\left\{ {\begin{array}{*{20}c} {T_{{int}} (r_{i} ) = \Delta T_{S} (r_{i} ) + \Delta T_{f} (r_{i} ) + T_{R} } \\ {\Delta T_{S} (r_{i} ) = (R_{1} \cdot \tau (r_{i} ) \cdot A_{S} V_{s} )/(\rho _{\omega } C_{\omega } A \cdot V)} \\ {\Delta T_{f} (r_{i} ) = 4\left( {1 - R_{{2S}} \left( {r_{i} } \right)} \right) \cdot q_{{fi}} .L_{2} (r_{i} )/3} \\ \end{array} } \right.\) | YES | NO | NO | NO |
Kalidas et al. 2002[14] | \(\left\{\begin{array}{c}{q}_{1}={\mathrm{\varnothing }}_{1}\left(\frac{L-Z}{L-{d}_{Z}}\right)\\ {q}_{2}={\mathrm{\varnothing }}_{2}\frac{{T}_{lips}\omega +{F}_{lips}{V}_{f}}{{A}_{lips}}\\ {q}_{3}={\mathrm{\varnothing }}_{3}\frac{{T}_{point}\omega +{F}_{point}{V}_{f}}{{A}_{point}}\end{array}\right.\) | YES | YES | NO | NO |
Wu et al. 2009[17] | \(\left\{\begin{array}{c}{q}_{t-c}={q}_{k}+{q}_{r}-{f}_{1}{q}_{g}\\ {q}_{t-w}=-{q}_{k}-{q}_{r}-{f}_{2}{q}_{g}\\ {q}_{g}=\eta \tau \frac{\Delta S}{\Delta t}\end{array}\right.\) | YES | NO | NO | NO |
Bono et al. 2002[9] | \(\left\{\begin{array}{c}{{q}{\mathrm{^{\prime}}\mathrm{^{\prime}}}}_{wp}=\frac{\left(1-{q}_{f}/q\right)\left(T\omega +{F}_{z}{V}_{f}\right)}{\pi \left({r}_{outer}^{2}-{r}_{inner}^{2}\right)}\\ {{q}{\mathrm{^{\prime}}\mathrm{^{\prime}}}}_{drill}=\frac{(1-{R}_{2})({q}_{f}/q)\left(T\omega +{F}_{z}{V}_{f}\right)}{area \space of \space element}\end{array}\right.\) | YES | NO | NO | NO |
Zhu et al. 2012[19] | \({q}_{0}=\frac{\alpha \left(T\omega +{F}_{z}{V}_{f}\right)}{\uppi {(d/2)}^{2}/\mathrm{sin}59^\circ }\) | YES | NO | NO | YES |
Patne et al. 2017[21] | \(\left\{\begin{array}{c}{q}_{tool}^{shear}=\left(1-{B}_{d}\right){V}_{C}.{\rho }_{\omega }.{C}_{\omega }.{T}_{s}.b.{t}_{2}\\ {q}_{tool}^{rake}=\left(1-{B}_{k}\right){q}_{f}=\left(1-{B}_{k}\right){F}_{f}.{V}_{c}\\ {q}_{tool}^{flank}=\left(1-{B}_{f}\right){q}_{flank}=\left(1-{B}_{f}\right){F}_{c\omega }.V\end{array}\right.\) | YES | NO | YES | NO |
Álvarez et al. 2014[23] | \(\left\{\begin{array}{c}dQ=d{W}_{T}+d{W}_{F}-d{E}_{f}\\ d{E}_{f}\left(\theta \right)={\omega }_{f}d{V}_{f}\left(\theta \right)\\ d{V}_{f}\left(\theta \right)=\pi {L}_{cut}^{2}{f}_{cut}\frac{d\theta }{2\uppi }\end{array}\right.\) | NO | NO | NO | YES |
Li et al. 2007[37] | \(\left\{\begin{array}{c}{Q}_{tool}^{friction}={B}_{2}{Q}_{f}={B}_{2}{F}_{f}{V}_{c}\\ {{q}{{^{\prime}}{^{\prime}}}}_{tool}=\frac{{B}_{2}{q}_{f}}{{l}_{c}l}\\ {B}_{2}={(1+0.45\frac{{K}_{t}}{{K}_{w}}\sqrt{\frac{\uppi {\alpha }_{\omega }}{{V}_{c}{l}_{c}}})}^{-1}\end{array}\right.\) | YES | YES | NO | NO |