# Optimization and Mapping of the Deep Drawing Force Considering Friction Combination
## 11 Conclusions
### Nomenclature  
\begin{tabular}{l l} Term & Definition \\ \(F_{d}\) & Punch load (deep drawing force) \\ \(\sigma_{1}\) & The principal stress (major stress) \\ \(F_{BH}\) & Blank holder load (force) \\ \(\mu\) & Friction coefficient \\ \(h\) & Drawing cup height (punch stroke) \\ \(t\) & Sheet metal thickness \\ \(n\) & The exponent of the strain hardening \\ \(wc\) & Radial clearance \\ \(\mu_{p}\) & Friction coefficient between punch and blank \\ \(\mu_{h}\) & Friction coefficient between holder and blank \\ \(\mu_{d}\) & Friction coefficient between die and blank \\ \(E\) & [PERSON]'s modulus \\ \(v\) & [PERSON]'s ratio \\ \(x\), \(y\), and \(z\) & The principal anisotropy axes \\ \(\sigma_{2}\) & Minor stress \\ \(\sigma_{0}\) & Yield stress in the rolling direction (0\({}^{\circ}\)) of the sheet metal \\ \(\sigma_{f=diag}\) & The mean flow stress in the die ring of the drawn cup (=\(\sigma_{f=nl}\)) \\ \(d_{Fmax}\) & The outside diameter of the flange when the drawing force is a maximum \\ \(a\) and \(\phi\) & Angles at the maximum deep drawing force \\ \(t^{\prime}\) & The instantaneous sheet metal thickness \\ \(r_{M}\) & The radius of curvature of the neutral fiber of the sheet metal \\ \(\overline{z}\) & The mean bending strain of the cross-section \\ \(\overline{z}_{total}\) & The total mean bending strain \\ \(\epsilon_{total}\) & The corresponding natural strain \\ \(\sigma_{f=max}\) & The maximum flow stress at point 2 \\ \(UTS\) & The ultimate tensile strength \\ \(F_{BH-tearing}\) & Blank holder force which caused tearing in the wall of the cup \\ \(K\) & The coefficient of the strain hardening \\ \(r\) & The coefficient of normal anisotropy \\ \(D\) & Blank diameter \\ \(d_{1}\) & Punch diameter \\ \(r_{p}\) & Punch nose radius \\ \(d_{D}\) & Die diameter \\ \(r_{d}\) & Die shoulder radius \\ \(\rho\) & Density \\ \(\sigma_{y0}\) & Yield strength \\ \(r_{0}\) & The coefficient of normal anisotropy in the rolling direction (0\({}^{\circ}\)) of the sheet metal \\ \(r_{45}\) & The coefficient of normal anisotropy in (45\({}^{\circ}\)) to the rolling direction \\  & of the sheet metal \\ \(r_{90}\) & The coefficient of normal anisotropy in (90\({}^{\circ}\)) to the rolling direction \\  & of the sheet metal \\ \(F\), \(G\), \(H\), \(L\), \(M\), and \(N\) & Factors particular to anisotropic condition of the material \\ \(\sigma_{f=m,flange}\) & The mean flow stress in the flange of the drawn cup (=\(\sigma_{f=nl}\)) \\ \(d_{m}\) & The mean diameter of the cup \\ \(d_{o}^{\prime}\) & The instantaneous blank diameter \\ \(F_{d=max}\) & Maximum deep drawing force \\ \(\epsilon_{\theta}\) & Circumferential strain \\ \(\epsilon_{t}\) & Thickness strain \\ \(\epsilon_{r}\) & Radial strain \\ \(\epsilon_{e}\) & The equivalent uniaxial strain \\ \(\epsilon_{s}\) & The incremental strain of the outside fiber of the sheet metal \\ \(\sigma_{f1=max}\) & The maximum flow stress at point 1 \\ \(\sigma_{f3-max}\) & The maximum flow stress at point 3 \\ \(F_{crack}\) & The cracking force \\ \(F_{BH-wrilling}\) & Blank holder force which caused wrinkling in the flange of the cup \\ \end{tabular}