1 Introduction
2 State of the art
3 Digital twin for TPRR
3.1 Ring rolling machine
3.2 FEM model
Name | A | B | n | C | \(T_{0}\) | \(T_{\mathrm {m}}\) | m |
---|---|---|---|---|---|---|---|
Unit | MPa | MPa | – | K | K | – | |
Value | 100 | 607 | 0.151 | 0.005 | 366 | 1000 | 1.04 |
3.3 Virtual sensors
3.4 Comparison with experiments
4 Soft sensor for TPRR
4.1 Concept
Name | \(h_c\) | \(v_t\) | \(\theta _{start}\) |
---|---|---|---|
Maximal value | 120 | 0.1 | 870 |
Minimal value | 0 | 0.3 | 1070 |
Units | \(\hbox {W}\,{\hbox {mm}^{-2}}\) | \(\hbox {mm}\,\hbox {s}^{-1}\) | K |
4.2 Hardening model
Name | Value | Units |
---|---|---|
K | 22 | \(\hbox {N}\,{\hbox {mm}^{{-2}/{3}}}\) |
\(k_{v}\) | 0.1 | – |
M | 2.7 | – |
G | 80 | GPa |
b | 2.6 | Å |
\(d_{0}\) | 20 | m |
\(\gamma ^{d}\) | 1.35 | – |
\(c_{1}\) | \(18 e^{{-9200}/{R\theta }}\) | \(\text {s}^{-1}\) |
\(c_{2}\) | 1.43 | – |
\(c_{3}\) | 0.08 | – |
\(Q_{0}\) | 20 | \(\text {s}^{-1}\) |
\({\bar{\rho }}_{c}\) | \(0.015 e^{{10000}/{R\theta }}\) | – |
\(N_{q}\) | 1.02 | – |
\(A_{0}\) | 30 | \(\text {s}^{-1}\) |
\(\alpha _{0}\) | 1.44 | \(\text {s}^{-1}\) |
\(\gamma _{0}\) | 3.07 | – |
\(\alpha _{2}\) | 78.68 | – |
\(\gamma _{2}\) | 0.12 | – |
\(\gamma _{3}\) | 1.06 | – |