Numerical Optimization of the Blank Dimensions in Tube Hydroforming Using Line-Search and Bisection Methods
Abstract
:1. Introduction
2. Materials and Methods
2.1. Part Geometries
- Long bulge height (Htarget) compared to the tube diameter (Htarget/Df equal to 1.9/1 and 1.5/1 respectively),
- Minimum wall thickness (wmin),
- Outer diameter corresponding to commercial blank tubes (available and suitable for the Company),
- AISI 316L material to comply with drinking water standards.
2.2. FEM Model
3. Process Optimization
- Step 1—process parameter curves. In this step, a FEM model was used to preliminary investigate the process and to identify which configurations enhance the feasibility of the part. At the end of the step, proper process parameters (pressure, punch strokes and counter-force curves) were identified and kept constant in the following steps so to focus the further analysis on less variables. Moreover, the limits where the model is stable (stability domain) were identified in terms of maximum and minimum tube dimensions (length and thickness).
- Step 2—numerical optimization. After the reduction of the number of free variables through the identification of the process curves, this step adopted a systematic approach based on numerical optimization techniques with the aim of identifying the dimensions of the tube (length and thickness, i.e., minimum amount of material) that guarantee the part requirements in terms of final height and thickness (Htarget and wmin). Their numerical optimization was constrained by the stability domain of the FEM.
- Step 3—experimental tests and final adjustments. The previous steps identified a process configuration, which is close to the optimum. Therefore, it was used as a starting point for an experimental campaign that tuned the industrial process. At the end of this step, the optimized process parameters for the production of the two parts were identified.
3.1. FEM Model
3.2. Tube Dimensions
3.2.1. Numerical Optimization Method—Description
- = (L, w),
- Constrain: L∈(Lmin; Lmax) ∧ w∈(wmin; wmax).
- Line–search method,
- Step direction: along ,
- Step length (ΔLi, Δwi): 1/10 of the domain amplitude.
- Bisection method,
- Step direction: along ,
- Step length (ΔLi, Δwi): ΔLi (or Δwi) halved at each inversion of sign for (or ),
- Convergence criterion: |ΔLi| ≤ 1 mm ∧ |Δwi| ≤ 0.02 mm.
3.2.2. Numerical Optimization Method—Implementation
3.3. Experimental Tests and Final Adjustments
4. Discussion
- H(wmin) = Htarget. It represents the most restrictive geometric requirement to focus on for the design of the process. Moreover, its achievement was very expensive in terms of blank material. In fact, a lot of material accumulated on the feeding sides during the process and only few materials reached the bulged branch of the part increasing H(wmin).
- Blank Tube Thickness (w). The numerical optimization showed that the optimum thickness of the initial blank tube was close to the minimum thickness allowed on the final part w = wmin.
- Blank tube Length (L). The length of the initial blank tube had a direct influence on H(wmin). However, the material accumulated along the feeding sides rather than reaching the expansion zone. Therefore, increasing L to enhance H(wmin) was not very efficient considering the need of raw material.
- Initial deformation. The deformation that occurred at the beginning of the process was crucial for the minimum thickness of the part. In particular, the minimum thickness in the free expansion area was mainly determined by the deformation of the tube during the initial phases. Therefore, it was important to improve these phases (see the following discussion on precrash and pressure). This result is opposite to what happens in the filling of closed die corners [23] where the minimum thickness is reached at the end of the forming process.
- Precrash. The use of a bulged counter-punch to preform the tube before expansion allowed us to reduce the thinning of the part so increasing its feasibility in accordance to [22].
- Pressure. A low pressure should be adopted in the early phase of the process so expanding the tube and reducing its thinning. After that, the pressure was less influent on thinning and it could be raised to contrast wrinkles. Moreover, as discussed in [24] the pressure is not expected to significantly enhance the height of the bulged branch, which is, as discussed, the most restrictive geometric requirement of the part.
- Other parameters. Process parameters as counter-punch force and punch velocity did not influence the feasibility of the part.
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Solver | PamStamp2G—Explicit |
Meshing | Die/Punches: Rigid Shell Tube: Deformable Shell–Double symmetry planes |
Material | AISI 316L—σ = 1453 × (ε + 0.159)0.634 |
Friction | Coulomb—Tube–Die: 0.057 Coulomb—Tube–Punch: 0.12 |
Small-Tee | Large-Tee | ||
Process | |||
Pressure (p) | p = 500 bar | p = 300 bar | |
Punch velocity (v) | v0 = 1 mm/s v = 5 mm/s | v0 = 1 mm/s v = 5 mm/s | |
Counter-punch (bulged) force (F) | F0 = 2.5 T 1 F = 1.5 T | F0 = 5 T 1 F = 3 T | |
Domain for Tube optimization | |||
Length (mm) | L ∈ (L1; L1 + 80) | L ∈ (L2; L2 + 100) | |
Thickness (mm) | w ∈ (w1; w1 + 1.25) | w ∈ (w2; w2 + 2.00) |
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Fiorentino, A.; Ginestra, P.S.; Attanasio, A.; Ceretti, E. Numerical Optimization of the Blank Dimensions in Tube Hydroforming Using Line-Search and Bisection Methods. Materials 2020, 13, 945. https://doi.org/10.3390/ma13040945
Fiorentino A, Ginestra PS, Attanasio A, Ceretti E. Numerical Optimization of the Blank Dimensions in Tube Hydroforming Using Line-Search and Bisection Methods. Materials. 2020; 13(4):945. https://doi.org/10.3390/ma13040945
Chicago/Turabian StyleFiorentino, Antonio, Paola Serena Ginestra, Aldo Attanasio, and Elisabetta Ceretti. 2020. "Numerical Optimization of the Blank Dimensions in Tube Hydroforming Using Line-Search and Bisection Methods" Materials 13, no. 4: 945. https://doi.org/10.3390/ma13040945