Non-Symmetrical Direct Extrusion—Analytical Modelling, Numerical Simulation and Experiment
Abstract
:1. Introduction
2. Theoretical Analysis
2.1. Eccentric Direct Extrusion Process
2.2. Formation of the Hollow Torus Profile
2.3. Volume of Material Flowing within the Gap
3. Experimental Apparatus and Methods
4. Experimental Results
4.1. Extrusion Process
4.2. Microstructural Examination
5. Numerical Modelling of Manufacture of Hollow Torus Pieces
6. Numerical Results and Discussion
6.1. Analysis of the Velocity and Flow Lines of the Lead Charge
6.2. Analysis of the State of Stress
7. Conclusions
- The obtained die stampings have uniform wall thicknesses and cross-sectional shapes around their circumference. They are characterised by good surface quality and favourable mechanical properties resulting from forming without damaging the metal structure. It ensures better operational properties of the elements obtained;
- The investigated technological process of forming the hollow toric elements makes it possible to obtain the desired arbitrary curvature of the torus axis in one operation, and does not require additional technological finishing;
- The value of the radius Rt of the elements formed by the direct extrusion method from a specific stock is inversely proportional to the value of the eccentric e. The height of the material does not directly affect the radius of the torus Rt. The proposed method of extrusion uses the phenomenon of a uniform flow of material with a different volume in relation to the symmetry plane of the calibrating pin in the die;
- In the case of using a die with a conical bottom with an angle close to the stabilization zone of the material flow, the extrusion force decreases. The derived geometrical relationships shows that the angle Θ of the cone of die bottom has no direct impact on the radius Rt of the torus curvature;
- By slide out of the calibrating mandrel below the plane of the die bottom, it is possible to experimentally increase the radius Rt of the extruded piece in relation to the analytically determined value of this radius;
- Along with the decreasing coefficient of friction between the extruded material and the die, the radius of the curvature of the extruded part Rt increases in relation to the calculated theoretical formula [9];
- A significant increase in the eccentric displacement of the calibration gap in the die may affect the proper flow of the workpiece material;
- The proposed design of the tooling for direct extrusion with an eccentric die opening shows a satisfactory durability, can be easily adapted in order to obtain a large range of dimensions of extruded elements, and enables simple operation.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Yield Stress Re, MPa | Ultimate Tensile Stress Rm, MPa | Elongation A5, % | Young’s Modulus E, MPa | Poisson’s Ratio ν |
---|---|---|---|---|
5 | 20 | 50 | 0.16×105 | 0.44 |
Eccentric e, mm | Number of Experiment | Radius of the Toric Part of the Pipe Rt, mm |
---|---|---|
1 | 1 | 78.7 |
2 | 76.8 | |
3 | 79.2 | |
2 | 1 | 40.1 |
2 | 39.1 | |
3 | 42.7 | |
3 | 1 | 27.2 |
2 | 27.5 | |
3 | 30.0 | |
5 | 1 | 20.1 |
2 | 17.3 | |
3 | 22.1 | |
7 | 1 | 14.7 |
2 | 13.3 | |
3 | 15.9 |
Eccentric e, mm | Number of Experiment | Radius of the Toric Part of the Pipe Rt, mm |
---|---|---|
1 | 1 | 85.4 |
2 | 84.5 | |
3 | 79.6 | |
2 | 1 | 37.6 |
2 | 42.0 | |
3 | 38.7 | |
3 | 1 | 25.4 |
2 | 31.9 | |
3 | 25.5 | |
5 | 1 | 15.8 |
2 | 18.9 | |
3 | 15.3 | |
7 | 1 | 11.1 |
2 | 12.6 | |
3 | 10.2 |
Eccentric e, mm | Radius of the Toric Part of the Pipe Rt, mm (Friction Coefficient 0.2) | Radius of the Toric Part of the Pipe Rt, mm (Friction Coefficient 0.5) |
---|---|---|
1 | 107.9 | 105.8 |
2 | 59.7 | 55.9 |
3 | 46.9 | 38.3 |
5 | 31.3 | 26.2 |
7 | 27.8 | 21.7 |
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Kowalik, M.; Paszta, P.; Trzepieciński, T.; Kukiełka, L. Non-Symmetrical Direct Extrusion—Analytical Modelling, Numerical Simulation and Experiment. Materials 2021, 14, 7856. https://doi.org/10.3390/ma14247856
Kowalik M, Paszta P, Trzepieciński T, Kukiełka L. Non-Symmetrical Direct Extrusion—Analytical Modelling, Numerical Simulation and Experiment. Materials. 2021; 14(24):7856. https://doi.org/10.3390/ma14247856
Chicago/Turabian StyleKowalik, Marek, Piotr Paszta, Tomasz Trzepieciński, and Leon Kukiełka. 2021. "Non-Symmetrical Direct Extrusion—Analytical Modelling, Numerical Simulation and Experiment" Materials 14, no. 24: 7856. https://doi.org/10.3390/ma14247856
APA StyleKowalik, M., Paszta, P., Trzepieciński, T., & Kukiełka, L. (2021). Non-Symmetrical Direct Extrusion—Analytical Modelling, Numerical Simulation and Experiment. Materials, 14(24), 7856. https://doi.org/10.3390/ma14247856