PSI - Issue 38

Martin Killmann et al. / Procedia Structural Integrity 38 (2022) 212–219 Killmann / Structural Integrity Procedia00 (2021) 000 – 000

217

6

for all interferences and geometries. The stress state in the critical area can therefore be improved by the use of gaps. The improvement is more pronounced for the elliptical geometry. For example, at an angle of 25° and an interference of 3‰ the increase in compressive prestress with gaps is about 500 MPa or 50% for the elliptical geometry and about 100 MPa or 7% for the functional elements. Similarly, the tensile stresses at process end decrease by about 400 MPa or 30% (elliptical) and 100 MPa or 6% (functional elements). A possible reason is the higher number of critical areas in the geometry with functional elements. This will be further discussed in section 3.2. It should be noted that the difference between the maximum compressive prestress and the maximum tensile stress at process end stays roughly the same with or without gaps. This shows, that the gaps only influence the compressive prestress in the beginning and not the load that is applied during forming. In absolute terms, the increase in prestress compared to the tool setup without gaps is more pronounced for high interferences. In the elliptical geometry with an angle of α = 25° it amounts to 500 MPa for 3‰ and to 1700 MPa for 9‰. Relatively, the increase is similar with about 50%, since the prestress is generally higher with a higher interference. While the stress state in the critical area is improved with the increase of compressive prestresses and decrease of fatigue-critical tangential stresses at process end, tensile stresses induced by the bending effect have to be taken into account. The analysis of the maximum tensile stresses in prestressing condition reveals that an increase in the angle α also causes higher bending stresses. For the geometry with functional elements, even the highest occurring tensile stresses during prestressing are small with 208 MPa for 9‰ and α = 35°. As was shown before, the effect of the gaps is increased for the elliptical geometry. Therefore, the tensile stresses induced by the gaps are also higher. The maximum value amounts to 811 MPa (9‰, α = 35°). Since the pressure leading to the bending effect increases with higher interferences, the tensile stresses in prestressing conditio ns are higher for 9‰ than for 3‰. At 3‰, the highest stresses are 265 MPa and occur for the elliptical geometry at α = 35°. It can be concluded, that with greater effect of the gaps, potentially critical tensile stresses due to bending also increase. This applies to different geometries as well as to higher interference fits. Having identified the effect of gaps on the inner die contour, Fig. 6 shows the contact pressure on the outer die wall depending on the angle γ for the elliptical part geometry. A higher angle γ signifies a smoother transition between the gap and the area of constant interference. The desired interference is only fully applied at the end of the angle. To use the entire prestressing effect, low angles would be desirable. However, a sharp transition leads to high and local contact pressures.

γ = 2.5

γ = 5

γ = 7.5

γ = 10

γ = 12.5

3‰ 9 ‰

p max = 2920 MPa

1600 MPa

1170 MPa

860 MPa

790 MPa

p max = 9470 MPa

6180 MPa

4090 MPa

3020 MPa

2280 MPa

Angle γ for elliptcial geometry α 30 β 5 a 0.2 mm b 0.1 mm

γ

p

0

5000 MPa

Fig. 6: Contact pressure depending on the angle γ