PSI - Issue 4

Ivo Černý / Procedia Structural Integrity 4 (2017) 35– 41

39 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

Dynamic stresses measured during rotating bending of the axle with frequency over 30 Hz, when dynamic bending force was introduced by a rotating eccentric mass at the axle top end, differed from static stresses with the exception of the distance 250 mm from the hub. The slope of the regression lines was significantly different, by almost 20 % - Fig. 7. A good agreement between the static and dynamic stresses only is at the distance 250 mm from the hub, which was the position of the machine controlling strain gauges. The controlling SGs were statically calibrated to the specified value and the machine controlled the fatigue loading exactly according to this static calibration. At different positions, the dynamic stresses did not correspond to the calibrated values due to the changes in the stress distribution along the axle. Note that such a remote position of the controlling SGs is recommended in the facility manual to avoid effects of some local worming, which may occur and actually usually occur near the hub due to microscopic friction movements under the press fit – Cervello (2016). A detailed comparison of dynamic stresses near the hub with static stresses is in Fig. 8. It can be seen that the actual dynamic average stress amplitude in the vicinity of the hub edge, at the distance 5 mm, was very significant. The difference was higher than 10%. It is clear that this phenomenon may affect the dynamic stress state under the press fit very considerably. If fatigue resistance of the axle body outside the axle seats is studied or verified, i.e. fatigue properties of the free axle surface between the wheels at the sufficient distance from the hub edge, the stress redistribution under the press fit does not matter – provided that a premature failure does not occur just under the press fit. However, if fatigue resistance under the press fit is to be verified or fatigue cracking mechanisms studied, it has to be kept in mind that high frequency tests may have unfavourable effects on the fatigue resistance – the characteristics F3 according to EN 13103 and 13104 standards and may change the damage mechanisms including the position of the main crack. Links between higher rotating bending frequency and reduced life under press fit, described e.g. by Song et al. (2014), can be connected with changes of contact forces values or their distribution, as both these factors can affect fatigue life under the press fit and fretting fatigue mechanisms – Yang et al. (2011), Lee et al. (2010). An example is given in Fig. 9, where the crack position under the press fit corresponds to the distance between 10 – 15 mm from the hub edge, which is very typical position for fretting fatigue cracking under press fits – Linhart and Černý (2011). The axle was tes ted using an older facility at frequency bellow 20 Hz. On the contrary, cracking of the axles tested within this experimental programme with the test frequency over 30 Hz occurred exactly at the hub edge, as described in Černý (2014). Similarly, fretting f atigue damage at the edge was described by Wang et al. (2011), where the investigation was performed, however, just on samples, under four point bending rotation. .

a

b

Fig. 9. Fretting fatigue crack under press fit at the distance 11 mm from the hub edge

Fig. 10. Illustrative scheme of axle deflection during rotating bending test at a) low frequency and b) high frequency

The dynamic effects on redistribution of stresses along the axle can be explained by an occurrence of additional dynamic centrifugal forces. Deformation of the axle during static calibration corresponded more or less to a beam fixed at its bottom end and loaded near the top end by lateral force acted in a single point. Calculation of lateral displacement w(x) at distance x from the point of load is not difficult, using simple relevant formula, e.g. Hoschl (1971), Klepš, Nožička et al. (1977):