Circumferential bending
Circumferential bending is the loading of a - mostly rod-shaped , in particular metallic - component perpendicular to its longitudinal axis by a bending force , the effective direction of which encircles the component radially , so that it suffers a circumferential elastic deformation .
In practice, it is mostly the reverse kinematically : the component, for example a shaft with a circular or circular cross-section , rotates around its longitudinal axis, while the bending force - from the point of view of an outside observer - maintains its effective direction unchanged. The result, namely a circumferential elastic deformation of the shaft, is of course the same for both variants.
From a structural point of view, in a first design, the bending force can act on the free end of a rotating shaft that is mounted on one side , like a cantilever beam . According to the second design, which is much more common in practice, the rotating shaft is supported at two points at a suitable axial distance and is subject to bending between the two support points.
example
A wheel axle rigidly connected to two wagon wheels at both ends bends elastically all around when the wagon moves under the wagon load carried by it (via a bearing) and lying between the wheels.
In the case of circumferential bending, it is therefore a question of changing loads on the shaft material . The risk of breakage depends on the level of the bending force as well as the number of bending stresses (load cycles) on the shaft, which follow one another continuously as a result of the shaft revolutions. The higher the bending force and / or the more load cycles take place, the greater the probability that the shaft will break (prematurely).
The dependence of the fracture behavior on the bending load (and the resulting stress in the material ) on the one hand and the number of load cycles (shaft revolutions) on the other hand can be graphically represented and illustrated by a Wöhler curve . Here, a concavely curved first (left) branch of the curve (the fatigue strength ) shows that the number of load cycles up to breakage will be smaller, the higher the tension generated by the bending force in the shaft material. As the load (tension) decreases, the Wöhler curve finally merges approximately tangentially into a second branch of the curve on the right, which has a straight horizontal course. This straight, horizontal branch of the curve is called fatigue strength . In this comparatively low load or voltage range, load cycles (shaft revolutions) of many millions are possible before the shaft breaks.
If the bending load is correspondingly strong and the bending frequency (shaft speed ) is high, circumferential bending can cause vibration cracking to occur in conjunction with a corrosion medium. This leads to (further) reductions in stress at break and number of cycles at break.
See also
literature
- Dubbels Taschenbuch für den Maschinenbau, 11th edition, Berlin / Göttingen / Heidelberg 1956, vol. 1
- HÜTTE, Des Ingenieurs Taschenbuch, 28th edition, Berlin 1955, Vol. I Theoretical Basics