Agitator nozzle fatigue from rotating bending

The vendor gives a shaft bending moment at the mounting flange. For a static check it is one load. For fatigue the point is that it rotates. A point on the nozzle wall sees the moment's full value on one side of the shaft, and its full value of opposite sign half a turn later. The agitator job builds a fatigue event that swings the bending between minus and plus the vendor's moment at operating pressure, so the range is twice the moment.

The weight, thrust and torque are steady while the machine runs. They set the mean stress the bending swings about, and they change only at start-up and shutdown, which are counted as a separate event.

At these counts the fatigue screening rules do not apply: above a million significant cycles VIII-2 asks for a fatigue analysis. And the welded joint curves keep falling with cycles, with no endurance limit below which a range does no damage. A small range repeated 10⁸ times still adds up.

The check runs along each weld line of the model: the nozzle-to-head junction on the head side and the nozzle side, and the pad's outer edge, at every node and on both faces. Each point is a possible crack site. The stress there is the structural stress, from a linearisation across the weld line: membrane and bending normal to the line. Against a solid model of a published example it reads 3 % low in membrane plus bending and does not change with the mesh.

• Method C turns the structural stress range into an equivalent range, with a thickness term for walls between 16 and 150 mm, a bending-ratio term and a mean-stress term, and reads it on the welded joint curve.
• Each event's cycles are counted against that curve, and the damage n/N is summed over the events: rotation and start-ups together.
• A point passes when the damage is at most 1.

The rotation and the start-ups are counted together. At each point the max-min method of VIII-2 Annex 5-B takes the largest range between any two load states first, counts it the smaller number of times the two states occur, and repeats until no range is left.

The dev log records the default agitator passing its stress checks at 34 % of the allowable while the welded-joint fatigue fails, with a damage of about 118 at 8.6 × 10⁸ cycles. The static ratio gives no hint of it. The levers are the bending moment itself, from the vendor, and the stiffness round the nozzle: a thicker neck, a pad, or gussets, each changing the range at the weld that governs.

Method A of the fatigue rules, an elastic stress range times a fatigue strength reduction factor read on the smooth-bar curves, is coded as well. For an as-welded joint Method C is the one to use: it is read at the weld line itself and does not depend on a factor chosen for the weld.