Stress, vibration and fatigue (FEA) analysis was performed on a bellows design. The 28-convolution bellows was intended to last for 5 years, or 13.14 billion cycles.
The bellows assembly is installed in a vertical orientation with its bottom end stationary. Its top end is subjected to a load that causes its top end to move in a circular motion. Both bellows ends remain parallel at a constant distance apart at all times. The resulting motion from the load placed upon this assembly causes the top end to circle around the bellows axis at a radius of 5 mm with a speed of 6,000 rpm.
Finite element analysis (FEA) was used for stress and fatigue evaluations. All geometry and operating data were provided by the client. We constructed a three-dimensional model (using Ansys 3-D solid elements) of the entire bellows, including all 28 convolutions and both ends.
Bellows convolutions and ends are geometrically symmetrical about any vertical planes through its axial centerline. However, the applied horizontal cyclic load acting on the top end, at any given time, is symmetrical only about the vertical plane that includes the applied load. Due to this symmetry condition, only one half of the bellows assembly was modeled and analyzed.
The material properties were obtained from the ASME Code Section II, Part D. The finite element analyses included two types of analysis: 1) fatigue analysis and 2) modal analysis. The fatigue analysis first involved determining the stress distributions during a typical rotation cycle. The resulting largest alternating stresses were then used to perform fatigue analysis to determine the life of the bellows. Natural frequencies of the bellows design were obtained from a modal analysis of the assembly.
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