Stress, Vibration and Fatigue (FEA) Analysis on Bellows

Stress, Vibration and Fatigue (FEA) Analysis was Performed on a Bellows. The 28-convolution Bellows was Designed 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.

Structural Analysis

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.

The analysis determined that for the original design, the imposed alternating stress level results in a 2,000,000 life cycle for the 28-
convolution bellows. This is less than the desired life of 13.14 billion.

One solution to reduce the stresses in the bellows is to make it more flexible by increasing the number of convolutions. New finite element models with 5 and 10 more convolutions were constructed. The number of elements was increased to 402,900 and 460,000, respectively.
Structural and fatigue analyses were performed on these alternate designs.

Analyses results indicated the number of expected life cycles to be about and over the goal of 13.14 billion cycles for the design with 33 and 38 convolutions, respectively. Generally failure is not expected in less than 3 to 5 times the calculated number of life cycles based on a design fatigue curve.

Modal Analysis

To enable the model to predict all possible natural frequencies of the assembly, a complete 360-degree model of the 28-convolution bellows was constructed. This model included over 1,027,000 nodes and 691,000 elements.

For the modal analysis boundary conditions, the bottom head was held stationary while allowing the top head to move in any direction in the horizontal plane. Both bellows ends remain parallel at a constant distance apart at all times. Modal analysis was initially performed on the 28-
convolution bellows. Since the addition of convolutions to the original design makes the bellows more flexible and consequently reduces the natural frequencies, We also performed modal analyses on the bellows with 33 and 38 convolutions. The image on the top-right depicts the 3rd Natural Frequency Mode Shape for the 28-Convolution Bellows.

O’Donnell Consulting Performs (Thermal, Stress, Vibration and Fatigue) Finite Element Analysis on Components including Vessels, Heat Exchangers and Bellows to various Engineering Codes.