Influence of simultaneous optimisation to enhance the stress-based fatigue life of bellows joint

ABSTRACT

Motion compensators utilized in process equipment pipe connections must be able to achieve maximum expansion-contraction cycle life with low stress levels. Due to bellows convolution complicated geometrical form and simultaneous necessity of optimum material flexibility and rigidity, the nature and magnitude of the stresses induced on the bellows convolution are multifaceted. Therefore, current research primarily focused on optimizing stress-based fatigue life and predicting cycles for a variety of bellows configurations. The integrated grey relational optimization methodology with principal components has been used.  Experiment and FEA methods are employed to validate stress and fatigue equations derived from the Expansion Joint Manufacturing Equations (EJMA) data, which are then used to build experimental design models.  The experimental PCA-GRG observed is 0.146 and the predicted PCA-GRG is 0.151, which is checked by the confirmatory test. It is shown that the life cycles calculated for the alternative optimal solution, as well as theL₂₅ Taguchi run, ranged from 1.133 x 10⁵ cycles to 9.083 x 10⁵ cycles, which is the low-cycle, finite fatigue regime of the bellows material. This study enables the suitability of the PCA-GRG technique for realizing complicated relationships between desrete design factors and responses at multiple levels.

KEYWORDS:

• Simultaneous optimisation
• regression analysis
• parametric design
• taguchi method
• stress-based life cycles
• grey relational approach
• principal components

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The author confirm that the data supporting the findings of this study are available within the article. Any other data if necessary could be available by corresponding author on reasonable request.

Nomenclature

$S_a$Ambient permissible stress

${\eta }_m$Average of grade relational grades

λ Coefficient for the characteristics equation

A_cCross-sectional area bellows

$K_o$Fatigue factor considering the material and manufacturing constant (forK_g factor less than 448 MPa)

$K_g$Fatigue strength reduction constant = 0.5

$\overline{{\eta }_i}$Highest values of the average GRG of the relevant significant optimal parameter

E_bModulus of Elasticity

$E_a$Modulus of elasticity of bellows at ambient temperature

$E_b$Modulus of elasticity of bellows at design temperature

• $x_i^{\ast }$Normalised comparative sequence

• $x_o^{\ast }$Normalised referential sequence

nNumber of plies

bNumber of significant parameters resulting from the ANOVA table

L_tTangent length of bellows

t_pThickness of convolution (total)

D_bTotal diameter of bellows

Additional information

Notes on contributors

N. D. Pagar

Dr. Nitin D. Pagar has obtained his Bachelor’s in Mechanical Engineering from Government College of Engineering, Aurangabad, Master’s in Design Engineering from Pune University and obtained PhD from in Mechanical and Materials Technology from the Department of Technology, SPPU, Pune. He has about 15 years of Teaching Experience and 4 years of Research / Industrial experience. His area of interest includes Structural Dynamics, Multi- Attributed Decision Making (MADM) Parametric Optimization, Stress Analysis, Materials and Design. Recently, he is working as a Teaching Faculty at MIT School of Engineering (Mechanical Department), MIT-ADT University, Pune. He is Permanent member of ISTE and Indian Institute of Metals (IIM). Author also working as a reviewer of many International peer-reviewed indexed international journals and conferences.