Multiple objective optimal design for an electrically assisted bicycle under dynamic finite element analysis

ABSTRACT

Electrically assisted bicycles have become increasingly popular in modern cities. This article presents an optimization design process to enhance the strength of an electrically assisted bicycle frame (EABF) model. This process includes several techniques such as uniform design (UD), Kriging interpolation (KGI), entropy weighting analysis (EWA), gray relational analysis (GRA), and genetic algorithm (GA). The EN 15,194 test standard is used to calculate the maximum deformation of the fork in an EABF, through falling mass (FM) and falling frame (FF) impact simulations with ANSYS/LS-DYNA software. Six geometry characteristics of an EABF are selected as control factors. The UD generates multiple simulation tests, as each control factor in the design space is continuous. Dynamic finite element analysis (FEA) is conducted to determine the maximum impact deformation (ID) of each experiment in the UD. Applying a multiple objective optimization process, the best design for an EABF is obtained. The newly designed model offers a maximum improvement of 4.20% over the original design for the largest distortion. In conclusion, the multiple objective optimization technique improves the maximum ID of an EABF.

CO EDITOR-IN-CHIEF:

• Hsieh, Sun-Yuan

ASSOCIATE EDITOR:

• Yuan, Shyan-Ming

KEYWORDS:

• Electric assisted bicycle frame
• EN 15194 standard
• maximum impact deformation
• ANSYS/LS-DYNA
• uniform design
• gray relational analysis

Nomenclature

$e_j$	=	entropy
$\mathit{G}$	=	n-dimensional column vector with all ones
$\mathit{R}$	=	a known square matrix
$\mathit{r}\left(\mathit{x}\right)$	=	n-dimensional vector
$W_j$	=	entropy weighting
$\mathit{x}$	=	a vector with unidentified input variables
$\mathit{Y}$	=	a known response vector
${\hat{y}}_{\mathit{m}}\left(\mathit{x}\right)$	=	regression function
$\mathit{\beta }$	=	a recognized constant
${\gamma }_{0\mathit{i}}\left(\mathit{j}\right)$	=	gray relational coefficients
${\mathrm{\Gamma }}_{0\mathit{i}}$	=	gray relational grade

Disclosure statement

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

Additional information

Funding

The authors would like to express our gratitude and appreciation for the financial support of the National Science and Technology Council (NSTC) under grant no’s. [109-2221-E-992 -022 and 111-2221-E-992-057]. Furthermore, I would like to thank the undergraduate research team for their collaborative effort.