# Assembly variation analysis of the non-rigid assembly with a deformation gradient model

Ibrahim Ajani (School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China)
Cong Lu (School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China)

ISSN: 0144-5154

Article publication date: 18 November 2021

Issue publication date: 11 January 2022

163

## Abstract

### Purpose

This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process.

### Design/methodology/approach

First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process.

### Findings

Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored.

### Originality/value

In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.

## Citation

Ajani, I. and Lu, C. (2022), "Assembly variation analysis of the non-rigid assembly with a deformation gradient model", Assembly Automation, Vol. 42 No. 1, pp. 40-53. https://doi.org/10.1108/AA-07-2021-0092

## Publisher

:

Emerald Publishing Limited

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