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Initial residual stress measurement based on piecewise calculation methods for predicting machining deformation of aeronautical monolithic components

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Abstract

Release and rebalance of initial residual stress of pre-stretched aluminum alloy plates in processing is the main factor affecting the machining deformation of aeronautic monolithic components. Precision measurement of the initial residual stress is of great significance for predicting and controlling the machining deformation. In this paper, two piecewise calculation methods for calculating the initial residual stress were presented. A test method based on superposition principle of elastic deformation was proposed to calculate the residual stress in the outer layer. Another method to calculate residual stress in the outer layer was crack compliance method using frontal strain instead of back strain. Then, the residual stress in the inner layer was calculated by the crack compliance method, and the influence of the order of interpolation polynomials on the results was studied. The accuracy of the two new methods were verified by finite element simulation and machining experiments. Considering only the initial residual stress, a relatively higher prediction accuracy of machining deformation can be obtained.

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Abbreviations

α :

Column vector of residual stress (MPa)

A :

Coefficient column vector

B 1 :

Frontal uniform stress compliance function (με/MPa)

B 2 :

Back uniform stress compliance function (με/MPa)

C 1 :

Frontal compliance function (με·mm/N)

C 2 :

Back compliance function (με·mm/N)

f :

Depth of each cut (mm)

m :

The number of segments of the thickness

n :

The number of orders of polynomials

s :

Root mean square of errors in calculation of back strain (με)

P:

Polynomial matrix (MPa)

\( \overset{\frown }{\mathbf{P}} \) :

Polynomial matrix containing P and α (MPa)

σ :

Initial residual stress (MPa)

\( \overset{\frown }{\boldsymbol{\upsigma}} \) :

Calculated initial residual stress (MPa)

σ inner :

Initial residual stress in the inner layer (MPa)

σ outer :

Initial residual stress in the outer layer (MPa)

ε 1 :

Measured frontal strain (με)

ε 2 :

Measured back strain (με)

ε 2 ′ :

Revised measured back strain (με)

\( {\overset{\frown }{\boldsymbol{\upvarepsilon}}}_2 \) :

Back strain calculated by \( \overset{\frown }{\boldsymbol{\upsigma}} \) (με)

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Funding

This work was supported by National Natural Science Foundation of China (Grant No. 51705281) and Shenzhen Foundational Research Project (Discipline Layout) (grant No. JCYJ20160428181916222).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Shuailei Fu, Pingfa Feng & Liping Wang

  2. Division of Advanced Manufacturing, Graduate School at Shenzhen, Tsinghua University, Shenzhen, 518055, People’s Republic of China

    Pingfa Feng & Yuan Ma

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  1. Shuailei Fu
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Correspondence to Yuan Ma.

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Fu, S., Feng, P., Ma, Y. et al. Initial residual stress measurement based on piecewise calculation methods for predicting machining deformation of aeronautical monolithic components. Int J Adv Manuf Technol 108, 2063–2078 (2020). https://doi.org/10.1007/s00170-020-05493-6

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