Abstract
Digital twin, a core technology for intelligent manufacturing, has gained extensive research interest. The current research was mainly focused on digital twin based on design models representing ideal geometric features and behaviors at macroscopic scales, which is challenging to accurately represent accuracy and performance. However, a numerical representation is essential for precision microstructures whose accuracy and performance are difficult to measure. The concept of a digital twin for an accurate representation, proposed in 2015, is still in the conceptual stage without a clear construction method. Therefore, the goal of accurate representation has not been achieved. This paper defines the concept and connotation of an accuracy and performance-oriented accurate digital twin model and establishes its architecture in two levels: geometric and physical. First, a geometric digital twin model is constructed by the contact surfaces distributed error modeling and virtual assembly with nonuniform contact states. Then, based on this, a physical digital twin model is constructed by considering the linear and nonlinear response of the structural internal physical properties to the external environment and time to characterize the accuracy and performance variation. Finally, the models are evaluated. The method is validated on microtarget assembly. The estimated values of surface modeling, center offset, and stress prediction accuracy are 94.22%, 89.3%, and 83.27%. This paper provides a modeling methodology for the digital twin research to accurately represent accuracy and performance, which is critical for product quality improvements in intelligent manufacturing. Research results can be extended to larger-scale precision structures for performance prediction and optimization.
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Abbreviations
- \({\mathrm{E}}_{i}\) :
-
Elastic modulus of material i
- \({\mathrm{E}}_{i}\left(T\right)\) :
-
Elastic modulus of material i, varying with temperature
- \(\mathrm{E}\) :
-
Elastic modulus
- \({\upnu }_{i}\) :
-
Poisson's ratio of material i
- \(\upmu \) :
-
Static friction coefficient
- \({\upmu }_{i}\) :
-
Static friction coefficient at contact position i
- \({\varepsilon }_{i}\left(t,T,\sigma \right)\) :
-
The creep strain of material i, varying with time, temperature T and loaded stress σ
- \({BC}_{i}\) :
-
The i-th vector element that characterizes the boundary conditions
- \({a}_{i}\) :
-
A representation of the acceleration of different entities (1,2…i…) in a physical system
- \(\mathrm{T}\) :
-
Temperature
- GDT:
-
Geometric digital twin model
- PDT:
-
Physical digital twin model
- \(\mathrm{GEM}\) :
-
Geometric error model
- \({\mathrm{GEM}}_{i}\) :
-
Geometric error model of part i
- GDES:
-
Geometric distribution error surface
- MAE:
-
Mean absolute error
- \({TP}_{i}\) :
-
Measured values of the parameter i characterizing the accuracy and performance of the structure
- \(\Delta {Q}_{i}\) :
-
Error of GEM at point i from experimentally measured data
- \({\Delta Z}\) :
-
Tolerance of the surface
- \({{\alpha }}_{i}\) :
-
The linear expansion coefficient of material i
- \({{\alpha }}_{i}\left(T\right)\) :
-
The linear expansion coefficient of material i, varying with temperature
- \({\alpha }\) :
-
The linear expansion coefficient
- \(\upvarepsilon \) :
-
Strain
- \(\upsigma \) :
-
Stress
- \({\upmu }_{i}\left(T\right)\) :
-
Static friction coefficient at contact position i, varying with temperature
- \({\sigma }_{i}\left(t,T\right)\) :
-
Stress when relaxation occurs in a material i, varying with time and temperature T
- \({F}_{i}\left(t,T\right)\) :
-
Force, applied on structure i, when stress relaxation occurs, varying with time t and temperature T
- \({A}_{T},{ m}_{T}, {n}_{T}\) :
-
Time- and temperature-dependent material constants in creep
- ADT:
-
Accurate digital twin model
- CM:
-
Condition matrix
- \(\overline{CM }\) :
-
Condition matrix of linear PDT
- \(\widetilde{CM}\) :
-
Condition matrix of nonlinear PDT
- \({\eta }_{GA}\) :
-
Geometric accuracy
- \({\eta }_{PA}\) :
-
Physical accuracy
- \({\eta }_{ADT}\) :
-
Accuracy of ADT
- \({MP}_{i}\) :
-
Model prediction values of the parameter i characterizing the accuracy and performance of the structure
- \({\eta }_{MAE}\) :
-
Relative error of the GEM and the measured data
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Funding
The work was supported by the Natural Science Foundation of China (Project No. U1937603) and the Natural Science Foundation of China (Project No. 52205512).
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All authors contributed to the study’s conception and design. The idea is supervised by ZZ. Material preparation, data collection, and analysis were performed by ZZ and QS. JX, WW, XJ and KS helped perform the analysis with constructive discussions. Experiments were done by QS, XC and DZ. The first draft of the manuscript was written by QS, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Saren, Q., Zhang, Z., Xiong, J. et al. An accuracy and performance-oriented accurate digital twin modeling method for precision microstructures. J Intell Manuf 35, 2887–2911 (2024). https://doi.org/10.1007/s10845-023-02169-2
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DOI: https://doi.org/10.1007/s10845-023-02169-2