Digital-twin-driven geometric optimization of centrifugal impeller with free-form blades for five-axis flank milling
Introduction
Centrifugal impeller (CI) has become the essential rotating component of power units such as small-scale gas turbine engine [1] and supercharger because of its simple structure and high efficiency at low flow rate [2]. For a CI product, although the performance parameters such as efficiency and pressure ratio are quite significant, small-scale power units pay more attentions to manufacturing costs from the viewpoint of the application object [3]. Generally, free-form surface blade (FFSB) [4] is mainly adopted in CI. Although the freedom degree of design is large enough [5], it can only be machined by end milling with relatively lower efficiency [6] (as the bottom of the cutter serves as the major cutting edge). Existing investigations reveal that if the blade surface is developable and ruled, the CI can be machined by flank milling [7]. By the means, the envelope surface [8] of the tool are tangent to the machined surface, and thus the side edge of the tool becomes the major cutting edge, which not only possesses high machining efficiency but also obviously improves surface finishment [9]. Therefore, for a CI_FFSB, an effective approach to improve machinability is to transform FFSB into approximately developable ruled surface blade (DRSB) through the geometry optimization [10,11]. However, accompanied deformations of blade surface usually lead to a negative effect on CI aerodynamic performance [12]. It is extremely challenging to take comprehensive consideration of both aerodynamic performance and machinability in the process of geometric optimization.
In recent years, many investigations have been implemented to improve the machinability by making a CI_FFSB approximately developable and ruled. Pyo Lim et al. [13] improved the machining efficiency of non-developable ruled surfaces through optimization. Zhang et al. [14] took the combination of points and lines as the subject of spatial transformation to form ruled surfaces by the point-line trajectory, which solved the issue of path planning of blade tools with rules surface. Fan et al. [15] presented a five-axis machining method based on bicubic NURBS surface to implement regional milling. Qiao et al. [16] introduced a generic rotation tool management module to realize the adaptive control of nonlinear error for major five-axis machine tools. Hu et al. [17] proposed a display method that could solve the problems of shape adjustment and shape control for developable surface. From aerodynamic optimization point of view, MS Campobasso et al. [18] used a two-stage multiple-objective optimization strategy to improve CI aerodynamic performance, which verified that the sensitivity to the error of the blade geometry can be depressed by reducing speed and moving the radial profile of CI upward. Do Yu et al. [19] developed two frame modules to improve the aerodynamic performance of blades. However, very few studies have considered both aerodynamic performance and machinability comprehensively. A. Panizza et al. [20] investigated the influence of machining parameters on CI aerodynamic performance, to optimize the machining parameters accordingly. The results indicated that the CI with ruled surface is more likely to produce secondary flow that easily results in the decline of efficiency and aerodynamic performance. Dong et al. [21] studied the impact of scallop height generated in the CI hub machining on aerodynamic performance. It can be concluded that the flow losses and the slip rate may decrease with the reduction of the scallop height. Although the above studies partly revealed the influence rule of DRSB on aerodynamic performance, the optimal balance point between machinability and aerodynamic performance has not been found from the perspective of comprehensive optimization strategy.
Industry 4.0 [22] and smart manufacturing [23,24] provide an effective resolution to forecast and optimize the behavior of CI production at each life cycle phase, which can be fully enabled by Digital Twin (DT) technology [25]. DT creates virtual model of physical entity through digitization [26] and simulates the behaviors of physical entity accompanied with fusion of Cyber-Physical Data [27]. By the integrated methods of, virtual-reality interactive feedback, data fusion analysis and decision-making iteration optimization, it has added or expanded new abilities for physical entity [28]. Besides, there have been some exploratory applications of DT technology in the field of turbomachinery. The DT five-dimension structure model [29,30] has greatly facilitated the theoretical applications of DT in the field of design and manufacture of CI. Wang [31] came up with a DT model for fault diagnosis of impeller rotor, and collected experimental data from simulating imbalance fault of rotor system. A Baldassarre [32] applied a new virtual prototype to the design of turbine blade, and built a DT model by the combination of experimental data of blade geometry structure, which could be used to trace and predict the structural changes and product life of CI.
Traditional CI development procedure experiences multiple iterative cooperations of CAD (Computer Aided Design), CAM (Computer Aided Manufacturing), CFD (Computational Fluid Dynamics) and Aerodynamics Test (AT) until the performance meets the requirements of design. The multiple-dimension and real-time of DT provide a novel idea for the integrated design and comprehensive optimization for CI. This paper presents a DT-based optimization strategy and the corresponding DT model. Reinforce Learning (RL) [33] is adopted to conduct iterative optimization of CI from two aspects of machinability and aerodynamic performance, so as to find the optimal CI model that satisfies the decision-making criteria. In addition, the verification has been carried out through machining experiment and performance test. The presented method can significantly accelerate the integrated design and manufacturing of CI as well as shorten the design cycle, which offers and identifies a new role of DT for CI smart manufacturing. The advantages of the presented method can be elaborated in the two aspects: ① The presented comprehensive optimization method facilitates to pursue an optimal balance between aerodynamic performance and machining efficiency for arbitrary CI based on DT technology, which improves the CI design technology. ② The CI real-world space can provide an immediate feedback to CI virtual DT model, which accelerates the integration of design and manufacturing and thus further facilitates CI smart manufacturing. The rest of this paper is arranged as follows: Section 2 introduces the DT model for CI optimization; Section 3 shows the method to achieve approximately developable and ruled surface so as to accommodate five-axis flank milling; Section 4 evaluates the impact of DRSB on aerodynamic performance; Section 5 introduces the DT-driven comprehensive optimization criteria of CI based on RL; Section 6 conducts experimental verification. This is followed by the concluding remarks in the final section.
Section snippets
Digital twin model for CI geometric optimization
This paper introduces the DT technology to develop the CI product. Accompanied with the iterative optimization and cooperation mechanism of physical products and virtual products, it integrates geometric modeling, machinability optimization and aerodynamic performance evaluation, which improves the design capability and accelerates the development of CI. Aiming at the universal DT model proposed by Tao Fei [34], the reified DT five-dimensional structure model for CI geometric optimization is
Digital-twin-driven geometric modeling
CI parametric model is pretty significant for the DT model due to not only the connected various sub-modules in the virtual model, but also the vector of DT data. MS, SGV and SSL are taken as parameters (as shown in Fig. 2) to set up a parametric geometric modeling platform.
The presented parametric platform facilitates the presented parameters to be transferred among various functional modules rapidly and effectively based on the previous researches of our group [39]. An integrated acquisition,
Influence of CI ruled-surface approximation on aerodynamic performance
Generally speaking, the transformation from CI_FFSB to CI_DRSB may produce a negative influence on aerodynamic performance, which can be evaluated in our DT model from two aspects, including CI characteristics and internal flow field [43].
Optimization decision-making based on reinforcement learning
For the service model, in order to make CI geometric parameters in DT model proposed in this paper dynamically updated and optimized, it is pretty necessary to conduct optimization decision-making. Taking aerodynamic performance and machinability as evaluation indexes, the CI optimization criterion is developed by reinforcement learning (RL) algorithm. In the early training stage, numerous methods are used to guide learning, such as continuous trial and error, as well as rewards obtained by
Machining experiment
In order to verify the improvement of machinability and provide immediate feedback to DT model, a contrast milling experiment with respect to two various CI models, CI_FFSB and CI_DRSB, is conducted. For both the two milling cases, Aluminum alloy (7075) is adopted as the material of workpiece. The machine tool is a five-axis machining center, JDGR200 V, as shown in Fig. 20. All the cutters for MS surface roughing, blade surface roughing and blade surface finishing are D8R1 ball-end milling
Conclusions
To conduct a comprehensive optimization on a centrifugal impeller (CI) dynamically and iteratively consider both machinability and aerodynamic performance, a DT-based optimization strategy is presented in this paper. Various simulations and experiments are implemented to accommodate virtual model and physical entity. Reinforce Learning is introduced to determine the optimization decision-making. The presented method connects the physical and virtual spaces, facilitates iterative optimization
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work is supported by the Basic Research Program of the National Natural Science Foundation of China (Grant Nos. 51775025, 51205015 and 11872015) and China Key Research and Development plan (Grant NO. 2018YFB0104100).
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