Development of a piezoelectrically actuated dual-stage fast tool servo
Introduction
Fast tool servo (FTS) diamond turning is very promising for the generation of micro/nanostructured functional surfaces [1], [2] which have been increasingly applied in optical fields due to its fantastic and superior performances [3]. However, the high intensity of the surface micro/nanostructures imposes significant challenge in the working bandwidth of FTS [4], leading to an essential requirement for the design of FTS having resonant frequency as high as possible [5], [6]. Generally speaking, the working bandwidth and motion stroke are two inherently conflict issues for oscillation generations [6], [7], [8], and in practice, the stroke is usually guaranteed in prior to satisfy the required cutting range by scarifying the performance of high-frequency tracking [9], [10].
To maximize the effective working bandwidth with an acceptable accuracy for FTS, one practical way is to implement the repetitive control [11], [12] and the iterative learning control [13] which outperforms other general control techniques in accurately tracking the trajectory over a wider frequency range. However, this kind of controllers would only be effective for periodic commands and periodic disturbances, and a small deviation from the desired periodicity may lead to a failure of the control system. An alternative solution for this issue is to employ the dual-stage actuation which has two actuating systems for one single-axial motion [14], [13]. With the dual-stage actuation, the primary coarse stage mainly provides large stroke with low working frequency. Meanwhile, the secondary stage with much higher bandwidth is combined to improve the motion accuracy of the end-effector in high frequency tracking. Nowadays, the dual-stage actuation has been extensively applied in a wide spectrum of fields, including the long stroke ultra-fine positioning [15], scanning probe microscopy [16], feed drive of machine tools [17], to mention a few. With respect to the application as FTS, the dual-stage actuation was also introduced for non-circular turning [13], [14]. Since large strokes are required for this application, the piezoelectric actuator (PEA) is normally employed for the secondary stage to jointly work with the primary Lorentz force based electromagnetic actuator [13], [14].
Currently, there are mainly three modes for the dual-stage actuation, namely the serial, parallel, and separate configuration. Although the parallel configuration has relatively compact size and better dynamic response of the coarse stage, there is inherent interference between the two stages [18]. With the serial configuration, the secondary stage including its actuator is totally embedded in the end-effector of the primary stage, having a simple structure with independent dual motions [15], [17]. The separate configuration is a special case of the dual-stage system which is mainly applied for the scanning probe microscope [16], [19]. As for this case, the tube PEA is designed to cooperatively work with the high frequency shear actuator without direct connection between the two actuators, and the interaction only occurs between the tip and sample at the two end-effectors of the two stages. Although it has the natural advantage of interference avoidance, the face-to-face arrangement of the two stages may significantly restrict its potential applications, for example, the application for dual-stage FTS diamond turning.
With the dual-stage actuation, two sensors are commonly employed to independently capture the displacement of each stage to construct the feedback control system [13], [14], [20]. To obtain high accurate control of the final end-effector, there are in general two main control methods which can be basically categorized into the cooperative control and master-slave control. As for the cooperative control, a low-pass and a high-pass filter are jointly employed to decompose the trajectory according to the bandwidth and stroke of each stage, and the two controlled stages are then cooperatively contributed to the final trajectory tracking [19], [21]. With respect to the master–slave control strategy, the tracking error of the primary stage was sent to the secondary stage as the desired reference for further eliminating the overall tracking error [14]. Essentially, the basic principle is the same for the two kinds of control strategies, and the primary stage may act as the low-pass filter in the master-slave control systems.
Therefore, to extend the manufacturing capability of FTS, the dual-stage actuation concept is adopted with the master–slave control strategy to construct a dual-stage FTS system. Unlike the pioneering work reported for non-circular turning [14], [13], the target micro/nanostructured surfaces makes it more challenging for the dual-stage FTS to achieve a much higher bandwidth in the micro/nanoscale. To satisfy the special requirement, a PEA instead of a electromagnetic actuator is selected for the primary stage in this study, and another PEA with shorter but quicker response is embedded in the platform of the primary stage. By adopting this configuration, the requirement for compact size and small moving mass imposes extra-challenge in placing an independent sensor for the secondary stage. In addition, since the primary PEA works with a relatively high frequency as that of conventional FTS, the working bandwidth of the secondary stage needs to be much higher to be effective to accurately track the control errors of the primary stage, which is usually limited by the servo periodicity of commercial controllers [11].
Accounting for these aforementioned challenges, a systematical study on the mechanical design, optimization, and control is conducted for the piezoelectrically actuated dual-stage FTS in this paper. The interference between the two stages as well as the high frequency tracking capability is also critically checked through experiments. The main contribution of this study is summarized as follows:
a) By taking the best of two PEAs having different bandwidth and stroke, a serially configured dual-stage FTS is developed to satisfy the ever-increasing requirement for ultra-fine tracking of high-frequency trajectory in the FTS turning of micro/nanostructured surfaces;
b) The stiffness model of two typical double parallelogram flexure mechanisms is analytically derived through the planar matrix based compliance modeling method, and the optimization model is accordingly established to optimize the mechanism for diamond turning;
c) The interference between the two stages is defined and comprehensively analyzed in the frequency domain, providing a measurement for the mutual coupling behavior of dual-stage systems;
d) Taking the best of the open-loop and closed-loop control, the master-slave control strategy using one displacement sensor is proposed which is simple and practical for industrial applications.
Section snippets
Mechanical structure configuration
As aforementioned, two PEAs are adopted to construct the dual-stage FTS. A PEA with longer stroke and larger capacitance is chosen for the primary stage (Stage-1). Meanwhile, another PEA with shorter stroke and smaller capacitance is employed for the secondary stage (Stage-2) to achieve quicker response. The diamond tool is mounted on the tool holder on the end-effector of Stage-2, and the accumulated motion from the two PEAs jointly contributes to the final motion of the diamond tool.
A
Stiffness modeling
With the linkage constructing the double parallelogram mechanism in Stage-1, the planar matrix based compliance modeling (MCM) method is employed to obtain the stiffness model [30], [31]. Assume the planar compliance of the RCFH relating the loads and deformations in its local coordinate system iswhere , and represents the planar compliance matrix of the RCFH [32].
By ignoring the elastic deformation of the middle flexure beam, the linkage
Experimental results and discussion
The prototype of the dual-stage FTS was produced through wire electrical-discharge machining using the material of spring steel, and the prototype is photographically shown in Fig. 6. One stack multilayer PEA (P-887.51, PI corporation, Germany) with nominal stroke of 15 μm and capacitance of 3.1 μF was employed to deliver a relatively larger but slower motion for Stage-1. Meanwhile, another chip actuator (PL055.3x, PI corporation, Germany) with nominal stroke of 2.2 μm and capacitance of
Conclusion
In this paper, a serially configured dual-stage fast tool servo driven by two piezoelectric actuators is developed using flexure hinges for motion guidance. Through analytical modeling and evolutionary computation, dimensions of the flexural structure are comprehensively optimized with full consideration of the strength and limitations of the two actuators. The optimized structure are then verified through finite element analysis with maximum modeling error around 15%.
Following the master-slave
CRediT authorship contribution statement
Dongpo Zhao: Writing - original draft, Methodology, Investigation, Software, Formal analysis, Data curation, Visualization. Zihui Zhu: Methodology, Investigation, Software, Formal analysis. Peng Huang: Resources, Data curation. Ping Guo: Formal analysis. LiMin Zhu: Supervision, Writing - review & editing. Zhiwei Zhu: Supervision, Resources, Project administration, Funding acquisition, Conceptualization, Writing - original draft, Writing - review & editing.
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.
Acknowledgments
This work is jointly supported by the National Natural Science Foundation of China (51705254), and the Natural Science Foundation of Jiangsu Province (BK20170836).
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