1. Introduction
Microstructures or free-form surfaces with specific functions have found widespread applications in aerospace, optics, and biomedicine [
1]. Single-point diamond turning (SPDT) based on fast tool servo (FTS) technology, which possesses high dynamic stiffness [
2,
3], can achieve high-frequency responses and micron-level displacements [
4,
5]. PZTs have been widely used in medicine [
6], microscopy [
7], aerospace, and metrology [
8], due to their excellent displacement control accuracy, excellent dynamic response characteristics, and strong load-bearing capacity. To a large extent, PZTs meet the needs of precision positioning by virtue of their significant advantages. Consequently, FTS based on piezoelectric actuators is regarded as one of the most effective and efficient techniques for machining free-form surfaces or microstructured surfaces. Despite its numerous advantages, the development of FTS technology is still constrained by the challenge of achieving large displacement under high-frequency vibrations [
9].
As a core component of the fast tool servo system, the design of the fast servo platform must carefully consider crucial factors such as output displacement and operating frequency, all of which significantly impact surface accuracy and machining efficiency. To achieve high-precision machining, Brinksmeier et al. developed two types of nano fast tool servo systems (nFTS), with travel ranges of 500 nm and 350 nm and frequencies reaching up to 5 kHz and 10 kHz, respectively [
10]. The closed-loop bandwidth of the fast tool servo system designed by Gao et al., which is driven by piezoelectric ceramics, can reach 2.5 kHz with a travel range of 0.45 μm, thereby achieving nanometer-level machining precision [
11]. Gan et al. developed a piezoelectric-driven fast tool servo system with an open-loop bandwidth of 1.4 kHz and a resolution of 1 nm, capable of achieving a displacement of 5 nm when the voltage frequency was set at 300 Hz [
12]. Additionally, the fast tool system developed by Zhu et al. can achieve a maximum bandwidth of 2 kHz and a maximum travel range of 10.25 μm [
13]. The utilization of FTS devices meticulously constructed using piezoelectric actuators has successfully enabled the achievement of a relatively high operating frequency. However, it should be noted that the displacement generated by these devices is markedly limited. This considerable limitation significantly constrains the range of applications for FTS.
Tilok Kumar Das et al. achieved amplification of the piezoelectric actuator output displacement by symmetrically connecting two lever mechanisms with a bridge mechanism. They optimized the design parameters of the microgripper mechanism through computational analysis to enhance its dynamic characteristics. When driving the micro gripper mechanism at 5 Hz drive frequency, the RMSE value of the micro gripper was 0.996 μm, which was 1.99% of the output displacement [
14]. Wang et al. employed a compound bridge amplifier to amplify the piezoelectric actuator displacement, resulting in a platform with a maximum single-axis output displacement of 42.9 μm; when tested with a 10 hz sinusoidal signal, the tracking error was 8.5% of travel [
15]. Ding et al. proposed a piezoelectric-driven flexible parallel mechanism, using a two-stage amplification mechanism to compensate for the limited stroke of the piezoelectric ceramics [
16]. Tian et al. introduced a novel spatially deployable three-degrees-of-freedom flexible nano-positioning platform with a three-stage motion amplification mechanism. By arranging three typical basic three-stage motion amplification modules with two sets of hook joints, the structure of the flexible nano-positioning platform was made more compact, achieving a maximum output displacement of 170 μm. In addition, when tracking a 50 Hz sinusoidal signal, the test yielded a maximum tracking error of 2.17% for the positioner on a single axis [
17]. Tang et al. used an improved lever displacement amplifier to enhance the displacement of the piezoelectric actuator, enabling planar positioning motion of the flexible positioning platform; single-axis output displacements of up to 1.035 mm and maximum inter-peak steady-state errors were maintained within ±0.2 μm, but the frequency of the sinusoidal signal applied to the PZT ω = 1.07 rad/s (0.17 Hz) [
18]. Although the use of flexible hinges with amplification mechanisms effectively enlarges the output displacement of piezoelectric ceramics, it also results in reduced overall structural stiffness of the platform, making it challenging to achieve both high response frequency and large output displacement simultaneously.
Based on the above context, in terms of frequency response and stroke, positioning platforms have only unilateral advantages, and few can guarantee high frequency response with a large stroke. The main purpose of this manuscript is to present a FPP (fast positioning platform) with a large stroke, based on a PZT (piezoelectric actuator) and quad-parallel flexible mechanism. The design method of the FPP (fast positioning platform), which is capable of achieving large displacement and a response at a high frequency is proposed. The remainder of this paper is organized as follows:
Section 2 establishes the mechanical model. Based on the mechanical model, the input and output characteristics of the FPP were analyzed and the working range of the FPP was obtained.
Section 3 describes the static structure and model analysis, which were carried out using the FEA method. In
Section 4, a prototype of the platform is presented; a series of experiments were conducted to validate the established theoretical model and the performance of the FPP.
Section 5 summarizes the findings of this paper.
4. Performance Testing Experiments
In this section, the experimental validation and study of the characteristics of the designed FPP experimental prototype are described, following the theoretical calculations and finite element analysis presented in the previous sections.
The modal test was conducted using the impact hammer excitation method to investigate the actual dynamic performance of the FPP.
Figure 12 illustrates the experimental setup for the modal analysis of the FPP. A B&K accelerometer was mounted on the moving platform (a tool holder was installed on the moving platform to facilitate the accelerometer installation, with the accelerometer attached to the tool holder) to measure the response induced by the impact force. The impact hammer provided pulse impact excitation to the platform, and the force sensor attached to the hammer measured the impact force. The force and corresponding acceleration signals were amplified by a charge amplifier and then fed into a dynamic analyzer (LMS SCADAS Mobile Testing System, Siemens, Berlin, Germany). Using modal analysis software, the frequency response function (FRF) of the developed positioning platform was obtained, and the experimental results are shown in
Figure 13. The discrepancies between the analytical calculation, finite element analysis, and experimental results were 6.87% and 8.67%, respectively. Considering the mass of the tool holder, which may cause a slight reduction in the measured first-order resonance frequency, it can be concluded that the experimental results are in good agreement with the analytical and finite element analysis results.
A series of experimental tests were conducted to verify the input/output characteristic and to establish performance measurements for the FPP. The experimental principle and experimental setup are shown in
Figure 14. The schematic diagram of performance testing is illustrated in
Figure 14a. The control signal was generated using a MicroLabBox (dSPACE, Paderborn, Germany) and amplified by the Trek PZD700A (Advanced Energy, Fort Collins, CO, USA) voltage amplifier to drive the P-025.80 (PI, Karlsruhe, Germany), enabling the forward and backward feed of the moving platform. Three capacitive displacement sensors CPL290 (Lion, Minneapolis, MN, USA) with a resolution of 1 nm and dynamic range of 1.5 kHz were utilized to measure the output displacement of the moving platform in the X, Y, Z axes, respectively. The real-time display and recording of experimental data were also carried out via the dSPACE MicroLabBox. To reduce external disturbance such as vibration, the experiments were performed on a vibration-isolated table VAIS AMT 045 (AMTEK, Berwyn, IL, USA).
A travel range test was conducted to determine the maximum working space of the moving platform. During the test, a 1000 V amplitude, 1 Hz frequency sine wave was applied to the PZT and the displacements of the moving platform in the X, Y, and Z directions were recorded. The test results, shown in
Figure 15, indicate that the maximum output displacement in the Z direction reached 53.13 µm. The coupling displacements in the X and Y directions were 0.35% and 0.66% of the Z displacement, respectively. These results demonstrate that FPP can achieve large displacements while maintaining good guiding performance.
The closed-loop step response test employed a controller established using the PID feedback control algorithm. Using a real-time displacement step signal ranging from 0 to 50 μm to drive the PZT, the output displacement signal of the platform is shown in
Figure 16. The experimental results indicated that when the step magnitude was 50 μm, the stabilization times of the moving platform for the falling and rising edges were 37 ms and 26 ms, respectively, with corresponding overshoots of 0.9% and 1.8%. Thus, by optimizing the feedback control algorithm and controller parameters, the platform can achieve good performance in terms of fast response and precision control.
During the motion resolution test, a step signal was applied to the PZT to observe the highest achievable motion resolution of the platform. The test results, shown in
Figure 17, indicate that the resolution of the FPP can reach 5 nm, effectively ensuring processing accuracy during machining.
Signal tracking capability is a crucial feature of the large-stroke fast position platform, reflecting its adjustment speed during operation. The signal tracking test employed sine waves with frequencies of 50 Hz and 200 Hz to measure the tracking error of the moving platform at displacements of 50 μm and 10 μm, respectively. To compensate for the hysteresis effect of the PZT, a control strategy combining PID and inverse PI models was used. The test results are shown in
Figure 18. When the amplitude and frequency of the signal were 50 μm and 50 Hz, respectively, the maximum tracking error was about ±1.96 μm (approximately 3.92% of the stroke); when the amplitude and frequency of the signal is 10 μm and 200 Hz, respectively, the maximum tracking error was about ±0.59 μm (approximately 5.9% of the stroke), demonstrating good signal tracking ability of the developed FPP. Higher response frequency can be realized by reducing the output displacement. These phenomena are consistent with the previous analysis and validate the theoretical model presented in this paper. Advanced control algorithms used for compensation of the tracking error as well as nonlinear characteristics of PZT will be fully considered and systematically applied in further research.
The end face turning experiments were conducted using a UPT250 precision lathe (JCSGY, Beijing, China) to validate the machining performance of the FPP. The specific experimental setup and cutting conditions are shown in
Figure 19 and
Table 3, respectively. The tool holder was installed on the FPP and was driven forward by the FPP to implement the precision feed operation. The tool position was initially set by the Z-axis feed drive of the UPT250 precision lathe; after the trial cutting was completed, the Z-axis was then fixed. Under the controlled cutting conditions, the cutting depth was set solely by the PZT of the FPP, while under the uncontrolled cutting condition, the cutting depth was set by the preload bolt and capacitive sensor. For both the uncontrolled and controlled cutting conditions, except for cutting depths, all of the cutting parameters were identical. Four sets of cutting experiments were conducted based on different cutting depths and tool position settings. The magnified images of the two processed surface topographies captured at 1000x magnification by VHX970F (Keyence, Osaka, Japan) are shown in
Figure 20. For both the cutting depths, the surface integrity under controlled cutting conditions was better than uncontrolled cutting conditions. The roughness of the machined surface was measured using ContourGT (Bruker, Berlin, Germany), and the surface roughness of the processed workpieces is shown in
Figure 21. The comparison of the results between controlled and uncontrolled cutting conditions is illustrated in
Figure 22. When the cutting depths were 5 μm and 10 μm, the surface roughness was 34.7 nm and 52.9 nm under uncontrolled conditions, respectively; the surface roughness was 26.4 nm and 46.2 nm under controlled conditions, respectively. Compared with the uncontrolled conditions, the values of surface roughness under controlled conditions decreased by 23.9% and 12.7%, respectively. The cutting test results indicate that the developed FPP device has excellent precision machining performance.
5. Conclusions
In this paper, a FPP (fast positioning platform) with a large stroke based on a PZT and quad-parallel flexible mechanism for application in precision machining is proposed. The conceptual design and mechanical model as well as input and output characteristic of the FPP were analyzed. The stiffness and resonant frequency of the FPP were obtained through both mathematical and FEA results. A series of experimental tests were conducted to verify the input/output characteristics, and the resonant frequency, output displacement, step response, motion resolution, and tracking error of the FPP were measured. The main conclusions can be drawn as follows:
The proposed quad-parallel flexible hinge mechanism can provide excellent planar motion capability with high stiffness and good guiding performance, guaranteeing outstanding dynamics characteristics. The driving capability of the PZT driver, capacitance value and stiffness of the PZT, and the stiffness of the flexible hinge play an important role on the input and output characteristics of the FPP. The contradiction between large output displacement and high-frequency response can be resolved by selecting drivers with high driving capability and matching the stiffness of the PZT with flexible hinge stiffness. The design method for a FPP that is capable of achieving large displacement while responding at a high frequency is proposed.
The developed FPP shows excellent performance in terms of fast response and output displacement. The natural frequency of the FPP is 1315.6 Hz, the maximum output displacement and the motion resolution of the FPP in a static state is 53.13 μm and 5 nm, respectively. Step response testing showed that under the step magnitude 50 μm, the stabilization times of the moving platform for the falling and rising edges were 37 ms and 26 ms, respectively. The tracking error was about 1.96 μm, when the amplitude and frequency of the signal were 50 μm and 50 Hz, respectively. A surface with a roughness of 0.1 was obtained by cutting experiments, proving the new FPP’s good performance.
Experiments were carried out in series. The experimental results indicate that the developed FPP showed excellent performance for fast response, output displacement, and precision machining performance. The tracking error was about ±1.96 μm and ±0.59 μm, when the amplitude and frequency of the signal were 50 μm, 50 Hz and 10 μm, 200 Hz, respectively. Compared with the uncontrolled conditions, the values of surface roughness under controlled conditions decreased by 23.9% and 12.7%, respectively.