Taking advantages of high stiffness, compact size, unlimited displacement resolution, large force generation, fast response as well as low power consumption, piezoactuators have been widely used in the fields of precision positioning [1–3], nanofabrication [4–7], micromanipulation [8–10], scanning probe microscopes [11,12] and nanomechanical testing systems [13–16].

For different applications, various kinds of piezo driving platforms have been proposed by previous researchers. One important category among them is the actuator that integrates displacement sensors to realize high precision positioning via closed-loop control. Zhu [4], Kim [6,7] and Tian [17,18] designed the fast tool servo to realize precision turning or grinding by integrating laser or capacitive displacement sensors and piezoactuators. Shimamoto [14] proposed a nanoindentation tester by integrating the piezoactuator and an optical fiber displacement sensor. Park [13] also presented a precision indentation and scratching system by integrating the piezoactuator and a capacitive displacement sensor. Shiou [19] developed a real-time control closed-loop micro-/nano-positioning system by integrating a capacitive displacement sensor to overcome the problem of the hysteresis and nonlinearity of the piezoactuator and to increase the positioning speed of the positioning stage. The works mentioned above realize different applications by integrating the piezoactuator and commercial displacement sensors. Though accuracy or resolution of these sensors is high, dimensions are a little big which makes the size of the platforms large. For some special applications requiring limited dimensions, such as in situ nanomechanical tests inside the scanning electron microscope, applications of commercial displacement sensors are limited. In addition, complex mechanical assembly leads to stiffness degradation and decreased platform sensitivity. Also measurement errors arise from the installation of sensors or quality of measuring surface, so more compact structures and direct measuring methods should be developed.

Fleming [20] presented a new technique of strain and force feedback scheme for reduction of creep, hysteresis and vibration in piezoelectric actuated systems. The proposed scheme can be integrated into the piezoactuator which minimizes parts count and overall system cost. In [21], a piezoelectric strain sensor was bonded to a flexure-based nanopositioner as a displacement sensor for damping and tracking control. With damping and integral tracking control, a closed-loop bandwidth of 1.86 kHz was achieved. AFM imaging results demonstrate the efficacy of using a piezoelectric strain sensor for damping and tracking control of high-speed nanopositioners.

In this paper, a compact precision positioning platform integrating strain gauges and a piezoactuator is designed for a future application of in situ nanoindentation inside the scanning electron microscope. Four strain gauges are glued at the root of two parallel elastic plates to measure the output displacement of the piezoactuator directly. The work principle was introduced and the mathematical model of the strain gauge sensor was established. Effects of geometric parameters of two parallel plates on Von Mises stress distribution as well as static and dynamic characteristics of the structure were studied by the finite element method. Results of the calibration experiment and output performance testing demonstrate that the developed precision positioning platform has good linearity and it can be integrated into an in situ nanoindentation device to realize in situ nanoindentation tests of materials inside a scanning electron microscope.

Figure 1 is the schematic diagram of the developed platform, which mainly consists of a piezoactuator, four strain gauges and a flexure hinge frame. The piezoactuator is an AE0505D16F type piezoelectric stack (NEC Tokin) with maximum displacement of 17.4 ± 2.0 μm and a maximum generated force of 850 N. The strain gauges are BFC-350-3AA-11 type and the grid material is constantan with a resistance of 350 Ohm. The flexure hinge frame has two parallel elastic plates processed by wire cutting using the material 65 Mn and the strain gauges are adhered in the root of plates with M-Bond 610 adhesive. These two parallel plates, the piezoactuator and the frame form the positioning platform. Strain gauges and two parallel plates form the displacement sensor. The piezoactuator will extend when voltage signal is applied to it, and then pushes the two parallel plates to output precision displacement. At the same time, strain gauges will deform with deformation of the two parallel plates, causing their electrical resistance to change.

The resistance change is converted to voltage change using the Wheatstone bridge as shown in Figure 2, which is conveniently measured by an A/D card, so the precision positioning platform is established. Compared with other platforms integrating commercial displacement sensors, such as the laser sensor or the capacitance sensor, the proposed platform can be designed with kinds of structures and also more compact because of the embedded strain gauges. The cost is also low.

Figure 3 shows the principle of the strain gauge. The resistance R increases when tension is applied to it. In contrast, the resistance R decreases when it is compressed. Whether the force applied to the strain gauge is tension or compression, is decided by the installation location of the strain gauge.

Now we will illustrate the strained condition of each strain gauge in detail. For purposes of analysis, the upper plate of the two parallel plates is simplified as shown in Figure 4. F is the driving force coming from the piezoactuator. l₁, w₁ and t₁ are length, width and thickness of the elastic plate, respectively. l₂, w₂ and t₂ are the length, width and thickness of the strain gauge, respectively. According to material mechanics, the location where strain gauges are installed in Figure 4 is tensioned, so resistance of these two strain gauges increases and the strain can be expressed by: (1) ɛ = 3 F l 1 2 E w 1 t 1 2where E is the elastic modulus of 65 Mn.

Similarly, resistance of strain gauges installed on the lower elastic plate decreases. Assuming that changes in resistance of strain gauges are ΔR₁, ΔR₂, ΔR₃ and ΔR₄ respectively, the voltage change in Figure 2 can be expressed by: (2) Δ U = E 0 4 ( Δ R 1 R 1 - Δ R 2 R 2 + Δ R 3 R 3 - Δ R 4 R 4 )

The gauge factor K_i is defined as: (3) K i = Δ R i / R i ɛ i ( i = 1 , 2 , 3 , 4 )where ΔR_i is the change in resistance caused by strain; R_i is the resistance of the undeformed strain gauge, and ε_i is strain.

Considering that four strain gauges are the same and the installation location is symmetric, if the size of strain is ε, then: (4) ɛ 1 = ɛ 3 = ɛ (5) ɛ 2 = ɛ 4 = - ɛ

So Equation (2) can be simplified to: (6) Δ U = E 0 K ɛwhere K is the gauge factor of the used strain gauges.

According to Equations (1) and (6), the voltage change ΔU is proportional to strain ε, and geometric parameters of two parallel plates and strain gauges will affect the strain significantly. Usually, as a user, geometric parameters of the strain gauges cannot be changed, so the effects of the geometric parameters of the strain gauges on the strain are not analyzed in this paper. In this section, finite element analysis was carried out to study effects of geometric parameters of two parallel plates on Von Mises stress distribution as well as static and dynamic characteristics of the precision positioning platform.

Figure 10 is a photograph of the developed precision positioning platform. The calibration experiment was carried out to evaluate the performance of the developed strain gauge sensor. Output performances of the platform were tested via the calibrated strain gauge sensor. The calibration experimental setup is shown in Figure 11. In order to reduce external disturbances on sensing and measurement system, the Newport precision vibration isolation table is used to mount the developed platform. The LK-G10 type laser displacement sensor with resolution of 10 nm is used to calibrate the developed gauge sensor.

This paper proposes a compact precision positioning platform. Using the embedded strain gauges, the output displacement of the developed platform is measured precisely. The work principle was introduced and the mathematical model of the strain gauge sensor was established. Effects of geometric parameters of two parallel plates on Von Mises stress distribution were studied by the finite element method. Analysis results show that length l₁ and thickness t₁ affect the Von Mises stress of the elastic plate obviously, while width w₁ has smaller effect. The stress in the root of the plate or near the loading area is larger than other places, so strain gauges are suitable for gluing on the root of the plate or near the loading area. Results of static and dynamic analysis of the structure demonstrate that the structure has enough strength, with a high first order frequency of 1,870 Hz.

The calibration experiment of the strain gauge sensor was carried out. The linear correlation coefficient R² of the calibration curve is equal to 1, which indicates that the sensor has good linearity. Sensitivity of the developed strain gauge sensor was obtained and it is about 0.0468 mV/μm.

The output performance of the proposed platform with open-loop control was measured by the calibrated strain gauge sensor. Corresponding to the maximum applied voltage of 100 V, the maximum output displacement is about 11.62 μm, agreeing well with the theoretical prediction values. With open-loop control, the portion of displacement increasing expresses good linearity, but obvious nonlinearity is observed during the portion of decreasing displacement.

The closed-loop control system was established to solve the problem of nonlinearity of the platform. Experimental results demonstrate that for the displacement control process, both the displacement increasing portion and the decreasing portion have good linearity, verifying that the control system is functional.

Through analysis and experiments, we can conclude that the proposed compact precision positioning platform was successfully designed. It has a small size but can realize displacement measurements with the embedded strain gauges, which is useful for the closed-loop control and structure miniaturization of piezo devices. It has potential applications in nanoindentation and nanoscratch tests, especially in field of in situ nanomechanical tests which require compact structures.