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Miniaturization precision positioning platforms are needed for

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 [

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 [

Fleming [

In this paper, a compact precision positioning platform integrating strain gauges and a piezoactuator is designed for a future application of

The resistance change is converted to voltage change using the Wheatstone bridge as shown in

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 _{1}, _{1} and _{1} are length, width and thickness of the elastic plate, respectively. _{2}, _{2} and _{2} are the length, width and thickness of the strain gauge, respectively. According to material mechanics, the location where strain gauges are installed in

Similarly, resistance of strain gauges installed on the lower elastic plate decreases. Assuming that changes in resistance of strain gauges are Δ_{1}, Δ_{2}, Δ_{3} and Δ_{4} respectively, the voltage change in

The gauge factor _{i} is defined as:
_{i}_{i}_{i}

Considering that four strain gauges are the same and the installation location is symmetric, if the size of strain is

So

According to

The strain gauge is glued on the upper surface while the loading area is added on the upper surface using Boolean operation of ANSYS 10.0 software. Elastic modulus and Poisson ratio of the elastic plate are 206 GPa and 0.288 respectively. While for the strain gauge, they are set to be 150 GPa and 0.3. Solid 95 is selected to mesh the model and key portions are refined to improve the simulation accuracy. On the left side of the elastic plate, all degrees of the freedom are constrained. The displacement load of 10 μm is applied on the loading area along the negative _{1} = 36 mm, _{2} = 4 mm, _{1} = 6 mm, _{2} = 5 mm, _{1} = 0.7 mm, _{2} = 0.05 mm. When analyzing effect of a single parameter of the elastic plate, other parameters are set to be the values of basic parameters.

Because the strain gauge is glued on the upper surface of the elastic plate, strain of the strain gauge can be thought as the same as that on the upper surface of the elastic plate. Accord to Hooke's Law of Elasticity, strain is proportional to stress. Through analyzing stress distribution of the elastic plate with different geometric parameters, as shown in

_{1}, different thickness _{1} and different width _{1}, respectively. Von Mises stress increases when length _{1} decreases, while stress of the middle part is very low and the lowest stress trends to 0 MPa for different length _{1}. Like the result of different length _{1}, Von Mises stress varies obviously with different thickness _{1} and it increases with the increasing of thickness _{1}. Being different from length _{1} and thickness _{1}, Von Mises stress is not sensitive to width change. So selection of length _{1} and thickness _{1} should be more careful.

Also, there are some common characteristics for these three parameters. Because of existence of the gauge, stress distribution has some variation though it is not sharp. Stress in the root of the plate or near the loading area is larger than other places, so strain gauges are suitable to be glued in the root of the plate or near the loading area. Due to space limit near the loading area where the piezoactuator is installed or stage existed, strain gauges were glued in the root of two parallel plates.

In order to make sure that the flexure hinge frame has enough strength and good dynamic performances, static and modal analysis of the structure were carried out. Geometric parameters of the elastic plate are selected as follows. Length _{1} is 40 mm, width _{1} is 6 mm and thickness _{1} is 0.8 mm. Considering that size of strain gauges is so small that they affect the flexure hinge frame very lightly, the analysis model does not include these four strain gauges and the mesh model is shown in

The main purpose of static analysis is to verify the structure strength, so the worst condition that two parallel plates have deformation of 18 μm is applied on the area on which the piezoactuator is installed. The upper surface is fixed. The analysis result is shown in

The maximum stress is 33.19 MPa less than the yield strength of 65 Mn being 432 MPa. Like the analysis results in Section 4.1, larger stress occurs in the root of parallel plates and near the loading area.

Modal analysis is one of the effective methods to examine the dynamic performance of mechanical structures and systems. From modal analysis, natural frequencies and mode shapes which are important parameters when the structure subjects to dynamic loads can be obtained easily.

The calibration experimental system was established as shown in ^{2} is equal to 1, which indicates that the sensor has good linearity.

Considering the stiffness of the flexure hinge frame along driving direction of the piezoactuator, the maximum steady-state output displacement of the precision positioning platform can be given as [_{max} is the actual maximum steady-state output displacement of the precision positioning platform. _{0} is the nominal maximum output displacement of the piezoactuator. _{pzt} and _{fh} are the equivalent stiffnesses of the piezoactuator and the flexure hinge frame. The equivalent stiffness of the used piezoactuator is about 48.9 N/μm and the equivalent stiffness of the flexure hinge frame with the structure illustrated in

According to the Formula (8), the stiffness of the flexure hinge is 0.618 N/μm. Then the maximum steady-state output displacement of the precision positioning platform can be given as:

Corresponding to the maximum applied voltage of 150 V, the nominal maximum output displacement of the piezoactuator is 17.4 ± 2 μm. Usually, the maximum applied voltage does not exceed 100 V during the applications, especially for the nanoindentation application, so corresponding to the maximum applied voltage of 100 V, the theoretical maximum output displacement is in the range of 10.3 μm∼12.9 μm.

The open-loop control experiment was carried out to test the output performance of the precision positioning platform manually and the results are shown in

The closed-loop control system is shown in

The closed-loop control curves are shown in

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 _{1} and thickness _{1} affect the Von Mises stress of the elastic plate obviously, while width _{1} 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 ^{2} 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

This research is funded by the National Natural Science Foundation of China (Grant No. 50905073, 51105163), National Hi-tech Research and Development Program of China (863 Program) (863 Program) (Grant No. 2012AA041206), Key Projects of Science and Technology Development Plan of Jilin Province (Grant No. 20110307), International Science and Technology Cooperation Program of China (Grant No. 2010DFA72000) and Graduate Innovation Fund of Jilin University (Grant No. 20121080)

Schematic diagram of the developed platform.

Wheatstone bridge.

The principle of the strain gauge.

The simplified upper plate with strain gauges.

The simplified model of the strain gauge sensor.

Von Mises stress distribution along the elastic plate with (_{1}; (_{1}; (_{1}.

The mesh model of the flexure hinge frame.

Stress distribution of the flexure hinge frame.

The first three order mode shapes of the precision positioning platform.

The photograph of the developed precision positioning platform.

The experimental setup.

The curve between the output displacement (

The output curve of the precision positioning platform with open-loop control.

Schematic of the closed-loop control system.

The closed-loop control curves with different maximum output displacement.