A piezoelectric stick–slip drive nanopositioner with large velocity under high load

Nanopositioners capable of high precise positioning and large velocity are of central importance in in situ SEM nanorobotic systems. Micro–nano-scale materials have become of significant interest for both research and industrial applications due to their unique chemical, electrical, and mechanical properties.^1–3 The precise characterization of individual nano-objects is a big challenging task that needs in situ SEM nanorobotic systems. These robots, such as the AFM, nanomanipulation system, and nanoindentation instrument, can move, manipulate, and characterize objects with a SEM visual feedback.^4–8 The precise alignment and contact are bask tasks for all nanohandling operations. However, the fragile materials might be destroyed due to the large force generated by using less accurate motion robotic systems. Moreover, the works with repeatability and high efficiency in the micro–nano-range cannot be accomplished without the help of micro–nano-positioning devices. Therefore, nanopositioners with nanometer resolution, millimeter stroke, high positioning accuracy, and large motion velocity are developed.^9–12 

Piezo-actuators produce smooth continuous motion with nanometer and sub-nanometer resolution. These properties make them useful in precision positioning. However, piezo-actuators typically have short stroke outputs of up to 0.1% of their whole length. Thus, the travel ranges of piezo-actuators are limited, and stroke amplified mechanisms with step-type motion are combined for assembling nanopositioners. These trans-scale technique-enabled designs include the inchworm drive nanopositioner, ultrasonic drive nanopositioner, and stick–slip drive nanopositioner.^13–17 An inchworm drive nanopositioner uses multiple piezo-actuators to make sliders walk in order to produce unlimited motion. However, the inchworm drive nanopositioner has a large size mechanism, and its movement includes a small displacement in the reverse direction at the beginning of each step. The ultrasonic drive nanopositioner creates high-speed motion using a vibrating piezo-actuator. However, it has relatively poor positioning accuracy.¹⁸ The stick–slip drive nanopositioner relies on contact friction and inertial force to realize one limited step displacement. Theoretically, infinitely long travels can be achieved by repeating one step motion. They can also achieve high resolution and large motion velocity.¹⁹ Miniaturized stick–slip drive nanopositioners are widely used in research and commercially for positioning samples and tools for micro- and nano-handling inside the SEM.

Despite many benefits and the widespread use of the piezoelectric stick–slip drive nanopositioner, its low speed under high load is still a limiting factor. The stick–slip motion of the positioner shows the SEM image of vibrations, and vibrations appear as zigzags on the SEM image due to raster scanning and frame averaging of the SEM image.¹⁸ Because of the huge disadvantage, piezoelectric stick–slip drive nanopositioners are used for coarse positioning. The loads, such as the indenter head and AFM head, are mounted on the load platform to manipulate or characterize materials. However, the positive pressure changes the piezoelectric stick–slip drive nanopositioner when the load to the drive changes. As a result, the contact friction is affected, which undesirably leads to inconsistent displacements. When sufficiently high, a load can make one step displacement of the nanopositioner almost zero.²⁰ 

In our previous works, we used a form-closed cam mechanism to separate the driving unit and moving unit to reduce the effect of load variations on positioning performance. However, the structure is highly large, which is not SEM-compatible, and the load capacity is less, which is 150 g.²⁰ Yu et al. proposed a load unit to separate the driving unit and moving unit of a piezoelectric stick–slip nanopositioning stage, but the stage has a large size of 85 × 50 × 32 mm³.²¹ Gao et al.,²² Guo et al.,²³ and Cheng et al.²⁴ all designed a flexure hinge mechanism with a spherical shape indenter to adjust the contact force, but the designs have large size and low resolution. This paper proposed a compact piezoelectric stick–slip drive nanopositioner with high velocity under high load. The driving unit is designed as an independent module, and contact friction is changed by adjust bolts. A MATLAB simulation model is created to optimize the nanopositioner for a certain velocity, and the FEM is used to confirm that the leaf hinge has sufficient stiffness. A series of experiments are undertaken to study the performances of the proposed nanopositioner.

This work focuses on decoupling the driving unit and moving unit because of its capability to adjust contact friction, low sensitivity to vibration, and compact size. Figure 1 shows the nanopositioner. It mainly consists of a driving unit, a moving unit, and a base. The driving unit is the key part of the nanopositioner, and it is assembled by one piezo-actuator, one preload screw, one preload block, one leaf hinge, one hinge frame, and one inertial mass block, as shown in Fig. 2. The leaf hinge, hinge frame, and inertial mass block are manufactured as one component. The piezo-actuator is nested between the block and the inertial mass block to deform the leaf hinge. The block prevents damage from the preload screw. The moving unit includes two cross roller guide rails (IKO Company, Japan) and one platform. Two friction plates with ZrO₂ ceramic are mounted on the upper faces to decrease the friction during motion. Both driving and moving units are installed on the base carefully.

Figure 3 shows the working principle of the designed nanopositioner, which mainly includes the following steps:

• Step 1:

  From time T₀ to T₁, the piezoelectric transducer (PZT) extends slowly with a displacement, leading to a slider displacement. At time T₁, the slider reaches the maximum displacement d_I.

• Step 2:

  From time T₁ to T₂, the PZT retracts quickly and the slider generates the backward displacement d_R due to the kinetic friction force. One step displacement is given as d_C = d_I − d_R. Repeating the above motion cycle, the nanopositioner could achieve a large working stroke.

• Step 3:

  The friction between the driving unit and the moving unit changes by adjusting the adjust bolts when the load on the load platform changes.

In this design, the driving unit and moving unit are fully separated. When the load on the load platform enlarges, the friction between the driving unit and moving unit decreases by turning the adjust bolts, as shown in Fig. 4(a). With the advantages of independent driving unit module, precise positioning and the rigidity of the nanopositioner are not affected. Furthermore, the piezoelectric stick–slip drive nanopositioner has a compact structure of 30 × 32 × 25 mm³. Figure 4(b) shows our previously proposed design.²⁰ We used a cam, actuated by a piezoelectric ceramic, to contact the slider. The positive force F_cp adjusts the contact force, and lateral force F_cl moves the slider. However, the main actuating force from the piezoelectric ceramic is used to change the contact force, which enlarges the size and lowers the stiffness of the nanopositioner. Figure 4(c) shows the design from the studies of Gao et al.,²² Guo et al.,²³ and Cheng et al.²⁴ They proposed an indenter with a spherical shape, actuated by a piezoelectric ceramic, to contact the slider. The positive force F_dp changes the contact force, and lateral force F_dl moves the slider. It has the same disadvantage as our previous design and a bad resolution of 60 nm.²³ 

A MATLAB model has been created to calculate the quantitative velocity response of the nanopositioner to an applied sawtooth-shaped voltage. This enables the optimization of the nanopositioner for a certain target velocity. The dynamic model of the system can be simplified as two spring–damper systems connected in series. In the simplified model, during the driving phase, the piezo-actuator is simulated as an electrical model and a mechanical model. The driving voltage is translated into displacement and force. Together with the mechanical model of the leaf hinge, the displacement and force are then translated into the speed of inertial mass. Based on the LuGre friction model,^25–27 the platform moves. Figure 5(a) shows the transfer function of the piezoelectric stick–slip drive nanopositioner. Figure 5(b) shows the simulation model that is used in MATLAB to analyze the effects of key parameters on the velocity of the nanopositioner. In the simulation model, the input sawtooth-shaped control signals are translated into displacements at the output. As shown in Fig. 5(b), when the positive pressure between the contact surfaces increases, the sliding displacement between the platform and the inertial mass block decreases, which impacts the one step displacement of the platform. In the meanwhile, the maximal static friction of the contacting surfaces changes, resulting in the changes in the viscous force between the platform and the inertial mass block. Figure 5(c) shows that when the force increases from 0.3 N to 6 N, the velocity decreases from 0.369 mm/s to 0.071 mm/s. Thus, the contact friction should be minimized in order to produce the desired velocity of the nanopositioner.

A series of values of load mass m_s and hinge equivalent mass m_f are selected to optimize the output velocity of the nanopositioner. The results are shown in Fig. 6. It can be seen that the velocities rise with the increase in m_s, but the velocities decrease with the increase in m_f. Based on the simulation results, the optimized values of load mass m_s and hinge equivalent mass m_f are selected, as given in Table I. The target maximum velocity is 3.657 mm/s at a driving voltage of 150 V, 1 kHz.

The leaf hinge is the key component in the driving unit module, and it is checked by both mechanical calculation and finite element (FE) simulation approaches. The length, width, thickness, and elasticity modulus are defined as L, W, T, and E, respectively, as shown in Fig. 2. According to Refs. 28 and 29, the stiffness of the leaf hinge is given by

Finite element simulation was conducted using ANASYS. The 10-node Solid 92 tetrahedron element was used. The material was specified to be 7075-T651 aluminum (Young’s modulus value: 71 GPa and Poisson’s ratio: 0.33) because of its high strength, better elastic module, and SEM-compatibility. The geometric dimensions of the leaf hinge were set to be L = 8.2 mm, W = 3.0 mm, and T = 1.5 mm. With an input force of 15 N, the maximum displacement of 11.722 µm was outputted. The simulation stiffness result of 1.302 N/μm was nearly equal to the value obtained from Eq. (1), namely, 1.285 N/μm. This indicates that the analysis of the leaf hinge can be performed by the FE simulation method. With an input displacement of 10 µm, the maximum stress in the root of the flexure hinge was ∼41.98 MPa, while the yield strength of the material is 520 MPa. Modal finite element analysis showed that the first, second, third, and fourth modes were 15 336 Hz, 16 485 Hz, 35 413 Hz, and 36 926 Hz, respectively. To avoid excitation of the mechanical resonance, the frequency of the driving signal was limited to around 1%–10% of the resonance frequency. Thus, it was determined that the frequency of the voltage driving signal for the nanopositioner should be less than 1.5 kHz.

The standard sawtooth-type driving signal is often used for the stick–slip drive nanopositioner, but how to improve the velocity is still challenging. In order to drive the designed piezoelectric drive nanopositioner with high speed, a novel driving power circuit is designed and fabricated. As shown in Fig. 7(a), the core element of the circuit is the operational amplifier PA92 (APEX Company, China). The stepping time of the outputted sawtooth wave is 1.84 µs, which is highly close to zero, and shown in Fig. 7(b). Compared with other sawtooth waves,^23,30 the retract displacement of the nanopositioner is constrained using the newly developed driving power circuit. As a consequence, one step displacement and the velocity of the nanopositioner are improved. The developed power circuit for the nanopositioner enables to output the maximum sawtooth voltage signal to 150 V and 1 kHz.

A prototype of the designed piezoelectric stick–slip drive nanopositioner was constructed using electro-discharge machining with 0.5 mm machining resolution. The overall dimension of the nanopositioner was 30 × 32 × 25 mm³. Both the base and platform were fabricated from AL7075. The piezo-actuator measured 3 × 3 × 5 mm³, outputting a maximum displacement of 5 µm and a force of 330 N at 150 V. Figure 8(a) shows the established experimental system. The experimental system worked as follows: a personal computer equipped with an NI PCI-6221 DAQ card provided the needed voltage signal. Then, the self-designed driving power circuit amplified the signals to drive the piezo-actuator. A laser interferometer (POLYTEC OFV3001) was adopted to measure the moving displacement of the nanopositioner. The whole system was placed on a vibration isolation table. Figure 8(b) shows the working principle of the experimental system. A laser is generated from the laser vibrometer and emitted to one end of the slider. When the slider of the nanopositioner moves one step displacement d, the laser vibrometer measures and records the motion data of the nanopositioner. When a sawtooth-shape signal is supplied to the nanopositioner, the slider moves continuously and the laser vibrometer records the displacement–time data of the nanopositioner.

Figure 9(a) illustrates the resolution results of the nanopositioner. A sinusoidal voltage signal with a 1 s cycle was inputted, and voltage amplitude was increased from 0 V to 0.7 V. With each 0.1 V input voltage increase, the nanopositioner generated a displacement of 6 nm through fitting the noise that comes from the driving circuit. The data shown in Fig. 9(b) were measured when a sawtooth voltage (150 V, 1 kHz) was supplied to the piezo-actuator. There was no obvious retract displacement, which shows and proves the advantage of the newly designed driving power circuit. One step displacement is 5.7 µm, and the maximum velocity is 3.507 mm/s. For precise quantification, the velocity at each voltage was repeated 15 times. The average value of the 15 velocities was taken as the nominal displacement under that particular voltage. Figure 9(c) summarizes the precision test results. The maximum velocity is 3.467 mm/s at a driving voltage of 150 V and 1 kHz. Experiments reveal that the maximum velocity of the nanopositioner is slightly lower than that obtained in simulation. This is mainly due to that the practical stepping time of the sawtooth-shaped driving signal is not zero. As shown in Fig. 9(d), the standard deviations of 15 velocity values of the nanopositioner at 80 V and 90 V are 0.025 and 0.028, and the standard deviations of 15 velocity values of the nanopositioner at 140 V and 150 V are 0.045 and 0.04. When the driving voltage was increased from 80 V to 150 V, the velocity fluctuations become larger, which are attributed to the inherent creep characteristics of the piezo-actuator.

In this design, the contact friction between the driving unit and moving unit is reduced by turning the adjust bolts when the load exerted on the platform increases. Two cross roller guide rails with high stiffness are utilized to drive the platform. In experiments, we placed weights on the platform from 0.4 kg to 2 kg and applied the driving voltage at 150 V and 1 kHz. Figure 10 shows the velocities under different loads. When the load was increased from 0.4 kg to 2 kg, the maximum velocities decreased from 3.457 mm/s to 3.143 mm/s. This result confirms that when the load was increased five times, the maximum velocity of the nanopositioner was reduced only by less than 9.08%. As the inertia of the load platform increases with increased loads, more transmission energy is consumed, resulting in the reduction of one step displacements. The developed piezoelectric stick–slip drive nanopositioner enables fast movement under high load.

A compact piezoelectric stick–slip drive nanopositioner with large velocity under high load and its design, optimization, and characterization have been presented. It has been designed such that the driving unit and moving unit are fully separated, and the contact friction changes by turning the adjust bolts. A MATLAB simulation model has been created to optimize the nanopositioner for a certain maximum velocity, and the FEM is used to confirm that the leaf hinge has sufficient stiffness. The testing results indicate that the nanopositioner achieved the maximum velocity of 3.467 mm/s, and it has a minimum resolution of 6 nm. Under the high load of 2 kg, the maximum velocity of 3.143 mm/s is acquired.

Peng et al.³¹ designed and fabricated a new portable micro-indentation device, which shows big advantages compared with the existing portable indentation devices. The maximum driving force and displacement of the portable micro-indentation device are 10 N and 1 mm, respectively. The maximum driving force and displacement of the designed nanopositioner are 2 N and 18 mm, respectively, such that the range of the driving force is limited if the designed nanopositioner is used as the actuator for the portable micro-indentation device. However, the designed nanopositioner has the capabilities of larger working stroke and high load. The designed nanopositioner can be used to actuate the sample such that the sample surface area to be indented and sample weight can be enlarged.

The main contributions of this work are as follows:

• ●

  The independent driving unit module, enabling the contact friction of the nanopositioner to be decreased by turning adjust bolts under high load.

• ●

  Compact structure, large velocity under high load, and using materials that are SEM-compatible, enabling the nanopositioner to be integrated to SEM-based nanorobotic systems.

• ●

  Compared with the existing piezoelectric stick–slip nanopositioner with high load, the proposed nanopositioner has better positioning resolution.

This research was supported by the National Natural Science Foundation of China (Grant No. 61774107) and the Construction Project of Suzhou Late-model R&D Institutions (Grant No. SZS2018337).

The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

The data that support the findings of this study are available from the corresponding author upon reasonable request.