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ISSN : 1975-6291(Print)
ISSN : 2287-3961(Online)
Journal of Korea Robotics Society Vol.12 No.1 pp.78-85
DOI : https://doi.org/10.7746/jkros.2017.12.1.078

# Optimal Design of 3D Printer based Piezo-driven Vertical Micro-positioning Stage

Jung Hyun Kim†
Corresponding author : Mechatronics Engineering, Kyungsung University, 48434. 309, Suyeong-ro, Nam-gu, Busan, Republic of Korea (dwellnom@ksu.ac.kr)
October 29, 2016 January 12, 2017 February 20, 2017

## Abstract

This paper presents the development of a 3D printer based piezo-driven vertical micro-positioning stage. The stage consists of two flexure bridge structures which amplify and transfer the horizontal motion of the piezo-element into vertical motion of the end-effector. The stage is fabricated with ABS material using a precision 3D printer. This enables a one-body design eliminating the need for assembly, and significantly increases the freedom in design while shortening fabrication time. The design of the stage was optimized using response surface analysis method. Experimental results are presented which demonstrate 100nm stepping in the vertical out-of-plane direction. The results demonstrate the future possibilities of applying 3D printers and ABS material in fabricating linear driven motion stages.

# 3D 프린터 기반 수직형 마이크로 모션 스테이지의 최적설계

김 정 현†

## 1.Introduction

Many measurement and fabrication processes in stateof- the-art semiconductor manufacturing and nano-technology require motion control with near nanometer precision. At the same time, 3D printing is emerging as a game changer in many manufacturing areas such as aero-space, optics among many others. This paper presents a novel effort to develop a piezo-driven linear motion stage using 3D printing technology, which can possibly greatly decrease the cost and simplify the process of building stages.

Piezo-driven linear motion stages can perform various motions ranging from 1 to 6 degree-of-freedom depending on various design factors such as number of actuators used, the degree of motion amplification, etc. Previous work on 1 degree-of-freedom motion stages include inquiries into parallel mechanisms and monolithic structures [1,2], bridge-type flex hinges [3], 3D bridge type hinges [4], tilt tables using half-bridges [5] and etc. Further work on 2, 3 & 6 degree-of-freedom has also been done [6,7,8,15].

Recently, due to the advancement in 3D printer technology and its many advantages, 3D printing is gaining much interest not only in technology but also in general society. Advantages include simplified manufacturing processes, one body manufacturing eliminating the need for assembly, various materials and etc. As a result, governments in United States, United Kingdom, China and many other countries are leading various R&D efforts [9], while industries such as automotive, aerospace, medicine, robotics, art, education and etc. are pursuing research into applying this emerging technology.

3D printers enable rapid prototyping of virtual 3D models drastically shortening design and fabrication time and is shown to increase the accuracy of design optimization [10]. In die casting, Kim et.al [11] has developed a novel rapid tooling process where a wax pattern fabricated with a 3D printer is used. In motion stages, Jung et.al [12] developed a micro-positioning stage using 3D printer.

This paper presents a 3D printer fabricated vertical-type piezo-driven linear motion stage employing two types of flexible bridge typed hinges (Fig. 1). Unlike previous stages which mostly use aluminum [4,5], we use ABS (Acrylonitrile - Butadiene - Styrene copolymer). Compared to previous materials, the stage structure exhibits significantly less structural stress which allows for more freedom of design. Furthermore, the required force to actuate the motion stage decreases. This relaxes power requirements for the piezoelectric element. Using a 3D printer, we simplified the manufacturing process, lowered costs and with ABS material created a more efficient stage.

## 2.Flexible Bridge-type Hinge

### 2.1.Motion Amplification Structure

In general, when designing a flexure stage two types of motion amplification structures are employed: the lever type shown in Fig. 2-(a) and the bridge type shown in Fig. 2-(b). The lever type allows for a large amplification ratio (b/a) that is proportional to the length of the structure. However, the structural stress also increases proportionally. This renders the need for stronger materials. Overall, the lever-type is more appropriate for in-plane motion amplification. The bridge-type has a smaller symmetric form-factor allowing for a denser design and has better vibrational characteristics making it better for out-of-plane motion structures. In this paper, we are implementing out-of-plane motion, therefore, the bridgetype hinge is employed.

### 2.2.Bridge-type Flexure Hinge

Two types of flexure hinges have been designed. First, as shown in Fig. 3-(a), the bridge transforms the x-axis motion of the piezo-element into y-axis motion. Second, as shown in Fig. 3-(b), a half-bridge transforms the y-axis bridge motion into z-axis motion.

These two bridges have been used to design a dense structure which can transform x-axis motion into z-axis motion. Furthermore, stress concentration is avoided by avoiding a notch type hinge. Although this can lead decreased flexibility, it is beneficial for performance with regards to stress.

### 2.3.Amplification structure of Bridge-type Flexure Hinge

A kinematic model of bridge-type amplification mechanism can be expressed as Figure 4. Defining the velocity of point A and B,

$V A = ∂ x ∂ t$
(1)

$V B = ∂ y ∂ t$
(2)

Where x is the displacement of the piezo-element and y is the displacement of the bridge. Expressing equations (1) and (2) as an amplification ratio

$V A = ∂ x ∂ t$
(3)

$V B = ∂ y e ∂ t$
(4)

Where x is the displacement of the piezo-element and y is the displacement of the bridge. Expressing equations (3) and (4) as an amplification ratio,(5)

$D amp = ∂ y ∂ x = ∂ y/ ∂ t ∂ x/ ∂ t = V B V A$
(5)

Defining O (Figure 4) as the instantaneous center of rotation of rigid body AB, as the instantaneous angular velocity, velocity of A and B can be expressed as,

$V A = ω ⋅ I x$
(6)

$V B = ω ⋅ I y$
(7)

Expressing (6) and (7) as amplification ratio, the following equation is obtained,(8)

$D amp = ω ⋅ I y ω ⋅ I x = I y I x =cotα$
(8)

It is evident from the above equation that determines the amplification ratio, therefore is the critical design factor.

## 3.Design Optimization and Simulation

### 3.1.Design Optimization

The optimization method employed in this paper is Response surface analysis. For Design of Experiment (DOE) the Central Composite Design (CCD) was used. The design factor used is α (Fig. 4) of the Bridge-type flexure hinge, which has been shown to have a critical effect on the amplification ratio of the motion amplification structure.

Design variables θ1, θ2 (Fig. 5) which correspond to the critical design factor α (Eq. 8) for each bridge structure are chosen as the optimization variables. Optimization is divided into a two-step process where θ1 of the bridge moving in the y-axis is optimized first, then θ2 of the bridge moving in the z-axis is

optimized next. The range of variables θ1, θ2 are set to,(9)(10)

(9)

(10)

Where the maximum of θ1 and the minimum of θ2 were each set near angles that render a flat bridge structure. The minimum of θ1 and the maximum of θ2 were set heuristically so that the total range would be approximately 20 degrees. The output variable is the maximum displacement of the stage structure. The input value is set at 20 μm according to the specification of the piezo-element to be used in the experiment (Table 1).

### 3.2.Simulation

Fig. 6 and Fig. 7 show the response surface analysis for the variables θ1, θ2 where the results are almost identical for both Al 7075-T6 and ABS. Both materials have a motion amplification ratio of 4.0. Also for both materials, the maximum displacement for θ1 occurs between 165° and 170° and for θ2 occurs between 100° and 105°. Based on these simulation results, the values chosen for θ1, θ2 are 168.1 and 101.0 respectively for designing the motion stage.

Table 2 shows the results of the response surface analysis. Although the displacements for Al 7075-T6 and ABS are almost identical, note that the stress level of the ABS is approximately 31 times lower. The yield stress for Al 7075-T6 and ABS are respectively 570 MPa, 40 MPa. Therefore, the simulation results for stress are each 4.1 vs 9 times smaller than the yield stress for Al 7075-T6 and ABS. This shows that ABS material compared to Al 7075-T6 is less restricted due to stress in designing flexure structures.

Fig. 8 and Fig. 9 each show the maximum displacement and maximum stress simulation results for the ABS material.

## 4.Experimental Results

### 4.1.Experiment Description

Based on the optimization results presented in Section 3, a Vertical micro-positioning stage has been fabricated using a 3D printer with ABS material. The stage is shown in Fig. 10. The 3D printer used is the Projet® 5000(3D Systems), which uses the MJM (Multi-Jet Modeling) method. MJM method sprays a photopolymer resin and wax from the printer head followed by a UV light which hardens the structure in layers. This 3D printer has maximum fabrication volume of this device is 550 × 393 × 300 mm, 0.025-0.05 mm precision, 375× 375 × 790 DPI (xyz) in HD mode, a minimum layer thickness of 32 μm. This resolution is sufficient to manufacture our motion stage.

The measurement of the vertical motion was performed using an interference microscope as shown in Figure 11. In order to measure vertical motion, the method developed by Kim et. al [13,14] was employed. The measurement method measures the movement of interference fringes using a CCD camera to estimate the vertical motion of the motion stage. Fig. 12 shows the flow diagram of the measurement process which is implemented in Labview. First, the fringe image model Mi(x, y) is defined. As the stage moves, the image of the stage I(x, y) is obtained. The model is found in the image using the correlation function,(11)

$r ( u, v ) = ∑ I ( x, y ) M i ( x-u, y-v ) - I ¯ ⋅ M i ¯ [ I ( x, y ) 2 - I ¯ 2 ] ⋅ [ ∑ M 1 ( x-u, y-v ) 2 - M ¯ i 2 ]$
(11)

and the position $( x ^ 1 , y ^ 1 )$ of the model is found where,(12)

$r ( x ^ 1 , y ^ 1 ) = max { r ( u , υ ) }$
(12)

Further details of the measurement method can be found in the literature [13].

### 4.2.Experiment Results

The input voltage to the piezo-element was varied from 0 to 40 V in 9 steps while the displacement of the end-effector, i.e. the half bridge, was measured. The experimental results are shown in Table 3. Amplification ratio is approximately 4 which agree with the simulation results. Fig. 13 plots the applied input voltage vs piezoelement displacement while Fig. 14 plots input voltage vs end effecter displacement.

In order to test the performance of the motion stage, 100 nm step inputs were applied to the stage (see Fig. 15). Measurement noise in the interference microscope is currently approximately 10 nanometers which attribute to the noise at each step. Furthermore, a gradual drift can also be seen at each step. It is thought that in the future improving the CCD camera performance and introducing further feedback control can improve motion control performance. Utilizing the motion measurement as feedback for close-loop control could especially correct for drift and non-linearity.

## 5.Conclusion & Remarks

This paper presented the development of a piezodriven vertical micro-positioning stage fabricated with a 3D printer using ABS material. Two bridge structures were constructed which amplified and transferred the horizontal motion of the piezo-element into vertical motion of the end-effector. It was shown that the use of 3D printed ABS material for creating flexure motion stages has less restriction on stress compared to traditional material. Compared to previous materials, the stage structure exhibits significantly less structural stress which allows for more freedom of design. Furthermore, the required force to actuate the motion stage decreases which relaxes power requirements for the piezoelectric element. Overall, we have the demonstrated the future possibilities of applying 3D printers and ABS material in fabricating linear driven motion stages. Due to the many advantages of 3D printing technology, various motion stage designs having multiple degrees-of-freedom and larger motion amplification should be possible.

## Figure

Diagram of vertical micropositioning stage

Topology of amplification mechanism

Bridge mechanism

Kinematic model of bridge-type amplification mechanism

Optimization Factor

Response surface of Al 7075-T6

Response surface of ABS

Maximum Displacement

Maximum Stress

Image of 3D printed Motion Stage (ABS material)

Microscope used for displacement measurement

Microscope used for displacement measurement

Piezo displacement

End effector displacement

100nm Stepping

## Table

Piezo Specification

Optimization result

Experimental results

## Reference

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## 저자소개

• 김 정 현 (Jung Hyun Kim)
• 1999 서울대학교 컴퓨터공학과(공학사)
• 2003 Ohio State University, Dept. Mechanical Eng. (석사)
• 2007 Ohio State University, Dept. Mechanical Eng. (박사)
• 2008 ~ 2010 미 Lam Research Corp. 근무
• 2010 ~ 현재 경성대학교 메카트로닉스공학과에서 교수로 근무
• 관심분야: 정밀계측, Fault Detection Diagnosis
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