micromachines Article
Development of a Contactless Air Conveyor System for Transporting and Positioning Planar Objects Xirui Chen 1,2 , Wei Zhong 1,2, * , Chong Li 1,2 , Jiwen Fang 1,2 and Fanghua Liu 1,2 1
2
*
School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
[email protected] (X.C.);
[email protected] (C.L.);
[email protected] (J.F.);
[email protected] (F.L.) Jiangsu Provincial Key Laboratory of Advanced Manufacture and Process for Marine Mechanical Equipment, Jiangsu University of Science and Technology, Zhenjiang 212003, China Correspondence:
[email protected]; Tel.: +86-511-84445385
Received: 30 July 2018; Accepted: 20 September 2018; Published: 24 September 2018
Abstract: In this study, we developed a completely contactless air conveyor system for transporting and positioning planar objects. The air conveyor forms a thin film underneath the object for support and simultaneously generates a controlled airflow that results in viscous traction. It is potentially applicable in the manufacturing process for semiconductor wafer or flat foodstuffs, where mechanical contact is expected to be avoided during transportation of the products to minimize contamination. The air conveyor employs duplicated arrays of actuating cells that are square pockets with a surrounding dam. A simple model is proposed to characterize the viscous force. The theoretical analysis reveals that the total force is the composition of an actuating force generated in the pocket areas and the side areas and a drag force generated in the dam areas. Experimental investigations are conducted on the basic characteristics of the film pressure distribution and the viscous force. The results show that the air film pressure is symmetrically distributed in the width direction but nonsymmetrically distributed in the length direction. The viscous force increases if the suction flow rate is enlarged or the gap thickness is narrowed. Comparison of the experimental results and the calculated results indicates that the model can provide an accurate prediction. A proportional–integral–derivative (PID) controller is applied for 1D-position control and position tracking. The actuating direction is selected using fast switching valves and the amplitude of the actuating force is adjusted using a control valve to vary the suction flow rate. The simulated and the experimental results verify the feasibility of the air conveyor system and the control method. Keywords: air conveyor; viscous force; contactless transport; pressure distribution; position control
1. Introduction Many industries require contactless transport of delicate or clean products such as silicon wafers, flat foodstuffs, and freshly painted objects. Transport by means of pneumatics technology is widely used in practical applications since it is clean, free from magnetism, and generates little heat [1–3]. Noncontact vacuum grippers [4–8] and air-cushion conveyors [9–13] are the most commonly used methods to avoid mechanical contact. The vacuum grippers generate an upward lifting force and thereby can pick-and-place a planar object. However, an object handled in this way is very likely to drop when tilted and thus locating pins or rubber friction pads are generally equipped on the grippers. The air-cushion conveyor uses arrays of bearing elements which supply pressurized air to form an air film under the object. The two methods are similar in that the object is levitated at an equilibrium
Micromachines 2018, 9, 487; doi:10.3390/mi9100487
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position where its weight is balanced by the lifting force. Unfortunately, both methods cannot completely avoid backside contact when moving the object in the horizontal direction. The conventional air-cushion method forms an air film to support the object but cannot provide a horizontal actuating force because the supplied airflow is perpendicular to the surface. Both the actuating function and the supporting function can be realized if a tilted airflow relative to the surface is in use. Paivanas et al. [14] described a system for wafer handling and transport applications using inclined air jets, and Biegelsen et al. [15] developed a paper mover using directed air jets. However, in these cases, the apertures are fixed and the object can only be moved in a predetermined direction that cannot be easily realized if the object needs to change direction. Therefore, researchers have found approaches to improve moving mechanisms. Konishi and Fujita [16] designed a fluidic microactuator which involves two on-off nozzles to transport tiny objects by changing the airflow direction. Zeggari et al. [17] presented the design and testing of a pneumatic conveyor which can levitate and move flat objects to a desired position using tilted air-flow. Fukuta et al. [18] reported the design, fabrication, and control of arrayed microelectromechanical systems (MEMS)-based actuators for distributed micromanipulation by generation and control of the air-flow force field. D. El Baz et al. [19] introduced a smart surface for conveying and positioning microparts; they established a mathematical model for discrete state acquisition and proposed several distributed synchronous and asynchronous discrete state acquisition algorithms. In addition to tilted air jets, some researchers used the aerodynamic-traction principle to move objects. Airflow across the surface of an object induces shear stress at the boundary and this might be used for actuation. Chen et al. [20] used viscous shear by air flow around a rotor shaft to drive a spindle, and Delhaes [21] presented a high-speed spindle which is both driven and supported by a viscous turbine. In these cases, the spindle is driven by exerting viscous force on the smooth surface, and similarly, the same principle can be applied to linear actuation. Moon and Luntz [22] accomplished this by generating the manipulation flow field on the top surface of an object while a standard air table generates an air cushion for support. Delettre [23] developed a 120 mm × 120 mm positioning system which uses individually controlled vertical jets for propulsion. Laurent et al. [24] utilized this system to perform experiments with several objects, but unfortunately they did not present a model for viscous force as a function of gap thickness. Ku et al. [25] developed a surface device using a 4 mm × 4 mm array of 100 capillary glass tubes which are individually connected to valves to generate a controllable pressure field. The Mechatronics System Design Group at the Technical University of Delft (TU Delft) has conducted long-term and meticulous research on product transport by means of using arrays of actuator cells to produce horizontal air flow underneath the object. The idea was originally raised by van Ostaijen in the patent published in 2008 [26]. The patent introduces a kind of air actuator which carries and transports a planar product by forming a thin layer of compressed air underneath the substrate to float and move the object in a desired direction. Afterwards the research group continuously advanced this research. In 2008, van Rij et al. [27] explained the operating principles of the new contactless transport system and its detailed mathematical modeling process. The computation results indicated that the generated acceleration approximates 2.5 m/s2 for a glass substrate with a surface area of 2 m2 and a thickness of 0.7 mm. In 2009, van Rij et al. [28] optimized the air actuator by means of grooves connecting the inlet points and outlet points; the simulation results by a finite element method (FEM) model indicated that more traction force can be generated after optimization. Later, van Ostayen et al. [29] and Jasper Wesselingh et al. [30] comprehensively studied and detailed the theory, modeling, design, implementation, testing, and evaluation of the developed air actuator. In 2017, Krijnen et al. [31] developed a novel contactless positioning system for silicon wafers with the application of fractional-order proportional–integral–derivative (PID). Their research on the topic of product transport continues currently and more results will be reported in future. Objectively, the systematic work by the research group of TU Delft has greatly enriched the implementation of contactless transport using a pneumatic approach. The present work is greatly
mathematical modeling and apparatus design. In this paper, we have designed a completely contactless air conveyor system for object transportation and positioning in a similar way as previously published [30]. First, a simplified theoretical model is deduced and used for calculating the viscous2018, force. Micromachines 9, 487Next, the film pressure distribution and viscous force are experimentally 3 of 21 measured. Then, a detailed analysis of the film pressure distribution and viscous force is provided. Finally, theoretical and experimental results with a PID controller—used for dimension position inspiredand by position the previous research ofpresented. TU Delft and actually follows some of the ideas in mathematical control tracking—are modeling and apparatus design. In this paper, we have designed a completely contactless air conveyor system for object transportation 2. Mechanism of the Air Conveyorand positioning in a similar way as previously published [30]. First, a simplified theoretical model is deduced and used for calculating the viscous force. Next, the film Figure 1a shows a photograph of the air conveyor. A flat object is levitated by the formed air pressure distribution and viscous force are experimentally measured. Then, a detailed analysis of the film, and can be moved and positioned using controlled airflow in the gap. The air conveyor film pressure distribution and viscous force is provided. Finally, theoretical and experimental results employs duplicated arrays of actuating cells. To facilitate analysis and experiments, as shown in with a PID controller—used for dimension position control and position tracking—are presented. Figure 1b, a representative unit is focused. The unit is a 74 mm square consisting of 25 actuating cells. Each cell of is the actually a 10 mm square pocket (depth: 150 μm) surrounded by a dam with a 2. Mechanism Air Conveyor width of 4 mm. In the pocket, two pairs of inlet/outlet ports (φ = 1 in diameter) are opened. The two Figure 1a shows a photograph of the air conveyor. A flat object is levitated by the formed inlet ports are connected with a groove, which has a dimension of 1 mm width and 1 mm depth, and air film, and can be moved and positioned using controlled airflow in the gap. The air conveyor similarly, the two outlet ports are also connected with a groove. We consider that these grooves can employs duplicated arrays of actuating cells. To facilitate analysis and experiments, as shown in stabilize the flow in the pocket. In this study, we aim to achieve one dimensional transport and Figure 1b, a representative unit focused. The unitlocated is a 74 in mm consisting 25 actuating cells. positioning. Accordingly, all theisinlet/outlet ports thesquare same column areofconnected with an Each cell is actually a 10 mm square pocket (depth: 150 µm) surrounded by a dam with a width internal perforation which is then connected to an independent fast switching valve (3/2 normally of 4 mm. In theBy pocket, two pairs inlet/outlet (ϕ =for 1 in diameter) are opened. The two inlet opened valve). this means, eachofcolumn can beports selected positive pressure or negative pressure ports are connected with a groove, which has a dimension of 1 mm width and 1 mm depth, by switching the valves as required. and similarly, the two outlet ports are also in connected with a groove. We consider that these grooves The working principle is illustrated Figure 1c. The inlet ports are connected to positive can stabilize the flow in the pocket. In this study, we aim to achieve one dimensional transport pressure while the outlet ports are connected to negative pressure. Therefore, a horizontal airflow is and positioning. Accordingly, inlet/outlet ports located in the same generates column area connected with formed in the pocket due to all thethepressure difference that accordingly viscous force, an internal which is then connected to an independent fast switching (3/2 normally namely, theperforation shear stress at the boundary. Meanwhile, the entering air formsvalve a supporting film opened valve). By this means, each column can be selected for positive pressure or negative pressure underneath the object. Because of the supporting function and the actuating function, the object can by switching the valves as required. be transported without mechanical contact.
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(b) Figure 1. Cont.
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(c) Figure 1. 1. Air unit consisting of of 25 Figure Air conveyor. conveyor. (a) (a) Photograph Photographof ofthe theair airconveyor. conveyor.(b) (b)AArepresentative representative unit consisting actuating cells. (c) (c) Cutaway view that shows thethe working principle. 25 actuating cells. Cutaway view that shows working principle.
The principle is illustrated in Figure 1c. The inlet are connected to positive pressure The working fabrication process of the device is described as ports follows. The material used was 7050 while the aluminum-alloy. outlet ports are connected to negative pressure. a horizontal airflow formed aviation First, a cuboid-shaped plate, Therefore, with dimensions of 204 mm ×is 228 mmin× the pocket pressure that accordingly generates viscous force, namely, the shear 20.15 mm, due was to cutthe down fromdifference the raw material. The upper and thealateral surfaces of the plate were stress at the boundary. air forms supporting film underneath the with object. roughly polished to a Meanwhile, roughness ofthe Raentering = 6.3 μm. Then, athirty-two internal perforations, a Because supporting function the actuating object can without diameterofofthe 4 mm, were drilled at and intervals of 7 mmfunction, into the the lateral side ofbe thetransported plate. Next, 16 × 8 mechanical contact. square pockets distributed in the arrays were fabricated on the upper surface of the plate by means fabrication the devicedepth is described follows. The material used was 7050 of a The milling process,process with aoftemporary of 300 as μm. In each pocket, two grooves wereaviation milled aluminum-alloy. First, a cuboid-shaped plate, dimensions of pairs 204 mm × 228 mm × 20.15 according to the locations and sizes shown inwith Figure 1, and two of inlet/outlet ports at mm, two was down from were the raw material. The upper the lateral surfaces of the perforation. plate were roughly endscut of the grooves drilled until they were inand connection with the internal Finally, polished a roughness of Ramachining = 6.3 µm. process Then, thirty-two perforations, with diameter of the plate to underwent a finish to ensure internal a roughness of Ra = 0.8 μmaon the upper 4surface mm, were at intervals 7 mm of into the lateral side of the plate. Next, 16 × 8 square pockets and drilled a final depth of theof pockets 150 μm. distributed in the arrays were fabricated on the upper surface of the plate by means of a milling 3. Theoretical process, with a Modeling temporary depth of 300 µm. In each pocket, two grooves were milled according to the locations and sizes shown in Figure 1, and two pairs of inlet/outlet ports at two of theequation grooves It is easy to understand that establishing a theoretical model based on ends Reynolds were drilled until they were in connection with the internal perforation. Finally, the plate underwent coupling and incompressible Navier–Stokes equation could help analyze and understand certain abasic finishcharacteristics, machining process a roughness of Ra = 0.8and µm on the upper and asolving final depth suchtoasensure film pressure distribution viscous force.surface However, the of the pockets of 150 µm. model with a finite difference method requires a large amount of calculating time and therefore such a model can never be used for motion control of the object in a real scenario. Therefore, there 3. Theoretical Modeling exists a crucial need to develop simple mathematical models with good real-time performance. In a is easy understand that establishing a theoretical modelbased based equation past It paper [30],toJasper Wesselingh proposed correlating equations onon theReynolds fundamental flow coupling and incompressible Navier–Stokes equation could help analyze and understand certain regime to predict the viscous force. This method greatly simplified the flow analysis on duplicated basic such as film distribution and viscous force. However, solving the model arrayscharacteristics, of the actuating cells and pressure proved to be effective. Therefore, we followed their treatments for with a finite differenceand method requiresofamodeling large amount of calculating time and therefore such a model region segmentation the method in this work. can never be used for motion of the object in a real scenario. Therefore, there exists a crucial As shown in Figure 1b, acontrol 3D-Cartesian coordinate is established at the bottom left point. The need to width, developand simple mathematical models with good In a past paper length, thickness directions are denoted as x,real-time y, and zperformance. coordinates, respectively. In [30], this Jasper Wesselingh proposed correlating equations based on the fundamental flow regime to predict study, the actuating force is only considered in the x-direction. Owing to the complexity of flowthe in viscous This method greatly simplified flow analysis on duplicated arrays of the actuating the gap,force. the following assumptions are made the to simplify the theoretical modeling. cells and proved to be effective. Therefore, we followed their treatments for region segmentation and 1. Airflow in the gap is laminar, dominated by viscous effects. the method of modeling in this work. 2. Pressure distribution in the z-direction is negligible. As shown in Figure 1b, a 3D-Cartesian coordinate is established at the bottom left point. The length, width, the andNavier–Stokes thickness directions are as x, y, z coordinates, respectively. Consequently, equation in denoted the x-direction is and simplified as the following. In this study, the actuating force is only considered in 2the x-direction. Owing to the complexity of flow p u in the gap, the following assumptions are made (1) tosimplify 0 the theoretical modeling.
x
z 2
1. Airflow in the gap is laminar, dominated by viscous effects. where p is the film pressure, μ is the air viscosity, and u is the flow velocity. 2. Pressure distribution in the z-direction is negligible.
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Consequently, the Navier–Stokes equation in the x-direction is simplified as the following.
−
∂2 u ∂p +µ 2 = 0 ∂x ∂z
(1)
where p is the film pressure, µ is the air viscosity, and u is the flow velocity. With the boundary condition that u = 0 (z = 0) and u = V 0 (z = h), integrating Equation (1) with 5 of 21 respect to Micromachines z yields: 2018, 9, x V0 p2 − p1 2 With the boundary condition =z0) − and V0 (z =zh), integrating Equation (1) with hzu = + u =that u = 0 (z (2) 2µl h respect to z yields:
where p1 is the pressure of the inlet ports, p2 is the pressure of the outlet ports, and l is the length of p p1 2 u 2 (2) z hz Vh0 z the pocket. 2l The shear stress τ is linearly proportional to the velocity gradient as below. where p1 is the pressure of the inlet ports, p2 is the pressure of the outlet ports, and l is the length of the pocket. ∂u τ =to − µ velocity gradient as below. The shear stress τ is linearly proportional the
(3)
∂z
u
(3) Figure 2a shows a typical actuating cell consisting z of three areas. They are the pocket area, dam area, and side area. The airflow in the pocket area and the side area is assumed along the x-direction, Figure 2a shows a typical actuating cell consisting of three areas. They are the pocket area, dam and the airflow inside thearea. dam area is the opposite. The thickness for the dam and the pocket area, and The airflow in the pocket area andfilm the side area is assumed along thearea x-direction, area is denoted d and d isThe thefilm distance the lower surface of the floating and theas airflow in h, therespectively. dam area is theHere, opposite. thicknessfrom for the dam area and the pocket area is denoted as d and h, respectively. Here, d is the distance from the lower surface of the floating object to the upper surface of the air conveyor, while h is the distance from the lower surface of the object to the upper surface of the air conveyor, while h is the distance from the lower surface of the floating object to the surface of the pocket (refer to Figure 2c). floating object to the surface of the pocket (refer to Figure 2c).
(a) II
I
......
III
Pocket Side
w
Dam
l l
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w
A
y w
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(c) Figure 2. Typical cells and modeling of the airflow in the gap. (a) Area segmentation of a typical cell. Typical cells and modeling of the airflow in the gap. (a) Area segmentation of a typical (b) Area segmentation of a representative row. (c) Velocity profile in the gap.
Figure 2. (b) Area segmentation of a representative row. (c) Velocity profile in the gap.
cell.
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With the boundary condition that z = h, submitting Equation (2) into Equation (3) obtains the shear stress τ p in the pocket area. p − p2 h µ − V0 (4) τp = 1 l 2 h Similarly, the shear stress τ d in the dam area is obtained as below. p − p2 d µ + V0 τd = − 1 2w 2 d
(5)
The shear stress, τ s , in the side area is thus expressed as: τs =
p1 − p2 d µ − V0 l 2 d
(6)
For multiple cells in a representative row, as shown in Figure 2b, the row is divided into three zones, designated as I, II, and III, respectively. Zone I is the leftmost cell that consists of a pocket area, a dam area, and two side areas. Zone II contains middle reduplicate cells which have similarity to that of zone I. Zone III is the rightmost dam area. The total viscous force is the composition of the force in the pocket, dam, and side areas (Fp , Fd , and Fs ). For zone I, the viscous force can be calculated by Equations (7)–(9), respectively. p1 − p2 µ hl − V0 l 2 2 h p − pa d µ + V0 × [w × (l + 2w)] Fd = − 1 w 2 d p1 − p2 d µ − V0 × 2wl Fs = l 2 d Fp =
(7) (8) (9)
For zone II, the viscous force (Fp , Fd , and Fs ) is calculated by Equations (10)–(12), respectively. p1 − p2 µ hl − V0 l 2 2 h p − p2 d µ Fd = − 1 + V0 × [2w × (l + 2w)] 2w 2 d p1 − p2 d µ − V0 × 2wl Fs = l 2 d Fp =
(10) (11) (12)
For zone III, the viscous force is calculated only in the dam area by Equation (13). Fd = −
pa − p2 d µ + V0 w 2 d
× [w × (l + 2w)]
(13)
As an example for the case of a covered region including M × N (Width × Length) cells in an array, the total force F is calculated as below, F = M × FI + M × ( N − 1) × FII + M × FIII
(14)
where FI , FII , and FIII denotes the viscous force of zones I, II, and III, respectively. Figure 2c shows the velocity profile in the gap. The film pressure at the edge remains at atmospheric pressure (pa ). The object is moved by an actuating force formed in the pocket area and the side area, but is also simultaneously subjected to a drag force formed in the dam area. This does not include the rightmost dam area where air exhausts to the atmosphere in the x-direction and exerts positive effects on the movement.
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Integrating Equation (2) with respect to cross-sectional area obtains the volumetric flow rate Qp in the pocket area. p − p2 3 hl Qp = 1 h + V0 (15) 12µ 2 The theoretical deduction of the equations above is greatly inspired by works in the literature [27–30]. When applying the equations to calculate the viscous force, there is a problem that the effective flow rate through the gap is necessary for calculating the pressure difference p1 -p2 . We thus made an extension to the modeling to accommodate for this in the present study. A fitting equation (Equation 16) is proposed to approximate the effective flow rate through the gap including the effect from the inlet/outlet flow and the gap thickness. The fitting coefficients are determined experimentally. This treatment improves the modeling and is especially appropriate for the present study since the position control of the object is implemented by varying the suction flow rate (detailed in Section 5.2). n d0 Qp = (αQ1 + βQ2 ) (16) d0 + δd where Q1 is the inlet flow rate, Q2 is the suction flow rate, α, β, and n are undetermined parameters, d0 is the initial thickness, and δd is the changed thickness. It should also be noted that in the actual case variation of the suction flow rate would affect the floating height of the object. However, the accompanying effect was not included in the theoretical model but its inclusion would be expected in future work. 4. Basic Characteristics 4.1. Pressure Distribution Since pressure distribution is very sensitive to inclination of the gap, the measuring table must be strictly parallel with the test device and the gap thickness should be finely adjusted. An experimental apparatus is proposed to accomplish this, as schematically shown in Figure 3. A measuring table with a sliding bar which has a small tap hole and an internal connecting perforation was used to measure the film pressure. First, the measuring table was installed at the bottom of an elevating table. Then, the measuring table was fixed by the following steps: (1) The measuring table was placed inversely on the conveyor surface and then set down three pins to make sure that their tips touched the top of the elevating table. (2) The pin clamps we turned until the pins were held tightly, and then we used a spring to fix the elevating table to the support. The vertical position of the measuring table is adjustable and can be read through a laser displacement sensor (LK-G30, Keyence Co., Ltd., Osaka, Japan, resolution: 0.1 µm). Another displacement sensor was used to measure the position of the sliding bar. A pressure sensor (KL17, Nagano Keiki Co., Ltd., Tokyo, Japan) with a range of 0–2 kPa was connected to the pressure tap through the internal perforation. In this way, the pressure distribution can be measured by recording the film pressure and position while slowly moving the sliding bar.
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Figure distribution measurement. measurement. Figure 3. 3. Schematic Schematic of of the the apparatus apparatus for for pressure pressure distribution Figureperformed 3. Schematic of the apparatus for pressure distribution measurement. Experiments were were with supplyflow flow rate = 50 L/min (ANR), suction rate Experiments performed with supply rate Q1Q=1 50 L/min (ANR), suction flowflow rate Q 2= Q = 2030 and 30 L/min (ANR), andthickness gap thickness h =and 150200 andμm, 200respectively. µm, respectively. Figure 4 shows the 202 and L/min (ANR), and gap h = 150 Figure 4 shows the film Experiments were performed with supply flow rate Q1 = 50 L/min (ANR), suction flow rate Q2 = film pressure distribution on line AA’ (cf. Figure 1b), which is perpendicularthe to the direction of airflow pressure distribution on line AA’ Figure which is perpendicular direction of airflow in 20 and 30 L/min (ANR), and gap(cf. thickness h1b), = 150 and 200 μm, respectively.toFigure 4 shows the film in the pockets. In each pocket, there are two high pressure peaks concentrated around the center of the the the pockets. each pocket, there high concentrated around of the centerinof pressure In distribution on line AA’are (cf.two Figure 1b),pressure which is peaks perpendicular to the direction airflow inlet ports. The pressure distributed symmetrically withconcentrated respect to the centerline, andofa the uniform pockets. Infilm each pocket,isthere are two high pressure peaks around thecenterline, center inletthe ports. Thefilm pressure is distributed symmetrically with respect to the and a distribution is recognizable in the grooves. The amplitude of the pressure is influenced by the suction inlet ports. The film pressure is distributed symmetrically with respect to the centerline, and a uniform distribution is recognizable in the grooves. The amplitude of the pressure is influenced by uniform distribution is recognizable in experiments the grooves. The amplitude of were the pressure is influenced by their flow rate andflow the gap Contrast were performed to clarify their effects. When the the suction ratethickness. and the gap thickness. Contrast experiments performed to clarify the suction flow rate and the gap thickness. Contrast experiments were performed to clarify their gap is narrowed, the pressure distribution shifts upward but maintains a nearly unchanged shape. effects. When the gap is narrowed, the pressure distribution shifts upward but maintains a nearly effects. Whenthe theviscous gap is narrowed, the pressure distribution shifts upward but maintainsThe a nearly This is because impedance of theimpedance gap is determined clearance. narrower unchanged shape. This is because the viscous of the gapbyis the determined by the clearance. unchanged shape. This is because the viscous impedance of the gap is determined by the clearance. the the viscous impedance; hence,impedance; the entire film pressure increases the gap Theclearance, narrower the thelarger clearance, the larger the viscous hence, the entire filmaspressure The narrower the clearance, the larger the viscous impedance; hence, the entire film pressure impedance is enlarged. If the suction flow rate, Q , is enlarged, the amount of air that escapes into the increases as the gapgap impedance the2suction suctionflow flow rate, is enlarged, the amount increases as the impedanceisisenlarged. enlarged. If If the rate, Q2,Qis2,enlarged, the amount of air of air dam area would reduce and thus lead to decreased pressure distribution. The symmetrical pressure that that escapes intointo thethe dam area and thus thuslead leadtotodecreased decreased pressure distribution. escapes dam areawould wouldreduce reduce and pressure distribution. The The distribution indicates that the viscous force generated in the width direction is considerably small symmetrical pressure distribution indicates that the viscous force generated in the width direction is symmetrical pressure distribution indicates that the viscous force generated in the width direction is and therefore can be neglected. considerably small and thereforecan canbe beneglected. neglected. considerably small and therefore
1200
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Figure4. 4. Film Film pressure Figure pressuredistribution. distribution.
Figure 4. Film pressure distribution.
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Figure 5 shows the film pressure distribution on line BB’ (cf. Figure 1b), which is distributed 5 shows pressure on line BB’ there (cf. Figure is distributed alongFigure the direction ofthe the film airflow in the distribution pockets. In each pocket, is only1b), onewhich high pressure peak along the direction of the airflow in the pockets. In each pocket, there is only one high pressure at the center of the inlet ports, and the pressure distribution is asymmetrical with respect to the peak at theThe center of thearound inlet ports, and the pressure distribution asymmetrical withofrespect to centerline. pressure the outlet port is apparently lower is compared with that the inlet the centerline. The pressure around the atmospheric outlet port ispressure. apparently compared thatsuction of the port; however, it is still higher than the As lower the gap thicknesswith or the inlet rate port;changes, however, is still higher than the atmospheric gap thickness or the flow theitpressure distribution shifts upward or pressure. downwardAs butthe also maintains a nearly suction flowshape. rate changes, the pressure distribution shifts upward or downward also maintains unchanged As is well-known, the pressure distribution shape reflects thebut flow behavior. In a nearly unchanged shape. As is well-known, the pressure distribution shape reflects the flow behavior. the pockets, the decreasing pressure indicates that air flows from the inlet ports to the outlet ports. In the pockets, the decreasing pressure indicates thatthat air flows fromthe theobject. inlet ports to the outlet The generated airflow therefore produces a force actuates In the dam area,ports. the The generated airflow therefore produces a force that actuates the object. theneighboring dam area, the pressure pressure gradient shows an opposite trend because of the airflow fromInthe cells. This gradient shows an airflow oppositeacross trend because the airflow fromcounteractive the neighboring This confirms confirms that the the damofarea is actually to cells. the movements of that the the airflow across the dam area is actually counteractive to the movements of the object. object.
1200 1000 800 600 400 200 0 0
14.8
29.6
44.4
59.2
74
Figure Figure 5. 5. Film Film pressure pressure distribution. distribution.
4.2. Viscous Viscous Force Force 4.2. Measuring the the viscous viscous force force is is important important since since it it is is an an effective effective way way to to evaluate evaluate the the accuracy accuracy of of Measuring the mathematical research groupgroup of TU of Delft [30]Delft reported well-designed experimental the mathematicalmodel. model.The The research TU [30] a reported a well-designed −3 N. In this apparatus which ensures adequate measuring accuracy of viscous force in the order of 10 experimental apparatus which ensures adequate measuring accuracy of viscous force in the order work, experimental is designed in a similar way asinschematically in Figure 6. of 10−3 the N. In this work, apparatus the experimental apparatus is designed a similar wayshown as schematically A flat plate is supported by aconveyor pressurized air film. force sensorair (LVS-5GA, shown in Figure 6. A flatupon platethe is conveyor supportedsurface upon the surface by aApressurized film. A Kyowa Electronic Instruments, Tokyo, Japan) is installed on a sliding track, and its mounting head force sensor (LVS-5GA, Kyowa Electronic Instruments, Tokyo, Japan) is installed on a sliding track, contacts with the lateral side of the plate measure force.to The force sensor was calibrated and and its mounting head contacts with thetolateral sideviscous of the plate measure viscous force. The force a preamplifier was used. The position of the sliding track can be finely adjusted using the micrometers. sensor was calibrated and a preamplifier was used. The position of the sliding track can be finely The air conveyor unit is placed onThe a stationary table,unit which is mounted a slight tilt by adjusting adjusted using the micrometers. air conveyor is placed on a on stationary table, which is three adjustable screws. Thus, the mounting head of the force sensor is in contact with the plate, mounted on a slight tilt by adjusting three adjustable screws. Thus, the mounting head of the force and viscous force measurement can be obtained by subtracting the component of gravity of the sensor is in contact with the plate, and viscous force measurement can be obtained by subtractingplate. the Moreover, the thickness be varied by slowly changing the can massbeofvaried the floating objectchanging and detected component of film gravity of thecan plate. Moreover, the film thickness by slowly the using of a laser displacement (LK-G30,using Keyence Co., displacement Ltd., Osaka, Japan, resolution: µm). Co., mass the floating objectsensor and detected a laser sensor (LK-G30,0.1 Keyence Ltd., Osaka, Japan, resolution: 0.1 μm).
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Figure 6. Schematic of the apparatus for viscous force measurement. Figure Figure 6. 6. Schematic Schematic of of the the apparatus apparatus for for viscous viscous force force measurement. measurement.
During the experiments, all the inlet ports in the same column were connected with positive During experiments, all same column were with pressure and outlet portsall with pressure. supply flow rateconnected Q1 was fixed atpositive 40 L/min During thethe experiments, thenegative inlet ports in the The pressure and the outlet ports with negative pressure. The supply flow rate Q was fixed at 40 while the suction flowports rate Q 2 was set to 20, 25, andThe 30 L/min. 7 plots the fixed measured viscous with negative pressure. supplyFigure flow rate Q11 was at 40L/min L/min while suction flow rate Q2Qwas seth. toClearly, 20,20, 25, 25, and 30 L/min. Figure 7 upward plots the as measured viscous force forcethe F versus gap thickness theand F–h moves suction flow rate the suctionthe flow rate 2 was set to 30curve L/min. Figure 7 plots thethe measured viscous F versus the gap thickness h. Clearly, the F–h curve moves upward as the suction flow rate increases. increases. With a constant suction flow rate, the viscous force decreases with gap thickness. Airflow force F versus the gap thickness h. Clearly, the F–h curve moves upward as the suction flow rate With a constant flow rate, the rate, viscous force decreases with gap thickness. Airflow inthus the a in the pockets accelerated by enhancing the flow reducing the gap and increases. With aissuction constant suction flow the suction viscous forceordecreases with gapthickness thickness. Airflow pockets is accelerated by enhancing the suction flow orflow reducing the gap thickness and thus a thus larger larger viscous can thus be generated. calculated were obtained using Equations in the pockets is force accelerated by enhancing the The suction or results reducing the gap thickness and a viscous force can thus be generated. The calculated results were obtained using Equations (14)–(16). (14)–(16). First, the can effective rate through gap in the pocket areas is estimated Equation larger viscous force thus flow be generated. The the calculated results were obtained using by Equations First, effective flow rateflow through the gapthe indifference the pocket estimated by Equation (16). the Then, with Equation (15),rate thethrough pressure 1areas -p2 is is obtained. Equation is(16). the (14)–(16). First, the effective gap in theppocket areas is estimated by (14) Equation Then, with Equation (15), the pressure differencedifference p1 -psum is obtained. Equation (14) is the integration of integration of Equations (7)–(13) representing the of generated viscous force. Observations in (16). Then, with Equation (15), the pressure p 1 -p 2 is obtained. Equation (14) is the 2 Equations (7)–(13) representing the sum of generated viscous force. Observations in Equations (7)–(13) Equations of (7)–(13) show(7)–(13) that ifrepresenting p1-p2 is known, the viscous force with different flow rate caninbe integration Equations the sum of generated viscous force. Observations show that if p isshow known, with flow can be calculated. The fitting calculated. The coefficients in2 Equation (16) are experimentally determined as α =rate β = 0.12 and Equations (7)–(13) thatthe if viscous p1-p is force known, thedifferent viscous forcerate with different flow can be 1 -p2fitting coefficients in Equation (16) are experimentally determined as α = β = 0.12 and n = 0.03. An error n = 0.03. An error less than 5% is estimated by the root-sum-square method indicating that the calculated. The fitting coefficients in Equation (16) are experimentally determined as α = β = 0.12 and less than 5% iserror estimated by the indicating that method the calculated results afford calculated afford sufficient n = 0.03. Anresults less than 5%root-sum-square is accuracy. estimated bymethod the root-sum-square indicating that the sufficient accuracy. calculated results afford sufficient accuracy.
Viscous force (mN) Viscous force (mN)
2.5 2.5 2 2 1.5 1.5 1 1 0.5 0.5 0 50 0 50
100 100
150 150
200 200
Figure7.7.Viscous Viscousforce forceversus versusgap gapthickness. thickness. Figure Figure 7. Viscous force versus gap thickness.
250 250
The height of of thethe plate is actually influenced by the flowflow rate.rate. Figure 8 shows the Thefloating floating height plate is actually influenced by suction the suction Figure 8 shows relation for a plate of weight 89.5 g. From the results of the pressure distribution it is clear that film the The relation for a plate of weight 89.5 g. From the results of the pressure distribution it is clear that floating height the plate is actually influenced by the suction flow rate. Figure 8 shows pressure changes flow89.5 rate. the plate would float at distribution afloat lower greater film pressure with suction flow rate. the Obviously, the plate would atheight a lower with the relation for changes a with platesuction of weight g.Obviously, From results of the pressure it with is height clear that suction flow rate. So if with we theoretical to correlate the viscousfloat force with theforce suction flow greater suction flow rate.use Sothe if we use rate. the model theoretical model to correlate theatviscous with the film pressure changes suction flow Obviously, the plate would a lower height with rate, we should take into account the resulting variation in gap thickness. Accordingly, an approximate suctionsuction flow rate, should into the account the resulting in gap thickness. Accordingly, greater flowwe rate. So iftake we use theoretical model variation to correlate the viscous force with the suction flow rate, we should take into account the resulting variation in gap thickness. Accordingly,
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11 of 21 an approximate curve was fitted to the data points using a 4th-order polynomial regression (R2 > 0.99) to representcurve the relation of h-Q an approximate was fitted to2.the data points using a 4th-order polynomial regression (R2 > 2 0.99)was to represent the data relation of h-Q 2. a 4th-order polynomial regression (R > 0.99) to represent the curve fitted to the points using relation of h-Q2 . 200
Gap thickness (μm) (μm) Gap thickness
200 180
Exp. Fitting Exp.
180 160
Fitting
160 140 140 120 120 100 5 100 5
10 10
25
30
35
Suction flow rate (L/min)
15
30
35
15
20 20
25
Suction flow rate (L/min)
Figure 8. Gap thickness versus suction flow rate. Figure Figure8.8.Gap Gapthickness thicknessversus versussuction suctionflow flowrate. rate.
Figure 9 shows the calculated viscous force versus gap thickness with different suction flow the calculated viscous versus gap with different suction flow rateFigure Q 2. For9 the motion of the object,force the viscous is expected to be variable and this can Figure 9shows shows thecontrol calculated viscous force versusforce gapthickness thickness with different suction flow rate Q . For the motion control of the object, the viscous force is expected to be variable and this can be be achieved by connecting a control valve to the outlet port to vary the suction flow rate. Increasing 2 2. For the motion control of the object, the viscous force is expected to be variable and this can rate Q the suction flow rate and decreasing thethe gap thickness a positive on the viscous achieved by connecting a control valvevalve to port port toboth vary the suction floweffect rate. rate. Increasing the be achieved by connecting a control tooutlet the outlet to exert vary the suction flow Increasing force. Therefore, when Q 2 increases, the viscous force actually exhibits a more significant upward suction flow rate and decreasing the gap thickness both exert a positive effect on the viscous force. the suction flow rate and decreasing the gap thickness both exert a positive effect on the viscous trend due to the Q accompanied decrease inviscous gap thickness. An adjustable range of the viscous force can Therefore, when the viscous force actually exhibits a more upward trend 2 increases, force. Therefore, when Q2 increases, the force actually exhibits asignificant more significant upward be discerned according to the upper and lower limits of the suction flow rate. Furthermore, since the due to the accompanied decrease in gap thickness. An adjustable range of the viscous force can be trend due to the accompanied decrease in gap thickness. An adjustable range of the viscous force can trend curve heavily relies on the relation of h-Q 2, itof would move left or right depending on whether discerned according to the upper and lower limits the suction flow rate. Furthermore, since the be discerned according to the upper and lower limits of the suction flow rate. Furthermore, since the the weight ofheavily the object changes. trend curve relies on 2 ,2it trend curveheavily relies onthe therelation relationofofh-Q h-Q , itwould wouldmove moveleft leftororright rightdepending dependingon onwhether whether the weight of the object changes. the weight of the object changes.
2.4
Viscous forceforce (mN)(mN) Viscous
2.4 2 2 1.6 1.6 1.2 1.2 0.8 0.8 0.4 50 0.4 50
100
150
200
250
100
150
200
250
Figure9.9.Calculated Calculatedviscous viscousforce forceversus versusgap gapthickness. thickness. Figure Figure 9. Calculated viscous force versus gap thickness.
The forceisisthe thecomposition composition of the actions the pocket areas,areas, damand areas, Thetotal total viscous force of the actions in theinpocket areas, dam side and sideFigure areas. Figure 10the plots the calculated viscous force versus the suction flow rate to demonstrate areas. 10 plots calculated viscous force versus the suction flow rate to demonstrate the The total viscous force is the composition of the actions in the pocket areas, dam areas, and side the contributions of different areas. The positive value means that the airflow in the pocket areas contributions of different The positive airflow in the areas and the the areas. Figure 10 plots theareas. calculated viscousvalue forcemeans versusthat the the suction flow ratepocket to demonstrate and the sideproduces areas produces an actuating force, while the negative value for theareas dam represents areas represents side areas an actuating force, while the negative value for the dam a drag contributions of different areas. The positive value means that the airflow in the pocket areas and the a force. drag force. Clearly, the actuating force anddrag the drag showincreasing an increasing trend suction Clearly, both both the the forceforce show withwith suction flow side areas produces an actuating actuating force force,and while the negative valueanfor the dam trend areas represents a drag flow rate, and, the greatest contribution is from the pocket areas. Careful observation shows that the rate, and, the greatest is from areas. Careful observation shows the force force. Clearly, both thecontribution actuating force and the the pocket drag force show an increasing trend withthat suction flow force contributed by the side areas is almost in equilibrium with that contributed by the dam areas. rate, and, the greatest contribution is from the pocket areas. Careful observation shows that the force
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contributed by the side areas is almost in equilibrium with that contributed by the dam areas. This means that the theoretical model can be further simplified, only considering the effects from the This means that the theoretical model can be further simplified, only considering the effects from the pocket areas. pocket areas.
2
Viscous force (mN)
1.5 1 0.5 0 -0.5 -1 -1.5 0
5
10
15
20
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Figure areas. Figure10. 10.Viscous Viscousforce forcecontributed contributedbybydifferent different areas.
5.5.Position PositionControl Control 5.1. Experimental Setup 5.1. Experimental Setup Figure 11a shows the photograph of the experimental apparatus for position control of Figure 11a shows the photograph of the experimental apparatus for position control of a planar a planar object. The air conveyor is a 228 mm × 204 mm rectangle consisting of 128 actuating cells. object. The air conveyor is a 228 mm × 204 mm rectangle consisting of 128 actuating cells. The upper The upper surface was carefully leveled by turning the supporting screws. A charge-coupled device surface was carefully leveled by turning the supporting screws. A charge-coupled device (CCD) (CCD) Camera (Manta G-031B, Allied Vision, Stadtroda, Germany) was placed above the conveyor Camera (Manta G-031B, Allied Vision, Stadtroda, Germany) was placed above the conveyor to to obtain the position of the object. Light sources were installed to improve the accuracy of the obtain the position of the object. Light sources were installed to improve the accuracy of the vision vision detection. Figure 11b shows the air supply circuit, which includes a pressurized air branch detection. Figure 11b shows the air supply circuit, which includes a pressurized air branch and a and a vacuum branch. The vacuum branch was created using a vacuum generator (vacuum ejector vacuum branch. The vacuum branch was created using a vacuum generator (vacuum ejector or or vacuum pump). Two buffer tanks were placed to stabilize the supplied positive pressure and the vacuum pump). Two buffer tanks were placed to stabilize the supplied positive pressure and the negative pressure, respectively. For 1D-position control, the inlet/outlet ports that share a column are negative pressure, respectively. For 1D-position control, the inlet/outlet ports that share a column interconnected and can be selected for the air circuit or the vacuum circuit using a 3/2 fast switching are interconnected and can be selected for the air circuit or the vacuum circuit using a 3/2 fast valve (MHA3-M1H-3/2G-3-K, Festo Co., Ltd., Esslingen, Germany); a total of 32 valves are in use. switching valve (MHA3-M1H-3/2G-3-K, Festo Co., Ltd., Esslingen, Germany); a total of 32 valves are Ports P, A, and B of the valve are connected with positive pressure and inlet/outlet ports of the air in use. Ports P, A, and B of the valve are connected with positive pressure and inlet/outlet ports of conveyor are connected with negative pressure. Two thermal-type flow sensors were used to indicate the air conveyor are connected with negative pressure. Two thermal-type flow sensors were used to the steady flow rate in the air circuit and vacuum circuit, respectively. A proportional directional indicate the steady flow rate in the air circuit and vacuum circuit, respectively. A proportional control valve (abbreviated as “control valve” in the following) was connected in the vacuum circuit to directional control valve (abbreviated as “control valve” in the following) was connected in the adjust the suction flow rate. During the experiments, the supply pressure was regulated to 500 kPa, vacuum circuit to adjust the suction flow rate. During the experiments, the supply pressure was and a choked flow rate of 100 L/min was produced using an orifice. In this case, the pressure in the regulated to 500 kPa, and a choked flow rate of 100 L/min was produced using an orifice. In this buffer tank was approximately 10 kPa. For the vacuum branch, the supply pressure was −20 kPa. case, the pressure in the buffer tank was approximately 10 kPa. For the vacuum branch, the supply A software package was developed on the computer using VC++ (Microsoft, Redmond, WA, USA) to pressure was −20 kPa. A software package was developed on the computer using VC++ (Microsoft, receive and process the images transmitted from the camera. Electrical control signals were sent by Redmond, WA, USA)to receive and process the images transmitted from the camera. Electrical computer via multichannel digital output boards with a 5 V/24 V amplifier circuit. control signals were sent by computer via multichannel digital output boards with a 5 V/24 V amplifier circuit.
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(a)
(b) Figure Photographofofthe the experimental experimental setup. AirAir supply circuit. Figure 11. 11. (a)(a) Photograph setup.(b)(b) supply circuit.
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5.2. Control Method 5.2. Method 5.2. Control Control In thisMethod work, the direction and the amplitude of the actuating force are separately controlled. this work, the the of and the actuating actuating force are separately separately controlled. TheIn actuating direction can beand selected by opening closing the appropriate valves. Figure 12 In this work, the direction direction and the amplitude amplitude of the force are controlled. The actuating direction can be selected by opening and closing the appropriate valves. Figure 12 shows shows three different smallby filled blackand circle represents that the port is selected for The actuating direction cases. can beThe selected opening closing the appropriate valves. Figure 12 three different cases. The small filled black circle represents that the port is selected for negative negative pressure while the empty circle for positive pressure. For cases 1 and 2, the arrow denotes shows three different cases. The small filled black circle represents that the port is selected for pressure while the empty circle for positive pressure. cases 1 and the arrow denotes the direction the direction of the generated force. Forfor case 3, allFor of the ports are2, supplied pressure negative pressure while the empty circle positive pressure. For cases 1 andwith 2, thepositive arrow denotes of the generated force. For case 3, all of the ports are supplied with positive pressure and therefore there anddirection therefore is no actuating generated. theare covered area, thepositive ports arepressure selected the ofthere the generated force. force For case 3, all of Within the ports supplied with is notherefore actuating force generated. Within the covered area, the ports are selected the control for the controlthere pressure switching thegenerated. fast switching valves. However, forfor the uncovered area, all and is no by actuating force Within the covered area, the ports are pressure selected by switching the fast switching valves. However, for the uncovered area, all of the ports are connected of the thecontrol ports are connected with positive pressure butvalves. no pressurized can be formed. for pressure by switching the fast switching However,air forfilm the uncovered area, The all with positive pressure but no pressurized air film can be formed. The aforementioned analysis on the aforementioned analysis on the viscous force implies that the amplitude of the actuating force can be of the ports are connected with positive pressure but no pressurized air film can be formed. The viscous force implies that the amplitude of the actuating force can be adjusted by varying the suction adjusted by varying the suction flow rate. To verify this, open loop control experiments were aforementioned analysis on the viscous force implies that the amplitude of the actuating force can be flow rate. by Toto verify this, open loop flow control were performed compare theThe movements performed compare movements of experiments theTo object with different flow rates. test were object adjusted varying thethe suction rate. verify this, open suction loop tocontrol experiments of the object with different suction flow rates. The test object is a circular plate (diameter: ϕ = 80, is a circular plate (diameter: φ = 80, weight: 16.9 g), which covers five columns of actuating cells. The performed to compare the movements of the object with different suction flow rates. The test object weight: 16.9 g), which covers five columns of actuating cells. The supply flow rate is set to 100 L/min, flow rate(diameter: is set to φ100 L/min, and theg),suction flow rate set to of 10,actuating 13, and cells. 16 L/min, issupply a circular plate = 80, weight: 16.9 which covers five is columns The and the flow suction flow rate is set 10, 13, and the 16 L/min, theversus measured respectively. Figure 13to shows the measured results in therate form of displacement time. supply rate is set 100toL/min, and suctionrespectively. flow isFigure set to13 10,shows 13, and 16 L/min, results in the form of13 displacement time. Evidently, object exhibits aand larger velocity as 4 Evidently, the object exhibits velocity as the suction flow rateofincreases, the velocity at respectively. Figure showsa larger the versus measured results in thethe form displacement versus time. the suction flow rate increases, and the velocity at 4 s is approximately 37.5 mm/s, 51.6 mm/s, s is approximately mm/s, 51.6 mm/s, and mm/s. As a result, we can accelerate, decelerate, Evidently, the object37.5 exhibits a larger velocity as80.1 the suction flow rate increases, and the velocity at 4 and 80.1 mm/s. As a result, we can accelerate, decelerate, and reverse the movement by adjusting the and reverse the movement by adjusting the actuating force and the direction. s is approximately 37.5 mm/s, 51.6 mm/s, and 80.1 mm/s. As a result, we can accelerate, decelerate, actuating force the direction. and reverse theand movement by adjusting the actuating force and the direction.
Case 1
Case 2
Case 3
Case 1 Figure 12. Three cases Case Case 3 for2the actuating direction. Figure 12. 12. Three Three cases cases for for the the actuating actuating direction. direction. Figure
180
Displacement (mm) Displacement (mm)
180 150
10 L/min L/min 1013L/min
150 120
L/min 1316L/min 16 L/min
120 90 90 60 60 30 30
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0.5 0.5
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1.5 1.5
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Time 2 (s)2.5
3 3
3.5 3.5
4 4
Time (s)
Figure Figure13. 13.Displacement Displacementversus versustime timeduring duringopen openloop loopcontrol controlexperiment. experiment.
Figure 13. Displacement versus time during open loop control experiment.
The u sent toto thethe control valve is an analog voltage thatthat ranges from 0 to05toV.5 Theactual actualcontrol controlsignal signal u sent control valve is an analog voltage ranges from The upper plot in Figure 15 shows the relations for F-u and Q -u . The suction flow rate, Q , changes 1 2 1 2 V. The in Figure shows relations foris F-u and Qvoltage 2-u1. The suction The upper actual plot control signal u15 sent to thethe control valve an 1analog that rangesflow fromrate, 0 toQ52, from 18 upper tofrom 0 L/min, and the viscous force approximately from 0.9 mN to 0.30.9 mN. We observe 18 toin 0Figure L/min, and the viscous force approximately mN torate, 0.3 mN. V.changes The plot 15 shows the relations forchanges F-u1 and Qchanges 2-u1. Thefrom suction flow Q2, that the viscous force cannot be adjusted to zero by only changing the suction flow rate while the We observe that the viscous force cannot be adjusted to zero by only changing the suction flow rate changes from 18 to 0 L/min, and the viscous force approximately changes from 0.9 mN to 0.3 mN. inlet flow rate is kept unchanged. This means that a continuous control signal can be sent when the while the inlet rate is kept This means thatby a continuous control signal can berate sent We observe thatflow the viscous forceunchanged. cannot be adjusted to zero only changing the suction flow whenthe theinlet object is far from the targetThis position, to be changed tosignal the discrete while flow rateaway is kept unchanged. meansbut thatit ahas continuous control can be mode sent when the object is far away from the target position, but it has to be changed to the discrete mode
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object is far away from the target position, but it has to be changed to the discrete mode when the when object is adequately to the desired position. authors’ previous [32–34] object the is adequately close to theclose desired position. The authors’The previous work [32–34]work implies that implies another method using the number of activecolumns actuating columns (e.g., an integer from to anotherthat method using the number of active actuating (e.g., an integer from 0 to +5) as0the +5) as the control also makes sense. shows examples of thesignal control (anfrom integer) control signal alsosignal makes sense. Figure 14 Figure shows 14 examples of the control (ansignal integer) +5 from to −5. Thefilled smallblack filledcircle blackrepresents circle represents a port connected to negative pressure the to −5.+5The small a port connected to negative pressure and theand empty empty circle represents a port connected to pressure. positive pressure. theforce actuating force as is circle represents a port connected to positive Naturally,Naturally, the actuating is enlarged enlarged as the number of activecolumns actuating columnsThe increases. The slow objectdown can slow down motion or reverse the number of active actuating increases. object can or reverse by motion bythe switching positive negative pressure for theports. appropriate ports. The switching positivethe pressure andpressure negativeand pressure for the appropriate The lower plot in lower in Figure 15 showsofthe of F-u2. The discrete-valued control is effective if Figureplot 15 shows the relation F-urelation output controloutput is effective if the sampling 2 . The discrete-valued the sampling period is sufficiently small. period is sufficiently small.
u2=+5
u2=+4
u2=0
u2=+1
u2=−2
u2=−3
u2=+2
u2=+3
u2=−1
u2=−4
u2=−5
Figure Figure 14. 14. Definition Definition of of the the control control signal signal for for method method 2. 2.
Two controlmethods methodsare areintroduced introduced above: selecting number of actuating columns by Two control above: (1)(1) selecting thethe number of actuating columns by fast fast switching valves (abbreviated as “method 2” in the following). In this method, both the switching valves (abbreviated as “method 2” in the following). In this method, both the actuating direction actuating direction amplitude ofbethe viscous only forcewith canthe befast controlled with(2)the fast and amplitude of theand viscous force can controlled switchingonly valves; adding switching valves; (2) to adding control valve to adjust the suction 1” flow ratefollowing). (abbreviated as an extra control valve adjust an theextra suction flow rate (abbreviated as “method in the In this “method in the following). In this servo to valve is the connected to the vacuum to method, a1” servo valve is connected to themethod, vacuumabranch adjust suction flow rate therebybranch changing adjust the suction rateforce thereby changing the amplitude the viscous force while the actuating the amplitude of theflow viscous while the actuating direction isof controlled using the fast switching valves. direction is is controlled using fast switching valves. Ancontrol example is raised here for1, au1more clear An example raised here for athe more clear explanation for the signals. For method = 1 means explanation the control 1, u1 =For 1 means ofthe 1 Vleftmost is sent that an analogfor voltage of 1 V signals. is sent toFor the method control valve. methodthat 2, u2an= analog 1 meansvoltage that only to the control For 2, actuating u2 = 1 means that(refer only to theFigure leftmost column of cellsvalve. is used as method the active column 14).column of cells is used as the active actuating column (refer to Figure 14).
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1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.40.4 0.20.2 0 0 0 0
1 1
22
33
44
55
1 1
22
33
44
55
1.21.2 1 1 0.80.8 0.60.6 0.40.4 0.20.2 0 00 0
Figure 15. Relationship between the viscous force and the control signal. Figure Figure 15. 15. Relationship Relationship between between the the viscous viscous force force and and the the control control signal. signal.
thus conduct experiments to compare the two control methods. A circular plate (diameter: WeWe thus conductexperiments experiments to compare the control two control methods. circular plate We thus conduct to compare the two methods. A circularAplate (diameter: φ = 80, weight: 10.4 g) is floated on the air conveyor, and a smooth wall is set to prevent it from (diameter: ϕ = 80, weight: 10.4 g) is the air conveyor, and a smooth set to prevent it φ = 80, weight: 10.4 g) is floated onfloated the aironconveyor, and a smooth wall is wall set tois prevent it from slipping away. The control signals are sent and the fluctuations of the floating object are recorded. from slipping The control signals are sent fluctuations floatingobject objectare arerecorded. recorded. slipping away.away. The control signals are sent andand thethe fluctuations of of thethe floating For method 2, the control signals (5, 4, and 3) are sent by turns and held for a while (5, 4, and 3 for For method method 2,2,the thecontrol controlsignals signals(5, (5,4,4,and and3)3) are sent turns and held a while (5,and 4, and For are sent byby turns and held forfor a while (5, 4, 3 for3 stages 1, 2, and 3, respectively), while for method 1, an analog voltage corresponding to the actuating for stages 2,3,and 3, respectively), while for method 1, anvoltage analogcorresponding voltage corresponding to the stages 1, 2, 1, and respectively), while for method 1, an analog to the actuating force, which are roughly the same as that of the method 2, are sent. Figure 16 shows the experimental actuating force, which are asmethod that of 2, theare method 2, are16 sent. Figure 16 shows the force, which are roughly theroughly same asthe thatsame of the sent. Figure shows the experimental results. When the control signal is switched, the flotation height for method 2 exhibits an experimental Whenover the control signal thethe flotation for method 2 exhibits results. Whenresults. the control signal switched, the flotation height for method exhibits exaggerative fluctuation 100 is μm, whichisisswitched, induced by suddenheight flow. But for 2method 1 it an is an exaggerative fluctuation over 100 µm, which is induced by the sudden flow. But for method it exaggerative fluctuation over 100 μm, which is induced by the sudden flow. But for method is only 20 μm. In the case that an object is being transported, the fast switching valves need 1toit1be is only 20 µm. In the case that an object is being transported, the fast switching valves need to be onlyfrequently 20 μm. In the caseinthat antoobject is being transported, the the fastmoving switching valves needcontact to be switched order vary the viscous force. Because object does not frequently switched in order to vary the viscous force. Because the moving object does not contact frequently switched in order to vary the viscous force. Because the moving object does not contact the device, it is very likely to slip way when subjected to large disturbances. From this perspective, the we device, it is isthat very likely1to toisslip slip way when whensuperior subjected to itlarge large disturbances. From this this perspective, the device, it very likely way subjected to disturbances. perspective, believe method comparatively and is employed in the From current work. we believe believe that that method method 11 is is comparatively comparatively superior superior and we and it it is is employed employed in in the the current current work. work.
300 300 250 250 200 200 150
Stage 1 Stage 2 Stage 3
Stage 1 Stage 2 Stage 3
150 100 100
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Control method 1 Control method 2 Control method 1
Control method 2
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6 Time (s)
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Time (s) by the two control methods. Figure 16. Fluctuations of the floating object
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The PID controller is used for 1D position control. The position of the object on the conveyor surface, which is required to settle on a reference value, is measured continuously by the camera. The error between the measured signal and the reference signal is used as feedback. The control structure is given in Equations (17) and (18): e(t) = yref − y u ( t ) = Kp e ( t ) + Ki T
Z t 0
e(τ )dτ +
(17) Kd . e(t) T
(18)
where e is the error between the reference position (yref ) and the measured position (y), Kp is the proportional gain, Ki is the integral gain, Kd is the derivative gain, and T is the sampling time. The image is processed at a rate of 50 frames per second so that the sampling time is 0.02 s. The coefficients Kp , Ki , and Kd are obtained by trial-and-error in order to achieve a good performance. The control signal u is calculated by the controller and its value is limited to a range of −5–5. The sign indicates the actuating direction, which is changed using the fast switching valves, and the amplitude related to the actuating force, are adjusted by the control valve. 5.3. Results and Discussion Experimental control has been made with two planar objects and the designed PID controller. The two objects have a diameter of 80 mm and a weight of 16.9 g and 10.4 g, designated as #1 and #2, respectively. During the experiments, the initial rest position of the object is set at 0 and the desired position is set as 100 mm. Results are shown in Figure 17 and the performances are summarized in Table 1. The rise time is almost the same for the two objects (3.7 s and 3.6 s). The overshoot for the heavy object exhibits a bigger value (13.3%) than that of the light object (7.3%). The static error is commonly over 0.3 mm due to the limited resolution of the used camera, and if an advanced camera is in use it can be improved. Simulated results are provided in comparison with the experimental results. In the simulation, dynamic characteristics of the valve are neglected because its response is much faster than that of the system. Furthermore, the relation of the floating height against the suction flow rate for the test object was experimentally measured and has been included. However, flow perturbation, which occurs at the opening and closing of the valves, has not been taken into account. This, to a certain extent, causes a difference between the simulations and the experimental results. Nevertheless, observation shows that the simulated curve is in accordance with the experimental data, and this verifies the effectiveness of the theoretical modeling and control method. The PID parameters slightly change with different objects because the controller is not adequately robust. Note that the use of steps as reference signals allows for the understanding of performances in the most unfavorable case. Taking a smooth reference signal would obtain a better result. It should be noted that there are some limitations for the size of the transported object. In theory, transport of large glass substrates with areas of approximately 2–3 m2 is feasible if the designed air conveyor is adequately large. However, the current air conveyor has an effective area of 228 × 110 mm2 (16 × 8 square pockets distributed in arrays), and therefore, for a circular plate, the maximum diameter should be less than 110 mm. Meanwhile, the minimum size for the plate should ensure the coverage of four complete pockets for stable movements. Therefore, the minimum diameter should be larger than 34 mm. In addition, the weight of the object produces a noticeable effect on the floatation height and thereby affects the actuating force. In this work, for a ϕ = 50 mm plate, transport is difficult to realize if the object’s weight is less than 5 g.
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Figure17. 17.Simulated Simulatedand andexperimental experimentalresults resultsfor forstep stepresponse. response. Figure Table 1. Step response performance of the PID controller. Table 1. Step response performance of the PID controller. Object Object MassMass (g) (g) amplitude (mm) StepStep amplitude (mm) Kp K p Ki K i Kd K d Rise time (s) Rise time (s) Overshoot Overshoot Static error (mm) Static error (mm)
#1 #1 10.4 10.4 100 100 0.08 0.08 0.005 0.005 1.5 1.5 3.7 3.7 7.3% 7.3% 0.45 0.45
#2 16.9 16.9 100 100 0.07 0.07 0.0050.005 1.2 1.2 3.6 3.6 13.3% 13.3% 0.35 0.35 #2
Figure results. The Thereference referencesignal signalis isa sine a sine signal with a period of s Figure18 18shows shows the the tracking tracking results. signal with a period of 20 20 s and amplitude of 55 mm. The results show that good tracking is realized but large deviations and amplitude of 55 mm. The results show that good tracking is realized but large deviations unexpectedly unexpectedlyappear. appear.This Thisisisbecause becausethe theobject objectisistransported transportedwithout withoutany anymechanical mechanicalcontact contactand and even tiny disturbance might exert influences on the tracking results. Theoretically, a tracking frequency even tiny disturbance might exert influences on the tracking results. Theoretically, a tracking offrequency 0.1 Hz is viable; however, it ishowever, difficult to experimentally actualize due to unavoidable of 0.1 Hz is viable; it is difficult to experimentally actualize due todisturbances. unavoidable These results areThese compared with those of a previous For the step response, overshoot disturbances. results are compared with work those [33,34]. of a previous work [33,34].the For the step isresponse, negligiblythe small in the previous work but considerably large in the current work. This is to overshoot is negligibly small in the previous work but considerably largedue in the differences in theThis experimental work, aapparatus. smooth wall edgea current work. is due to apparatus. differencesIninthe theprevious experimental In that the touches previousthe work, ofsmooth the object is set in order to make the object move along a straight line, and thus friction exists. wall that touches the edge of the object is set in order to make the object move along a 2 . However, in the The maximum was 5.2 mm/s andThe the maximum was5.2 1.6mm/s mm/sand straight line, velocity and thus friction exists. maximumacceleration velocity was the maximum current work, was the geometry the air conveyor and thework, controlthe method haveofbeen optimized and such acceleration 1.6 mm/s2of . However, in the current geometry the air conveyor and the acontrol block ismethod not required. Overshoot easily occurs in the absence of friction, but the maximum velocity have been optimized and such a block is not required. Overshoot easily occurs in the 2 . In addition, was increased to 17.2 but mm/s, the maximum acceleration to 5.4 mm/s absence of friction, the while maximum velocity was increasedincreased to 17.2 mm/s, while the maximum 2. In addition, the the relative error evaluated bymm/s the root-sum-square method was approximately11.5% the previous acceleration increased to 5.4 relative error evaluated by the for root-sum-square work and was 3.2%approximately11.5% for the current work. for From comparisons, method withFrom suction method thethe previous work we andconclude 3.2% forthat thethe current work. the flow rate as thewe control variable, rather thanwith the number of actuating columns, superior because comparisons, conclude that the method suction flow rate as the control is variable, rather than the number of actuating columns, is superior because it can reduce the disturbance induced by the
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it can reduce the disturbance induced by the opening and closing of the valves, and thus the object opening and closing of the results valves,are and thus the object movescan more smoothly. Better results are moves more smoothly. Better expected if disturbances be further reduced, and this will expected if disturbances can be further reduced, and this will be a part of future works. be a part of future works.
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Figure18. 18.Simulated Simulatedand andexperimental experimentalresults resultsfor forposition positiontracking. tracking. Figure
6.6.Conclusions Conclusions In a completely contactless air conveyor systemsystem is developed to transport and position Inthis thisstudy, study, a completely contactless air conveyor is developed to transport and planar objects. A simplified model derived from the film flow behavior is proposed to correlate the position planar objects. A simplified model derived from the film flow behavior is proposed to viscous force the suction flow the ratesuction and the flow gap thickness. Experimental setupsExperimental were established to correlate thewith viscous force with rate and the gap thickness. setups measure the film pressure distribution andpressure the viscous force, andand the basic characteristics werethe studied. were established to measure the film distribution the viscous force, and basic The film pressurewere is symmetrically in the direction distributed but nonsymmetrically distributed characteristics studied. Thedistributed film pressure is width symmetrically in the width direction in thenonsymmetrically length direction. distributed This meansinthat thedirection. viscous force airflow direction the but the only length This along meansthe that only the viscousinforce pockets needs consideration. the totalconsideration. viscous force is the composition an actuating along the airflow direction inMoreover, the pockets needs Moreover, the totalof viscous force is force generated inofthe areas andgenerated the side areas a drag force generated the and dama area. the composition anpocket actuating force in theand pocket areas and the side in areas drag The viscous force if theThe suction flow rate is enlarged the gap thickness is narrowed. force generated inincreases the dam area. viscous force increases if theor suction flow rate is enlarged or the Actually, the viscous force exhibits a more variation than aexpected as did the variation change ofthan the gap thickness is narrowed. Actually, thesignificant viscous force exhibits more significant suction flow which would influence the which floatingwould heightindirectly of the object and thus expected as rate, did the change ofindirectly the suction flow rate, influence thereinforce floating the effects. Comparison the experimental the simulated results indicates that theand model height of the object andofthus reinforce theresults effects.and Comparison of the experimental results the can accurately predict the viscous force, which is necessary for the motion simulation. A PID controller simulated results indicates that the model can accurately predict the viscous force, which is was appliedfor forthe 1D-position control andAposition tracking.was Theapplied direction the amplitude of the necessary motion simulation. PID controller forand 1D-position control and actuating force are separately controlled. control of method that varies theare suction flow rate rather position tracking. The direction and the The amplitude the actuating force separately controlled. than number of the actuating columns it can reduce disturbance to The the control method that varies the suctionwas flowused rate because rather than thegreatly number of thethe actuating columns the object. it can greatly reduce the disturbance to the floating object. wasfloating used because In comparison works by by the the research researchgroup groupofofTU TUDelft Delft[27–30] [27–30]and and In comparison with with the previous works R. R. Zeggarietetal.al.[17], [17],the thehighlights highlightsof of the the present present work work mainly mainly lie lie in Zeggari in the the aspects aspects of of control control method, method, improvements improvementstotomodeling, modeling,and andsome somemeasuring measuringmethods methodsasasfollows. follows. (1) The The actuating actuating direction thethe viscous force are are separately controlled, with (1) direction and andthe theamplitude amplitudeof of viscous force separately controlled, switching valves used for selecting the actuating direction and a servo valve for varying the with switching valves used for selecting the actuating direction and a servo valve for varying the suction flow rate. This control method can effectively reduce the flow perturbation which easily occurs at the opening and closing of the fast-switching valves. (2) An extension to the modeling is made using a fitting equation to approximate the effective flow rate through the gap for the case that the suction flow rate is changeable.
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suction flow rate. This control method can effectively reduce the flow perturbation which easily occurs at the opening and closing of the fast-switching valves. An extension to the modeling is made using a fitting equation to approximate the effective flow rate through the gap for the case that the suction flow rate is changeable. Apparatuses for measuring the film pressure distribution and conducting position control of planar objects were developed. The model-based calculated results agree with the experimental results indicating that the measuring method is feasible.
Author Contributions: Conceptualization, W.Z.; Methodology, X.C. and J.F.; Resources, C.L.; Writing—original draft, X.C. and W.Z.; Writing—review & editing, F.L. Funding: This study was supported by the National Natural Science Foundation of China (Grant No. 51675247), the Natural Science Foundation of Jiangsu Province (Grant No. BK20181467) and the Postgraduate Research&Practice Innovation Program of Jiangsu Province (Grant No. KYCX_2313). Conflicts of Interest: The authors declare no conflicts of interest.
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