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An optimization dust-removing electrode design method aiming at improving dust mitigation efficiency in lunar exploration
Journal Pre-proof An optimization dust-removing electrode design method aiming at improving dust mitigation efficiency in lunar exploration Jing Jiang, Yifan Lu, Xiaoteng Yan, Lei Wang PII:
S0094-5765(19)31310-4
DOI:
https://doi.org/10.1016/j.actaastro.2019.10.004
Reference:
AA 7689
To appear in:
Acta Astronautica
Received Date: 12 April 2019 Revised Date:
25 June 2019
Accepted Date: 6 October 2019
Please cite this article as: J. Jiang, Y. Lu, X. Yan, L. Wang, An optimization dust-removing electrode design method aiming at improving dust mitigation efficiency in lunar exploration, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.10.004. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
An optimization dust-removing electrode design method aiming at improving dust mitigation efficiency in lunar exploration Jing Jiang1,2, Yifan Lu1,2*, Xiaoteng Yan1, Lei Wang1 1
State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China
2
These authors contributed equally to this work.
Email address: [email protected]
Abstract The photovoltaic lunar dust removal technology has proved to own potential application for future space exploration. In this new technology, based on the high voltage characteristics of the photoelectric material lanthanum-modified lead zirconate titanate (PLZT), a dust-removing electrode is used to polarize and remove the lunar dust. The influence of the area and the shape of the dust-removing electrode on the dust removal performance is analyzed in this paper. An optimization of dust-removing electrode design method is proposed and comb-shaped electrodes are designed to improve the dust mitigation efficiency of the system. The configuration of the comb-shaped electrode is optimized by theoretical analysis. A series of experiments are performed to reveal the influence of different factors, such as electrode area, electrode shape, light intensity, copper foil thickness, insulation film and geometric parameters of electrode, etc. on the dust removal performance. Research results of this work can serve as guidelines for optimization electrode design to maximize the efficiency of this photovoltaic lunar dust removal system for future lunar exploration.
Keywords: Lunar exploration; dust-removing electrode; PLZT; dust mitigation.
1 Introduction Due to the influence of meteorites and micrometeorites impact, solar wind, high-energy cosmic rays, and the dramatic change in temperature between day and night, rocks on the surface of the moon are gradually pulverized and therefore form the lunar soil. Particles with a diameter of less than 1mm among lunar soil are called lunar dust. From 1969 to 1972, six Apollo programs were completed by the US. With the results and experience gained through the Apollo missions, NASA has pointed out that for the future exploration of the moon, the effect of lunar dust is an issued which must be addressed [1]. According to the standard sieve analysis on lunar soil samples returned from the Apollo 11 mission, scientists have found that the particle size of lunar soil ranges from 0.002mm to 1.2mm, and the average mean particle size is 0.072mm [2]. Since the moon dust is perennially bombarded by the solar wind plasma as well as the solar ultraviolet (UV) radiation, the surface of the particle is activated and exhibits strong adhesive characteristics. The dust is therefore apt to stubbornly adhere to the surface of space instrumentation such as optical systems, solar panels and thermal radiators, and then degrade their working performance. Thus, to develop a reliable dust mitigation technique for protecting a specific instrument surface from the threat of dust adhesion is of great significance in future lunar exploration. The properties of lunar dust have been investigated using varies methods in the past few decades. The charging properties of lunar dust grains charged by photoelectric emission induced by the solar UV radiation were explored and the first laboratory measurements of the photoelectric efficiencies were presented by Abbas et al. [3]. Physicochemical properties of fine lunar dust of respirable-size were tested and the size distribution and shape, chemistry, iron content and magnetic resonance of various size fractions were investigated by McKay et al. [4]. Numerical modeling as well as experimental study on charging and transport of lunar dust simulants under the UV radiation in vacuum environment were carried out by Champlain et al. [5]. The physical/dynamic properties and investigation techniques of lunar dust were reviewed [6] and charging mechanism and dynamics of lunar dust grains on the moon surface were analyzed theoretically [7,8]. A lunar dust simulant named CLDS-i was developed by the Institute of Geochemistry Chinese Academy Sciences which has similar properties with real lunar dust and can therefore be applied to many fields such as the scientific researches, the treatment technology and toxicological study of lunar dust [9]. A comprehensive review on dust transport mechanism and mitigation technologies including fluidal, mechanical, electrical and passive self-cleaning methods for lunar and Martian missions was presented by Afshar-Mohajer et al. [10]. Advantages and disadvantages of different approaches were discussed and suggestions were given for choosing the most suitable dust removal technology in different situations. An electrodynamic dust shield (EDS) was designed by Calle et al. based on the electric curtain concept which could prevent the accumulation of dust on surfaces and remove the dust adhering to those surfaces by using electrostatic and dielectrophoretic forces [11]. However, there is still some limitations of this technique. It has proved that when an amount of dust greater than 300g/m2 accumulated on the protected surface, the performance of this cleaning system declines dramatically [12]. Since 2010, a series of systematic studies on lunar dust removal/mitigation methods were carried out by Kawamoto et al. Electrostatic and magnetic cleaning system/device for removing lunar dust
adhering to space suits were proposed and the dust removal rate could reach a value of 82% [13-15]. A dust cleaning system utilizing the electrostatic traveling wave with small energy consumption was developed and improved to achieve the mitigation of lunar dust on solar panels and other optical elements with a dust removal rate of more than 90% [16-19]. In 2011, an Electrostatic Lunar Dust Collector (ELDC) was proposed by Afshar-Mohajer et al. to collect the charged lunar dust particles on the protected surface and a mathematical model and discrete element method were used respectively to determine the dust collection efficiency in vacuum condition [20,21]. In 2012, Afshar-Mohajer et al. developed another Electrostatic Lunar Dust Repeller (ELDR) which consists of a series of needle-shaped electrodes in front of the protected surface to repel the charged lunar dust. Finite element analysis showed that a complete removal of 20µm sized particles from a 30cm×30cm surface could be achieved with 2.2kV applied to the 5cm length electrode [22]. However, the installation of both ELDC and ELDR are quite complicated. Furthermore, the ELDC/ELDR would inevitably shield the solar panel from sunlight which will reduce the working performance of the solar panel. Dust mitigation for solar panels with electric curtains were also explored by Marshall et al. and the dynamics of dust particles under the effect of traveling waves were analyzed by Zhang et al. using an electrostatic discrete-element method (EDEM) [23-25]. Recently, a novel Spacesuit Integrated Carbon nanotube Dust Ejection/Removal system was developed aiming at protecting spacesuits from lunar dust [26]. Upon carbon nanotube technology, a scaled knee joint prototype of the spacesuit with self-cleaning property was fabricated and the experimental results showed a promising application of this technique in future planetary exploration missions [27]. A new photovoltaic lunar dust removal technique based on the photoelectric characteristics of PLZT was proposed by Jiang et al. [28,29]. A Lunar Dust Collector (LDC) which consists of an array of dust-removing electrodes is used in this technique to polarize and remove the dust deposited on the protected surface. This technique could overcome the obstacles of the previous dust mitigation methods reported in the literature. It can not only work well when the protected surface is covered by a mass of dust, but also has almost no influence on the working performance of the solar cell/panel. The dust removal system could be small in size and light in weight, which is very promising for lunar exploration. However, from previous research we found that to achieve dust removal performance for large areas, multiple PLZTs are required to drive the dust-removing electrode when the area of the electrode is relatively large, which will complicate the entire dust removal device [28]. Therefore, how to maximize the driving capability of a single-chip PLZT to achieve a maximum dust removal area is an issue worthy of study. In this paper, a physical model of the lunar dust particle subjected to electric field force is established. The influence of the surface area of the dust-removing electrode on the dust removal effect was analyzed. It was verified by experiments that under the driving of a single-chip PLZT, when the surface area of the dust-removing electrode is larger than a certain value, the dust cannot be removed reliably. Then the comb-shaped dust-removing electrode is designed to maximize the driving capability of a single-chip PLZT. The effect of the electrode geometric parameters on the dust removal efficiency was investigated experimentally. Research results disclose that dust removal effect is relatively good when the tooth width and the tooth gap are both 1mm. In this manner, the dust removal efficiency can be improved by nearly 100% within the scope of the processing technique.
2 The influence of electrode area on the dust removal efficiency 2.1 Photovoltaic lunar dust removal system based on PLZT The schematic diagram of the photovoltaic lunar dust removal system is shown in Figure 1. A dust-removing electrode is used to remove the dust on the protected surface, which could be solar panels, reflectors and thermal radiators, etc. The dust-removing electrode is a laminae of an insulation layer, a copper foil, and an insulating substrate. The structural composition of the electrode is shown in the partial enlarged drawing. The dust-removing electrode is connected to the positive pole of the PLZT and the protected surface is connected to the negative pole of the PLZT. When the PLZT is irradiated by ultraviolet light (365nm) with an intensity of about 5KW/m2, it will generate several thousand volts in the polarized direction. If the dust-removing electrode is placed close enough to the protected surface (≤5mm), a strong electrostatic field (approximately 500V/mm) could be built up between the electrode and the protected surface. The dust on the protected surface will be charged by the strong electrostatic field and then absorbed by the electrode. In this method, the protected surface need to be electrically conductive. For the non-conductive surface, this could be achieved by laminating a transparent indium tin oxid (ITO) film on it. The forces acting on a specific dust particle is also presented in Figure 1 and this will be discussed in the next section. In practical application, the dust-removing electrode should be fixed on a travel mechanism which can move around the protected surface and thereby achieve the dust cleaning task of the whole surface. For future lunar exploration, the UV light can be obtained from the solar radiation by a fresnel lens concentrator, a secondary concentrator and a UV filter. When the sun light passes through the fresnel lens concentrator, the secondary concentrator and the UV filter, a strong enough UV light with a wavelength of 365nm will be generated. By adjusting the concentrator radius, the intensity of the UV light can be above 5KW/m2, which is enough to polarize the PLZT. Dust-removing electrode Insulation layer Copper foil UV light
−
Insulating substrate
+
Lunar dust
PLZT
Protected surface
FE G FVan
Figure 1. Dust removal principle schematic diagram
2.2 Force analysis on lunar dust particle 2.2.1 Photovoltage output of PLZT PLZT will produce photoelectric effect under UV light irradiation. Since the temperature of PLZT will inevitably increase due to illumination, PLZT will also exhibit pyroelectric effect and positive piezoelectric effect. The voltage generated by the positive piezoelectric effect is opposite to the polarity of the other two voltages. Considering the environment, wire connection and other factors, there will be
a certain voltage loss in the polarization direction, and the total voltage can be described as
U p (t ) = Uθ (t ) + U v (t ) − U e (t ) − U l (t ) = U vs (1 − e
−
t
τv
) + (Uθs − U es )(1 − e
−
t
τθ
) − U ls (1 − e
−
(1)
t
τl
)
where Uv(t) is the voltage generated by the photovoltaic effect; Uθ(t) is the voltage generated by the pyroelectric effect; Ue(t) is the voltage generated by the positive piezoelectric effect; Ul(t) is the loss voltage; the superscript ‘s’ denotes the saturation voltage based on these three effects; and τ is a time constant based on these three effects. The electrical model of PLZT can be equivalent to a parallel connection of a current source Ip, a resistor Rp and a capacitor Cp. When the UV light intensity is constant, the photocurrent output by PLZT is approximately constant. At this time we have U p = I p R p [1 − exp( −
t t )] = U ps [1 − exp( − )] RpC p τp
(2)
where τp = RpCp is a time constant; U ps is the saturation voltage.
2.2.2 Mathematical model of dust removal electric field force When PLZT is connected to a dust-removing electrode, it can be regarded as the PLZT being connected to a capacitor C1 and a resistor R1 in parallel. Thus, the dust removal voltage can be written as U = Ip
R1 R p R1 + R p
(1 − e
−
t ( C1 + C p ) R1 R p ( R1 + R p )
) = I p R (1 − e
−
t RC
−
t
) = U s (1 − e τ )
(3)
where the load capacitance C1 can be obtained by
C1 =
εS
(4)
d
where S is the area of the dust-removing electrode, ε is the relative dielectric constant and d is the distance between the dust-removing electrode and the protected surface. Therefore, the intensity of the dust removal electric field can be given by t
E=
− U I p R1 R p (ε s / d + C p ) R1 R p / ( R1 + R p ) = (1 − e ) d d R1 + R p
(5)
Assume that the total amount of charge carried by the dust is q, then the electric field force acting on the dust is
FE = Eq
(6)
2.2.3 Effective dust removal conditions The lunar dust on the protected surface is mainly affected by electric field force, lunar gravity and Van der Waals force. Since the gravity on the moon is roughly 1/6 of the gravity on the earth, if the density of the lunar dust is assumed to be ρ, then the gravity of the lunar dust is
2 1 G = π ( d p )3 ρ g 9 2
(7)
The Van der Waals force acting on a spherical particle with an infinite plane can be approximately calculated by [30]
FVan =
1 Ad p 12 z02
(8)
where A is the Hamaker constant of lunar dust; dp is particle diameter; z0 is the minimum distance between two contacted particles. If the electric field force received by the lunar dust is greater than the combination of the gravity and Van der Waals force, as shown in Eq. (9), the dust could be removed by the electrode.
FE ≥ G + FVan
(9)
Combine Eqs. (5-9) one can get the following equation qI p R1 R p d R1 + R p
(1 − e
−
t (ε s / d + C p ) R1 R p / ( R1 + R p )
)≥
2 1 1 Ad p π ( d p )3 ρ g + 9 2 12 z02
(10)
which gives the effective dust removal condition. From Eq. (10) one can find that there are many factors which influence the dust removal effect. Since the size of the dust-removing electrode affects the equivalent capacitance and equivalent resistance in the dust-removing electrical model, it therefore influences the magnitude of the dust-removing electric field force. It is noteworthy that the force analysis in this section is only used for qualitatively analyzing the effective dust removal condition of the dust particles. The specific calculations of forces acting on the particles are not performed. Therefore, the shape of the lunar dust particle is simplified to spherical. The effects of the dust removing electrode area on the dust removal efficiency will be experimentally investigated next.
2.3 Dust removal efficiency tests on different electrodes area Theoretically, when the area of the dust-removing electrode becomes larger, the equivalent capacitance will become larger which means that the equivalent resistance and the saturation voltage of the dust-removing voltage will become smaller, and the response speed will become slower as well. This indicates that when the area of the dust-removing electrode is large to a certain extent, the lunar dust will not be adsorbed by the electrode or can only be partially adsorbed. An experimental platform was built up to verify the above conclusion as shown in Figure 2. In order to investigate the influence of dust-removing electrode area on the dust removal effect, two kinds of simulated lunar dust were used in this experiment. The sizes of the simulated lunar dust are 0.05-0.075mm and 0.075-0.1mm, respectively. The area of the copper foil of the dust-removing electrode is divided into three groups, which are 80×70mm2, 80×100mm2 and 80×130mm2, respectively. The distance between the protected surface and the dust-removing electrode is 4mm. The lunar dust simulant used in the experiment is CLDS-i which is developed by the Institute of Geochemistry Chinese Academy Sciences [9].
Figure 2. Experimental setup for dust removal efficiency tests In order to better explain the dust removal effect of the dust removal experiment, the concept of dust removal efficiency is proposed and defined as:
η0 =
m1 m2
(11)
where η0 is the dust removal efficiency, m1 is the mass of the lunar dust removed by the electrode, and m2 is the mass of the lunar dust on the protected surface before dust removal. The values of m1 and m2 are measured by a high precision electronic balance with an accuracy of 0.01g. Each experiment is repeated for three times and the average dust removal efficiency is reported in this paper. As shown in Figure 3 and Figure 4, when the light intensity and the distance between the protected surface and the dust-removing electrode are constant, as the surface area of the dust-removing electrode increases, the dust removal efficiency is decreasing. Therefore, in the latter part of this paper, we will focus on how to increase the effective area of a dust-collecting electrode driven by a single piece of PLZT, and thereby improve the dust removal efficiency.
(a) S = 80×70mm2, η0=85% (b) S = 80×100mm2, η0=79% (c) S = 80×130mm2, η0=70% 2 Figure 3. Dust removal test Ⅰ, light intensity 350mW/cm , particle size range 0.05-0.075mm
(a) S = 80×70mm2, η0=95%
(b) S = 80×100mm2, η0=84%
(c) S = 80×130mm2, η0=78%
Figure 4. Dust removal test Ⅰ, light intensity 350mW/cm2, particle size range 0.075-0.1mm
3 Design of comb-shaped dust-removing electrodes When PLZT is connected to a common type of dust-removing electrode, the charge density at the edge of the electrode is much larger than the center area of the electrode due to the edge effect, so the dust removal ability of different regions of the same dust-removing electrode is different. This phenomenon makes it impossible to maximize the area of a common type of dust-removing electrode that can be driven by a single piece of PLZT. Therefore, the dust-removing electrode is formed into a comb shape, so that the charge distribution in each region is more uniform, so as to fully exert the driving ability of a single piece of PLZT.
3.1 Comparison of dust removal effect between different electrodes When PLZT is connected to the dust-removing electrode for dust removal, it is equivalent to connecting a capacitor and a resistor to the PLZT in parallel. So even if the material of the dust-removing electrode and the area of the copper foil are the same, the dust removal voltage may also vary depending on the shape of the electrode. Theoretically, changing the shape of the dust-removing electrode to comb-shaped has little effect on the capacitance of the dust-removing electrode, but the influence of this change on the resistance is difficult to verify. For these reasons, the same copper foil area with different shapes of the dust-removing electrode are selected and the influence of the shape on the dust removing voltage is explored by experiments. The total surface area of the copper foil is 80×100mm2, and the distance between the dust-removing electrode and the protected surface is 4mm. Three types of electrodes were selected: a common electrode, a comb-shaped electrode with tooth width of 10mm and gap width of 3mm, and a comb-shaped electrode with a tooth width of 5mm and gap width of 2mm. Two different light intensities, i.e., 270mW/cm2 and 530mW/cm2 were used in the experiment. The selected dust-removing electrodes are shown in Figure 5. The dust removal voltage of the electrode of different shapes measured by this experiment is shown in Figure 6.
(a) Common type (b) 10mm type (c) 5mm type Figure 5. Three types of dust-removing electrode with the same copper foil area
Common type 10mm type 5mm type
Voltage (V)
1000 800 600 400 200 0 0
5
10 15 20 25 30 35 40
Voltage (V)
1400 1200
1600 1400 1200 1000 800 600 400 200 0
Common type 10mm type 5mm type
0
5
10 15 20 25 30 35 40
Time (s) Time (s) (a) Light intensity 270mW/cm2 (b) Light intensity 530mW/cm2 Figure 6. Dust removal voltages of different type electrodes The experimental results show that when the copper foil area of the dust-removing electrode is the same, the dust removing voltages of the three kinds of electrode are almost the same which means that the influence of the electrode shape change on the dust removal voltage can be neglected. Previous experiments have shown that the larger the area of the copper foil is, the worse the dust removal ability becomes [28]. For the dust-removing electrode with the same electrode area, the area of the copper foil of the comb-shaped electrode is smaller than that of the common electrode, so the dust removal effect of the comb-shaped electrode should be better than that of the common electrode. Therefore, the common electrode and comb-shaped electrode with the same electrode area are used to compare the dust removal effect under the light intensities of 334mW/cm2. The electrode area is 80×127mm2, the distance between the dust-removing electrode and the protected surface is 4 mm, and the tooth width of the comb-shaped electrode is 10mm and the gap width is 3mm. The dust removal experiment results are shown in Figure 7.
(a) 10mm type electrode, η0=94% (b) Common type electrode, η0=32% Figure 7. Comparison of dust removal effect of different electrode The experimental results show that when the light intensity is 334mW/cm2, the dust removal efficiency of common electrode and comb-shaped electrode are 32% and 94%, respectively. Therefore, when the comb-shaped electrode is used, the area of the dust-removing electrode that can be driven by a single-chip PLZT can be greatly improved under the same dust-removing condition, and the dust-removing effect is more reliable. When a comb-shaped electrode is used, the increase in efficiency is defined as
η=
S1 − S2 ×100% S2
(12)
where η is the increased efficiency, S1, S2 are the area of the comb-shaped dust-removing electrode and
the common dust-removing electrode that can be driven by a single piece of PLZT, and their conductor areas remain the same. Since S1 is related to the geometric parameters of the comb-shaped electrode, the increase in efficiency is related to the number of teeth, the tooth width and the tooth gap of the comb-shaped electrode. In order to optimize the geometric parameters of the comb-shaped electrode, the electric field distribution of the comb-shaped electrode is analyzed in the next part.
3.2 Analysis on electric field distribution of dust-removing electrodes Whether the dust-removing electrode adsorbs the lunar dust depends on the intensity of the electric field generated by the electrode on the protected surface. The charge distribution on a single-piece of dust-removing electrode is obtained by the moment method, and the electric field intensity distribution of the dust-removing electrode acting on the protected surface is obtained according to the charge distribution. The electrode and the protected surface can be modelled as a parallel plate capacitor, with a distance d, and side lengths of a and b respectively, as shown in Figure 8.
Figure 8. A parallel plate capacitor model Assume that the electric potential at infinity is zero and the potential of the upper electrode of the capacitor is ϕ. The electrode plate is evenly divided into N tiny rectangular regions. If the value of N is large enough, it can be assumed that electric charge density σ in each tiny rectangular region ∆s is a constant; and each tiny region can be considered equivalent to a point charge with a charge quantity of q=σ∆s. Considering the m-th region ∆sm among the N tiny rectangular regions, the electric potential of
∆sm caused by the charges on the upper and lower electrodes can be obtained by
φm =
1 4πε 0
b 2 b − 2
a 2 a − 2
∫ ∫
σ ( x, y )
1
( x − x ) 2 + ( y − y )2 m m
−
dxdy ( x − xm )2 + ( y − ym ) 2 + d 2 1
(13)
where σ(x,y) denotes the electric charge density at an arbitrary point on the electrode, and at the same spatial coordinates, the charge densities of the upper and lower electrodes are equal but opposite in sign. Since the electrode plate is an equipotential body, for an arbitrary m, the equation ϕm=ϕ is satisfied. The above integral equation can be solved by moment method. The electric charge density can be expressed as N
σ ( x, y ) = ∑ σ n ∏ n ( x, y ) n =1
where σn is the charge density of the n-th region ∆sn, and
(14)
) ( ∏ ( x, y ) = 0, ( x, y ) ∈ ∆s
1, x, y ∈ ∆sn
n
(15)
n
Thus, Eq. (13) can be rewritten as
φm =
1 1 − ∆sn 2 2 2 ( x − xm ) + ( y − ym )2 + d 2 ( x − xm ) + ( y − ym )
N
1 4πε 0
∑ σ ∫∫ n
n =1
dxdy
(16)
One can find from above equations that the contribution of charges in ∆sn to the electric potential of
∆sm can be described by Zmn as follows
Z mn =
1 4πε 0
1 1 − ∆sn 2 2 2 ( xn − xm ) + ( yn − ym ) 2 + d 2 ( xn − xm ) + ( yn − ym )
∫∫
dxdy
(17)
When m≠n, assume that all the charges concentrate at the center of the rectangle, which gives
Z mn =
1 1 ∆sn − 2 ( x − x )2 + ( y − y ) 2 4πε 0 ( xn − xm ) + ( yn − ym ) 2 + d 2 n m n m 1
(18)
When m=n, to avoid the situation where the denominator becomes zero, assume that the charges are uniformly distributed in an circular area ∆sn, which leads to Z nn =
1 4πε 0
∫
R
0
1 1 − 2 r + d2 r
2π 1 rdr ∫0 dθ = 2ε 0
∆ sn ∆ sn − + d2 + d π π
(19)
Rewritten the integral equation in the following matrix form
[ Z ]N × N [σ ]N ×1 = [φ ]N ×1
(20)
where
Z11 L Z = M O Z N 1 L
σ1 1 Z1N σ 1 ,σ = 2 ,φ =φ M M M Z NN N × N 1 N ×1 σ N N ×1
(21)
Upon Eq. (20), the charge density matrix [σ] can be solved and the electric field intensity at any position between the two electrodes can be obtained by using the formula of electric field intensity caused by a point charge. r N r 1 σ n ∆S n rn E ( x, y, z ) = ∑ ⋅ r r 2 rn rn n =1 4πε 0
(22)
r rn = ( x − x n , y − y n , z − z n )
(23)
where
The distribution of electric field intensity on the protected surface generated by a common type electrode and different comb-shaped electrodes are solved by MATLAB based on Eq. (22) and are presented in Figure 9. The distance between the electrode and the protected surface is 4mm. The total copper foil area of each electrode is 100×80mm2. For the comb-shaped electrodes, the tooth length is 80mm, the tooth width is 5mm/10mm, the gap width is 2mm/3mm/4mm. Figure 9(a, b) present the electric field generated by the common type electrode from front view and top view. We can find that the edge effect of the common type electrode is quite obvious. Although the electric field intensity near the boundary of the electrode is strong (about 6.73×105V/m), it drops significantly at the inner part of the electrode to a minimum of 4.79×105V/m, which is reduced by approximately 30%. Since the dust
removal performance strongly depends on the uniformity of the electric field, one can imagine that the dust removal efficiency of the common type electrode will decrease dramatically when the size of the electrode is relatively large. The previous experiments have also proved that for a 80×127mm2 common type electrode, the dust removal efficiency is only 32%, while the efficiency of the comb shaped electrode is 94% (see Figure 7).
(a) Common type electrode (front view)
(b) Common type electrode (top view)
(c) Tooth width 10mm, gap width 4mm
(d) Tooth width 5mm, gap width 4mm
(e) Tooth width 10mm, gap width 3mm
(f) Tooth width 5mm, gap width 3mm
(g) Tooth width 10mm, gap width 2mm (h) Tooth width 5mm, gap width 2mm Figure 9. Field strength distribution of common type and comb-shaped dust-removing electrodes
Figure 9(c-h) indicates that the comb-shaped dust-removing electrodes can provide better electric field distributions compared with the common type electrode and thus lead to a more effective dust removal performance. Furthermore, it can be concluded from Figure 9 that when the tooth width is 10 mm or 5mm, the gap width is between 2mm to 4mm, the electric field is relatively uniform. Additionally, when the tooth width is 10mm, the increased efficiency is between 18% and 36%, and when the tooth width is 5mm, the increased efficiency is between 38% and 57% which means that within a certain range, reducing the tooth width may contribute to a greater improvement in dust removal efficiency. It is noteworthy that although Eq. (12) indicates that when the tooth width is a constant, the larger the tooth gap is, the higher the dust removal efficiency is, however, when the gap width is too large, the electric field strength at the gap is insufficient, and thereby it is difficult to remove the lunar dust reliably, which occurs as shown in Figure 10 below.
Figure 10. Dust removal effect of an electrode with 20mm tooth width and 10mm gap width Based on the theoretical analysis presented above, a series of experiments will be carried out in the next section to optimize the geometric parameters of the comb-shaped electrodes.
4 Experiments on parameter optimization of comb-shaped electrodes Theoretical analysis indicates that within a certain range, reducing the tooth width can lead to a greater improvement in dust removal efficiency. However, since the manufacturing process limits the tooth width of the electrode being infinitely reduced, the optimum tooth width and tooth gap of the comb-shaped dust-removing electrode will be explored by an experimental method in this work.
4.1 Fabrication of comb-shaped electrodes The comb-shaped electrode is made by a chemical etching method. The specific steps are as follows and the manufacturing process is shown in Figure 11.
1) Apply the photosensitive ink (TOYO INK, FD-O-NEW-blue-M-G3) evenly on the copper-plated polyimide film and then blow dry it with a blower; 2) Print a comb-shaped electrode pattern on the transparent film, wherein the transparent portion will be retained. Then place the film on the polyimide film in step 1 and irradiate it with ultraviolet light for four minutes; 3) Clean the film in step 2 with the developer (KONICA MINOLTA, C220). Since the ink irradiated by the ultraviolet light cannot be washed away, it will overlay on the film; 4) Put the film into the etchant (DAIKIN, PFC-14(CF4)) and shake it for ten minutes to remove the copper that is not blocked by the ink (the temperature of the etchant is required to be greater than 60Ⅰ ); 5) Place the film treated in step 4 in the release agent, and the ink on the film which is irradiated with ultraviolet light can be washed away.
(a) Ink coated film Light
(b) Blow dry with a blower
(c) Irradiated with ultraviolet
(e) Film treated by etchant (f) Comb-shaped electrode and release agent attached to an epoxy board Figure 11. Process for making comb-shaped dust-removing electrode by chemical etching method (d) Clean with the developer
4.2 Influence of insulation film type and copper foil thickness The dust-removing electrode is composed of an insulating film and a copper foil electrode, so the dust removal effect may be affected by the material of the insulating film, the thickness of the copper foil and the shape of the electrode. Hence, the effects of these factors on the dust removal effect should be investigated respectively. In this section, the influence of insulation film type and copper foil thickness were explored first by experiments. A polyimide film and a vinyl film were selected as the insulating film, respectively. The area of the copper foil was 160×50mm2 and the thickness was 0.01mm, 0.05mm, and 0.1mm, respectively. Two kinds of light intensity was used: 590mW/cm2 and 350mW/cm2. Other dust removal conditions were consistent. The dust removal effects of different kinds of electrodes are shown in
Figure 12 and the dust removal efficiencies are collected in Table 1. In each subfigure, from the left side to the right side, the thickness of the copper foil increases.
(a) Polyimide insulating film, 590mW/cm2
(b) Vinyl insulating film, 590mW/cm2
(c) Polyimide insulating film, 350mW/cm2 (d) Vinyl insulating film, 350mW/cm2 Figure 12. Dust removal effect of electrodes with different film type and different copper foil thickness
Table 1. Dust removal efficiency corresponding to different insulating film materials and different copper foil thicknesses Film
Copper foil
Dust removal
intensity (mW/cm )
material
thickness (mm)
efficiency η0
590
Polyimide
0.01
97%
590
Polyimide
0.05
98%
590
Polyimide
0.1
96%
590
vinyl
0.01
96%
590
vinyl
0.05
97%
590
vinyl
0.1
97%
350
Polyimide
0.01
35%
350
Polyimide
0.05
31%
350
Polyimide
0.1
40%
350
vinyl
0.01
37%
350
vinyl
0.05
41%
350
vinyl
0.1
40%
Ultraviolet light 2
The experimental results show that all these dust-removing electrodes can clean the dust satisfactorily when the light intensity is 590mW/cm2, and the dust removal effect is not ideal when the light intensity drops to 350mW/cm2. Therefore, it should be considered that the dust removal effect does not change significantly when the type of the insulating film or the thickness of the copper foil electrode varies, and the influence of these factors on the dust removing effect will not be considered in the following experiment.
4.3 Influence of geometric parameters of comb-shaped electrodes
Theoretical analysis has shown that, within a certain range, reducing the tooth width of the comb-shaped electrode can improve the dust removal efficiency. Since the electrode is difficult to be manufactured if the tooth width is less than 1mm, the influence of the tooth width on the dust removal efficiency is explained by the tooth width of 10mm, 5mm, and 1mm in this study. According to the theoretical calculation, the gap width is selected to be 3mm, 2mm and 1mm, respectively. First, an electrode with a tooth width of 10mm, a gap width of 3mm (15 teeth) and an electrode with a tooth width of 5mm, a gap width of 2mm (28 teeth) were compared. The length of the former electrode is 192mm, the latter 194mm, and the widths of both are 80mm. The experimental results are shown in Figure 13(a). Then, an electrode with a tooth width of 5mm, a gap width of 2mm (31 teeth) and an electrode with a tooth width of 1mm, a gap width of 1mm (108 teeth) were compared. Both electrodes are 215mm in length and 80mm in width. The experimental results are presented in Figure
13(b). Finally, an electrode with a tooth width of 1mm, a gap width of 1mm (108 teeth) and an electrode with a tooth width of 1mm, a gap width of 1.5mm (87 teeth) were compared. The widths of the electrodes are also 80mm and the lengths of the two electrodes are 215mm and 216mm, respectively. The experimental results are displayed in Figure 13(c). Dust removal efficiency η0 and the increased efficiency η of each experimental group are shown in Table 2.
(a) (b) (c) Figure 13. Electrode configuration optimization experiments
Table 2. Dust removal efficiency and increased efficiency of different electrode configurations Experimental group a b c
Tooth(mm)
Gap(mm)
Dust removal efficiency η0
Increased efficiency η
10
3
51%
28%
5
2
85%
38.6%
5
2
63%
38.6%
1
1
87%
99.1%
1
1
95%
99.1%
1
1.5
32%
148.2%
From the experimental results one can find that when the tooth width is narrowed, not only the dust removal efficiency is improved, but also the dust removal performance becomes better. Therefore, the most suitable dust-removing electrode is considered to have a tooth width of 1mm. However, if the gap width of the comb-shaped electrode increases from 1mm to 1.5mm (the accuracy is difficult to ensure when the gap width is reduced to 1mm or less), although the theoretical dust removal efficiency is improved, the actual dust removal effect is greatly weakened. In summary, the optimum geometric
parameters of the comb-shaped electrode in the range allowed by the processing conditions are the tooth width and the gap width being both 1mm. In this situation, the dust removal efficiency can be increased by nearly 100%.
5 Conclusions In this study, to increase the driving capability of a single piece of PLZT, the configuration of the comb-shaped dust-removing electrode was proposed and the geometric parameters were optimized. The equivalent electrical model of PLZT was established to analyze the effect of the copper foil area of the dust-removing electrode on the dust removal effect and the experimental verification was carried out. The electric field model of the dust-removing electrode is established by the method of moments, and the electric field distribution of the comb-shaped electrode is obtained. The model is used to guide the experiment to obtain the optimal comb-shaped dust-removing electrode configuration. By theoretical analysis and experimental validation, this study leads to the following conclusions: (1) When the other conditions are constant, the larger the copper foil area of the dust-removing electrode is, the worse the dust removing ability of the dust-removing electrode becomes. (2) When the copper foil area of the dust-removing electrode is constant, the influence of the shape of the dust-removing electrode on dust removal voltage of PLZT can be neglected. (3) When the area of the dust-removing electrode is constant, the comb-shaped electrode can distribute charge more evenly and has a stronger dust removing ability than the common electrode. (4) The material parameters of the dust-removing electrode, such as the type of insulating film and the thickness of the copper foil, do not have much influence on the dust removing effect. (5) When the tooth width of the electrode is narrowed, the dust removal performance will be bettered and the dust removal efficiency will be improved. In the range allowed by the processing conditions, analysis suggests the optimal electrode geometric parameters: 1mm tooth width and 1mm gap width, which contribute to an approximate 100% dust removal efficiency improvement.
Acknowledgements This research is supported, in part, by grant from the National Natural Science Foundation of China (No. 51575125, 51175123) and the China Postdoctoral Science Foundation (2014M561358).
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Research Highlights
1.
A new photoelectric lunar dust removal technique is proposed.
2.
An optimization dust-removing electrode design method is presented.
3.
Electric field intensity distribution of the dust-removing electrode is obtained.
4.
Dust removal efficiency is improved by approximately 100% with this method.
S0094-5765(19)31310-4
DOI:
https://doi.org/10.1016/j.actaastro.2019.10.004
Reference:
AA 7689
To appear in:
Acta Astronautica
Received Date: 12 April 2019 Revised Date:
25 June 2019
Accepted Date: 6 October 2019
Please cite this article as: J. Jiang, Y. Lu, X. Yan, L. Wang, An optimization dust-removing electrode design method aiming at improving dust mitigation efficiency in lunar exploration, Acta Astronautica, https://doi.org/10.1016/j.actaastro.2019.10.004. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
An optimization dust-removing electrode design method aiming at improving dust mitigation efficiency in lunar exploration Jing Jiang1,2, Yifan Lu1,2*, Xiaoteng Yan1, Lei Wang1 1
State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China
2
These authors contributed equally to this work.
Email address: [email protected]
Abstract The photovoltaic lunar dust removal technology has proved to own potential application for future space exploration. In this new technology, based on the high voltage characteristics of the photoelectric material lanthanum-modified lead zirconate titanate (PLZT), a dust-removing electrode is used to polarize and remove the lunar dust. The influence of the area and the shape of the dust-removing electrode on the dust removal performance is analyzed in this paper. An optimization of dust-removing electrode design method is proposed and comb-shaped electrodes are designed to improve the dust mitigation efficiency of the system. The configuration of the comb-shaped electrode is optimized by theoretical analysis. A series of experiments are performed to reveal the influence of different factors, such as electrode area, electrode shape, light intensity, copper foil thickness, insulation film and geometric parameters of electrode, etc. on the dust removal performance. Research results of this work can serve as guidelines for optimization electrode design to maximize the efficiency of this photovoltaic lunar dust removal system for future lunar exploration.
Keywords: Lunar exploration; dust-removing electrode; PLZT; dust mitigation.
1 Introduction Due to the influence of meteorites and micrometeorites impact, solar wind, high-energy cosmic rays, and the dramatic change in temperature between day and night, rocks on the surface of the moon are gradually pulverized and therefore form the lunar soil. Particles with a diameter of less than 1mm among lunar soil are called lunar dust. From 1969 to 1972, six Apollo programs were completed by the US. With the results and experience gained through the Apollo missions, NASA has pointed out that for the future exploration of the moon, the effect of lunar dust is an issued which must be addressed [1]. According to the standard sieve analysis on lunar soil samples returned from the Apollo 11 mission, scientists have found that the particle size of lunar soil ranges from 0.002mm to 1.2mm, and the average mean particle size is 0.072mm [2]. Since the moon dust is perennially bombarded by the solar wind plasma as well as the solar ultraviolet (UV) radiation, the surface of the particle is activated and exhibits strong adhesive characteristics. The dust is therefore apt to stubbornly adhere to the surface of space instrumentation such as optical systems, solar panels and thermal radiators, and then degrade their working performance. Thus, to develop a reliable dust mitigation technique for protecting a specific instrument surface from the threat of dust adhesion is of great significance in future lunar exploration. The properties of lunar dust have been investigated using varies methods in the past few decades. The charging properties of lunar dust grains charged by photoelectric emission induced by the solar UV radiation were explored and the first laboratory measurements of the photoelectric efficiencies were presented by Abbas et al. [3]. Physicochemical properties of fine lunar dust of respirable-size were tested and the size distribution and shape, chemistry, iron content and magnetic resonance of various size fractions were investigated by McKay et al. [4]. Numerical modeling as well as experimental study on charging and transport of lunar dust simulants under the UV radiation in vacuum environment were carried out by Champlain et al. [5]. The physical/dynamic properties and investigation techniques of lunar dust were reviewed [6] and charging mechanism and dynamics of lunar dust grains on the moon surface were analyzed theoretically [7,8]. A lunar dust simulant named CLDS-i was developed by the Institute of Geochemistry Chinese Academy Sciences which has similar properties with real lunar dust and can therefore be applied to many fields such as the scientific researches, the treatment technology and toxicological study of lunar dust [9]. A comprehensive review on dust transport mechanism and mitigation technologies including fluidal, mechanical, electrical and passive self-cleaning methods for lunar and Martian missions was presented by Afshar-Mohajer et al. [10]. Advantages and disadvantages of different approaches were discussed and suggestions were given for choosing the most suitable dust removal technology in different situations. An electrodynamic dust shield (EDS) was designed by Calle et al. based on the electric curtain concept which could prevent the accumulation of dust on surfaces and remove the dust adhering to those surfaces by using electrostatic and dielectrophoretic forces [11]. However, there is still some limitations of this technique. It has proved that when an amount of dust greater than 300g/m2 accumulated on the protected surface, the performance of this cleaning system declines dramatically [12]. Since 2010, a series of systematic studies on lunar dust removal/mitigation methods were carried out by Kawamoto et al. Electrostatic and magnetic cleaning system/device for removing lunar dust
adhering to space suits were proposed and the dust removal rate could reach a value of 82% [13-15]. A dust cleaning system utilizing the electrostatic traveling wave with small energy consumption was developed and improved to achieve the mitigation of lunar dust on solar panels and other optical elements with a dust removal rate of more than 90% [16-19]. In 2011, an Electrostatic Lunar Dust Collector (ELDC) was proposed by Afshar-Mohajer et al. to collect the charged lunar dust particles on the protected surface and a mathematical model and discrete element method were used respectively to determine the dust collection efficiency in vacuum condition [20,21]. In 2012, Afshar-Mohajer et al. developed another Electrostatic Lunar Dust Repeller (ELDR) which consists of a series of needle-shaped electrodes in front of the protected surface to repel the charged lunar dust. Finite element analysis showed that a complete removal of 20µm sized particles from a 30cm×30cm surface could be achieved with 2.2kV applied to the 5cm length electrode [22]. However, the installation of both ELDC and ELDR are quite complicated. Furthermore, the ELDC/ELDR would inevitably shield the solar panel from sunlight which will reduce the working performance of the solar panel. Dust mitigation for solar panels with electric curtains were also explored by Marshall et al. and the dynamics of dust particles under the effect of traveling waves were analyzed by Zhang et al. using an electrostatic discrete-element method (EDEM) [23-25]. Recently, a novel Spacesuit Integrated Carbon nanotube Dust Ejection/Removal system was developed aiming at protecting spacesuits from lunar dust [26]. Upon carbon nanotube technology, a scaled knee joint prototype of the spacesuit with self-cleaning property was fabricated and the experimental results showed a promising application of this technique in future planetary exploration missions [27]. A new photovoltaic lunar dust removal technique based on the photoelectric characteristics of PLZT was proposed by Jiang et al. [28,29]. A Lunar Dust Collector (LDC) which consists of an array of dust-removing electrodes is used in this technique to polarize and remove the dust deposited on the protected surface. This technique could overcome the obstacles of the previous dust mitigation methods reported in the literature. It can not only work well when the protected surface is covered by a mass of dust, but also has almost no influence on the working performance of the solar cell/panel. The dust removal system could be small in size and light in weight, which is very promising for lunar exploration. However, from previous research we found that to achieve dust removal performance for large areas, multiple PLZTs are required to drive the dust-removing electrode when the area of the electrode is relatively large, which will complicate the entire dust removal device [28]. Therefore, how to maximize the driving capability of a single-chip PLZT to achieve a maximum dust removal area is an issue worthy of study. In this paper, a physical model of the lunar dust particle subjected to electric field force is established. The influence of the surface area of the dust-removing electrode on the dust removal effect was analyzed. It was verified by experiments that under the driving of a single-chip PLZT, when the surface area of the dust-removing electrode is larger than a certain value, the dust cannot be removed reliably. Then the comb-shaped dust-removing electrode is designed to maximize the driving capability of a single-chip PLZT. The effect of the electrode geometric parameters on the dust removal efficiency was investigated experimentally. Research results disclose that dust removal effect is relatively good when the tooth width and the tooth gap are both 1mm. In this manner, the dust removal efficiency can be improved by nearly 100% within the scope of the processing technique.
2 The influence of electrode area on the dust removal efficiency 2.1 Photovoltaic lunar dust removal system based on PLZT The schematic diagram of the photovoltaic lunar dust removal system is shown in Figure 1. A dust-removing electrode is used to remove the dust on the protected surface, which could be solar panels, reflectors and thermal radiators, etc. The dust-removing electrode is a laminae of an insulation layer, a copper foil, and an insulating substrate. The structural composition of the electrode is shown in the partial enlarged drawing. The dust-removing electrode is connected to the positive pole of the PLZT and the protected surface is connected to the negative pole of the PLZT. When the PLZT is irradiated by ultraviolet light (365nm) with an intensity of about 5KW/m2, it will generate several thousand volts in the polarized direction. If the dust-removing electrode is placed close enough to the protected surface (≤5mm), a strong electrostatic field (approximately 500V/mm) could be built up between the electrode and the protected surface. The dust on the protected surface will be charged by the strong electrostatic field and then absorbed by the electrode. In this method, the protected surface need to be electrically conductive. For the non-conductive surface, this could be achieved by laminating a transparent indium tin oxid (ITO) film on it. The forces acting on a specific dust particle is also presented in Figure 1 and this will be discussed in the next section. In practical application, the dust-removing electrode should be fixed on a travel mechanism which can move around the protected surface and thereby achieve the dust cleaning task of the whole surface. For future lunar exploration, the UV light can be obtained from the solar radiation by a fresnel lens concentrator, a secondary concentrator and a UV filter. When the sun light passes through the fresnel lens concentrator, the secondary concentrator and the UV filter, a strong enough UV light with a wavelength of 365nm will be generated. By adjusting the concentrator radius, the intensity of the UV light can be above 5KW/m2, which is enough to polarize the PLZT. Dust-removing electrode Insulation layer Copper foil UV light
−
Insulating substrate
+
Lunar dust
PLZT
Protected surface
FE G FVan
Figure 1. Dust removal principle schematic diagram
2.2 Force analysis on lunar dust particle 2.2.1 Photovoltage output of PLZT PLZT will produce photoelectric effect under UV light irradiation. Since the temperature of PLZT will inevitably increase due to illumination, PLZT will also exhibit pyroelectric effect and positive piezoelectric effect. The voltage generated by the positive piezoelectric effect is opposite to the polarity of the other two voltages. Considering the environment, wire connection and other factors, there will be
a certain voltage loss in the polarization direction, and the total voltage can be described as
U p (t ) = Uθ (t ) + U v (t ) − U e (t ) − U l (t ) = U vs (1 − e
−
t
τv
) + (Uθs − U es )(1 − e
−
t
τθ
) − U ls (1 − e
−
(1)
t
τl
)
where Uv(t) is the voltage generated by the photovoltaic effect; Uθ(t) is the voltage generated by the pyroelectric effect; Ue(t) is the voltage generated by the positive piezoelectric effect; Ul(t) is the loss voltage; the superscript ‘s’ denotes the saturation voltage based on these three effects; and τ is a time constant based on these three effects. The electrical model of PLZT can be equivalent to a parallel connection of a current source Ip, a resistor Rp and a capacitor Cp. When the UV light intensity is constant, the photocurrent output by PLZT is approximately constant. At this time we have U p = I p R p [1 − exp( −
t t )] = U ps [1 − exp( − )] RpC p τp
(2)
where τp = RpCp is a time constant; U ps is the saturation voltage.
2.2.2 Mathematical model of dust removal electric field force When PLZT is connected to a dust-removing electrode, it can be regarded as the PLZT being connected to a capacitor C1 and a resistor R1 in parallel. Thus, the dust removal voltage can be written as U = Ip
R1 R p R1 + R p
(1 − e
−
t ( C1 + C p ) R1 R p ( R1 + R p )
) = I p R (1 − e
−
t RC
−
t
) = U s (1 − e τ )
(3)
where the load capacitance C1 can be obtained by
C1 =
εS
(4)
d
where S is the area of the dust-removing electrode, ε is the relative dielectric constant and d is the distance between the dust-removing electrode and the protected surface. Therefore, the intensity of the dust removal electric field can be given by t
E=
− U I p R1 R p (ε s / d + C p ) R1 R p / ( R1 + R p ) = (1 − e ) d d R1 + R p
(5)
Assume that the total amount of charge carried by the dust is q, then the electric field force acting on the dust is
FE = Eq
(6)
2.2.3 Effective dust removal conditions The lunar dust on the protected surface is mainly affected by electric field force, lunar gravity and Van der Waals force. Since the gravity on the moon is roughly 1/6 of the gravity on the earth, if the density of the lunar dust is assumed to be ρ, then the gravity of the lunar dust is
2 1 G = π ( d p )3 ρ g 9 2
(7)
The Van der Waals force acting on a spherical particle with an infinite plane can be approximately calculated by [30]
FVan =
1 Ad p 12 z02
(8)
where A is the Hamaker constant of lunar dust; dp is particle diameter; z0 is the minimum distance between two contacted particles. If the electric field force received by the lunar dust is greater than the combination of the gravity and Van der Waals force, as shown in Eq. (9), the dust could be removed by the electrode.
FE ≥ G + FVan
(9)
Combine Eqs. (5-9) one can get the following equation qI p R1 R p d R1 + R p
(1 − e
−
t (ε s / d + C p ) R1 R p / ( R1 + R p )
)≥
2 1 1 Ad p π ( d p )3 ρ g + 9 2 12 z02
(10)
which gives the effective dust removal condition. From Eq. (10) one can find that there are many factors which influence the dust removal effect. Since the size of the dust-removing electrode affects the equivalent capacitance and equivalent resistance in the dust-removing electrical model, it therefore influences the magnitude of the dust-removing electric field force. It is noteworthy that the force analysis in this section is only used for qualitatively analyzing the effective dust removal condition of the dust particles. The specific calculations of forces acting on the particles are not performed. Therefore, the shape of the lunar dust particle is simplified to spherical. The effects of the dust removing electrode area on the dust removal efficiency will be experimentally investigated next.
2.3 Dust removal efficiency tests on different electrodes area Theoretically, when the area of the dust-removing electrode becomes larger, the equivalent capacitance will become larger which means that the equivalent resistance and the saturation voltage of the dust-removing voltage will become smaller, and the response speed will become slower as well. This indicates that when the area of the dust-removing electrode is large to a certain extent, the lunar dust will not be adsorbed by the electrode or can only be partially adsorbed. An experimental platform was built up to verify the above conclusion as shown in Figure 2. In order to investigate the influence of dust-removing electrode area on the dust removal effect, two kinds of simulated lunar dust were used in this experiment. The sizes of the simulated lunar dust are 0.05-0.075mm and 0.075-0.1mm, respectively. The area of the copper foil of the dust-removing electrode is divided into three groups, which are 80×70mm2, 80×100mm2 and 80×130mm2, respectively. The distance between the protected surface and the dust-removing electrode is 4mm. The lunar dust simulant used in the experiment is CLDS-i which is developed by the Institute of Geochemistry Chinese Academy Sciences [9].
Figure 2. Experimental setup for dust removal efficiency tests In order to better explain the dust removal effect of the dust removal experiment, the concept of dust removal efficiency is proposed and defined as:
η0 =
m1 m2
(11)
where η0 is the dust removal efficiency, m1 is the mass of the lunar dust removed by the electrode, and m2 is the mass of the lunar dust on the protected surface before dust removal. The values of m1 and m2 are measured by a high precision electronic balance with an accuracy of 0.01g. Each experiment is repeated for three times and the average dust removal efficiency is reported in this paper. As shown in Figure 3 and Figure 4, when the light intensity and the distance between the protected surface and the dust-removing electrode are constant, as the surface area of the dust-removing electrode increases, the dust removal efficiency is decreasing. Therefore, in the latter part of this paper, we will focus on how to increase the effective area of a dust-collecting electrode driven by a single piece of PLZT, and thereby improve the dust removal efficiency.
(a) S = 80×70mm2, η0=85% (b) S = 80×100mm2, η0=79% (c) S = 80×130mm2, η0=70% 2 Figure 3. Dust removal test Ⅰ, light intensity 350mW/cm , particle size range 0.05-0.075mm
(a) S = 80×70mm2, η0=95%
(b) S = 80×100mm2, η0=84%
(c) S = 80×130mm2, η0=78%
Figure 4. Dust removal test Ⅰ, light intensity 350mW/cm2, particle size range 0.075-0.1mm
3 Design of comb-shaped dust-removing electrodes When PLZT is connected to a common type of dust-removing electrode, the charge density at the edge of the electrode is much larger than the center area of the electrode due to the edge effect, so the dust removal ability of different regions of the same dust-removing electrode is different. This phenomenon makes it impossible to maximize the area of a common type of dust-removing electrode that can be driven by a single piece of PLZT. Therefore, the dust-removing electrode is formed into a comb shape, so that the charge distribution in each region is more uniform, so as to fully exert the driving ability of a single piece of PLZT.
3.1 Comparison of dust removal effect between different electrodes When PLZT is connected to the dust-removing electrode for dust removal, it is equivalent to connecting a capacitor and a resistor to the PLZT in parallel. So even if the material of the dust-removing electrode and the area of the copper foil are the same, the dust removal voltage may also vary depending on the shape of the electrode. Theoretically, changing the shape of the dust-removing electrode to comb-shaped has little effect on the capacitance of the dust-removing electrode, but the influence of this change on the resistance is difficult to verify. For these reasons, the same copper foil area with different shapes of the dust-removing electrode are selected and the influence of the shape on the dust removing voltage is explored by experiments. The total surface area of the copper foil is 80×100mm2, and the distance between the dust-removing electrode and the protected surface is 4mm. Three types of electrodes were selected: a common electrode, a comb-shaped electrode with tooth width of 10mm and gap width of 3mm, and a comb-shaped electrode with a tooth width of 5mm and gap width of 2mm. Two different light intensities, i.e., 270mW/cm2 and 530mW/cm2 were used in the experiment. The selected dust-removing electrodes are shown in Figure 5. The dust removal voltage of the electrode of different shapes measured by this experiment is shown in Figure 6.
(a) Common type (b) 10mm type (c) 5mm type Figure 5. Three types of dust-removing electrode with the same copper foil area
Common type 10mm type 5mm type
Voltage (V)
1000 800 600 400 200 0 0
5
10 15 20 25 30 35 40
Voltage (V)
1400 1200
1600 1400 1200 1000 800 600 400 200 0
Common type 10mm type 5mm type
0
5
10 15 20 25 30 35 40
Time (s) Time (s) (a) Light intensity 270mW/cm2 (b) Light intensity 530mW/cm2 Figure 6. Dust removal voltages of different type electrodes The experimental results show that when the copper foil area of the dust-removing electrode is the same, the dust removing voltages of the three kinds of electrode are almost the same which means that the influence of the electrode shape change on the dust removal voltage can be neglected. Previous experiments have shown that the larger the area of the copper foil is, the worse the dust removal ability becomes [28]. For the dust-removing electrode with the same electrode area, the area of the copper foil of the comb-shaped electrode is smaller than that of the common electrode, so the dust removal effect of the comb-shaped electrode should be better than that of the common electrode. Therefore, the common electrode and comb-shaped electrode with the same electrode area are used to compare the dust removal effect under the light intensities of 334mW/cm2. The electrode area is 80×127mm2, the distance between the dust-removing electrode and the protected surface is 4 mm, and the tooth width of the comb-shaped electrode is 10mm and the gap width is 3mm. The dust removal experiment results are shown in Figure 7.
(a) 10mm type electrode, η0=94% (b) Common type electrode, η0=32% Figure 7. Comparison of dust removal effect of different electrode The experimental results show that when the light intensity is 334mW/cm2, the dust removal efficiency of common electrode and comb-shaped electrode are 32% and 94%, respectively. Therefore, when the comb-shaped electrode is used, the area of the dust-removing electrode that can be driven by a single-chip PLZT can be greatly improved under the same dust-removing condition, and the dust-removing effect is more reliable. When a comb-shaped electrode is used, the increase in efficiency is defined as
η=
S1 − S2 ×100% S2
(12)
where η is the increased efficiency, S1, S2 are the area of the comb-shaped dust-removing electrode and
the common dust-removing electrode that can be driven by a single piece of PLZT, and their conductor areas remain the same. Since S1 is related to the geometric parameters of the comb-shaped electrode, the increase in efficiency is related to the number of teeth, the tooth width and the tooth gap of the comb-shaped electrode. In order to optimize the geometric parameters of the comb-shaped electrode, the electric field distribution of the comb-shaped electrode is analyzed in the next part.
3.2 Analysis on electric field distribution of dust-removing electrodes Whether the dust-removing electrode adsorbs the lunar dust depends on the intensity of the electric field generated by the electrode on the protected surface. The charge distribution on a single-piece of dust-removing electrode is obtained by the moment method, and the electric field intensity distribution of the dust-removing electrode acting on the protected surface is obtained according to the charge distribution. The electrode and the protected surface can be modelled as a parallel plate capacitor, with a distance d, and side lengths of a and b respectively, as shown in Figure 8.
Figure 8. A parallel plate capacitor model Assume that the electric potential at infinity is zero and the potential of the upper electrode of the capacitor is ϕ. The electrode plate is evenly divided into N tiny rectangular regions. If the value of N is large enough, it can be assumed that electric charge density σ in each tiny rectangular region ∆s is a constant; and each tiny region can be considered equivalent to a point charge with a charge quantity of q=σ∆s. Considering the m-th region ∆sm among the N tiny rectangular regions, the electric potential of
∆sm caused by the charges on the upper and lower electrodes can be obtained by
φm =
1 4πε 0
b 2 b − 2
a 2 a − 2
∫ ∫
σ ( x, y )
1
( x − x ) 2 + ( y − y )2 m m
−
dxdy ( x − xm )2 + ( y − ym ) 2 + d 2 1
(13)
where σ(x,y) denotes the electric charge density at an arbitrary point on the electrode, and at the same spatial coordinates, the charge densities of the upper and lower electrodes are equal but opposite in sign. Since the electrode plate is an equipotential body, for an arbitrary m, the equation ϕm=ϕ is satisfied. The above integral equation can be solved by moment method. The electric charge density can be expressed as N
σ ( x, y ) = ∑ σ n ∏ n ( x, y ) n =1
where σn is the charge density of the n-th region ∆sn, and
(14)
) ( ∏ ( x, y ) = 0, ( x, y ) ∈ ∆s
1, x, y ∈ ∆sn
n
(15)
n
Thus, Eq. (13) can be rewritten as
φm =
1 1 − ∆sn 2 2 2 ( x − xm ) + ( y − ym )2 + d 2 ( x − xm ) + ( y − ym )
N
1 4πε 0
∑ σ ∫∫ n
n =1
dxdy
(16)
One can find from above equations that the contribution of charges in ∆sn to the electric potential of
∆sm can be described by Zmn as follows
Z mn =
1 4πε 0
1 1 − ∆sn 2 2 2 ( xn − xm ) + ( yn − ym ) 2 + d 2 ( xn − xm ) + ( yn − ym )
∫∫
dxdy
(17)
When m≠n, assume that all the charges concentrate at the center of the rectangle, which gives
Z mn =
1 1 ∆sn − 2 ( x − x )2 + ( y − y ) 2 4πε 0 ( xn − xm ) + ( yn − ym ) 2 + d 2 n m n m 1
(18)
When m=n, to avoid the situation where the denominator becomes zero, assume that the charges are uniformly distributed in an circular area ∆sn, which leads to Z nn =
1 4πε 0
∫
R
0
1 1 − 2 r + d2 r
2π 1 rdr ∫0 dθ = 2ε 0
∆ sn ∆ sn − + d2 + d π π
(19)
Rewritten the integral equation in the following matrix form
[ Z ]N × N [σ ]N ×1 = [φ ]N ×1
(20)
where
Z11 L Z = M O Z N 1 L
σ1 1 Z1N σ 1 ,σ = 2 ,φ =φ M M M Z NN N × N 1 N ×1 σ N N ×1
(21)
Upon Eq. (20), the charge density matrix [σ] can be solved and the electric field intensity at any position between the two electrodes can be obtained by using the formula of electric field intensity caused by a point charge. r N r 1 σ n ∆S n rn E ( x, y, z ) = ∑ ⋅ r r 2 rn rn n =1 4πε 0
(22)
r rn = ( x − x n , y − y n , z − z n )
(23)
where
The distribution of electric field intensity on the protected surface generated by a common type electrode and different comb-shaped electrodes are solved by MATLAB based on Eq. (22) and are presented in Figure 9. The distance between the electrode and the protected surface is 4mm. The total copper foil area of each electrode is 100×80mm2. For the comb-shaped electrodes, the tooth length is 80mm, the tooth width is 5mm/10mm, the gap width is 2mm/3mm/4mm. Figure 9(a, b) present the electric field generated by the common type electrode from front view and top view. We can find that the edge effect of the common type electrode is quite obvious. Although the electric field intensity near the boundary of the electrode is strong (about 6.73×105V/m), it drops significantly at the inner part of the electrode to a minimum of 4.79×105V/m, which is reduced by approximately 30%. Since the dust
removal performance strongly depends on the uniformity of the electric field, one can imagine that the dust removal efficiency of the common type electrode will decrease dramatically when the size of the electrode is relatively large. The previous experiments have also proved that for a 80×127mm2 common type electrode, the dust removal efficiency is only 32%, while the efficiency of the comb shaped electrode is 94% (see Figure 7).
(a) Common type electrode (front view)
(b) Common type electrode (top view)
(c) Tooth width 10mm, gap width 4mm
(d) Tooth width 5mm, gap width 4mm
(e) Tooth width 10mm, gap width 3mm
(f) Tooth width 5mm, gap width 3mm
(g) Tooth width 10mm, gap width 2mm (h) Tooth width 5mm, gap width 2mm Figure 9. Field strength distribution of common type and comb-shaped dust-removing electrodes
Figure 9(c-h) indicates that the comb-shaped dust-removing electrodes can provide better electric field distributions compared with the common type electrode and thus lead to a more effective dust removal performance. Furthermore, it can be concluded from Figure 9 that when the tooth width is 10 mm or 5mm, the gap width is between 2mm to 4mm, the electric field is relatively uniform. Additionally, when the tooth width is 10mm, the increased efficiency is between 18% and 36%, and when the tooth width is 5mm, the increased efficiency is between 38% and 57% which means that within a certain range, reducing the tooth width may contribute to a greater improvement in dust removal efficiency. It is noteworthy that although Eq. (12) indicates that when the tooth width is a constant, the larger the tooth gap is, the higher the dust removal efficiency is, however, when the gap width is too large, the electric field strength at the gap is insufficient, and thereby it is difficult to remove the lunar dust reliably, which occurs as shown in Figure 10 below.
Figure 10. Dust removal effect of an electrode with 20mm tooth width and 10mm gap width Based on the theoretical analysis presented above, a series of experiments will be carried out in the next section to optimize the geometric parameters of the comb-shaped electrodes.
4 Experiments on parameter optimization of comb-shaped electrodes Theoretical analysis indicates that within a certain range, reducing the tooth width can lead to a greater improvement in dust removal efficiency. However, since the manufacturing process limits the tooth width of the electrode being infinitely reduced, the optimum tooth width and tooth gap of the comb-shaped dust-removing electrode will be explored by an experimental method in this work.
4.1 Fabrication of comb-shaped electrodes The comb-shaped electrode is made by a chemical etching method. The specific steps are as follows and the manufacturing process is shown in Figure 11.
1) Apply the photosensitive ink (TOYO INK, FD-O-NEW-blue-M-G3) evenly on the copper-plated polyimide film and then blow dry it with a blower; 2) Print a comb-shaped electrode pattern on the transparent film, wherein the transparent portion will be retained. Then place the film on the polyimide film in step 1 and irradiate it with ultraviolet light for four minutes; 3) Clean the film in step 2 with the developer (KONICA MINOLTA, C220). Since the ink irradiated by the ultraviolet light cannot be washed away, it will overlay on the film; 4) Put the film into the etchant (DAIKIN, PFC-14(CF4)) and shake it for ten minutes to remove the copper that is not blocked by the ink (the temperature of the etchant is required to be greater than 60Ⅰ ); 5) Place the film treated in step 4 in the release agent, and the ink on the film which is irradiated with ultraviolet light can be washed away.
(a) Ink coated film Light
(b) Blow dry with a blower
(c) Irradiated with ultraviolet
(e) Film treated by etchant (f) Comb-shaped electrode and release agent attached to an epoxy board Figure 11. Process for making comb-shaped dust-removing electrode by chemical etching method (d) Clean with the developer
4.2 Influence of insulation film type and copper foil thickness The dust-removing electrode is composed of an insulating film and a copper foil electrode, so the dust removal effect may be affected by the material of the insulating film, the thickness of the copper foil and the shape of the electrode. Hence, the effects of these factors on the dust removal effect should be investigated respectively. In this section, the influence of insulation film type and copper foil thickness were explored first by experiments. A polyimide film and a vinyl film were selected as the insulating film, respectively. The area of the copper foil was 160×50mm2 and the thickness was 0.01mm, 0.05mm, and 0.1mm, respectively. Two kinds of light intensity was used: 590mW/cm2 and 350mW/cm2. Other dust removal conditions were consistent. The dust removal effects of different kinds of electrodes are shown in
Figure 12 and the dust removal efficiencies are collected in Table 1. In each subfigure, from the left side to the right side, the thickness of the copper foil increases.
(a) Polyimide insulating film, 590mW/cm2
(b) Vinyl insulating film, 590mW/cm2
(c) Polyimide insulating film, 350mW/cm2 (d) Vinyl insulating film, 350mW/cm2 Figure 12. Dust removal effect of electrodes with different film type and different copper foil thickness
Table 1. Dust removal efficiency corresponding to different insulating film materials and different copper foil thicknesses Film
Copper foil
Dust removal
intensity (mW/cm )
material
thickness (mm)
efficiency η0
590
Polyimide
0.01
97%
590
Polyimide
0.05
98%
590
Polyimide
0.1
96%
590
vinyl
0.01
96%
590
vinyl
0.05
97%
590
vinyl
0.1
97%
350
Polyimide
0.01
35%
350
Polyimide
0.05
31%
350
Polyimide
0.1
40%
350
vinyl
0.01
37%
350
vinyl
0.05
41%
350
vinyl
0.1
40%
Ultraviolet light 2
The experimental results show that all these dust-removing electrodes can clean the dust satisfactorily when the light intensity is 590mW/cm2, and the dust removal effect is not ideal when the light intensity drops to 350mW/cm2. Therefore, it should be considered that the dust removal effect does not change significantly when the type of the insulating film or the thickness of the copper foil electrode varies, and the influence of these factors on the dust removing effect will not be considered in the following experiment.
4.3 Influence of geometric parameters of comb-shaped electrodes
Theoretical analysis has shown that, within a certain range, reducing the tooth width of the comb-shaped electrode can improve the dust removal efficiency. Since the electrode is difficult to be manufactured if the tooth width is less than 1mm, the influence of the tooth width on the dust removal efficiency is explained by the tooth width of 10mm, 5mm, and 1mm in this study. According to the theoretical calculation, the gap width is selected to be 3mm, 2mm and 1mm, respectively. First, an electrode with a tooth width of 10mm, a gap width of 3mm (15 teeth) and an electrode with a tooth width of 5mm, a gap width of 2mm (28 teeth) were compared. The length of the former electrode is 192mm, the latter 194mm, and the widths of both are 80mm. The experimental results are shown in Figure 13(a). Then, an electrode with a tooth width of 5mm, a gap width of 2mm (31 teeth) and an electrode with a tooth width of 1mm, a gap width of 1mm (108 teeth) were compared. Both electrodes are 215mm in length and 80mm in width. The experimental results are presented in Figure
13(b). Finally, an electrode with a tooth width of 1mm, a gap width of 1mm (108 teeth) and an electrode with a tooth width of 1mm, a gap width of 1.5mm (87 teeth) were compared. The widths of the electrodes are also 80mm and the lengths of the two electrodes are 215mm and 216mm, respectively. The experimental results are displayed in Figure 13(c). Dust removal efficiency η0 and the increased efficiency η of each experimental group are shown in Table 2.
(a) (b) (c) Figure 13. Electrode configuration optimization experiments
Table 2. Dust removal efficiency and increased efficiency of different electrode configurations Experimental group a b c
Tooth(mm)
Gap(mm)
Dust removal efficiency η0
Increased efficiency η
10
3
51%
28%
5
2
85%
38.6%
5
2
63%
38.6%
1
1
87%
99.1%
1
1
95%
99.1%
1
1.5
32%
148.2%
From the experimental results one can find that when the tooth width is narrowed, not only the dust removal efficiency is improved, but also the dust removal performance becomes better. Therefore, the most suitable dust-removing electrode is considered to have a tooth width of 1mm. However, if the gap width of the comb-shaped electrode increases from 1mm to 1.5mm (the accuracy is difficult to ensure when the gap width is reduced to 1mm or less), although the theoretical dust removal efficiency is improved, the actual dust removal effect is greatly weakened. In summary, the optimum geometric
parameters of the comb-shaped electrode in the range allowed by the processing conditions are the tooth width and the gap width being both 1mm. In this situation, the dust removal efficiency can be increased by nearly 100%.
5 Conclusions In this study, to increase the driving capability of a single piece of PLZT, the configuration of the comb-shaped dust-removing electrode was proposed and the geometric parameters were optimized. The equivalent electrical model of PLZT was established to analyze the effect of the copper foil area of the dust-removing electrode on the dust removal effect and the experimental verification was carried out. The electric field model of the dust-removing electrode is established by the method of moments, and the electric field distribution of the comb-shaped electrode is obtained. The model is used to guide the experiment to obtain the optimal comb-shaped dust-removing electrode configuration. By theoretical analysis and experimental validation, this study leads to the following conclusions: (1) When the other conditions are constant, the larger the copper foil area of the dust-removing electrode is, the worse the dust removing ability of the dust-removing electrode becomes. (2) When the copper foil area of the dust-removing electrode is constant, the influence of the shape of the dust-removing electrode on dust removal voltage of PLZT can be neglected. (3) When the area of the dust-removing electrode is constant, the comb-shaped electrode can distribute charge more evenly and has a stronger dust removing ability than the common electrode. (4) The material parameters of the dust-removing electrode, such as the type of insulating film and the thickness of the copper foil, do not have much influence on the dust removing effect. (5) When the tooth width of the electrode is narrowed, the dust removal performance will be bettered and the dust removal efficiency will be improved. In the range allowed by the processing conditions, analysis suggests the optimal electrode geometric parameters: 1mm tooth width and 1mm gap width, which contribute to an approximate 100% dust removal efficiency improvement.
Acknowledgements This research is supported, in part, by grant from the National Natural Science Foundation of China (No. 51575125, 51175123) and the China Postdoctoral Science Foundation (2014M561358).
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Research Highlights
1.
A new photoelectric lunar dust removal technique is proposed.
2.
An optimization dust-removing electrode design method is presented.
3.
Electric field intensity distribution of the dust-removing electrode is obtained.
4.
Dust removal efficiency is improved by approximately 100% with this method.