Dust removal on solar panels of exploration rovers using Chladni patterns

Abstract

The buildup of dust on solar panels has significantly reduced the operational lifespan and mission performance of exploration rovers, and traditional dust removal techniques have proven inadequate for the Martian environment. The present study proposes a novel method for removing dust from the solar panels of Mars exploration rovers using Chladni patterns, addressing the persistent issue of efficiency loss due to Martian dust accumulation. To overcome these challenges, the proposed method leveraged Chladni patterns, generated by specific frequencies, to effectively clear dust from the panels. We conducted experiments that identified optimal frequencies, frequency sequences, and plate shapes for dust removal, demonstrating the method’s effectiveness. In conclusion, our approach not only enhances the efficiency of solar panels but also has the potential to improve the overall performance and longevity of Mars exploration missions.

Introduction

Most Martian exploration rovers utilize solar power as their primary energy source, relying on solar panels not only for energy generation but also for collecting data that contribute to our understanding of Martian weather phenomena and inform the design of future rovers^1,2. However, since the landing of the Mars Pathfinder in 1997, rovers such as the Spirit and Curiosity have consistently faced the challenge of a daily average power loss of 0.2% owing to dust accumulation on their solar panels³.

The concentration of atmospheric dust on Mars is a key factor that directly affects the efficiency of solar panels. This issue is particularly pronounced during the Martian summer, when frequent dust storms increase the amount of airborne dust, thereby reducing panel efficiency⁴. These dust storms can contribute to the accumulation of dust on solar panels⁵. Consequently, predicting the lifespan of solar panels on Martian rovers is challenging.

For example, NASA’s stationary InSight lander had to cease operation because of problems caused by dust accumulation^6,7. Fig. 1 illustrates a comparison between the lander’s clean solar panels at its initial landing in 2018 and the significantly reduced output caused by dust buildup four years later in 2022. Similarly, China’s Mars rover Zhurong, which entered hibernation after landing, has been unable to resume operations for over five months due to dust accumulation, preventing it from awakening⁸.

Fig. 1

Comparison of the amount of dust on InSight’s solar panels⁷.

Therefore, removing the dust accumulated on solar panels is essential for extending the lifespan of rovers, and various methods exist to address this issue. One approach involves the use of an electrodynamic dust shield (EDS) to remove accumulated dust^9,10,11, which employs electrodes that periodically receive voltages to create an electric field. The electric field generated by EDS can remove the dust accumulated on solar panels and serve as a coating-like barrier, reducing further dust accumulation. However, this approach, which leverages electrostatic and electrodynamic properties, is still in the development stage and has the limitation of requiring additional energy to generate an electric field.

Another approach involves the use of hybrid hydrophobic coatings to reduce dust accumulation¹². Martian dust tends to adhere firmly to the panels because of static electricity and humidity, making the removal through Martian winds difficult. The hybrid hydrophobic coating method involves applying a coating to solar panels to prevent dust from sticking to the panels owing to static electricity and moisture, thereby making the removal easier. However, this method is not entirely independent and may require additional measures such as tilting the panels or utilizing Martian winds. Moreover, factors such as the Martian climate and the lifespan of the coating must be considered. Additional efforts to address the issue of dust accumulation on Mars include attaching wipers to solar panels for dust removal¹³ and studying optimal panel angles to mitigate the impact of dust storms¹⁴.

The present study introduces a novel dust removal method that overcomes the limitations of previous approaches by using the Chladni pattern generated by the vibration of a rover’s solar panels. Unlike traditional dust removal methods that rely primarily on wind or electrical techniques, which may not be effective in extreme environments such as Mars or the Moon, the proposed method uses modal patterns for dust removal. The proposed technique is expected to significantly enhance the efficiency of solar panels and ensure the sustained operational capability of rover missions.

Chladni plates

A Chladni plate is a classical physical system used to study the vibration modes of a flat solid surface. The patterns formed by sand or other particles on this vibrating plate are known as Chladni patterns and are named after Ernst Chladni (first demonstration in the late eighteenth century)¹⁵. These patterns visually represent the nodal lines, where there is no vibration on the plate.

The vibrations of the Chladni plate can be explained using elasticity theory and wave dynamics¹⁶. The key to understanding the Chladni patterns lies in solving the wave equation for a thin elastic plate. The related mathematical model involves the following biharmonic equation. Eq. (1)¹⁶ for the transverse displacement w of the plate is expressed as follows:

$$D{\nabla }^{4}w+\rho h\frac{{\partial }^{2}w}{\partial {t}^{2}}=0, D=\frac{E{h}^{3}}{12(1-{\nu }^{2})}$$

(1)

where D is the bending stiffness, E represents the Young’s modulus, and ν is the Poisson’s ratio. The operator ${\nabla }^{4}$ is the biharmonic operator, ρ denotes the density of the plate material, and ℎ is defined as the thickness of the plate.

Assuming free vibration, the plate motion can be described by the Eq. (2)¹⁶:

$$w=W\text{cos}\omega \text{t}$$

(2)

where ω represents the angular frequency, and W(x, y) is a function of the spatial coordinates. By combining Eqs. (1) and (2), we can rearrange and simplify the expression into Eq. (3) for the position function (x, y) as follows:

$$D{\nabla }^{4}W-\rho h{\omega }^{2}W=0$$

(3)

Iguchi¹⁷ solved the problem using a series expansion and provided the following general solution presented in Eq. (4):

$$\begin{array}{c}W=\sum_{n}{X}_{n}\text{cos}n\pi \left(\frac{1}{2}+\eta \right)+\sum_{m}{Y}_{m}\text{cos}m\pi \left(\frac{1}{2}+\xi \right), \xi =\frac{x}{a}, \eta =\frac{y}{b} \left(m,n=0, 1, 2 \cdots \right)\end{array}$$

(4)

In Eq. (4), a and b are the lengths of the plate in the horizontal and vertical directions, respectively; x and y are coordinates with the center of the square plate as the origin. The functions ${X}_{n}$ and ${Y}_{m}$ in Eqs. (5) and (6) are defined as follows:

$${X}_{n}={A}_{n}\frac{\text{cosh}\pi {\lambda }_{\alpha n}\xi }{\text{sinh}\frac{\pi }{2}{\lambda }_{\alpha n}}+{A}_{n}^{\prime}\frac{\text{cosh}\pi {\lambda }_{\alpha n}^{\prime}\xi }{\text{sinh}\frac{\pi }{2}{\lambda }_{\alpha n}^{\prime}}+{A}_{n}^{{\prime}{\prime}}\frac{\text{sinh}\pi {\lambda }_{\alpha n}\xi }{\text{cosh}\frac{\pi }{2}{\lambda }_{\alpha n}}+{A}_{n}^{{\prime}{\prime}{\prime}}\frac{\text{sinh}\pi {\lambda }_{\alpha n}^{\prime}\xi }{\text{cosh}\frac{\pi }{2}{\lambda }_{\alpha n}^{\prime}}$$

(5a)

$${Y}_{m}={B}_{m}\frac{\text{cosh}\pi {\lambda }_{\beta m}\eta }{\text{sinh}\frac{\pi }{2}{\lambda }_{\beta m}}+{B}_{m}^{\prime}\frac{\text{cosh}\pi {\lambda }_{\beta m}^{\prime}\eta }{\text{sinh}\frac{\pi }{2}{\lambda }_{\beta m}^{\prime}}+{B}_{m}^{{\prime}{\prime}}\frac{\text{sinh}\pi {\lambda }_{\beta m}\eta }{\text{cosh}\frac{\pi }{2}{\lambda }_{\beta m}}+{B}_{m}^{{\prime}{\prime}{\prime}}\frac{\text{sinh}\pi {\lambda }_{\beta m}^{\prime}\eta }{\text{cosh}\frac{\pi }{2}{\lambda }_{\beta m}^{\prime}}$$

(5b)

$${\lambda }_{\alpha n},{\lambda }_{\alpha n}^{\prime}=\sqrt{{\alpha }^{2}{n}^{2}\pm \mu }, (\mu =\frac{\omega {\alpha}^{2}}{{\pi }^{2}}\sqrt{\frac{\rho }{D}}, \alpha =\frac{a}{b})$$

(6a)

$${\lambda }_{\beta m},{\lambda }_{\beta m}^{\prime}=\sqrt{{\beta }^{2}{m}^{2}\pm \mu^{\prime} }, (\mu^{\prime} =\frac{\omega {\beta}^{2}}{{\pi }^{2}}\sqrt{\frac{\rho }{D}}, \beta =\frac{b}{a})$$

(6b)

The boundary conditions for a free edge of a square plate are detailed in Iguchi¹⁷. These equations describe the various modes and vibration frequencies of the Chladni plate depending on the physical properties and boundary conditions. In the reference¹⁸, this determinant was truncated to a finite order, and the equation was solved according to the features of the Chladni patterns, resulting in the determination of specific shapes.

When vibrations are applied to a square plate, certain points on the plate do not experience displacement; these points are known as nodes. The particles tend to accumulate along these nodal lines, forming Chladni patterns. These mode shapes vary depending on the vibration frequency, and each mode exhibits a unique pattern. The Chladni patterns visually represent these nodal lines, and different frequencies produce distinct configurations, with each characteristic of a particular vibration mode.

Vibration-induced dust removal on solar panels: exploring Chladni patterns and plate shapes

In this section, we propose a dust removal method for solar panels that leverages the shape variations resulting from different frequencies. Chladni patterns, which change with frequency, offer an effective means of removing dust accumulated on the surface through vibration or mechanical movement. This dust removal technique, based on mode shapes, aims to enhance the efficiency of solar panels and sustain the operational capabilities of exploration rovers.

To validate this approach, we examined Chladni patterns corresponding to different frequencies for various plate shapes. Based on these results, we selected three frequencies that appeared to be the most suitable for dust removal. Finally, we aimed to identify the most effective factors for dust removal by comparing the performances of square and octagonal plates.

Chladni patterns based on plate shape

Given the sensitivity of the Chladni patterns to changes in the shape of the underlying plate, we investigated the Chladni patterns based on the shape of the plate to which the solar panel was attached. For this experiment, a shaker was required because of the nature of the Chladni patterns. We used a speaker unit with a diameter of 143 mm (5.5 in) and a power output of 70 W as the shaker. The speaker unit was connected to a laptop through an amplifier (TPA3116D2), and the frequency was adjusted using an online frequency control site¹⁹. We used a Delona DC power supply with a maximum output of 30 V. Fig. 2 illustrates the experimental setup used to study dust removal from solar panels using Chladni patterns. The setup consists of several key components: a DC power supply on the left, which powers the system, a halogen lamp used to simulate environmental lighting conditions, and an amplifier connected to a shaker (speaker), which is placed under the Chladni plate to generate vibrations at different frequencies. The Chladni plate was covered with solar cells, and a shaker induced vibrations to create the desired Chladni patterns on the plate. A multimeter was used to monitor the electrical output of the solar cells during the experiment, and a laptop controlled the frequency settings of the shaker through an online frequency generator. The setup was designed to evaluate the effectiveness of dust removal from solar panels via mechanical vibration.

Fig. 2

Experimental setup for dust removal on solar panels.

The shapes of the base plates selected for the experiment were a square plate, which represented the majority of rover solar panel shapes, and an octagonal plate, inspired by the panel design of the “InSight” lander. Both plates were symmetrically structured with identical dimensions of 380 mm × 380 mm × 5 mm. Nine solar cells were attached to each plate in the same arrangement, i.e., one 165 mm × 165 mm cell with a 6 V output and eight 82.5 mm × 100 mm cells with a 5 V output each. A gap of approximately 5 mm was created between the base plate and solar cells to allow sand to escape during the vibration process. This design ensured that the sand could disperse naturally as vibrations were applied, thereby preventing its accumulation in specific areas. Fig. 3 shows the base plates used in this experiment, including both square and octagonal shapes. The plate is made of a solar cell and PVC foam board.

Fig. 3

Base plates used in this experiment: (a) square plate and (b) octagonal plate.

For the experiment, we installed a speaker unit that served as a shaker for the vibration source at the central point of the base plate. A spirit level was used to ensure that the plate was perfectly horizontal to prevent shape distortion due to the tilting of the plate. Using an online frequency adjustment tool¹⁹, we then observed shape changes within the frequency range of 30–500 Hz. To simulate Martian dust and clearly observe the Chladni patterns, we used fine turquoise sand. Based on the data from the reference²⁰, the particle size of the sand we used is approximately in the range of 0.075 to 0.425 mm. To ensure reliability, the experiment was repeated three times for both square and octagonal plates. Fig. 4 shows the experimental layout for the observation of the Chladni pattern. Figs. 5 and 6 present the results of the experiment with shapes selected based on the frequencies at which the patterns are clearly defined.

Fig. 4

Experimental layout for observation of Chladni pattern.

Fig. 5

Shapes selected based on the frequencies with clearly defined patterns on square plates.

Fig. 6

Shapes selected based on the frequencies with clearly defined patterns on octagonal plates.

Effective frequency for dust removal

In the previous process, we identified the Chladni patterns corresponding to different base plate shapes and frequencies. Based on these results, we determined the most suitable patterns for dust removal. Because the primary goal of this study was to remove dust from solar panels, we prioritized frequencies where the movement of sand was most active during the formation of patterns on both square and octagonal plates. Additionally, we chose the frequencies where the patterns were most clearly defined as the key criteria.

For the square plate, patterns were formed in three frequency ranges: 35–110 Hz (frequency band 1), 150–230 Hz (frequency band 2), and 320–400 Hz (frequency band 3). For the efficiency experiments, we used the frequencies within each range where the patterns were most clearly defined, i.e., 50, 180, and 380 Hz, referred to as ${f}_{S,1}$, ${f}_{S,2}$, and ${f}_{S,3}$, respectively. Once vibration is applied to the plates, the pattern forms within 10 s. Therefore, we applied vibration to the plate for 10 s at each frequency. Fig. 7 shows the Chladni patterns at these specific frequencies for the square plates.

Fig. 7

Selected patterns corresponding to specific frequencies on square plates.

For the octagonal plate, the patterns were observed within three frequency ranges: 40–70 Hz (frequency band 1), 180–230 Hz (frequency band 2), and 250–370 Hz (frequency band 3). These ranges were selected because the overall pattern shape tendencies were similar within each range. The specific frequencies of 50, 220, and 350 Hz (${f}_{O,1}$, ${f}_{O,2}$, and ${f}_{O,3}$, respectively) were chosen because they produced the most clearly defined patterns, as shown in Fig. 8.

Fig. 8

Selected patterns corresponding to specific frequencies on octagonal plates.

Effects of dust removal on solar panel efficiency: a comparative study of frequency sequences and shape of plates

To assess the effectiveness of the dust removal method using Chladni patterns, we conducted experiments to measure the electrical power output and evaluate the performance based on frequency sequences and plate shapes. To eliminate variables, such as weather conditions, that could affect the efficiency of the solar panel, we used a portable halogen lamp with a maximum output of 500 W instead of natural sunlight. The power generated by solar panels was measured using a digital multimeter (GT100).

Electric power measurement in the presence and absence of sand on solar panels

To compare the electric power output, measurements were performed under two conditions: with and without sand. Fig. 9 illustrates the states of the panels for both scenarios. Power measurements were conducted for both square and octagonal plates. The average of the measurements was used as the result for each base plate. Fig. 10 shows the experimental setup used to assess the dust removal performance on the solar panels. A halogen lamp was positioned above the solar panel to provide consistent illumination, and the panel was covered with fine sand to simulate dust. The panel was mounted on a Chladni plate, and vibrations were applied using a shaker placed underneath. A multimeter was used to measure the electrical output of the solar panel during the experiment. In addition, a DC power supply unit is visible on the right side of Fig. 10, providing the necessary power to the system, and an amplifier is connected to control the frequency of the shaker. The setup was designed to assess the performance of dust removal from a solar panel subjected to specific frequencies and vibrations.

Fig. 9

Illustration of the presence and absence of sand.

Fig. 10

Experimental setup for assessing dust removal performance through electric power measurements.

Fig. 11

Comparison of electric power with and without sand.

Fig. 11 shows the effect of dust removal on the plates, comparing the electric power output of a solar panel under two conditions: with sand and without sand. The bar corresponding to the “with sand” condition shows a significantly lower power output (2.262 W), whereas the bar for the “without sand” condition shows a much higher power output (8.977 W). This comparison clearly illustrates that the presence of sand significantly reduces the efficiency of the solar panel, with the power output being substantially higher in the absence of sand.

Electric power measurement across frequency sequences and shape of plates

In this section, we measure the electric power at selected frequencies for square plates (${f}_{S,1}$, ${f}_{S,2}$, and ${f}_{S,3}$) and octagonal plates (${f}_{O,1}$, ${f}_{O,2}$, and ${f}_{O,3}$). The power output of the solar cells was measured immediately after the vibrations ceased. Fig. 12 shows the measured power output from the nine cells at each frequency in both square and octagonal plates. The results indicated that sand was most effectively removed at frequencies ${f}_{S,2}$ and ${f}_{O,2}$ in both square and octagonal plates.

Fig. 12

Comparison of electric power in each frequency: (a) square and (b) octagonal plates.

Subsequently, the order of the frequencies ${f}_{1}$, ${f}_{2}$, and ${f}_{3}$ was varied to determine the optimal sequence, and six different combinations were tested. Table 1 lists the frequency change sequences used to test the power performance, covering all possible combinations. Six sequences (S1–S6) are presented, and each one is designed to evaluate the power efficiency under different frequency transitions. Each sequence involved different arrangements of the three frequency settings, ${f}_{1}$, ${f}_{2}$, and ${f}_{3}$, which allowed for varied testing conditions. For example, S1 follows the order ${f}_{1}$, ${f}_{2}$, and ${f}_{3}$, whereas S6 uses the reverse order ${f}_{3}$, ${f}_{2}$, and ${f}_{1}$. These sequences enable the evaluation of how different frequency transitions affect the power output, providing critical insights into optimizing the power performance based on frequency variations. The results of these tests are presented in Fig. 13, where the electric power output is compared across six different frequency change sequences (S1–S6) under two conditions: square (blue, left) and octagonal (green, right) plates. This trend showed that S2 consistently resulted in the highest power output, reaching 7.026 W with square plates and 7.235 W with octagonal plates. The results indicated that sequence S2 for both square and octagonal plates was the most effective in removing sand. Each frequency (${f}_{1}$, ${f}_{2}$, and ${f}_{3}$) has specific pattern characteristics for the Chladni plates. Frequency ${f}_{1}$ tends to gather sand in a circular pattern, covering the center of the cells. Frequency ${f}_{2}$ pushes sand towards the edges of the solar cells. Frequency ${f}_{3}$ spreads the sand more widely, thus assisting its dispersion more effectively across the surface. The effectiveness of the S2 sequence, regardless of the plate shape, can be attributed to the specific manner in which the sand moves at each frequency. When applying the S2 sequence, ${f}_{1}$ initially dislodged sand from the cells and gathered it into a circular pattern. Then, ${f}_{3}$ spread the sand across a wider area, making it easier to remove the subsequent pattern. Finally, ${f}_{2}$ moved the dispersed sand off the cells and towards the edges to maximize the output voltage.

Table 1 Frequency change sequences for testing power efficiency performance.

Fig. 13

Comparison of electric power across predetermined frequency sequences: (a) square and (b) octagonal plates.

Conversely, the lowest power output was observed for S3 and S6 in both plates, indicating a correlation in which certain frequency sequences yielded lower efficiency, regardless of the shape of the plates. Notably, the power output from the octagonal plate is generally higher across all sequences, reinforcing the concept that sand affects negatively the system power efficiency. This consistent trend highlights the importance of sequence selection in optimizing power performance.

Fig. 14 compares the electric power output between the square and octagonal geometric configurations. The electric power ranges from 7.026 W to 7.235 W, and the data indicate that the octagonal configuration yields slightly higher electric power output, reaching 7.235 W, compared to the square configuration, which produces 7.026 W. Evidently, the octagonal plate demonstrates a higher power production when Chladni patterns are used for dust removal from solar panels. This suggests that the octagonal shape of the proposed dust removal method is more efficient in terms of power output, probably because its geometry offers better performance characteristics in the tested system.

Fig. 14

Comparison of electric power with square and octagonal plates under the S2 sequence.

In real-world applications, Martian rovers must achieve landing and navigate uneven terrain on Mars. For instance, the Perseverance rover traversed a crater slope with an incline of approximately 23 degrees [3]. This suggests that vibration-induced transport could be used to simply move dust downslope, rather than channeling it via nodal lines. To investigate this, we conducted additional experiments to assess the performance of the proposed dust removal method at varying slope angles: 5°, 10°, 15°, 20°, and 25°. Fig. 15 compares the electric power output of solar panels at slope angles ranging from 0° to 25° during the S2 sequence with 10-s vibration intervals. This vibration interval was chosen to ensure consistent and reliable results in the clearing effect analysis across the varying slope angles. In both plate configurations, power output increases as the slope angle rises from 0° to around 15°–20°, after which it plateaus. This trend suggests that tilting the solar panel to a specific angle enhances power output, likely due to improved dust removal or optimized light exposure associated with each frequency’s effect on dust distribution. These results indicate that at a slope of 15 degrees or more, with power outputs reaching 8.645 W for the square plate and 8.897 W for the octagonal plate, all dust was effectively removed from the panels.

Fig. 15

Comparison of electric power as an effect of slope angle under the S2 sequence.

Conclusion

In this paper, we present a novel dust removal method for solar panels using Chladni patterns. We conducted a series of experiments to validate the effectiveness of the proposed approach. First, we investigated two types of base plates and observed the Chladni patterns formed at various frequencies that varied depending on the shape of the plate. Based on these observations, we identified three distinct frequencies that resulted in significant sand movement, labeled as ${f}_{1}$, ${f}_{2}$, and ${f}_{3}$ for each plate shape.

We then measured the power output across various frequency sequences, taking into account the shape of the base plates. The results indicated that, on average, power output was approximately four times higher when sand was present on the solar cells. Among the selected frequencies, ${f}_{2}$ consistently produced the highest power output for both plate shapes. Each frequency (${f}_{1}$, ${f}_{2}$, and ${f}_{3}$) generated distinct pattern characteristics on the Chladni plates: at frequency ${f}_{1}$, sand tended to gather in a circular pattern, concentrating in the center of the cells; at frequency ${f}_{2}$, sand was pushed toward the edges of the solar cells; and at frequency ${f}_{3}$, sand was more broadly dispersed, aiding in effective distribution across the surface.

Further testing of different frequency sequences revealed that the S2 sequence achieved the highest efficiency for both base plates, likely due to the specific movement of sand and the distinctive pattern characteristics at these frequencies. Additionally, the octagonal plate showed effectiveness in dust removal compared to the square plate, suggesting that plate shape influences the efficiency of sand dispersion and removal. These findings underscore the role of frequency selection and plate shape in optimizing power output and dust management on solar panels.

Although this study focused on square and octagonal base plates, the proposed dust removal method could be adapted to other plate shapes using a similar experimental approach. Furthermore, integrating this technique with additional methods such as solar cell coatings or electrostatic dust removal could enhance dust mitigation and significantly extend the operational lifespan of solar panels, particularly in environments such as those encountered by exploration rovers.