Analysis of Removing Barnacles Attached on Rough Substrate with Cleaning Robot

: In this paper, a cleaning robot is designed to remove the marine fouling attached to a marine steel pile. In the following study, in order to analyse the process of cleaning marine fouling attached to a rough substrate, the barnacle is taken as a typical case in order to study the horizontal cutting force in the scarping process for removing barnacles on a rough substrate. The adhesion model of the barnacle was established on a rough rigid substrate. Considering both right angle cutting theory and the Peel Zone method, a scraping means and horizontal cutting force model for rough surface cleaning are proposed for the study of the surface cleaning of steel piles. In order to make the model more accurate, the ﬁnite element method is used to analyze and compare its errors. Through comparative analysis, it is known that the relative average errors about the cutting force in the horizontal direction are less than 15%. The analysis shows that the blade rake angle and rough substrate have a great inﬂuence on the horizontal cutting force. It can be concluded that the cutting force needed to clean the barnacle attached to the surface decreases correspondingly as the rake angle of the blade increases; and the rougher the substrate is, the greater the horizontal cutting force required. It is recommended to use 60 ◦ for blade rake angle. We can use the model to predict the horizontal cutting force and blade rake angle in the design of a cleaning robot.


Introduction
In recent years, with the development of offshore engineering, pile foundation has been extensively used for offshore wind mills, drilling platforms, ports, piers, etc. Most of the steel piles stand in the splash zone [1] and endure seawater corrosion as well as marine fouling [1,2]. As a result, the pile life cycle is affected severely [3], and further leads to a heavy cost in both man power and finance for maintenance [4]. Therefore, it is imperative to regularly clean steel piles and/or prevent marine fouling from accumulating on the surface of steel piles.
The anti-corrosion treatment of the steel pile surface generally includes four methods: cleaning marine fouling, applying anti-corrosion paste, wrapping up with anti-corrosion tape, and putting on protective covers [5]. Chemical, mechanical, water jet, sonic, and ultraviolet methods have been used to remove marine fouling. The chemical method involves using chemicals or biological fungicides to kill microorganisms. The chemicals are toxic to microorganisms, and the biological fungicides can destroy cell structure and function [6], but this causes water pollution [7] as well as equipment The cleaning robot can also be operated underwater. The range of cleaning robot operations is ±15 m about sea level. Marine fouling needs to be cleaned to protect against corrosion in the area where marine steel piles are located. At present, the cleaning robot can clean the marine steel pile with a diameter of 1 m. Rotation speed range is 10 to 20°/min. The cleaning robot moves up and down along the steel pile with a speed range from 1 m/20 min to 1 m/30 min. The scraping tool material is Alloy Tool Steel, ISO 210Cr12, and the frame work material is aluminum alloy to reduce the overall weight of the robot.
After the cleaning robot is installed, with crane ship, to hug the steel pile, it can be operated automatically to clean the steel piles. When starting to install the cleaning robot so that it is hugging the steel pile, it needs cooperation of a crane ship and manual assistance. The the cleaning robot holds the frame stably with clamps, and it can clean the steel piles automatically with scraping tools vertically. The gears rotate at a certain angle, after the vertical cleaning, and continue to repeat vertical cleaning until whole surface is finished. The lower set of clamps release and three hydraulic cylinders 1 and 2 extend at the same time. When the hydraulic cylinder is extended to the limit, the lower set of clamps lock. Then, the upper set of clamps release, three hydraulic cylinder 1 and 2 draw back to the limit, and the upper set of clamps lock. At this time, the cleaning robot completes the downward movement and moves to a new position, which can clean up the new surface as above.

Barnacle Geometric Model and Cleaning Methods
In order to analyze the effect of the barnacle on the vortex-induced vibration of the cylinder, a model of a barnacle was created by Jadidi [25], which attached to the cylinder surface. This model was a trapezoidal cross section. The barnacle idealized model is as shown in Figure 2. The trapezoidal mound is used to represent the calcareous shell of the barnacle and the bottom layer represents the viscoelastic cement, which attach the barnacle to the rough substrate. The cleaning robot can also be operated underwater. The range of cleaning robot operations is ±15 m about sea level. Marine fouling needs to be cleaned to protect against corrosion in the area where marine steel piles are located. At present, the cleaning robot can clean the marine steel pile with a diameter of 1 m. Rotation speed range is 10 to 20 • /min. The cleaning robot moves up and down along the steel pile with a speed range from 1 m/20 min to 1 m/30 min. The scraping tool material is Alloy Tool Steel, ISO 210Cr12, and the frame work material is aluminum alloy to reduce the overall weight of the robot.
After the cleaning robot is installed, with crane ship, to hug the steel pile, it can be operated automatically to clean the steel piles. When starting to install the cleaning robot so that it is hugging the steel pile, it needs cooperation of a crane ship and manual assistance. The the cleaning robot holds the frame stably with clamps, and it can clean the steel piles automatically with scraping tools vertically. The gears rotate at a certain angle, after the vertical cleaning, and continue to repeat vertical cleaning until whole surface is finished. The lower set of clamps release and three hydraulic cylinders 1 and 2 extend at the same time. When the hydraulic cylinder is extended to the limit, the lower set of clamps lock. Then, the upper set of clamps release, three hydraulic cylinder 1 and 2 draw back to the limit, and the upper set of clamps lock. At this time, the cleaning robot completes the downward movement and moves to a new position, which can clean up the new surface as above.

Barnacle Geometric Model and Cleaning Methods
In order to analyze the effect of the barnacle on the vortex-induced vibration of the cylinder, a model of a barnacle was created by Jadidi [25], which attached to the cylinder surface. This model was a trapezoidal cross section. The barnacle idealized model is as shown in Figure 2. The trapezoidal mound is used to represent the calcareous shell of the barnacle and the bottom layer represents the viscoelastic cement, which attach the barnacle to the rough substrate. The bottom diameter of the geometrical model is d1, the top diameter is d2 = 7d1/12, the average height of one-year-old barnacle is, h1 = 5d1/12, and the height of cement layer is, h2 = d1/24, as shown in Figure 3. The parameters in Figure 3 are also shown in Appendix A. The size/diameter of barnacles range from 8 to 43 mm [26]. The barnacle used was Balanomorpha genus, in particular, the Semibalanus balanoides (previous name Balanus balanoides). The S. balanoids is a sessile barnacle that attaches to hard substrates. This species has a highly synchronized settlement. The diameter can be measured and has a certain representativeness [27,28]. The adhesion force increased monotonously with the area and time of barnacle attachment. And and Walker [27,28] presented the relationship between barnacle size and adhesion, and concluded the adhesion strength of adult barnacles was p = 9.252 × 10 5 N/m 2 . The relation between the adhesion and barnacle diameter is as shown in Figure 4.  The bottom diameter of the geometrical model is d 1 , the top diameter is d 2 = 7d 1 /12, the average height of one-year-old barnacle is, h 1 = 5d 1 /12, and the height of cement layer is, h 2 = d 1 /24, as shown in Figure 3. The parameters in Figure 3 are also shown in Appendix A. The bottom diameter of the geometrical model is d1, the top diameter is d2 = 7d1/12, the average height of one-year-old barnacle is, h1 = 5d1/12, and the height of cement layer is, h2 = d1/24, as shown in Figure 3. The parameters in Figure 3 are also shown in Appendix A. The size/diameter of barnacles range from 8 to 43 mm [26]. The barnacle used was Balanomorpha genus, in particular, the Semibalanus balanoides (previous name Balanus balanoides). The S. balanoids is a sessile barnacle that attaches to hard substrates. This species has a highly synchronized settlement. The diameter can be measured and has a certain representativeness [27,28]. The adhesion force increased monotonously with the area and time of barnacle attachment. And and Walker [27,28] presented the relationship between barnacle size and adhesion, and concluded the adhesion strength of adult barnacles was p = 9.252 × 10 5 N/m 2 . The relation between the adhesion and barnacle diameter is as shown in Figure 4. The size/diameter of barnacles range from 8 to 43 mm [26]. The barnacle used was Balanomorpha genus, in particular, the Semibalanus balanoides (previous name Balanus balanoides). The S. balanoids is a sessile barnacle that attaches to hard substrates. This species has a highly synchronized settlement. The diameter can be measured and has a certain representativeness [27,28]. The adhesion force increased monotonously with the area and time of barnacle attachment. And and Walker [27,28] presented the relationship between barnacle size and adhesion, and concluded the adhesion strength of adult barnacles was P = 9.252 × 10 5 N/m 2 . The relation between the adhesion and barnacle diameter is as shown in Figure 4.
The Peel Zone method was proposed by Pesika [29,30] to calculate the cutting force in barnacle cleaning. This paper proposed a method of cleaning barnacles based on the right angle cutting method and the Peel Zone method, namely scraping means. The scraping process of barnacles can be divided into two stages-cut-in stage A and peeling stage B-as shown in Figure 5. a sessile barnacle that attaches to hard substrates. This species has a highly synchronized settlement. The diameter can be measured and has a certain representativeness [27,28]. The adhesion force increased monotonously with the area and time of barnacle attachment. And and Walker [27,28] presented the relationship between barnacle size and adhesion, and concluded the adhesion strength of adult barnacles was p = 9.252 × 10 5 N/m 2 . The relation between the adhesion and barnacle diameter is as shown in Figure 4.  The Peel Zone method was proposed by Pesika [29,30] to calculate the cutting force in barnacle cleaning. This paper proposed a method of cleaning barnacles based on the right angle cutting method and the Peel Zone method, namely scraping means. The scraping process of barnacles can be divided into two stages-cut-in stage A and peeling stage B-as shown in Figure 5. The cut-in stage is as shown in Figure 5A. The blade with a rake angle of γ0 moves towards the barnacle with a certain speed, when the blade cuts into the cement by S(t1) at t1, the rake face of the blade contacts the calcareous shell and produces a peel angle θ1.
The peeling stage, B, is as shown in Figure 5B. The blade further moves to S(t2) at t2, whereby the peeling-produced cement damage happens. The calcareous shell bears the normal and tangential forces produced by the rake face of the blade in this stage. The normal force of the rake face is the main force for peeling, which causes the calcareous shell to be deformed and gradually lifted up. At this moment, t2, the remaining adhesion length is S1, the Peel Zone length is S2, and d1 = S1+ S2+S(t2). The theoretical peel angles is at the range about 0° < θ ≤ 90°. After t2, the resultant force of adhesion and friction decreases, until the barnacle is peeled off the substrate completely.

Force Modeling
Barnacles were tightly attached to rigid substrates with their cement. It was very difficult to clean up because of the calcareous shell tightly attached to the substrate and cement. In this paper, a scraping means was presented to analyze the cutting force on the surface of the barnacle. This method used the right angle cutting theory and the Peel Zone method used by Pesika [29,30]. The process of cleaning up the barnacle can be divided into two stages, as shown in Figure 5.
The parameters in the formula are shown in Appendix A. Assume that: (1) The cutting tip of the blade is fully sharp; and (2) there is no friction on the flank face [31,32]. The cutting force F on the rake face can be decomposed into two components (the normal force Fn and the tangential friction force Ft), the calcareous shell is mainly deformed by the normal force Fn, and Fn can be decomposed into Fnx and Fny, as shown in Figure 6 and F` is the counterforce of F. The counterforce F` can be decomposed into FH and FV, in horizontal and vertical directions, respectively, and FH can be expressed as: The cut-in stage is as shown in Figure 5A. The blade with a rake angle of γ 0 moves towards the barnacle with a certain speed, when the blade cuts into the cement by S(t1) at t1, the rake face of the blade contacts the calcareous shell and produces a peel angle θ 1 .
The peeling stage, B, is as shown in Figure 5B. The blade further moves to S(t2) at t2, whereby the peeling-produced cement damage happens. The calcareous shell bears the normal and tangential forces produced by the rake face of the blade in this stage. The normal force of the rake face is the main force for peeling, which causes the calcareous shell to be deformed and gradually lifted up. At this moment, t2, the remaining adhesion length is S 1 , the Peel Zone length is S 2 , and d 1 = S 1 + S 2 + S(t2). The theoretical peel angles is at the range about 0 • < θ ≤ 90 • . After t2, the resultant force of adhesion and friction decreases, until the barnacle is peeled off the substrate completely.

Force Modeling
Barnacles were tightly attached to rigid substrates with their cement. It was very difficult to clean up because of the calcareous shell tightly attached to the substrate and cement. In this paper, a scraping means was presented to analyze the cutting force on the surface of the barnacle. This method used the right angle cutting theory and the Peel Zone method used by Pesika [29,30]. The process of cleaning up the barnacle can be divided into two stages, as shown in Figure 5.
The parameters in the formula are shown in Appendix A. Assume that: (1) The cutting tip of the blade is fully sharp; and (2) there is no friction on the flank face [31,32]. The cutting force F on the rake face can be decomposed into two components (the normal force F n and the tangential friction force F t ), the calcareous shell is mainly deformed by the normal force F n , and F n can be decomposed into F nx and F ny , as shown in Figure 6 and The barnacle bottom area can be divided into three zones: divided zone, peeling zone and adhesion zone, as shown in Figure 7. The following relations applies: where FA is the adhesion force in the adhesion zone, FPZ is the peeling force in the peel zone, and Ff is the horizontal friction force and can be calculated individually.

Calculation of FPZ
The normal force Fn on the rake face acts on the calcareous shell and make it deformed. We assume that the trapezoidal bottom cross section deformation of the calcareous shell is actually a F is the counterforce of F. The counterforce F can be decomposed into F H and F V , in horizontal and vertical directions, respectively, and F H can be expressed as: where the angle β between F and Fn is the friction angle. γ 0 is the fake angle of the blade. The angle between F and F H is β−γ 0 . The barnacle bottom area can be divided into three zones: divided zone, peeling zone and adhesion zone, as shown in Figure 7. The following relations applies: where F A is the adhesion force in the adhesion zone, F PZ is the peeling force in the peel zone, and F f is the horizontal friction force and can be calculated individually.
adhesion zone, as shown in Figure 7. The following relations applies: where FA is the adhesion force in the adhesion zone, FPZ is the peeling force in the peel zone, and Ff is the horizontal friction force and can be calculated individually.

Calculation of FPZ
The normal force Fn on the rake face acts on the calcareous shell and make it deformed. We assume that the trapezoidal bottom cross section deformation of the calcareous shell is actually a

Calculation of F PZ
The normal force F n on the rake face acts on the calcareous shell and make it deformed. We assume that the trapezoidal bottom cross section deformation of the calcareous shell is actually a circular arc, the cement deformation changes with the calcareous shell, the bottom surface is also circular arc with a radius of R . We assume that the bottom surface keeps the same arc when the cement is peeled off, and L 2 is the arc length between x 1 and x 2 . When θ is smaller, L 2 = R θ≈S 2 . The area is the Peel Zone, which is surrounded by points x 1 , x 2 , and M. The cement starts to scrape off the substrate at x 1 . The last fiber of cement scrapes off the substrate at x 2 , which is the critical point. M is the critical point at which the last fiber of the cement is removed by blade tip. The θ is the peel angle which is between x 1 and x 2 . The relationship according to the formula between the radius of curvature, R , and the peel angle, θ, is R = 4215 × θ −1.35 [30]. The B represents the width of the Peel Zone (as shown in Figure 7) between x 1 and x 2 , which is B = 2 R 2 − (R − S) 2 . The adhesion force of the Peel Zone is written as [30]: A represents the Hamaker constant and D is represents the surface gap. We know that the gecko spatula pad is made of β-keratin [29], that is a certain protein. In addition, the majority of barnacle cement is made of multi-protein complex [26]. Their adhesion mechanism is almost the same, which is caused by the intermolecular interactions [26,29,30]. The size of the gecko spatula pad and barnacle cement is of equal magnitude. Due to the similar properties mentioned, we make some similar assumptions to the gecko spatula pad to ensure that formulas of the Peel Zone can be calculated in this paper.

Calculation of F A and F f
A Z is the area of the adhesion zone, which is shown Figure 7: with R = 0.012 m, where S 1 = d 1 − S 2 − S and S 2 ≈R θ. The adult barnacle's adhesion strength is P = 9.252 × 10 5 N/m 2 [27,28]. Assuming that all barnacles to be removed are adult barnacles, the remaining adhesion force F A can be written as: Substituting Equations (5) and (7) into (4), F ny can be rewritten as: F nx in the horizontal direction can be expressed as [30]: where µ is the friction coefficient between substrate and cement.
For smooth substrates, because there is no F f and F nx , through the trigonometric relationship F n = F ny /sinγ 0 , the cutting force can be expressed as F H .
For rough substrates, there is F f = F nx , thus the cutting force can be expressed as F H .

Effect of Friction
A typical curve is shown in the Figure 8, showing a 3D image of cutting force vs. displacement. The cutting force F H can also be drawn as a 3D picture, which is about the influence of rake angle. The rake angle of blade has a great influence on the cutting force. Increasing the rake angle can greatly decrease the cutting force in (0, 45 • ), and the trend is relatively gentle in (45-90 • ). Considering the cutting force and the design of the scraping tools, the rake angle can be compromised. The blade rake angle could be recommended to [30 • A typical curve is shown in the Figure 8, showing a 3D image of cutting force vs. displacement. The cutting force FH can also be drawn as a 3D picture, which is about the influence of rake angle. The rake angle of blade has a great influence on the cutting force. Increasing the rake angle can greatly decrease the cutting force in (0, 45°), and the trend is relatively gentle in (45-90°). Considering the cutting force and the design of the scraping tools, the rake angle can be compromised. The blade rake angle could be recommended to [30°, 60°]. Among [30°, 60°], we select 45° and 60° as examples. In the process of removing attached barnacles, the surface roughness of the substrate is considered to play a significant role in the scraping behavior. In nature, the smooth surface does not exist completely, and even highly polished surfaces are rough. The surface roughness shows a significant effect. Assume that the surface roughness changes monotonically with the relative friction coefficient under dry friction. In order to analyze the effect of relative friction coefficient on the cutting force in the process of removing barnacles, in the case of the blade rake angle of 45 ° and 60 °, according to the formulas (10) and (12), we drew a 3D plot of rake angles 45° and 60°, different friction coefficients, and displacement vs. horizontal cutting force, as shown in Figure 9. In the process of removing attached barnacles, the surface roughness of the substrate is considered to play a significant role in the scraping behavior. In nature, the smooth surface does not exist completely, and even highly polished surfaces are rough. The surface roughness shows a significant effect. Assume that the surface roughness changes monotonically with the relative friction coefficient under dry friction. In order to analyze the effect of relative friction coefficient on the cutting force in the process of removing barnacles, in the case of the blade rake angle of 45 • and 60 • , according to the Formulas (10) and (12), we drew a 3D plot of rake angles 45 • and 60 • , different friction coefficients, and displacement vs. horizontal cutting force, as shown in Figure 9. It is found that the cutting force FH increases with the increase monotonically with friction coefficient, and a larger friction coefficient corresponds to a greater amplitude of cutting force. At the same time, we also made contrast curves on smooth and rough substrates at rake angles 45°and 60°, as shown in Figure 10. We can see straight away that the horizontal cutting force on the rough surface is much larger than that on the relatively smooth one at the same blade rake angle. It is found that the cutting force F H increases with the increase monotonically with friction coefficient, and a larger friction coefficient corresponds to a greater amplitude of cutting force. At the same time, we also made contrast curves on smooth and rough substrates at rake angles 45 • and 60 • , as shown in Figure 10. We can see straight away that the horizontal cutting force on the rough surface is much larger than that on the relatively smooth one at the same blade rake angle.
It is found that the cutting force FH increases with the increase monotonically with friction coefficient, and a larger friction coefficient corresponds to a greater amplitude of cutting force. At the same time, we also made contrast curves on smooth and rough substrates at rake angles 45°and 60°, as shown in Figure 10. We can see straight away that the horizontal cutting force on the rough surface is much larger than that on the relatively smooth one at the same blade rake angle.

Simulation and Results
In order to study the data and validation results of the mathematical model on smooth and rough substrates, we chose 60° and 45°, respectively, to represent different blade rake angles. Therefore, the difference in results can be more intuitively presented in different rake angles. We established 3D finite element models in Hypermesh, as shown in Figure 11. The diameter of barnacle was d1 = 0.024 m. The size of height, cement thickness, and top can be drawn according to Figure 3. The blade rake angles were 60° and 45°, respectively. The velocity of blade wass set as 0.7 m/s. The blade, barnacle shell, and cement were set as a solid element, but the substrate was set as the shell element to facilitate convergence of the results.
The failure contact command was set between the cement and substrate; The no failure contact command was set among the calcareous shell, cement, and blade. The blade and substrate was set as elastic material with density ρ = 7.93 × 10 3 kg/m 3 , the bulk modulus was K = 1.95 × 10 5 MPa, the Poisson's ratio was γ = 0.247. The calcareous shell was set as plastic material with density ρ = 2.6 × 103 kg/m 3 , the bulk modulus was K = 5 × 10 4 Mpa, the Poisson's ratio was γ = 0.3; the cement was set as viscoelastic material with density ρ = 1.19 × 10 3 kg/m3, bulk modulus was K = 100 MPa. The whole 3D finite element model was meshed with 12,162 units and 15,405 nodes. The whole 3D finite element

Simulation and Results
In order to study the data and validation results of the mathematical model on smooth and rough substrates, we chose 60 • and 45 • , respectively, to represent different blade rake angles. Therefore, the difference in results can be more intuitively presented in different rake angles. We established 3D finite element models in Hypermesh, as shown in Figure 11. The diameter of barnacle was d1 = 0.024 m. The size of height, cement thickness, and top can be drawn according to Figure 3. The blade rake angles were 60 • and 45 • , respectively. The velocity of blade wass set as 0.7 m/s. The blade, barnacle shell, and cement were set as a solid element, but the substrate was set as the shell element to facilitate convergence of the results. The results of horizontal cutting forces FH of the simulation and analytical curves are drawn in Figure 12 with regard of the blade displacement. When the blade rake is 60°, the results of the analytical and simulation smooth and rough curves of the cutting forces, FH, are drawn in Figure 12a. The trends of smooth simulations agree with the analytical curve. Both smooth substrate curves of the cutting force, FH, intersect at three points-A, B and C. The relative average error between both curves is less than 10%. Although the trends of analytical rough curves agree with the simulations, it is not good as smooth curves. Both rough substrate curves of the cutting force, FH, intersect at the point of D only. The relative average error between both curves are less than 20%. When the blade rake is 45°, the results of the analytical and simulation smooth and rough curve of forces FH are drawn in Figure 12b. The trends of the smooth simulations agree with the analytical curve also. Both smooth substrate curves of force FH intersect at three points-E, F and G. Both rough substrate curves of force FH intersect at three points also-H, I and J. The relative average errors between smooth and rough curves are less than 10%. Overall, the relative average error is less than 15%. The average error between both results is because of the assumption of the mathematical model. The error is also related to meshing the model, the number of units, and the blade speed. The failure contact command was set between the cement and substrate; The no failure contact command was set among the calcareous shell, cement, and blade. The blade and substrate was set as elastic material with density ρ = 7.93 × 10 3 kg/m 3 , the bulk modulus was K = 1.95 × 10 5 MPa, the Poisson's ratio was γ = 0.247. The calcareous shell was set as plastic material with density ρ = 2.6 × 103 kg/m 3 , the bulk modulus was K = 5 × 10 4 Mpa, the Poisson's ratio was γ = 0.3; the cement was set as viscoelastic material with density ρ = 1.19 × 10 3 kg/m3, bulk modulus was K = 100 MPa. The whole 3D finite element model was meshed with 12,162 units and 15,405 nodes. The whole 3D finite element model was set to four couple groups in the contact system. The bottom substrate was fixed in six degrees of freedom and the velocity of the blade was set as 0.7 m/s in the x negative direction.
The results of horizontal cutting forces F H of the simulation and analytical curves are drawn in Figure 12 with regard of the blade displacement. When the blade rake is 60 • , the results of the analytical and simulation smooth and rough curves of the cutting forces, F H , are drawn in Figure 12a. The trends of smooth simulations agree with the analytical curve. Both smooth substrate curves of the cutting force, F H , intersect at three points-A, B and C. The relative average error between both curves is less than 10%. Although the trends of analytical rough curves agree with the simulations, it is not good as smooth curves. Both rough substrate curves of the cutting force, F H , intersect at the point of D only. The relative average error between both curves are less than 20%. When the blade rake is 45 • , the results of the analytical and simulation smooth and rough curve of forces F H are drawn in Figure 12b. The trends of the smooth simulations agree with the analytical curve also. Both smooth substrate curves of force F H intersect at three points-E, F and G. Both rough substrate curves of force F H intersect at three points also-H, I and J. The relative average errors between smooth and rough curves are less than 10%. Overall, the relative average error is less than 15%. The average error between both results is because of the assumption of the mathematical model. The error is also related to meshing the model, the number of units, and the blade speed.
The results of horizontal cutting forces FH of the simulation and analytical curves are drawn in Figure 12 with regard of the blade displacement. When the blade rake is 60°, the results of the analytical and simulation smooth and rough curves of the cutting forces, FH, are drawn in Figure 12a. The trends of smooth simulations agree with the analytical curve. Both smooth substrate curves of the cutting force, FH, intersect at three points-A, B and C. The relative average error between both curves is less than 10%. Although the trends of analytical rough curves agree with the simulations, it is not good as smooth curves. Both rough substrate curves of the cutting force, FH, intersect at the point of D only. The relative average error between both curves are less than 20%. When the blade rake is 45°, the results of the analytical and simulation smooth and rough curve of forces FH are drawn in Figure 12b. The trends of the smooth simulations agree with the analytical curve also. Both smooth substrate curves of force FH intersect at three points-E, F and G. Both rough substrate curves of force FH intersect at three points also-H, I and J. The relative average errors between smooth and rough curves are less than 10%. Overall, the relative average error is less than 15%. The average error between both results is because of the assumption of the mathematical model. The error is also related to meshing the model, the number of units, and the blade speed.

Conclusions
In this paper, a marine steel pile cleaning robot is designed to analyze the process of removing barnacles attached to a rough substrate. In addition, the mathematical model of cutting force is put

Conclusions
In this paper, a marine steel pile cleaning robot is designed to analyze the process of removing barnacles attached to a rough substrate. In addition, the mathematical model of cutting force is put forward for the barnacle scraping process, which is based on the right angle cutting theory and the Peel Zone method. Based on the verification, the following conclusions can be obtained: (1) Through the finite element simulation, the mathematical analysis model is verified, and the verification results show that the relative average error of the mathematical model is less than 15%. During the operation of barnacle scraping, the mechanical analysis process can be presented to estimate the horizontal cutting force in order to optimize the angle of the scraping blade for the cleaning robot design. (2) During the scraping process, the blade rake angle and substrate roughness have a big effect on the horizontal cutting force. The blade rake angle could be recommended to [30 • , 60 • ]. It could be seen that the smaller the blade rake angle, the greater the horizontal cutting force needed to clean up the barnacles, Additionally, the rougher the substrate is, the greater the horizontal cutting force required. Finally, it is recommended that a 60 • blade rake angle is more suitable for the cleaning robot design.
In the next stage, further research is required to select the suitable conditions and methods for the experiment. Firstly, the samples of marine fouling are multi-sample symbiosis on the actual marine steel piles. There is no single sample condition available for the experiment. The typical objects are required for experiment under the conditions of multi-sample symbiosis. Secondly, a statistics model is required to represent the actual condition of fouling and control the statistical parameters to approximate the actual situation. Finally, combining the cutting force model and statistic model, the total cutting force of the cleaning robot can be predicted and the results can be compared with the experiment. For example, we can select a steel plie with a typical barnacle distribution (with regard to sample concentration in unit area and sample size percentage), input these data into the statistics and cutting force combined model to predict the total cutting force, and compare with experiment results. With this comparison, the model can be further improved to minimize the prediction errors to support the clean robot design.

Conflicts of Interest:
The authors declare no conflict of interest.
Appendix A   Table A1. The parameters in the formula.

Symbol
Significance Unit d 1 The bottom diameter of the barnacle geometrical model mm d 2 The top diameter of the barnacle geometrical model mm h 1 The average height of one-year-old barnacle mm h 2 The