### Permanent magnetic wheel system for water-jetting wall-climbing robot

**Design of permanent magnetic wheel-type adhesion-locomotion system for water-jetting wall-climbing robot**

Regular surface-maintenances are necessary for high structures to increase service life. The traditional manual operation has shortcomings like limited maneuverability, poor operating quality, low operating efficiency, and high risk of physical harm, which makes it urgent to develop wall-climbing robot for carrying out surface-maintenances of high structures with high efficiency, low cost, and good protection of operators. In this article, we have developed a wheeled wall-climbing robot that uses a permanent magnet adhesion system to climb on large steel surfaces. Wheel traction to avoid slippage is increased by using inflated rubber tire while maintaining a desired air gap for the magnet system. Research is directed at designing a lightweight magnet system to provide an optimum adhesion force and at determining required tire pressures to maintain a specified air gap between the magnets and the surface.

Keywords : Wall-climbing robot, surface cleaning, water-jet cleaning, permanent magnet adhesion optimization, adhesion-locomotion

**Introduction**

Ships, offshore platforms, petroleum storage tanks, and sea-crossing bridges are important structures to industry and economy. They make sure global distribution of products, energy supply, and transportation in the world, which is the basics of modern life.1 Currently, those structures are as high as dozens of meters, even over 100 m. In addition, they are usually located at the seaside or directly operating in the sea. This special environment causes the structures suffered from many problems, such like corrosion, perish, and biofouling.2,3 Taking ships, for example, biofouling not only weakens strength of hull but also leads to more fuel consumption, which can get an increment as much as 25%–30%.4 In order to keep them working for longer time, it is very necessary to conduct regular surface-maintenances to those high structures at some intervals, including non-destructive testing, removal of rust, and stripping of corrosion.

Traditionally, the surface-maintenances are carried out manually by operators. Since the target surface is always located at a high altitude, it is a major challenge of accessing to the target surface, especially with heavy operating tools. Usually, scaffolding and aerial working platform are used to help operators to reach the desired area, which causes an ineffective preparation process with additional cost of time and money. Moreover, the manual surface-maintenance operation has other critical shortcomings, such like limited maneuverability, poor operating quality, low operating efficiency, and high risk of physical harm.5–9 Additionally, in some cases like nuclear industry and chemical industry, the working environments could cause serious harm to operator’s health.10–12 Therefore, developing a wall-climbing robot to carry out surface-maintenances of high structures with high efficiency, low cost and good protection of operators is extremely necessary.

Technologies of wall-climbing robots have been researched for a few decades.5–9,13–39 Considering the high working surfaces, adhesion-locomotion system plays an important role in a wall-climbing robot. On one hand, it provides an adhesive force to produce enough friction for sustaining the weight of robot and payloads, which should not be too great to make robot stuck in place or locomotion jerkily. On the other hand, it provides a climbing movement on the surface with high velocity and maneuverability. Obviously, adhesion-locomotion system determines the operating performance and payload capacity of a wall-climbing robot, which is the research focus in this field. Until today, there are different adhesion-locomotion principles for wall-climbing robots. Considering the surface-maintenances requiring good capacity of payload, high speed, and maneuverability, permanent magnetic wheel-type adhesion-locomotion system is the most preferred choice in the design of wall-climbing robot, which works on ferrous surfaces.1,8,38 Cai et al.38 presented a wall-climbing robot with three magnetic wheels. The magnetic wheel includes two permanent magnetic rings magnetizing radially in opposite directions, a copper ring and a yoke. The arrangement constitutes a magnetic circuit with most of the magnetic flux flowing through the surface and then produces a larger adhesive force compared to a whole piece of permanent magnetic ring. Easily to understand, only the part near the surface is effective to produce adhesive force in a magnetic ring, which means most part of the magnetic ring does not function but increases the weight of robot. To make best of the magnet, Howlader and Sattar8 mounted flat permanent magnets beneath the chassis. Without magnetic flux concentrator, quite a part of magnetic flux leaks into the air, which is still not good enough for getting a large adhesive force with a lightweight magnet. To solve this problem, Ross et al.5 arranged permanent magnets in a Halbach array. This array can form a one-sided strong magnetic field and then produce a large adhesive force. However, considering the adhesive force as large as several thousand newtons, it is not convenient to assemble permanent magnets with a Halbach array, which costs a lot of time and money. Furthermore, the above wheels all had a hard outer-part and caused a small deflection under the contact force from the surface, which leads to a small friction and makes the robots easily to slip.

In this article, a permanent magnetic wheel-type adhesion-locomotion system for water-jetting wall-climbing robot, which uses the high-velocity water jet to clean rust, biofouling, and corrosion,40 is presented. An annular-sector shaped magnetic adhesion system is used, which performs well in producing a large adhesive force with a lightweight magnet. In addition, a pneumatic tire is employed to increase the friction between wheel and surface, which is much lighter than solid one. However, there is a coupling interrelationship between the magnetic adhesion system and the pneumatic tire, which must be considered in order to determine two important designed parameters of wall-climbing robots, initial air gap and inflation pressure. Here, initial air gap is used to set the assembling dimensions between the magnetic adhesion system and the robot, and inflation pressure is used to set the air pressure inside the tire before robot climbing on the surface. Clearly, the adhesive force produced under an initial air gap causes a tire deflection under the inflation pressure, which then reduces the air gap and increases the adhesive force. Afterward, the tire deflection decreases the air gap and obtains a larger adhesive force, which will increase the tire deflection. At the same time, tire deflection compresses the air inside the tire and leads to a rise of air pressure, which will make the tire hard to deflection. This process will not stop until the adhesive force and the tire deflection gets balanced. Apparently, since adhesive force and tire deflection are all changing in nonlinear patterns, the above interaction process must have a strongly nonlinearity, which brings difficulty to determine the values of initial air gap of magnet and inflation pressure of tire. To the best knowledge of authors’, there are few researches about the above process.4–39

In the following, a structure of the wall-climbing robot is introduced first. With consideration of avoiding slip and overturn, a mechanical model of robot is proposed to get the theoretical value of adhesive force. Afterward, an optimization of magnetic adhesion system is carried out with the help of simulation software Ansoft Maxwell, which determines the dimensions of magnetic components. Then, the curves of adhesive force under different air gaps and tire deflection under different normal pushing forces are obtained based on experiments. With the above two curves, the working point of permanent magnetic wheel-type adhesion-locomotion system can be determined, which is used to set the values of initial air gap and inflation pressure. Finally, the design of permanent magnetic wheel-type adhesion-locomotion system is proven feasible by robot prototype experiments in the lab and in the shipyard.

**Robot structure and its mechanical model**

As demonstrated by Figure 1, water-jetting wall-climbing robot has two adhesion-locomotion systems of the same structure, which includes two wheels and a permanent magnetic adhesion system attached to the wheel support, whose details are shown in Figure 2, distributed on both sides and two universal wheels amounted at the front. There is a small permanent magnetic adhesion system amounted between the universal wheels, which has function of avoiding overturning from the surface. And a vacuum shroud is mounted in the center of the robot and completes an enclosed environment-friendly cleaning process with the help of water-jet nozzles inside, which has a inclination angle of 15° and vacuum pump located on the ground. As demonstrated by Figure 2, two coaxial driving wheels are arranged outside and encloses a space containing servo motor, reducer, and magnetic adhesion system inside. This arrangement has a compact volume and is helpful to protect motor, reducer, and magnetic components from dust and collision.

To determine the value for required adhesive forces, a free body diagram of robot is built on the boundary conditions ensuring that robot operates on the surface without slipping or overturning. As demonstrated by Figure 3, equations (1)–(3) are obtained

??1+??2+??−?sin?=?1+?2+??+?? (1)

?cos?=??1+??2+?fs (2)

?cos?×ℎ+?sin?×?1+(??+??−??)?2+(?2−??2)?3<0 (3)

where Ff1 is the sum of friction forces between driving wheels and surface, Ff2 is the sum of friction forces between universal wheels and surface, Ffs is the friction force between vacuum shroud and surface, Fm1 is the sum of adhesive forces from magnetic adhesion systems at driving wheels, Fm2 is the adhesive force from magnetic adhesion system at universal wheels, Fj is the reaction-propulsion force from water jets obtained by equation (4),20Fv is the vacuum suction force at vacuum shroud obtained by equation (5), G is the gravitational force acting on the robot, N1 is the sum of support forces at driving wheels, N2 is the sum of support forces at universal wheels, Ns is the support force at vacuum shroud, and β is the inclination angle between surface and vertical direction. To describe clearly, four points are defined in Figure 3. Point A is the contact point between driving wheel and surface, point B is the contact point between universal wheel and surface, point C is the point where Ns acts, and point O is the gravity center of robot. Therefore, three distances along the surface are defined as follows: l1 is the distance between points A and O, l2 is the distance between points A and C, and l3 is the distance between points A and B. And h is the vertical distance from point O to surface

??=0.745???⎯⎯⎯√

(4)

??=??24??

(5)

where d is the inner diameter of vacuum shroud, pj is operation pressure of water jet, pv is negative air pressure in the vacuum shroud, and Q is the flow rate of water jet. Here, the above pressures have units of MPa and flow rate have units of L/min.

Given the statically indeterminate problem exiting, equations (6)–(8) are obtained

??1<?1?1

(6)

??2<?2?2

(7)

?fs<???? (8) where μ1 is the static friction coefficient between driving wheel and surface, μ2 is the static friction coefficient between universal wheel and surface, and μs is the static friction coefficient between vacuum shroud and surface. To simplify the calculation, it is assumed that the above three static friction coefficients have the same values and all are represented by μ. Then, with equations (1), (2) and (4)–(8), equation (9) can be derived and is used to determine the total values of adhesive forces to avoid slip ??1+??2>?cos??+?sin?+0.745???⎯⎯⎯√−??24??

(9)

When the robot is about to overturn, it is known that value of N2 equals zero and value of Ns is very small, which can be seen as zero. According to equation (3), equation (10) is derived and determines the value of adhesive force from magnetic adhesion system at universal wheels to avoid overturn

??2>?cos?×ℎ+?sin?×?1+(0.745???⎯⎯⎯√−??24??)?2?3

(10)

In practice, when the robot just adsorbs on the surface, the negative suction of vacuum shroud does not work because the air pressure in the vacuum shroud is zero. It requires more adhesive force than operating mode for robot to avoid slip and can be used to determine the values of Fm1 and Fm2 approximately, which actually increases the reliability of design. Then, equations (9) and (10) can yield equations (11) and (12)

??1+??2=?cos??+?sin?+0.745???⎯⎯⎯√

(11)

??2=?cos?×ℎ+?sin?×?1+0.745???⎯⎯⎯√×?2?3

(12)

Equations (11) and (12) yield

??1=?cos?(?3−?ℎ)??3+?sin??3−?1?3+0.745???⎯⎯⎯√?3−?2?3

(13)

With the help of MATLAB, solutions of equations (12) and (13) can be obtained as illustrated by Figure 4. Here, values of some parameters are listed in Table 1 and the value of β varies from zero to 90°. Clearly, Fm1 has a maximum value of 2503.2 N when β is 26° and Fm2 has a maximum value of 719.5 N when β is 32.09°. Therefore, the design goal of magnetic adhesion systems can be determined: the adhesive force from one magnetic adhesion system at driving wheels should be about 1252 N and the adhesive force from the small magnetic adhesion system at universal wheels should be about 720 N. With the above design goal, design and optimization of magnetic adhesion system can be carried out. Since the two above magnetic adhesion systems have similar structures, only the study of magnetic adhesion system at driving wheels, which is larger and heavier, is involved in the article for brevity. Without special note, the term magnetic adhesion system refers to that mounting at driving wheels in the following.

**Design of magnetic adhesion system**

Figure 5 shows the designed magnetic adhesion system. It includes four pieces of permanent magnets, one aluminum magnetic-flux insulator, and one yoke. The permanent magnets are separated into two groups by the magnetic-flux insulator. As demonstrated in Figure 6, the magnetic-flux insulator forces the magnetic flux flow from one group of permanent magnets, through surface with a ferromagnetic material, to the other group of permanent magnets while not flowing from one group directly into the other group. Moreover, the yoke concentrates most of the magnetic flux into the circuit. This structure makes sure a rather large adhesive force produced.

In this part, the aim is to obtain an optimal design of magnetic adhesion system, which could produce an adhesive force of 1252 N to make robot climb on the surface normally with a lightweight magnet. Here, an index γ is introduced to evaluate the performance of magnetic adhesion system, which equals the ratio of adhesive force to mass and is defined by equation (14)

?=????

(14)

where Fm is the adhesive force and Mm is the mass.

Considering the robot size and the limited assembly space, some dimensions of magnetic adhesion system are defined as demonstrated in Figure 7. There are three dimensions involved in the optimization, which are the thickness of permanent magnet, the width of permanent magnet, and the thickness of yoke, represented by Tm, Wm, and Ty, respectively. Before finding a proper set of the above three dimensions, the magnet layout and magnetizing direction should be determined for increasing the adhesive force.

**Influence of dimensions of magnetic adhesion system**

It is known that adhesive force is positively associated with dimensions of permanent magnets under the specific magnetic material, air gap, and surface thickness. However, a large permanent magnet has a heavy weight, which requires more adhesive force for making robot climb on the surface normally. Obviously, there should be an optimal set of dimensions of magnetic adhesion system, which could achieve the necessary value of adhesive force and get a light weight at the same time. Based on the determined magnet layout, magnetizing direction and some magnet dimensions mentioned above, influences of Tm, Ty, and Wm on adhesive force and γ are obtained by Ansoft Maxwell, as illustrated in Figures 12–14. To increase adhesive force, the three dimensions increase in the simulation and the other two dimensions remain the same when one target dimension increases. Here, the initial values of Tm, Ty, and Wm are set to 20, 8, and 50 mm, respectively.

As demonstrated in Figure 12, increasing the width of permanent magnet Tm gets a large γ with increasing adhesive force. When Tm is greater than 30 mm, adhesive force increases gradually, which also happens to γ with a Tm greater than 25 mm. Considering the light-weight and required adhesive force, Tm is set to 30 mm, which gets an adhesive force of 1448 N.

Figure 13 shows that increasing Ty increases adhesive force with a saturation occurring at a value of 18 mm and γ decreasing. It is concluded that a thick yoke gets magnet flux more easily flowing through and then increases the adhesive force. However, the increment of adhesive force is not large enough to gets a smaller γ, which indicates that a too thick yoke has little positive effect while leading to a heavy magnet. Moreover, there is a rather small variation of adhesive force as Ty changing. Therefore, the value of Ty keeps the same and is set to 8 mm.

As demonstrated by Figure 14, increasing Wm is very helpful to increase the adhesive force and γ. However, the total dimension of robot limits the value of Wm. Additionally, the width of magnetic-flux insulator should be large enough to leave the mounting space for bolts. Here, the width of permanent magnet is set to 55 mm, which leads to an adhesive force of 1284.5 N.

Based on the above analysis, the final dimensions of magnetic adhesion system are determined, which have a Tm of 30 mm, a Ty of 8 mm, and a Wm of 55 mm. Then, magnetic adhesion system is manufactured and its adhesive force under different air gaps can be measured by a tension testing machine, which are shown by Figure 15. During the measurements of adhesive force, pieces of A4 paper are inserted into the gap. By measuring the thickness of those pieces of paper, the value of air gap is indirectly obtained. To decrease the error, five tests are carried out and the average value is used. However, there are still unavoidable errors occurred. A peak value of adhesive force exists at 11 mm air gap, which leads to a peak value of ratio of experimental result to simulation result. Here, we ignore the influences of peak value and the two adjacent values.

**Conclusion**

This article has proposed a permanent magnetic wheel-type adhesion-locomotion system for water-jetting wall-climbing robot, which comprises of an annular-sector shaped magnetic adhesion system and a pneumatic tire. This type of adhesion-locomotion system could produce a large adhesive force and a large friction force with a small mass. Meanwhile, the coupling interrelationship between magnetic adhesion system and pneumatic tire brings difficulty to determine the values of initial air gap and inflation pressure, which is important for adhesion-locomotion system normally operating in the robot. Combining simulations and experiments, dimension optimization of magnetic component and determination of values of initial air gap and inflation pressure are completed. According to the tests in the lab, the adhesion-locomotion system makes robot prototype climb well with a maximum payload of 62.9 kg, an average velocity of 4 m/min, and an obstacle-crossing capability 6 mm on the surface. Finally, robot prototype is tested in the shipyard, which proves the design of adhesion-locomotion system feasible.

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