Sage Journals: Discover world-class research

Abstract

For developing a climbing robot which is used to inspect and maintain a wind power tower, the magnetic unit is one of the key components. Based on analysis of the working conditions of the robot, the approach in this paper is to use four common kinds of magnetic units for adapting to the conical surface. The magnetic circuit of these units is given by theory analysis and is simulated using ANSYS. Moreover, the magnetic force is analysed in detail and the results prove that the magnetic force is greatly influenced by the gap between the unit and the wall surface. In this paper, the design procedures and selection criteria based on the analytical results are given. Meanwhile, these units are compared with each other with the aid of ANSYS. From the results of this comparison, it can be ascertained that the unit using Installation C has the better performance. Furthermore, the effectiveness of the magnetic unit using Installation C is verified by a prototype. The simulations and experiments show that the magnetic unit can allow the robot to keep in contact with the conical wall surface as well as the plane wall surface.

Keywords

Climbing robot magnetic units wind power tower

1. Introduction

As specialized robots, climbing robots have so far been studied because they work in high altitude environments on varied wall surfaces. These robots are widely and effectively used in many industrial environments instead of human beings such as in the inspection of nuclear waste and oil store tanks [1 –4], maintenance of boiler water-cooling tubes [5], sand-blasting and painting in the ship building industry [6], cleaning high building surfaces [7 –12] and rescuing in emergency situations [13–14].

Traditional climbing robots can be classified into four types according to the adhesion methods: vacuum or negative pressure robots, robots with propellers, bionic adhesion robots and magnetic adhesion robots [15]. The adsorption function of vacuum or negative pressure robots is accomplished by the pressure difference inside and outside of the sucker. They can work on various wall surfaces, but the demand for smoothness is high. Robots with propellers take advantage of the high-speed airflow produced by the propeller which means the robot inclines toward the wall surface. While they do not have leakage problems and can climb on wall surfaces of various shapes and materials, they have the shortcoming of annoying noise, large size and inefficiency. Bionic adhesion robots imitate the adhesion methods of geckos or snails. They have the advantages of low power demand and novel structure, but they are of low load capacity and are limited by the development of biology, material and microfabrication techniques, etc. Magnetic adhesion robots make use of the magnetic force between a magnet and an iron wall surface. Although the magnet unit of the robot can easily adhere to the iron wall surface, it cannot adapt to anomalous surfaces stably. So it is important to design an adhesion mechanism for these robots.

For the purpose of inspecting and maintaining a wind power tower, several conditions should be considered when designing a wall climbing robot. Firstly, the payload of the robot is as large as possible because it not only carries its own weight but also the work device. Secondly, it should be capable of overcoming the adverse effects caused by strong winds, ash and welding areas, etc. Thirdly, the robot must be qualified to work on a wall surface with variable sections because the surface is conical. Finally, it should be able to climb in portrait orientation and landscape orientation to detect the defects of the vertical and horizontal welding seams inon the tower. The appropriate adsorption force is one of the basic requirements for the robot. If the magnetic force is too weak, the climbing robot cannot adhere to the wall surface. However, if the magnetic force is too strong, the power consumption would be too high and the mobility would be reduced. Much research effort has been made to improve the magnetic adsorption units. Xueshan Gao, Dianguo Xu and Yan Wang et al. presented a kind of special magnetic block structure which was used in their multifunctional robot to maintain boiler water-cooling tubes [16]. Weimin Shen, Jason Gu and Yanjun Shen presented the design of a permanent magnetic system for a wall climbing robot [17]. Yao Pingxi and Li Dewei introduced a new permanent-magnet adhesion device of an adjustable pole for their wheel-type robot [18]. Yi Zhengyao, Gong Yongjun and Wang Zuwen et al. analysed the magnetic sucking mechanism unit of a large load wall climbing robot [19]. Zeliang Xu and Peisun Ma presented a permanent magnetic sucker mechanism used for a wall-climbing robot which measured oil tank volumes [20]. At present, these magnetic units can be applied to plane wall surfaces or arc wall surfaces with a large radius. But, for executing the task on a wind power tower, the unit has difficulty in adhering to the surface with a small radius and working on the high-raised tower carrying a heavy operating device. So the question of how to design a magnetic adhesion unit which has strong adsorbability and adaptability is very important for developing the inspection robot. We will focus on the unit which uses the least magnets to gain the biggest magnetic force. A unit which has prominent integrated performance is put forward.

In this paper, the selection criterion of magnetic unit is given by the theory analysis and simulation. The paper is organized as follows. The force analysis and force relation of the robot on the wall surface is explained in Section 2. In Section 3, the common structures of the magnetic unit mounted on the climbing robot are discussed. In Section 4, the unit is analysed by theory analysis and simulation, and compared by using ANSYS. The stability and efficiency of the chosen magnetic unit are verified by experiments in Section 5. In Section 6, the conclusions and future works are discussed.

2. Force analysis

The steel wind power tower has a conical wall surface, the height of which is 70–80m and the radius changes from bottom to top in the range of 10m to 3m. When the robot climbs on such a wall surface, its trajectory is a conical helix as shown in Fig.1. There are two major risks when it is doing so: first, the robot may fall over from the wall and second, sliding along the wall. In each case the robot will not stay on the wall safely. Hence it is necessary to analyse these two situations in particular. The analyses are shown in Fig.2.

Figure 1.

Robot's trajectory

Figure 2.

Force analysis of the robot

At y direction, the following equation can be attained: $\begin{array}{l} G_{y} + (N_{1} + N_{2} + \dots + N_{m - 1} + N_{m}) - \\ - (F_{1} + F_{2} + \dots + F_{m - 1} + F_{m}) = 0 \end{array}$ (1)

where

F_i is the magnetic force provided by the magnetic unit numbered i; N_i is the support force of the magnetic unit numbered i.

G_y is the gravity at y direction and it can be expressed as follows: ${\begin{cases} G_{x} = \frac{G}{2} \cos θ \\ G_{y} = - \frac{G}{2} \sin θ \end{cases}$

The magnetic force provided by each magnetic unit is the same due to the same magnets and the same magnetic circuits. Nevertheless, the support force acting on the bottom of the track is bigger than that on the top. Assume that there is a relationship as follows: ${\begin{cases} N_{2} = N_{1} + ξ \\ N_{3} = N_{2} + ξ \\ \begin{matrix} ⋮ & ⋮ & ⋮ & ⋮ \end{matrix} \\ N_{m - 1} = N_{m - 2} + ξ \\ N_{m} = N_{m - 1} + ξ \end{cases}$

There is no relative motion between the magnetic units and the wall surface, so static force f_s acts on the robot. Then the following relationship can be attained: $G_{x} = f_{s} \leq (N_{1} + N_{2} + \dots + N_{m - 1} + N_{m}) {μ^{'}}_{\max}$ (2)

Referring to Eq. (1) and Eq. (2), in order to overcome the gliding tendency, the magnetic force F_i should satisfy the following condition: $F_{i} \geq \frac{G \cos θ}{2 {μ^{'}}_{\max} m} - \frac{G \sin θ}{2 m}$ (3)

To the bottom of the track there is the torque balance equation as follows: $\begin{array}{l} F_{i} (l_{1} + l_{2} + \dots l_{m - 1} + l_{m}) + \frac{G}{2} \sin θ \frac{(m - 1) l}{2} = \\ = (N_{1} l_{1} + N_{2} l_{2} + \dots N_{m - 1} l_{m - 1} + N_{m} l_{m}) + \frac{G h \cos θ}{2} \end{array}$ (4)

where

l_i is the distance between the bottom of the track and the magnetic unit numbered i; h is the height of the robot's centre; the distances between each magnetic unit are the same and they are assumed as l.

In order to prevent the robot from overturning, the support force between the wall surface and the robot should be bigger than zero. Therefore F_i should satisfy the following condition: $F_{i} \geq \frac{2 G h \cos θ - G (m - 1) l \sin θ}{2 m (m - 1) l}$ (5)

Eq. (3) and Eq. (5) show the conditions which the magnetic force should satisfy when the climbing robot makes itself adhere reliably to the tower wall. The force needed is influenced by conical angle θ and the number of the magnetic units adhering to the wall m.

3. Common magnetic units

In order to provide enough adsorption force, the magnetic flux of units should flow through the iron wall surface rather than the gap. There are four types of magnetic units that can meet the demand.

The magnetic unit using Installation A is shown in Fig.3. There is one magnet in the unit. Both poles of the magnet are fixed by a yoke iron with high permeability. The bottom of the magnet is fixed by a copper block or other materials with low permeability and the top of the magnet adheres directly to the wall surface.

Figure 3.

Magnetic unit using Installation A

As seen in Fig.4, by using Installation B, there is one magnet fixed by a yoke iron. One pole of the magnet adheres to the wall surface and the other is fixed by the yoke iron.

Figure 4.

Magnetic unit using Installation B

In Installation C shown in Fig.5, there are several magnets and each magnet is installed with the same pole. The bottoms of the magnets are fixed by a copper block or other materials with low permeability and the top of the magnets adhere to the wall surface directly. Each magnet is separated by a yoke iron with high permeability.

Figure 5.

Magnetic unit using Installation C

Fig.6 shows the magnetic unit using Installation D. There are several small magnets in one magnetic unit. One pole of the magnets is used to contact with the wall surface and the other pole is fixed by a yoke iron. Copper blocks or other materials with low permeability are used to separate magnets.

Figure 6.

Magnetic unit using installation D

4. Analyses and comparisons of magnetic units

4.1 Theory analyses of magnetic units

Usually, the magnets used in these magnetic units are NdFeB which has good magnetic capability, such as great coercivity, good magnetic property consistency and a lower temperature coefficient. As shown in Fig.7, a permanent magnet will work on the demagnetization curve when the magnetizing field is reduced. Nevertheless, when the demagnetizing field is reduced, the magnetic field recovers along the recovery curve with a small radian which can be simplified as a line. Fig.8 shows that the recovery curve and the demagnetization curve of NdFeB can be simplified as the same line on account of their coincidence [21].

Figure 7.

Performance of general permanent magnets

Figure 8.

Performance of NdFeB

4.1.1 Theory analysis of magnetic units using Installation A and C

The magnetic unit using Installation A is a single-loop unit while Installation C is a multiloop unit. Installation A can be seen as the simplification of Installation C, so the analysis of Installation A can be applied for Installation C equally. Fig.9 shows the magnetic circuit of Installation A. When the robot works, there are three possible states. Most of the magnetic flux flows through the iron wall surface when the unit adheres to the wall surface, as shown in Fig.9 (1). When the magnetic unit is out of contact with the wall surface, as shown in Fig.9 (2), some magnetic flux flows through the iron wall surface whilst the other flux leaks to the gap between the magnet and the wall. As shown in Fig.9 (3), all of the magnetic flux flows through the gap when the magnetic unit is separated from the tower wall.

Figure 9.

Magnetic circuit of Installation A

Looking back at Fig.8, when the magnetic unit contacts with the wall surface, all of the magnetic flux flows through the wall surface and the operating point can be described as E(B_r,0). Some magnetic flux leaks to the gap between the magnetic unit and the wall when the unit is out of contact with the wall surface, so the operating point in this situation can be seen as D(H₂,B2). When the magnetic unit is separated from the wall surface, the corresponding operating point can be assumed as A(H',B'). In other words, the operating point moves between A and E when the robot climbs on the wall surface.

The relationship between the magnetic force F_a and the gap is shown as follows: [21–22] $F_{a} = \frac{B_{g} H_{g}}{2} S_{g} = \frac{B_{g}^{2}}{2 μ_{0}} S_{g}$ (6)

where

B_g – Magnetic induction in gap

H_g – Magnetic field intensity in gap

S_g – Gap area

μ₀ – Vacuum magnetic conductance constant

The operating point of NdFeB is F(H_m,B_m) when the climbing robot moves to a certain location. The magnetic induction in gap can be expressed as follows: $B_{g} = \frac{B_{r}}{\frac{S_{g}}{S_{m}} + (μ_{r e c} μ_{0} + \frac{B^{'}}{H^{'}}) \frac{f L_{g}}{μ_{0} L_{m}}}$ (7)

According to Eq. (6), the magnetic force which acts on the wall surface is shown as follows: $F_{a} = \frac{B_{g}^{2}}{2 μ_{0}} S_{g} = \frac{S_{g}}{2 μ_{0}} {[\frac{B_{r}}{\frac{S_{g}}{S_{m}} + (μ_{r e c} μ_{0} + \frac{B^{'}}{H^{'}}) \frac{f L_{g}}{μ_{0} L_{m}}}]}^{2}$ (8)

where

B_r – The residual magnetic flux density of the magnet

L_m – The length of magnetic pole

L_g – The length of the gap

μ_rec – Recoil permeability

S_m – The area of the magnetic pole

If the magnet used in the unit is as shown in Fig.10, the magnetic force can be expressed as follows: $F_{a} = \frac{2 l a^{'} + l a}{2 μ_{0}} {[\frac{B_{r}}{\frac{2 a^{'} + a}{h} + (μ_{r e c} μ_{0} + \frac{B^{'}}{H^{'}}) \frac{f L_{g}}{μ_{0} a}}]}^{2}$ (9)

Figure 10.

Magnet used in Installation A

When the magnetic unit works on the initial point A, the situation of NdFeB is shown in Fig.9 (3) and the magnetic circuit is open. Yoke irons are fixed on both poles of the magnet and their sections are different from the magnet, therefore, the initial point A of the unit using installation A is shown as follows [23]. $\frac{B^{'}}{H^{'}} = {\begin{cases} \frac{{(\frac{a + 2 a^{'}}{\sqrt{l h}})}^{(1 + 0.05 \frac{a + 2 a^{'}}{\sqrt{l h}})}}{0.41} (a^{'} < l h) \\ \frac{{(\frac{a + 2 \sqrt{l h}}{\sqrt{l h}})}^{(1 + 0.05 \frac{a + 2 \sqrt{l h}}{\sqrt{l h}})}}{0.41} (a^{'} \geq l h) \end{cases}$ (10)

where the unit of B is Gauss and the unit of H is Oe.

It is assumed that there is no leakage flux when the magnetic unit adheres closely to the wall surface and the saturation induction density of the yoke iron is B_s. Then, the following formula can be attained to make the magnetic flux in the iron yoke unsaturated. $a^{'} \geq \frac{B_{r} h}{B_{s}}$ (11)

l, h, a and a' are shown in Fig.10.

4.1.2 Theory analysis of magnetic unit using Installation B

The magnetic circuit of the unit using Installation B is shown in Fig.11. It shows that the magnetic flux which flows through the wall surface is small because of the yoke iron around the magnet. The magnetic force which Installation B provides is small.

Figure 11.

Magnetic circuit of Installation B

4.1.3 Theory analysis of magnetic unit using Installation D

The magnetic unit using Installation D can be simplified as shown in Fig.12. When the unit keeps contact with the wall surface, as shown in Fig.12 (1), all of the magnetic flux flows through the wall surface with high permeability. However, as shown in Fig.12 (2), when the magnetic unit is out of contact with the wall surface, only a portion of magnetic flux flows through the wall surface. The rest of the flux is lost in the gap between the wall and the unit. Fig.12 (3) shows that when the magnetic unit is separated from the iron wall, all of the magnetic flux flows through the gap just like the unit using installation A.

Figure 12.

Magnetic circuit of Installation D

This is similar to Installation A. The operating point is assumed as E(0, B_r) when the robot adheres closely to the wall surface. If there is a gap between the magnetic unit and the wall, the operating point can be seen as D(H₂, B₂). When the robot is separated from the surface, the operating point is expressed by A(H', B'). The operating point is moving between A and E.

The same as in Installation A, the magnetic force of Installation D can be explained as follows.

F_{a} = \frac{B_{g}^{2}}{2 μ_{0}} S_{g} = \frac{S_{g}}{2 μ_{0}} {[\frac{B_{r}}{\frac{S_{g}}{S_{m}} + (μ_{r e c} μ_{0} + \frac{B^{'}}{H^{'}}) \frac{f L_{g}}{μ_{0} L_{m}}}]}^{2}

(12)

If the magnet used in Installation D is shown in Fig.13, the magnetic force is expressed as follows. $F_{a} = \frac{h l}{μ_{0}} {[\frac{B_{r}}{2 + (μ_{r e c} μ_{0} + \frac{B^{'}}{H^{'}}) \frac{f L_{g}}{μ_{0} a}}]}^{2}$ (13)

Figure 13.

Magnet used in the magnetic unit using Installation D

Fig.13 shows that there is a yoke iron between the magnets installed in Installation D. Therefore the effective length L_φ can be seen as zero, i.e., L_φ = 0 [23]. Then the initial operating point can be expressed as follows.

\frac{B^{'}}{H^{'}} = \frac{{[\frac{a (l + h)}{2 l h}]}^{[1 + \frac{0.05 a (l + h)}{2 l h}]}}{0.41}

(14)

The same as in Installation A, the magnetic flux in the yoke iron cannot be saturated. Then, the relationship between the thickness of the yoke iron and the size of magnet is shown as follows.

a^{'} \geq \frac{B_{r} h}{B_{s}}

(15)

Where

The means of B_s, B_r, L_g, L_m, B_g, S_g, S_m, f, μ₀ and μ_rec are the same as in Installation A.

l, h, a and a' are shown in Fig.13.

4.2 Simulation analysis and comparisons of the magnetic units

Fig.14 shows the ANSYS simulations of these units and there is a small gap between the magnetic units and the wall surface. Fig.14 (1) is the simulation of Installation A, Fig.14 (2) is the simulation of Installation B, Fig.14 (3) is the simulation of Installation C and Fig.14 (4) is the simulation of Installation D. Most of the magnetic flux of these units used in Installation A, C and D flows through the wall surface and the leakage is small. Whereas most of magnetic flux of Installation B flows through the yoke iron around the magnet and little of the flux flows through the wall.

Figure 14.

ANSYS simulations of the magnetic circuit of the unit

The magnetic force of the unit is simulated using ANSYS. In addition, the simulation results are compared with the analysis results. The simulation and analysis results of Installation A, C and D are shown in Fig.15 (1), (3) and (4). The simulation result of installation B is shown in Fig.15 (2). Therefore the following issues can be ascertained from Fig.15: the magnetic force of a magnetic unit descends dramatically when the gap increases; the magnetic force of the unit using Installation B is small because the majority of the magnetic flux flows through the yoke iron around the magnet; the magnetic force analysed by theory is a little bigger than simulations, for some influencing factors of magnetic force, such as ash, are neglected.

Figure 15.

Simulation results and analysis results of magnetic units

The magnetic forces of the units using Installation A, B, C and D are compared in Fig.16. The size of the magnets used in these units is the same. In Fig.16, the magnetic force of Installation D is the biggest when the gap is small, but the force drops dramatically as the gap increases. The initial magnetic force of Installation C is smaller than Installation D. However, the influence of the gap is smaller. The magnetic force provided by Installation B is the smallest. This is because most of the magnetic flux flows through the yoke iron rather than the wall surface.

Figure 16.

Comparison of the magnetic units

When the robot with single-loop magnetic units encounters obstacles, the magnetic circuit of the unit would be damaged. Fig.17 (1) and Fig.17 (2) show that when the multiloop magnetic unit encounters an obstacle, although a part of the magnetic circuit is destroyed, high magnetic force can still be attained by other magnets whose circuits are not damaged completely. Hence the multiloop magnetic unit is preferred.

Figure 17.

Single-loop and multiloop magnetic unit encounter an obstacle

For multiloop magnetic units, sufficient magnetic force is provided by Installation C. Moreover, the anti-interference capability and damage resistance capability of Installation C are better than that of Installation D whose magnets are directly attached to the wall surface.

Therefore, the magnetic unit using Installation C is used for the magnetic climbing robot.

5. Prototype and experiment

A robot prototype whose magnetic units are that of Installation C was designed. The prototype is made of aluminium alloy and its weight is 30kg. 5 × 6 × 36 NdFeB magnets whose pole is on the 6 × 36 plane are used in its magnetic unit. The magnetic force is tested in Fig.18 and the result is shown in Table 1. The force of only one unit can achieve 140N, which is strong enough for the robot to keep attached to the wall surface if a number of the units are mounted on the robot moving mechanism.

Figure 18.

Test of one of the magnetic units

Table 1.

Testing and analysis result of the magnetic unit

Testing result (N)	135
Analysis result (N)	145.4

In installation C, as shown in Table 1, the error between the testing result and the analysis result is small -allowable in engineering design. The analysis result is a little bigger than the testing result because the factors influencing magnetic adsorption are simplified in the analysis and the wall surface is not very smooth.

The relationship between the magnetic force needed and the number of the unit adhering is shown in Fig.19. The force decreases exponentially when the number of the unit which keeps contact with the wall surface increases.

Figure 19.

Relationship between the magnetic unit amount and adhering force

In the prototype, there are six magnetic units in one row track which keep in contact with the wall surface due to the structure. Referring to the relationship shown in Fig. 15, the gap can be reached at 3mm, so the adaptability of the robot on the surface could be promoted.

In the laboratory, the maximum radius of the tower is 10m, which is sufficiently large compared to the size of the robot. Therefore it is reasonable to assume the tower surface as a plane. As for the smallest radius in the area of the tower, this is simplified as a cylindrical wall with a radius of 2m. The experiments are shown in Fig.20. Fig.20 (1) shows that the prototype can adhere closely and steadily to the wall surface. In order to detect the horizontal as well as the vertical welding seam, the robot should be able to climb horizontally and vertically and the experiments are shown in Fig.20 (2) and Fig.20 (3). Fig.20 (2) and Fig.20 (3) show that the prototype can overcome the affects of its weight to keep in contact with the cylindrical iron surface.

Figure 20.

Experiments of the robot prototype in the laboratory

6. Conclusions and future works

Based on inspection and maintenance of a wind power tower, the specially designed magnetic units for the climbing robot have been described. In order to attain the optimal magnetic force with the fewest magnets, the magnetic unit should be made the most of the magnetic flux flows through the wall surface, so there are four common types of magnetic units which satisfy the condition mentioned above.

The analyses of the magnetic units have been described comprehensively. Installation A and B are single-loop, and the magnetic force provided by Installation B is weaker than others because the magnetic flux leakage is the greatest. Installation C and D are multiloop magnetic units with better performance than the single-loop unit. The initial magnetic force provided by D is the stronger of the two. But the force of Installation C is sufficient for climbing action. The magnetic unit using Installation D is easily damaged and influenced by the environment. Hence, the optimal choice for the climbing robot magnetic unit is Installation C. Through the experiments in the laboratory, it has been proved that the robot prototype with Installation C performed effectively and reliably.

Further work needs to improve the stabilization and adaptability of the magnetic unit in continuous practical cases.

Footnotes

7. Acknowledgments

This work was supported by the National Nature Science Foundation of China (grant no. 60975070) and the State Key Laboratory of Robotics and Systems (HIT) (grant no. SKLRS-2010-ZD-04).

References

Eich

and Vogele

(2011) Design and Control of a Lightweight Magnetic Climbing Robot for Vessel Inspection. 2011 19th Mediterranean Conference on Control and Automation, Corfu, Greece. 1200–1205.

Zhang

Houxiang

Zhang

Jianwei

Liu

Rong

Wang

Wei

and Zong

Guanghua

(2005) Design of a Climbing Robot for Cleaning Spherical Surfaces. 2005 IEEE International Conference on Robotics and Biomimetics, Shatin, N.T., China. 375–380.

Sabater

J.M.

Saltaren

R.J.

Aracil

Yime

and Azorin

J.M.

(2006) Teleoperated parallel climbing robots in nuclear installations. Industrial Robot. 33: 381–386.

Love

Kalra P

and Meng

(2006) A wall climbing robot for oil tank inspection. 2006 IEEE International Conference on Robotics and Biomimetics (ROBIO), Kunming, China. 1523–1528.

Gao

Xueshan

Jiang

Zhihong

Gao

Junyao

Dianguo

Wang

Yan

and Pan

HuanHuan

(2008) Boiler maintenance robot with multi-operational schema. 2008 IEEE International Conference on Mechatronics and Automation(ICMA2008), Takamatsu, Japan. 610–15.

Zhengyao

Yongju

Gong

Zuwen

Wang

and Wang

Xingru

(2009) Development of a wall climbing robot for ship rust removal. 2009 IEEE International Conference on Mechatronics and Automation (ICMA), Changchun, China. 4610–4615.

Zhihong

Zhu

Jize

Jinmin

Peng

Jun

and Xueshan

Gao

(2011) Mobile platform of miniature wall-climbing robot for building surface inspection. Journal of Mechanical Engineering. 47: 49–54.

Hillenbrand

Schmidt

and Berns

(2008) CROMSCI: Development of a climbing robot with negative pressure adhesion for inspections. Industrial Robot. 35: 228–237.

Jun

Xueshan

Gao

(2010) Adsorption performance of sliding wall-climbing robot. Chinese Journal of Mechanical Engineering. 23: 733–41.

10.

Jun

Xueshan

Gao

Ningjun

Fan

Kejie

Zhihong

Jiang

and Zhijian

Jiang

(2009) BIT climber: A centrifugal impeller-based wall climbing robot. Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation, Changchun, China. 4605–4609.

11.

Hirose

Nagakubo

and Toyama

(1991) Machine that can walk and climb on floors, walls and ceilings. Fifth International Conference on Advanced Robotics. Robots in Unstructured Environments (ICAR), Pisa, Italy. 1: 753–8.

12.

Akihiko

Nagakubo

and Shigeo

Hirose

(1994) Walking and running of the quadruped wall-climbing robot. Proceedings – IEEE International Conference on Robotics and Automation, San Diego, CA, USA, 2: 1005–1012.

13.

Liu

Shuyan

Gao

Xueshan

Kejie

Jun

and Duan

Xingguang

(2008) A small-sized wall-climbing robot for anti-terror scout. 2007 IEEE International Conference on Robotics and Biomimetics (ROBIO), Yalong Bay, Sanya, China. 1866–1870.

14.

Eich

Grimminger

and Kirchner

(2008) A versatile stair-climbing robot for search and rescue applications. 2008 IEEE International Workshop on Safety, Security and Rescue Robotics, Sendai, Japan. 35–40.

15.

Song

Young Kouk

Lee

Chang Min

Koo

Ig Mo

Tran

Duc Trong

Moon

Hyungpil

and Choi

Hyouk Ryeol

(2008) Development of wall climbing robotic system for inspection purpose. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, Nice, France. 1990–1995. 2008.

16.

Xueshan

Gao

Dianguo

Yan

Wang

Huanhuan

Pan

and Weimin

Shen

(2009) Multifunctional robot to maintain boiler water-cooling tubes. Robotica. 27: 941–948.

17.

Shen

Weimin

and Shen

Yanjun

(2005) Permanent magnetic system design for the wall-climbing robot. International Conference on Mechatronics and Automation, ICMA, Niagara Falls, Canada. 2078–2083.

18.

Pingxi

Yao

and Dewei

(2009) The magnetic field analysis and optimization of permanent-magnetic adhesion device for a novel wall-climbing robot. International Technology and Innovation Conference 2009, ITIC, Xi'an, China. 5: 556–561.

19.

Zhengyao

Yongjun

Gong

Zuwen

Wang

Xingru

Wang

and Jie

(2010) Analysis on turning stress states of magnetic Sucking Mechanism Unit of a Large Load Wall Climbing Robot. 2010 International Conference on Measuring Technology and Mechatronics Automation, ICMTMA, Changsha City, China. 570–3.

20.

Zeliang

and Ma

Peisun

(2002) A wall-climbing robot for labelling scale of oil tank's volume. Robotica. 20: 209–212.

21.

Zhao

Han

and Tian

Jie

(2009) Magnet Mechanics (in Chinese). Beijing: Higher Education Press.

22.

Lin

Qiren

and Zhao

Youmin

(1987) Magnetic Circuit Design Principle (in Chinese). Beijing: China Machine Press.

23.

Zhong

Wending

(1987) Ferromagnetics (in Chinese). Beijing: Science Press.