`Advances in Mechanical EngineeringVolume 2013 (2013), Article ID 791295, 7 pageshttp://dx.doi.org/10.1155/2013/791295`
Research Article

## Numerical Analysis of the Frictional Characteristics of a Magnetic Suspended Flying Vehicle

School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan, Hubei 430070, China

Received 11 March 2013; Accepted 8 July 2013

Copyright © 2013 Xiaoguang Wang and Yongwei Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper explores a novel approach to the calculation of the dynamic magnetic field under the feedback control and analyzes the frictional characteristics of a magnetic suspended flying vehicle by ANSYS. The numerical calculation result is compared with the experimental data to verify the accuracy and the effectiveness of the approach which suggests a method of the calculation of the dynamic magnetic field under the feedback control by ANSYS. Research results indicate that the equivalent friction coefficient of the magnetic suspended flying vehicle is not a constant which is not only related to the running speed and the weight of the vehicle but also to the resistivity of material of the guide rail and some control parameters of the vehicle. In other words, the smaller the air gap of the vehicle, the smaller the equivalent friction force. The equivalent friction force increases as the running speed increases. With the same air gap and running speed, the equivalent friction force increases with the increase of the weight of the vehicle.

#### 1. Introduction

The magnetic suspended flying vehicle (MSFV) is a novel rail transport mode with a propeller-driven approach that takes the advantage of the magnetic suspension technology to suspend the vehicle body under the guide rail [1]. When the vehicle is running, there is no mechanical friction for noncontact between the vehicle body and the guide rail. The characteristics of which are no wear and no need for lubrication are ideal for high-speed movement. Although MSFV has no friction in the traditional sense, there still exists friction-like phenomenon because of the magnetic field. Paper [2] points out that air resistance and electromagnetic resistance exist when the maglev train is running. It focuses on the calculation of the electromagnetic resistance and the forms of the resistance at different running speeds. Paper [3] indicates that rotor losses have windage loss and iron loss in chief and derives the computing on loss in the state of suspension. Paper [3] also points out that the generation mechanism of the friction loss mainly has eddy Joule heat loss, alternating hysteresis loss and rotational hysteresis loss in the suspension. Paper [4] adopts the laminated rotors of heteropolar magnetic bearing as the mode to extend a method for predicting rotational loss on the condition of suspension. It compares the analytical solution to the experimental data to verify the accuracy. Paper [5] shows the relationship between rotor energy loss with speed and the number of poles and other relevant parameters with theoretical and rundown experimental methods in the state of suspension. Paper [6] proposes the concept of electromagnetic friction and states that the order of magnitude of the electromagnetic friction coefficient measured is 10−2, which is only concerned with the moving speed and not related to the payload by researching on the rotational and translational movement under the support of magnetic suspension with an energy conservation principle. Paper [1] measured the equivalent static friction coefficient and the equivalent kinetic friction coefficient of MSFV with the experimental method and came to the conclusion that the order of magnitude of the equivalent kinetic friction coefficient is 10−4 and the equivalent kinetic friction force is greater than the equivalent static friction force. However, the order of magnitude of the equivalent friction coefficient obtained in papers [1, 6] is greatly different. Paper [7] points out that the energy loss of the rotor is related to the size of air gap, the rotational speed, and the magnetic flux density but independent of the number of magnetic poles which are measured with the experimental method under the support of the same pole radial magnetic bearings. The relation between the power loss, the air gap, the bias current was given in paper [8], which theoretically and experimentally studied the flying vehicle when it ran at a lower speed. It came to the conclusion that the smaller the magnetic flux density in the magnetic bearing, the smaller the power loss. The earlier papers verify the existence of the friction phenomenon theoretically and experimentally in the state of magnetic suspension but do not provide the method of calculating the friction force. Only paper [8] utilized the method of numerical calculation to study the frictional characteristics of MSFV at low speed. Paper [9] includes weight optimization method of rotor and analysis of total power loss in radial magnetic bearing consisting of four, eight, and twelve poles. The total loss characteristics are compared with different number of poles which will decide suitable number of poles for given configuration of bearing system. Paper [10] proposes a novel radial hybrid magnetic bearing (RHMB), which has integrative magnetic pole boards and continuous working air gaps that reduce the hysteresis and eddy-current losses of the traditional homopolar structure.

This paper adopts the method of numerical calculation to explore the frictional characteristics of MSFV. It aims to research the factors that affect the frictional characteristics and their relationship to each other. It also discusses the feasibility of applying ANSYS to calculate the dynamic magnetic field under the feedback control and suggests a method of numerical calculation to compute the dynamic magnetic field under the feedback control.

#### 2. Introduction of the Experimental Device

To simplify the analysis of the experimental results and facilitate the research, the two-degree-of-freedom experimental device is illustrated in Figure 1.

Figure 1: Structure of MSFV.

MSFV is suspended with the electromagnetic force generated by the two U-shaped electromagnets beneath the guide rail. Some main parameters of MSFV are shown in Table 1. The propeller thrust makes the vehicle body move along the horizontal guide rail.

Table 1: Main parameters of MSFV.

The conventional definition of friction is based upon two objects which are in contact with each other. When there is relative movement or motion trend between body surfaces under an external force, the tangential moving resistance generated between the contact surfaces is called friction force and the phenomenon is called friction. The two objects that generate friction are called friction pairs. Referring to the conventional definition of friction, the paper describes the friction phenomenon in the state of magnetic suspension as the equivalent friction and explores the frictional characteristics with the equivalent friction coefficient, the equivalent friction force, and the equivalent friction pairs.

#### 3. ANSYS Computational Model

MSFV has two structurally identical U-shaped electromagnets to suspend the vehicle body. The research is on one of them for generality. Its computational model is shown in Figure 2. In the calculation of the two-dimensional static magnetic field with ANSYS, theoretically the guide rail is fixed, while the vehicle moves in the -axis direction, but in order to simplify the language of APDL analysis, the assumptions are that the vehicle is immobile and the guide rail moves relatively in the -axis positive direction.

Figure 2: Computational model of MSFV.

A one-half model of the vehicle structure was established by applying symmetric boundary conditions in ANSYS, and the magnetic field distribution of electromagnet longitudinal section was simulated by making use of a two-dimensional field. The assumptions are as follows: the guide rail is infinitely long; there is no consideration of the end effect and the magnetic flux leakage of the outer edge of the electromagnet.

Here, air relative permeability , iron core coil relative permeability , and rail materials Q235 in China (GB/T 700) are Fe360A in ISO (ISO 600). Its resistivity is approximately . The material of iron core is a silicon steel sheet. In the calculation, it is ensured that the number and the size of grid are the same each time as shown in Figure 3, which reduces the errors due to the irregularity of the grid.

Figure 3: Meshing of computational model.

It turns out that the magnetic lines of force have changed in the computational process when the MSFV is still or moves as shown in Figure 4. Magnetic field lines of force appear to tilt when the guide rail moves in the -axis direction, and the degree of inclination increases as the moving speed increases.

Figure 4: Distribution of magnetic field lines of force (,  m/s).

The numerical computation results are as follows: when keeping average coil current constant, with the increase of the speed of MSFV, the force in the horizontal direction increases, while the force in the vertical direction decreases. Namely, the force hindering the movement of MSFV is increasing, and the suspended force is decreasing. As shown in Figure 5, it means that the vehicle will drop down. However, the MSFV runs stably in the same suspension air gap because of the feedback control system. The control system will adjust the coil current in real time to keep the force in vertical direction constant, which raises the problem of how to use ANSYS to calculate the dynamic magnetic field under the control of feedback.

Figure 5: Force in the moving flying vehicle.

Paper [11] employs the moving boundary to link the stator with the rotor. The stator is in the stationary coordinate system, while the rotation of the rotor is in the rotating coordinate system, and it uses the main program to calculate the electromagnetic field step by step. A static magnetic field calculation approach is given to achieve the calculation of the dynamic magnetic field step by step. Paper [12] shows the method of the time-stepping finite element that solves the coupling between the control circuit and electromagnetic field, which takes the method of interpolated motion boundary to solve magnetic field computational problems of the rotor.

This paper uses for reference the idea of papers [11, 12] that transforms the calculation of the dynamic magnetic field to the one of a static magnetic field step by step. It converts the calculation of the dynamic electromagnetic field under the real-time feedback control to the calculation of the electromagnetic field under the specific control current and at a specific speed. The specific control current can be obtained on condition that MSFV moves steadily at the specific speed in the same suspension air gap without dropping from the guide rail. As a result, the unpredictable problem of the real-time control current under the feedback control condition can be solved.

#### 4. Analysis of Numerical Calculation Results

##### 4.1. The Static Frictional Characteristics of MSFV

The weight of MSFV is 94 N, and an electromagnet must bear 47 N to guarantee the stable suspension. When MSFV moves at an extremely low speed, the equivalent static friction coefficient that was calculated by ANSYS in the different air gap is shown in Table 2.

Table 2: Parameters of calculation.

In the light of the conventional definition of friction, the transient friction force generated when the flying vehicle at a moment from still to motion is called the equivalent static friction force. The corresponding friction coefficient is called the equivalent static friction coefficient.

##### 4.2. The Frictional Characteristics of MSFV at Low Speed

To ensure the constant suspension air gap of the vehicle in its movement, which means to keep the suspension force of the electromagnetic constant in the vertical direction, it is essential to increase the excitation current in the coil, as shown in Figure 6.

Figure 6: Relation between Coil Current and Speed When MSFV Runs at Low Speed.

The trends of the equivalent friction force are unchanged when the flying vehicle runs in the different suspension air gaps. The equivalent friction force increases as the speed increases, as shown in Figure 7. When MSFV runs at the same speed, the greater the suspension air gap, the greater the equivalent friction force.

Figure 7: Relation between the Equivalent Friction Force and Speed When MSFV Runs at Low Speed.
##### 4.3. Comparison of Calculated and Experimental Results

In order to verify the validity of the calculating method, the paper compared the calculated results with the experimental data in paper [1].

An inclined plane method was used in the experimental measurements of the equivalent static friction force in paper [1] as shown in Figure 8, where is the equivalent friction force measured by experimental methods; is quality of the MSFV; is acceleration of gravity; is tilt angel of the guide rail; a is acceleration of MSFV.

Figure 8: Measurement theory diagram for the equivalent friction force.

The experimental procedures for measuring equivalent static friction force are as follows: the MSFV is magnetic suspended steadily on the guide rail and tilts the guide rail gradually until the MSFV starts to move. Equivalent static friction force was determined at a moment the MSFV from still to motion by visual inspection in the experiment.

The equivalent static friction force did not change significantly when the suspension air gap was changed. The experimental data and the calculated results by ANSYS are shown in Table 3. They match well with each other. Compared with Table 3, equivalent static friction force has small variations when MSFV is suspended with different air gaps. Therefore, the change of equivalent static friction force cannot be observed by visual inspection in the experiment.

Table 3: Experimental and calculated equivalent static friction force.

The experimental procedures for measuring equivalent friction force are as follows: the MSFV is magnetic suspended steadily on the guide rail, tilts the guide rail to a certain angel, and lets the MSFV slides down freely under the action of the gravity just as shown in Figure 8.

There is a dynamic equation:

The equivalent friction force can be calculated if the acceleration and tilted angels are measured.

Paper [1] shows the relation between displacement and time with different air gaps in the experiment, as shown in Figure 9. The maximum speed of the experimental vehicle was 0.7 m/s.

Figure 9: Relation between displacement and time.

The smaller the air gap, the farther the flying vehicle travels at the equal time. It shows that the smaller the air gap, the smaller the equivalent frictional resistance. The experimental results agree with the ANSYS calculation results. The equivalent frictional resistance is gradually increasing with the increase of the air gap.

Paper [8] researches MSFV when it moves at a speed varying from 0 to 0.7 m/s and collects the average current in the coil with the different air gaps. This paper calculates the average coil current in the moving vehicle with speed ranges from 0 to 0.7 m/s. The comparison is in Table 4.

Table 4: Average coil current with different air-Gap at low speed.

It can be seen from Table 4 that the average current calculated in the coil matches well with the one measured experimentally when the flying vehicle runs at low speed.

The experimental results of papers [1, 8] verify that it is feasible to convert the calculation of the dynamic electromagnetic field under the real-time feedback control to the calculation of the static electromagnetic field under the specific control current and at a specific speed.

##### 4.4. Frictional Characteristics of MSFV at Medium Speed

The relation between the coil current and the speed is shown in Figure 10 when MSFV runs at medium speed.

Figure 10: Relation between coil current and speed when MSFV runs at medium speed.

The trends of the equivalent friction force are the same when MSFV runs stably with different suspension air gaps. It is shown that the equivalent friction force increases as the speed increases in Figure 11. The change of suspension air gaps has less impact on the equivalent friction force.

Figure 11: Relation between the equivalent friction force and Speed.

This paper uses the coil current on condition that vehicle does not drop down with the same suspension air gap as control current. Moreover, it uses this control current to calculate the equivalent friction force of the flying vehicle at a specific speed. The suspension force calculated is  N. The calculation error range is .

Under the control of feedback from the control system, the coil current during the running process of MSFV is greater than that in the static state to ensure the unchanged suspended air gap. As shown in Figure 10, the compensation of the control current can be clearly seen to keep the suspension force unchanged.

##### 4.5. Impact of Rail Resistivity on the Equivalent Friction Force

In the calculation, increasing the rails resistivity can reduce the degree of deformation of the magnetic field lines when MSFV is in the same air gap and at the same speed. Namely, it can reduce the equivalent friction force. It can be concluded that selecting a larger material of resistivity as the rail can obviously reduce the equivalent friction force of MSFV.

##### 4.6. Impact of Positive Pressure on the Equivalent Friction Force

With the change of the weight of the MSFV, the relation between equivalent friction force and the weight of the MSFV can be seen in Figure 12.

Figure 12: Relationship between the Equivalent Friction Force and the Weight of MSFV (Air gap: 2.5 mm).

It can be concluded that when the suspension air gap and the weight of MSFV are certain, equivalent friction force is proportional to the running speed; with the same air gap and running speed, the greater the weight of the flying vehicle, the greater the equivalent friction force.

When the suspension air gap and the running speed are certain, the greater the weight is, the more suspension current is needed, as shown in Figure 13.

Figure 13: Relationship between the Weight of MSFV and the Coil Current (Air gap: 2.5 mm).

#### 5. Conclusions

(1)This paper uses the coil current on condition that vehicle does not drop with the same suspension air gap as control current in the calculation of the electromagnetic field. It is feasible to convert the calculation of the dynamic electromagnetic field under the real-time feedback control to the calculation of the static electromagnetic field with the control current under a specific control current and at a specific speed.(2)The equivalent static friction force changes little when the air gap changes. The equivalent friction force increases as the running speed increases. With a certain speed, the equivalent friction force increases with the increase of the air gap. With the same air gap and running speed, the equivalent friction force increases with the increase of the weight of the vehicle. (3)It can be seen that the equivalent friction coefficient of MSFV is not a constant from the results calculated by ANSYS. It is not only related to the running speed, its weight, and the resistivity of the material of guide rail but also to some control parameters of MSFV. (4)The earlier findings match well with the experimental results of papers [1, 8], which verify their reliability.

#### Acknowledgment

The authors gratefully acknowledge the support of this research by the National Natural Science Foundation of China grants on “Study on Energy Loss Mechanism of Magnetic Suspended Flywheel Battery” (no. 51147004).

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