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In-situ steering dynamics analysis of skid steering for articulated motor-driven vehicle.

ABSTRACT

The traditional hydraulic steering mode in articulated motor-driven vehicle makes the vehicle structure complex. Further more, the forces between the front and rear part of the articulated vehicle could damage the articulated joint body in the process of vehicle steering. However, skid steering mode could make the vehicle steer with the different speed of each wheel, which is flexible without hydraulic steering system. The purpose of this paper is to introduce the principle of skid steering mode in articulated motor-driven vehicle. In this paper, the theory of traditional wheeled vehicle's skid-steering mode and hydraulic steering mode of articulated vehicle are used to establish the in-situ skid-steering kinematic and dynamic model. Based on the model, the vehicle trajectory and the dynamic relationships among the body structure of the vehicle, longitudinal forces, lateral forces of each wheel are described. With these analyses, the kinematic and dynamic simulations are implemented according to the parameters of an underground mine articulated vehicle, which could provide references for the designing and studying of articulated motor-driven vehicle with skid steering mode.

CITATION: Xu, T., Shen, Y. , and Zhang, W., "In-Situ Steering Dynamics Analysis of Skid Steering for Articulated Motor-Driven Vehicle," SAE Int. J. Passeng. Cars - Mech. Syst. 9(2):2016.

1. INTRODUCTION

The articulated vehicle is widely used in engineering machinery technology. It can realize the 2WD or 4WD mode for the articulated vehicle with motorized wheels, which is also called articulated motor-driven vehicle. For the 4WD articulated motor-driven vehicle, each wheel is controlled independently. With the analysis of structure feature of the articulated motor-driven vehicle, it can be simplified to three parts, which include the front part of the vehicle, the rear part of the vehicle and the articulated joint body.

The hydraulic steering mode is mainly used in articulated motor-driven vehicle. It could realize the vehicle steering in different working conditions. However, there still exist several problems considering vehicle structure and response time of hydraulic steering system. Firstly, the tire wears seriously because of the slipping of wheel in the process of vehicle steering. [1] Secondly, the steering of the vehicle mainly relies on the hydraulic cylinders and articulated joint body, which the forces in the joint body could not be ignored. [2] Thirdly, the steering angle of the articulated vehicle is generally about 45 degrees that is limited by the structure of hydraulic cylinder. [3] Finally, there still exist the response problems of vehicle steering due to the delay action of the hydraulic steering system.

Comparing with the hydraulic steering mode, skid steering mode use the different speed of each wheel to change the direction of the vehicle since there is no steering device. [4] The vehicle with skid steering mode could implement in-situ steering mode or zero-radius steering mode, which make the vehicle have better steering performance and maneuverability. In the process of the vehicle steering, the wheels are in the state of torsional deformation, thus there will be less generation of tire wear. [5] Currently, skid steering mode is mainly used in crawler vehicles, skid steer loaders and some multi-axis vehicles. Yi et al. [4], Maclaurin,[5] Fauroux et al. [6] , Ren et al. [7] , Michihisa et al. [8] and Fahim et al. [9] used the skid steering mode in different vehicles according to the steering principle. They studied the force characteristics of each wheel in the skid steering process. However, none of these works investigate the skid steering mode in 4WD articulated vehicle that each wheel can be controlled independently.

In this paper, skid steering mode is applied to articulated motor-driven vehicle that the wheels can be controlled independently. The organization of the rest of this paper is as follow. In section 2, the articulated motor-driven vehicle with skid steering mode will be introduced with several assumptions; and a kinematic model of articulated motor-driven vehicle is established to study the motion characteristics of the vehicle. The front part of the vehicle is taken as a research object to discuss the dynamic characteristics of skid steering mode, and investigate the relations among the structure of the vehicle, the force and speed of the wheels in section 3. In section 4, the dynamic and kinematic simulations are implemented according to the structure of an underground mine articulated vehicle with motor-driven wheels to verify the model. The results could provide references for the designing and controlling of skid steering mode in articulated motor-driven vehicle.

2. IN-SITU STEERING KINEMATIC ANALYSIS OF SKID STEERING FOR ARTICULATED MOTOR-DRIVEN VEHICLE

Skid steering mode is used in the articulated motor-driven vehicle with the purpose of taking the minimum force of articulated joint body. Some rules should be set with several assumptions.

1. The load of the rear part is heavier than the front part of the articulated motor-driven vehicle. The turning center of the vehicle could be made at the center of the rear axle by actively controlling of the rear wheels' speed. (Articulated vehicle with motorized wheels has a virtual axle that is the equivalent of the vehicle axle.) Then, the front wheels speed is controlled based on the motion of articulated joint body, which could make the front part turning with that of the rear part of the vehicle. The steering process is shown in Figure 1(a). This assumption will be an example in the following analysis of the paper

2. The load of the front part is heavier than the rear part of the articulated motor-driven vehicle. The steering process is contrary to the first assumption. The front wheels speed could be actively controlled to make the turning center of the vehicle being at the front axle. The rear wheels speed is passively controlled based on the motion of articulated joint body, which is shown in Figure 1(b).

The speed of rear wheels is actively controlled when the heavier load is at rear part of the vehicle. The front wheels speed is controlled based on the particular motion trajectory of joint part with the purpose of minimum forces of the articulated joint body. With the analysis above, a kinematic model of articulated vehicle at time t is established in Figure 2.

In Figure 2, a global coordinate system x-F-y is established at the center of rear axle F where the x coordinate is parallel to the rear axle of the vehicle. The y coordinate is perpendicular to the rear axle. A local coordinate system [x.sub.0]-[O.sub.1] -[y.sub.0] is assigned to the front part at the center of articulated joint body [O.sub.1]. The positive direction of [x.sub.0] is the right direction of the articulated joint body vertical to the front part of the vehicle, and the positive direction of [y.sub.0] is the forth direction of the articulated joint body parallel to the front part of the vehicle. In the kinematic mode, [A.sub.1], [B.sub.1], [C.sub.1], [D.sub.1] represent left front wheel, right front wheel, rear wheel of right side and left side at time t, respectively. E2 is the instantaneous steering center of front axle. The speed of the ith wheel (i represent A, B, C or D, which is the same with the following analysis) is [V.sub.i]. [alpha] and [beta] represent steering angle of the front and rear part of the vehicle, respectively. [theta] is the steering angle of the articulated vehicle. [[omega].sub.1] and [[omega].sub.2] are the steering angular velocity of the front and rear part of the vehicle. W is the wheel track. [L.sub.1] and [L.sub.2] represent the distances from the front axle center and the rear axle center to the articulated joint body, respectively.

2.1. Kinematic Analysis of In-Situ Skid Steering for Rear Part of the Articulated Motor-Driven Vehicle

According to the in-situ skid steering analysis of articulated motor-driven vehicle above, this paper make the speed of rear wheels being v and -v in the in-situ skid steering process, which is shown in equation (1). Thus the turning center of the articulated vehicle could be at the rear axle center F.

[V.sub.c] = -[V.sub.D]= v (1)

where v is the speed of rear wheels, which is actively controlled and related to the steering angular velocity.

The trajectory of the rear wheels and articulated joint body will be a circle which the circle center is at point F in the global coordinate system x-F-y. These trajectories could be obtained by equation (2).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where ([x.sub.1], [y.sub.1]) represent the coordinate of rear wheels C and D, ([x.sub.2], [y.sub.2]) represent the coordinate of articulated joint body O.

The steering angular velocity of rear part of the vehicle [omega]2 is as follow:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Based on equation (3) and structural parameters of the articulated motor-driven vehicle, speed of the articulated joint body at rear part of the vehicle could be given by equation (4).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [V.sub.oxr] and [V.sub.oyr] are the speed of articulated joint body at rear part of the vehicle in [x.sub.0] and [y.sub.0] direction of the local coordinate system, respectively.

2.2. Kinematic Analysis of In-Situ Skid Steering for Front Part of the Articulated Motor-Driven Vehicle

For the front part of articulated motor-driven vehicle, the center of the front axle E ([x.sub.3], [y.sub.3]) can be modeled by equation (5) with the coordinate of the point O ([x.sub.2], [y.sub.2]).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Combining the point E and point O, the motion trajectory of point E can be expressed by equation (6).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

The speed of the articulated joint body at front part of the vehicle could be given by equation (7) with the speed of front wheels.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [V.sub.oxf] and [V.sub.oyf] are the speed of articulated joint body at front part of the vehicle along [x.sub.0] and [y.sub.0] direction in the local coordinate system, respectively.

The movements of both the front and rear part of the vehicle should be reasonable to minimize the force of articulated joint body, which means that, the articulated joint body of front and rear part of the vehicle should have the same motion relationships. Thus the speed of the front wheels could be expressed by equation (8) with the analysis of equation (7).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

Therefore, the steering angular velocity [[omega].sub.1] can be given by equation (9).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

2.3. In-Situ Skid Steering Angle [theta] of the Articulated Motor-Driven Vehicle

According to the equations (3), (9) and the relations among angle [theta], [alpha] and [beta], the steering angle of the articulated motor-driven vehicle is determined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Integrating the equation (10), the steering angle [theta] could be simplified to equation (11).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where C and B are constant and their value are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

3. IN-SITU STEERING DYNAMICS ANALYSIS OF SKID STEERING FOR THE ARTICULATED MOTOR-DRIVEN VEHICLE

Based on the kinematic analysis of in-situ skid steering in section 2, the speed of each wheel should meet the special relations to minimize the force of the articulated joint body in the steering process. In this condition, the front and rear part of the vehicle will be mutual independence. Its trajectory is a circle which the circle center is at the instantaneous center [E.sub.2] and F, respectively. For the rear part of the vehicle, the turning center F is fixed while the center [E.sub.2] of the front part of the vehicle change from the center to the one side of the front axle in the vehicle steering process. The motion trajectories of articulated joint body, front and rear parts of the vehicle are shown in Figure 3.

With the analysis of Figure 3 and equations (8), the difference of two wheels in front part of the vehicle will increase with the steering of vehicle, which make the instantaneous steering center [E.sub.2] move toward one side of the axle. The speed of front and rear part at articulated joint body O is similar whose motion direction is the tangential direction of rear part movement. Therefore, the dynamic analysis of front and rear part should be considered alone. In a certain time, the steering mode of rear part is similar to the front part of the vehicle, thus the front part of the vehicle could be a research object in dynamic analysis.

For the front part of the vehicle in skid steering process, there are two kinds of steering mode on the basis of the location of turning center [E.sub.2], which is shown in the Figure 4 and Figure 5.

In the process of in-situ steering, the actual steering position of wheels lags behind the theoretical steering position. Thus for the tire, there are torsional and lateral deformation, which will produce steering force to make wheel steering. In the beginning of wheels steering, the deformation of tire produces angle that include slip angle and torsional angle, which could meet the requirement of large steering radius. The steering is realized in the state of tire deformation. (The steering radius is defined as the distance from the instantaneous steering center to the axle center). When the steering radius decreases, the maximum tire deformation could not meet the requirement of the steering radius, the wheels are forced to move by the torsional moment. In this case, it will happen slip steering.

It could be obtained by Figure 4 and Figure 5 that there is mainly transverse and torsional deformation before the steering of the wheel is steady. When the tire deformation meet the requirement of the certain steering radius, the wheel will steer steadily. In steady steering state, wheels A and B bear constant lateral force that make tire defection. The defection angles are [[delta].sub.1] and [[delta].sub.2]. Torsion moment of the wheels make the torsional deformation being constant, which the angles are [[zeta].sub.1] and [[zeta].sub.2]. In Figure 4 and 5, [[gamma].sub.i] is the angle with influence of torsion and defection of tires. [[DELTA].sub.i] is the lateral defection distance of each wheel at the steady steering moment. [R.sub.Ai], [R.sub.Bi] and R' represent the steering radius of left front wheel, right front wheel and front part of the vehicle, respectively.

The force diagram of each wheel in front part of the vehicle is shown in Figure 5 and Figure 6.

In Figure 6 and 7, [F.sub.j] (j represents [A.sub.2] or [B.sub.2], which is the same as the following analysis) is the driving force of each wheel, F[f.sub.j] denote rolling resistance force, [T.sub.fj] represent steering resistance moment, [F.sub.rj] is the lateral force caused by front axle.

With the dynamic analysis of Figure 6 and 7, the driving and resistance moment of front wheels should be balanced at instantaneous steering center [E.sub.2], which is expressed by equation (13).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

where y =min([y.sub.A1] , [y.sub.B1]).

3.1. Deflection Angle [gamma] and Steering Radius R

The angle between the tire carcass and the tread is y which is also the angle of tire defection. It is assumed that 1/n turns of the wheel will make the wheel steer y degrees in the skid steering of front part of the vehicle. The relationship between the slip angle y and the steering radius R of front wheels is shown in equation (14).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

where r is the rolling radius of wheel, n denote the recovery coefficient of tire, R represent [R.sub.Ai] or [R.sub.Bi].

3.2. Lateral Force Frj Caused by Front Axle

The lateral deformation of the tire carcass at the two sides is the same in value but opposite in direction, which could be expressed by equation (15).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Based on the analysis of equation (15), the lateral forces of axle are the same in value but opposite in direction. According to Yu and Lin's research [10], the lateral force [F.sub.r] could be derived in equation (16).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

where [[rho].sub.y] represent the lateral stiffness of tire.

3.3. Steering Resistance Moment Tf and Rolling Resistance Ff

According to the steering process of front part of the vehicle, it could get that the slip angles [y.sub.A] and [y.sub.B] are the same in value. Therefore, the steering resistance moment of tire caused by torsional deformation could be obtained by equation (17) according the equations (14) and the Zhuang's studies [11].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where torsional stiffness of tires k'=[[pi]kr'.sup.3], k is cornering stiffness of tire.

The longitudinal rolling resistance force [F.sub.f] is proportional to the vertical force of tire [F.sub.Z], which the relation could be expressed by equation (18) when the rolling resistance coefficient is f.

[F.sub.f]=f * [F.sub.z]=mgf (18)

where m is vertical mass of each wheel.

3.4. Driving Force F

With the analysis of Figure 6, 7 and equations (13), the driving force of front wheels is shown in equation (19) and (20) when the turning center [E.sub.2] is inside or outside of the two wheels of front part of the vehicle, respectively.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

3.5. Critical Steering Radius [R.sub.min]

As shown in Figure 4 and 5, the steering of tread of the vehicle is lag behind the tire carcass in the steering process of front wheels. Thus for the tires, there are torsional and lateral deformation, which cause steering force to make the tire move. In the beginning of steering, the deformation of tire produces angle y that include slip angle and torsional angle could meet the requirement of large steering radius. The steering of front wheels is realized with the tire deformation. When the steering radius R' of front part decreases, the maximum tire deformation could not meet the requirement of the steering radius, the tire is forced to steer by the torsional moment. In this case, it will happen slip steering. Therefore, there is a critical steering radius [R.sub.min] that is related to the minimum deformation between tread and tire carcass in the steering process of wheels. And this critical radius [R.sub.min] divides the radius [R.sub.1] into two parts. The wheel steering with the tire deformation when the radius [R.sub.1] belong to 0 ~[R.sub.min] and it will be slip steering when the radius R[greater than or equal to][R.sub.min] .

The minimum deformation of front wheels is related to the friction resistance moment [T.sub.fmax] which is caused by the interaction of tires and ground. When the contact surface between the tires and ground is simplified as a circle, the relation between the steering resistance moment and the vertical force could be obtained by the equation (21) according to the Talblick Formula introduced in literature [12].

[T.sub.fmax] = mgf * K (21)

where, K is the equivalent radius of the contact circle which could be expressed by Eq. (22).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

where, [I.sub.P] is the polar moment inertia while A is the area of contact surface, r' represent the radius of contact circle of the tire that connect with ground.

Based on the equation (14) and the relations among y, (and S, the critical steering radius [R.sub.min] of wheels without slip steering in skid steering mode could be expressed by equation (23).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

where [y.sub.max] is critical deformation of tire, which could be obtained by equation (24) with the analysis of equation (21) and (22).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

It is difficult to solve the [[gamma].sub.max] and [R.sub.min], but we can analyze the change process of these two parameters with the numerical method of [[gamma].sub.max] and [R.sub.min].

4. KINEMATIC AND DYNAMIC SIMULATION FOR UNDERGROUND MINE ARTICULATED MOTOR-DRIVEN VEHICLE

In order to analyze the steering process and wheel forces of articulated vehicle, an underground mine articulated vehicle are taken as the research object. The parameters of this articulated vehicle are shown in Table 1.

4.1. In-Situ Experiment of the Underground Articulated Motor-Driven Vehicle with Hydraulic Steering Mode

The steering mode of the underground mine articulated vehicle is hydraulic steering. When we use the angle transducer (whose liner measure range is [+ or -]60[degrees] and the signal deviation is less than [+ or -]2%) to measure the in-situ steering angle of the articulated vehicle on concrete road, the voltage change of the transducer will reflect the steering angle, which is shown in Figure 8 and 9.

The experiment results show that the vehicle with hydraulic steering mode could turn about 40 degrees in 3s. Therefore, the skid steering mode could be designed with the reference above.

4.2. Kinematic Simulation of the Underground Articulated Motor-Driven Vehicle with Skid Steering Mode

When the speed of rear wheels v=0.08km/h, the change process of steering angles [theta] including [alpha], [beta] and the speed of each wheel are shown in Figure 10 and Figure 11, respectively.

Some conclusion could be obtained with the analysis of Figure 10 and Figure 11.

1. The slope of the defection angle curve that represents the steering angular velocity [omega] declines with time t gradually.

2. The maximum of the vehicle steering angle could reach to 60 degrees or more. Therefore, skid steering mode could deal with the problems that the vehicle steering angle is constrained by the hydraulic cylinder dimension which is shown in Figure 9.

Analysis above shows that the speed of rear wheels determines the motion trajectory of each wheel, speed of front wheels and steering angular velocity of articulated vehicle. Figure 12 shows the variations of steering angle of the vehicle with the steering process at different speeds of rear wheels.

Figure 12 shows that the vehicle steering angular velocity is inversely proportional to the rear wheel speed. When the rear wheel speed increases, the time of vehicle steering for the same angles will decrease. Consequently, the angular speed of vehicle in-situ steering can be implemented by controlling the rear wheel speed during skid steering process.

4.3. Dynamic Simulation of the Underground Articulated Motor-Driven Vehicle with Skid Steering Mode

For the rear part, the fixed turning center is at point F. In the vehicle steering process, the steering radius R' is 0. The wheel is always in slip steering state, and the driving force keeps 2105 N.

For the front part of the articulated vehicle, the in-situ steering process could be divided into two kinds of mode according to the steering center [E.sub.2], which is introduced in section 3. Referencing to the equations (13) to (20), the driving force and resistance of each wheel changed with the corresponding steering radius R' are shown in Figure 13 and Figure 14.

In the vehicle steering process, the driving force is mainly used to overcome the rolling resistance, torsion resistance and lateral force of front wheels. It could be obtained by the Figures 13 and 14 that the rolling resistances of the wheels are constant without the impact of inertial force while the torsion resistance and lateral force change with the steering radius R'.

If vehicle moving straight ahead, which means that the steering radius is infinite, the wheel trajectory will be a line. The driving force is mainly used to overcome rolling resistance. When the steering radius decreases, the driving force at the left wheels increases while decreases at the right wheels. The smaller the steering radius is, the larger difference of the driving force of front wheel will be. If the steering radius is less than half of the wheelbase, the driving forces of wheels are the same in value. The lateral force will cause the wheels to steer.

5. CONCLUSIONS

In this paper, the skid steering mode is applied to articulated vehicle that the wheels could be controlled independently. Based on the kinematic and dynamic model, the characteristics of articulated vehicle with skid steering mode are discussed. The main conclusions of this paper are as following.

1. Articulated vehicles with hydraulic steering could be replaced by skid steering, which could realize the steering in small radius or insitu steering. In skid steering mode, the steering angular velocity of the vehicle could be controlled by the speed of the rear wheels, and the steering angle could reach to 60 degrees or more.

2. For the articulated vehicle with skid steering mode, the steering angular velocity of front part are decided by the rear wheels' speed when the heavier load is at rear part.

3. The steering radius R' of front part is the principal factor that influences the motion of the front wheels. The wheels will be slip steering if the radius is less than the critical steering radius [R.sub.min]. When the radius is larger than the critical steering radius [R.sub.min] the wheels will steer with the influence of tire deformation

REFERENCES

[1.] Wang Jianchun, Yang Wenhua, "The Dynamic Response of Articulated Vehicle to Steering Input," Journal of Wuhan Yejin University of Science and Technology, 1996.

[2.] Wang Jianchun, "Dynamical Mathematical Model of in Situ Steering of Articulated Vehicles," Construction Machinery, ISSN 1001-554X, 06-0086-05, 2008, doi: 10.3969/j.issn.1001-554X.2008.06.016.

[3.] Wang Jianchun, "Mechanical Analysis of In-situ Steering of Articulated Loader," Coal Mine Machinery, 2009, doi: 10.3969/j.issn.1003-0794.2009.03.034.

[4.] Jingang Yi, Hongpeng Wang, Junjie Zhang, Dezhen Song, Suhada Jayasuriya, Jingtai Liu, "Kinematic Modeling and Analysis of Skid-Steered Mobile Robots with Applications to Low-cost Inertial-Measurement-Unit-Based Motion Estimation," IEEE Transactions on robotics, 2009, doi:10.1109/TRO.2009.2026506.

[5.] Maclaurin B, "Comparing the Steering Performances of Skid-and Ackermann-steered Vehicle," Journal of Automobile Engineering, 2007.

[6.] Fauroux J. C., Vaslin P. P. P. P., "Modeling, Experimenting, and Improving Skid Steering on a 6x6 All-Terrain Mobile Platform," Journal of Field Robotics, 2010.

[7.] Feng Ren, Xin-hui Liu, Jin-shi Chen, Ping Zeng, Xue-Feng Jia, "Analysis of Skid Steer Loader Steering Characteristic," Advances in Mechanical Engineering, 2004.

[8.] Michihisa Iida, Hiroshi Nakashima, Hiroki Tomiyama, Toho Oh, Taku Nakamura, "Small-radius Turning Performance of an Articulated Vehicle by Direct Yaw Moment Control," Computer and Electronics in Agriculture, 2010.

[9.] Fahim F. Al Hamdani, "Dynamic Analysis of Steering Articulated Tracked Vehicle," Journal of Engineering and Development, 2006.

[10.] Yu Fan, Lin Yi, "Vehicle Dynamics," ISBN 978-7-111-16895-9, China Machine Press, Beijing, 2005.

[11.] Zhuang Jide, "Automobile Tire," ISBN 7-81045-781-0, Beijing Institute of Technology Press, Beijing, 2001.

[12.] Gao Jianming, Wang Tongjian, Xu Jinyong, Zhang Zida, "Simulation and Experimental Research on Steering Kinematics and Dynamics of Articulated Loaders," Journal of Construction Machinery, 2005.

CONTACT INFORMATION

Tao Xu, Postgraduates

School of Mechanical Engineering, University of Science and Technology Beijing

Beijing, 30 Xueyuan Road, Haidian District Beijing, P. R. China

ustb_xt@163.com

Yanhua Shen, Associate Professor

School of Mechanical Engineering, University of Science and Technology Beijing

Beijing, 30 Xueyuan Road, Haidian District Beijing, P. R. China

yanhua_shen@ces.ustb.edu.cn

Wenming Zhang, Professor

School of Mechanical Engineering, University of Science and Technology Beijing

Beijing, 30 Xueyuan Road, Haidian District Beijing, P. R. China

wmzhang@ustb.edu.cn

Tao Xu, Yanhua Shen, and Wenming Zhang

University of Science and Technology Beijing

Table 1. The parameters of an underground articulated vehicle and ground

Structures                           Values

Front part loads /[m.sub.1]          8700kg
Rear part loads /[m.sub.2]          16300kg
Front wheelbase /[L.sub.1]           1670mm
Rear wheelbase /[L.sub.2]            2600mm
Wheel track/ W                       1530mm
Tire rolling radius/ [r.sub.g]        810mm
Tire width/ r'                        400mm
Carcass lateral stiffness/[rho]y   -40000N/mm
Carcass cornering stiffness/ k     -40000N/rad
Carcass recovery coefficient /n         4
Adhesion coefficient/[phi]              0.7
Rolling resistance coefficient /f       0.02
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Author:Xu, Tao; Shen, Yanhua; Zhang, Wenming
Publication:SAE International Journal of Passenger Cars - Mechanical Systems
Article Type:Report
Date:Jun 1, 2016
Words:4763
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