Research on Leveling Strategy of Suspension System of Roadway Heavy-Load Transport Vehicle

Abstract

As a transport device for underground equipment, the roadway heavy-load transport vehicle needs to ensure its safety and stability during loading and transportation. In order to reduce the overturning risk and improve the stability during transportation, the improved position error leveling method is proposed, and the effectiveness of the scheme is verified by simulation analysis and actual results.

1 Introduction

In the underground construction operation of coal mine, the mining efficiency is limited by the transportation speed of mining hydraulic supports, continuous mining machines, shearers and other equipment in the roadway. Although some equipment, such as continuous mining machines, can perform short-distance transportation by their own hydraulic drive system, considering the moving speed and damage to the road surface, the continuous mining machine itself cannot perform long-distance transportation [1, 2]^. Therefore, it is necessary to carry out research on Heavy-load transport vehicles in roadways.

In order to suppress the body overturning problem caused by different suspension forces when the heavy-load transport vehicle is transporting, the leveling strategy, after the heavy-load transport vehicle is fully loaded, is studied to reduce the risk of accidents.

Based on the angle error leveling method, Wang et al. adopted the leveling strategy of ‘only lifting without lowering’ and ‘low-leg raising’ to solve the weak leg in the leveling process [3]. Guo Yakui et al. used the angle error leveling strategy to control the opening of the proportional valve to perform leveling by the measurement of the two-axis horizontal sensor [4]. Wang Tianhui et al. adopted the ‘height-by-height method’ control strategy to improve the problem of weak leg in leveling through pressure feedback [5]. Liu Zhi et al. used pressure sensors to make the four legs of the aerial work platform support separately and ensure no weak leg, and then used the chasing leveling strategy to control the platform leveling [6]. Li Xiangyu proposed a fuzzy PID control scheme based on particle swarm optimization, which improved the response speed and adaptive ability of the leveling control system [7]. Based on the integral separation PID control method and the chasing leveling strategy, Xia Xin proposed the automatic leveling control system of radar vehicle [8]. Jonnavittula used a two-axis horizontal sensor to obtain the tilt angle, and realized the leveling control of the omnidirectional vehicle platform through the Arduino Mega 2850 micro-controller [9]. Foley invented an intelligent platform with all-terrain automatic leveling. By analyzing the current working conditions, the platform predicts the future working conditions to prevent or reduce the influence of working conditions on the stability of the platform [10].

It can be seen from the above researches that the weak leg, which may occur in the leveling process, is still the main concern. At the same time, considering the disadvantage of long overall leveling time in the angle error leveling strategy, the improvement research on the position error leveling strategy is carried out.

2 Research on Leveling Strategy

2.1 Common Leveling Strategies

At present, the leveling strategies used for engineering transport equipment mainly include position error leveling strategy and angle error leveling strategy. The two leveling control strategies have their own advantages and disadvantages [11, 12].

The position error leveling strategy contains three different forms, namely, the highest point fixation, the center point fixation and the lowest point fixation. In the process of leveling with different methods, the position of the corresponding point is kept unchanged, so that it becomes the target point. By reducing the position error between the other legs and the target point in the vertical direction, it is gradually close to the target point. Usually, in the process of adjusting other legs close to the reference point, the speed of each leg is proportional to its position error relative to the target point in the vertical direction, so as to eliminate the position error and achieve the purpose of leveling. The advantage of this method is that the inertia force acting on the plunger cylinder is small, and the speed mutation is relatively small, which is conducive to the stability and accuracy of leveling. However, it cannot maintain the uniform force of each fulcrum during the adjustment process, so it is prone to occur the failure of the weak leg of the plunger cylinder.

The principle of the angle error leveling strategy is that the platform plane, parallel to the ground, of the large engineering transport vehicle is used as the datum plane, and the platform is divided into X and Y directions. Then, α is used to represent the offset angle between the platform plane and the X axis direction, and β is used to represent the offset angle between the platform plane and the Y axis direction. Before leveling, α and β are generally not equal to 0, so it is necessary to adjust α and β to achieve the purpose of rebalancing the vehicle platform. Compared with the position error leveling strategy, the principle and implementation algorithm of the angle error leveling strategy are simpler, and the coupling relationship between each support point is ignored. However, in the leveling process, when one of the directions of X and Y is adjusted, it will always interfere with one or two support points in the other direction, which will affect the offset angle in the other direction. Therefore, this method needs to repeat the leveling in both directions many times, makes the overall leveling time longer. And this method is only applicable to the three-point or four-point leveling system, which cannot complete the multi-point participation leveling task.

2.2 Improved Position Error Leveling Strategy

The coordinate system before and after the leveling of the four-point support platform is shown in Fig. 1. OXYZ is the coordinate system when the platform is horizontal, which is called the reference coordinate system. The center point of the coordinate system is the geometric center point of the body platform, and the coordinate system remains horizontal. The platform coordinate system is OX₁Y₁Z₁, which rotates with the rotation of the body platform. The coordinate center point always coincides with the OXYZ center point, and the coordinate system is called the platform coordinate system. The inclination angles of the platform coordinate system relative to the reference coordinate system in two directions are α and β respectively, that is, the angle of rotation around the X axis is α, and the angle of rotation around the Y axis is β. The angle can be measured by a biaxial sensor installed at the geometric center of the body platform.

Fig. 1

Four-point support platform coordinate system

If the body platform rotates angle α around the X-axis and then rotates angle β around the Y-axis relative to the reference coordinate system, the conversion matrix between the platform coordinate system and the reference coordinate system is as follows:

$$ A_{1} = Rot\left( {Y,\alpha } \right)Rot\left( {X,\alpha } \right) = \left[ {\begin{array}{*{20}c} {cos\beta } & {sin\alpha sin\beta } & {sin\beta cos\alpha } \\ 0 & {cos\alpha } & { - sin\alpha } \\ { - sin\beta } & {sin\alpha cos\beta } & {cos\alpha cos\beta } \\ \end{array} } \right] $$

If the body platform rotates angle β around the Y-axis and then rotates angle α around the X-axis relative to the reference coordinate system, the conversion matrix between the platform coordinate system and the reference coordinate system is as follows:

$$ A_{2} = Rot\left( {X,\alpha } \right)Rot\left( {Y,\alpha } \right) = \left[ {\begin{array}{*{20}c} {cos\beta } & 0 & {sin\beta } \\ {sin\alpha sin\beta } & {cos\alpha } & { - sin\alpha cos\beta } \\ { - sin\beta } & {sin\alpha } & {cos\alpha cos\beta } \\ \end{array} } \right] $$

Considering that the inclination angle of the body platform is very small in the actual working process, the trigonometric functions can be transformed according to the following relations: $sin\alpha =\alpha$, $sin\beta =\beta$, $cos\alpha =cos\beta =1$, $sin\alpha sin\beta =0$, $cos\alpha cos\beta =1$ by means of Limit Thought and equivalent infinitesimal substitution. Therefore, the transformation matrix ${A}_{1}$ and the transformation matrix ${A}_{2}$ are simplified to the following forms:

$$A={A}_{1}={A}_{2}=\left[\begin{array}{ccc}1& 0& \beta \\ 0& 1& -\alpha \\ -\beta & \alpha & 1\end{array}\right]$$

The scope of application of the small angle approximation is briefly discussed, and the following conclusions are drawn through simple calculations: (1) When the arc degree is <0.244, the error between sinα and α is <1%. (2) When the arc degree is <0.141, the error between cosα and 1 is <1%. Therefore, it is considered that when the arc degree is <0.141, the small angle approximation can be performed.

It can be seen that in the leveling process of the body platform, the platform firstly rotates around the X axis or firstly rotates around the Y axis has no effect on the conversion matrix, so the two processes can be seemed as one case. For any point B on the platform, assuming that the body platform is horizontal, its coordinates in the platform coordinate system are $\left({x}_{1},{y}_{1},{z}_{1}\right)$. When the platform rotates relative to the X-axis rotation angle α and relative to the Y-axis rotation angle β, the coordinates of point B in the reference coordinate system are $\left(x,y,z\right)$, and the transformation relationship between the two is as follows:

$$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=A\cdot \left[\begin{array}{c}{x}_{1}\\ {y}_{1}\\ {z}_{1}\end{array}\right]$$

B is the point on the platform, that is ${z}_{1}=0$, so the coordinates of any point on the platform in the vertical direction (i.e., Z axis) can be obtained as follows:

$$z=-\beta {x}_{1}+\alpha {y}_{1}+{z}_{1}=-\beta {x}_{1}+\alpha {y}_{1}$$

In order to overcome the weak leg of the plunger cylinder that may occur in the position error leveling strategy, the position error leveling strategy is analyzed from the geometric direction. It is known that in space, three points which are not on the same line, can only determine one plane; in the actual working process, the inclination arc degree of the body platform is very small. Therefore, it can be considered that in the three-point support, the position error leveling strategy will not appear the weak leg of the plunger cylinder. Therefore, the improvement of the position error leveling strategy is to convert the four-point support into three-point support. The specific scheme is as follows.

The four supporting points of the body platform are recorded as the highest point A, the second highest point B, the lowest point C and the second lowest point D. During the leveling process, the second highest point B and the second lowest point D move at a speed proportional to the error value of their respective vertical direction with the highest point A. A plane can be determined by the three points A, B and D, and the lowest point C pursuing surface ABD can ensure that the four points are located on the same plane. In addition, the pressure of each plunger cylinder is monitored by the pressure sensor, which can effectively prevent the weak leg of plunger cylinder in the leveling process.

3 Simulation Verification

The leveling process of the suspension system using the improved position error leveling strategy is established by MatLab. The model is shown in Fig. 2. The four points of A, B, C and D correspond to the piston cylinder 1–3 respectively. Through the input step signal simulation system, the platform lifting signal is issued. The signal is processed by the PID controller and output to the control valve. The mathematical model of the valve converts the displacement signal into a flow signal and outputs it to the plunger cylinder 1. After the sensor 1 monitors the displacement and pressure signals, the signals are fed back to the controller to complete the closed-loop control, and it is also used as the input signal of the piston cylinder 2 and 3 to control the action of the two cylinders. The displacement and pressure signals collected by sensors 2 and 3 are input into the controller together with the signals of sensor 1. The controller converts the position coordinate of the piston cylinder 4 obtained by the operation into signal to control the action of the piston cylinder 4. In addition, the displacement and pressure signals collected by sensors 1–4 are plotted into corresponding curves.

Fig. 2

Suspension system leveling control simulation model

The lifting and falling processes of the suspension system are calculated by the model, and the results are shown in Figs. 3 and 4.

Fig. 3

Leveling error of lifting process

Fig. 4

Leveling error of falling process

It can be seen from the simulation results that the displacement error between the suspension groups is kept within 2.0 mm, and the pressure error is <0.1 MPa, whether in the lifting process or the falling process. It can be judged that there is no weak leg.

4 Experimental Verification

The rated load of the roadway transporter is up to 150 t, the maximum speed is 10 km/h, the length of the whole vehicle is 6200 mm, and the width of the whole vehicle is 3500 mm. The test load is 100 t.

In the real machine test, after loading, the whole-body platform lifted by 170 mm and stayed for 20 s, and then the platform dropped to the initial position. The displacement and pressure curves during the synchronous lifting process were recorded by the sensor, as shown in Fig. 5.

Fig. 5

Synchronous lifting leveling error

It can be seen from the curves that the displacement error is <5.0 mm in the actual operation process, which is close to the simulation results. At the same time, according to the vehicle length of 6200 mm and the vehicle width of 3500 mm, the inclination arc degree of the body platform in the length direction is calculated to be 8.06 × 10^–4, and the inclination arc degree in the length direction is 1.43 × 10^–3, both of which are <0.141. Therefore, it can be seen that in actual work, the small angle approximation is still valid. The pressure error is <2.5 MPa, and there is a certain error between the simulation results. After analysis, it was found that the pressure error was mainly caused by the different tire pressure between the tires. The leveling control accuracy meets the requirements.

5 Conclusion

• (a) Through calculation and simulation verification, an improved position error leveling strategy is proposed to improve the weak leg of the position error leveling strategy.

• (b) Through the actual test, it is proved that the improved position error leveling strategy plays a role in preventing the occurrence of weak leg.