Based on the Lagrange equation in system dynamics, aiming at the horizontal cutting process, the dynamical coupling model of boom-type roadheader’s body pose was established. According to input problem of solving the model, a calculation method of the cutting head load was proposed, and the relationship between the cutting head load and pressure of the driving cylinders and swing angle of the cutting arm was obtained through simulating analysis. The simulation model was established to solve the dynamical coupling model. The cutting head load, horizontal swing angle of the cutting arm, and dip angle of coal seam were regarded as independent variables to perform changing parameter analysis in variations of the body pose. The field experiment was carried out, and the measured data is basically consistent with the simulation values. The results show that lateral displacement of the body can reach up to 6.5 cm, backward displacement can reach up to 5.2 cm, floor-based quantity can reach up to 11 cm, pitch angle of the body can reach up to 7.8°, and roll angle can reach up to 2.1°. Variations of the body pose parameters are influenced greatly by the cutting head load, while the influence from horizontal swing angle of the cutting arm and dip angle of coal seam is slighter. Among the pose parameters, floor-based quantity and pitch angle of the body vary relatively greatly, which tend to seriously influence forming quality of the roadway and should be mainly considered in deviation rectification of the roadheader’s body pose.
Coal is the main energy source in China, accounting for 65% of China’s primary energy consumption, which supports sustainable development of national economy and society. At present, the depth of coal mining in China keeps increasing, and some coal mines have exceeded 1000 m; therefore coal mining faces more and more difficulty. The mining and excavating operation are the most important and difficult production links. There are high risk factors in deep coal seam, so it is very significant to study the key basic problems of the fully mechanized excavation face [
Boom-type roadheader is the most important equipment in the fully mechanized excavation face, mainly used for excavation of the roadway to prepare the working face for coal mining. Due to the complexity and changeableness of the occurrence condition and physical mechanical properties of coal and rock in roadway cross-section, the hardness of coal and rock during cutting process is changing constantly and randomly; therefore the cutting head load is also continuously changing during the cutting process [
Some domestic and international scholars have done some researches on related aspects of roadheaders. Ergin and Acaroglu and Acaroglu and Erdogan established the mathematical model of the cutting system of a longitudinal axial roadheader during the horizontal cutting process and obtained the three-dimension forces on the cutting head through theoretical calculation and field test methods, then analyzed stability of the cutting system during cutting process and the influencing factors through simulations, and finally ascertained the maximum working range of the cutting system under stable state [
In conclusion, some researches conducted on dynamical behaviors of key mechanisms of the boom-type roadheader during cutting process, vibration characteristics of the overall unit, and measurement of the body pose have been certainly achieved. However, research on the regularities of roadheader’s body pose responses under influence of various factors during cutting process is still vacant. Based on EBZ-160 type roadheader, aiming at the horizontal cutting process and the three factors of the cutting head load, horizontal swing angle of cutting arm, and dip angle of coal seam, this paper is going to analyze the regularities of roadheader’s body pose responses through overall unit dynamical modeling and simulation.
Theoretically, due to the extremely complex working environment of coal mine, the boom-type roadheader should be a system with infinite degree of freedom during the horizontal cutting process. Therefore, in order to establish the dynamical coupling model of roadheader’s body pose, it is necessary to make reasonable and appropriate simplification and assumption for the working state of roadheader [
According to the actual structure and working environment of roadheader, its working state is simplified and assumed as follows.
Take the initial position of roadheader’s center of gravity as the origin to establish a three-dimensional fixed rectangular coordinate system
The coordinate system in vertical view of the overall machine.
The coordinate system in left view of the overall machine.
In Figure
Since a roadheader can be considered as a complete system during cutting process, the differential equations of roadheader’s body pose can be established based on the Lagrange equation in system dynamics, so as to accurately describe the overall unit dynamical behaviors of roadheader during the horizontal cutting process.
The second-kind Lagrange equation in system dynamics [
Considering viscous resistance, Rayleigh dissipation function
Separating the potential forces from the right side of (
In (
Based on the Lagrange equation (
The above equations are plugged into (
In the same way, the differential equations of motion to describe
According to (
The cutting arm of roadheader is driven by a pair of angling cylinders during the horizontal cutting process and driven by a pair of lifting cylinders during the vertical cutting process. The pressure of angling cylinders and lifting cylinders is changing with different hardness of coal and rock, and there is a positive correlation between them [
The cutting arm is fixedly connected to the revolving platform and driven by a pair of symmetrically arranged cylinders. The cylinder pole is connected to the revolving platform and the cylinder barrel is connected to the frame. At work, the cylinder on one side is elongated and the cylinder on the other side is shortened synchronously, and the synergistic motion drives the revolving platform to revolve, leading the cutting arm to swing around its center of gyration. As shown in Figure
Two-dimensional diagram of the cutting arm during the horizontal swing process.
Take the horizontal swing process towards the right side as an example. As the cutting arm swinging horizontally towards the right, the component force of the cutting head load in the horizontal direction presents towards the left. During this process, the hydraulic oil is entering into the head port of the left cylinder to push the revolving platform, and the hydraulic oil is entering into the rod port of the right cylinder to pull the revolving platform. When the cutting arm swings towards the left, the force condition is oppositely symmetrical to the above analysis.
Taking the center of the revolving platform as the base point
The moment of pull force of the right cylinder about the point
The moment of the cutting head load about the point
The revolving platform bears a large unilateral pressure while the roadheader is drilling into the coal wall, but the pressure to the revolving platform is very small and relatively dispersed during the section cutting process. The revolving platform and its support are connected with sufficiently lubricated rolling bearing. Therefore, the friction moment of the revolving platform itself is negligible relative to the driving force of the cylinder and the resistance of the coal wall to the cutting head.
According to (
In the above formula,
The component force of the cutting head load in the horizontal direction is
The cutting arm is driven by a pair of lifting cylinders arranged parallelly and symmetrically to each other during the vertical swing. The cylinder pole is connected to the cutting arm and the cylinder barrel is connected to the revolving platform. At work, lifting cylinders are elongated or shortened synchronously, driving the cutting arm to swing up or down. As shown in Figure
Two-dimensional diagram of the cutting arm during the vertical swing process.
Take the vertical upward swing process as an example. With the cutting arm swinging vertically upward, the component force of the cutting head load in the vertical direction presents downward, and the hydraulic oil is entering into the head port of the lifting cylinders to push the cutting arm to swing upward. When the cutting arm swings downward, the force condition is oppositely symmetrical.
Taking the hinge point
The moment of the gravity of the cutting arm about the point
The moment of push force of the lifting cylinders about the point
According to (
In the above formula,
The component force of the cutting head load in the vertical direction is
The component force of the cutting head load perpendicular to the coal wall can be calculated through addition of the component forces of the circumferential forces in the horizontal and vertical direction. As shown in Figure
As shown in Figure
In summary, the component force of the cutting head load perpendicular to the coal wall is
Based on underground engineering experiment, the pressure data of angling cylinders and lifting cylinders on the EBZ-160 type roadheader was acquired by the BYD-60 type mining explosion-proof pressure transmitter, and the experiment data was processed. During the cutting process, the pressure of angling cylinders is changing in the range of 5~21 MPa, as shown in Figure
The pressure of the angling cylinders.
The component force
The pressure of the lifting cylinders.
The component force
The component force
According to the dynamical coupling model of roadheader’s body pose during the horizontal cutting process, namely, (
The simulation model to solve roadheader’s body pose during the horizontal cutting process.
The simulation system to solve roadheader’s body pose
The simulation model to solve
The simulation model to solve
The simulation model to solve
The simulation model to solve
The simulation model to solve
The horizontal swing process of EBZ160 type roadheader’s cutting arm has the characteristic of axial symmetry, and the maximum of the swing angle is 28° in both left and right side. In coalfields of different areas, the dip angle of coal seam is different, but it is no more than 15° in most areas [
Initial parameters of simulation.
Parameters | Value | Unit |
---|---|---|
| 1600 | Kg |
| 5700 | Kg |
| 37700 | Kg |
| 6.31 × 107 | N⋅m−1 |
| 7.45 × 106 | N⋅m−1 |
| 1 × 104 | N⋅m−1 |
| 400 | N⋅s⋅m−1 |
| 3.49 × 104 | N⋅s⋅m−1 |
| 10 | N⋅s⋅m−1 |
| 118123 | Kg⋅m2 |
| 25381 | Kg⋅m2 |
| 1.15 | m |
| 2.95 | m |
| 3.9 | m |
| 1.75 | m |
The dynamical coupling model was simulated and solved in the simulation model. The cutting head load, horizontal swing angle of the cutting arm, and dip angle of coal seam were regarded as independent variables to perform changing parameter analysis in variation of the five body pose parameters, which are displacement of the body in the
The response results of displacement of the body in the
The relationship between
The relationship between
The relationship of
The response results of displacement of the body in the
The relationship between
The relationship between
The relationship of
The response results of displacement of the body in the
The relationship between
The relationship between
The relationship of
The response results of the pitch angle of the body
The relationship between
The relationship between
The relationship of
The response results of the roll angle of the body
The relationship between
The relationship between
The relationship of
According to Figure
According to Figure
According to Figure
According to Figure
According to Figure
EBZ160 type roadheader is selected to conduct field experiments in YunJiaLing mine, the depth of which is between 580 and 1200 m. Environments and conditions of the fully mechanized excavation face are highly representative, so it is suitable for experiments.
BYD-60 type mining explosion-proof pressure transmitter is selected to detect the pressure of the driving cylinders. Intrinsic safety type GUC360 mining angle sensor is selected to detect the vertical swing angle of the cutting arm. W18LD type dual speed sensor is selected to detect the horizontal swing angle of the cutting arm. TS15-A type explosion-proof automatic total station with high precision is selected to measure the pose of roadheader. All the detected data are stored in the onboard large-capacity data recorder. The pictures of experiment equipment are shown in Figure
The pictures of the experiment equipment.
Angle sensor
Dual speed sensor
Pressure transmitter
Onboard large-capacity data recorder
Automatic total station
Round prism
While measuring the horizontal swing angle of the cutting arm, two arc-shaped steel racks are installed in the inside torus of the revolving platform. One rack is fixed, and the other one rotates with the revolving platform. The tooth width of the rack is 4 mm, corresponding to 1° of horizontal swing angle of the cutting arm. The sensitive surface of W18LD type dual speed sensor faces the rack, and the range of reaction is 0~2 mm, as shown in Figure
Installation position of dual speed sensor and measurement schematic diagram.
Installation position
Measurement schematic diagram
While measuring the roadheader’s body pose, a round prism was fixed on the upper surface of the body above the center of gravity of roadheader and the automatic total station was set behind the roadheader at a certain distance. Before the cutting operation, the three-dimensional coordinate of the prism in the coordinate system of the total station was measured by the total station and expressed by
Pressure of the driving cylinders and swing angle of the cutting arm during the cutting process were detected by the sensors. According to the calculation method of the cutting head load in Section
The experiment results of roadheader’s body pose.
Experiment result of
Experiment result of
Experiment result of
Experiment result of
Experiment result of
According to Figure
In this paper, a calculation method of the cutting head load is proposed, and the relationship between the cutting head load and pressure of the driving cylinders and swing angle of the cutting arm was obtained. Based on the experimental data of pressure of the driving cylinders, the spectrum of cutting head load was obtained.
Based on the Lagrange equation method, the dynamical coupling model of roadheader’s body pose during the horizontal cutting process and the corresponding simulation model were established. The dynamical coupling model was simulated and solved, and the regularities of roadheader’s body pose responses influenced by different factors during the horizontal cutting process were obtained through the processing and changing parameter analysis of the simulation results. Finally, the simulation results are verified through field experiment.
The cutting head load is calculated based on the pressure of the driving cylinders and swinging angle of the cutting arm, and pressure of the driving cylinders, swinging angle of the cutting arm, and the dip angle of coal seam can be detected and obtained in real time. Therefore, the regularities of roadheader’s body pose responses during the horizontal cutting process can provide important theoretical basis for rectification of roadheader’s body pose and control of automatic cutting operation.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work is supported by the National Basic Research Program of China (973 Project) (2014CB046306).