Analysis and experimental validation of the load characteristics of the hydraulic rod in a shearer

Abstract

The joint surface of the preloaded structure of the hydraulic rod in a shearer is prone to bending and slitting. In this study, to systematically evaluate this phenomenon, critical load characterization parameters of the hydraulic rod are first determined based on its critical load, preload, working load, and residual preload. A critical load equation of the hydraulic rod is further established based on the principle of compatibility of small deformation. Finally, the integral solution method is used to solve the load equation of the hydraulic rod of the shearer by combining the deflection and rotation equation of the fuselage and the hydraulic rod on the upper side of the coal wall to obtain the deformation and load value of the hydraulic rod. The results show that the maximum load applied on the upper hydraulic rod on the coal wall, lower hydraulic rod on the coal wall, lower hydraulic rod on the gob side, and upper hydraulic rod on the gob side are 538.15, 500.3, 445.95, and 375.15 kN, respectively. The corresponding maximum deformation of the upper hydraulic rod on the coal wall, lower hydraulic rod on the coal wall, and lower hydraulic rod on the gob side are 2.4696, 1.653, and 0.9652 mm, respectively. Compressive deformation occurred on the upper hydraulic rod on the gob side with a magnitude of −1.6346 mm. Results of numerical calculations agree well with instantaneous measurements of the load in the hydraulic rod in a shearer using wireless sensing technology. The maximum error between the calculation and measurement is less than 4%, thus validating the accuracy of the proposed load model. Using the proposed load model, we further analyzed the load characteristics of the hydraulic rod under straight cutting working conditions with different pitch and roll angles. Our findings provide an important basis for understanding the load characteristics of the entire shearer, optimizing the structure of the hydraulic rod, and improving the lifetime of the shearer.

INTRODUCTION

The hydraulic rod is an important auxiliary part that connects the left and right walking mechanism with the fuselage in a shearer through high-strength bolts and nuts. Under the preload force, the fuselage and the walking mechanism can form a tightly connected unit. When a shearer is operated for hours, the reduction in preload will result in the formation of slits along the joint surface between the fuselage and walking mechanism. Fluctuations of shear induced by various factors cause collision between the contact surfaces, which eventually leads to fatigue failure of the hydraulic rod.¹ Furthermore, under an extremely large preload force, high local stress may be induced on the joint surface, which greatly reduces the service life of the shearer. Therefore, investigating the loading characteristics of the hydraulic rod is important for improving the service life of the shearer and increasing work efficiency.

Loading characteristics of the hydraulic rod have been explored by only a few scholars in china and abroad. For example, through mechanical analysis of the entire shearer and the hydraulic rod, Mao et al.² studied the mechanism of changes in the tension of the hydraulic rod under different roll angles and pitch angles. They further predicted the fatigue life of the hydraulic rod based on the cumulative fatigue damage theory, which accurately reflected its mechanical properties. Song et al.³ analyzed several fracture accidents of the hydraulic rod in a certain type of shearer manufactured by Xi'an Coal Mine Machinery Co., Ltd. They identified the causes of fatigue fracture of the hydraulic rod and proposed an improvement method. Hao et al.⁴ solved the overdetermined equation of the spatial mechanical model of the left traction part of the shearer and obtained the shear load spectrum of the connecting rod of the fuselage. The rain flow counting method was used to compile the load spectrum, and the frequency domain characteristics and time domain continuous characteristics of the load spectrum were obtained. Ma⁵ used three-dimensional solid modeling and finite element simulation method to establish the dynamic simulation model of the whole shearer, analyzed the load variation characteristics of the hydraulic rod under the dynamic load of the drum and obtained the maximum stress and corresponding deformation of the four rods, which provided the basis for the optimization design of the hydraulic rod of the shearer.

Meanwhile, the bolt preload has been explored by many domestic and foreign scholars. Cavallaro et al.⁶ determined changes in the bolt assembly preload in a friction damper by monitoring the preload force continuously through experimental studies. Matos et al.⁷ analyzed the effects of extraction temperature using a calibrated nonlinear Hammerstein–Wiener model and further estimated long-term loss in preload. Their results indicate that maintaining a lower temperature when tightening the bolt can effectively reduce the long-term loss in preload. Vires et al.⁸ determined the actual bolt preload based on the measurement of the strain, bolt mechanics, and geometric changes in the bolt bar without calibrating each bolt. DeAngelis et al.⁹ determined the basic dimensions and strength of the preloaded bolt drive amplitude to ensure an adequate threading match between the bolt and screw. Shahani et al.¹⁰ performed experimental studies using a specially designed fixture to analyze the effect of preload on the fatigue life of bolts. Their results showed that the preload reduces the endurance limit of the bolt, beyond a significant mean stress, the endurance limit increases too. Duan and Su¹¹ analyzed the relationship between the deformation of the integrated frame in a forging press and the residual preload applied on the hydraulic rod. In particular, their study considered the mismatch between basic assumptions in the parameter design of the multi-hydraulic rods preloaded integrated frame. Lin¹² performed finite element analysis of the bolt using ABAQUS Inc. FEA to explore the local yielding phenomenon commonly found in the root of high-strength bolt threads. The results revealed the stress-strain condition of bolted components and the nonuniform load distribution on the screw thread. Ai et al.¹³ studied the relationship between contact radius and multiple bolt parameters, such as the preload force, coupling material, and thickness ratio. The results obtained by the experimental test and the calculation results are within a reasonable range. Hui et al.¹⁴ constructed an analytical theoretical model of bolt joints based on the static characteristics of the joint surface and further solved the model using an equivalent distributed load method. Their results showed a linear relationship between the tangential deformation of the joint surface and external load when the tangential load is smaller than the static friction force. Wen et al.¹⁵ created a fractal model of normal contact stiffness on the joint contact surface, incorporating the impact of the domain expansion factor of the microcontact size distribution. Zhang et al.¹⁶ established a bolt contact model using the hybrid unit method and derived the actual contact area and distribution of contact compressive stress.

Thus far, numerous studies have explored preload, but investigations of the load condition of the hydraulic rod in a shearer are lacking. This study establishes a characteristic equation describing the load on the hydraulic rod in a shearer, considering critical load, preload, the working load, and residual preload. Along with the deflection and rotation angle equations of the fuselage and hydraulic rod, this equation was solved using the integration method. The accuracy of the proposed equation was validated by comparing analytical results calculated from the equation with real-time transmission measurements of the load on the hydraulic rod. Finally, using the proposed equation, load distribution in the hydraulic rod in a shearer was analyzed under straight cutting working conditions with varied pitch and roll angles. The results provide an important basis for understanding the load characteristics of the entire shearer and optimizing the structure of the hydraulic rod.

DESCRIBING EQUATION OF THE LOAD ON THE HYDRAULIC ROD

Shearer is composed of many functional components such as fuselage, walking part, and cutting part, such as Figure 1A. The compact unit of the left and right walking mechanism and the fuselage connected through hydraulic rods and bolts is shown in Figure 1B. The hydraulic rod of the shearer is arranged on the coal wall side and the upper and lower ends of the goaf, respectively, and the shearer hydraulic rod is installed to the inside of the shearer fuselage, only the end of the upper hydraulic rod can be displayed. $${F}_{lu1}$$, $${F}_{lu2}$$, $${F}_{ld1}$$, and $${F}_{ld2}$$ represent pulling forces while $${F}_{s}$$ is the shear force, such as Figure 1C.

Figure 1. Schematic of a shearer showing. (A) The hydraulic rod of shearer structure diagram. (B) Connection of preloaded combined structural bolts (C) Distribution of bolts on the walking mechanism.

Hydraulic rod remnant preload of shearer

From Deng et al.,¹⁷ it can be known that during the working process of the shearer hydraulic rod, the deformation of the four hydraulic rods under the action of the working load can be obtained according to the following equation: [Image Omitted. See PDF]where $$x$$ denotes the relative displacement of the walking part to the fuselage, $$\delta $$ denotes the transverse swing angle, $$\gamma $$ denotes the longitudinal swing angle, $${L}_{B}$$ denotes the distance between the center of gravity of fuselage and the lower end of the fuselage, $${L}_{C}$$ denotes the distance between the center of gravity of the fuselage and the upper-end face of the fuselage, $${L}_{D}$$ denotes the distance between the center of gravity of the fuselage and the left end face of the fuselage, $${L}_{E}$$ denotes the distance between the center of gravity of the fuselage and the right end face of the fuselage.

When the shearer is working, the force acting on the end face of the fuselage from the hydraulic rod is the residual preload, as shown in Figure 2. The residual preload on each individual hydraulic rod is proportional to its deformation.

Figure 2. Load distribution on the end face of the fuselage

Therefore, we have [Image Omitted. See PDF]where $${F}_{x}$$ denotes the residual load on the fuselage when it is loaded.

Due to the existence of friction forces $${F}_{m}^{y},{F}_{m}^{z}$$, and the supportive load $${F}_{N}$$ acting on the connecting bolt in Y-direction, the total force F_m, proportional to the pulling force in Axial, can be expressed as [Image Omitted. See PDF]

Establishment of load equation for hydraulic rod of shearer

During the normal cutting of coal wall by shearer, the load on the hydraulic rod is not only affected by the critical slitting load, preload, working load, and residual preload but also closely related to the stiffness of the hydraulic rod $${C}_{b}$$ and the stiffness of the fuselage $${C}_{m}$$. Therefore, the load on the hydraulic rod is derived according to the relationship between the force acting on the joint surface and the corresponding deformation.

It can be known from Deng et al.¹⁷ that the load variation and working load of the four rods in the working process of the shearer hydraulic rod can be obtained by solving according to the following equation: [Image Omitted. See PDF]where, $${K}_{u1}=\frac{{E}_{2}{A}_{2}}{{L}_{u1}}$$; $${K}_{u2}=\frac{{E}_{2}{A}_{2}}{{L}_{u2}}$$; $${K}_{d1}=\frac{{E}_{2}{A}_{2}}{{L}_{d1}}$$; $${K}_{d2}=\frac{{E}_{2}{A}_{2}}{{L}_{d2}}$$, $${E}_{2}{A}_{2}$$ denotes the bending strength of hydraulic rod, $${A}_{2}$$ denotes the cross-sectional area of the hydraulic rod, $${F^{\prime} }_{<mpadded lspace="-4pt">u</mpadded><mpadded lspace="-4pt">(d)</mpadded>}$$ denotes preload.

Figure 3A shows that no deformation occurs at the moment the hydraulic rod comes into contact with the fuselage because mutual interacting forces do not exist. Figure 3B depicts a scenario when the bolt is tightened and no working load is applied. Figure 3C shows a scenario when the working load is applied to the hydraulic rod. The pulling force exerted on the hydraulic rod increases from the initial preload force $${F^{\prime} }_{<mpadded lspace="-4pt">u</mpadded><mpadded lspace="-4pt">(d)</mpadded>}$$ to working loads $${F}_{\mathrm{left}}$$ and $${F}_{\mathrm{right}}$$. Simultaneously, the length of the hydraulic rod is also increased by $$\Delta {\lambda }_{1}$$ and $$\Delta {\lambda }_{2}$$. In contrast, compression in the fuselage decreases as the hydraulic rod is being stretched, which causes the fuselage to return to its original shape. According to the principle of compatibility of joint deformation, the change in the compressive deformation of the fuselage should be equal to the change in the elongation of the hydraulic rod $$\Delta {\lambda }_{1}$$ and $$\Delta {\lambda }_{2}$$. The force acting on the fuselage should also decrease from $${F}_{u(d)}^{^{\prime} }$$ to the residual load force $${F}_{x}$$.

Figure 3. Deformation of the hydraulic rod when subjected to a tensile load. (A) no deformation, (B) deformation under tightened bolt without working load, and (C) deformation under working load.

Forces acting on the hydraulic rod and the fuselage as well as the corresponding deformations are shown in Figure 4. Figure 4A,B show the force and deformation of the hydraulic rod and the bolt on the right side of the fuselage when the bolt is tightened and no working load is applied. Figure 4C shows the force and deformation of the hydraulic rod and the two sides of the fuselage when the shearer is working. O_b as the origin corresponds to the force and deformation of the hydraulic rod affected by the right-side walking mechanism, and $${O}_{b}^{^{\prime} }$$ as the origin corresponds to that affected by the left-side walking mechanism.

Figure 4. Schematic of joint deformation of the hydraulic rod. (A) Contact state between hydraulic rod and fuselage; (B) bolt tightening state; (C) Working load state of hydraulic rod

As shown in Figure 4A,B the initial preload force is $${F^{\prime} }_{<mpadded lspace="-4pt">u</mpadded><mpadded lspace="-4pt">(d)</mpadded>}$$. The forces acting on the hydraulic rod and the fuselage are proportional to the corresponding deformations as [Image Omitted. See PDF]

In Figure 4C, with $${O}_{b}$$ as the origin, the working pulling force exerted from the right side walking mechanism is $${F}_{\text{right}}$$ and the corresponding deformation in elongation for both the hydraulic rod and the fuselage is $$\Delta {\lambda }_{2}$$. Therefore, the total stretching deformation of the hydraulic rod and the total compressive deformation of the fuselage are $${\lambda }_{b}+{\rm{\Delta }}{\lambda }_{2}$$ and $${\lambda }_{m}-{\rm{\Delta }}{\lambda }_{2}$$, respectively. With $${O}_{b}^{^{\prime} }$$ as the origin, the working pulling force exerted from the left side walking mechanism is $${F}_{\mathrm{left}}$$ and the corresponding deformation in elongation for both the hydraulic rod is $$\Delta {\lambda }_{1}$$. Then the total stretching deformation of the hydraulic rod is $${\lambda }_{b}+{\rm{\Delta }}{\lambda }_{1}+{\rm{\Delta }}{\lambda }_{2}$$. As shown in the figure, the total load applied on the hydraulic rod $$F$$ equals the sum of the working pulling force $${F}_{\mathrm{left}}$$ and $${F}_{\text{right}}$$ and the residual preload force $${F}_{x}$$. [Image Omitted. See PDF]

Then the loads of four hydraulic rods are: [Image Omitted. See PDF]

SOLVING THE LOAD EQUATION OF THE HYDRAULIC ROD

As the load Equation (7) for the hydraulic rod involves multiple unknown variables, the bending moment equation, rotating angle equation, and deflection curve differential equation are used to determine such unknown variables.

Figure 5 shows the force and deformation diagram of the fuselage. Point A is set as the origin of the coordinate. When the shearer is working, a uniform load bear on the fuselage in the Y direction, originating from the supporting force of the joint bolt and self-gravity force, is denoted as $${q}_{1}$$. The friction force between the fuselage and the walking mechanism is $${F}_{m}^{y}$$. The residual preload acting on the fuselage in X-direction, originating from the hydraulic rod, is denoted as $${F}_{x}$$. The bending moment at the end of the connection between the fuselage and the walking part is expressed as $${M}_{1}$$.

Figure 5. Schematic diagram of the force and deformation in the fuselage

Setting A as the origin, the force balance equation in the Y-direction is $$\sum Y=0$$, which can be expressed as [Image Omitted. See PDF]where $${l}_{1}$$ denotes the length of the fuselage.

Now set $${M}_{e}={M}_{1}-{F}_{x}{L}_{C}$$, the bending momentum balance equation of the fuselage is given by [Image Omitted. See PDF]

Without any supporting frame on the bottom, the fuselage is supported only by the hydraulic rod and the connecting bolts. However, only the connecting bolts can take shear force in the Y-direction. This means that [Image Omitted. See PDF]where $${m}_{1}$$ is the mass of the fuselage.

For the bending deformation of the fuselage, the integral method is used to solve the approximate differential equation of the deflection curve of the fuselage bending deformation, and the deflection and rotation equations of the fuselage bending are obtained. [Image Omitted. See PDF]

Substituting the bending momentum equation of the fuselage into Equation (11) and imposing the boundary conditions of the fuselage and the smooth continuous condition $${\theta }_{1}(\frac{{l}_{1}}{2})=0$$, $${\omega }_{1}(0)=0$$, we can determine the constant terms in the equation and further obtain the rotating angle and deflection equation of the fuselage as [Image Omitted. See PDF]where $${E}_{1}{A}_{1}$$ is the flexural rigidity of the fuselage.

Taking the upper hydraulic rod on a coal wall as the object in the study, a force and deformation diagram of the upper hydraulic rod can be plotted, as shown in Figure 6, where D is the origin of the coordinate.

Figure 6. Schematic diagram of the force and deformation in the upper hydraulic rod on a coal wall

The hydraulic rod on the coal wall is subjected to both self-gravity force and the force exerted by the fuselage in the Y-direction. Therefore, we have [Image Omitted. See PDF]where $${m}_{2}$$ and $${l}_{1}+2{l}_{2}$$ are the mass and length of the hydraulic rod on the coal wall, respectively.

The mid-section of the hydraulic rod on the coal wall supports the fuselage, while the two ends of the hydraulic rod are connected with the left and right walking mechanism. Therefore, the entire hydraulic rod needs to be segmented into different sections for the analysis. Then the torque balance equation can be expressed as [Image Omitted. See PDF]where, $${F}_{2y}$$ denotes the constraint force of the bolt on the hydraulic rod on the coal wall upper side in the Y direction, $${q}_{3}$$ denotes the support load of the walking part on both ends of the hydraulic rod on the coal wall upper side, $${M}_{2}$$ denotes the moment of the hydraulic rod on the coal wall upper side of goaf at point A.

The force balance equation in the Y-direction, $$\sum Y=0$$, can be expressed as [Image Omitted. See PDF]

After substituting Equation (15) into Equation (14), we can obtain: [Image Omitted. See PDF]

Substituting Equation (16) into Equation (11) and imposing the boundary conditions of the hydraulic rod and the smooth continuous condition, we can obtain the rotating angle and deflection equations of the hydraulic rod on the coal wall as [Image Omitted. See PDF] [Image Omitted. See PDF]

The hydraulic rod on the coal wall is in close contact with the fuselage. Based on the deformation relationship, both parts must share the same rotating angle at point A and the same deflection at point B, as given by [Image Omitted. See PDF]where [Image Omitted. See PDF] [Image Omitted. See PDF]

According to Figure 6, the two ends of the hydraulic rod are subject to the same force and deformation along the Y-direction. Therefore, they also share the same rotating angle at point D and E, that is, [Image Omitted. See PDF]where [Image Omitted. See PDF]

Simplifying the equation yields [Image Omitted. See PDF]

Set [Image Omitted. See PDF]

Equations for $${M}_{2}$$, $${F}_{2y}$$, $${F}_{N}$$ can be obtained [Image Omitted. See PDF]

Rearranging Equation (22), we can obtain the following matrix equation: [Image Omitted. See PDF]where $$\tilde{X}={[{M}_{2}{F}_{2y}{F}_{N}]}^{T};\tilde{A}=\left[\begin{array}{ccc}{A}_{11} & {A}_{12} & {A}_{13}\\ {A}_{21} & {A}_{22} & {A}_{23}\\ {A}_{31} & {A}_{32} & {A}_{33}\end{array}\right];\tilde{B}=\left[\begin{array}{c}{B}_{1}\\ {B}_{2}\\ {B}_{3}\end{array}\right];\left\{\begin{array}{c}{A}_{11}=12\\ {A}_{12}=(6b-6){l}_{1}\\ {A}_{13}=a{l}_{1}\end{array}\right.$$ [Image Omitted. See PDF]

$${M}_{2}$$, $${F}_{2y}$$, and $${F}_{N}$$ can be obtained by solving the matrix Equation (23). The remaining unknown variables can be obtained by substituting these values in the corresponding equations. The residual preload in each individual hydraulic rod can be obtained by substituting the residual preload $${F}_{x}$$ into Equation (2). Based on the solution of the entire shearer model developed in previous studies,^18,19 we can derive the loads on the guide support plate and plane support plate in different directions as well as the three-way loads of the roller. Substituting these values in Equations (1), (4), and (7), we can obtain the values of $$x$$, $$\delta $$, and $$\gamma $$, and ultimately derive the deformation and load of each hydraulic rod.

ANALYSIS OF SOLUTION RESULTS OF THE LOAD MODEL

Based on the load model of the hydraulic rod and solution developed in this study, as well as the previously measured three-way load of the roller and the counterforce of the support plate,^18,19 brought into Equation (23) to solve, the deformation and load of the hydraulic rod in the shearer can be derived, as shown in Figures 7 and 8.

Figure 7. Deformation of the hydraulic rod. (A) Upper hydraulic rod on the coal wall, (B) lower hydraulic rod on the coal wall, (C) upper hydraulic rod on the gob side, and (D) lower hydraulic rod on the gob side.

Figure 8. Loads acting on the hydraulic rod. (A) Upper hydraulic rod on the coal wall, (B) lower hydraulic rod on the coal wall, (C) upper hydraulic rod on the gob side, and (D) lower hydraulic rod on the gob side.

The upper and lower hydraulic rod on the coal wall exhibit the largest and second-largest deformation with maximum deformation magnitudes of 2.4696 and 1.653 mm, respectively (Figure 7). The lower hydraulic rod on the gob side exhibits the smallest deformation with a maximum deformation magnitude of 0.9652 mm. The upper hydraulic rod on the gob side is subjected to compressive deformation with a maximum deformation magnitude of −1.6346 mm.

The average elongation of the upper hydraulic rod on the coal wall, lower hydraulic rod on the coal wall, and lower hydraulic rod on the gob side are 2.0885, 1.197, and 0.58 mm, respectively. The average compression of the upper hydraulic rod on the gob side is 2.2474 mm.

As shown in Figure 8, the upper and lower hydraulic rod on the coal wall are subjected to the largest and second-largest loads with maximum values of 561.16 and 527.941 kN, respectively. The maximum loads applied on the lower and upper hydraulic rods on the gob side are 459.202 and 404.54 kN, respectively.

The average loads acting on the upper hydraulic rod on the coal wall, the lower hydraulic rod on the coal wall, the lower hydraulic rod on the gob side, and the upper hydraulic rod on the gob side are 538.1483, 500.299, 445.952, and 375.125 kN, respectively.

These results can be mainly attributed to the upper hydraulic rod on the coal wall being the closest strut to the drum. While cutting through the coal wall, the drum generates vibrations, which influence the load and deformation. Therefore, the load applied on the upper hydraulic rod on the coal wall experiences the most intense fluctuations. When coal and rocks are cut off from the coal wall, some materials are scattered on the pin rail. As the shearer travels on the track, these scattered materials affect the engagement between the wheel and the rail, which will further result in large fluctuations in the load on the lower hydraulic rod on the gob side near the guide support plate. The plane support plate provides only a supportive load and is not subjected to any force in both the X- and Z- directions. Consequently, the plane support plate has a relatively simple force structure and is more prone to the impact of the scattered coal. As a result, the lower hydraulic rod on the coal wall near the plane support plate also exhibits a certain level of load fluctuation. Finally, the upper hydraulic rod on the gob side is the farthest strut away from the equivalent vibration center of the shearer. Therefore, it experiences the least load fluctuation.

EXPERIMENTAL VALIDATION

To validate the accuracy of the load model of hydraulic rod in a shearer, on-site simulation experiments were performed at the “Coal Mining Machinery Equipment R&D Experimental Center” in Zhangjiakou National Energy Center Key Laboratory. A coal wall with a 1:1 ratio was constructed at the experimental center. The hardness, height, and length of the simulated coal wall were f₃, 3 m, and 70 m, respectively. The MG500/1180 shearer and SGZ1000/1050 scraper conveyor were used in the study. Figure 9 shows the image of the experimental site. The experimental system is capable of measuring the mechanical properties of the entire mining system. To ensure proper data acquisition and transmission, a wireless data transmission method was used.^20-22 The installation of the data acquisition sensor and data transmission flowchart are shown in Figure 10. During the experiment, the cutting speed of the shearer, cutting depth of the drum, and the rotating speed of the roller were 3 m/min, 500 mm, and 28 r/min.

Figure 9. Experimental site

Figure 10. Installation of the sensor and methods for wireless data transmission

The mechanical properties of the hydraulic rod and the bolt were tested using a pressure ring sensor manufactured by Beijing Beetech Inc. Primary technical parameters are shown in Table 1.

Table 1 Primary technical parameters of pressure ring sensor

Range	Accuracy	Safety overload	Operating temperature	Thermal drift at zero degree	Sensitivity thermal drift
65 T	0.02%Fs or above	150%Fs	−20–65°C	< 0.05%Fs/10°C	<0.03%Fs/10°C

To ensure the accuracy of data acquisition, the pressure ring sensor must be calibrated properly before the experiments.²² In addition, the load required application in small increments. Therefore, the load was increased from 0 to 50 kN with a 10 kN gap during the calibration. The calibration procedure was repeated for multiple times until an average of actual known values was reached. The calibration values of the pressure ring sensor are summarized in Table 2.

Table 2 Calibration values of the pressure ring sensor

Loading force (kN)	0	10	20	30	40	50
Output from the pressure ring sensor (mV)	0.1	88.4	165	250.6	338.6	423.6

The calibration values were fitted with a third order polynomial curve using the cftool tool in MATLAB, as shown in the following equation: [Image Omitted. See PDF]

The working pressure of the shearer during a 50 s cutting operation was measured by the pressure ring sensor. The voltage output from the sensor was converted to the force output using the conversion correlation provided by the sensor manufacturer, as shown in Figure 11.

Figure 11. Experimental measurements of the load on the hydraulic rod. (A) Upper hydraulic rod on the coal wall, (B) lower hydraulic rod on the coal wall, (C) upper hydraulic rod on the gob side, and (D) lower hydraulic rod on the gob side.

As shown in Figure 11, when the shearer cut across the coal wall during normal operation, the upper hydraulic rod on the coal wall was subjected to the largest load with a maximum value of 525.86 kN, followed by the lower hydraulic rod on the coal wall and lower hydraulic rod on the gob side with 506.59 and 497.73 kN, respectively. The upper hydraulic rod on the gob side experienced the smallest load with a maximum value of 379.64 kN.

As shown in Table 3, the values calculated using the load equation generally agree with the measurements. The upper hydraulic rod on the coal wall was subjected to the largest load, followed by the lower hydraulic rod on the coal wall, lower hydraulic rod on the gob side, and upper hydraulic rod on the gob side. The error between the calculated and measured values was found to be quite large for the upper hydraulic rod on the coal wall but relatively small for the rest of the struts. For application in large-scale facilities such as coal mine machinery, such error is within the acceptable range of accuracy.

Table 3 Calculated and measured values of the load on hydraulic pulling struts and the corresponding error

Average load on the hydraulic pulling strut	Calculated value (kN)	Measured value (kN)	Error between calculated and measured values (%)
Upper hydraulic rod on coal wall ($${l}_{u1}$$)	538.148	519.257	3.5
Lower hydraulic rod on gob side ($${l}_{u2}$$)	375.1247	376.601	0.4
Lower hydraulic rod on coal wall ($${l}_{d1}$$)	500.299	506.59	1.26
Lower hydraulic rod on gob side ($${l}_{d2}$$)	445.952	497.73	1.2

The above error can be attributed to the difference between the working environments of the mathematical model and actual underground mining. The mathematical model is established under ideal working conditions, but actual underground mines are much more complex and may involve many uncertain factors. Therefore, although comprehensive efforts have been made to reflect real conditions through the coal wall simulation, differences between the simulation and practical conditions are inevitable. When the drum cuts across the coal wall, falling coal materials induce more complexity in the running resistance of the support plate. Furthermore, the force analysis of the walking mechanism and the fuselage only consider the bending deformation of the hydraulic pulling strut and the fuselage themselves. In reality, the shearer itself may also experience a certain level of deformation.

LOAD CHARACTERISTICS OF THE HYDRAULIC ROD UNDER DIFFERENT PITCH AND ROLL ANGLE CONDITIONS

With the development of the coal mine itself and mining activities, the working faces of the coal mine may develop significantly different pitch and roll angles. With large pitch and roll angles, the force applied to the hydraulic rod in the shearer can change drastically. Using the proposed theoretical load model of the hydraulic rod of the MG500/1180 shearer, we derived load conditions on the hydraulic rod under different scenarios.

Relevant parameters of the shearer are set as follows. The swing angle of the front rocker arm is $${\alpha }_{1}=22^\circ $$, the swing angle of the rear rocker arm is $${\alpha }_{2}=8^\circ $$, and the pitch angle is $$\alpha =-5^\circ $$. The roll angle $$\beta $$ is 0°, 5°, 10°, 15°, 20°, and 25°. Loads applied on the hydraulic rod when the shear cuts through the coal wall under different roll angles are shown in Figure 12.

Figure 12. 3D load surfaces under different roll angles for the hydraulic rod. (A) Upper hydraulic rod on the coal wall, (B) lower hydraulic rod on the coal wall, (C) upper hydraulic rod on the gob side, (D) lower hydraulic rod on the gob side.

Figure 12A shows that the maximum load on the upper hydraulic rod on the coal wall increases with increasing roll angle. When the roll angle increases from 0° to 25°, the maximum load on the hydraulic rod also increases from 574.28 to 643.91 kN with a 12.1% increment. These results show that the roll angle significantly affects the load on the hydraulic rod on the coal wall.

Figure 12B shows that the load on the lower hydraulic rod on the coal wall decreases with increasing roll angle. In particular, when the roll angle increases from 0° to 25°, the maximum load on the hydraulic rod decreases from 541.02 to 530.83 kN with a 1.9% reduction. Therefore, the roll angle has a small effect on the load on the hydraulic rod. A small fluctuation of the curve is observed at a roll angle of approximately 15°.

Figure 12C shows that the load on the upper hydraulic rod on the gob side decreases with increasing roll angle. In particular, when the roll angle increases from 0° to 25°, the maximum load on the hydraulic rod decreases from 378.62 to 359.85 kN with a 4.9% reduction.

Figure 12D shows that the load on the lower hydraulic rod on the gob side first increases and then decreases with increasing roll angle. In particular, when the roll angle increases from 0° to 25°, the maximum load on the hydraulic rod first increases from 454.82 to 462.57 kN with a 1.7% increment, and then decreases from 462.57 to 451.71 kN, with a 2.4% decrement. Overall, the impact of roll angle change on the load on the upper hydraulic rod on the gob side is relatively small. The maximum load on the hydraulic rod is reached with a roll angle of 15°.

Maintaining the same parameters of the shearer, the loads applied on the hydraulic rod when the shear cuts through the coal wall under different pitch angles were investigated, as shown in Figure 13. The roll angle is $$\beta =5^\circ $$, and the pitch angles $$\alpha $$ are −10°, −5°, 0°, 5°, and 10°.

Figure 13. 3D load surfaces under different pitch angles for the hydraulic rod. (A) Upper hydraulic rod on the coal wall, (B) lower hydraulic rod on the coal wall, (C) upper hydraulic rod on the gob side, and (D) lower hydraulic rod on the gob side.

Figure 13A shows that the maximum load on the upper hydraulic rod on the coal wall increases with increasing pitch angle. When the pitch angle increases from −10° to 10°, the maximum load on the hydraulic rod also increases from 618.85 to 636.31 kN with a 3.1% increment.

Figure 13B shows that the load on the lower hydraulic rod on the coal wall decreases with increasing pitch angle. When the pitch angle increases from −10° to 10°, the maximum load on the hydraulic rod decreases from 542.54 to 530.22 kN with a 2.3% reduction.

Figure 13C shows that the load on the upper hydraulic rod on the gob side increases with increasing pitch angle. When the pitch angle increases from −10° to 10°, the maximum load on the hydraulic rod also increases from 354.86 to 355.75 kN with a 0.25% increment.

Figure 13D shows that the load on the lower hydraulic rod on the gob side decreases with increasing pitch angle. When the pitch angle increases from −10° to 10°, the maximum load on the hydraulic rod decreases from 458.57 to 448.54 kN with a 2.2% reduction.

These results show that the pitch angle change has significant and small impacts on the load on the upper and lower hydraulic rods on the coal wall, respectively. In addition, the pitch angle change has negligible and relatively small impacts on the load on the upper and lower hydraulic rods on the gob side, respectively.

CONCLUSION

• (1)

  Taking the critical load, preload, working load, and residual load on hydraulic rods in a shearer into consideration, the load equation of the hydraulic rod could be established based on the principle of compatibility of small deformation.

• (2)

  The load equation of the hydraulic rod, together with the deflection and rotation angle equations of the fuselage and hydraulic rod, were solved using the integration method. Maximum deformation magnitudes of 2.4696, 1.6530, and 0.9652 mm were calculated for the upper hydraulic rod on the coal wall, lower hydraulic rod on the coal wall, and lower hydraulic rod on the gob side, respectively. The upper hydraulic rod on the gob side was subjected to compressive deformation with a maximum deformation magnitude of −1.6346 mm.

• (3)

  By solving the load equation, the upper hydraulic rod on the coal wall was found to experience the largest load with a maximum value of 561.16 kN, followed by the lower hydraulic rod on the coal wall at 527.941 kN. The lower and upper hydraulic rods on the gob side experienced maximum loads of 459.202 and 404.54 kN, respectively. These calculation results were compared with the experimental measurements and the error was found to be less than 3.5%. Such error meets the accuracy requirements and validates the accuracy of the proposed model.

• (4)

  From the calculated results of the load on the hydraulic rod under different pitch and roll angles, changes in pitch and roll angles were found to have a significant impact on the load on the upper hydraulic rod on the coal wall. In particular, the change in roll angle could lead to changes in the maximum load by high as 12.1%. The loads on the rest three hydraulic rods were less sensitive to changes in the pitch and roll angles. In particular, changes in pitch angle had negligible effects on the load on the upper hydraulic rod on the gob side (0.25%).

Overall, the findings of this study provide an important basis for understanding the load characteristic of the entire shearer, optimizing the structure of the hydraulic rod, and improving the lifetime of the shearer.

ACKNOWLEDGMENTS

This study was supported by the National Natural Science Foundation of China (52104134, 51974159), the Young Elite Scientists Sponsorship Program by CAST (2021QNRC001), the China Postdoctoral Science Foundation (No. 2020M682268), and Major Scientific and Technological Innovation Project of Shandong Province (2019SDZY04).