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Abstract

In order to improve the drilling performance of polycrystalline diamond compact bit and prolong its service life during drilling in coal rock under the action of wind cycle, the theoretical calculation model of polycrystalline diamond compact bit cutting teeth temperature was derived based on the theory of tribology and heat transfer. The theoretical temperature field of polycrystalline diamond compact bit-cutting teeth was analyzed. Using the joint simulation of EDEM–FLUENT, the temperature variation law of polycrystalline diamond compact bit cutting teeth under the thermo-fluid–solid coupling was analyzed to verify the validity of the theoretical calculation model of polycrystalline diamond compact bit cutting teeth temperature. By building a rotary drilling test platform and conducting drilling experiments on polycrystalline diamond compact bit under different drilling parameters respectively, the correctness of the theoretical model and the simulation data were verified. In addition, a response surface analysis model was established to study the influence of different drilling parameters on the polycrystalline diamond compact bit cutting teeth temperature during drilling in coal rock. The analysis results show that the influence degree of various drilling parameters on the polycrystalline diamond compact bit cutting teeth temperature from large to small is drilling pressure, drilling speed, coal rock properties, and wind speed. Compared with the working condition without wind cycle, the drilling efficiency of polycrystalline diamond compact bit can be increased by 14.38% and the temperature is reduced by 8% when it drills in coal. The drilling efficiency of polycrystalline diamond compact bit can be increased by 17.79% and the temperature is reduced by 10.5% when it drills in coal gangue.

Keywords

Polycrystalline diamond compact bit thermo-fluid–solid coupling response surface analysis cutting teeth temperature temperature variation

Introduction

Polycrystalline diamond compact (PDC) is a special super-hard material synthesized by artificial diamond and cemented carbide in one-time synthesis under high-temperature conditions,¹ which not only has the advantages of high hardness and wear resistance of diamond, but also has the characteristics of strong impact resistance and large blade emergence. Using it as the bit cutting teeth can improve the drilling efficiency.² Nowadays, PDC bits are widely used in coalfield drilling and mining, petroleum drilling, geological exploration, and other industries.^3–5 In order to determine the effect of tilt angle on the frictional force on the cutting surface of a single cutting tooth within a certain depth of cut, Rostamsowlat conducted cutting experiments on two different rock samples by using state-of-the-art rock cutting equipment and a unique tool holder and concluded that the normal contact stress on the contact surface between the cutting surface and the rock depends on the depth of cut, but in the region of elastic contact, the contact stress changes as the depth of cut increases.⁶ Zhou et al.⁷ considered the wear process of circular tools and derived a simple model for the relationship between depth of cut and mechanical specific energy, and found that the wear of cutting teeth usually leads to lower efficiency, increased mechanical specific energy, or lower drilling speed. Li et al.⁸ used ABAQUS software to establish a numerical model of single tooth-rock interaction of PDC bit, the cohesive force and compressive stress of rock material are alternately distributed in the damage area, and the highest rock breaking efficiency is obtained when the impact conditions are the same and the axial impact frequency is 1/2 of the torsional impact frequency; if the impact frequency is too small, the rock cannot be broken effectively and the drilling process will occur viscous slip vibration.

The tool wear rate is highly influenced by the temperature distribution.^9,10 In bit drilling, Han et al.¹¹ established a mathematical model of bit-cutting force based on the principle of coal rock cutting and conducted drilling experiments under different drilling conditions. The results showed that the rotational speed was inversely proportional to the feed resistance. The drilling torque and feed resistance were the lowest when the coal rock surrounding pressure was 7 MPa.¹² At the same time, the drilling temperature has been studied.^13,14

More than 70% of PDC drill failures are caused by damage to the PDC cutting teeth, mainly in the appearance of wear and fracture of the cutting teeth. Glowka et al.^15,16 developed a model to predict the average wear temperature of the PDC bit by simulating the working conditions of the PDC bit under steady-state as well as transient operating conditions and concluded that the wear rate of the PDC bit will increase significantly when the drilling temperature is higher than 350 °C. What's more, a numerical analysis model was established for predicting the temperature of the PDC bit under drilling with fluid flow. Appl et al.¹⁷ used thermocouples to measure the temperature of water and air jet-assisted cooling tools cutting the granite separately. A tool wear model was established, and to the conclusion was drawn that as the tool temperature increases, the tool wear rate gradually increases and the tool will be born out quickly when the critical temperature (700 °C) is reached. Li et al.¹⁸ established a temperature field model and a thermal stress calculation model for water jet-assisted rock drilling in combination with the boundary conditions such as heat flow density and interface temperature, and concluded that thermal stress was the main reason for tool failure and that thermal stress was related to parameters such as tool and rock material properties, geometric dimensions, cutting parameters and jet pressure. Gao et al.¹⁹ established a temperature calculation model in order to study the influence of parameters and rock type on the temperature of the bit in drilling. The temperature of PDC cutting teeth under different parameter combinations was qualitatively analyzed with temperature tests, the experimental results were obtained to be in good agreement with the simulation results, in which the drilling speed would increase the temperature of cutting teeth. Under the same working parameters, the cutting teeth temperature is highly correlated with the type of rock drilled and the value of drilling speed. Yang et al.²⁰ established an equation of temperature variation during the drilling process of a drill bit into rocks and concluded that the drilling temperature of the bit is affected by geometric conditions, thermo-physical properties, and drilling parameters. The average temperature of bit is positively proportional to the square of bit feed speed. Li et al.²¹ established a temperature field model and a thermal stress calculation model for water jet-assisted rock drilling in combination with the boundary conditions such as heat flow density and interface temperature, and concluded that thermal stress was the main reason for tool failure and that thermal stress was related to parameters such as tool and rock material properties, geometric dimensions, cutting parameters and jet pressure. Li et al.²² simulated the temperature field of PDC bit cutting teeth during the cutting process based on the finite element analysis software and discussed the temperature distribution of cutting teeth during the cutting process to provide an effective basis for the future design of PDC bits. Zhang et al.²³ used the finite element method to simulate the temperature field of the PDC bit during rock breaking by thermo-solid coupling, and concluded that the main failure part of the cutting teeth was concentrated on the top of the crown of the cutting teeth; and the temperature of the cutting teeth of granite was found to be about two times that of marble and three times that of sandstone under the verification of experiments. Beaton et al.²⁴ proposed a new technique that can eliminate bit wear and improve the drilling ability as well as the drilling life when compared with the wear of conventional bits. Karasawa et al.²⁵ proposed a calculation model for estimating cutting teeth wear, conducted room experiments using different types of bits, and proposed a method for measuring wear on cutting teeth surfaces based on the experimental results. Based on this, Karasawa et al.²⁶ conducted drilling experiments using three bits on various types of rock samples and found that the wear of each bit was torque-dependent. Kazi et al.²⁷ used two different methods to estimate the cutting-specific energy, and the results of the study found that the higher the rock strength, the greater the wear of the PDC bit, the drilling efficiency will be reduced, the drilling cycle will be prolonged, and the drilling cost will increase.²⁸

In recent years, driven by computing power, response surface analysis has been widely used in various industries at home and abroad.^29–32 Liu et al. used the discrete element method to study the wear behavior of auger bit picks and conducted the response surface analysis on ribbed picks.³³ Zhang proposed a method that combined the numerical computational model with the response surface method. This method can optimize the model of blade-type forgings and construct the strain and temperature functions that characterize each part of the blade. So, the optimal shape of the forging blank can be determined to obtain satisfactory forming results.³⁴

If the thermal stress exceeds the allowable strength of the bit material, the bit deformation, wear, and failure will occur, which not only affects the drilling efficiency, but also greatly affects the lifetime of the bit. Researchers at home and abroad have conducted in-depth research on the temperature of the drill bits during operation and the methods to reduce the bit temperature. However, few people have participated in the calculation of the temperature of bit-cutting teeth using the discrete element method. Previous research has not considered the effect of the wind cycle on bit temperature. In this article, a temperature calculation model of PDC bit based on wind cycle is established based on wind cycle, which not only improves the calculation model of PDC bit drilling temperature, but also improves the prediction accuracy of PDC bit drilling temperature. Based on the research of the bit temperature field, this paper will further analyze the temperature rise mechanism of PDC bit during drilling under wind circulation, and use the response surface analysis method to study and predict the relationship between factors such as drilling speed, drilling pressure, wind speed coal rock properties and the cutting teeth temperature during working.

Temperature model of PDC bit cutting teeth

During the drilling process of PDC bit in coal rock, the bit-cutting teeth are easy to be damaged, which will determine the working efficiency of the bit. The tri-wing PDC bit is mainly composed of the bit body, composite cutting teeth, air hole, chip removal groove, and diameter maintaining bar which is shown in Figure 1. The diameter and thickness of composite cutting teeth are 13.4 and 3 mm, respectively. The thickness of polycrystalline diamond is 0.5 mm. The outer diameter of the bit body is 72 mm and the inner hole diameter is 62 mm.

Figure 1.

Structure of polycrystalline diamond compact (PDC) bit.

The cutting heat of the PDC bit when drilling in coal rock mainly comes from the friction between the bit and the coal rock in the deformation zones during drilling. As shown in Figure 2, the heat generation zones are mainly in the three cutting deformation zones near the cutting teeth which are the shear deformation zone I, teeth front end deformation zone II, and teeth lower end deformation zone III.

Figure 2.

Cutting deformation zones.

The forces on the single cutting tooth when cutting coal rock is analyzed and the mechanical and velocity relationship equations are established.

The speed of cutting V is

V = 2 π R n

(1)

where R is the radius of bit and n is the rotation speed.

The friction velocity between coal rock and cutting tooth $V_{1}$ is

V_{1} = \frac{V \sin r_{0}}{\cos (φ - r_{0})}

(2)

where

r_{0}

is the top rake of cutting teeth and

φ

is the shear angle.

The shear speed of cutting tooth and coal rock $V_{s}$ is

V_{s} = \frac{V \cos r_{0}}{\cos (φ - r_{0})}

(3)

The shear stress on the shear surface of a coal rock chip

F_{s}

F_{s} = F_{t} \cos φ - F_{b} \sin φ

(4)

The friction between the chip and the front of the tooth

F_{1}

F_{1} = F_{t} \sin r_{0} - F_{b} \cos r_{0}

(5)

The main cutting force during cutting

F_{t}

F_{t} = F_{N f} \cos r_{0} + F_{b} μ

(6)

The coal rock force on a bit during drilling

F_{b}

F_{b} = b \cdot P_{m} [\frac{0.6}{\cos α} + \frac{1}{3} (△ L_{f} - \frac{0.6}{\cos α})]

(7)

where

F_{N f}

is the combined force of positive stresses uniformly distributed over the coal rock shear body,

μ

is the coefficient of friction between the wear surface of the cutting tooth and the coal rock,

P_{m}

is the maximum value of coal rock stress, expressed as

P_{m} = k σ_{s}

△ L_{f}

is the wear length of the cutting tooth.

The heat generated on the shear surface can be expressed as

q_{ts 1} = \frac{F_{s} V_{s}}{a_{c} a_{w} \csc φ}

(8)

where

a_{c}

is the cutting thickness and

a_{w}

is the cutting width.

The proportion of heat transmitted from the shear surface to the bit is

R_{1} = \frac{q_{ts 1}}{V c_{1} ρ_{1} \sin φ (\frac{q_{ts 1}}{V c_{1} ρ_{1} \sin φ} + \frac{377 a_{c} q_{ts 1}}{1000 \sqrt{L_{1}} k_{1} \sin φ})}

(9)

where

c_{1}

is the specific heat capacity of coal rock,

ρ_{1}

is the density of coal rock,

k_{1}

is the thermal conductivity of coal and

L_{1}

is the calculation parameter and

L_{1} = V_{s} a_{c} \csc φ ε / 4 K_{1}

K_{1}

is the thermal diffusivity of coal rock and

ε

is the shear deformation coefficient and

ε = \cos r_{0} / \sin φ \cos (φ - r_{0})

The temperature rise of the shear surface can be expressed as

Δ T_{1} = \frac{R_{1} q_{t s_{1}} \csc φ}{V c_{1} ρ_{1}}

(10)

The heat generated on the end face of the teeth front angle can be expressed as

q_{ts 2} = \frac{F_{1} V_{1}}{l_{f} a_{w}}

(11)

where

l_{f}

is the contact length of cutting teeth end face with coal rock.

The proportion of heat transferred to coal rock can be expressed as

R_{2} = 1 - \frac{377 k_{3} - 1000 \sqrt{L_{2}} k_{2} + 1000 \bar{A} \sqrt{L_{2}} k_{2}}{377 k_{3} + 1000 \bar{A} \sqrt{L_{2}} k_{2}}

(12)

where

k_{3}

is the thermal conductivity of bit,

k_{2}

is the thermal conductivity of coal chips, and

\bar{A}

is the area factor of moving plane heat source. Due to the length–width ratio of the heat source of the PDC bit during drilling in coal rock

\frac{m}{l}

is bigger than 20,

\bar{A}

can be expressed as

\bar{A} = \frac{2}{π} [\ln \frac{2 m}{l} + \frac{1}{2} + \frac{1}{3} \frac{l}{m}]

, and

L_{2}

is the calculation parameter and

L_{2} = V_{1} l_{f} / 4 K_{2}

K_{2}

is the thermal diffusivity of coal rock chips.

The temperature rise of the teeth front angle end face can be expressed as

Δ T_{2} = \frac{0.377 (1 - R_{2}) q_{t s_{2}} l_{f}}{k_{2} \sqrt{L_{2}}}

(13)

The frictional heat between the rest part of the bit and the coal rock can be expressed as

q_{ts 3} = (f_{1} + f_{2}) V

(14)

The temperature rise from the friction of the rest part of the bit with coal rock can be expressed as

Δ T_{3} = \frac{q_{ts 3}}{c_{2} m_{2}}

(15)

where

c_{2}

is the specific heat capacity of bit and

m_{2}

is the mass of bit.

The process of wind force passing through the interior of the PDC bit to the cutting teeth can be regarded as the outward swept flat plate convection heat exchange:

From Newton's cooling equation, the heat flow from the bit to the wind cycle q is

q = h A_{c} = h A_{c} (t_{1} - t_{2})

(16)

Substituting into Newton's cooling equation, the heat flow absorbed during the wind cycle is

Q = 0.332 π r_{n}^{2} (t_{1} - t_{2}) \frac{k_{4}}{l} {(\frac{u l}{ν})}^{\frac{1}{2}} {(\frac{ν}{a})}^{\frac{1}{3}} = c_{3} m_{3} Δ T_{F}

(17)

m_{3} = ρ_{3} π r_{n}^{2} d s

(18)

where q is the heat flow from the bit to the wind cycle, h is the convective heat transfer coefficient,

A_{c}

is the heat transfer area between cutting tooth and wind cycle,

t_{1}

is the temperature of bit,

t_{2}

is the temperature of air,

r_{n}

is the inner radius of the drill pipe,

k_{4}

is the thermal conductivity of the wind, u is the wind speed, l is the total length of the drill pipe and bit,

ν

is the kinematic viscosity, and a is the thermal diffusivity,

a = k_{4} / ρ_{3} c_{3}

c_{3}

is the specific heat capacity,

m_{3}

is the mass of the wind fluid involved in the heat transfer, and

d s

is the thickness of the wind cycle on the cutting tooth.

The wind fluid absorbs the temperature $Δ T_{F}$ is

Δ T_{F} = \frac{Q}{c_{3} m_{3}}

(19)

The temperature during drilling and with wind circulation is

T_{f} = Δ T_{1} + Δ T_{2} + Δ T_{3} + T_{0} - Δ T_{F}

(20)

From equations (10), (13), (15), and (17), the average temperature rise of the cutting teeth of a bit under the wind cycle can be deduced as:²⁶

Δ T = \frac{1}{2} (\begin{matrix} \frac{R_{1} q_{t s_{1}} \csc ϕ}{V c_{1} ρ_{1}} + \frac{0.377 (1 - R_{2}) q_{t s_{2}} l_{f}}{k_{2} \sqrt{L_{2}}} \\ + \frac{q_{ts 3}}{c_{2} m_{2}} + \frac{0.332 A_{c} (t_{1} - t_{2}) \frac{k_{F}}{l} {Re}^{\frac{1}{2}} {Pr}^{\frac{1}{3}}}{c_{F} M} + T_{0}^{'} \end{matrix})

(21)

where

c_{F}

is the specific heat capacity of air in wind cycle and

T_{0}^{'}

is the initial temperature of air.

After ensuring the steady-state temperature of the bit, the temperature of the PDC bit cutting teeth at any distance from the interface at any time can be expressed as:³⁶

T (p, t) = e r f c [\frac{p}{2 \sqrt{\frac{k_{3} t}{ρ_{2} c_{2}}}}] Δ T + T_{0}^{″}

(22)

where p is the distance to the PDC bit cutting teeth, t is the cutting time,

ρ_{2}

is the density of cutting teeth, and

T_{0}^{″}

is the environmental temperature.

Theoretical model solution

To simplify the calculation, the relevant parameters are shown in Table 1. This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn. The temperature calculation flow of the bit during drilling under the wind cycle is shown in Figure 3, and the numerical calculation software MATLAB is applied to create the program to calculate the temperature field of the bit.

Figure 3.

Calculation flowchart.

Table 1.

Related parameters of model calculation.³⁷

Material	Parameter name	Value
Coal	Poisson ratio $(v_{1})$	0.32
	Elastic modulus $(GPa)$	7.85
	Density $(kg / m^{3})$	1280
	Thermal conductivity $(W / (m \cdot^{\circ} C))$	0.415
	Specific heat capacity $(J / (kg \cdot^{\circ} C))$	1.082
Gangue	Poisson ratio $(v_{1})$	0.23
	Elastic modulus $(GPa)$	40
	Density $(kg / m^{3})$	2630
	Thermal conductivity $(W / (m \cdot^{\circ} C))$	3.15
	Specific heat capacity $(J / (kg \cdot^{\circ} C))$	800
Cutting teeth	Poisson ratio $(v_{1})$	0.07
	Elastic modulus $(GPa)$	897
	Density $(kg / m^{3})$	3510
	Thermal conductivity $(W / (m \cdot^{\circ} C))$	543
	Specific heat capacity $(J / (kg \cdot^{\circ} C))$	790
Cemented carbide (bit substrate）	Poisson ratio $(v_{1})$	0.22
	Elastic modulus $(GPa)$	579
	Density $(kg / m^{3})$	15,000
	Thermal conductivity $(W / (m \cdot^{\circ} C))$	100
	Specific heat capacity $(J / (kg \cdot^{\circ} C))$	230
Air	Density $(kg / m^{3})$	1.225
Air	Dynamic viscosity $(kg / (m \cdot s))$	1.7894 × 10⁻⁵

Figure 4 shows the theoretical temperature of PDC bit cutting teeth for drilling coal rock, gangue, and coal-gangue model when the drilling pressure is 4 kN, wind speed is 0 m/s, and drilling speed is 100, 300, and 500 r/min, respectively. It can be seen that the temperature of bit-cutting teeth will increase with the increase of time. The higher the drilling speed, the higher the temperature of PDC bit cutting teeth. Because of the different properties of coal rock, the rate of temperature rise will also change. Under the same drilling conditions, when drilling in the gangue, the temperature rise is the fastest, followed by the coal-gangue model, and the temperature rise drilling in the coal-rock model is the slowest.

Figure 4.

The theoretical temperature of cutting teeth under windless conditions ( $V_{F} = 0 m / s$ ), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

Figure 5 shows the theoretical temperature of PDC bit cutting teeth for drilling the coal rock, gangue, and coal-gangue model when the drilling pressure is 4 kN, wind speed is 20 m/s and drilling speed is 100, 300, and 500 r/min, respectively. Under the same drilling parameters, the temperature rise trend is the same as that when the wind speed is 0 m/s. At the same time, the temperature of PDC bit cutting teeth under the wind cycle condition is lower than that under the no-wind cycle condition. So, the temperature rise rate of PDC bit cutting teeth under the wind cycle conditions is lower than that of PDC bit cutting teeth under the no-wind cycle condition.

Figure 5.

The theoretical temperature of cutting teeth under wind conditions ( $V_{F} = 20 m / s$ ), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

Simulation model analyze

In order to verify the accuracy of the theoretical model of PDC bit cutting teeth temperature, the Executive Diploma in Export Management (EDEM) and FLUENT software are used to jointly simulate the temperature rise process of PDC bit drilling different coal rock under the condition of wind cycle. In EDEM, the principle of frictional heat transfer between the bit and coal chips follows the Hertzian contact theory. The source of heat is mainly the friction heat between the particles and between the particles and bit:³⁸

q_{av} = \sum_{n = 1}^{2} μ_{n} \cdot F_{i j} \cdot v_{r n}

(23)

where

F_{i j}

is the normal contact force between particles as well as particles and bit,

μ_{1}

is the friction coefficient between particles,

μ_{2}

is the friction coefficient between particles and bit,

v_{r 1}

is the relative velocity between particles, and

v_{r 2}

is the relative velocity between particles and bit.

Firstly, EDEM is used to calculate the temperature data generated by drilling the bit with different groups of working parameters to obtain the temperature rise curves of the bit during the working time. The curve functions are transformed into heat flow density-related functions, and the temperature information is organized and input into FLUENT, which calculates the bit temperature under different wind cycle speeds according to the input heat flow density functions and the wind speed. The calculation process is shown in Figure 6.

Figure 6.

Simulation flowchart.

EDEM calculation settings

The coal rock and gangue models are created by using spherical particles with a diameter of 6 mm which are shown in Figure 7. In EDEM, the Hertz-Mindlin bonding model is adopted as the bonding contact model between coal rock or gangue particles, which is mainly defined by normal stiffness, shear stiffness, critical normal stress, critical shear stress as well and bonded disk radius. The calculation equations are as follows:³⁹

\begin{aligned} S_{n} = \frac{4}{3000} R^{*} \frac{1}{E^{*}} \\ S_{t} = f \cdot S_{n} \\ F_{n} = \frac{1}{2} (σ_{\max} + σ_{\min}) + \frac{1}{2} (σ_{\max} - σ_{\min}) \cos 2 α \\ F_{t} = C + F_{n} \tan β \\ R^{*} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} \\ \frac{1}{E^{*}} = \frac{1 - v_{1}^{2}}{E_{1}} + \frac{1 - v_{2}^{2}}{E_{2}} \end{aligned}

(24)

where

S_{n}

is the critical normal stress between coal particles,

R^{*}

is the equivalent contact radius between coal particles,

E^{*}

is the equivalent elastic modulus between coal particles,

S_{t}

is the critical shear stress between coal particles, f is the stiffness coefficient,

F_{n}

is the normal contact stress,

σ_{max}

is the maximum primary stress between coal particles,

σ_{min}

is the minimum primary stress between coal particles,

α

is the shear damage angle of coal,

F_{t}

is the tangential contact stress, C is the cohesive force of coal,

β

is the internal friction angle of coal,

R_{1}

and

R_{2}

are the radio of two bonded coal particles, respectively,

E_{1}

and

E_{2}

are the modulus of elasticity of the particles, respectively, and

v_{1}

and

v_{2}

are the Poisson's ratio of particles, respectively.

Figure 7.

Different coal rock models in the Executive Diploma in Export Management (EDEM), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

Import the 3D model of the bit into the EDEM and set the API contact model which is regenerated based on the changing physical properties of the coal or gangue particles within the EDEM. The simulation RayLeigh step is set to 20% and the overall simulation motion time is 1 s.

FLUENT calculation settings

The tetrahedral structured grid is used to mesh the bit model and divide the flow field calculation domain. The model is shown in Figure 8. To improve the mesh quality, the cutting teeth is approximated from cylinder to cuboid. The wind enters through the hole in the lower part of the bit and flows out through the air hole to complete the heat dissipation by air. In FLUENT, the turbulence model adopts the standard $k - ε$ model. In order to study the influence of different wind cycle speeds on the temperature of bit-cutting teeth, the velocity inlet is adopted and the outlet type is set as outflow. There is no slip condition on the wall surface and the convergence residual of the calculation simulation is $< 10^{- 5}$ .

Figure 8.

Bit three-dimensional (3D) model and wind cycle flow field diagram, should be listed as (a) a description of bit meshing; and (b) a description of a schematic diagram of wind circulation flow field of bit.

Simulation results and discussion

The simulation results are shown in Figures 9 and 10. After comparing with the theoretical calculation results in Figures 4 and 5, it can be seen that the starting time of the rapid rise of simulation temperature is slightly later than the theoretical value under the same drilling parameters. This is because there is a certain gap between the initial position of the bit and coal rock in the simulation setting. However, the overall temperature rise trend is more consistent with that of the theoretical value.

Figure 9.

Simulation temperature of cutting teeth under windless conditions ( $V_{F} = 0 m / s$ ), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

Figure 10.

Simulation temperature of cutting teeth under wind cycle ( $V_{F} = 20 m / s$ ), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

The graph shows the temperature cloud expression of the bit when the wind circulation speed is 0 m/s and the drilling pressure is 4 kN. From Figure 11, it can be seen that the main area of the highest temperature region is concentrated in the part, of the cutting teeth at the bottom of the bit and the head of the bit retaining bar which are in contact with the coal rock. Due to the particle model in the discrete element model being composed of small particles, the display area of drilling temperature is striped, and as the temperature increases, the wear rate also increases.

Figure 11.

The temperature cloud of the bit ( $V_{F} = 0 m / s$ ), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

Different from Figure 11, the cloud maps in Figure 12 were taken at a wind cycling speed of 20 m/s. Then the temperature difference can be seen with the same drilling parameters at different wind cycle speeds. When the wind speed increases, the temperature decrease is obvious in the base part of the bit. The highest temperature region remains in the cutting teeth part of the bit, which is also the reason why the cutting teeth of the bit are most prone to wear.

Figure 12.

The temperature cloud of the bit ( $V_{F} = 20 m / s$ ), should be listed as (a) a description of gangue; (b) a description of coal; and (c) a description of coal-gangue.

Experimental verification

In order to verify the theoretical and the simulation calculation results, an experimental platform is built, which consists of a drilling system, a screw feeding system, and a data acquisition system. It is shown in Figure 13.

Figure 13.

Schematic diagram of the overall structure of the test and experiment platform. 1—Experimental control panel; 2—three-phase asynchronous motor; 3—coupling; 4—bearing support; 5—drill rod; 6—conductive slip ring; 7—PDC (polycrystalline diamond compact) bit; 8—coal rock box; 9—lead screw feed device; 10—stepping motor; 11—air compressor; 12—signal test and analysis system; 13—thermocouple; and 14—computer.

The variable frequency motor drives the drilling rod and bit to rotate through a coupling. The coal rock box is fixed on the sliding table of the screw feeding device which is fixed on the fixed bracket and operated by a stepping motor type of $110 B Y G 350 E$ . The data acquisition system has consisted of thermocouples, conductive slip rings, temperature isolators, and acquisition software, which can realize the real-time detection and storage of the drilling parameters. At the same time, an oil-free air compressor is used to provide the wind for cooling the bit. The wind speed is tested by the wind meter.

The cutting temperature generated during the cutting process was measured empirically to explore the effect of drilling parameters such as wind cycle, feeding rate, and drilling speed on the generation of cutting heat.

The drilling speed was set as 1, 2, 3, and 4 mm/s, the speed was 100 r/min, and the drilling time was controlled within 100 s to investigate the effect of different drilling speeds on the bit temperature. From the data in Table 2, it can be seen that the temperature of the PDC bit is easily affected by the drilling speed, and the temperature of the bit is positively correlated with the drilling speed.

Table 2.

Temperature of polycrystalline diamond compact (PDC) bit at different feeding rates.

Material	Feeding rate (mm/s)	Drilling speed (r/min)	Initial temperature (°C)	Final temperature (°C)
Coal rock	1	100	8	46.256
Coal rock	2	100	8	54.559
Coal rock	4	100	8	70.971

The test data were fitted to obtain equation (25) for the temperature variation with feeding rate.

Y_{1} = 11.05 x_{1} + 38.75686

(25)

The drilling speed was set to 100, 200, and 300 r/min, the feeding rate was 1 mm/s, and the drilling time was controlled within 100 s to investigate the effect of different drilling speeds on the temperature of the bit. The relationship between the drilling speed and the maximum temperature of the bit can be derived from Figure 14. The drilling speed also shows a positive correlation with the temperature rise of the bit.

Figure 14.

Temperature variation of polycrystalline diamond compact (PDC) bit at different feeding rates.

The data from Figure 15 were fitted to obtain equation (26) for the temperature variation with drilling speed.

Y_{2} = 0.12231 x_{2} + 55.367

(26)

Figure 15.

Temperature variation of polycrystalline diamond compact (PDC) bit at different drilling speeds.

The drilling speed was set to 200 r/min and the feeding rate was set to 3 mm/s. The temperature of the bit was measured when the wind speed was 0, 10, and 20 m/s, respectively. It can be noted that as the wind speed increases, the temperature of the bit decreases. This is due to the fact that as the wind speed increases, the amount of heat exchange with the bit increases, resulting in less heat in the bit and a lower temperature.

The data from Figure 16 were fitted to obtain equation (27) for the temperature variation with wind speed

Y_{3} = - 0.24747 x_{3} + 68.5729

(27)

Figure 16.

Temperature variation of polycrystalline diamond compact (PDC) bit with different wind speeds.

The theoretical and simulated values were compared with the fitted experimental data respectively. As shown in Table 3, the results show that the error between the theoretical values calculated by the developed theoretical model of cutting tooth temperature and the simulation results is < 10%. Therefore, the theoretical model of the cutting tooth temperature of the drill bit can be effectively used to calculate the temperature of the cutting tooth of the PDC drill bit during coal rock drilling.

Table 3.

Maximum error between theoretical and simulation temperature at 1 s.

Drilling speed 300 r/min	Theoretical calculation value (°C)	Simulation calculation value (°C)	Fitted experimental data (°C)	Error₁ (%)	Error₂ (%)
Ganguage $V_{F} = 0 m / s$	244.63	241.50	237.9	2.75	1.49
Coal $V_{F} = 0 m / s$	158.86	152.70	148.5	6.52	2.75
Coal-ganguage $V_{F} = 0 m / s$	218.09	211.40	201.6	7.56	4.64
Ganguage $V_{F} = 20 m / s$	236.13	232.09	221.4	6.24	4.61
Coal $V_{F} = 20 m / s$	148.65	143.09	134.3	9.65	6.14
Coal-ganguage $V_{F} = 20 m / s$	207.20	202.09	196.9	4.97	2.57

Response surface analysis

Response surface analysis plan and variance simulation

Response surface analysis is a method to simulate the experimental results under limited state conditions based on a series of experiments with multiple variables and different response values. It is possible to study the interaction of several factors and has a good predictive performance. The Box-Benhnken principle is used to analyze the effects of cutting parameters and coal rock materials on the cutting temperature of the bit under wind circulation. In this analysis, factors such as drilling pressure, drilling speed, material, and wind circulation speed are taken as the independent variables in the experiment, and the temperature of the bit is the response value. The quadratic regression equation is used to fit the functional relationship between the independent variables and the response value. This functional relationship is represented by analyzing the regression equations and through the use of graphical techniques.

The design values and the coded values are shown in Table 4.

Table 4.

Design factor codes and levels.

Factor	Variable	Coded variable level
Factor	Variable	−1	0	1
Drilling speed (r/min)	A	100	400	500
material	B	Coal	Coal-ganguage	Ganguage
Drilling pressure (kN)	C	1	4	5
$V_{F}$ (m/s)	D	0	20

The theoretical model of PDC bit cutting teeth temperature is used to calculate the theoretical temperature when drilling with different working parameters, as shown in Table 5.

Table 5.

Temperature of drill cutting teeth under different working conditions.

Run	Real variable level
Run	Drilling speed (r/min)	Material	Drilling pressure (kN)	$V_{F}$	Theoretical value
1	100	Ganguage	4	0	295.53
2	100	Coal-ganguage	4	0	288.28
3	100	Coal	4	0	218.54
4	400	Ganguage	1	0	185.03
5	400	Ganguage	4	0	703.75
6	400	Ganguage	5	0	951.44
7	400	Coal-ganguage	1	0	131.86
8	400	Coal-ganguage	4	0	675.75
9	400	Coal-ganguage	5	0	830.64
10	400	Coal	1	0	136.12
11	400	Coal	4	0	492.71
12	400	Coal	5	0	734.91
13	500	Ganguage	4	0	780.65
14	500	Coal-ganguage	4	0	712.54
15	500	Coal	4	0	630.57
16	100	Ganguage	4	20	271.33
17	100	Coal-ganguage	4	20	264.14
18	100	Coal	4	20	194.42
19	400	Ganguage	1	20	159.41
20	400	Ganguage	4	20	678.46
21	400	Ganguage	5	20	925.78
22	400	Coal-ganguage	1	20	106.29
23	400	Coal-ganguage	4	20	650.41
24	400	Coal-ganguage	5	20	805.04
25	400	Coal	1	20	110.45
26	400	Coal	4	20	467.33
27	400	Coal	5	20	709.16
28	500	Ganguage	4	20	755.76
29	500	Coal-ganguage	4	20	687.63
30	500	Coal	4	20	605.66

Based on the regression analysis of the quadratic response surface, the multiple quadratic response surface fitting regression equation of drilling speed, coal rock properties, drilling pressure, and wind speed on the PDC bit cutting teeth temperature is established. It is shown as

Y_{4} (X) = 492.75 + 220.05 X_{1} + 70.36 X_{2} + 343.98 X_{3} - 25.14 X_{4}

(28)

where

X_{1}

is the drilling speed of bit,

X_{2}

is the coal rock type,

X_{3}

is the drilling pressure of bit, and

X_{4}

is the wind speed.

The variance analysis of the regression equation related to theoretical temperature is shown in Table 6. Among them, the larger the F-value and the smaller the P-value in the table represent the more significance of the correlation coefficient. So, the P-value of the model is < 0.0001, and the model F-value is required to be < 0.01 in the table of the regression equations, which indicates that the response surface regression model reaches a highly significant level. The fitting accuracy is good enough and the response surface approximation model can be used in the subsequent research. It can be seen that A, B, C, and D are significant in the temperature of bit-cutting teeth, and there is a relationship between the factors. According to the magnitude of the F-value, it is known that the influence degree of the above factors on the temperature of the bit-cutting teeth from large to small is drilling pressure, drilling speed, coal rock properties, and wind speed.

Table 6.

Variance analysis table for regression equations.

Source	Sum of squares	df	Mean square	F-value	p-value
Model	2.105 × 10⁶	4	5.262 × 10⁵	110.87	< 0.0001	Significant
A—Drilling speed	5.810 × 10⁵	1	5.810 × 10⁵	122.43	< 0.0001
B—Material	99,019.88	1	99,019.88	20.86	0.0001
C—Drilling pressure	1.420 × 10⁶	1	1.420 × 10⁶	299.19	< 0.0001
D—Wind speed	4738.65	1	4738.65	0.9985	0.3273
Residual	1.186 × 10⁵	25	4745.87
Cor total	2.223 × 10⁶	29

Further, the error statistical analysis of the regression equation is presented in Table 7. The larger the multiple correlation coefficient, the better the correlation. The predicted R² is 0.9303 while the adjusted R² is 0.9381. The difference is < 0.2, indicating that the model can fully reflect the drilling process. The adeq precision is 30.3592, which is > 4. So, the model has good adaptability and can be used to analyze and predict the bit-cutting teeth temperature.

Table 7.

Error statistical analysis of regression equation.

Statistical items	Value	Statistical items	Value
Std.Dev	68.89	R ²	0.9466
Mean	505.32	Adjusted R²	0.9381
CV%	13.63	Predicted R²	0.9303
		Adeq precision	30.3592

Glowka et al.¹⁶ using the same methodology found that the wear rate of PDC bits increased significantly when drilling temperatures were higher than 350 °C. Based on the above response surface analysis, the results are shown in Table 8. For coal, it is seen that the drilling pressure (N) increases at the rate of 14.38% due to increasing V_F. As the magnitude of V_F increases for coal language, the drilling pressure (N) increases at the rate of 17.79%. For coal, it is worth observing that the temperature decreases at the rate of 8% due to higher V_F and decreases at the rate of 10.5% due to higher V_F for ganguage. When the bit is drilling the coal rock, the upper-temperature limit is set to 350 °C. Under the same drilling speed, the increase of drilling pressure further can effectively improve the drilling efficiency when there is wind circulation.

Table 8.

Drilling parameters below 350 °C.

Material	$V_{F}$	Drilling speed (r/min)	Drilling pressure (N)	Temperature (°C)
Coal	0	400	3130	347.002
Coal	20	400	3580	347.724
Coal-ganguage	0	400	2530	349.884
Coal-ganguage	20	400	2980	349.411
Ganguage	0	400	1900	347.461
Ganguage	20	400	2350	349.782

Discussion

Taking the parameters of drilling pressure, drilling speed, and coal rock properties as the influencing factors, the response diagram of bit cutting teeth temperature is drawn according to the response surface fitting regression equation, which can visually reflect the influence of each cutting parameter on the bit cutting teeth temperature.

As shown in Figure 17, the influence of drilling speed and drilling pressure on bit-cutting teeth temperature is greater than that of coal rock properties. At the same time, the wind cycle can effectively reduce the steady-state convergence temperature of bit drilling in coal rock, which can effectively improve the drilling efficiency of bit-cutting teeth.

Figure 17.

Response surface diagram analysis; should be listed as (a) a description of when $V_{F} = 0 m / s$ ; and (b) a description of when $V_{F} = 20 m / s$ .

Conclusions

Based on the theory of tribology and heat transfer, the theoretical calculation model of PDC bit cutting teeth temperature was derived and the theoretical temperature field was analyzed. The temperature variation law of PDC bit cutting teeth under the thermal-fluid–solid coupling effect was analyzed by using the joint simulation of EDEM–FLUENT. The validity of the theoretical calculation model of bit-cutting teeth temperature was further verified by test. By establishing the response surface analysis model, the influence law of different drilling parameters on the temperature of PDC bit cutting teeth during drilling coal rock was studied. The results show that:

The error between the theoretical calculation results and the simulation calculation results and the experimental values is within 10%, which indicates that the theoretical model of the temperature of the cutting teeth of the PDC bit can be effectively used to calculate the temperature change of the cutting teeth of the PDC bit during the coal rock drilling process.

Based on the response surface analysis, a multivariate quadratic response surface fitting regression equation is established for the effects of drilling speed, coal rock properties, drilling pressure, and wind speed on the temperature of the cutter teeth of the PDC bit. The final results of the analysis show that the factors affecting the temperature of the bit cutter teeth in the process of coal rock drilling are drilling pressure, drilling speed, nature of coal rock, and wind speed in descending order.

With the regression equation and visualization analysis, the drilling efficiency increases by 14.38% and the temperature decreases by 8% for coal while the drilling efficiency increases by 17.79% and the temperature decreases by 10.5% for coal gangue when the critical temperature of cutting teeth is 350 °C, the drilling speed of bit is 400 r/min and the wind speed is 20 m/s. The maximum drilling pressures are 3580, 2980, and 2350 N, respectively.

In the future, we will further investigate the influence of the angle between the coal seam and the drilling direction of the bit on the drilling performance and the temperature of the bit when the bit is inclined to drill into the composite coal seam containing the gangue.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the Key Discipline of Mechanical Engineering in Henan Polytechnic University, the Key Research Projects of Colleges and Universities in Henan Province (grant number 22A440013) and Henan Province Science and Technology Project (grant number 232102320341).

ORCID iDs

Xiaoming Han

Liubing Xue

Author biographies

Xiaoming Han was graduated from China University of Mining Technology, majoring in the Mechanical Engineering. Now, Han is an associate professor at Henan Polytechnic University.

Liubing Xue is a postgraduate under the guidance of Professor Xiaoming Han. Xue's research interest is gas extraction technology and equipment in coal mines.

Jin Xu is a postgraduate under the guidance of Professor Xiaoming Han. Xu's research interest is gas extraction technology and equipment in coal mines.

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Influence mechanism of polycrystalline diamond compact bit temperature rise based on thermo-fluid–solid coupling

Abstract

Keywords

Introduction

Temperature model of PDC bit cutting teeth

Theoretical model solution

Simulation model analyze

EDEM calculation settings

FLUENT calculation settings

Simulation results and discussion

Experimental verification

Response surface analysis

Response surface analysis plan and variance simulation

Discussion

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iDs

Author biographies

References