Research on deep-hole drilling quality of high-strength steel with slender gun drill

There are a lot of problems exist in the processing of long and thin deep hole gun drilling of high strength steel, such as insufficient of the machining mechanism and characteristics of gun drilling, difficulty in selecting machining parameters, unknown influence mechanism of machining parameters on drilling force, drilling temperature and machining quality. In this paper, 42CrMo high strength steel is selected as the workpiece material. A numerical model of cutting force is established based on the mechanism of gun drill, and then the finite element simulation and processing test are carried out. The results show that the cutting force decreases with the increase of cutting speed, and increases with the increase of feed speed; the error between the theoretical and actual value is less than 10%. Cutting speed and feed speed have a great influence on machining quality, and the cutting fluid pressure mainly affects the surface roughness.


Introduction
Deep hole drilling is an important machining method in the field of machining and manufacturing.
With the development of machining technology and equipment manufacturing, deep hole drilling becomes more and more widely used and important [1] . At present, deep hole processing is mainly used in energy and chemical industry, automobile engine, construction machinery and shipbuilding industry [2] . However, it has become one of the most difficult machining technologies due to the complicated machining system and tool design, poor tool rigidity caused by large length-diameter ratio, and closed machining environment which is difficult to monitor.
Gun drill is the first processing system to realize large-scale and mature application in the field of deep hole processing. It is with the advantages of high processing efficiency, good processing quality and long tool life [3] . As shown in Fig. 1, gun drill is composed with drill bit, drill pipe and drill handle.
Generally, small diameter gun drills are formed by welding once, and the drill bit cannot be replaced.
Larger diameter gun drills with blades can be replaced after the blades are worn out. The drill bit is the most important part of the gun drill, which undertakes the main drilling work. It is generally made of hard alloy and tool steel, with higher requirements on strength and wear resistance [4] . The tip part of the drill bit is the cutting edge, and the circumference part is distributed with the guide block with the function of guiding and polishing, which can improve the machining accuracy of the hole. Generally, there is no need for reaming. In addition, since the gun drill has a unilateral cutting edge, the guide strip also has the function of balancing the radial cutting force on the cutting edge, and a reasonable guide block layout can keep the drilling process more stable. The drill pipe is used for chip removal and cutting fluid flow. It is usually made of seamless steel pipe. The drill pipe usually has a "V" groove structure, and the multi-blade gun drill has two V-grooves , through which the chip is discharged under the action of high pressure cutting fluid. The diameter of the drill pipe is slightly smaller than that of the bit, and the drill pipe is hollow inside, which is used for transmitting cutting fluid. The size design of the V-shaped groove and the through-oil hole should consider the rigidity of the drill pipe and the efficiency of through-oil and chip removal. The drill handle is mainly used to transfer power and connect the fuel injection device. The model and geometry are adapted according to the machine tool selected. At present, some studies have been conducted in-depth on the improvement of processing structure, processing technology and drilling stability of gun drill. Viktor P et al [5] comprehensively analyzed the tool parameters of gun drill and the influence of machining parameters on tool life through a large number of experimental studies. Woon. K. S. et al. [6] studied the influence of radius of the inner and outer edges of fillet on the straightness of the hole in the process of drilling thin-wall deep hole with gun drilling. Dirk Biermann et al. [7] studied the influence of drill edge radius on drilling force, tool wear, tool life, chip length and surface roughness. Jung J [8] ，Wang Y [9] established a mathematical drilling force model of gun drills based on the energy principle and micro cutting tools, and the correctness of the model were verified by drilling experiments. Astakhov et al. [10] studied the formation principle of trumpet mouth under gun drilling. Galitsky et al. [11] established a tool life model for gun drilling by group data analysis method (GMDH) including tool angle parameters and process parameters, which was a relatively perfect tool life prediction model. Klocke et al. [12] established a finite element analysis model of gun drilling process based on Deform-3D, and the simulation results were basically consistent with the experimental results by adjusting the radius of cutter blade circle and friction coefficient in the model. Yongguo Wang et al. [13] studied the corresponding relationship between the chip morphology and surface morphology under different tool wear conditions during gun drilling. On machining stability and straightness control, Alexander [14] studied the nonlinear bending vibration and torsional vibration in the gun drilling process, simplified the drill pipe into a continuous beam model, then proposed a new bending-torsional coupled vibration drilling model combined with the intermittent cutting theory. Tarng [15] developed a flutter identification system based on the ART2 neural network method, which could effectively identify the drill pipe vibration in the process of gun drilling. Kirsanov [2] , Chin et al [16] . used finite element method to simulate the vibration and bending of drill pipe in the process of gun drilling.
However, there are still some problems in the gun drilling process, such as insufficient processing mechanism, lack of quantitative research on the influence of machining parameters, clamping error, tool parameters and other factors on machining quality, and low simulation accuracy. In this paper, the drilling force, drilling heat and machining quality of gun drilling are studied, especially for the influence of machining parameters on drilling force, drilling temperature and machining quality by combining theory, experiment and simulation.

Experimental procedures
A high strength steel 42CrMo round bar is used as the workpiece. The processing equipment adopted is the deep-hole gun drilling machine tool, Beijing Jinuo deep-hole equipment company. The tool is German Cobalt Collar gun drill, the bit parameters are generally standard parameters, shown in Table 1. The drilling machine is a horizontal machine tool. The cutting fluid is pumped into the spindle and the drilling hole of the gun from the tail of the machine tool by the high pressure pump. It flows out through the head of the bit and discharges the chips into the chip container. The workpiece is fixed onto the dynamometer, and the dynamometer sensor collects the cutting force signals in the drilling process. After signal processing and amplification, the measured cutting force values are presented on DynoWare . The schematic diagram of test platform construction is shown in Fig. 2, and the experimental parameters are shown in Table 2.  Hole diameter (mm) 4 After processing, the axis deviation, roundness and aperture size are measured using Hexagon Global Advantage coordinate measuring machine. The workpiece coordinate system is established based on the process datum (front and left side of the workpiece) corrected during machining. The diameter, roundness and center coordinates of the hole entrance-side and exit-side are measured respectively under the workpiece coordinate system, shown in Fig. 3.

Fig. 3 Sketch of workpiece coordinate system
The surface morphology of the inner hole and the surface roughness were measured using Keyence 3D laser scanning microscope. In this paper, the machining hole is planed along the axis by wire cutting method, and then the surface topography is taken at three positions, i.e. 4 mm from the hole entrance, 4 mm from the middle of the hole and 4 mm from the exit of the hole, respectively. As shown in Fig. 4, each position was measured three times, and roughness was calculated in VK analysis software. The force of the drill bit is complicated [17] , which can be divided into normal force, circumferential and axial friction force on the support surface of the guide strip, normal force and tangential friction force on the inner and outer cutting edges, and normal force formed by the cutting fluid on the outer diameter clearance surface. The overall stress analysis is shown in Fig. 5. As shown in Fig. 6, the normal force on the support surface of the guide bar is simplified as and the circumferential friction force is decomposed into and along X and Y directions. can be described by the following formula : Where, p is the unit normal force, is the drilling radius, 1 and 2 is the starting angle and the ending angle of the drilling guide bar, is the contact area between the guide bar and the inner wall of the hole in the Z-axis direction. The direction is at the center of the drill and the action point is Simplified force decomposition on guide bar The circumferential friction force on the guide bar is decomposed into and , According to the triangle decomposition in the figure, when 1 ≤ ≤ /2, the element's circumferential friction force along the minus X axis, can be expressed as: along the minus X axis, can be expressed as: is the friction coefficient, is the angle variable.
Therefore, at the top 1 ≤ ≤ 2 , can be expressed as: 12 (cos cos ) Similarly, along the Y axis, and the expression of is： Suppose the axial friction coefficient on the guide bar is , the axial friction force on the guide bar can be expressed as: Due to the special single-edge structure of the gun drill, the cutting speed at each point of the inside and outside edges is different, and the cutting force distributed along the cutting edge is un-uniform.
Therefore, the internal and external cutting edges are divided into countless micro elements by the micro element method, and each micro element can be regarded as a cutting element. If the number of microelement is large enough and the area of micro-element is small enough, the cutting speed on each microelement can be considered as unchanged [18] . After the cutting force on each micro-element is obtained, the cutting force on the whole cutting edge can be obtained by integrating along the cutting edge.
Then the normal force 1 and friction force 1 on the outer edge can be expressed as: Similarly, the normal force 2 and friction force 2 on the inner edge can be expressed as: In the process of gun drilling, the cutting force mainly comes from the decomposition of the normal force and friction force on the guide bar and cutting edge as well as the clearance water pressure in XYZ directions. According to the principle of force balance, the forces are decomposed in X and Y directions, seen as follows [9] : 3.2 Thermodynamic coupling finite element model Due to the small heat dissipation space in the drilling process, the workpiece and tool absorb most of the cutting heat, and the chip takes away only about 30% of the heat. The workpiece expansion caused by the cutting heat will affect the machining precision, especially in the deep hole machining, the cutting heat has a great influence on the diameter deviation of the machining hole [19] .
In this paper, the finite element model of gun drilling is established by Deform-3D. In this model, the radius of the cutting edge circle is not considered, and the it is assumed to be absolutely sharp. The effect of the cutting fluid and the through-oil hole are also without considered . In order to facilitate the grid division, the through-oil hole is removed and simplified. For reduce the number of grids and improve the computational efficiency, only a small part of bits involved in cutting are retained in the simulation. The shapes of the meshed workpiece and cutter are shown in Fig. 7. The material model of the workpiece is defined as the Johnson-Cook model, and the parameters are shown in Table 3 [14] .  For the contact conditions between the workpiece and the tool, the contact tolerance is set as 0.0002, and the contact calculation method is penalty function method. The friction type is shear friction, and the average friction coefficient in the calculation is set as 0.4. The heat transfer coefficient between the workpiece and the tool is determined by the pressure, sliding speed, contact temperature, etc. As shown in Table 4 [20] , in order to facilitate the simulation, the heat transfer coefficient between the workpiece and the tool is determined as a function of pressure. The tool wear model is Usui model, which is applicable to simulate the tool wear in cutting, with the empirical coefficient = 1 × 10 −7 , = 855.   Fig. 10 shows the surface temperature field distribution of workpiece and cutting tool at time step=900. The highest temperature of the workpiece at the same time is higher than that of the tool. The main reasons are as follows: first, the temperature rise is different due to the different thermal characteristics of the two materials; second, it takes a certain time for the temperature to be transferred from the workpiece to the tool, and there is a heat loss in the transfer process. The highest temperature of the workpiece is concentrated in the cutting part, where the chip and the workpiece just separated, and the temperature decreases gradually along the processed surface and the chip surface. The temperature on the chip is higher than that on the machined surface, and the temperature field distribution on the workpiece is basically consistent with the theoretical analysis. The highest temperature of the tool appears on the tip and the inner and outer edges, and the temperature field is distributed symmetrically on the flank and rake face with the inner and outer cutting edges as the center, with a large temperature gradient. The thermal load on the outer edge is significantly higher than that on the inner edge, which is related to the larger average cutting speed of the outer edge. The cutting temperature of the outer edge is higher than that of other positions due to the largest contact area between the cutting surface and the chip. As the cutting depth increases, friction occurs between the outer cylinder of the drill bit and the inner surface of the hole, and the temperature also begins to appear on the outer cylinder. As shown in Fig. 11, the workpiece cutting area is divided along depth to analyze the distribution of temperature field. It can be seen that the temperature starts from the cutting area and gradually decreases along the depth, indicating that the drilling heat is transferred from the cutting area to the workpiece interior, which cause the workpiece interior temperature to rise. By magnifying the chip root position, it can be seen that the temperature contour distribution is dense and the temperature gradient is large. At the same time, the distribution of temperature field also exists in the area between the chip and the rough surface (the first deformation area), indicating that the cutting heat is generated in this area, which is consistent with the mechanism of cutting heat generation. Fig. 11 Distribution of workpiece temperature field along depth The vertical cutting edge dissects the bit along the axis are shown in Fig. 12, .Compared with the workpiece, the temperature distribution on the bit is more concentrated, and the heat transfer range along the axis is shallow. It shows that in the process of drilling, a lot of heat is gathered near the drill tip and cutting edge, and the heat diffuses slowly to the inside of the drill bit. The heat dissipation mainly depends on the heat dissipation medium. It can be seen that good cutting fluid cooling is important for gun drilling.
It can be predicted from the characteristics of the cutting temperature field that the wear of the gun drill should mainly occur on the front surface near the outer edge and tip.   In this paper, the temperature at the drill tip was used to represent the cutting temperature to extract the temperature simulation results under each parameter, and the average temperature between (0.02-0.05) s was calculated to draw the graph shown in Fig. 15. As the cutting speed increases, the cutting temperature shows a linear trend of increasing, and the growth rate is faster at high feed speed. When the cutting speed is constant, the cutting temperature increases with the increase of feed speed, and it is sensitive to the change of the feed speed at low feed rate. In the process of gun drilling, there are problems of drill pipe length, poor rigidity, gap between drill bit and guide sleeve, drill pipe vibration, rotary vibration in the guide sleeve clearance repeatedly, which lead to the deviation between drill hole diameter and tool diameter and hole roundness error. Tool wear, cutting heat and other factors also lead to hole inlet and outlet diameter deviation.
It can be seen from Fig. 16 and Fig. 17 that the diameter of entrance of the hole should be larger than that of the exit. With the increases of cutting speed, the diameter of the exit decreases more and more, and that of the entrance also fluctuates to a certain extent, but the range is relatively small. The diameter deviation of the entrance and exit shows a linear rising trend with the increases of cutting speed. The diameter change at the entrance can be attributed to the wear of the guide bar and the random error of measurement. The diameter of the hole outlet is obviously smaller than the gun drill, which is related to the cutting temperature. According to the simulation analysis, in the process of gun drilling, the drilling temperature is relatively high, and increases with the increase of cutting speed. A large amount of cutting heat is transferred to the workpiece, and the temperature near the hole is high, and rises rapidly due to the slow heat dissipation of the workpiece with larger hole depth. Due to the effect of thermal expansion and cold contraction, the workpiece expanded during drilling, and then its temperature gradually returned to room temperature after drilling, leading to the shrinkage of the material and the reduction of the hole diameter. The faster the cutting speed, the higher the cutting temperature. The obvious effect of heat expansion and cold contraction results in the hole inlet and outlet diameter deviation.
It can be seen from the roundness error curve in Fig. 18 that the roundness error at the entrance of the hole is smaller than the exit, which is related to the inconsistency of the internal shrinkage rate of the material. With the increase of feed velocity, the diameters of inlet and outlet are with some fluctuation, but the variation range is small, and the diameter deviation has little change. The roundness error of the inlet is smaller than that of the outlet, but the feed velocity has little influence on the diameter error and roundness error of the inlet and outlet. With the increase of cutting fluid pressure, the hole exits basic remain stable, the diameter difference of the inlet and outlet is less. That is because as the cutting fluid pressure and flow rate increases, the cooling performance of gun drill system reduces the cutting temperature. But the pressure strengthen the pipe eddy effect and the drill string vibration, resulting in the hole roundness error increases.  oil pressure (c) The axis deviation of long and thin deep holes is the most important parameter to represent their machining quality. For spatial cross holes with high position accuracy, the axis deviation will lead to the exit position deviation, which will affect the intersection of the hole system and oil transfer efficiency, and even lead to the scrap of the workpiece. Axis deviation is mainly caused by the bending of the drill, which is related to machining parameters, clamping accuracy, vibration and other factors. The surface micro morphologies of each hole measured position are shown in Table 5. It can be seen from the micro morphology of the processed hole that the surface of the hole has surface defects such as cracks, scratches, dense grooves and pits formed by material hard points falling off. With the decrease of oil pressure, there are more scratches on the processed hole surface, and the surface will be rougher. In According to the test results, the influence of chip length and thickness on the surface roughness is enhanced after the feed rate is 0.01mm /r. Therefore, for the long and thin deep hole processing with high surface quality requirements, the feed rate should not exceed 0.01mm /r. With the increase of cutting fluid pressure, the chip length gradually becomes shorter, and the chip form also changes from a seriously deformed long tapered strip to a regular short spiral, indicating that the chip discharge ability of the processing system is enhanced. Chip discharge is smooth without blocking, and the friction of the chip on the surface is reduced, so the surface roughness is reduced.

Conclusion
In this paper, 42CrMo high-strength steel is selected as the experimental material. Based on the drilling mechanism of gun drilling, combined with finite element simulation and processing test, the influence of processing parameters on drilling force, drilling temperature and processing quality is analyzed. The main contents of the study are summarized as follows： (1) Numerical model analysis and experimental verification of drilling force are carried out. The drilling force tends to increase rapidly and then become stable with the increase of hole depth, and decreases with the increase of cutting speed and increases with feed speed. The maximum error between experimental data and theoretical value is less than 10%.
(2) The finite element simulated temperature and temperature gradient near the chip root are the largest, and the temperature in the uncut area of the workpiece rises in a stepped manner with the tool feed.
The temperature and temperature gradient near the cutting edge and the drill tip are maximum, and increases with the increase of cutting speed and feed speed, with the cutting speed is the main influencing factor.
(3) Cutting speed and feed speed have a great influence on the machining quality, and cutting fluid pressure mainly affects surface roughness.

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