Research on chip mechanism of Inconel 718 with ultrasonic assisted drilling by step drill

Nickel-based high-temperature alloys (Inconel 718) are considered to be difficult-to-machine materials with high yield strength and high-temperature strength properties and are widely used in the aerospace industry. Due to the low thermal conductivity of Inconel 718 material, it leads to severe machining hardening and easy to cause tool wear. In this paper, three step drills with different second point angles are proposed, the thrust force and torque models of twist and step drill bits are established, and then the critical burr generating states of the drills are analyzed. The experimental and finite element simulation analyses of the four drills showed that the thrust force, torque, burr, effective stress, and chip flow rate generated by the step drill under conventional drilling conditions were less than those of the twist drill. The torque and thrust force decrease as the angle of the second point angle of the step drill decreases. The smaller the second point angle of step drill, the higher the chip flow rate, the lower the maximum effective stress and the better the machining quality. In addition, the step drill is then compared with conventional drilling (CD) and ultrasonic-assisted drilling (UAD) to analyze the differences in temperature and chip morphology, and the results show that the machining temperature is lower and chip breaking performance is better under ultrasonic-assisted drilling.


Introduction
Inconel 718 material is a versatile material due to its high resistance to corrosion and temperature, while its excellent properties make drilling inconvenient [1,2]. Inconel 718 is widely used in the aerospace industry and biomedical applications, such as guide vanes and turbine blades in hightemperature environments in the aerospace industry [3]. At high temperatures, the mechanical properties of Inconel 718 such as tensile strength, fracture strength, and fatigue strength are at a high level [4].The low thermal conductivity and high temperature strength of Inconel 718 lead to high tool wear and premature tool failure, limiting productivity and reducing economic efficiency [5]. The quality of drilling operations in difficult materials has been the subject of many studies in the literature, such as the study of temperature, thrust force, torque, burr formation, and chip analysis during drilling [6]. In order to improve the life of the drill and the reliability of the machining, many scholars have proposed to modify the drill geometry for the purpose of drilling difficult materials. Also, there are many studies on ultrasonic-assisted machining of difficult materials to improve drilling accuracy.
Beer et al. designed a new bit that modified the geometry of the flank face of the twist drill to improve the cooling effect of the cutting area when drilling Inconel 718. The temperature in the cutting area was reduced, the friction between the drill and the workpiece was reduced, and the width of the drill flank wear was reduced [7]. Oezkaya et al. obtained a new type of drill bit for machining Inconel 718 by grinding the flank face of the cutting edge of the drill bit. The simulation calculation of fluid mechanics shows that the supply of cutting fluid can be increased, the friction between the drill bit and the drilling surface can be reduced and the tool life can be prolonged [8]. Singh et al. used auxiliary machining technology to drill Inconel 718. By low frequency vibration, intermittent contact between the drill bit and the workpiece was created, which facilitated chip discharge and reduced the wear on the tool [9]. Chen et al. designed axial ultrasonic vibration-assisted drilling and studied its drilling effect on Inconel 718 material. The optimal natural frequency and vibration amplitude are obtained by simulation. The conditions of chip breaking are obtained by applying the geometric chip breaking theory of ultrasonic vibration drilling [10]. Ucak et al. studied the influence of TiAlN coated tools and uncoated tools on Inconel 718 material drilling, and analyzed the drilling force, torque, and tool wear. The results show that the coated tool can reduce the drilling force and torque and improve the tool life [11]. Khanna et al. studied the influence of drilling Inconel 718 material at low temperature. The low-temperature environment was able to reduce tool wear, increase tool life by more than 80%, reduce production costs, and increase productivity [12].
Alonso et al. investigated the effect of tool geometry on machining performance by machining CFRP/Ti6Al4V stacked materials, and analyzed the cutting edge profile evolution to prove that stepped geometry can obtain lower wear and lower thrust force [13]. Wang et al. proposed a new composite stepped tapered diamond bit and performed comparative machining tests with twist drills, and the results showed that the composite bit can reduce the thrust force, which can effectively reduce the tear size at the exit of C/ SiC composite materials holes [14]. Wang et al. in order to reduce the chip damage in CFRP/Al tacks laminated primary drilling, a new structure of step drill bit was researched and developed, proposing to add chip breaking structure on the front cutter face of the second step to effectively crushing the aluminum chips into small sizes and improving the surface quality of CFRP [15]. Qiu et al. designed a step drill with different diameter ratios for drilling CFRP with different cutting parameters in order to reduce the influence of crossedge on CFRP delamination, and the results showed that the best hole exit quality could be obtained with a diameter ratio of 0.5 [16]. Pérez et al. compared and analyzed the effect of step geometry and double-tip geometry on CFRP material for drilling, and found that the double-tip drill bit produced greater thrust force and torques [17]. Kwon et al. found that the step drill has the effect of inhibiting delamination and uncut fiber production when drilling CFRP, and the effect of core diameter, step angle, and front angle on the machining quality of CFRP by the step drill was investigated [18]. Tamer et al. designed a new step drill, and through experimental analysis, a step drill with tip angle can shorten the operation time and improve the hole formation quality of the CFRP material [19].
UAD is the application of ultrasonic vibrations to the drill bit to increase drilling process efficiency, produce smaller chips, reduce tool wear, extend tool life and improve drilling process accuracy [20][21][22][23]. Moghaddas et al. used 16-mm drill bits on 4340 steel for both conventional drilling and ultrasonic-assisted drilling tests. The results showed that CD resulted in continuous cutting and high frequency vibration resulted in intermittent cutting. UAD breaks the chips into smaller pieces, makes chip evacuation easier, and reduces thrust force and torque [24]. Safar et al. designed a rotary ultrasonic transducer in order to study ultrasonic-assisted drilling. By experimentally comparing the CD and UAD processes, it was found that the drilling force was much lower under UAD conditions, and decreased when the amplitude increased [25]. Shao et al. investigated the application of ultrasonic vibration to the drilling of CFRP/Ti stacked materials. UAD was effective in reducing cutting forces, cutting temperatures, burr height, drill wear, and surface roughness [26]. Zhu et al. conducted UAD experiments on DD6 high-temperature alloys, and the results showed that the surface roughness increased with increasing feed speed and decreased with increasing spindle speed, and the thrust force decreased with decreasing feed speed and decreased with increasing spindle speed. The higher the amplitude of ultrasonic waves, the greater the decrease in thrust force [27].
These studies on drill geometry have contributed to the improvement of the quality of machining of difficult materials, and very little literature has considered the effect on hole quality when drilling Inconel 718 materials with step drills. In this paper, three step drills with different second point angles are proposed for comparison with twist drills, combined with finite element simulation analysis and experimental analysis to fully ensure the reliability of the research results. The main work of this paper is as follows: firstly, we establish the thrust force and torque models of twist drill and step drill, and analyze the influence of tool geometry on the thrust force and torque. Secondly, a finite element simulation model of twist drill and step drill is established to compare and analyze the differences in thrust force, torque, exit burr, effective stress, and chip flow rate between twist drill and step drill to obtain the step drill with the best second point angle. Meanwhile, experiments are conducted to compare and analyze the prediction model and simulation model of thrust force and torque to ensure the correctness of the simulation model. Finally, the effect of step drilling on hole quality under CD and UAD conditions is investigated to understand the advantages of UAD in terms of chip breaking performance and cutting temperature.

Geometric model of drill bit
The geometric structure models of twist drill and step drill are shown in Fig. 1. The point angle, helix angle, and bit diameter of the twist drill are 2 , , and D . The cutting area of the twist drill consists of a chisel edge and two main cutting edges. The step drill is cutting the main cutting edge of the twist drill by dividing it into two parts. The first part is the main cutting edge with the same geometry as the twist 1 3 drill and the same point angle of 2 . The second part is the secondary cutting edge with a point angle of 2 ′ . The step drill has the same diameter and helix angle as the twist drill. The cutting area of the step drill consists of a chisel edge, two main cutting edges and two secondary cutting edges. The drilling force generated by the step drill is the sum of the three cutting areas of the chisel edge, the main cutting edge and the secondary cutting edge.

Force and torque model
The force on the main cutting edge of the drill is divided into two main parts: the thrust force exerted by the main cutting edge and the torque exerted [28]. The thrust force and torque generated on the main cutting edge of twist and step drills are modeled using mechanical methods to analyze the change of force on the main cutting edge when the cutting angle changes during the drilling process [29]. It has been found that the thrust force during drilling comes mainly from the chisel edge and the main cutting edge, where the chisel edge accounts for the major part. Since the chisel edge of the step drill and the twist drill are the same, only the difference in thrust force on the main cutting edge is studied here [30,31]. The torque during drilling also comes mainly from the chisel edge and the main cutting edge, where the main cutting edge accounts for the major part and the chisel edge has little effect on the torque, so only the difference of the torque on the main cutting edge is studied here [32,33]. To model the thrust force and torque on the main cutting edge, first draw the schematic diagrams of twist drill and step drill, then split the main cutting edge into finite elements with unit length dh, analyze the cutting force generated on each micro-element, and finally integrate and sum up the cutting force on all micro-element to obtain the cutting force on the main cutting edge. The forces on the main cutting edges of the twist drill and step drill at each unit length are shown in Fig. 2a and Fig. 2b. F y is the feed cutting force exerted by the main cutting edge of the twist drill, F z is the main cutting force exerted by the main cutting edge of the twist drill, F y ′ is the feed cutting force exerted by the main cutting edge of the step drill, F z ′ is the main cutting force exerted by the main cutting edge of the step drill, R represents the radius of the final drill hole, the chisel angle and web thickness of the twist drill are and 2 , the chisel angle and web thickness of the step drill are 1 and 2 ′ . According to the orthogonal cutting model, a c is the cutting thickness, and is the yield stress and shear stress of Inconel 718 high temperature alloy, respectively. The feed cutting force and the main cutting force for each micro-element are as follows: where is the dynamic shear angle.
According to the mechanical prediction model of thrust force and torque by Langella et al. [34], with the center of the drill bit as the pole, the right-angle coordinate system is converted into a polar coordinate system, and the length of each micro-element unit is dr . If = r∕R , then dr = Rd . i( ) is cutting angle, dh can be expressed as dh = cosi( )dr . The force dF y and dF z on the main cutting edge and can be shown in Eqs. (3) and (4). Similarly, the thrust force and torque generated by step drilling Inconel 718 can be derived. Since the step drill is divided into the first main cutting edge and the secondary cutting edge, a and c are the starting positions of the first main cutting edge of the step drill, c and b are the starting positions of the secondary cutting edge, the thrust force on the first main cutting edge is F d1 , the thrust force on the secondary cutting edge is F d2 . The torque on the first main cutting edge is T d1 , and the torque on the secondary main cutting edge is T d2 . The equation of thrust force and torque is as follows: With the above equation it can be concluded that the thrust force and torque generated during drilling is related to the length of the first and secondary cutting edges, which will increase as the drilling depth of the bit increases.

Exit burr model
In CD, burr formation consists of four stages. The first stage is the steady drilling state, the second stage is the critical state, the third stage is the initial fracture, and the fourth stage is the burr formation [35]. A diagram of the burr formation process is shown in Fig. 3.
It has been shown that burr formation is related to cutting forces, strain rates, and the type of material deformation [36]. The size of the burr is influenced by the material properties, cutting conditions, and the drill bit. The structural design of the drill bit has an impact on the burr formation [37]. It has also been found that the burr height is related to the feed rate, and the higher the feed rate, the higher the burr height [38]. For the prediction of burrs in (10)

Fig. 3 Burr formation process
Inconel 718 material, the accumulated axial force along the cutting edge of the drill is studied. Treating the material in front of the drill as a uniformly stressed plate, burrs will occur when the axial force is equal to or greater than the resistance to Inconel 718 plastic deformation. For the burr model of Inconel 718 material, only the process after the drill bit starts to drill out the material and after the final drill bit is fully drilled out was observed [39,40], as shown in Fig. 4. The material in front of the drill bit will continue to be subjected to thrust force, and when the stress reaches the ultimate stress of the material, the remaining material begins to deform and form a burr. The equilibrium equation is as follows: where Q is the shear force per unit length, E is the modulus of elasticity, is the Poisson's ratio of the material, h is the thickness of the plate and h = c ⋅ r , c is the slope of the plate thickness and c is a constant value, D is the bending stiffness, k is the slope of the reamed material. Combining Eqs. (13) and (14), using the second-order Euler method, the radial and tangential stresses are: From r = e z , then Eq. (13) can be transformed to be expressed as: which, Compare the Mises stress with the radial and tangential stresses of Inconel 718 material. If the Mises stress is high, the material bends under the action of the cutting edge and a burr is formed. Based on the geometry of the drill, the critical distance for burr formation can be calculated using Rp.

UAD kinematics analysis
The essential difference between UAD and CD lies in the fact that UAD produces a periodic, controlled relative motion between the drill, and the workpiece with the help of external excitation [41][42][43][44].
During CD, the displacement of any point on the tool relative to the workpiece is: where, x (mm) is the displacement in x direction, y (mm) is the displacement in y direction, z f (mm) is the axial feed displacement at a point on the tool edge, r (mm) is the vertical distance from a point on the tool to the tool axis, (rad) is the circumferential angular displacement of the tool relative to the workpiece, f r (mm/r) is the feed per revolution of the tool, n (r/min) is the tool speed, and t (s) is the machining time.
Under UAD conditions, the axial vibration displacement of the drill bit can be expressed as: W h e n r = 3mm , f = 100kHz , n = 3000rpm , f r = 0.2um∕r , and A = 0.1um draw the three-dimensional motion trajectory of the outer edge point of the main cutting edge, as shown in the Fig. 5.
According to Fig. 6a, the synthetic cutting velocity V e in CD can be expressed as: According to Fig. 6b, the synthetic cutting velocity V e in UAD can be expressed as: V c is the tangential velocity (mm/s), V f is the tool axial feed velocity (mm/s), V F is the velocity of ultrasonic vibration (mm/s), and V e is the synthetic cutting velocity (mm/s).
During the UAD drilling process, the chip breaking capacity and chip removal capacity are greatly improved. The trajectory length of each tool tooth of UAD and CD in unit time interval can be expressed as:

Finite element model
The workpiece material is Inconel 718, and the drill bit material is WC. The simulation model was developed using DEFORM-3D software. In this paper, four different drill bits with different geometrical parameters were used to simulate the Inconel 718 material and study the effect of different geometrical parameters of step drill on Inconel 718 for drilling. The twist drill has a diameter of 6 mm, a point angle of 135°and a helix angle of 30°, based on which three step drills with the same first point angle and different second point angles were designed, as shown in Table 3. The finite element model of Inconel 718 material is shown in Fig. 7, where the workpiece is a plastic body and the drill bit is a rigid body. The workpiece is Inconel 718 material with 3 mm thickness and 20 mm diameter. The drill bit is moved axially downward, and the workpiece is fixed boundary immobile so that its velocity in X, Y, and Z directions is zero. The number of mesh for the drill bit is 40,000 and the mesh ratio is 4. The number of mesh for the workpiece is also 40,000, and the mesh ratio is 7. The contact surface is shear friction, and the friction coefficient is 0.6. The heat transfer coefficient is set to 45. In order to study, the effect of drill geometry parameters on the drilling at different spindle speeds and different feed rates, simulation experiments were done for four types of drills at rotation speeds of 3000 r/min, 4000 r/min, and 5000 r/min and feed rates of 0.1 mm/r, 0.15 mm/r, and 0.2 mm/r, respectively.

Experiment and validation
The experimental setup is shown in Fig. 8. The drilling experiments were performed on a 3-axis CNC machining center, and the Inconel 718 material sample was fixed with fixtures on both sides. The fixture is connected to a piezoelectric force gauge on the bench for measuring thrust force and torque. The ultrasonic device transmits ultrasonic energy to the drill bit, which causes the drill bit to vibrate axially. The frequency of ultrasonic vibration is 20 kHz. All drilling experiments were performed without the use of coolant,  and all were performed under dry cooling conditions. Each drill bit drills three holes under each set of parameters to prevent the effect of inaccurate experimental results caused by drill bit wear. To ensure the reliability of the measurement results, each experiment was repeated three times, and the average value was taken. Experiments were conducted on four types of drills at speeds of 3000r/min, 4000r/min, and 5000r/min and feed rates of 0.1 mm/r, 0.15 mm/r, and 0.2 mm/r, respectively. Drilling of Inconel 718 material with twist drill under CD conditions. The comparison of the experimental results, simulation results and predicted results of the average thrust force during stable drilling is shown in Fig. 9, and the comparison of the experimental results, simulation results and predicted results of the average torque during stable drilling is shown in Fig. 10. The variables here mainly consider the effect of spindle speed on thrust force and torque. As can be seen in Figs. 9 and 10, both thrust force and torque decrease when the spindle speed increases. When the feed  Fig. 9 Comparison of experimental results, simulation results and predicted results of average thrust force for stable drilling Inconel 718 with twist drill at a feed rate of 0.2 mm/r under CD conditions rate is 0.2 mm/r, and the speed is 4000r/min, the maximum error models between experimental results and simulation results, experimental results and prediction results, and simulation results and prediction results for thrust force are 3.0%, 3.4%, and 6.3%, respectively, and the maximum error models between experimental results and simulation results, experimental results and prediction results, and simulation results and prediction results for torque are 3.2%, 3.3%, and 4.8%, respectively. The er rors are all within acceptable limits. Figure 11 shows the variation of thrust force with drilling depth for four different geometries of drill bits drilling Inconel 718 material at a feed rate of 0.2 mm/r and a spindle speed of 4000 r/min. As can be seen in Fig. 11, when the drill bit starts drilling into Inconel 718 material, the thrust force rises quickly and reaches its maximum when the cutting edge is in complete contact with the Inconel 718 material and enters the stable drilling phase [46]. Figure 12 shows a comparison of the average thrust force during stable drilling Inconel 718 material with four different geometries at different spindle speed conditions. As can be seen from Fig. 12, for twist drill and step drill, the thrust force decreases with increasing spindle speed when the feed rate is constant. Because increasing the spindle speed makes it easier to discharge the chips, it reduces the friction between the drill and the chips and between the workpiece and the chip contact surface, thus reducing the average thrust force. At a speed of 4000 r/min, compared to the twist drill, the thrust force of the step drill (A, B, and C) decreased by 32.3%, 23.0%, and 17.7%, respectively. The results show that the step drill can reduce the thrust force compared with the twist drill, and the smaller the second point angle, the better the step drill can reduce the thrust force. In the stable drilling process of the step drill, when the second point angle is smaller than the first point angle, the core thickness of the secondary cutting edge is smaller than the main cutting edge, and it is known from Eq. (10) that the generated thrust force will be reduced.   Figure 13 shows the distribution curves of torque with drilling time for four different geometries of drill bits for drilling Inconel 718 material at a feed rate of 0.2 mm/r and a spindle speed of 4000 r/min. The comparison shows that the step drill takes longer to generate torque, with the step drill (A) taking the longest to drill. Because the second point angle of the step drill (A) is smaller than that of the step drill (B) and step drill (C), the secondary cutting edge is longer, increasing the total length of the main cutting edge and thus extending he time to generate torque. According to Eqs. (8) and (11)(12), when the twist and step drills start drilling into Inconel 718 material, the torque gradually rises to its maximum value and enters stable drilling. The difference in torque produced by twist drill and step drills at this stage is not significant. When the drill tip starts to drill out the Inconel 718 material, the torque of the twist drill drops sharply, while the torque of the step drill drops more slowly because the secondary cutting edge of the step drill is still drilling [47]. Figure 14 shows a comparison of the average torque during stable drilling Inconel 718 material with four different drill geometries at different spindle speeds. As can be seen in Fig. 14, for twist drill and step drill, the torque decreases with increasing spindle speed when the feed rate is constant. At 4000 r/min, the torque of the step drill (A, B, and C) decreases by 12.9%, 9.7%, and 6.4% respectively compared to the twist drill. The results show that the step drill can reduce the torque compared with the twist drill, and the smaller the second point angle the more effective the step drill is in reducing the torque. In the stable drilling process of the step drill, when the second point angle is smaller than the first point angle, the core thickness of the secondary cutting edge is smaller than the main cutting edge, and it is known from Eq. (12) that the generated torque will be reduced.

Analysis of chip flow rate and effective stress
Studying the size of chip flow rate plays an important role in chip removal and chip breaking. When the chip flow rate is high, the chips can be easily discharged and the friction between the chips and the drill and workpiece can be reduced, thus reducing the wear on the drill and improving the surface quality of the drill. Figure 15 shows the chip flow analysis in the simulation for drilling Inconel 718 material with twist drill and step drills (A, B, C) at a feed rate of 0.2 mm/r and a spindle speed of 4000 r/min. From the graph, it can be seen that the step drill (A) has the highest chip flow rate. The chip flow rate increases as the length of the main cutting edge increases, making chip discharge easier and more conducive to chip deformation and chip breakage. The smaller the point angle, the longer the secondary cutting edge of the step drill, and therefore the higher the chip flow rate of the step drill (A). Figure 16 shows the effective stress distribution of Inconel 718 material drilled with twist drill and step drill (A, B, C) at a feed rate of 0.2 mm/r and a spindle speed of 4000 r/min in the simulation, from which it can be seen that the step drill (A) has the lowest maximum effective stress. From the figure, it can be seen that the highest stresses always occur where the edge of the main cutting edge is in contact with the workpiece. Compared to twist drill, the secondary cutting edge of step drill is more conducive to chip evacuation, which reduces the contact time between the drill and the workpiece. Thus step drill reduces

Burr analysis
Burrs can cause many problems in machining and assembly, affecting the quality of the process and reducing the accuracy of the assembly. Burr height is one of the easiest features to analyze for drill exit quality. The different configurations of the drills have an effect on the burr height. Experiments were conducted with twist drill and step drills (A, B, C) at a feed rate of 0.2 mm/r and a spindle speed of 4000 r/min for drilling Inconel 718 material. Figure 17 shows the burr height measured by drilling experiments to analyze the effect of drill geometry on burr height. As you can see from the graph, the step drill is able to reduce the burr height and have a better surface quality of drilling compared to the twist drill. The step drill has two main cutting edges, and it can be seen from Eq. (10) that the total thrust force of the step drill is the sum of the thrust force generated by the two main cutting edges. When the first step is drilled out, the second step has relatively less pressure on the workpiece material and does not reach the critical condition of Inconel 718 plastic deformation, thus producing less burr and reducing the exit burr height. [48]. In addition, the smaller the second point angle the smaller the thrust force generated by the step drill in the second step, the smaller the deformation of the workpiece and the smaller the burr generated. So the step drill (A) has the smallest burr height.

Temperature and chip analysis
Cutting temperature affects tool wear and service life. Due to the poor thermal conductivity of Inconel 718 material, it is essential to study the drilling temperature. Figure 18 shows the temperature distribution of the twist drill and step drill (A) under CD conditions and the step drill (A) under UAD conditions at a spindle speed of 4000 r/min and a feed rate of 0.2 mm/r. Under CD conditions, the step drill (A) has a higher drilling temperature than the twist drill. The  second point angle of the step drill (A) is smaller than the first point angle, then the secondary cutting edge is larger than the main cutting edge. The total cutting edge length of the step drill (A) is larger than that of the twist drill. Therefore the cutting edge of the step drill (A) has a larger contact area with the workpiece, which increases the friction and increases the drilling temperature. With UAD, the vibration reduces the contact time between the cutting edge and the workpiece, and the intermittent motion allows more cooling time for the workpiece, thus reducing the drilling temperature. Figure 19 shows a comparison of the simulation results of the maximum temperature of the twist drill and step drill (A) for drilling Inconel 718 material under CD conditions and the step drill (A) under UAD conditions. As can be seen from the graph, the drilling temperature increases with the increase of feed rate at a certain spindle speed. In addition, UAD was 14.96% lower than CD temperature at a feed rate of 0.2 mm/r, indicating that UAD can significantly reduce the drilling temperature [49,50].
Drilling is a continuous cutting process. Chip formation and fracture have a great impact on the quality of drilling, which can be analyzed in terms of the length of chips produced. Figure 20 shows a chip comparison between drilling simulations using twist drill and step drill (A) in CD, and using step drill (A) in UAD. Simulation results show that step drills can effectively reduce chip length. The addition of the secondary cutting edge of the step drill increases the drilling temperature and reduces the strength and hardness of the Inconel 718 material, making it more conducive to chip breakage. Figure 21 shows the chip morphology comparison of Inconel 718 material in simulation and experiment by using twist bit in CD, 2 mm/r and the feed rate of 4000 r/ min. CD is a continuous cutting process without separation, which produces spiral continuous chips. UAD is intermittent motion, producing segmented discontinuous chips, intermittent contact between tool and workpiece, reducing the friction between chips and workpiece, better drilling results. Figure 22 is a comparison of the average chip length of Inconel 718 material by using twist drill in CD, step drill (A) in CD and step drill (A) in UAD at different feed speeds. It can be seen from the figure that the chip length decreases with the increase of feed speed [51].

Conclusion
In this paper, we conducted drilling simulation experiments on Inconel 718 by changing the geometry of twist drill and designing three step drills with different second point angles. Mathematical models of thrust force and torque of twist drill and step drill were established. Simulations and experimental analyses were performed to verify the reliability of both models. The effects of four types of drills on the thrust force, torque, effective stress, chip flow rate, and burr of Inconel 718 high-temperature alloy under CD conditions were mainly analyzed to determine the step drill with the best machining performance. The best step drill was used to drill 718 under CD and UAD conditions to compare drilling temperatures and chip morphology. The main findings of this study are summarized as follows: (1) Through simulation and experimental analysis, the average thrust force of the step drill (A, B, and C) decreases by 32.3%, 23%, and 17.7%, and the average torque of the step drill (A, B, and C) decreases by 12.9%, 9.7%, and 6.4%, respectively, when comparing with the twist drill at a feed rate of 0.2 mm/r and a spindle speed of 4000r/ min. It proves that the thrust force and torque of the step drill are smaller than the twist drill, and the torque and thrust force decrease with the decrease of the second point angle of the step drill. The torque and thrust force of the twist drill and step drill decrease with increasing spindle speed, indicating that increasing the spindle speed helps to improve the machining performance. (2) The simulation analysis shows that the chip flow rate and maximum effective stress of the step drill are smaller than the twist drill. The longer total main cutting edge of Comparison of average chip length at different feed rates at a spindle speed of 4000r/min the step drill makes chip discharge easier and increases the chip flow rate. The smaller the second point angle, the higher the chip flow rate and the better the chip evacuation. The maximum effective stress is reduced because the step drill reduces the contact time between the drill and the workpiece and the chips. The lower the second point angle of the step drill, the lower the maximum effective stress and the better the machining quality. (3) Compared to twist drill, step drill produces a lower burr height. As the first step of the step drill is drilled out, the second step exerts relatively less pressure on the workpiece and does not reach the critical conditions for plastic deformation of Inconel 718 high-temperature alloy, resulting in fewer burrs and lower exit burr heights. When Inconel 718 is drilled using the step drill (A), less deformation of the workpiece occurs and a lower burr height is produced. (4) Under CD conditions, the step drill (A) has a higher drilling temperature than the twist drill. The second point angle of the step drill (A) is smaller than the first point angle, then the secondary cutting edge is larger than the main cutting edge. The total cutting edge length of the step drill (A) is larger than that of the twist drill. Therefore the cutting edge of the step drill (A) has a larger contact area with the workpiece, which increases the friction and increases the drilling temperature. UAD reduces the contact time between the cutting edge and the workpiece, which reduces the drilling temperature. Drilling temperature increases with increasing feed rate for both CD and UAD conditions. Using step drill increases the drilling temperature and reduces the strength and hardness of the Inconel 718 material, which is more conducive to chip breakage. Ultrasonic-assisted drilling produces segmented discontinuous chips with good chip breakage. Chip length decreases with increasing feed rate for both conventional and ultrasonic-assisted drilling conditions.
Author contribution Conceptualization, Qi Wang; software, Dazhong Wang; writing review and editing, Yu Fang. All authors have read and agreed to the published version of the manuscript.
Funding This study was supported by a research project financed by the National Natural Science Foundation of China (number 5217052158).