1 Introduction Hole deflection is an unavoidable technical problem in deep hole drilling [1]. For various reasons, such as the arbor bearing deflection, the deflection of the guide sleeve, and the asymmetry of the cutting force, the initial deflection amount of the drill bit will be generated, and the deflection amount will increase as the drilling depth increases. Finally, the drilling direction of the drill bit will eventually deviate from the axis of rotation of the workpiece, and when it is severe, the drill bit will be drilled from the side wall of the machined part, causing a machining accident. Although there are many corrective measures for deep-hole drilling [2,3], but the method of more application is still based on the size of the deflection after the completion of drilling, with the center of the hole as a reference to re-turn the workpiece outer circle In order to achieve the purpose of correction. However, this method of correction has a limited range of use, and it cannot fundamentally eliminate the phenomenon of skew expansion. 2. Analysis of the Mechanism of Drilling Hole Deflection (1) Ordinary Drilling Hole Deflection In the deep hole machining system shown in Fig. 1, the initial deflection of the drill bit plays an important role in the deflection of the hole, due to the presence of the initial deflection, the bit axis Deflection occurs relative to the axis of rotation of the workpiece, and the amount of deflection gradually increases as the drilling depth increases, and the trajectory of the drill bit axis also moves away from the theoretical drilling axis. By simplifying the drilling process, a mechanical model for drilling and drilling into the drilling stage is shown in Figure 2. Fig.1 Schematic diagram of common drilling hole deflection Figure 2 Drilling and drilling stage mechanical model Assuming that the axial force during drilling is p and the radial force is R, under the action of these two forces, the drill tip is offset from the center of the drill bit to a point where the displacement is q, and is in equilibrium at this point. From this we can get the differential equation of bit deflection In the formula E, the modulus of elasticity of the drill pipe material I—the inertia moment of the drill pipe According to the boundary conditions x=0, y=0 and x=L,y=-q, the solution of equation (2) is Finding both sides of equation (3) From Fig. 2, it can be seen that the influence of the deviation of the hole center is the radial force R, and the boundary condition is When x=L, the angle of deviation of the drill at the free end of the drill is make In equation (7), the minus sign indicating the skew direction is removed. When the external load P is much smaller than the buckling limit load Pc, the initial skew angle of the drill bit can be reduced to Deflection of drilling in equation (8) So you can get That is, in the case of a certain length of the drill pipe, the amount of deviation of the hole center for ordinary drilling is related to the amount of ingression deviation q0 and the length ln of drilling. Same reason Comparison formula (10) and formula (12) shows that when drilling the same depth deep hole with the same bit, compared with ordinary drilling, the hole drilling deflection at drilling depth is significantly reduced. That is, q vibration <q general. 3 drilling processing comparison test In order to verify the correctness of the above-mentioned theoretical analysis, a comparative experiment was conducted on the eccentricity of the boreholes in the two drilling methods of ordinary drilling and vibration drilling. Fig. 3 Vibratory drilling system The test bit is 7.9mm small-diameter DF internal chip deep hole drilling, tool length L = 630mm, blade material is YT798; test piece is 14 x 130mm TC-4 titanium alloy bar material; amplitude of the vibration device is 0.05mm The frequency is 90Hz; the feed rate is 0.008mm/r, the spindle speed is 1250r/min, and the cutting fluid in the machining uses 5# mechanical oil and the oil pressure is 4MPa. Fig. 4 compares the borehole deflection test results for ordinary drilling and vibration drilling. It can be seen from the figure that the hole deflection under the state of vibration drilling is small, which is consistent with the above theoretical analysis results. Fig. 4 Comparison of the hole deflection of two drilling methods 4. in conclusion Vibratory drilling changes the cutting mechanism of the drill, changing the one-time continuous drilling of ordinary drilling into a periodic pulse wedge. Vibration drilling has a dynamic process of cutting-resetting-recutting. Compared with ordinary drilling, this feature of vibratory drilling not only improves the drill's entry accuracy, but also slows down the accumulative speed of the deviation of the hole center in the depth of cut. Therefore, vibration drilling can significantly reduce the depth of the hole. Hole center deflection error during cutting.
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Experimental studies and machining practices show that vibratory drilling is a new type of process that can significantly improve the quality of deep hole machining [4]. The difference between vibratory drilling and ordinary drilling is that the relative vibration between the drill and the workpiece is generated through the vibration device during the drilling process, thereby changing the drilling mechanism and improving the drilling quality. Vibratory drilling can significantly improve the deviation of the hole center. Many literatures have discussed the mechanism of action. Literature [5] believes that the combined effect of the “stationary effect†and “rigidization effect†of the high-frequency vibration of the bit can effectively suppress the drilling deflection and improve the straightness of the drilling. However, because the "static effect" and "rigidization effect" of the drill that oscillates in the low frequency range are very weak, the above theory has certain limitations. Based on the research results in [6], this paper considers the pulse cutting characteristics of vibratory drilling, discusses the inherent mechanism of vibratory drilling to reduce the deviation of small hole center, and verifies the theoretical derivation results through vibration drilling test. 
, finishing (1) 
Into (4), there are 
, R value is returned to formula (4) 
, and expand equation (6) 
.
In the ordinary drilling process, as the drilling depth increases, the deviation of the tool tip from the target axis gradually increases under the influence of the initial deflection amount (see FIG. 1 ). Set the tool's instantaneous feed amount to Δl, and the hole depth to ln. Then, the deflection amount at any position of the hole is 
(2) The amount of hole deflection for vibration drilling When discussing the amount of hole deflection for vibration drilling, it is first necessary to analyze the vibration drilling process. In vibratory drilling, the drill tip retracts immediately after impacting the surface of the workpiece once. The deformation caused by the momentary action of the transverse force is reset and straightened after the drill bit disengages from the workpiece, and is then re-entered. Therefore, compared with ordinary drilling, the hole deflection of the vibration drilling has two characteristics: 1 In the drilling stage, the vibration drilling changes the one-time continuous cutting of the drill bit into multiple pulse cutting in the ordinary drilling. Since the drill tip impacts the workpiece again after the offset is recovered, the offset of the drill is corrected so that the drill tip can be drilled into the workpiece with a small offset, that is, there is q0 vibration. 2 In the drilling stage, due to the pulse action of the drill bit, each entry of the drill bit is not performed on the basis of all the previous drilled deviations, but drilling is continued on the basis of the reduced last drilled deviation. By setting the deviation reduction coefficient to δ (δ<1), the deviation of the hole center at the drilling depth ln at vibration drilling can be obtained as 
Figure 3 shows the vibratory drilling system we designed. The vibration device adopts a mechanical double eccentric mechanism, and the amplitude can be continuously adjusted in the range of 0-0.5mm. The DC motor speed is controlled by a DC power supply, and the vibration frequency can be selected by adjusting the DC power supply current within 100Hz. Therefore, the vibration drilling system is used. It can meet the requirements of amplitude and vibration frequency under different working conditions. 
