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Experimental study on drilling basalt with self-vibratory drilling head
Journal Pre-proofs Experimental study on drilling basalt with self-vibratory drilling head Xiaogan Peng, Liang Li, Bo Chen, Shen Yin, Zhongwang Yin, Yinfei Yang PII: DOI: Reference:
S0273-1177(19)30852-X https://doi.org/10.1016/j.asr.2019.12.002 JASR 14568
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
17 June 2019 6 October 2019 2 December 2019
Please cite this article as: Peng, X., Li, L., Chen, B., Yin, S., Yin, Z., Yang, Y., Experimental study on drilling basalt with self-vibratory drilling head, Advances in Space Research (2019), doi: https://doi.org/10.1016/j.asr. 2019.12.002
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© 2019 Published by Elsevier Ltd on behalf of COSPAR.
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Experimental study on drilling basalt with self-vibratory drilling head o
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Xiaogan Penga, Liang Lia, Bo Chenb, Shen Yinc, Zhongwang Yinc, Yinfei Yanga
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
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Xi'an Aircraft Industry (Group) Co., Ltd. Xi'an 710089, China
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Beijing Spacecrafts. Beijing 100094, China
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Abstract Based on the goal of improving the rock breaking ability when drilling asteroid rock samples under limited energy conditions, this paper proposes a method of drilling rock using self-vibratory drilling head and develops a small self-vibratory drilling head for drilling rock. In order to analyze the dynamic characteristics of drilling rock with self-vibratory drilling head, a rock model hypothesis that the rock consists of a series of micro-segment uniform continuous media is put forward. Base on the hypothesis, the model of drilling rock is constructed, the stability lobes diagram of self-vibratory drilling head drilling basalt is plotted, and the energy mechanism of drilling rock system with self-vibratory drilling head is discussed. The comparison tests of drilling basalt by three kinds of self-vibratory drilling head with different spring stiffness and the conventional method are carried out. The rotational speed is a variable in the comparative tests. The test results show that under the specific rotational speed and spring stiffness, self-excited vibration is produced in self-vibratory drilling head drilling basalt. When self-excited vibration drilling is conducted, although the amplitude fluctuation range of the drilling thrust force is wider than that of conventional drilling, the average drilling thrust force is smaller than the conventional drilling. The amplitude of drilling thrust force increases with an increase in spring stiffness. The method of drilling rock by self-vibratory drilling head is proved to be a potential method for viable drilling of asteroid rock samples. Keywords: Self-vibratory drilling head; Basalt; Self-excited vibration; Drilling thrust force
1. Introduction Asteroids are celestial bodies in the solar system that are similar to the planets moving around the sun, but much smaller in volume and mass. The asteroid is loosely organized, like a huge pile of gravel combined by gravity. Asteroids are rich in mineral resources and can provide a source of material for humans to move into space (Badescu 2013; Bonneville 2018). Therefore, asteroid attachment and sampling return detection are one of the main contents of deep space exploration. The energy of asteroid detectors is generally supplied by solar power systems. During the drilling of the asteroid rock sample, the power of the drilling mechanism of the asteroid detector is set within a specific range. Consequently, improving drilling capacity and rock breaking efficiency of the drilling mechanism under limited power has become a key technical problem and research hotspot (Sorenson 2000; Zacny and Bar-cohen 2009). From the perspective of the drilling process, the impact of the vibration drilling will cause the rock to produce micro-cracks and expand the micro-cracks, or activate and propagate the existing micro-cracks in the rock, thereby improving the rock breaking
Corresponding author. E-mail addresses: [email protected] (Liang Li), [email protected] (Xiaogan Peng), [email protected] (Bo Chen), [email protected] (Shen Yin), [email protected] (Zhongwang Yin), [email protected] (Yinfei Yang).
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spacesystems developed a low force sample acquisition system using the principle of rotary impact (Stanley et al., 2007). The Mars Sample Return core drill designed by Honeybee Robotics also uses a rotary impact drilling method (Zacny et al., 2011). The Luna-24 detector of the former Soviet Union also adopts the method of rotary impact drilling and uses threshold judgment to automatically control the opening and closing of the impact motor. According to the telemetry results, the impact motor is frequently opened during drilling. Twice it has happened that the drilling pressure was large enough to have triggered the alarm (Zacny and Bar-cohen 2009; Zacny et al., 2013). The rotary impact method is based on forced vibration, and its impact energy is generally a fixed value. However, due to the heterogeneity, discontinuity, and anisotropy of rocks, the physical-mechanical properties of rocks of the same composition are also quite different. The impact energy required for different mechanical properties of the rock is also different. Therefore, the self-vibratory drilling method is a potential method for vibration drilling of a rock. Self-vibratory drilling method has a series of research and application in the field of metal cutting. Brun-Picard et al. (1999) proposed a technique of self-excited vibration drilling in which a low energy flutter is excited at the specific process parameters by a low stiffness component (spring) mounted between the machine tool and the tool or workpiece. Tichkiewitch et al. (2002) proposed a nonlinear dynamic model of self-excited vibration drilling, and simulated and analyzed the phenomenon of "finite amplitude instability" in the time domain. Based on the principle of self-excited vibration drilling, Paris et al. (2005) designed a self-vibrating drilling head that can be conveniently used on ordinary CNC machine tools. The processing performance of the self-vibrating drilling head is proved by experimental research. Gouskov et al. (2005) proposed to replace nine physical quantities in self-excited vibration drilling with three dimensionless parameters, which can be used to select cutting conditions conveniently in the experiment. Guibert et al. (2008) constructed dynamic model of self-vibratory drilling head, cutting force and plowing force, and material removal based on the problem of chip breakage in deep drilling. The model is used to simulate the cutting conditions and then predict the vibration condition. Forestier et al. (2012) associated self-vibratory drilling head drilling with machine tool systems to construct the finite element model of the machining system based on machine tool spindle, self-vibratory drilling head and drill bit, which is used to evaluate the dynamic characteristics of the machining system. However, there are few public reports on self-vibratory drilling head drilling rock in the space. Although the amplitude of drilling thrust force fluctuates greatly during self-excited vibration drilling, the average drilling thrust force is much smaller than that of conventional drilling under the same drilling parameters (Paris et al., 2005; Paris 2018). The rock generates and expands the crack under the influence of vibration impact force, which is beneficial to improve the efficiency of drilling rock. Therefore, this paper proposes a method of drilling rock samples using self-vibratory drilling head (SVDH). This method uses SVDH to perform self-excited vibration drilling rock under particular cutting parameters. The vibration impact of the drilling tool on the rock can improve the rock breaking ability. In this paper, the SVDH for drilling rock is developed, and an experimental study of drilling basalt is carried out. The model of SVDH drilling rock is constructed in the second part, and the comparison experiment of drilling basalt with SVDH and conventional method is carried out in the third part. In the fourth part, the test results are analyzed and discussed. Finally, the conclusions are obtained. 2. Model of drilling rock system with self-vibratory drilling head The physicist A. A. Harkevich defines the self-vibration system as a closed-loop system consisting of the main vibration body, energy, controller and feedback unit. The self-excited vibration of the self-vibration system requires neither external force excitation nor external action to change the structural parameters of the system but relies on the interaction of various components within the system to maintain steady-state periodic motion (Ding 2009). According to the regenerative flutter theory, in the self-vibration system of SVDH drilling rock, the main vibration body is the arbor and the drilling tool, the energy is the drilling 2
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e r-s o ft w a r improve the drilling efficiency under limited power. Based on the NASA Mars instrument development project, Alliance
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ability of the drilling tool (Hu et al., 2002). The vibration effect is also beneficial to chip removal. The vibration drilling can
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thrust force, the controller is the drilling depth, and the feedback unit is the drilling machined surface generated in the previous
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2.1. Self-vibratory drilling head As shown in Fig. 1, a small SVDH for drilling rock is developed, which consists of a front drilling head body, an arbor, a spring, an adjusting screw, and a rear drilling head body. The maximum diameter of SVDH is Φ 30 mm, and the total length is 65mm (not including the cemented carbide triangular bit). The extended length of the cemented carbide triangular bit (CCTB) is 35mm. The total mass of SVDH is 212 g, and the main vibration body (arbor and CCTB) has a mass of 24g. The CCTB is mounted on the arbor, the arbor is splined with the front drilling head body, the spring is installed in the front drilling head body, and the adjusting screw is installed at the rear end of the front drilling head body. The spring is compressed by rotating the adjusting screw to maintain it in contact with the arbor. The vibration mode of the SVDH can be adjusted by replacing the internal spring. The output shaft on the rear drilling head body can be fixed with the tool holder.
Fig. 1 Self-vibratory drilling head
2.2. Dynamic model of drilling rock system with self-vibratory drilling head 2.2.1. Hypothesis of rock model In the elastoplastic model of rock, rock is regarded as a continuous medium. However, natural rock is an uneven, discontinuous medium with irregular cracks and pores inside. If the natural rock is divided into sufficiently thin micro-layers along the drilling direction, then the rock medium on each micro-layer should satisfy the basic hypothesis of the elastoplastic model of the rock (Xie and Chen 2004). Therefore, in this paper, based on the elastoplastic model of rock, a rock model hypothesis is proposed, that is, the rock is a combination of a series of micro-segment uniform continuous medium. The rock hypothesis model can be described as follows: Let the thickness of the rock is hr and the threshold of
mechanical properties is [MRmin, MRmax]. Then, the rock can be considered as a combination of a series of continuous uniform micro-segment rock of thickness hri (i = 1, 2, ...), hri is a random value less than hr, MRi is the mechanical property of the hri micro-segment rock, and MRmin≤MRi ≤MRmax. 2.2.2. Dynamic model of drilling rock system with self-vibratory drilling head The SVDH drilling rock system needs to have the following two points to generate self-excited vibration. One is that the SVDH drilling system is unstable near the equilibrium point. The other is the presence of a disturbance that forces the working point of the SVDH drilling rock system to deviate from the equilibrium point. Thus, when the SVDH is used for drilling on each micro-segment uniform continuous rock medium, the condition for generating self-excited vibration will be satisfied. Therefore, the self-excited vibration characteristics of the SVDH drilling rock system can still be studied by the regenerative flutter method, but the form of self-excited vibration is more complicated. 3
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The model of the SVDH drilling rock system is shown in Fig. 2, and the general equation of the machining system can be
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(1)
Where m is the mass of the vibrating part, which is the sum of m1 (arbor) and m2 (CCTB), c is the damping coefficient between the arbor and front drilling head body, k is spring stiffness, z(t) is the instantaneous axial position of the vibrating portion, and P is the drilling thrust force. The empirical formula for the drilling thrust force can be expressed as: P kc zc d h(t )
(2)
Where kc is the coefficient determined by the rock material and the drilling tool geometry parameters such as axial lip length (all),
blade thickness (bt) and apex angle (aa), zc is the number of drill lips on drilling tool, d is the diameter of the drilling tool, and h(t) is the instantaneous cutting thickness.
In each uniform continuous micro-segment of rock, h(t) in Eq. (2) can be described as: h (t ) h0 z (t ) z (t T )
(3)
Where h0 is the theoretical cutting thickness, [z(t)-z(t-T)] is the dynamic cutting thickness produced by the two adjacent cutting vibrations. The period of the drill lip passes through a specific point in the cutting layer:
T
60 n zc
(4)
Where n is the rotational speed of the SVDH. Substituting Eq. (2) and Eq. (3) into Eq. (1), the motion equation of self-excited vibration drilling rock system on each uniform continuous micro-segment rock can be obtained: m z (t ) c z (t ) k z (t ) k c z c d h0 z (t ) z (t T )
(5)
Fig. 2 Model of drilling rock with self-vibratory drilling head
2.2.3. Block diagram of drilling rock system with self-vibratory drilling head According to the regenerative flutter theory, the Laplace transformation of Eq. (5) is carried out, and then the block diagram 4
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In the block diagram, the transfer function of the SVDH is:
(s)
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Where, the natural frequency is n
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of drilling rock with SVDH can be constructed, as shown in Fig. 3.
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(6) k m , the damping ratio is c 2 k m .
The transfer function between the instantaneous cutting thickness and the theoretical cutting thickness is:
H (s) 1 sT H 0 ( s ) 1 (1 e )kc zc d ( s )
(7)
According to the rock model hypothesis that the rock is a combination of a series of micro-segment uniform continuous medium, it can be inferred that when the SVDH drills the rock at a specific feed rate, the stable self-excited vibration may occur on the micro-segment uniform continuous medium under a specific rotational speed and spring stiffness.
Fig. 3 Block diagram of drilling rock with self-vibratory drilling head
2.3. Energy mechanism of drilling rock system with self-vibratory drilling head The self-excited vibration of the SVDH drilling rock system is not “self-sufficient vibration”, and it cannot be “autarky” in energy, but needs to rely on the external energy supply to supplement the energy dissipation caused by a system damping. In the self-excited vibration of the SVDH drilling rock system, the magnitude of the drilling thrust force is periodically changed. when the drilling thrust force is in the decreasing stage, the drilling tool and the arbor compression spring are acting in the axial direction, and the drilling thrust force does the positive work to the system, and the input energy to the system; When the drilling thrust force is in the increasing stage, the arbor relax the spring in the axial direction. In this stage, the energy of the vibration system is divided into three parts dissipation. The first part is transmitted into the rock inside through the impact work, the second part is dissipated by drilling the rock in the form of net negative work, and the remaining part is dissipated by the system damping. Thus, the following equation can be obtained. WP Wdi Wc Wim Wdo
(8)
Where WP is the input energy of the drilling process, Wdi is the damping loss energy when inputting energy, Wc is energy dissipated by the cutting work, Wim is the impact energy consumed during drilling, and Wdo is the damping loss energy when drilling. According to the rock model hypothesis, if the mechanical properties of each micro-segment are uniform, then the amplitude of self-excited vibration generated by the SVDH drilling rock system is stable when equation (8) is tenable. If the mechanical properties of the micro-segments are inconsistent from one micro-segment to the adjacent micro-segment, then two situations may occur for Eq. (8): WP Wdi Wc Wim Wdo
(9)
WP Wdi Wc Wim Wdo
(10)
For Eq. (9), the amplitude of self-excited vibration is incremented until the amplitude is increased to a specific value. A new 5
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generated, and Eq. (8) is tenable, producing self-excited vibration with new amplitude. If a new energy balance cannot be generated, the system tends to be stable and does not generate self-excited vibration. 3. Experiment on drilling basalt with self-vibratory drilling head 3.1. Experimental setup The test device is composed of vertical machining center, tool holder, SVDH, CCTB, fixture and force measuring system, as shown in Fig. 4. The SVDH is mounted on the tool holder, the tool holder is fixed on the spindle of machining center, and the three-direction piezoelectric dynamometer is mounted on the machining center table. The fixture is fixed on the upper plane of the dynamometer. The vertical machining center (Model: XK2174, SHENJI ZHONGJIE CNC Machine Tool Co., Ltd.) has a spindle power of 4 KW, a maximum spindle speed of 8000 r/min, and a feed rate range of 1-4000 mm/min. The Φ4mm commercial CCTB is selected as the drilling tool with an axial lip length of 7 mm, a blade thickness of 1 mm and the apex angle of 31.9°. The force measuring system is composed of Kistler 9265B three-direction piezoelectric dynamometer, Kistler 5019A charge amplifier and corresponding data acquisition and processing system. Basalt is selected as the test material, its drillability classification grade is 8, and the compressive strength and tensile strength is 205±45 MPa and 5.8±1.3 MPa, respectively.
Fig.4 Test device, (a) The actual image, (b) The schematic diagram
3.2. Experimental procedure The spring stiffness in SVDH is an important parameter that directly determines the vibration characteristics of the SVDH. In this experiment, three springs of different stiffness values are selected, and the SVDH with different spring is used to carry out the single factor test of drilling basalt with rotational speed as a variable. For comparison purpose, a single factor test of drilling basalt with the same parameters is carried out using a conventional drilling method (without SVDH). The experiment in this paper consists of four group tests. The Experimental parameters are shown in table 1. The drilling depth for all the four group tests is 15mm. The drilling thrust force is taken as the test result. The drilling thrust force data are collected by the force measurement system, which consists of Kistler 9265B three-way piezoelectric dynamometer and Kistler 5019A charge amplifier. The drilling thrust force data are processed using MATLAB and Origin. Table 1 Experimental parameters Number
Feed rate (mm/min)
Spring Stiffness (N/mm)
Rotational speed (r/min)
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energy balance is generated, and Eq. (8) is tenable, producing self-excited vibration with new amplitude. In the case of Eq. (10),
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3.3. Stability lobes diagram of drilling rock system with self-vibratory drilling head The vibration when drilling rock with SVDH is regenerative flutter. Linear stability theory is an important method to explain and analyze the stability of flutter (Altintas 2000). Therefore, the linear stability theory is used to analyze the stability of self-excited vibration drilling rock systems. The characteristic equation of Eq. (7) can be expressed as
D( s ) 1 (1 e sT )kc zc d ( s ) 0
(11)
Let the characteristic root of Eq. (11) be s=+jω. When > 0, the system is unstable; when <0, the system is stable; when
= 0, the system is in a critical stable state. In order to analyze the system state with the critical stability boundary line, let the characteristic root of Eq. (11) is s= jωc. Then Eq. (11) can be rewritten as: D ( j c ) 1 k c z c d (1 e jc T ) ( j c ) 0
(12)
The transfer function Φ (jωc) can be expressed as the sum of the real part G (ωc) and the imaginary part H (ωc), as follows: ( jc ) G (c ) jH (c )
(13)
Then equation (12) can be rewritten as follows:
D( jc ) 1 kc zc d 1 cos(cT ) j sin(cT ) G (c ) jH (c ) 0
(14)
When equation (14) is tenable, its real and imaginary parts are equal to zero, as follows
Re D( jc ) 0 Im D( jc ) 0
(15)
According to the rock model hypothesis, although the mechanical properties of each micro-segment uniform continuous medium along the drilling direction cannot be accurately predicted, there is a particular understanding of the threshold range of the macroscopic mechanical properties of the rock. Therefore, based on the principle of extreme value, the mechanical properties of the micro-segment uniform continuous medium can be replaced by the macroscopic mechanical properties of the rock. The minimum macroscopic mechanical properties of the rock are used to set the parameter kc in the Eq. (2). And then the stability lobes diagram of SVDH drilling basalt is drawn, as shown in Fig. 5. The area below the critical stability curve of the stability lobes diagram is not a completely stable drilling area, but the area above the curve must be an absolutely unstable drilling area. It can be seen from Fig. 5 that when the compliance is greater than 1.09X10-5 m/N, that is, the spring stiffness is less than 91.74 N/mm. The SVDH drilling basalt system may be in an unstable drilling area.
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Fig. 5 Stability lobes diagram of self-vibratory drilling head drilling basalt (kc=4.8X103 N/m, d=4X10-3 m, m=0.024Kg, ζ=0.05, zc=2, h0 = 3.5X10-5 m, all=7mm, bt=1mm, aa=31.9°)
4. Results and discussion Drilling thrust force is an important indicator of drilling rock samples on asteroids. According to the rock model hypothesis presented above, the drilling thrust force at one or several time points cannot fully characterize the characteristics of SVDH drilling rock, and only the average drilling thrust force within a sufficiently long period of time can be characterized. Therefore, when discussing the test results, the average drilling thrust force during the CCTB full-edge drilling basalt is taken as the test result. 4.1. Effect of rotational speed on drilling thrust force The drilling thrust force data of the CCTB full-edge drilling basalt are selected in each test, and the average value is calculated separately. And then the histogram of the average drilling thrust force with the rotational speed is constructed, as shown in Fig. 6. In order to compare the time-domain diagram of the drilling thrust force under different drilling conditions, four typical drilling states (a) - (d) are selected from the histogram, and four sub-graphs of drilling thrust force varying with time are drawn, as shown in Fig. 6 (a) - (d). It can be seen from Fig. 6 that the average drilling thrust force of the four groups of tests does not have a uniform law as the rotational speed increases. With the increase of the rotational speed, the fluctuation range of the average drilling thrust force of the four group tests can be arranged in the following sequence: Group3> Group2> Group1> Group4. For three groups of SVDH drilling basalt tests, the average drilling thrust force at 800 r / min is the minimum for each group of the tests. The average drilling thrust force of SVDH drilling is lower than that of conventional drilling under some drilling conditions, such as condition (b). It can be seen from Figure 6 (b) that the self-excited vibration is produced under the drilling conditions (b). Therefore, it is proved that self-excited vibration drilling has the characteristics of smaller average drilling thrust force. It can be seen from Fig. 6 (a) - (d) that the amplitude fluctuation range of the drilling thrust force when drilling with SVDH is significantly larger than that during conventional drilling. According to Eq. (2), for conventional drilling, when the feed rate is fixed, the instantaneous cutting thickness h(t) is constant. On the other hand, the coefficient kc is a random value within a specific 8
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c .c e. r-s o SVDH drilling, the drilling system changes from a rigid system to a weakly rigid system due to the presence of the spring. k eThe ft w a r
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instantaneous cutting thickness h(t) is not constant. At the appropriate rotational speed and spring stiffness, the self-excited vibration is produced when drilling basalt. According to the Eq. (8) of the energy mechanism of SVDH drilling rock system, the damping loss energy always exists in the self-excited vibration drilling. Therefore, the amplitude of the drilling thrust force of the self-excited vibration cannot be increased indefinitely, and it experiences random fluctuations within a specific range.
Fig. 6 Average drilling thrust force histogram and drilling thrust force domain diagram
4.2. Effect of spring stiffness on drilling thrust force The drilling thrust force data collected from the three group tests of SVDH drilling basalt are pre-processed, and the time domain diagram of drilling thrust force is constructed. It is found that the drilling thrust force diagrams under the six test conditions are consistent with the characteristics of self-excited vibration drilling. The six test conditions are (7.32 N/mm, 600 r/min), (7.32 N/mm, 800 r/min), (11.46 N/mm, 500 r/min), (19.42 N/mm, 500 r/min), (19.42 N/mm, 600 r/min) and (19.42 N/mm, 800 r/min). The drilling thrust force data for the specified period are selected on the time domain diagrams of the above six test
conditions respectively, and the Fast Fourier transform is performed, as shown in Fig.7. It can be seen from Fig. 7 that the lower envelope of the drilling thrust force of all the time domain diagrams is almost straight and the value is small, which is the characteristic of self-excited vibration drilling. It can be seen from Fig.7 (a) and (b) that when the spring stiffness is 7.32 N/mm, the vibration frequency component is relatively cluttered and the vibration amplitude is small. As can be seen from Fig. 7(c), when the spring stiffness is 11.46 N/mm, although the vibration frequency component is concentrated, the amplitude is small. From Fig.7 (d), (e) and (f), it can be seen that when the spring stiffness is 19.42 N/mm, the vibration frequency component is more concentrated and has certain regularity, and the amplitude is also significantly increased. Comparing the amplitude fluctuation 9
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range. Therefore, the drilling thrust force P does not tend to be a specific value, but a random value within a specific range. For tra
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with the increase of spring stiffness. The wider the amplitude fluctuation range of the drilling thrust force, the greater the impact energy of drilling tool to basalt, which is beneficial to breaking rock and improving drilling efficiency. According to Fig. 5 Stability lobes diagram of self-vibratory drilling head drilling basalt, it can be inferred that when the rotational speed is constant, as the spring stiffness increases, the working state point of the system is closer to the critical stable curve, and the self-excited
vibration drilling is better.
Fig. 7 Drilling thrust force time-frequency domain diagram of SVDH drilling basalt
4.3. Effect of drilling method on drilling thrust force In this paper, two methods are used for basalt drilling, one is the method of SVDH drilling, and the other is the conventional drilling method. The average drilling thrust force of the two drilling methods is comparatively analyzed in Section 4.1. In this section, the drilling thrust force of the two drilling methods is discussed in detail. Two sets of drilling thrust force at 500 r/min and 600 r/min in the third group of SVDH drilling basalt test are selected for the discussion purpose. In both cases, self-excited vibration occurs in the drilling process. In addition, two sets of the drilling thrust force at 500 r / min and 600 r / min in the fourth 10
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e r-s o ft w a r amplitude fluctuation range of the drilling thrust force, and the amplitude fluctuation range of the drilling thrust force increases
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range of the drilling thrust force under the six conditions, as shown in Fig. 7, it can be seen that the spring stiffness is related to the
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drilling thrust force is constructed, as shown in Figure 8. It can be seen from Fig. 8 (a) that the lower envelope of the drilling thrust force diagram is almost a straight line, and the upper envelope has obvious random fluctuation characteristics. From the four detailed sub-graphs of Fig. 8 (a), it can be seen that all the drilling thrust forces have obvious periodic vibrations, but their amplitudes and waveforms are different. A similar phenomenon can also be observed in Figure 8(b). It can be seen from Fig. 8(c) that the two envelopes of the drilling thrust force are approximately parallel curves with random fluctuations. It can be seen from the four detailed sub-graphs of Fig. 8 (c) that the drilling thrust force is in a disordered vibration state. The phenomenon similar to Fig. 8 (c) can also be observed in Fig. 8 (d). Compared with the detailed sub-graphs of Figures 8(a) and (b), it can be seen that the vibration amplitude in detailed sub-graphs of Fig. 8 (c) and (c) are significantly smaller. It can be seen from Fig. 8(a) and (b) that the self-excited vibration generated by the SVDH drilling basalt is not a stable self-excited vibration, but a dynamically changing self-excited vibration. In the system of SVDH drilling basalt, when the rotational speed and feed rate are fixed, the basalt material properties become the main factor affecting the self-excited vibration of the system. According to the rock model hypothesis proposed in this paper, self-excited vibrations with different amplitude are generated on different micro-segments in the drilling direction. When the micro-segment self-excited vibration transition to the adjacent micro-segment, the self-excited vibration either tends to be gentle or more intense. This explains the reason for the random fluctuation of the upper envelope of the drilling thrust force diagram, as shown in Fig. 8 (a) and (b).
Fig. 8 Comparison of drilling thrust forces between SVDH drilling and conventional drilling. (a)SVDH drilling (500 r/min, 19.42 N/mm),
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-s o ft w a r e continuous drilling thrust force data with the time duration of 1s are selected. Subsequently, the time domain diagram of rthe
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group of conventional drilling basalt tests are also selected. In the selected four sets of drilling thrust force data, four segments of
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5. Conclusions
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(b) SVDH drilling (600 r/min, 19.42 N/mm), (c) Conventional drilling (500 r/min), (d) Conventional drilling (600 r/min) tra
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In this paper, the method of drilling rock with self-vibratory drilling head is proposed. A small SVDH for drilling rock is developed. And a series of comparison test of drilling basalt with SVDH and conventional method is carried out. The following conclusions are drawn: 1) The rock model hypothesis, which states that rock is composed of a series of micro-segment uniform continuous medium, is proposed. The thickness of the micro-segment is a random value, and the mechanical properties are a specific value within the threshold range of the macro-mechanical performance of the rock. 2) Under the specific rotational speed and spring stiffness, self-excited vibration is produced in SVDH drilling basalt. In self-excited vibration drilling, although the amplitude fluctuation range of the drilling thrust force is wider than that of the conventional drilling, the average drilling thrust force is smaller than that of the conventional drilling. 3) When basalt is drilled under self-excited vibrations using SVDH, the amplitude of drilling thrust force increases with an increase in spring stiffness.
References Altintas Y. 2000. Manufacturing automation: Metal cutting mechanics, Machine tool vibrations, and CNC design. Cambridge University Press. (Chapter 3) Badescu V., 2013. Asteroids: prospective energy and material resources. Springer Berlin Heidelberg. (Chapter 4, 12) Bonneville R., 2018. A truly international lunar base as the next logical step for human spaceflight. Advances in Space Research, 61, 2983–2988. Brun-Picard D, Gouskov A, Lesage D, Vincenti J., 1999. Vibration drilling By use of self-vibrating drilling head, PPF Workshop, ENSAM, Aix-en-Provence, France. 11-22. Deng Yong, Chen Mian, Jin Yan, et al., 2016. Prediction model and numerical simulation for rock fissure length under impact load. Petroleum Drilling Techniques. 44(4), 41-46. Ding Wenjing., 2009. Self-excited vibration. Tsinghua University Press. 245-280. Forestier F, Gagnol V, Ray P, et al., 2012. Model-based cutting prediction for a self-vibratory drilling head - spindle system. International Journal of Machine Tools & Manufacture. 52:59–68. Gouskov A, Peigné G, Kamnev E, et al., 2005. Self-excited vibratory drilling: a dimensionless parameter approach for guiding experiments. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture. 219(219):73-84. Guibert N, Paris H, Rech J., 2008. A numerical simulator to predict the dynamical behavior of the self-vibratory drilling headed. International Journal of Machine Tools & Manufacture. 48(6):644-655. Hu Liuqing, Li Xibing, Zhao Fujun. 2002. Study on energy consumption in fracture and damage of rock induced by impact loadings. Chinese Journal of Rock Mechanics and Engineering, 21(12): 2304-2308. Paris H, Tichkiewitch S, Peigné G., 2005. Modelling the vibratory drilling process to foresee cutting parameters. CIRP Annals - Manufacturing Technology. 54(1): 367-370. Paris H., 2018. Self-vibratory drilling. The International Academy for Production Engineering et al. (eds.), CIRP Encyclopedia of Production. 1-7. Sorenson A C., 2000. Asteroids: more than just chunks of rock. The Seventh International Conference & Exposition of Engineering, Space 2000, 1007-1010. Stanley S, Dougherty S, Laramee J., 2007. The low-force sample acquisition system. 2007 NASA Science and Technology Conference Proceedings. 1-5. Tichkiewitch S, Moraru G, Brun-Picard D, et al., 2002. Self-excited vibration drilling models and experiments. CIRP Annals - Manufacturing Technology. 51(1): 311-314. Xie Heping, Chen Zhonghui., 2004. Rock Mechanics. Science Press. 45-63. Zacny K, Bar-cohen Y., 2009. Drilling in extreme environments: penetration and sampling on Earth and other planets. Wiley-VCH. (Chaps. 6, 10) Zacny K, Paulsen G, Mckay C P, et al., 2013. Reaching 1m deep on Mars: the icebreaker drill. Astrobiology, 13(12):1166-1198. Zacny K, Wilson J, Chu P, et al., 2011. Prototype rotary percussive drill for the Mars sample returned mission. 2011 Aerospace Conference. IEEE: 1-8.
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S0273-1177(19)30852-X https://doi.org/10.1016/j.asr.2019.12.002 JASR 14568
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
17 June 2019 6 October 2019 2 December 2019
Please cite this article as: Peng, X., Li, L., Chen, B., Yin, S., Yin, Z., Yang, Y., Experimental study on drilling basalt with self-vibratory drilling head, Advances in Space Research (2019), doi: https://doi.org/10.1016/j.asr. 2019.12.002
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier Ltd on behalf of COSPAR.
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Experimental study on drilling basalt with self-vibratory drilling head o
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Xiaogan Penga, Liang Lia, Bo Chenb, Shen Yinc, Zhongwang Yinc, Yinfei Yanga
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
a
Xi'an Aircraft Industry (Group) Co., Ltd. Xi'an 710089, China
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Beijing Spacecrafts. Beijing 100094, China
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Abstract Based on the goal of improving the rock breaking ability when drilling asteroid rock samples under limited energy conditions, this paper proposes a method of drilling rock using self-vibratory drilling head and develops a small self-vibratory drilling head for drilling rock. In order to analyze the dynamic characteristics of drilling rock with self-vibratory drilling head, a rock model hypothesis that the rock consists of a series of micro-segment uniform continuous media is put forward. Base on the hypothesis, the model of drilling rock is constructed, the stability lobes diagram of self-vibratory drilling head drilling basalt is plotted, and the energy mechanism of drilling rock system with self-vibratory drilling head is discussed. The comparison tests of drilling basalt by three kinds of self-vibratory drilling head with different spring stiffness and the conventional method are carried out. The rotational speed is a variable in the comparative tests. The test results show that under the specific rotational speed and spring stiffness, self-excited vibration is produced in self-vibratory drilling head drilling basalt. When self-excited vibration drilling is conducted, although the amplitude fluctuation range of the drilling thrust force is wider than that of conventional drilling, the average drilling thrust force is smaller than the conventional drilling. The amplitude of drilling thrust force increases with an increase in spring stiffness. The method of drilling rock by self-vibratory drilling head is proved to be a potential method for viable drilling of asteroid rock samples. Keywords: Self-vibratory drilling head; Basalt; Self-excited vibration; Drilling thrust force
1. Introduction Asteroids are celestial bodies in the solar system that are similar to the planets moving around the sun, but much smaller in volume and mass. The asteroid is loosely organized, like a huge pile of gravel combined by gravity. Asteroids are rich in mineral resources and can provide a source of material for humans to move into space (Badescu 2013; Bonneville 2018). Therefore, asteroid attachment and sampling return detection are one of the main contents of deep space exploration. The energy of asteroid detectors is generally supplied by solar power systems. During the drilling of the asteroid rock sample, the power of the drilling mechanism of the asteroid detector is set within a specific range. Consequently, improving drilling capacity and rock breaking efficiency of the drilling mechanism under limited power has become a key technical problem and research hotspot (Sorenson 2000; Zacny and Bar-cohen 2009). From the perspective of the drilling process, the impact of the vibration drilling will cause the rock to produce micro-cracks and expand the micro-cracks, or activate and propagate the existing micro-cracks in the rock, thereby improving the rock breaking
Corresponding author. E-mail addresses: [email protected] (Liang Li), [email protected] (Xiaogan Peng), [email protected] (Bo Chen), [email protected] (Shen Yin), [email protected] (Zhongwang Yin), [email protected] (Yinfei Yang).
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spacesystems developed a low force sample acquisition system using the principle of rotary impact (Stanley et al., 2007). The Mars Sample Return core drill designed by Honeybee Robotics also uses a rotary impact drilling method (Zacny et al., 2011). The Luna-24 detector of the former Soviet Union also adopts the method of rotary impact drilling and uses threshold judgment to automatically control the opening and closing of the impact motor. According to the telemetry results, the impact motor is frequently opened during drilling. Twice it has happened that the drilling pressure was large enough to have triggered the alarm (Zacny and Bar-cohen 2009; Zacny et al., 2013). The rotary impact method is based on forced vibration, and its impact energy is generally a fixed value. However, due to the heterogeneity, discontinuity, and anisotropy of rocks, the physical-mechanical properties of rocks of the same composition are also quite different. The impact energy required for different mechanical properties of the rock is also different. Therefore, the self-vibratory drilling method is a potential method for vibration drilling of a rock. Self-vibratory drilling method has a series of research and application in the field of metal cutting. Brun-Picard et al. (1999) proposed a technique of self-excited vibration drilling in which a low energy flutter is excited at the specific process parameters by a low stiffness component (spring) mounted between the machine tool and the tool or workpiece. Tichkiewitch et al. (2002) proposed a nonlinear dynamic model of self-excited vibration drilling, and simulated and analyzed the phenomenon of "finite amplitude instability" in the time domain. Based on the principle of self-excited vibration drilling, Paris et al. (2005) designed a self-vibrating drilling head that can be conveniently used on ordinary CNC machine tools. The processing performance of the self-vibrating drilling head is proved by experimental research. Gouskov et al. (2005) proposed to replace nine physical quantities in self-excited vibration drilling with three dimensionless parameters, which can be used to select cutting conditions conveniently in the experiment. Guibert et al. (2008) constructed dynamic model of self-vibratory drilling head, cutting force and plowing force, and material removal based on the problem of chip breakage in deep drilling. The model is used to simulate the cutting conditions and then predict the vibration condition. Forestier et al. (2012) associated self-vibratory drilling head drilling with machine tool systems to construct the finite element model of the machining system based on machine tool spindle, self-vibratory drilling head and drill bit, which is used to evaluate the dynamic characteristics of the machining system. However, there are few public reports on self-vibratory drilling head drilling rock in the space. Although the amplitude of drilling thrust force fluctuates greatly during self-excited vibration drilling, the average drilling thrust force is much smaller than that of conventional drilling under the same drilling parameters (Paris et al., 2005; Paris 2018). The rock generates and expands the crack under the influence of vibration impact force, which is beneficial to improve the efficiency of drilling rock. Therefore, this paper proposes a method of drilling rock samples using self-vibratory drilling head (SVDH). This method uses SVDH to perform self-excited vibration drilling rock under particular cutting parameters. The vibration impact of the drilling tool on the rock can improve the rock breaking ability. In this paper, the SVDH for drilling rock is developed, and an experimental study of drilling basalt is carried out. The model of SVDH drilling rock is constructed in the second part, and the comparison experiment of drilling basalt with SVDH and conventional method is carried out in the third part. In the fourth part, the test results are analyzed and discussed. Finally, the conclusions are obtained. 2. Model of drilling rock system with self-vibratory drilling head The physicist A. A. Harkevich defines the self-vibration system as a closed-loop system consisting of the main vibration body, energy, controller and feedback unit. The self-excited vibration of the self-vibration system requires neither external force excitation nor external action to change the structural parameters of the system but relies on the interaction of various components within the system to maintain steady-state periodic motion (Ding 2009). According to the regenerative flutter theory, in the self-vibration system of SVDH drilling rock, the main vibration body is the arbor and the drilling tool, the energy is the drilling 2
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e r-s o ft w a r improve the drilling efficiency under limited power. Based on the NASA Mars instrument development project, Alliance
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ability of the drilling tool (Hu et al., 2002). The vibration effect is also beneficial to chip removal. The vibration drilling can
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thrust force, the controller is the drilling depth, and the feedback unit is the drilling machined surface generated in the previous
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2.1. Self-vibratory drilling head As shown in Fig. 1, a small SVDH for drilling rock is developed, which consists of a front drilling head body, an arbor, a spring, an adjusting screw, and a rear drilling head body. The maximum diameter of SVDH is Φ 30 mm, and the total length is 65mm (not including the cemented carbide triangular bit). The extended length of the cemented carbide triangular bit (CCTB) is 35mm. The total mass of SVDH is 212 g, and the main vibration body (arbor and CCTB) has a mass of 24g. The CCTB is mounted on the arbor, the arbor is splined with the front drilling head body, the spring is installed in the front drilling head body, and the adjusting screw is installed at the rear end of the front drilling head body. The spring is compressed by rotating the adjusting screw to maintain it in contact with the arbor. The vibration mode of the SVDH can be adjusted by replacing the internal spring. The output shaft on the rear drilling head body can be fixed with the tool holder.
Fig. 1 Self-vibratory drilling head
2.2. Dynamic model of drilling rock system with self-vibratory drilling head 2.2.1. Hypothesis of rock model In the elastoplastic model of rock, rock is regarded as a continuous medium. However, natural rock is an uneven, discontinuous medium with irregular cracks and pores inside. If the natural rock is divided into sufficiently thin micro-layers along the drilling direction, then the rock medium on each micro-layer should satisfy the basic hypothesis of the elastoplastic model of the rock (Xie and Chen 2004). Therefore, in this paper, based on the elastoplastic model of rock, a rock model hypothesis is proposed, that is, the rock is a combination of a series of micro-segment uniform continuous medium. The rock hypothesis model can be described as follows: Let the thickness of the rock is hr and the threshold of
mechanical properties is [MRmin, MRmax]. Then, the rock can be considered as a combination of a series of continuous uniform micro-segment rock of thickness hri (i = 1, 2, ...), hri is a random value less than hr, MRi is the mechanical property of the hri micro-segment rock, and MRmin≤MRi ≤MRmax. 2.2.2. Dynamic model of drilling rock system with self-vibratory drilling head The SVDH drilling rock system needs to have the following two points to generate self-excited vibration. One is that the SVDH drilling system is unstable near the equilibrium point. The other is the presence of a disturbance that forces the working point of the SVDH drilling rock system to deviate from the equilibrium point. Thus, when the SVDH is used for drilling on each micro-segment uniform continuous rock medium, the condition for generating self-excited vibration will be satisfied. Therefore, the self-excited vibration characteristics of the SVDH drilling rock system can still be studied by the regenerative flutter method, but the form of self-excited vibration is more complicated. 3
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The model of the SVDH drilling rock system is shown in Fig. 2, and the general equation of the machining system can be
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(1)
Where m is the mass of the vibrating part, which is the sum of m1 (arbor) and m2 (CCTB), c is the damping coefficient between the arbor and front drilling head body, k is spring stiffness, z(t) is the instantaneous axial position of the vibrating portion, and P is the drilling thrust force. The empirical formula for the drilling thrust force can be expressed as: P kc zc d h(t )
(2)
Where kc is the coefficient determined by the rock material and the drilling tool geometry parameters such as axial lip length (all),
blade thickness (bt) and apex angle (aa), zc is the number of drill lips on drilling tool, d is the diameter of the drilling tool, and h(t) is the instantaneous cutting thickness.
In each uniform continuous micro-segment of rock, h(t) in Eq. (2) can be described as: h (t ) h0 z (t ) z (t T )
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Where h0 is the theoretical cutting thickness, [z(t)-z(t-T)] is the dynamic cutting thickness produced by the two adjacent cutting vibrations. The period of the drill lip passes through a specific point in the cutting layer:
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Where n is the rotational speed of the SVDH. Substituting Eq. (2) and Eq. (3) into Eq. (1), the motion equation of self-excited vibration drilling rock system on each uniform continuous micro-segment rock can be obtained: m z (t ) c z (t ) k z (t ) k c z c d h0 z (t ) z (t T )
(5)
Fig. 2 Model of drilling rock with self-vibratory drilling head
2.2.3. Block diagram of drilling rock system with self-vibratory drilling head According to the regenerative flutter theory, the Laplace transformation of Eq. (5) is carried out, and then the block diagram 4
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In the block diagram, the transfer function of the SVDH is:
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Where, the natural frequency is n
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(6) k m , the damping ratio is c 2 k m .
The transfer function between the instantaneous cutting thickness and the theoretical cutting thickness is:
H (s) 1 sT H 0 ( s ) 1 (1 e )kc zc d ( s )
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According to the rock model hypothesis that the rock is a combination of a series of micro-segment uniform continuous medium, it can be inferred that when the SVDH drills the rock at a specific feed rate, the stable self-excited vibration may occur on the micro-segment uniform continuous medium under a specific rotational speed and spring stiffness.
Fig. 3 Block diagram of drilling rock with self-vibratory drilling head
2.3. Energy mechanism of drilling rock system with self-vibratory drilling head The self-excited vibration of the SVDH drilling rock system is not “self-sufficient vibration”, and it cannot be “autarky” in energy, but needs to rely on the external energy supply to supplement the energy dissipation caused by a system damping. In the self-excited vibration of the SVDH drilling rock system, the magnitude of the drilling thrust force is periodically changed. when the drilling thrust force is in the decreasing stage, the drilling tool and the arbor compression spring are acting in the axial direction, and the drilling thrust force does the positive work to the system, and the input energy to the system; When the drilling thrust force is in the increasing stage, the arbor relax the spring in the axial direction. In this stage, the energy of the vibration system is divided into three parts dissipation. The first part is transmitted into the rock inside through the impact work, the second part is dissipated by drilling the rock in the form of net negative work, and the remaining part is dissipated by the system damping. Thus, the following equation can be obtained. WP Wdi Wc Wim Wdo
(8)
Where WP is the input energy of the drilling process, Wdi is the damping loss energy when inputting energy, Wc is energy dissipated by the cutting work, Wim is the impact energy consumed during drilling, and Wdo is the damping loss energy when drilling. According to the rock model hypothesis, if the mechanical properties of each micro-segment are uniform, then the amplitude of self-excited vibration generated by the SVDH drilling rock system is stable when equation (8) is tenable. If the mechanical properties of the micro-segments are inconsistent from one micro-segment to the adjacent micro-segment, then two situations may occur for Eq. (8): WP Wdi Wc Wim Wdo
(9)
WP Wdi Wc Wim Wdo
(10)
For Eq. (9), the amplitude of self-excited vibration is incremented until the amplitude is increased to a specific value. A new 5
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generated, and Eq. (8) is tenable, producing self-excited vibration with new amplitude. If a new energy balance cannot be generated, the system tends to be stable and does not generate self-excited vibration. 3. Experiment on drilling basalt with self-vibratory drilling head 3.1. Experimental setup The test device is composed of vertical machining center, tool holder, SVDH, CCTB, fixture and force measuring system, as shown in Fig. 4. The SVDH is mounted on the tool holder, the tool holder is fixed on the spindle of machining center, and the three-direction piezoelectric dynamometer is mounted on the machining center table. The fixture is fixed on the upper plane of the dynamometer. The vertical machining center (Model: XK2174, SHENJI ZHONGJIE CNC Machine Tool Co., Ltd.) has a spindle power of 4 KW, a maximum spindle speed of 8000 r/min, and a feed rate range of 1-4000 mm/min. The Φ4mm commercial CCTB is selected as the drilling tool with an axial lip length of 7 mm, a blade thickness of 1 mm and the apex angle of 31.9°. The force measuring system is composed of Kistler 9265B three-direction piezoelectric dynamometer, Kistler 5019A charge amplifier and corresponding data acquisition and processing system. Basalt is selected as the test material, its drillability classification grade is 8, and the compressive strength and tensile strength is 205±45 MPa and 5.8±1.3 MPa, respectively.
Fig.4 Test device, (a) The actual image, (b) The schematic diagram
3.2. Experimental procedure The spring stiffness in SVDH is an important parameter that directly determines the vibration characteristics of the SVDH. In this experiment, three springs of different stiffness values are selected, and the SVDH with different spring is used to carry out the single factor test of drilling basalt with rotational speed as a variable. For comparison purpose, a single factor test of drilling basalt with the same parameters is carried out using a conventional drilling method (without SVDH). The experiment in this paper consists of four group tests. The Experimental parameters are shown in table 1. The drilling depth for all the four group tests is 15mm. The drilling thrust force is taken as the test result. The drilling thrust force data are collected by the force measurement system, which consists of Kistler 9265B three-way piezoelectric dynamometer and Kistler 5019A charge amplifier. The drilling thrust force data are processed using MATLAB and Origin. Table 1 Experimental parameters Number
Feed rate (mm/min)
Spring Stiffness (N/mm)
Rotational speed (r/min)
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energy balance is generated, and Eq. (8) is tenable, producing self-excited vibration with new amplitude. In the case of Eq. (10),
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3.3. Stability lobes diagram of drilling rock system with self-vibratory drilling head The vibration when drilling rock with SVDH is regenerative flutter. Linear stability theory is an important method to explain and analyze the stability of flutter (Altintas 2000). Therefore, the linear stability theory is used to analyze the stability of self-excited vibration drilling rock systems. The characteristic equation of Eq. (7) can be expressed as
D( s ) 1 (1 e sT )kc zc d ( s ) 0
(11)
Let the characteristic root of Eq. (11) be s=+jω. When > 0, the system is unstable; when <0, the system is stable; when
= 0, the system is in a critical stable state. In order to analyze the system state with the critical stability boundary line, let the characteristic root of Eq. (11) is s= jωc. Then Eq. (11) can be rewritten as: D ( j c ) 1 k c z c d (1 e jc T ) ( j c ) 0
(12)
The transfer function Φ (jωc) can be expressed as the sum of the real part G (ωc) and the imaginary part H (ωc), as follows: ( jc ) G (c ) jH (c )
(13)
Then equation (12) can be rewritten as follows:
D( jc ) 1 kc zc d 1 cos(cT ) j sin(cT ) G (c ) jH (c ) 0
(14)
When equation (14) is tenable, its real and imaginary parts are equal to zero, as follows
Re D( jc ) 0 Im D( jc ) 0
(15)
According to the rock model hypothesis, although the mechanical properties of each micro-segment uniform continuous medium along the drilling direction cannot be accurately predicted, there is a particular understanding of the threshold range of the macroscopic mechanical properties of the rock. Therefore, based on the principle of extreme value, the mechanical properties of the micro-segment uniform continuous medium can be replaced by the macroscopic mechanical properties of the rock. The minimum macroscopic mechanical properties of the rock are used to set the parameter kc in the Eq. (2). And then the stability lobes diagram of SVDH drilling basalt is drawn, as shown in Fig. 5. The area below the critical stability curve of the stability lobes diagram is not a completely stable drilling area, but the area above the curve must be an absolutely unstable drilling area. It can be seen from Fig. 5 that when the compliance is greater than 1.09X10-5 m/N, that is, the spring stiffness is less than 91.74 N/mm. The SVDH drilling basalt system may be in an unstable drilling area.
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Fig. 5 Stability lobes diagram of self-vibratory drilling head drilling basalt (kc=4.8X103 N/m, d=4X10-3 m, m=0.024Kg, ζ=0.05, zc=2, h0 = 3.5X10-5 m, all=7mm, bt=1mm, aa=31.9°)
4. Results and discussion Drilling thrust force is an important indicator of drilling rock samples on asteroids. According to the rock model hypothesis presented above, the drilling thrust force at one or several time points cannot fully characterize the characteristics of SVDH drilling rock, and only the average drilling thrust force within a sufficiently long period of time can be characterized. Therefore, when discussing the test results, the average drilling thrust force during the CCTB full-edge drilling basalt is taken as the test result. 4.1. Effect of rotational speed on drilling thrust force The drilling thrust force data of the CCTB full-edge drilling basalt are selected in each test, and the average value is calculated separately. And then the histogram of the average drilling thrust force with the rotational speed is constructed, as shown in Fig. 6. In order to compare the time-domain diagram of the drilling thrust force under different drilling conditions, four typical drilling states (a) - (d) are selected from the histogram, and four sub-graphs of drilling thrust force varying with time are drawn, as shown in Fig. 6 (a) - (d). It can be seen from Fig. 6 that the average drilling thrust force of the four groups of tests does not have a uniform law as the rotational speed increases. With the increase of the rotational speed, the fluctuation range of the average drilling thrust force of the four group tests can be arranged in the following sequence: Group3> Group2> Group1> Group4. For three groups of SVDH drilling basalt tests, the average drilling thrust force at 800 r / min is the minimum for each group of the tests. The average drilling thrust force of SVDH drilling is lower than that of conventional drilling under some drilling conditions, such as condition (b). It can be seen from Figure 6 (b) that the self-excited vibration is produced under the drilling conditions (b). Therefore, it is proved that self-excited vibration drilling has the characteristics of smaller average drilling thrust force. It can be seen from Fig. 6 (a) - (d) that the amplitude fluctuation range of the drilling thrust force when drilling with SVDH is significantly larger than that during conventional drilling. According to Eq. (2), for conventional drilling, when the feed rate is fixed, the instantaneous cutting thickness h(t) is constant. On the other hand, the coefficient kc is a random value within a specific 8
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instantaneous cutting thickness h(t) is not constant. At the appropriate rotational speed and spring stiffness, the self-excited vibration is produced when drilling basalt. According to the Eq. (8) of the energy mechanism of SVDH drilling rock system, the damping loss energy always exists in the self-excited vibration drilling. Therefore, the amplitude of the drilling thrust force of the self-excited vibration cannot be increased indefinitely, and it experiences random fluctuations within a specific range.
Fig. 6 Average drilling thrust force histogram and drilling thrust force domain diagram
4.2. Effect of spring stiffness on drilling thrust force The drilling thrust force data collected from the three group tests of SVDH drilling basalt are pre-processed, and the time domain diagram of drilling thrust force is constructed. It is found that the drilling thrust force diagrams under the six test conditions are consistent with the characteristics of self-excited vibration drilling. The six test conditions are (7.32 N/mm, 600 r/min), (7.32 N/mm, 800 r/min), (11.46 N/mm, 500 r/min), (19.42 N/mm, 500 r/min), (19.42 N/mm, 600 r/min) and (19.42 N/mm, 800 r/min). The drilling thrust force data for the specified period are selected on the time domain diagrams of the above six test
conditions respectively, and the Fast Fourier transform is performed, as shown in Fig.7. It can be seen from Fig. 7 that the lower envelope of the drilling thrust force of all the time domain diagrams is almost straight and the value is small, which is the characteristic of self-excited vibration drilling. It can be seen from Fig.7 (a) and (b) that when the spring stiffness is 7.32 N/mm, the vibration frequency component is relatively cluttered and the vibration amplitude is small. As can be seen from Fig. 7(c), when the spring stiffness is 11.46 N/mm, although the vibration frequency component is concentrated, the amplitude is small. From Fig.7 (d), (e) and (f), it can be seen that when the spring stiffness is 19.42 N/mm, the vibration frequency component is more concentrated and has certain regularity, and the amplitude is also significantly increased. Comparing the amplitude fluctuation 9
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range. Therefore, the drilling thrust force P does not tend to be a specific value, but a random value within a specific range. For tra
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with the increase of spring stiffness. The wider the amplitude fluctuation range of the drilling thrust force, the greater the impact energy of drilling tool to basalt, which is beneficial to breaking rock and improving drilling efficiency. According to Fig. 5 Stability lobes diagram of self-vibratory drilling head drilling basalt, it can be inferred that when the rotational speed is constant, as the spring stiffness increases, the working state point of the system is closer to the critical stable curve, and the self-excited
vibration drilling is better.
Fig. 7 Drilling thrust force time-frequency domain diagram of SVDH drilling basalt
4.3. Effect of drilling method on drilling thrust force In this paper, two methods are used for basalt drilling, one is the method of SVDH drilling, and the other is the conventional drilling method. The average drilling thrust force of the two drilling methods is comparatively analyzed in Section 4.1. In this section, the drilling thrust force of the two drilling methods is discussed in detail. Two sets of drilling thrust force at 500 r/min and 600 r/min in the third group of SVDH drilling basalt test are selected for the discussion purpose. In both cases, self-excited vibration occurs in the drilling process. In addition, two sets of the drilling thrust force at 500 r / min and 600 r / min in the fourth 10
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range of the drilling thrust force under the six conditions, as shown in Fig. 7, it can be seen that the spring stiffness is related to the
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drilling thrust force is constructed, as shown in Figure 8. It can be seen from Fig. 8 (a) that the lower envelope of the drilling thrust force diagram is almost a straight line, and the upper envelope has obvious random fluctuation characteristics. From the four detailed sub-graphs of Fig. 8 (a), it can be seen that all the drilling thrust forces have obvious periodic vibrations, but their amplitudes and waveforms are different. A similar phenomenon can also be observed in Figure 8(b). It can be seen from Fig. 8(c) that the two envelopes of the drilling thrust force are approximately parallel curves with random fluctuations. It can be seen from the four detailed sub-graphs of Fig. 8 (c) that the drilling thrust force is in a disordered vibration state. The phenomenon similar to Fig. 8 (c) can also be observed in Fig. 8 (d). Compared with the detailed sub-graphs of Figures 8(a) and (b), it can be seen that the vibration amplitude in detailed sub-graphs of Fig. 8 (c) and (c) are significantly smaller. It can be seen from Fig. 8(a) and (b) that the self-excited vibration generated by the SVDH drilling basalt is not a stable self-excited vibration, but a dynamically changing self-excited vibration. In the system of SVDH drilling basalt, when the rotational speed and feed rate are fixed, the basalt material properties become the main factor affecting the self-excited vibration of the system. According to the rock model hypothesis proposed in this paper, self-excited vibrations with different amplitude are generated on different micro-segments in the drilling direction. When the micro-segment self-excited vibration transition to the adjacent micro-segment, the self-excited vibration either tends to be gentle or more intense. This explains the reason for the random fluctuation of the upper envelope of the drilling thrust force diagram, as shown in Fig. 8 (a) and (b).
Fig. 8 Comparison of drilling thrust forces between SVDH drilling and conventional drilling. (a)SVDH drilling (500 r/min, 19.42 N/mm),
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group of conventional drilling basalt tests are also selected. In the selected four sets of drilling thrust force data, four segments of
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5. Conclusions
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(b) SVDH drilling (600 r/min, 19.42 N/mm), (c) Conventional drilling (500 r/min), (d) Conventional drilling (600 r/min) tra
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In this paper, the method of drilling rock with self-vibratory drilling head is proposed. A small SVDH for drilling rock is developed. And a series of comparison test of drilling basalt with SVDH and conventional method is carried out. The following conclusions are drawn: 1) The rock model hypothesis, which states that rock is composed of a series of micro-segment uniform continuous medium, is proposed. The thickness of the micro-segment is a random value, and the mechanical properties are a specific value within the threshold range of the macro-mechanical performance of the rock. 2) Under the specific rotational speed and spring stiffness, self-excited vibration is produced in SVDH drilling basalt. In self-excited vibration drilling, although the amplitude fluctuation range of the drilling thrust force is wider than that of the conventional drilling, the average drilling thrust force is smaller than that of the conventional drilling. 3) When basalt is drilled under self-excited vibrations using SVDH, the amplitude of drilling thrust force increases with an increase in spring stiffness.
References Altintas Y. 2000. Manufacturing automation: Metal cutting mechanics, Machine tool vibrations, and CNC design. Cambridge University Press. (Chapter 3) Badescu V., 2013. Asteroids: prospective energy and material resources. Springer Berlin Heidelberg. (Chapter 4, 12) Bonneville R., 2018. A truly international lunar base as the next logical step for human spaceflight. Advances in Space Research, 61, 2983–2988. Brun-Picard D, Gouskov A, Lesage D, Vincenti J., 1999. Vibration drilling By use of self-vibrating drilling head, PPF Workshop, ENSAM, Aix-en-Provence, France. 11-22. Deng Yong, Chen Mian, Jin Yan, et al., 2016. Prediction model and numerical simulation for rock fissure length under impact load. Petroleum Drilling Techniques. 44(4), 41-46. Ding Wenjing., 2009. Self-excited vibration. Tsinghua University Press. 245-280. Forestier F, Gagnol V, Ray P, et al., 2012. Model-based cutting prediction for a self-vibratory drilling head - spindle system. International Journal of Machine Tools & Manufacture. 52:59–68. Gouskov A, Peigné G, Kamnev E, et al., 2005. Self-excited vibratory drilling: a dimensionless parameter approach for guiding experiments. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture. 219(219):73-84. Guibert N, Paris H, Rech J., 2008. A numerical simulator to predict the dynamical behavior of the self-vibratory drilling headed. International Journal of Machine Tools & Manufacture. 48(6):644-655. Hu Liuqing, Li Xibing, Zhao Fujun. 2002. Study on energy consumption in fracture and damage of rock induced by impact loadings. Chinese Journal of Rock Mechanics and Engineering, 21(12): 2304-2308. Paris H, Tichkiewitch S, Peigné G., 2005. Modelling the vibratory drilling process to foresee cutting parameters. CIRP Annals - Manufacturing Technology. 54(1): 367-370. Paris H., 2018. Self-vibratory drilling. The International Academy for Production Engineering et al. (eds.), CIRP Encyclopedia of Production. 1-7. Sorenson A C., 2000. Asteroids: more than just chunks of rock. The Seventh International Conference & Exposition of Engineering, Space 2000, 1007-1010. Stanley S, Dougherty S, Laramee J., 2007. The low-force sample acquisition system. 2007 NASA Science and Technology Conference Proceedings. 1-5. Tichkiewitch S, Moraru G, Brun-Picard D, et al., 2002. Self-excited vibration drilling models and experiments. CIRP Annals - Manufacturing Technology. 51(1): 311-314. Xie Heping, Chen Zhonghui., 2004. Rock Mechanics. Science Press. 45-63. Zacny K, Bar-cohen Y., 2009. Drilling in extreme environments: penetration and sampling on Earth and other planets. Wiley-VCH. (Chaps. 6, 10) Zacny K, Paulsen G, Mckay C P, et al., 2013. Reaching 1m deep on Mars: the icebreaker drill. Astrobiology, 13(12):1166-1198. Zacny K, Wilson J, Chu P, et al., 2011. Prototype rotary percussive drill for the Mars sample returned mission. 2011 Aerospace Conference. IEEE: 1-8.
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