# Research on Impact Stress Transfer Characteristics of Lunar Rock Coring Drill

Authors: Peng Li; Yizhuo Wang; Bo Xu; Junwei Liu; Weiwei Zhang
Journal: Shock and Vibration
 (2021)

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## Abstract

In the whole lunar surface drilling and sampling task, it is critical to make the operation of the drilling and sampling impact system efficient and reliable. This paper focuses on how to improve the impact stress obtained at the cutting edge of the drill bit. Firstly, with the objective of maximizing the output impact energy, the design parameters of the percussive mechanism are optimally selected; based on the one-dimensional stress wave transfer theory, the collision input model and transfer models of impact stress in the drilling tool are established. Secondly, in order to verify the above design parameters and theoretical models, the percussive drive characteristics’ test and the transfer characteristics’ tests of impact stress in the drill stem and drilling tool joints are carried out in turn. The experimental results are consistent with the theoretical analysis, which clarifies the transfer characteristics of the impact stress at the various stages of generation, incidence, and transfer to the cutting edge. It was finally found that increasing the percussive frequency and impact energy of the percussive mechanism as well as the contact stiffness of the collision surface can increase the incident impact stress of the drilling tool, while reducing the length of the screw connection between the drill bit and the drill stem can reduce the impact stress loss. This provides a theoretical reference for the design of the percussive mechanism and drilling tools in lunar surface drilling and sampling tasks.


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## Body

## 1. Introduction

Sampling of lunar regolith samples for return is an important part of lunar exploration missions [1], among which drilling sampling is widely adopted by various countries because of many advantages such as high efficiency, stability, and effective retention of rational information of the lunar regolith layer [2, 3]. Compared with geological drilling, lunar surface drilling and sampling faces the interference of low gravity, high vacuum, and unknown mechanical properties of the lunar regolith, and its drilling efficiency is significantly reduced [4, 5]. In order to improve the drilling crushing efficiency of lunar rock simulants, a certain impact force can be applied during rotary drilling to make it assist in crushing lunar rocks [6, 7]. However, due to the long length of the lunar rock coring auger, there is a large amount of energy loss in the transfer of impact force from the top of the auger to the drill bit, making it difficult to form a visible impact crushing pit on the lunar rock surface. In addition, the drilling tool system can only provide a limited amount of power due to the limitations of rocket carrying capacity and other factors [8, 9]. Therefore, in order to obtain greater energy at the drill bit, it is necessary to study the impact action of coring drilling tools and their transmission characteristics.At present, the mechanical response characteristics in drilling tools can be explained by the theory of impact stress waves. Among them, Li tested the stress wave curves of impact pistons with different lengths based on the stress wave testing technique and calculated the impact performance to obtain the relationship between impact force and collision coefficient of restitution [10]; Hustrulid and Mate et al. studied the energy transfer efficiency from the perspective of the shape size of the drill stem and drill bit and the contact conditions between the bit and the rock, respectively [11, 12]; Wang et al. introduced an elastic model of the drilling tool joint and carried out an experimental study [13]; Li and Ma developed a linear contact nonlinear spring-damped contact force model describing rigid body acceleration and stress wave acceleration based on the one-dimensional stress wave transfer theory [14]; Yang et al. conducted a computational analysis of the energy transfer efficiency of four stress waveforms in the drilling tool [15]; Yuan et al. studied the influence law of axial static load on the stress amplitude of the variable cross section [16]. In this paper, we focus on how to improve the impact stress obtained at the cutting edge of the drill bit and carry out experimental research from two perspectives of increasing the stress input and reducing the loss in the transmission process, respectively. Firstly, the design parameters of the percussive mechanism are optimally selected with the objective of maximizing the output impact energy; secondly, the impact stress collision input model and stress transfer model in the drilling tool are established according to the stress wave transfer theory; finally, the above design parameters and the theoretical model are verified experimentally.


## 2. Stress Transfer Model in the Coring Drilling Tool under Impact Action

The transmission path of impact stress in the drilling tool during the lunar rock drilling and sampling is shown in Figure1, in which the percussive drive mechanism in the drilling mechanism provides kinetic energy to the percussive hammer and generates a single impact energy; the impact force is generated by the percussive hammer after collision with the anvil and is sequentially transferred to the lunar rock through the anvil, drill stem, drill bit, and finally by the cutting edge. Table 1 shows the relevant parameters in the impact stress transfer process.Figure 1
The transmission diagram of impact stress in the lunar rock drilling process.Table 1
Constant parameters used in the transmission analysis of impact stress on drill.
ParametersSymbolsNumerical valueUnitInput impact energyWP0.8∼4JPercussive frequencyfP0∼20HzAnvil lengthLD230mmDrill stem lengthLA2600mmLength of the drill bitLB46mmOutside diameter of the drill stemDAo31mmDrill stem inner diameterDAi25.5mmCross-sectional area of the drill stemAD189mm2MaterialsSteel grade 45Elastic modulusE210 × 109N·m−1Densityρ7850kg·m−3


### 2.1. Parameter Optimization of the Percussive Mechanism

The percussive drive mechanism is loaded by intermittent cams to drive the spring mass block to achieve reciprocating motion. Therefore, with certain drive power consumption, the output impact energy can be increased by a reasonable design of the percussive mechanism [17, 18].Figure2 shows the three-dimensional model of the percussive mechanism and the force analysis diagram; then, the percussive mechanism power consumption PC, cam rotation speed nC, and cam torque TC are(1)PC=2π⋅nC⋅TC60,nC=60⋅fPnCb,TC=mP⋅g+kP⋅sC+Fp0+mp⋅sC1−tanαC+Eδ/1−Eδ⋅tanαC⋅μC⋅tanαC+Eδ1−Eδ⋅tanαC⋅RC,where fP is the percussive frequency; nCb is the number of convex contour line bumps; SC is the percussive hammer displacement; FP0 is the percussive spring preload; Eδ is the percussive hammer roller equivalent rolling friction coefficient; αC is the pressure angle; μC is the sliding friction coefficient; RC is the cylindrical cam base circle radius; kP is the percussive spring stiffness coefficient; and mP is the percussive hammer mass. The percussive spring stiffness coefficient in equation (1) can be obtained by inversely calculating the required impact energy, i.e.,(2)kP=2WPhp0+hC2−hp02,where hp0 is the percussive spring preload displacement and hC is the maximum action displacement of the percussive hammer. Among the above parameters, the percussive frequency and single impact energy are the initial optimization indexes of the system, the roller radius and rolling friction coefficient depend mainly on the material of the cam and roller and the contact stiffness, while the percussive spring stiffness and spring preload are related to its initial installation position. Therefore, the variable parameters can be summarized as follows:(3)XP=kp,hC,hP0,mp,nCb,βC1,RCT,where βC1 is the cylindrical cam thrust motion angle and needs to meet(4)2hCRC⋅tanαC≤βC1≤2πnCb⋅1−fP⋅mPkp⋅acoshP0hC+hP0.Figure 2
(a) 3D configuration of the percussive mechanism. (b) Force analysis model.
(a)(b)The remaining parameters of the design variables need to satisfy the constraints of the structural dimensions of the percussive mechanism in addition to the two constraints mentioned above. Therefore, the constraint parameters of the percussive mechanism can be discretized in Table2, and the parameters can be optimized by the enumeration method.Table 2
The constraint parameters of the percussive mechanism.
Parameter nameSymbolsValue intervalOptimum resultSpring stiffness coefficientkP＜2000013500 N/mHammer amplitudehC5, 6, …, 208 mmSpring preload displacementhP05, 6, …, 2020 mmHammer massmP180, 280, …, 580180 gNumber of convex contour line bumpsnCb2, 3, 42Cam thrust motion angleβC110, 55, …, 180155°Cam base circle radiusRC25, 26, …, 3533 mmOptimum indexes: percussive frequencyfP = 20 Hz; single impact energy WP = 2.6 J. Constraint parameters: cam speed nC < 3000; roller equivalent rolling friction coefficient RCf = 0.0039; sliding friction coefficient μC = 0.5; permissible pressure angle (αC) < 20.After arranging and combining the above design parameters, 49104 groups of parameters can be obtained. Then, the minimum power consumption of the percussive mechanism is found, and its corresponding design parameter group is the results of optimal selection, as shown in Table2.


### 2.2. Model of Impact Stress Collision Input Drilling Tools

It can be seen from Figure2 that the impact force is formed on the contact surface between the percussive hammer and the anvil. The collision model can be regarded as a spring damping model, and the equivalent model is shown in Figure 3 [19, 20].Figure 3
The mechanics simplified model of the hammer impact drill process.According to the characteristic equation of one-dimensional stress wave transfer, it can be deduced that the impact force generated by the collision of the mass block and the elastic rod should satisfy the following equation:(5)mPx¨P=−ksxP−xD−csx˙P−x˙D,csx˙P+ksxP=cs+EADCx˙D+ksxD.From the state of the mass block and elastic rod at the moment before contact (t = 0), the initial boundary conditions of the model are determined as follows:(6)xP=0,x˙P0=v0,xD=0,where v0 is the impact velocity; ks is the contact stiffness of the percussive hammer-drilling tool collision; cs is the equivalent damping coefficient of the percussive hammer-drilling tool collision; xP is the percussive hammer displacement; xD is the displacement of the mass point on the contact surface; AD is the contact area of the percussive hammer-drilling tool collision; E is the elastic modulus of the drill stem; and C is the stress wave propagation velocity. The Laplace transform of equation (5) is(7)s2+2ξs+ω02xP∗−2ξs+ω02xD∗=v0,2ξs+ω02xP∗−2ξ+ηs+ω02xD∗=0,where xP∗s is the Laplace transform of xPt and xD∗s is that of xDt. ζ, η, and ω0 are as follows:(8)ξ=cs2mP,η=EAD2CmP,ω02=kSmP.Then, the inverse Laplace transform of equation (7) can be obtained as follows:(9)xPt=v02η1−e−αtcosωt+β1e−αtsinωt,xDt=v02η1−e−αtcosωt−β1e−αtsinωt,where(10)α=ω02+4ξη4ξ+η,β1=8η2−ω02+4ξη4ξ+ηω,β=ω02−4ξη4ξ+ηω,ω2=16η2w02−ω02−4ξη216ξ+η2,φ=arcsinα−ωβ1+β2α2+ω2.Combining the above equation, the incident impact stress obtained by the drilling tool is(11)σit=mPv01+β2α2+ω2AD⋅e−αtsinωt+φ.The above equation is the attenuation equation of the impact stress at the position coordinate of 0. From equation (11), it can be seen that the impact stress obtained by the drilling tool is a sinusoidal function of time, and its amplitude decay trend is exponential. In addition, by substituting each parameter of Table 2 into the above equation, the trend of impact stress with initial velocity v0 and contact stiffness ks can be obtained as shown in Figure 4.Figure 4
The waveform diagram of incident impact stress. (a) Curves of impact stress vs. impact velocity. (b) Curves of impact stress vs. hammer contact stiffness.
(a)(b)As can be seen from Figure4, the incident impact stress obtained by the drilling tool increases with the speed of the percussive hammer, and it basically follows a linear trend of increase. In addition, the stress amplitude increases gradually with the increase of contact stiffness of the collision surface, and the time taken to reach the peak becomes smaller.


### 2.3. Transfer Model of Impact Stress in Drilling Tools

#### 2.3.1. Transfer Model in the Drill Stem

In order to analyze the attenuation characteristics of impact stress along the axial direction of the drilling tool, the following assumptions are made: (I) since the length of the anvil and bit is much smaller than that of the drill stem (the length of the drill stem is 2510 mm, while the length of the drill bit and the anvil is 50 mm and 150 mm, respectively), the stress attenuation in the above two components can be disregarded, and only the attenuation of impact stress in the drill stem is considered; (II) the drill stem is treated as a thin-walled smooth rod, i.e., the cross-sectional area of each section is the same size; (III) the drill stem material is treated as uniform, i.e., the value of impact stress attenuation rate is constant.An infinitesimal in the drill stem is taken for analysis (as shown in Figure5), and it can be obtained:(12)σησdx=σ−σ+dσ.Figure 5
The drilling tool impact stress transmission diagram.The impact stress at the position coordinatex = 0 of the drilling stem is set to σ0. The attenuation equation of the impact stress with displacement is obtained by integrating equation (12) as(13)σ=σ0e−ησx,where ησ is the impact stress attenuation coefficient in m−1.


#### 2.3.2. Transfer Model at the Drilling Tool Joints

The drilling tool joints mainly include the flange connection interface between the anvil and the drill stem and the screw connection interface between the drill stem and the drill bit. Based on the presence or absence of axial relative motion during the impact process, the stress transfer models at the connection interface are equated to the rigid body mass model and mass damping model, respectively. The equivalent models are shown in Figure6.Figure 6
Stress transfer analysis of the flange/screw interface. (a) The rigid body mass model (flange interface). (b) The mass damping model (screw interface).
(a)(b)According to the equivalent model, the incident and transmitted stresses at the flange interface and the incident and transmitted stresses at the screw interface can be derived to satisfy the following differential equations, respectively:(14)MF2Zdσtdt+σt=σi,(15)MT2Zdσtdt+1+cT2Zσt=σi,where MF is the equivalent rigid body mass of the flange interface; Z is the drilling tool wave resistance coefficient; σi is the incident stress of the interface; σt is the transmitted stress of the interface; MT is the equivalent mass of the screw interface; and cT is the equivalent damping of the screw interface.When solving the transfer efficiency, in order to simplify the calculation model, incident impact stress equation (11) obtained above is simplified to the exponential form shown in the following equation:(16)σi=σ0e−Z/mpt.Then, substituting equation (16) into equations (14) and (15), respectively, the impact stress transfer efficiency at the flange interface and screw interface can be obtained as ηF and ηT, respectively.(17)ηF=EtEi=AFc/E∫0∞σt2dtAFc/E∫0∞σi2dt=22+KFmr,(18)ηT=EtEi=ATc/E∫0∞σt2dtATc/E∫0∞σi2dt=4+4KTmr/2+KTczr−16KTmr/KTmr+KTczr+2KTczr−KFmr+22,where Ei is the energy of the incident stress wave; Et is the energy of the transmitted stress wave; KFmr = MF/mP; KTmr = MT/mP; and KTczr = cT/Z.Figure7(a) shows the curve of stress transfer efficiency ηF versus KFmr, and Figure 7(b) shows the trend of stress transfer efficiency ηT with KTmr when changing KTczr.Figure 7
The drill flange/screw interface impact stress transmission efficiency. (a) Transmission efficiency of the flange interface. (b) Transmission efficiency of the screw interface.
(a)(b)


## 2.1. Parameter Optimization of the Percussive Mechanism

The percussive drive mechanism is loaded by intermittent cams to drive the spring mass block to achieve reciprocating motion. Therefore, with certain drive power consumption, the output impact energy can be increased by a reasonable design of the percussive mechanism [17, 18].Figure2 shows the three-dimensional model of the percussive mechanism and the force analysis diagram; then, the percussive mechanism power consumption PC, cam rotation speed nC, and cam torque TC are(1)PC=2π⋅nC⋅TC60,nC=60⋅fPnCb,TC=mP⋅g+kP⋅sC+Fp0+mp⋅sC1−tanαC+Eδ/1−Eδ⋅tanαC⋅μC⋅tanαC+Eδ1−Eδ⋅tanαC⋅RC,where fP is the percussive frequency; nCb is the number of convex contour line bumps; SC is the percussive hammer displacement; FP0 is the percussive spring preload; Eδ is the percussive hammer roller equivalent rolling friction coefficient; αC is the pressure angle; μC is the sliding friction coefficient; RC is the cylindrical cam base circle radius; kP is the percussive spring stiffness coefficient; and mP is the percussive hammer mass. The percussive spring stiffness coefficient in equation (1) can be obtained by inversely calculating the required impact energy, i.e.,(2)kP=2WPhp0+hC2−hp02,where hp0 is the percussive spring preload displacement and hC is the maximum action displacement of the percussive hammer. Among the above parameters, the percussive frequency and single impact energy are the initial optimization indexes of the system, the roller radius and rolling friction coefficient depend mainly on the material of the cam and roller and the contact stiffness, while the percussive spring stiffness and spring preload are related to its initial installation position. Therefore, the variable parameters can be summarized as follows:(3)XP=kp,hC,hP0,mp,nCb,βC1,RCT,where βC1 is the cylindrical cam thrust motion angle and needs to meet(4)2hCRC⋅tanαC≤βC1≤2πnCb⋅1−fP⋅mPkp⋅acoshP0hC+hP0.Figure 2
(a) 3D configuration of the percussive mechanism. (b) Force analysis model.
(a)(b)The remaining parameters of the design variables need to satisfy the constraints of the structural dimensions of the percussive mechanism in addition to the two constraints mentioned above. Therefore, the constraint parameters of the percussive mechanism can be discretized in Table2, and the parameters can be optimized by the enumeration method.Table 2
The constraint parameters of the percussive mechanism.
Parameter nameSymbolsValue intervalOptimum resultSpring stiffness coefficientkP＜2000013500 N/mHammer amplitudehC5, 6, …, 208 mmSpring preload displacementhP05, 6, …, 2020 mmHammer massmP180, 280, …, 580180 gNumber of convex contour line bumpsnCb2, 3, 42Cam thrust motion angleβC110, 55, …, 180155°Cam base circle radiusRC25, 26, …, 3533 mmOptimum indexes: percussive frequencyfP = 20 Hz; single impact energy WP = 2.6 J. Constraint parameters: cam speed nC < 3000; roller equivalent rolling friction coefficient RCf = 0.0039; sliding friction coefficient μC = 0.5; permissible pressure angle (αC) < 20.After arranging and combining the above design parameters, 49104 groups of parameters can be obtained. Then, the minimum power consumption of the percussive mechanism is found, and its corresponding design parameter group is the results of optimal selection, as shown in Table2.


## 2.2. Model of Impact Stress Collision Input Drilling Tools

It can be seen from Figure2 that the impact force is formed on the contact surface between the percussive hammer and the anvil. The collision model can be regarded as a spring damping model, and the equivalent model is shown in Figure 3 [19, 20].Figure 3
The mechanics simplified model of the hammer impact drill process.According to the characteristic equation of one-dimensional stress wave transfer, it can be deduced that the impact force generated by the collision of the mass block and the elastic rod should satisfy the following equation:(5)mPx¨P=−ksxP−xD−csx˙P−x˙D,csx˙P+ksxP=cs+EADCx˙D+ksxD.From the state of the mass block and elastic rod at the moment before contact (t = 0), the initial boundary conditions of the model are determined as follows:(6)xP=0,x˙P0=v0,xD=0,where v0 is the impact velocity; ks is the contact stiffness of the percussive hammer-drilling tool collision; cs is the equivalent damping coefficient of the percussive hammer-drilling tool collision; xP is the percussive hammer displacement; xD is the displacement of the mass point on the contact surface; AD is the contact area of the percussive hammer-drilling tool collision; E is the elastic modulus of the drill stem; and C is the stress wave propagation velocity. The Laplace transform of equation (5) is(7)s2+2ξs+ω02xP∗−2ξs+ω02xD∗=v0,2ξs+ω02xP∗−2ξ+ηs+ω02xD∗=0,where xP∗s is the Laplace transform of xPt and xD∗s is that of xDt. ζ, η, and ω0 are as follows:(8)ξ=cs2mP,η=EAD2CmP,ω02=kSmP.Then, the inverse Laplace transform of equation (7) can be obtained as follows:(9)xPt=v02η1−e−αtcosωt+β1e−αtsinωt,xDt=v02η1−e−αtcosωt−β1e−αtsinωt,where(10)α=ω02+4ξη4ξ+η,β1=8η2−ω02+4ξη4ξ+ηω,β=ω02−4ξη4ξ+ηω,ω2=16η2w02−ω02−4ξη216ξ+η2,φ=arcsinα−ωβ1+β2α2+ω2.Combining the above equation, the incident impact stress obtained by the drilling tool is(11)σit=mPv01+β2α2+ω2AD⋅e−αtsinωt+φ.The above equation is the attenuation equation of the impact stress at the position coordinate of 0. From equation (11), it can be seen that the impact stress obtained by the drilling tool is a sinusoidal function of time, and its amplitude decay trend is exponential. In addition, by substituting each parameter of Table 2 into the above equation, the trend of impact stress with initial velocity v0 and contact stiffness ks can be obtained as shown in Figure 4.Figure 4
The waveform diagram of incident impact stress. (a) Curves of impact stress vs. impact velocity. (b) Curves of impact stress vs. hammer contact stiffness.
(a)(b)As can be seen from Figure4, the incident impact stress obtained by the drilling tool increases with the speed of the percussive hammer, and it basically follows a linear trend of increase. In addition, the stress amplitude increases gradually with the increase of contact stiffness of the collision surface, and the time taken to reach the peak becomes smaller.


## 2.3. Transfer Model of Impact Stress in Drilling Tools

### 2.3.1. Transfer Model in the Drill Stem

In order to analyze the attenuation characteristics of impact stress along the axial direction of the drilling tool, the following assumptions are made: (I) since the length of the anvil and bit is much smaller than that of the drill stem (the length of the drill stem is 2510 mm, while the length of the drill bit and the anvil is 50 mm and 150 mm, respectively), the stress attenuation in the above two components can be disregarded, and only the attenuation of impact stress in the drill stem is considered; (II) the drill stem is treated as a thin-walled smooth rod, i.e., the cross-sectional area of each section is the same size; (III) the drill stem material is treated as uniform, i.e., the value of impact stress attenuation rate is constant.An infinitesimal in the drill stem is taken for analysis (as shown in Figure5), and it can be obtained:(12)σησdx=σ−σ+dσ.Figure 5
The drilling tool impact stress transmission diagram.The impact stress at the position coordinatex = 0 of the drilling stem is set to σ0. The attenuation equation of the impact stress with displacement is obtained by integrating equation (12) as(13)σ=σ0e−ησx,where ησ is the impact stress attenuation coefficient in m−1.


### 2.3.2. Transfer Model at the Drilling Tool Joints

The drilling tool joints mainly include the flange connection interface between the anvil and the drill stem and the screw connection interface between the drill stem and the drill bit. Based on the presence or absence of axial relative motion during the impact process, the stress transfer models at the connection interface are equated to the rigid body mass model and mass damping model, respectively. The equivalent models are shown in Figure6.Figure 6
Stress transfer analysis of the flange/screw interface. (a) The rigid body mass model (flange interface). (b) The mass damping model (screw interface).
(a)(b)According to the equivalent model, the incident and transmitted stresses at the flange interface and the incident and transmitted stresses at the screw interface can be derived to satisfy the following differential equations, respectively:(14)MF2Zdσtdt+σt=σi,(15)MT2Zdσtdt+1+cT2Zσt=σi,where MF is the equivalent rigid body mass of the flange interface; Z is the drilling tool wave resistance coefficient; σi is the incident stress of the interface; σt is the transmitted stress of the interface; MT is the equivalent mass of the screw interface; and cT is the equivalent damping of the screw interface.When solving the transfer efficiency, in order to simplify the calculation model, incident impact stress equation (11) obtained above is simplified to the exponential form shown in the following equation:(16)σi=σ0e−Z/mpt.Then, substituting equation (16) into equations (14) and (15), respectively, the impact stress transfer efficiency at the flange interface and screw interface can be obtained as ηF and ηT, respectively.(17)ηF=EtEi=AFc/E∫0∞σt2dtAFc/E∫0∞σi2dt=22+KFmr,(18)ηT=EtEi=ATc/E∫0∞σt2dtATc/E∫0∞σi2dt=4+4KTmr/2+KTczr−16KTmr/KTmr+KTczr+2KTczr−KFmr+22,where Ei is the energy of the incident stress wave; Et is the energy of the transmitted stress wave; KFmr = MF/mP; KTmr = MT/mP; and KTczr = cT/Z.Figure7(a) shows the curve of stress transfer efficiency ηF versus KFmr, and Figure 7(b) shows the trend of stress transfer efficiency ηT with KTmr when changing KTczr.Figure 7
The drill flange/screw interface impact stress transmission efficiency. (a) Transmission efficiency of the flange interface. (b) Transmission efficiency of the screw interface.
(a)(b)


## 2.3.1. Transfer Model in the Drill Stem

In order to analyze the attenuation characteristics of impact stress along the axial direction of the drilling tool, the following assumptions are made: (I) since the length of the anvil and bit is much smaller than that of the drill stem (the length of the drill stem is 2510 mm, while the length of the drill bit and the anvil is 50 mm and 150 mm, respectively), the stress attenuation in the above two components can be disregarded, and only the attenuation of impact stress in the drill stem is considered; (II) the drill stem is treated as a thin-walled smooth rod, i.e., the cross-sectional area of each section is the same size; (III) the drill stem material is treated as uniform, i.e., the value of impact stress attenuation rate is constant.An infinitesimal in the drill stem is taken for analysis (as shown in Figure5), and it can be obtained:(12)σησdx=σ−σ+dσ.Figure 5
The drilling tool impact stress transmission diagram.The impact stress at the position coordinatex = 0 of the drilling stem is set to σ0. The attenuation equation of the impact stress with displacement is obtained by integrating equation (12) as(13)σ=σ0e−ησx,where ησ is the impact stress attenuation coefficient in m−1.


## 2.3.2. Transfer Model at the Drilling Tool Joints

The drilling tool joints mainly include the flange connection interface between the anvil and the drill stem and the screw connection interface between the drill stem and the drill bit. Based on the presence or absence of axial relative motion during the impact process, the stress transfer models at the connection interface are equated to the rigid body mass model and mass damping model, respectively. The equivalent models are shown in Figure6.Figure 6
Stress transfer analysis of the flange/screw interface. (a) The rigid body mass model (flange interface). (b) The mass damping model (screw interface).
(a)(b)According to the equivalent model, the incident and transmitted stresses at the flange interface and the incident and transmitted stresses at the screw interface can be derived to satisfy the following differential equations, respectively:(14)MF2Zdσtdt+σt=σi,(15)MT2Zdσtdt+1+cT2Zσt=σi,where MF is the equivalent rigid body mass of the flange interface; Z is the drilling tool wave resistance coefficient; σi is the incident stress of the interface; σt is the transmitted stress of the interface; MT is the equivalent mass of the screw interface; and cT is the equivalent damping of the screw interface.When solving the transfer efficiency, in order to simplify the calculation model, incident impact stress equation (11) obtained above is simplified to the exponential form shown in the following equation:(16)σi=σ0e−Z/mpt.Then, substituting equation (16) into equations (14) and (15), respectively, the impact stress transfer efficiency at the flange interface and screw interface can be obtained as ηF and ηT, respectively.(17)ηF=EtEi=AFc/E∫0∞σt2dtAFc/E∫0∞σi2dt=22+KFmr,(18)ηT=EtEi=ATc/E∫0∞σt2dtATc/E∫0∞σi2dt=4+4KTmr/2+KTczr−16KTmr/KTmr+KTczr+2KTczr−KFmr+22,where Ei is the energy of the incident stress wave; Et is the energy of the transmitted stress wave; KFmr = MF/mP; KTmr = MT/mP; and KTczr = cT/Z.Figure7(a) shows the curve of stress transfer efficiency ηF versus KFmr, and Figure 7(b) shows the trend of stress transfer efficiency ηT with KTmr when changing KTczr.Figure 7
The drill flange/screw interface impact stress transmission efficiency. (a) Transmission efficiency of the flange interface. (b) Transmission efficiency of the screw interface.
(a)(b)


## 3. Experimental Verification

In order to verify the design parameters of the percussive drive mechanism and the above theoretical model, it is necessary to carry out the percussive drive characteristics’ test and the transfer characteristics’ test of the impact stress in the drill stem and the drilling tool joints, respectively.


### 3.1. Percussive Drive Characteristics’ Experiment

Before conducting the experiment, the single impact energy of the percussive mechanism was first calibrated. The calibration method is to measure the maximum velocity of the percussive hammer before colliding with the drilling tool by using a high-speed camera and then solve for the single impact energy.After multiple measurements, the maximum velocity is −5.045 m/s, and the single impact energy can be calculated as 2.3 J (less than the design value of 2.6 J) from the following equation:(19)WP=12kP⋅hC+hp02−12kP⋅hP02=12mP⋅vP2.Then, the percussive mechanism is designed by using the above optimally selected parameters, and the experiment is carried out on the test platform. The velocity curve of the percussive hammer is shown in Figure8(a).Figure 8
Curves of (a) velocity of the hammer and (b) percussive driving power.
(a)(b)Figure8(b) shows the comparison curve between the experimental value of percussive driving power consumption and the theoretical optimization results. It can be seen from the figure that there is little difference between the theoretical value and the experimental value of the maximum driving power consumption, which are 141.8 W and 148.2 W, respectively, and the variation tendency of the two is basically the same. Therefore, the design parameters of the percussive mechanism optimally selected by the above method can meet the requirements of the drilling tool for the percussive frequency and impact energy in the sampling process.


### 3.2. Transfer Characteristics’ Experiment in the Drill Stem

Figure9 shows the drilling tool impact stress transfer characteristics’ test system. During the impact process, the penetration mechanism can apply a certain static pressure to the drilling tool, thus ensuring that the drilling tool is always in contact with the lunar rock simulant. Fiber optic grating sensors are attached to the drilling tool surface along the axial direction to measure the stress and strain at different locations of the drilling tool after the impact action.Figure 9
The drilling impact stress transfer characteristics’ test system.According to the previous simulation analysis experience of the impact stress transfer characteristics, the fiber grating sensor is pasted near the lower surface of the spiral wing [21], and four installation measuring points are necessary, while they should be installed at an interval of 800 mm. The relative position between the measuring point and the drilling tool is shown in Figure 10. In addition, in order to reduce the influence of temperature error, the fiber grating sensor at each measuring point is encapsulated with strong adhesive [22].Figure 10
The layout of the fiber Bragg grating in the impact stress transmission test.Firstly, the attenuation law of impact stress in the drill stem is studied. Taking the percussive frequency of 2 Hz and the single impact energy of 1.25 J as the impact input parameters and setting the static pressure between the drilling tool and the lunar rock simulant as 0 N, the variation trend of impact stress with time at different positions can be obtained, as shown in Figure11.Figure 11
Curves of impact stress on drill different positions.From Figure11, it can be seen that the impact stress reaches its maximum value successively during the transmission from measuring point 1 to measuring point 4, and the impact stress amplitude at each point decreases in turn. It is consistent with the theoretical analysis; the reason is that the drill stem material has anelasticity [23], and the impact stress amplitude decreases with the increase of displacement.In order to further clarify the attenuation law, the stress amplitude at each measuring point is then fitted according to equation (15), and the curve is obtained as shown in Figure 12. It can be seen that the stress attenuation trend in the drill stem basically satisfies the pure exponential attenuation equation. The stress at measuring point 4 was abruptly reduced due to the superposition effect of reflected stress, so this point was discarded in the curve fitting.Figure 12
Impact stress attenuation curve in the drill stem.Secondly, in order to study the impact stress transfer characteristics in the drill stem under different impact input parameters, the variable impact energy and variable percussive frequency tests are carried out, respectively. The impact input parameters are shown in Table3.Table 3
The input parameters of drilling tool impact stress.
Parameter nameParameter rangeFp (Hz){2, 4, 6, 8, 10, 12, 14, 16}WP (J){1.3, 2.25, 3.125, 4}Figure13(a) shows the variation trend of impact stress with single impact energy at different measuring points. It can be seen that the impact stress amplitude at different measuring points on the drill stem increases with roughly a quadratic growth trend when single impact energy increases. It is consistent with the theoretical analysis which is that the impact energy will affect the magnitude of the input energy, and when the input energy is high, the impact stress is large.Figure 13
The impact stress at each measuring point under different input parameters. (a) Curves of impact stress vs. impact energy. (b) Curves of impact stress vs. percussive frequency.
(a)(b)Figure13(b) shows the variation trend of impact stress with percussive frequency at different measuring points. It can be seen that the amplitude of impact stress at different measuring points on the drill stem increases with the increase of percussive frequency. This is because when the percussive frequency increases, the single impact energy of the percussive mechanism increases slightly. And as the frequency increases, the number of impact forces applied by the percussive mechanism per unit time also increases, which makes the impact stress interval transferred to the next measurement position decrease, thus increasing the probability of impact stress superposition.


### 3.3. Transfer Characteristics’ Experiment at the Joints of Drilling Tools

In order to study the transfer characteristics of impact stress at the drilling tool joints, a fiber grating sensor can be installed at each of the drilling tool flange interface and screw interface. Figure14 shows the variation trend of impact stress at the flange connection interface and screw connection interface, where the percussive frequency is 2 Hz and the static pressure is 100 N.Figure 14
The impact stress transfer characteristics at the drilling tool joints. (a) The impact stress at the flange interface. (b) The impact stress at the screw interface.
(a)(b)As can be seen from Figure14, the impact stress does not change significantly past the drilling tool flange interface. This is mainly because at the drilling tool flange interface, the cross section of the anvil is larger than the cross section of the drill stem, and the impact stress is slightly amplified during the transfer from the large cross section to the small cross section, and this amplification effect will compensate for the lost impact stress. On the contrary, the impact stress loss is obvious when passing through the screw interface. Thus, in order to improve the transfer efficiency of impact stress, the screw connection length between the drill bit and the drill stem should be as short as possible when designing the drilling tool.In order to make the theoretical model further predict the transfer efficiency at the drilling tool joints, the above test data need to be analyzed and calculated. After selecting the best equivalent mass ratio and equivalent damping ratio, the theoretical transfer efficiency can be obtained by substituting them into transfer models (17) and (18) and then compared with the measured transfer efficiency.Figure15 is the comparison of the theoretical and measured transfer efficiency. It can be seen that, under different impact energy conditions, the impact stress transfer efficiency at the flange interface and screw interface is basically consistent with the theoretical model. Therefore, the above transfer model can better predict the impact stress transfer efficiency at the drilling tool joints under different working conditions.Figure 15
Comparison of the theoretical and measured transfer efficiency at drilling tool joints under different impact energies. (a)KFmr = 0.13, flange interface. (b) KTmr = 0.42 and KTczr = 0.3, screw interface.
(a)(b)In addition, the impact stress may also be transmitted along the spiral direction on the drilling tool. Therefore, another fiber grating sensor can be placed at the same cross-sectional position of measuring point 3 to compare the difference between stress transmission characteristics along the axial and spiral directions on the drilling tool. Figure16 shows the variation trend of impact stress at measuring point 3, in which the percussive frequency is 2 Hz and the static pressure is 100 N.Figure 16
The impact stress transferred along the axial and spiral directions on the drilling tool.As can be seen from Figure16, there is also a certain impact stress along the spiral direction on the drilling tool, but it is much smaller than the impact stress transmitted along the axial direction of the drilling tool, and the change of impact energy has little effect on it. This indicates that the main transfer direction of impact stress in the drilling tool is axial, while the impact stress transferred along the spiral direction can be approximately neglected.


## 3.1. Percussive Drive Characteristics’ Experiment

Before conducting the experiment, the single impact energy of the percussive mechanism was first calibrated. The calibration method is to measure the maximum velocity of the percussive hammer before colliding with the drilling tool by using a high-speed camera and then solve for the single impact energy.After multiple measurements, the maximum velocity is −5.045 m/s, and the single impact energy can be calculated as 2.3 J (less than the design value of 2.6 J) from the following equation:(19)WP=12kP⋅hC+hp02−12kP⋅hP02=12mP⋅vP2.Then, the percussive mechanism is designed by using the above optimally selected parameters, and the experiment is carried out on the test platform. The velocity curve of the percussive hammer is shown in Figure8(a).Figure 8
Curves of (a) velocity of the hammer and (b) percussive driving power.
(a)(b)Figure8(b) shows the comparison curve between the experimental value of percussive driving power consumption and the theoretical optimization results. It can be seen from the figure that there is little difference between the theoretical value and the experimental value of the maximum driving power consumption, which are 141.8 W and 148.2 W, respectively, and the variation tendency of the two is basically the same. Therefore, the design parameters of the percussive mechanism optimally selected by the above method can meet the requirements of the drilling tool for the percussive frequency and impact energy in the sampling process.


## 3.2. Transfer Characteristics’ Experiment in the Drill Stem

Figure9 shows the drilling tool impact stress transfer characteristics’ test system. During the impact process, the penetration mechanism can apply a certain static pressure to the drilling tool, thus ensuring that the drilling tool is always in contact with the lunar rock simulant. Fiber optic grating sensors are attached to the drilling tool surface along the axial direction to measure the stress and strain at different locations of the drilling tool after the impact action.Figure 9
The drilling impact stress transfer characteristics’ test system.According to the previous simulation analysis experience of the impact stress transfer characteristics, the fiber grating sensor is pasted near the lower surface of the spiral wing [21], and four installation measuring points are necessary, while they should be installed at an interval of 800 mm. The relative position between the measuring point and the drilling tool is shown in Figure 10. In addition, in order to reduce the influence of temperature error, the fiber grating sensor at each measuring point is encapsulated with strong adhesive [22].Figure 10
The layout of the fiber Bragg grating in the impact stress transmission test.Firstly, the attenuation law of impact stress in the drill stem is studied. Taking the percussive frequency of 2 Hz and the single impact energy of 1.25 J as the impact input parameters and setting the static pressure between the drilling tool and the lunar rock simulant as 0 N, the variation trend of impact stress with time at different positions can be obtained, as shown in Figure11.Figure 11
Curves of impact stress on drill different positions.From Figure11, it can be seen that the impact stress reaches its maximum value successively during the transmission from measuring point 1 to measuring point 4, and the impact stress amplitude at each point decreases in turn. It is consistent with the theoretical analysis; the reason is that the drill stem material has anelasticity [23], and the impact stress amplitude decreases with the increase of displacement.In order to further clarify the attenuation law, the stress amplitude at each measuring point is then fitted according to equation (15), and the curve is obtained as shown in Figure 12. It can be seen that the stress attenuation trend in the drill stem basically satisfies the pure exponential attenuation equation. The stress at measuring point 4 was abruptly reduced due to the superposition effect of reflected stress, so this point was discarded in the curve fitting.Figure 12
Impact stress attenuation curve in the drill stem.Secondly, in order to study the impact stress transfer characteristics in the drill stem under different impact input parameters, the variable impact energy and variable percussive frequency tests are carried out, respectively. The impact input parameters are shown in Table3.Table 3
The input parameters of drilling tool impact stress.
Parameter nameParameter rangeFp (Hz){2, 4, 6, 8, 10, 12, 14, 16}WP (J){1.3, 2.25, 3.125, 4}Figure13(a) shows the variation trend of impact stress with single impact energy at different measuring points. It can be seen that the impact stress amplitude at different measuring points on the drill stem increases with roughly a quadratic growth trend when single impact energy increases. It is consistent with the theoretical analysis which is that the impact energy will affect the magnitude of the input energy, and when the input energy is high, the impact stress is large.Figure 13
The impact stress at each measuring point under different input parameters. (a) Curves of impact stress vs. impact energy. (b) Curves of impact stress vs. percussive frequency.
(a)(b)Figure13(b) shows the variation trend of impact stress with percussive frequency at different measuring points. It can be seen that the amplitude of impact stress at different measuring points on the drill stem increases with the increase of percussive frequency. This is because when the percussive frequency increases, the single impact energy of the percussive mechanism increases slightly. And as the frequency increases, the number of impact forces applied by the percussive mechanism per unit time also increases, which makes the impact stress interval transferred to the next measurement position decrease, thus increasing the probability of impact stress superposition.


## 3.3. Transfer Characteristics’ Experiment at the Joints of Drilling Tools

In order to study the transfer characteristics of impact stress at the drilling tool joints, a fiber grating sensor can be installed at each of the drilling tool flange interface and screw interface. Figure14 shows the variation trend of impact stress at the flange connection interface and screw connection interface, where the percussive frequency is 2 Hz and the static pressure is 100 N.Figure 14
The impact stress transfer characteristics at the drilling tool joints. (a) The impact stress at the flange interface. (b) The impact stress at the screw interface.
(a)(b)As can be seen from Figure14, the impact stress does not change significantly past the drilling tool flange interface. This is mainly because at the drilling tool flange interface, the cross section of the anvil is larger than the cross section of the drill stem, and the impact stress is slightly amplified during the transfer from the large cross section to the small cross section, and this amplification effect will compensate for the lost impact stress. On the contrary, the impact stress loss is obvious when passing through the screw interface. Thus, in order to improve the transfer efficiency of impact stress, the screw connection length between the drill bit and the drill stem should be as short as possible when designing the drilling tool.In order to make the theoretical model further predict the transfer efficiency at the drilling tool joints, the above test data need to be analyzed and calculated. After selecting the best equivalent mass ratio and equivalent damping ratio, the theoretical transfer efficiency can be obtained by substituting them into transfer models (17) and (18) and then compared with the measured transfer efficiency.Figure15 is the comparison of the theoretical and measured transfer efficiency. It can be seen that, under different impact energy conditions, the impact stress transfer efficiency at the flange interface and screw interface is basically consistent with the theoretical model. Therefore, the above transfer model can better predict the impact stress transfer efficiency at the drilling tool joints under different working conditions.Figure 15
Comparison of the theoretical and measured transfer efficiency at drilling tool joints under different impact energies. (a)KFmr = 0.13, flange interface. (b) KTmr = 0.42 and KTczr = 0.3, screw interface.
(a)(b)In addition, the impact stress may also be transmitted along the spiral direction on the drilling tool. Therefore, another fiber grating sensor can be placed at the same cross-sectional position of measuring point 3 to compare the difference between stress transmission characteristics along the axial and spiral directions on the drilling tool. Figure16 shows the variation trend of impact stress at measuring point 3, in which the percussive frequency is 2 Hz and the static pressure is 100 N.Figure 16
The impact stress transferred along the axial and spiral directions on the drilling tool.As can be seen from Figure16, there is also a certain impact stress along the spiral direction on the drilling tool, but it is much smaller than the impact stress transmitted along the axial direction of the drilling tool, and the change of impact energy has little effect on it. This indicates that the main transfer direction of impact stress in the drilling tool is axial, while the impact stress transferred along the spiral direction can be approximately neglected.


## 4. Conclusions

Aiming at how to improve the impact stress obtained at the cutting edge of the drill bit, this paper successively carried out the parameter optimization design of the percussive drive mechanism and the research on the transfer characteristics of the impact stress in the drilling tool. The transfer characteristics of the impact stress from generation, incidence to transfer to the cutting edge are clarified.Eventually, it was found that increasing the percussive frequency and impact energy of the percussive mechanism as well as increasing the contact stiffness of the collision surface could improve the incident impact stress of the drilling tool. In addition, reducing the length of the screw connection between the drill bit and the drill stem can reduce the impact stress transfer loss, while the stress transfer loss at the drilling tool flange connection interface and in the spiral direction can be neglected. This provides a theoretical reference for the design of the percussive mechanism and drilling tools in lunar surface drilling and sampling tasks.



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*Source: 1555295-2021-09-15.xml*