impact dynamics of a percussive system based on rotary...

Research ArticleImpact Dynamics of a Percussive System Based onRotary-Percussive Ultrasonic Drill

YinchaoWang Qiquan Quan Hongying Yu He Li Deen Bai and Zongquan Deng

State Key Laboratory of Robotics and System Harbin Institute of Technology No 92 Xidazhi Street Nangang DistrictHarbin 150001 China

Correspondence should be addressed to Qiquan Quan quanqiquanhiteducn

Received 3 June 2017 Accepted 23 August 2017 Published 9 October 2017

Academic Editor Dario Di Maio

Copyright copy 2017 Yinchao Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents an impact dynamic analysis of a percussive system based on rotary-percussive ultrasonic drill (RPUD) TheRPUD employs vibrations on two sides of one single piezoelectric stack to achieve rotary-percussive motion which improvesdrilling efficiency The RPUDrsquos percussive system is composed of a percussive horn a free mass and a drill tool The percussivehorn enlarges longitudinal vibration frompiezoelectric stack and delivers the vibration to the drill tool through the freemass whichforms the percussive motion Based on the theory of conservation of momentum and Newtonrsquos impact law collision process of thepercussive system under no-load condition is analyzed to establish the collision model between the percussive horn the free massand the drill tool The collision model shows that free mass transfers high-frequency small-amplitude vibration of percussive horninto low-frequency large-amplitude vibration of drill tool through impact As an important parameter of free mass the greater theweight of the free mass the higher the kinetic energy obtained by drill tool after collision High-speed camera system and drillingexperiments are employed to validate the inference results of collision model by using a prototype of the RPUD

1 Introduction

As rock samples of asteroid are rich in geological informationwhich contributes to getting a deeper understanding on theorigin of the universe acquiring rock samples is now animportant target in space exploration projects Drilling isan important method for rock samples collection [1ndash4] Inthe existing sample drilling devices ultrasonic drill is a kindof sampling device which can drill into the rocks underlow weight on bit and low power consumption Thereforethe ultrasonic drill has wider application prospect in spacesampling under low-gravity environments [5]

The developing process of the ultrasonic drill can bedivided into two stages In the initial stage ultrasonic drillonly has an impact function to break rocks such as Ultra-sonicSonic DrillerCorer (USDC) [6ndash8] Ultrasonic DrillTools (UDT) [9] and UltrasonicSonic Driller (USD) [10]Late development of the ultrasonic drill adds with rotaryfunction or torsional function [11] to improve drilling effi-ciency such as Auto-Gopher [12 13] Percussive Augmenter

of Rotary Drills (PARoD) [14] Ultrasonic Planetary CoreDrill (UPCD) [15 16] and Single Piezo-Actuator Rotary-Hammering Drill (SPaRH) [17] The typical representativeof the initial stage of ultrasonic drill is USDC whichconsists of four parts a piezoelectric transducer a tunedhorn a free mass and a drill tool Tuned horn amplifiesthe vibration generated from piezoelectric transducer anddelivers impact motion to the drill tool through free massUSDC can quickly break into the rocks depending on theimpact motion Though impact motion is helpful to removedrilling chips in a certain extent it is difficult to achievechips removal effectively especially when drilling to a certaindepth Torsional ultrasonic drill utilizes ultrasonic hornto generate longitudinal-torsional vibration to improve thedrilling chips removal efficiency However the improvementof drilling efficiency is limited the chips removal efficiencystill needs to be improved According to the difference ofpower mode rotary ultrasonic drill can be divided into twotypes motor-rotary and piezoelectric-rotary Motor-rotaryultrasonic drill uses electromagnetic motor to rotate the

HindawiShock and VibrationVolume 2017 Article ID 5161870 10 pageshttpsdoiorg10115520175161870

2 Shock and Vibration

drill tool to remove drilling chips which raises the drillingefficiency effectively Nevertheless adding a motor to theultrasonic drill may increase the degree of drilling whichalso brings complication to the power supply Piezoelectric-rotary ultrasonic drill utilizes piezoelectric ceramics as therotary and impact power which has a more compact systemstructure and stronger environmental adaptability comparedwith motor-rotary ultrasonic drill SPaRH is a representativeof the piezoelectric-rotary ultrasonic drill which consistsof four parts a piezoelectric transducer a grooved horn akeyed free mass and a drill tool The grooved horn translateslongitudinal vibration of the piezoelectric transducer intolongitudinal-torsional vibration After receiving vibrationfrom the horn the keyed freemassmakes the drill tool realizerotary-impact motion However as the rotary motion andimpact motion of SPaRH are coupled together it is difficultto adjust the rotation or impact parameters separately whichmay limit the scope of application of SPaRH

As is well known the piezoelectric ceramics transmitvibration to both sides The existing ultrasonic drill only usesthe vibration on front side and part of vibration on the backside is not used In our previous work a rotary-percussiveultrasonic drill (RPUD) based on one single piezoelectrictransducer is proposed to drill into rocks in rotary-percussivemotion which uses the vibration energy on both sides of thepiezoelectric ceramics [18] Drilling experiment shows thatthe RPUD can raise the drilling efficiency of rock sampling

To validate the energy delivering capability of the per-cussive system the dynamic analysis of impact between thepercussive horn the free mass and the drill tool needs to becarried out Nowadays the research on the collision processof percussive system can be divided into theoretical researchand experimental research In the research of [8] integratedmodelingmethod and finite elementmethod are employed toanalyze the impact contact between the ultrasonic horn andthe free mass But there is no research on collision of the drilltool According to the study of [19 20] it is assumed that thedrill tool is fixed and the ultrasonic horn canmove axially andset-oriented method is chosen to analyze the drilling systemwith contact interfaces However there is lack of experimentsto validate the collision model Based on the paper of [21] adrill rod is assumed to be consolidated with rock solid bodycollision is used to analyze ultrasonic horn and free massand free mass and drill rod impact process and the drill rodmodel for both undamped and damped states is discussedAnd a spherical mass is studied only through experiment bythe study of [22] The effects of multiple free mass and singlefree mass on the impact force are tested through ultrasonicdrilling experiments

Above all to the best knowledge of the authors theresearch about the collision process of the free mass is mostlyin the load condition of the ultrasonic drill which meansthat ultrasonic drill breaks into rocks and the drill tool isfixed with the rocks In order to describe the collision processof the free mass unit intuitively and clearly and eliminatethe interference factors this paper analyzes the free masscollision process under no-load condition In this paper thecollision process of the percussive system is studied based onthe RPUD Using Newtonrsquos impact law the collision model

of percussive horn free mass and drill tool is establishedAs the weight of free mass has a significant effect on theenergy transfer process based on the collision model theeffect of weight of free mass on the kinetic energy of drillingtool under no-load condition is discussed as well To verifythe collision model the vibration process of the percussivesystem under no-load condition is observed through high-speed camera Motion parameters of free mass are extractedand analyzed Moreover the effect of weight of free masson the kinetic energy of drilling tool is verified In order tofurther confirm the validity of the collisionmodel the drillingexperiments under load condition is carried out based on theRPUD

The remaining sections of the paper are organized asfollows In Section 2 the structure and working principle ofthe RPUD are proposed Section 3 presents a collision modelof percussive system under no-load condition including thecollision model of the free mass with percussive horn anddrill tool In Section 4 the simulation of collision model ispresented High-speed camera system and drilling experi-ments are employed to evaluate the collision performance inSection 5 Finally Section 6 concludes this paper

2 Structure and Working Principle

TheRPUD is proposed based on the vibration of piezoelectricceramics on both sides RPUD consists of PZT (piezoelectricceramics of PbZrO3-PbTiO3 system) ceramics a rotary unita percussive unit a sleeve and a drill tool as shown inFigure 1(a) PZT ceramics are composed of four piezoelectricceramics and placed between rotary unit and percussive unit

The rotary unit is located on the back of the PZT ceramicsand consists of a V type of longitudinal-torsional vibrationcoupling element (V-LT coupler) [23] a rotor and a preloadspring The bottom of the V-LT coupler is connected to thePZT ceramics by bolts The rotor is engaged with the drivingteeth of the V-LT coupler and the preload force is provided bythe preload spring The percussive unit is connected with thefront of the PZT ceramics and is composed of a percussivehorn a free mass and a restoring spring The same as V-LTcoupler the bottom of the percussive horn is linked with thePZT ceramics by bolts as well The free mass is fitted with thetop of the percussive horn and the preload force is providedby the restoring spring as shown in Figure 1(b) The drilltool is composed of a spiral drill pipe and a drilling bit Thepercussive horn the freemass and the drill tool constitute thepercussive system of the RPUD Preload force on the rotor isabout 18N and the preload force on the free mass is about5N The mass of the RPUD is about 590 g

Based on the composition of RPUD system ANSYS(ANSYS120 ANSYS Inc Canonsburg PA USA) [24] isemployed to establish the finite element model of the V-LT coupler and percussive horn (rotary-percussive composi-tion) as shown in Figure 2 The PZT ceramics use 11988933 work-ing mode for the excitations of longitudinal vibration andare polarized along their thickness directions Figure 3 givesthe vibration shape and displacement vector of the rotary-percussive composition inmodal analysis respectivelyWhenthe rotary-percussive composition works in resonant state

Shock and Vibration 3

+

+

v

PZTceramics

Rotaryunit

Percussiveunit

Drilltool

v

Sleeve

minus

minus

(a)

Freemass

Percussivehorn

Drillingbit

Rotor

Storingspring

V-LTcoupler

Preloadspring

278

Φ 64

(b)

Figure 1 Structure of the RPUD

~

Polarized positively Polarized negativelyminusminus minus

Fixed

++

Figure 2 Finite element model of the rotary-percussive composi-tion

the vibration modal analysis of the V-LT coupler and per-cussive horn is well matched with each other [25] and themaximum vibration value is reached simultaneously

After being excited by the voltage the PZT ceramicstransfer vibration to both sides simultaneously The rotary-percussive composition synchronously reaches the resonancestate and drives the drill tool to realize the rotary-percussivemotion respectively Figure 4 shows the detailed workingprinciple of rotary unit and percussive unit When the rotaryunit receives the vibration from the PZT ceramics V-LTcoupler transforms longitudinal vibration into longitudinal-torsional vibration and an elliptical motion is formed on the

Figure 3 Modal analysis of the rotary-percussive composition

top of driving teeth of the V-LT coupler With the preloadforce provided by preload spring friction is generated on thecontact surface between the driving teeth and the rotor whichdrives the rotor to rotate continuously In the percussive unitthe percussive horn enlarges the longitudinal vibration fromthe PZT ceramics and passes the vibration to freemassThenthe free mass transmits the percussive vibrating energy to thedrill tool based on the continuous impact movement with thedrill tool Since the driving voltage changes in accordance


Storingspring

Preloadforce

Rotor

V-LTcoupler

Free mass

Percussivehorn

Drill tool

Rotatingdirection

(a)

(b)

(c)

(d)

t = (n + 1)T

t = (n +1

4)T

t = (n +1

2)T

t = (n +3

4)T

Figure 4 Working principle of rotary unit and percussive unit

with the sinusoidal period the rotary unit and the impactunit also drive the drill tool to carry out periodic movementwhich follows the sequence of (a)-(b)-(c)-(d)

3 Collision Model of Percussive System

In the percussive system work process after being excitedby resonance voltage the PZT ceramics generate a firstlongitudinal vibrationmode and drive percussive hornwhichproduces longitudinal vibration As the percussive system iscomposed of the percussive horn the free mass and the drilltool the percussive horn transmits vibrations at an ultrasonicfrequency to the free mass and then free mass delivers thevibration to the drill tool The percussive motion of the drilltool is achieved by the collision process with the free massThe collision of freemass is a highly nonlinearmotion whichcontains lots of influencing factors In order to describe themotion of free mass more clearly some secondary factorsneed to be ignored So some assumptions should be madebefore establishment of the free mass collision model

(1) The PZT ceramics are fixed at the nodal plane thedisplacement of percussive horn is a simple harmonic

vibration and the vibration process is not affected bythe collision of free mass

(2) The rotary-percussive ultrasonic drill works in no-load condition and the drill tool can vibrate freelyalong the axial direction

(3) In the collision modeling process effect of frictionforce between the free mass the percussive horn andthe drill tool is ignored

(4) The centroid of the percussive horn the freemass andthe drill tool are coaxial during the collision process

(5) There is no aerodynamic drag and the coefficient ofrestitution is a constant

The collision process between the free mass the percus-sive horn and the drill tool is shown in Figure 5(a) Tipof the percussive horn makes a simple harmonic vibrationunder the driving of the PZT ceramicsThe freemass vibratesbetween the percussive horn and the drill tool passingthe vibration energy The modeling of the collision processbetween the free mass the percussive horn and the drill toolis shown in Figure 5(b) The top 119906(119905) is the displacement ofthe percussive horn the bottom V(119905) is the displacement of the


Percussivehorn

Free mass

Drill tool

(a)

u(t)

w(t)

v(t)

Y

O

X

v(0)

wk

wkwkminus1 wk+1 w

k+1

wi wi

wi+1 wi+1

L0

tkminus1 ti tk ti+1

(b)

Figure 5 Collision model of free mass (a) Composition of collision system (b) Modeling of collision system

drill tool and themiddle119908(119905) is the vibration of the freemassIn the coordinate system the OX direction is the center linedirection of the percussive horn vibration displacement andthe OY direction is the initial displacement direction of thepercussive systemThe initial interval between the percussivehorn and the drill tool is 1198710

The motion of the percussive horn can be written as

119906 (119905) = 1198600 cos (2120587119891119905) (1)

where 1198600 is the vibration amplitude of percussive horn and119891 is the vibration frequencySo the velocity of the percussive horn can be given as

(119905) = minus21205871198911198600 sin (2120587119891119905) (2)

The initial time of the calculation is assumed to be 119905119896minus1After the collisionwith the percussive horn the free massvelocity is 1015840119896minus131 Calculation of the Collision Time between Free Mass andDrill Tool 119905119894 The vibration parameters of free mass at time of119905119896minus1 can be written as

(119905) = minus119892119908 (119905119896minus1) = 119906 (119905119896minus1)

1015840 (119905119896minus1) = 1015840119896minus1(3)

where 119892 is acceleration of gravity As one assumes the OYdirection is positive 119892 is negative after 119905119896minus1

The vibration equation of free mass after 119905119896minus1 is119908 (119905) = 1199061015840119896minus1 minus 1198922 (119905 minus 119905119896minus1)2 + 1015840119896minus1 (119905 minus 119905119896minus1)

forall119905 isin [119905119896minus1 119905119894) (4)

After 119905119896minus1 free mass accelerates the velocity to the drilltool And the velocity of the free mass can be given as (119905) = 1015840119896minus1 minus 119892 (119905 minus 119905119896minus1) forall119905 isin [119905119896minus1 119905119894) (5)

In the percussive system the motion of the drill tool is afree vibration with viscous damping The equation of motioncan be expressed as follows [26]

V (119905) + 119888119898VV (119905) + 1198960119898V

V (119905) = 0 (6)

where 119888 is viscous damping coefficient of the drill tool and 1198960is equivalent stiffness coefficient of the drill tool

The equation of motion of the drill tool before the 119905119894thcollision can be written asV119894minus1 (119905)

= [119890minus120577120596119899119905 sin (120596119889119905 + 120593)] radicV119894minus12 + ( V1015840119894minus1 + 120577120596119899V119894minus1120596119889 )2

forall119905 isin (119905119894minus1 119905119894] (7)

where tan120593 = 120596119889V119894minus1(V1015840119894minus1 + 120577120596119899V119894minus1) 120596119899 = radic1198960119898V is thenatural frequency of the drill tool without damping 120596119889 =radic(1 minus 1205772)120596119899 and 120577 = 1198882119898V120596119899

At 119905119894 moment the contact condition of the free mass withthe drill tool can be given by

V (119905119894) = 119908 (119905119894) (8)That is

[119890minus120577120596119899119905119894 sin (120596119889119905119894 + 120593)] radicV119894minus12 + ( V1015840119894minus1 + 120577120596119899V119894minus1120596119889 )2

= 1199061015840119896minus1 minus 1198922 (119905119894 minus 119905119896minus1)2 + 1015840119896minus1 (119905119894 minus 119905119896minus1) (9)


By solving (9) 119905119894 is obtained The velocity of the freemass and the drill tool before collision can be obtained bysubstituting 119905119894 in the velocity equation of the free mass andthe drill tool The velocity can be expressed as

(119905119894) = 1015840119896minus1 + 1198922 (119905119894 minus 119905119896minus1)V (119905119894)

= 119890minus120577120596119899119905119894 [120596119889 cos (120596119889119905119894 + 120593) minus 120577120596119899 sin (120596119889119905119894 + 120593)]sdot radicV02 + ( V0 + 120577120596119899V0120596119889 )2

(10)

The collision process of the free mass and the drill toolsatisfies the momentum conservation theorem which can bewritten as [27]

119898VV (119905) + 119898119908 (119905) = 119898VV1015840 (119905) + 1198981199081015840 (119905) (11)

where 119898V is the mass of the drill tool and 119898119908 is the mass ofthe free mass

The coefficient of restitution 1198901 between the freemass andthe drill tool can be given by [28]

1198901 = 1015840119894 minus V1015840119894V119894 minus 119894 (12)

So the velocity of the free mass and the drill tool aftercollision of the time 119905119894 can be expressed as

V1015840 (119905119894) = V119894 + 119898119908119898V + 119898119908 (1 + 1198901) (119894 minus V119894)1015840 (119905119894) = 119894 minus 119898V119898V + 119898119908 (1 + 1198901) (119894 minus V119894) (13)

32 Calculation of the Collision Time between Free Mass andPercussive Horn 119905119896 The vibration parameters of free mass attime of 119905119894 can be written as

(119905) = minus119892119908 (119905119894) = V (119905119894)

1015840 (119905119894) = 1015840119894 (14)

The vibration equation of free mass after 119905119894 is119908 (119905) = V119894 minus 1198922 (119905 minus 119905119894)2 + 1015840119894 (119905 minus 119905119894) forall119905 isin [119905119894 119905119896) (15)

After 119905119894 free mass decelerates the velocity to the percus-sive horn At 119905119896 moment the contact condition of the freemass with the percussive horn can be given by

119906 (119905119896) = 119908 (119905119896) (16)

That is

1198600 cos (2120587119891119905119896)= 119890minus120577120596119899119905119894 [120596119889 cos (120596119889119905119894 + 120593) minus 120577120596119899 sin (120596119889119905119894 + 120593)]sdot radicV02 + ( V0 + 120577120596119899V0120596119889 )2 minus 1198922 (119905119896 minus 119905119894)2+ 1015840119894 (119905119896 minus 119905119894)

(17)

By solving (17) 119905119896 is obtainedThe velocity of the freemassand the percussive horn before collision can be obtained bysubstituting 119905119896 in the velocity equation of the free mass andthe percussive horn So the velocity can be expressed as

(119905119896) = 1015840119894 minus 119892 (119905119896 minus 119905119894) (119905119896) = minus21205871198911198600 sin (2120587119891119905119896) (18)

The collision process of the free mass and the percussivehorn satisfies the momentum conservation theorem whichcan be given as

119898119906 (119905119896) + 119898119908 (119905119896) = 1198981199061015840 (119905119896) + 1198981199081015840 (119905119896) (19)

The coefficient of restitution 1198902 between the freemass andthe percussive horn can be given by

1198902 = 1015840119896 minus 1015840119896119896 minus 119896 (20)

Considering that the percussive horn is the power sourceof the vibration system it is assumed that the vibration of thehorn is not affected by the collision process of the free massSo the velocity of the percussive horn and the free mass aftercollision of the time 119905119896 can be expressed as

1015840 (119905119896) = V119896

1015840 (119905119896) = 119896 minus 119898119906119898119906 + 119898119908 (1 + 1198902) (119896 minus 119896) (21)

4 Analysis of Collision Model

In order to get a visual understanding of the collision processMATLAB is employed for analysis of the collision modelof the percussive horn the free mass and the drill toolTo obtain the numerical solution of collision model theinitial parameters of the collision system are given in Table 1The collision process through time between the free massthe percussive horn and the drill tool is obtained throughcalculation

Figure 6 shows the vibration displacement for the first50 milliseconds of the percussive system The vibration dis-placement for the first 20 milliseconds is shown in Figure 7The vibration frequency of the free mass is varied during thecollision process and the average collision frequency of thefree mass is about 520Hz As the free mass and the drill toolare coupled together by the collision process the vibration


Table 1 The initial parameters of the percussive system

Parameters Symbols Unit ValueAcceleration of gravity 119892 ms2 98Coefficient of restitution between the freemass and the drill tool 1198901 mdash 08

Coefficient of restitution between the freemass and the percussive horn 1198902 mdash 09

Vibration amplitude of the percussive horn 1198600 120583m 15Vibration frequency of the percussive horn 119891 kHz 20Mass of percussive horn 119898119906 kg 008Mass of drill tool 119898V kg 005Mass of free mass 119898119908 kg 0008

Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0

02Percussive horn Free mass

Drill tool

Time (ms)

Figure 6The vibration displacement for the first 50milliseconds ofthe percussive system

of the drill tool follows with the free mass which changesthe state of vibration after each collision The free massconverts ultrasonic-frequency small-amplitude vibration ofthe percussive horn into a lower-frequency large-amplitudevibration of the drill tool through the collision process

To analyze the effect of the free mass on the energydelivering process the kinetic energy of the drill tool iscalculated after collision with different weight of free massas shown in Figures 8(a)ndash8(d) It is observed that with theweight of free mass changed from 2 g to 8 g the kineticenergy of the drill tool after collision is also increased andthe increase of kinetic energy is linear with the weight of freemass

5 Experiments

To verify the calculation results of the collision model high-speed camera system and drilling experiments are employedto evaluate the vibration process of the percussive system

51 VibrationMeasurement Using High-Speed Camera SystemHigh-speed camera is a device for recording fast-movingmotion which can measure the movement state of objects[29] To verify the collision model result this paper usesthe high-speed camera to measure the vibration process andanalyze the nonlinear dynamic behavior of the free mass

10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)

Figure 7The vibration displacement for the first 20 milliseconds ofthe percussive system

with percussive horn and drill tool The test uses PhantomV12 high-speed camera as shown in Figure 9(a) In orderto match the requirements of the tracking of free massmovement the camera parameter of the high-speed camerais set to 5000 frames per second Before test it is necessaryto identify the percussive horn the free mass and the drilltool as shown in Figure 9(b) High-speed camera is usedto measure the percussive motion of the free mass betweenthe percussive horn and the drill tool The displacement andvibration velocity of free mass are extracted respectively asshown in Figures 10 and 11 The maximum displacement offreemass is nearly 6mmand themaximumvibration velocityis nearly 80mms In order to determine the frequency rangeof the free mass in the collision process Fourier transformis performed on the time domain characteristics of thedisplacement of free mass The corresponding frequencyspectrum is obtained as shown in Figure 12 According tothe spectrum the vibration frequency of the free mass ismostly in the range of 0sim400Hz which is consistent with theprevious theoretical analysis result

To validate the effect of the weight of free mass on thepercussive energy of the drill tool in the collision modeldifferent weights of freemasses are assembled into the RPUDand the vibration velocity of the drill tool is measured withthe help of the high-speed camera systemThe average kineticenergy of the drill tool is measured and compared withthe theoretical results in the collision model as shown inFigure 13 With the weight of free mass changed from 0 gto 8 g the theoretical values and measured values of thekinetic energy of drill tool are gradually increased It canbe inferred that the larger the weight of the free massthe greater the percussive kinetic energy delivered to thedrill tool which verifies the aforementioned collision modelcalculation results in Figure 8

52 Drilling Experiments To further observe the effect ofthe free mass on the percussive kinetic energy of the drilltool drilling experiments of RPUD with load condition iscarried out under different weights of free mass To keep therationality of drilling experiments RPUD operates at bothrotary-percussive mode and percussive mode The drillingexperiments are accomplished under exciting voltage of


0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)

0 10 20 30 40 50Impact numbers

4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)

Figure 8 The kinetic energy of the drill tool after collision under different weights of free mass

(a) High-speed camera

Percussivehorn

Free mass

Drill tool

(b) Marked percussive system

Figure 9 Vibration measurement using high-speed camera system (a) Phantom V12 high-speed camera (b) Marked percussive system

225V and exciting frequency of 1995 kHz Diameter of drilltool is 3mm the drilling time is 5 minutes the weight on bitis 7N the drilling object is sandstone and the drilling depthis observed under different weights of free mass as shown inFigure 14

The rotary-percussive drilling and percussive drillingresults show that the drilling depth increases with the weightof free mass from 0 g to 8 g As the weight becomes 8 g thedrilling depth reaches the maximum value This is consistent

with the previous high-speed camera vibrationmeasurementresults The experiments also indicate that rotary-percussivedrilling has higher drilling efficiency than percussive drillingwhich validates the aforementioned advantages of the RPUD

6 Conclusions

This paper proposed an impact dynamics analysis of thepercussive system based on the rotary-percussive ultrasonic


minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)

Figure 10 The vibration displacement of free mass

0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)

Figure 11 The vibration velocity of free mass

001

0203

0600

1200

minus03

0

03

Time (s)Frequency (Hz)

Am

plitu

de (m

m)

Figure 12 The corresponding frequency spectrum of free mass

drill (RPUD) The proposed RPUD uses the vibrations ontwo sides of one single piezoceramic with achieved rotary-percussive motion which has higher drilling efficiency com-pared with percussive ultrasonic drill The theory of conser-vation of momentum and Newtonrsquos impact law are employedto analyze the collision process of the percussive systemunderno-load condition The collision process of the free massbetween the percussive horn and the drill tool is analyzed andthe effect of the weight of free mass on the kinetic energy ofdrill tool is discussed as well High-speed camera system anddrilling experiments are used to verify the analysis results

0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)

Weight of free mass (g)

Calculated energyMeasured energy

Figure 13 The average kinetic energy of the drill tool in theoreticalresults and measured results

Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25

Rotary-percussivePercussive


Dril

ling

dept

h (m

m)

(b)

Figure 14 Drilling experiment of RPUD (a) Test bed of RPUD (b)Drilling depth of RPUD under different weight of free mass

In the collision process of the percussive system the freemass transmits high-frequency small-amplitude vibrationof the percussive horn into low-frequency large-amplitudevibration and delivers the impact energy to the drill toolwhich achieved the percussive movement of the drill tool Inthe range of RPUD drive capability increasing the weight ofthe free mass can effectively raise the kinetic energy of thedrill tool during collision process


Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The project is financially supported by fundamental researchfunds for National Natural Science Foundation of China(61403106)

References

[1] K Zacny Y Bar-CohenM Brennan et al ldquoDrilling systems forextraterrestrial subsurface explorationrdquo Astrobiology vol 8 no3 pp 665ndash706 2008

[2] Y Bar-Cohen and K Zacny ldquoDrilling in Extreme Environ-mentsrdquo Chapter Extraterrestrial Drilling and Excavation pp347ndash546 2008

[3] K Zacny J Wilson P Chu and J Craft ldquoPrototype rotary per-cussive drill for theMars sample returnmissionrdquo in Proceedingsof the proceeding of the 2011 IEEE Aerospace Conference AEROrsquo11 9 pages Montana MT USA March 2011

[4] Z YOuyang ldquoScientific objectives of Chinese lunar explorationproject and development strategyrdquo Advance in Earth Sciencesvol 19 pp 351ndash358 2004

[5] P Harkness and M Lucas ldquoA brief overview of space applica-tions for ultrasonicsrdquo Ultrasonics vol 52 no 8 pp 975ndash9792012

[6] Y Bar-Cohen S Sherrit B P Dolgin et al ldquoUltrasonicsonicdrillercorer (USDC) as a sampler for planetary explorationrdquoIEEE Aerospace Conference Proceedings vol 1 pp 1263ndash12712001

[7] X Bao Y Bar-Cohen Z Chang et al ldquoModeling and com-puter simulation of ultrasonicsonic drillercorer (USDC)rdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 50 no 9 pp 1147ndash1160 2003

[8] M Badescu X Bao Y Bar-Cohen Z Chang and S SherritldquoIntegratedmodeling of the ultrasonicsonic drillcorer - Proce-dure and analysis resultsrdquo in Proceedings of the Smart Structuresand Materials 2005 - Smart Structures and Integrated Systemspp 312ndash323 March 2005

[9] P N H Thomas ldquoMagna Parva and ESArsquos ultrasonic drill toolfor planetary surface explorationrdquo in Proceedings of the 12thInternational Conference on Engineering Science Constructionand Operations in Challenging Environments - Earth and Space2010 pp 1235ndash1245 March 2010

[10] Q Quan H Li S Jiang Z Deng X Hou and D TangldquoA piezoelectric-driven ultrasonicsonic driller for planetaryexplorationrdquo in Proceedings of the 2013 IEEE InternationalConference on Robotics and Biomimetics ROBIO 2013 pp 2523ndash2528 December 2013

[11] A Cardoni P Harkness and M Lucas ldquoUltrasonic rock sam-pling using longitudinal-torsional vibrationsrdquo Physics Procediavol 3 no 1 pp 125ndash134 2010

[12] M Badescu S Sherrit X Bao Y Bar-Cohen and B ChenldquoAuto-Gopher - A wire-line rotary-hammer ultrasonic drillrdquo inProceedings of the Sensors and Smart Structures Technologies forCivil Mechanical and Aerospace Systems 2011 March 2011

[13] K Zacny G Paulsen Y Bar-Cohen et al ldquoWireline deep drillfor exploration of Mars Europa and Enceladusrdquo in Proceedingsof 2013 IEEE Aerospace Conference AERO 2013 March 2013

[14] M Badescu J Hasenoehrl Y Bar-Cohen et al ldquoPercussiveaugmenter of rotary drills (PARoD)rdquo in Proceedings of the SPIESmart Structures andMaterials +Nondestructive Evaluation andHealth Monitoring p 86921Q San Diego Calif USA

[15] X Li K Worrall P Harkness et al ldquoA Motion Control SystemDesign for an Ultrasonic Planetary Core Drill (UPCD) Unitrdquo inin Proceedings of AIAA SPACE 2015 Conference and Expositionpp 1ndash11 Pasadena Calif USA June 2015

[16] R Timoney P Harkness X Li A Bolhovitins A Cheneyand M Lucas ldquoThe Development of the European UItrasonicPlanetary Core Drill (UPCD)rdquo in Proceedings of the AIAASPACE 2015 Conference and Exposition Pasadena Calif USA

[17] S Sherrit L Domm X Bao Y Bar-Cohen and Z ChangldquoSingle piezo-actuator rotary-hammering (SPaRH) drillrdquo inProceedings of the Sensors and Smart Structures Technologies forCivil Mechanical and Aerospace Systems 2012 San Diego CalifUSA March 2012

[18] Y Wang H Li D Bai et al ldquoA rotary-percussive ultrasonicdrill for planetary rock samplingrdquo in Proceedings of the 2016IEEERSJ International Conference on Intelligent Robots andSystems IROS 2016 pp 2966ndash2971 October 2016

[19] N Neumann T Sattel and J Wallaschek ldquoOn the Analysisof a Simple Impact Drill Model using Set-Oriented NumericalMethodsrdquo PAMM vol 5 no 1 pp 119-120 2005

[20] N Neumann and T Sattel ldquoSet-oriented numerical analysis ofa vibro-impact drilling system with several contact interfacesrdquoJournal of Sound and Vibration vol 308 no 3-5 pp 831ndash8442007

[21] L J Vila and R B Malla ldquoAnalytical model of the contactinteraction between the components of a special percussivemechanism for planetary explorationrdquo Acta Astronautica vol118 pp 158ndash167 2016

[22] P Harkness M Lucas and A Cardoni ldquoArchitectures forultrasonic planetary sample retrieval toolsrdquo Ultrasonics vol 51no 8 pp 1026ndash1035 2011

[23] A Kumada ldquoA piezoelectric ultrasonicmotorrdquo Japanese Journalof Applied Physics vol 24 pp 739ndash741 1985

[24] T Stolarski Y Nakasone and S Yoshimoto ldquoEngineeringanalysis with ANSYS softwarerdquo in Chapter Mode Analysis pp143ndash185 2011

[25] Y Liu X Yang W Chen and D Xu ldquoA Bonded-Type Piezo-electric Actuator Using the First and Second Bending VibrationModesrdquo IEEE Transactions on Industrial Electronics vol 63 no3 pp 1676ndash1683 2016

[26] D E NewlandMechanical vibration analysis and computationvol 4 Courier Corporation 2013

[27] R M Brach ldquoMechanical impact dynamics rigid body colli-sionsrdquo Chapter Vibratory Impact pp 189ndash206 1991

[28] G Gilardi and I Sharf ldquoLiterature survey of contact dynamicsmodellingrdquoMechanism and Machine Theory vol 37 no 10 pp1213ndash1239 2002

[29] H-H Kim J-H Kim and A Ogata ldquoTime-resolved high-speed camera observation of electrosprayrdquo Journal of AerosolScience vol 42 no 4 pp 249ndash263 2011

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



drill tool to remove drilling chips which raises the drillingefficiency effectively Nevertheless adding a motor to theultrasonic drill may increase the degree of drilling whichalso brings complication to the power supply Piezoelectric-rotary ultrasonic drill utilizes piezoelectric ceramics as therotary and impact power which has a more compact systemstructure and stronger environmental adaptability comparedwith motor-rotary ultrasonic drill SPaRH is a representativeof the piezoelectric-rotary ultrasonic drill which consistsof four parts a piezoelectric transducer a grooved horn akeyed free mass and a drill tool The grooved horn translateslongitudinal vibration of the piezoelectric transducer intolongitudinal-torsional vibration After receiving vibrationfrom the horn the keyed freemassmakes the drill tool realizerotary-impact motion However as the rotary motion andimpact motion of SPaRH are coupled together it is difficultto adjust the rotation or impact parameters separately whichmay limit the scope of application of SPaRH

As is well known the piezoelectric ceramics transmitvibration to both sides The existing ultrasonic drill only usesthe vibration on front side and part of vibration on the backside is not used In our previous work a rotary-percussiveultrasonic drill (RPUD) based on one single piezoelectrictransducer is proposed to drill into rocks in rotary-percussivemotion which uses the vibration energy on both sides of thepiezoelectric ceramics [18] Drilling experiment shows thatthe RPUD can raise the drilling efficiency of rock sampling

To validate the energy delivering capability of the per-cussive system the dynamic analysis of impact between thepercussive horn the free mass and the drill tool needs to becarried out Nowadays the research on the collision processof percussive system can be divided into theoretical researchand experimental research In the research of [8] integratedmodelingmethod and finite elementmethod are employed toanalyze the impact contact between the ultrasonic horn andthe free mass But there is no research on collision of the drilltool According to the study of [19 20] it is assumed that thedrill tool is fixed and the ultrasonic horn canmove axially andset-oriented method is chosen to analyze the drilling systemwith contact interfaces However there is lack of experimentsto validate the collision model Based on the paper of [21] adrill rod is assumed to be consolidated with rock solid bodycollision is used to analyze ultrasonic horn and free massand free mass and drill rod impact process and the drill rodmodel for both undamped and damped states is discussedAnd a spherical mass is studied only through experiment bythe study of [22] The effects of multiple free mass and singlefree mass on the impact force are tested through ultrasonicdrilling experiments

Above all to the best knowledge of the authors theresearch about the collision process of the free mass is mostlyin the load condition of the ultrasonic drill which meansthat ultrasonic drill breaks into rocks and the drill tool isfixed with the rocks In order to describe the collision processof the free mass unit intuitively and clearly and eliminatethe interference factors this paper analyzes the free masscollision process under no-load condition In this paper thecollision process of the percussive system is studied based onthe RPUD Using Newtonrsquos impact law the collision model

of percussive horn free mass and drill tool is establishedAs the weight of free mass has a significant effect on theenergy transfer process based on the collision model theeffect of weight of free mass on the kinetic energy of drillingtool under no-load condition is discussed as well To verifythe collision model the vibration process of the percussivesystem under no-load condition is observed through high-speed camera Motion parameters of free mass are extractedand analyzed Moreover the effect of weight of free masson the kinetic energy of drilling tool is verified In order tofurther confirm the validity of the collisionmodel the drillingexperiments under load condition is carried out based on theRPUD

The remaining sections of the paper are organized asfollows In Section 2 the structure and working principle ofthe RPUD are proposed Section 3 presents a collision modelof percussive system under no-load condition including thecollision model of the free mass with percussive horn anddrill tool In Section 4 the simulation of collision model ispresented High-speed camera system and drilling experi-ments are employed to evaluate the collision performance inSection 5 Finally Section 6 concludes this paper

2 Structure and Working Principle

TheRPUD is proposed based on the vibration of piezoelectricceramics on both sides RPUD consists of PZT (piezoelectricceramics of PbZrO3-PbTiO3 system) ceramics a rotary unita percussive unit a sleeve and a drill tool as shown inFigure 1(a) PZT ceramics are composed of four piezoelectricceramics and placed between rotary unit and percussive unit

The rotary unit is located on the back of the PZT ceramicsand consists of a V type of longitudinal-torsional vibrationcoupling element (V-LT coupler) [23] a rotor and a preloadspring The bottom of the V-LT coupler is connected to thePZT ceramics by bolts The rotor is engaged with the drivingteeth of the V-LT coupler and the preload force is provided bythe preload spring The percussive unit is connected with thefront of the PZT ceramics and is composed of a percussivehorn a free mass and a restoring spring The same as V-LTcoupler the bottom of the percussive horn is linked with thePZT ceramics by bolts as well The free mass is fitted with thetop of the percussive horn and the preload force is providedby the restoring spring as shown in Figure 1(b) The drilltool is composed of a spiral drill pipe and a drilling bit Thepercussive horn the freemass and the drill tool constitute thepercussive system of the RPUD Preload force on the rotor isabout 18N and the preload force on the free mass is about5N The mass of the RPUD is about 590 g

Based on the composition of RPUD system ANSYS(ANSYS120 ANSYS Inc Canonsburg PA USA) [24] isemployed to establish the finite element model of the V-LT coupler and percussive horn (rotary-percussive composi-tion) as shown in Figure 2 The PZT ceramics use 11988933 work-ing mode for the excitations of longitudinal vibration andare polarized along their thickness directions Figure 3 givesthe vibration shape and displacement vector of the rotary-percussive composition inmodal analysis respectivelyWhenthe rotary-percussive composition works in resonant state


+

+

v

PZTceramics

Rotaryunit

Percussiveunit

Drilltool

v

Sleeve

minus

minus

(a)

Freemass

Percussivehorn

Drillingbit

Rotor

Storingspring

V-LTcoupler

Preloadspring

278

Φ 64

(b)


~


Fixed

++







Storingspring

Preloadforce

Rotor

V-LTcoupler

Free mass

Percussivehorn

Drill tool

Rotatingdirection

(a)

(b)

(c)

(d)

t = (n + 1)T

t = (n +1

4)T

t = (n +1

2)T

t = (n +3

4)T













Percussivehorn

Free mass

Drill tool

(a)

u(t)

w(t)

v(t)

Y

O

X

v(0)

wk

wkwkminus1 wk+1 w

k+1

wi wi

wi+1 wi+1

L0

tkminus1 ti tk ti+1

(b)




119906 (119905) = 1198600 cos (2120587119891119905) (1)


(119905) = minus21205871198911198600 sin (2120587119891119905) (2)



1015840 (119905119896minus1) = 1015840119896minus1(3)






V (119905) + 119888119898VV (119905) + 1198960119898V

V (119905) = 0 (6)







V (119905119894) = 119908 (119905119894) (8)That is







(10)


119898VV (119905) + 119898119908 (119905) = 119898VV1015840 (119905) + 1198981199081015840 (119905) (11)



1198901 = 1015840119894 minus V1015840119894V119894 minus 119894 (12)




(119905) = minus119892119908 (119905119894) = V (119905119894)

1015840 (119905119894) = 1015840119894 (14)



119906 (119905119896) = 119908 (119905119896) (16)

That is


(17)




119898119906 (119905119896) + 119898119908 (119905119896) = 1198981199061015840 (119905119896) + 1198981199081015840 (119905119896) (19)


1198902 = 1015840119896 minus 1015840119896119896 minus 119896 (20)


1015840 (119905119896) = V119896

1015840 (119905119896) = 119896 minus 119898119906119898119906 + 119898119908 (1 + 1198902) (119896 minus 119896) (21)









Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0


Drill tool

Time (ms)




5 Experiments



10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)






0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










+

+

v

PZTceramics

Rotaryunit

Percussiveunit

Drilltool

v

Sleeve

minus

minus

(a)

Freemass

Percussivehorn

Drillingbit

Rotor

Storingspring

V-LTcoupler

Preloadspring

278

Φ 64

(b)


~


Fixed

++







Storingspring

Preloadforce

Rotor

V-LTcoupler

Free mass

Percussivehorn

Drill tool

Rotatingdirection

(a)

(b)

(c)

(d)

t = (n + 1)T

t = (n +1

4)T

t = (n +1

2)T

t = (n +3

4)T













Percussivehorn

Free mass

Drill tool

(a)

u(t)

w(t)

v(t)

Y

O

X

v(0)

wk

wkwkminus1 wk+1 w

k+1

wi wi

wi+1 wi+1

L0

tkminus1 ti tk ti+1

(b)




119906 (119905) = 1198600 cos (2120587119891119905) (1)


(119905) = minus21205871198911198600 sin (2120587119891119905) (2)



1015840 (119905119896minus1) = 1015840119896minus1(3)






V (119905) + 119888119898VV (119905) + 1198960119898V

V (119905) = 0 (6)







V (119905119894) = 119908 (119905119894) (8)That is







(10)


119898VV (119905) + 119898119908 (119905) = 119898VV1015840 (119905) + 1198981199081015840 (119905) (11)



1198901 = 1015840119894 minus V1015840119894V119894 minus 119894 (12)




(119905) = minus119892119908 (119905119894) = V (119905119894)

1015840 (119905119894) = 1015840119894 (14)



119906 (119905119896) = 119908 (119905119896) (16)

That is


(17)




119898119906 (119905119896) + 119898119908 (119905119896) = 1198981199061015840 (119905119896) + 1198981199081015840 (119905119896) (19)


1198902 = 1015840119896 minus 1015840119896119896 minus 119896 (20)


1015840 (119905119896) = V119896

1015840 (119905119896) = 119896 minus 119898119906119898119906 + 119898119908 (1 + 1198902) (119896 minus 119896) (21)









Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0


Drill tool

Time (ms)




5 Experiments



10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)






0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Storingspring

Preloadforce

Rotor

V-LTcoupler

Free mass

Percussivehorn

Drill tool

Rotatingdirection

(a)

(b)

(c)

(d)

t = (n + 1)T

t = (n +1

4)T

t = (n +1

2)T

t = (n +3

4)T













Percussivehorn

Free mass

Drill tool

(a)

u(t)

w(t)

v(t)

Y

O

X

v(0)

wk

wkwkminus1 wk+1 w

k+1

wi wi

wi+1 wi+1

L0

tkminus1 ti tk ti+1

(b)




119906 (119905) = 1198600 cos (2120587119891119905) (1)


(119905) = minus21205871198911198600 sin (2120587119891119905) (2)



1015840 (119905119896minus1) = 1015840119896minus1(3)






V (119905) + 119888119898VV (119905) + 1198960119898V

V (119905) = 0 (6)







V (119905119894) = 119908 (119905119894) (8)That is







(10)


119898VV (119905) + 119898119908 (119905) = 119898VV1015840 (119905) + 1198981199081015840 (119905) (11)



1198901 = 1015840119894 minus V1015840119894V119894 minus 119894 (12)




(119905) = minus119892119908 (119905119894) = V (119905119894)

1015840 (119905119894) = 1015840119894 (14)



119906 (119905119896) = 119908 (119905119896) (16)

That is


(17)




119898119906 (119905119896) + 119898119908 (119905119896) = 1198981199061015840 (119905119896) + 1198981199081015840 (119905119896) (19)


1198902 = 1015840119896 minus 1015840119896119896 minus 119896 (20)


1015840 (119905119896) = V119896

1015840 (119905119896) = 119896 minus 119898119906119898119906 + 119898119908 (1 + 1198902) (119896 minus 119896) (21)









Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0


Drill tool

Time (ms)




5 Experiments



10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)






0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Percussivehorn

Free mass

Drill tool

(a)

u(t)

w(t)

v(t)

Y

O

X

v(0)

wk

wkwkminus1 wk+1 w

k+1

wi wi

wi+1 wi+1

L0

tkminus1 ti tk ti+1

(b)




119906 (119905) = 1198600 cos (2120587119891119905) (1)


(119905) = minus21205871198911198600 sin (2120587119891119905) (2)



1015840 (119905119896minus1) = 1015840119896minus1(3)






V (119905) + 119888119898VV (119905) + 1198960119898V

V (119905) = 0 (6)







V (119905119894) = 119908 (119905119894) (8)That is







(10)


119898VV (119905) + 119898119908 (119905) = 119898VV1015840 (119905) + 1198981199081015840 (119905) (11)



1198901 = 1015840119894 minus V1015840119894V119894 minus 119894 (12)




(119905) = minus119892119908 (119905119894) = V (119905119894)

1015840 (119905119894) = 1015840119894 (14)



119906 (119905119896) = 119908 (119905119896) (16)

That is


(17)




119898119906 (119905119896) + 119898119908 (119905119896) = 1198981199061015840 (119905119896) + 1198981199081015840 (119905119896) (19)


1198902 = 1015840119896 minus 1015840119896119896 minus 119896 (20)


1015840 (119905119896) = V119896

1015840 (119905119896) = 119896 minus 119898119906119898119906 + 119898119908 (1 + 1198902) (119896 minus 119896) (21)









Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0


Drill tool

Time (ms)




5 Experiments



10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)






0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(10)


119898VV (119905) + 119898119908 (119905) = 119898VV1015840 (119905) + 1198981199081015840 (119905) (11)



1198901 = 1015840119894 minus V1015840119894V119894 minus 119894 (12)




(119905) = minus119892119908 (119905119894) = V (119905119894)

1015840 (119905119894) = 1015840119894 (14)



119906 (119905119896) = 119908 (119905119896) (16)

That is


(17)




119898119906 (119905119896) + 119898119908 (119905119896) = 1198981199061015840 (119905119896) + 1198981199081015840 (119905119896) (19)


1198902 = 1015840119896 minus 1015840119896119896 minus 119896 (20)


1015840 (119905119896) = V119896

1015840 (119905119896) = 119896 minus 119898119906119898119906 + 119898119908 (1 + 1198902) (119896 minus 119896) (21)









Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0


Drill tool

Time (ms)




5 Experiments



10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)






0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Disp

lace

men

t (m

m)

0 10 20 30 40 50

minus06

minus03

0


Drill tool

Time (ms)




5 Experiments



10 20

Disp

lace

men

t (m

m)

minus06

minus03

0

02Percussive horn

Free mass

Drill tool

0Time (ms)






0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 500

05

10Ki

netic

ener

gy (J

)

Impact numbers

2 g

(a)

0

05

10

Kine

tic en

ergy

(J)


4 g

(b)

0

05

10

Kine

tic en

ergy

(J)


6 g

(c)

0

05

10

Kine

tic en

ergy

(J)


8 g

(d)



Percussivehorn

Free mass

Drill tool






6 Conclusions



minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus06

minus04

minus02

0

02

04

0 100 200 300 400Time (ms)

Disp

lace

men

t (m

m)


0 100 200 300 400Time (ms)

minus80

minus40

0

40

80

Velo

city

(mm

s)


001

0203

0600

1200

minus03

0

03


Am

plitu

de (m

m)



0 2 4 6 80

01

02

03

04

Impa

ct k

inet

ic en

ergy

(J)




Test bed of RPUD(a)

0 2 4 6 80

5

10

15

20

25



Dril

ling

dept

h (m

m)

(b)






Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Acknowledgments


References






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









impact dynamics of a percussive system based on rotary...

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