Effect of ultrasound on dynamics characteristic of the cavitation bubble in grinding fluids during honing process

Accepted Manuscript Effect of ultrasound on dynamics characteristic of the cavitation bubble in grinding fluids during honing process Ce Guo, Xijing Zhu PII: DOI: Reference:

S0041-624X(17)30581-4 https://doi.org/10.1016/j.ultras.2017.09.016 ULTRAS 5621

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Ultrasonics

Received Date: Revised Date: Accepted Date:

30 June 2017 29 August 2017 22 September 2017

Please cite this article as: C. Guo, X. Zhu, Effect of ultrasound on dynamics characteristic of the cavitation bubble in grinding fluids during honing process, Ultrasonics (2017), doi: https://doi.org/10.1016/j.ultras.2017.09.016

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Effect of ultrasound on dynamics characteristic of the cavitation bubble in grinding fluids during honing process Ce Guo1, 2, *, Xijing Zhu2 1

Shanxi Key Laboratory of Precision Machining, Taiyuan University of Technology, 030024

Taiyuan, China 2

Shanxi Key Laboratory of Advanced Manufacturing Technology, School of Mechanics and

Power Engineering, North University of China, 030051 Taiyuan, China * Corresponding author E-mail address: [email protected] Abstract: The effect of ultrasound on generating and controlling the cavitation bubble of the grinding fluid during ultrasonic vibration honing was investigated. The grinding fluid on the surface of the honing stone was measured by utilizing the digital microscope VHX-600ESO. Based on analyzing the cavitation mechanism of the grinding fluid, the bubble dynamics model under conventional honing (CH) and ultrasonic vibration honing (UVH) was established respectively. Difference of dynamic behaviors of the bubble between the cases in UVH and CH was compared respectively, and the effects of acoustic amplitude and ultrasonic frequency on the bubble dynamics were simulated numerically using the Runge-Kutta fourth order method with variable step size adaptive control. Finally, the cavitation intensity of grinding fluids under ultrasound was measured quantitatively using acoustimeter. The results showed that the grinding fluid subjected to ultrasound can generate many bubbles and further forms numerous groups of araneose cavitation bubbles on the surface of the honing stone. The oscillation of the bubble under UVH is more intense than the case under CH, and the maximum velocity of the bubble wall under UVH is higher two magnitudes than the case under CH. For lower acoustic amplitude, the dynamic behaviors of the bubble under UVH are similar to that case under CH. As increasing acoustic amplitude, the cavitation intensity of the bubble is growing increased. Honing pressure has an inhabitation effect on cavitation effect of the grinding fluid. The perfect performance of cavitation of the grinding fluid can be obtained when the device of UVH is in the resonance. However, the cavitation intensity of the grinding fluid can be growing weakened with increasing ultrasonic frequency, when the device of UVH is in the off-resonance. The experimental results agree with the theoretical and numerical analysis, which provides a method for exploring applications of the cavitation effect in ultrasonic assisted machining. Keywords: Ultrasound ; Cavitation; Honing; Bubble; Dynamics model 1.

Introduction 1

Honing is a precise machining process for finishing internal or external cylindrical surfaces such as cylinder liners for internal combustion engines [1]. Lubrication and cooling in the honing process play a primary role to avoid thermal damage much of material surface. In conventional honing machining, a spiral cross honing textured of the material surface for lubrication and oil storage can be prepared by applying honing pressure and honing velocity of reciprocating and rotation motion [2]. However, due to using lower-end technology, conventional honing (CH) has faced many challenges such as blockage of honing stones, low processing efficiency and low machining accuracy [3]. Thus, some new honing techniques have constantly appeared and been rapidly applied, such as plateau honing [4], ELID honing [5], laser honing [6], and ultrasonic vibration honing (UVH) [7]. In the application process of honing, the uneven material surface of plateau honing is often produced under the action of abrasives of honing stones, while the geometric deviation of the material surface of ELID honing is hard to correct. In addition, negative thermal effects caused by laser honing are difficult to overcome. Compared with CH, the technology of UVH is an advanced precision machining of ultrasonic vibration-assisted machining [8], which has been widely used to honing hard-brittle materials such as CrMoCu ally [9], NdFeB [10] and ZrO2 ceramics [11], etc. However, until now, the mechanism of effect of ultrasonic wave upon honing process has not been clearly revealed. The effect of ultrasound on the honing process is recognized primarily in the following two aspects. On the one hand, honing stones are employed with constant ultrasonic frequency (18-22 kHz) and amplitude (10-20 μm) [12]. On the other hand, grinding fluids under effect of ultrasound may cause cavitation effect, and then generates a great number of cavitation bubbles [13]. Generally, occurrence of cavitation accompanies with the extreme variation of a pressure gradient between the bubble interior and exterior. When the cavitation bubble in a liquid collapses violently, the extreme pressure (up to tens of GPa) and temperature (up to thousands K of GPa) can be released [14]. The first theoretical model for describing cavitation effect under ultrasound was derived by Rayleigh [15]. Philipp [16] reported that the collapse velocity of the bubble wall near to a rigid wall is one of a main reason of cavitation damages. Brujan [17-18] after a series of acoustic cavitation experiments has found that the bubble near to a rigid wall can generate a fast liquid micro-jet and a strong shock wave, which can further cause material damage. Those extreme conditions have been widely used in the applications of ultrasonic cleaning, acoustic chemical, water jet cutting and sewage treatment, etc. Although, many foundation investigations have been done to explore the cavitation effect, the method for predicting and controlling cavitation bubbles is always difficult to obtain effectively, due to the complex nature mechanism and numbers influence factors [19]. Especially for engineering fields, the cavitation bubble will be further affected by some specific engineered factors. Thus, the research of cavitation effect during processing is still in 2

the stage of exploring in quite a few fields of precision processing such as ultrasonic micro machining [20], ultrasonic drilling [21], ultrasonic assisted honing [22], and other fields. For UVH, the violently vibratory bubbles and their repeated collapse sending micro-jets and shocks and other effects can greatly improve the performance of grinding conditions. It plays very important role in honing processing, in particular for enhancing machining precision and efficiency, suppressing chatter and noise and optimizing honing conditions. However, it is not easy to exactly control and utilize cavitation in grinding fluids due to its numerous influencing factors such as grinding fluid properties, honing pressure and velocity, and ultrasonic driving parameters. Generally, the grinding fluid is needed to cooperate with honing machine and materials after a period of adjustment, and not convenient to adjust and control. The selection of honing pressure is more related to the material removal of workpiece and the wear of honing stones. In addition, the honing velocity is so lower compared with sound velocity in the liquid that its effect on cavitation is quite small. To obtain better parameters control of cavitation, we have conducted the research on the dynamics of cavitation bubbles in the grinding fluid under UVH and CH. Firstly, the grinding fluid bubble was examined using digital microscope. Secondly, the bubble dynamics model under CH and UVH were established respectively and accordingly comparative study was further addressed in detail. The effects of acoustic amplitude and ultrasonic frequency on the bubble oscillation and pressure pulse were then analyzed and discussed. Finally, the cavitation intensity of the grinding fluid was measured under various ultrasonic parameters to verify the results of numerical calculations. It will be favorable to predict and control the bubble in grinding fluids and further to understand the grinding mechanisms of ultrasonic assisted honing. 2.

Cavitation of the grinding fluid under ultrasonic vibration honing

2.1. Cavitation mechanism of the grinding fluid The schematic diagram of the work principle of UVH is shown in Fig.1. An ultrasound generator is used to send a signal to a piezoelectric transducer to generate ultrasonic vibration. The amplitude of ultrasonic vibration is then amplified by a horn, and finally transmitted to the honing stone using other transmission components of structural vibration [23]. In this process, honing pressure ph is commonly applied on the surface of honing stones using honing tool expansion and contraction mechanism. In addition, the same honing device can be used for both UVH and CH. Unlike UVH, the ultrasonic generator is switched off during the CH. In the machining of UVH or CH, the effect of lubrication and cooling for the grinding area should be examined cautiously. In order to ensure obtaining a more superior grinding area, a great number of grinding fluids are injected continuously with the help of a jet nozzle. 3

Fig.1. Schematic diagram of the work principle of UVH.

It is noticed that the space region of the grinding area during honing is usually narrow. Thus continuous grinding fluids under actions of the honing disturbances such as honing pressure and honing velocity can be easily scattered into tiny liquids or bubble nucleus. The honing velocity vh of a honing stone applied to the grinding fluid is given by

vh  va2  v 2

(1)

where, va is the reciprocating velocity of a honing stone, and v is the rotation velocity of a honing stone. The function v can also become another form v =πdn, here, d is the diameter of the honing head, and n is the revolving speed of the honing device. In fact, the stability of the cavity nuclei in the grinding fluid during honing is so weak that some of those nuclei may collapse directly, and others may be kept in the microstructure of honing stones or material surfaces. Perturbations of fluid pressure and velocity can lead to a state where cavitation occurs easily. The complexity of cavitation occurrence in a liquid can be expressed by the cavitation number σ [24].



pc  pv uc2 / 2

(2)

where, pc and uc are the ambient pressure and flow velocity without considering fluid perturbations respectively, pv is the vapor pressure, ρ is the density of the liquid. Eq. (2) shows the normalized cavitation numbers in a liquid. Different types of cavitation of liquid medium have different cavitation numbers. The smaller the cavitation number is, the more likely cavitation occurs. Thus, cavitation can be roughly viewed as caused by lower ambient pressure, higher ambient flow velocity or liquid temperature, in theory. However, experiments demonstrated that cavitation effect can be found actually with the cavitation number at 1~2.5[25]. For CH, honing pressure and honing velocity are significant external factors for generating cavitation and their effects on the grinding fluid are similar to the fluid under a 4

helical blade [26]. Thus, same types of hydrodynamic cavitation such as shifting cavitation and vortex cavitation may be noted in the machining of CH. Besides the types of cavitation in CH, for UVH, ultrasonic wave through the grinding fluid can become another important cause to generate ultrasonic cavitation. Although many theoretical and experimental investigations on the dynamic behaviors of cavitation bubbles under ultrasound have been carried out, the effective approach to reveal the cavitation mechanism of the grinding fluid under CH and UVH still has needed to be dealt with. For an actual pure liquid, a higher negative pressure is needed to produce cavities due to the large tensile strength of the liquid [27]. However, any grinding liquid, owing to its nature, always includes a suspension of submicroscopic particles and a few gaseous phase species in structural defects in the grinding area, which can act as cavity nuclei. Thus, a certain intensity ultrasonic wave through the grinding liquid will create a negative pressure zone around the structural defect, and cause the liquid-liquid or liquid-solid coupling interface fracture, and then result in the occurrence of cavitation bubbles. Anti-fracture ability of coupling interface can be described by the critical negative pressure p B , which is also called the cavitation threshold. Given any bubble of an initial radius R0 , the cavitation threshold p B can be expressed by [28]

p B  p0  pv 

(2 / R0 ) 3 p0  pv  2 / R0

2 3 3

(3)

where, p0 is the ambient static pressure, pv is the vapor pressure, and  is the liquid surface tension. For large bubbles, that is p0  2 / R0 and pv  p0 , Eq. (3) can be simplified to

p B  p0 

8 3 1 / 2 ( ) 9 2 p0 R0

(4)

And for small bubbles, that is p0  2 / R0 , and pv  p0 , Eq. (3) can be reduced to

pB  p0  0.77

 R0

(5)

Thus, the cavitation threshold should be influenced by various bubble sizes. If the bubble radius is relatively large, the cavitation threshold is mainly influenced by the liquid surface

tension (see Eq. (4)); otherwise the cavitation threshold is determined by ambient static pressure of the grinding fluid (see Eq. (5)). In the honing process, water and kerosene are usually selected as the grinding fluid. For the bubble in water at 20 ºC (σ =0.07275 N/m, pv = 2.34×103 Pa, p0 = 0.1 MPa), the cavitation threshold is 9.773×104-9.968×104 Pa when the bubble size is ranged of 10-100 μm. Similarly, for the bubble in kerosene at 20 ºC (σ =0.024 N/m, pv = 4.67×103 Pa, p0 = 0.1 MPa), the corresponding cavitation threshold is 5

9.534×104-9.574×104 Pa. The negative pressure zone is a key condition to form cavitation. In order to create a negative pressure zone more likely, the cavitation threshold must be overcame, under the action of comprehensive effects of ultrasonic wave, honing pressure and velocity and so on. Thus, it is much easier to produce cavitation in kerosene due to the lower cavitation threshold. This may be an important reason that water is usually selected in coarse honing and kerosene is chosen in fine honing. Moreover, owing to some structural defects

included in the grinding fluid, the actual cavitation threshold is far less than the theoretical calculation of Eq. (4) and Eq. (5). 2.2.

Experimental observation of bubbles of the grinding fluid

The time duration of a bubble oscillation under strong ultrasonic field is very rapid. It is sometimes difficult to capture visually the resonance state of the bubble motion. The technology of high speed imaging is usually used to record the dynamic behaviors of bubbles in a liquid. Image analysis for the bubble motion is examined according to the series images taken at a frame rate of same fixed frames per second. The target position of cavitation under UVH is focused on the grinding area. As shown in Fig.1, the grinding area is composed of the honing stone surface, workpiece surface and grinding fluids between them. Moreover, it can be regarded as a semi-closed or extremely narrow space, which is not easy to film the grinding fluid using high speed photography in real-time. In order to make the observation of grinding fluids possible, it is necessary to simplify the grinding area. The reciprocating and rotation of honing velocity are ignored due to their lower values and small contributions to cavitation. The honing pressure is not exerted during observation and its effect on cavitation can be obtained through a prediction for cavitation bubble dynamics. The grinding fluid is estimated to evenly distribute on the surface of honing stones. Thus, the grinding fluid on the surface of honing stones can become the object of concern, and it can be seen as a comparatively ideal observation study to explore cavitation under UVH. Taking into account facility and feasibility for users, the digital microscope is used to examine the dynamic behaviors of bubbles of the grinding fluid. Fig. 2(a) presents a schematic diagram of the experimental equipment. The experimental equipment consists of the following: Machine tool: ultrasonic vibration honing device Ф47, resonant frequency 18.6 kHz, amplitude of a honing stone 10 μm Ultrasound generator: H66MC, maximum power 250 W, frequency ranges of 18.0 to 22.0 kHz Observation instrument: digital microscope VHX-600ESO (Keyence, Japan), Microlens VH-Z500R, Zoom 5000, Speed 5000fps, 54 million pixels Other equipment: jet nozzle, sheet glass 50×100×3 mm, grinding fluid (water), etc 6

Fig.2. Schematic diagram of the experimental equipment

Fig.3. Measurements of cavitation bubbles on the surface of a honing stone. (a)Without ultrasonic vibration (×2000); (b) With ultrasonic vibration (×2000).

Before the measurement, the microscope lens should be shielded with the sheet glass. A certain amount of water with jet nozzle was sprayed evenly on the surface of a honing stone. And then, the ultrasound generator was switched on and the ultrasonic vibration honing device was regulated to its resonant state. After a few seconds, the ultrasound wave was switched off and then the glass was removed. The grinding fluid of the surface of a honing stone was measured by digital microscope VHX-600ESO, and the results were shown in Fig. 3. Fig. 3(a) shows the surface topography of the honing stone without ultrasonic vibration. The red circles in Fig. 3(a) are the dripping water solution sprayed on the surface of a honing stone. It can be observed that there are several groups of droplets at the surface of a honing stone. This may be due to the fact that the surface of a honing stone has always a layer of oil film after honing processing. It can form groups of droplets in water solution as the dispersed phase, under the actions of microstructures of the honing stone and surface tension of the oil film and so on. Fig. 3(b) shows the surface topography of the honing stone with ultrasonic vibration. In Fig. 3(b), the ultrasonic resonant frequency is 18.6 kHz, and the acoustic pressure is estimated as 1MPa. From Fig. 3(b), droplets under ultrasonic wave have become a mixture state including gas, liquid and solid phases. Since the acoustic pressure value of the 7

honing stone is more than the cavitation threshold (up to liquid static pressure, 0.1 MPa) of water, the cavities begin to appear and eventually form a great many of cavitation bubbles. These cavitation bubbles under the influence of their interactions and the surface tension of oil film and the microstructure of the honing stone may result in several groups of araneose bubbles. It means that ultrasonic vibration has an obvious effect on the production of cavitation bubbles in the grinding fluid. In addition, the actual behaviors of bubbles under UVH may be more complicated due to our experiment not taking honing velocity and pressure into consideration. 3.

Mathematical model and numerical method The motion of cavitation bubbles can be described by the bubble dynamics model. To gain

more easily engineering control for cavitation of the grinding fluid, the cavitation bubble dynamics under UVH should be discussed in detail. In the past, many scholars have carried out a series of studies in regards to modeling and analysis of a cavitation bubble. Rayleigh [14] firstly proposed an equation to account for the dynamic behaviors of a bubble and afterwards, the equation was modified by Plesset [29]. The revised model is well known as classical Rayleigh-Plesset equation. The Rayleigh-Plesset equation and its successive revised versions have been widely used in cavitation research and applications. Thus, in view of engineering environment of the grinding fluid, a modified Rayleigh-Plesset equation for honing will be proposed in this paper. 3.1.

Bubble dynamics model

The physical situation of the model during UVH is that a gas and vapor filled spherical bubble isolated in the grinding fluid under actions coupled with ultrasonic wave and honing parameters. The ultrasonic wave is assumed to be sinusoidal and beginning an expansion cycle at the initial stage. Honing disturbances including honing pressure, the velocity of honing rotating and reciprocating motion will be also added in the model. The pressure inside the bubble is assumed to be uniform spatially and the gas content of the bubble is the wan der Waals gas. The compressibility of the liquid as well as its thermal transmission and mass transfer are ignored since those factors are beyond our consideration. The hypothesis stems from the purpose of simplified engineering environment primarily. The effect of ultrasound on the cavitation bubble dynamics under different honing process is what we focused on. In the first place, let us consider the energy relation of the free bubble oscillation in the grinding fluid. Based on the principle of conversation of energy, the bubble energy under actions of the external force W can be converted to the kinetic energy Ek of the bubble and other energies ΔE, that is 8

W  Ek  E

(6)

The kinetic energy Ek of the bubble in the grinding fluid is mainly comprised of two parts, which are defined by

Ek  Ek1  Ek 2

(7)

where, Ek 1 is the energy for the bubble oscillation itself, and Ek 2 is the energy used for dealing with the bubble moving within the grinding fluid together. If the bubble oscillation is assumed to be a vibrator regarding the liquid as a load, the function Ek can be expressed as

Ek  



R

1 R 2 dR 2 2 (  vh ) 4r 2dr 2 r 2 dt

where, R is the radius of the bubble,

(8)

 is the density of the liquid and r is the distance

from the center of the bubble. In addition, the work of the external force W on the bubble can be represented as [30-31] R

W    p  4R 2dR R0

p  pg  pv 

2 4 dR   p0  ph  pa sin 2πft R R dt

(9) (10)

where, pg is the gas pressure inside the bubble, pv is the vapor pressure,  is the liquid surface tension,

 is the liquid viscosity, p0 is the ambient static pressure of the grinding

fluid, ph is the honing pressure, pa is the acoustic amplitude and f is the ultrasonic frequency. Substituting Eq. (8) -Eq. (10) into Eq. (6), and ignoring the term ΔE, the model describing the radial dynamic characteristic of the cavitation bubble under UVH can be derived as:

d 2 R 3 dR 2 3 2 1 2 4 dR R 2  ( )  vh  ( pg  pv    p0  ph  pa sin 2πft ) dt 2 dt 2  R R dt

(11)

Taking into account the acoustic radiation losses of the bubble caused by the compressibility of the grinding fluid, Eq. (11) can be represented as

R

d 2 R 3 dR 2 3 2 1 2 4  dR  ( )  vh  ( pg  pv   2 dt 2 dt 2  R R dt R d  p0  ph  pa sin 2πft )  ( p  pa sin 2πf )  c dt g

(12)

If without regarding to the factors of honing pressure and velocity, Eq. (12) can be described as

R

d 2 R 3 dR 2 1 2 4  dR  ( )  ( pg  pv   2 dt 2 dt  R R dt R d  p0  pa sin 2πft )  ( p  pa sin 2πf )  c dt g 9

(13)

The above equation can be used to describe the bubble dynamics in the grinding fluid with turning on ultrasound but without conducting honing process, which is the case of ultrasonic vibration (UV). It should be noted that the gas inside a bubble is usually assumed to be adiabatic for the reason that the gas undergoes so fast a cycle of expansion and collapse. This assumption may lead to a computational error, especially in the process of expansion and compression of the bubble calculated under higher pressure acoustic amplitude. As the variation of the radial of the bubble wall is relatively slow from growth to begin to collapse, this process may be assumed as isothermal. That is, when R0 ≤ R ≤ Rmax (Rmax is the maximum radius of the bubble), the gas pressure inside the bubble pg can be expressed as [32-33]

pg  pg 0 (

V0 3 R )  pg 0 ( 0 )3 V R

(14)

where, V is the volume of the bubble, V0 is the initial volume of the bubble, R0 is the initial radius of the bubble,  is the adiabatic index, pg = kp0 + 2σ/R0-pv, is the initial pressure inside the bubble, and k (0 < k ≤1) is the variation coefficient of the gas content of the bubble. Moreover, in the process of bubble compression and collapse, the strong nonlinear variation of the bubble wall is found out, which can be considered as an adiabatic process. That is, when Rmin ≤ R≤ R0 (Rmin is the minimum radius of the bubble), the gas pressure inside the bubble pg can be expressed as

V0 3 R03  pg  pg 0 ( )  pg 0 ( 3 ) V R  a3

(15)

where, a is used to describe the characteristic wan der Waals hard-core radius of the gas inside the bubble (R0 / a = 8.54). Comparing the revised model Eq. (11) with Zhu’s model [30], one can see that the model used in this study not only reserves the special terms of parameters of UVH such as ph , vh , but also revises the term of the gas pressure inside the bubble pg . In addition, the revised model considers the term of acoustic radiation losses of the bubble, which should be more accurate in calculating process. If we do not consider the effect of ultrasound wave but consider the effect of honing pressure and velocity, Eq. (12) can be represented as

R

d 2 R 3 dR 2 3 2 1 2S 4 dR R dpg  ( )  vh  ( pg  pv  p0  ph   ) 2 dt 2 dt 2  R Rdt  c dt 10

(16)

The above bubble model, that is Eq. (16), can be employed to describe the dynamic behaviors of the bubble under CH. Cavitation and bubble dynamics are a comprehensive phenomenon composed of many complex physical and chemical effects, such as extreme temperatures, pressures and cooling rates, etc. Each of these effects can be used to characterize the intensity of cavitation. In this study, a typical physical quantity is introduced to describe the cavitation intensity, which is referred to acoustic intensity. The acoustic intensity I released by the bubble is correlated with the pressure difference p between the bubble and the grinding liquid, using following expression:

1 p2 I   pdt  T c

(17)

The pressure difference p is calculated by Eq. (10), which can be rewritten as

p  pg  p where p  pv 

2 4 dR   p0  ph  pa sin t R R dt

(18) (19)

The gas pressure inside the bubble p g expands rapidly during the bubble compression ( R  Rmin ), and reaches a maximum pg  pmax at the end of the bubble collapse ( R  Rmin ). The maximum pressure pmax during the bubble collapse can be approximated by [32]

pmax  [ pv  pg 0 (

R0 3 Rmax 3 ) ]( ) Rmax Rmin

(20)

Note that, the maximum pressure inside the bubble is usually several orders higher than other pressures, that is pg  p , and thus one can take p  pg . Thus, combining Eq. (20) with Eq. (17), an approximation formula is obtained to describe and predict the cavitaiton intensity in the grinding fluid, as follows

I

1 R R [ pv  pg 0 ( 0 )3 ]2 ( max )6 c Rmax Rmin

(21)

where, Rmax and Rmin can be calculated from the bubble dynamics in the grinding fluid and then one can obtain I  Rmax / Rmin . 3.2. Numerical method and initial conditions Using Runge-Kutta fourth order method with variable step sizes adaptive control, integrating Eq. (14) and Eq. (15), the bubble model of Eq. (12), Eq. (13) and Eq. (16) can be numerically calculated respectively. The initial conditions for the simulation are when t = 0, R = R0, dR/dt=0. Based on previous experimental conditions of UVH and physical properties of 11

grinding fluids, we have used numerical simulation data from Refs. [22, 30, 31]. The values of the physical properties of liquid kerosene and the process parameters of ultrasonic vibration honing are ρ = 803 kg/m3, c = 1324 m/s, μ =1.92 mPa·s, σ = 0.024 N/m, γ = 5/3, k = 0.8, pv = 4.67×103Pa, p0 = 0.3 MPa, ph = 0.4 MPa, n = 80 r/min, va = 0.05 m/s, d = 47 mm. 4.

Results and discussion

4.1. Difference of dynamic behaviors of the bubble between the cases in UVH and CH It is well known that the initial radius of the bubble is a crucial parameter affecting cavitation experiment, particularly depending on the acoustic amplitude and ultrasonic frequency [34]. According to the experimental results of the observation for bubbles of the grinding fluid, there are lots of bubbles with various initial radii at random distributed in the microstructure of honing stones, material surfaces or grinding fluids. Usually, different initial radii of the bubble under the same ultrasonic wave can present different variation. The size of most of the bubbles for an ultrasonic frequency at around 20 kHz is usually in the range of a few hundred micrometers [35]. But because the grinding fluid always exists various dissolved gases and suspended impurities particles, the bubble size may be one to two orders of magnitude lower than the theoretical value. Numerical calculations for an ultrasonic frequency of 18.6 kHz and acoustic amplitude of 0.8 MPa have been performed for different initial radii of the bubbles (10, 20, 50 and 100 μm) under UVH. Normalized values of the bubble radius (R/R0) are shown in Fig. 4(a), as function of time (t) for the four selected initial radius of the bubble. From Fig. 4(a), it is quite clear that the bubble in the grinding fluid under UVH presents the dynamic behaviors of growth, expansion, rapid implosion collapse and rebound. As the initial radius of the bubble increases, the maximum radius of the bubble (Rmax) is growing decreased and oscillation interval is extended. This may be explained that for a higher initial radius of the bubble, the pressure inside the bubble makes the bubble being arduous to compress. Fig. 4(b) gives the bubble wall velocity dR/dt versus the normalized values of the bubble radius (R/R0) in the process of bubble compression. As can be viewed, the maximum velocity of the bubble wall can be gained instantaneously, when the bubble is compressed to the minimum radius (Rmin). With the initial radius of the bubble increasing, the minimum radius (Rmin) is gradually increased, and the maximum velocity of the bubble wall is also reduced. This observation indicates that the cavitation intensity produced by the collapsing bubble will be growing deduced with increasing initial radius of the bubble. Vignoli [36] reported that the high speed micro-jet and violent shock wave may be generated, when the bubble wall velocity during the final stage of collapse is much higher than even the speed of sound in the liquid. Thus, in Fig. 4(b), smaller bubbles with initial radii of 10, 20 μm can obtain the micro-jet and violent shock wave much 12

more easily than other sizes.

Fig.4. Dynamic behaviors of the bubble of the grinding fluid under UVH for various initial bubble radii. (a) Normalized values of the bubble radius (R/R0) versus time (t) curves. (b) Bubble wall velocity (dR/dt) versus the normalized values of the bubble radius (R/R0) in the process of bubble compression.

Unlike UVH, honing pressure, honing velocity and other external disturbances are the most critical influences on the dynamic behaviors of the bubble in the grinding fluid under CH. Thus, numerical simulations are done with the same situation as in Fig. 4, except for the ultrasonic frequency and acoustic amplitude. The dynamic behaviors of the bubble under CH are described in Fig. 5. Fig. 5 (a) is the normalized values of the bubble radius (R/R0) versus time (t) under CH for the initial radii of the bubble set at 10, 20, 50 and 100 μm, respectively. As showed in Fig. 5 (a), the bubble under CH is compressed directly to the minimum value and then rebound many times. What is more, the oscillation amplitude of the bubble decreases gradually, as the time continues by. From Fig. 5 (a), it is also found that as the initial radius of the bubble increases, the minimum radius of the bubble compression increases gradually, and the oscillation interval is extended. According to the initial conditions, the values of honing velocity are relatively small to the bubble wall velocity, and its effects on the bubble can be neglected. Thus, honing pressure is to be the main influences on the bubble dynamics under CH and its effect on the bubble dynamics is pronounced on the inhibition growth of the bubble. In actual machining of honing, higher honing pressure has put forward higher requirements on structural strength and stiffness of the machine tool and honing device [37, 38]. Moreover, from the point of this paper, higher honing pressure can weaken cavitation of the grinding fluid, and this can be different significant reason for selection of honing pressure. Fig. 5(b) gives the bubble velocity (dR/dt) versus the normalized values of the bubble radius (R/R0). As can be seen, evolution of the bubble velocity is similar to a spiral shape repeatedly and differences between the bubbles with various initial radii are relatively low. Compared with Fig. 4 and Fig. 5, it can be seen that the oscillation of the bubble in the case 13

under UVH is more intense than the case under CH, and the maximum velocity of the bubble wall in the case under UVH is higher two magnitudes than the case under CH. Thus, compared with CH, the produced oscillation bubble under UCH can provide more sufficient additional impact energy to remove and clean the materials’ internal surface, which improves the honing processing efficiency directly [39]. In the next section, how do the acoustic amplitude and ultrasonic frequency affect cavitation of grinding fluids will be discussed in the detail.

Fig.5. Dynamic behaviors of the bubble in the grinding fluid under CH for various initial bubble radii. (a) Normalized values of the bubble radius (R/R0) versus time (t) curves. (b) Bubble wall velocity (dR/dt) versus the normalized values of the bubble radius (R/R0).

4.2.

Effects of acoustic amplitude

Fig. 6(a) shows the normalized values of the bubble radius (R/R0) versus time (t) under UVH for an initial radius of the bubble of 20 μm under an ultrasonic frequency of 18.6 kHz for various acoustic amplitudes (0.4-1.0 MPa). As can be seen, when pa
of the acoustic amplitude, the shrinkage of the bubble radius is increasingly reduced during the bubble collapse phase. Such as for pa = 1.0 MPa, the bubble collapses highly violently up to 6% its maximum radius. Moreover, in the present model, the compression phase is assumed to be adiabatic and the mass transfer and heat exchange are neglected. That assumption can be explained as follows. The collapse time from the initial radius compressed to the minimum of the bubble is defined as tcollapse. Values of tcollapse are listed in Table 1. As can be show in Table 1, for smaller acoustic amplitude, the collapse time of the bubble is longer. With the increase of the acoustic amplitude, the collapse time of the bubble is induced. In addition, the collapse time of the bubble under UV is one order lower than that under UVH. That means the bubble under UV is a lot easier to collapse. The process of the bubble collapse is affected by the time scale of gas diffusion. The time scale of gas diffusion tdiff can be expressed as tdiff  R02 D , and D is the diffusion coefficient (D=10-9 m2/s) [41]. So that, when R0=20 μm, tdiff =0.4s. Compared tdiff with tcollapse, it is concluded that tcollapse << tdiff. In other words, for whatever UVH or UV, the pressure inside the bubble during the adiabatic collapse has insufficient time to escape and can be recognized as “trapped” in the bubble. Thus, it is reasonable to expect the adiabatic process during the bubble collapse. Table 1 Collapse time of various acoustic amplitudes under UVH and UV

tcollapse /μs

Pa /MPa 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

UV

0.15

0.05

0.02

0.01

0.01

0.01

0.01

0.01

UVH

0.79

0.79

0.768

0.68

0.13

0.03

0.03

0.02

The energy of the collapsing bubble is proportional to the expansion-compression ratio of the bubble (Rmax /Rmin). The ratio (Rmax /Rmin) can be used to describe indirectly the intensity of cavitation. Fig. 6(b) shows the expansion-compression ratio of the bubble versus acoustic amplitude under UVH and VH, setting the initial parameters same as Fig. 6(a). It can be seen that as the increase of acoustic amplitude, the ratio (Rmax /Rmin) is growing increased both in the UVH and the VH cases. However, the ratio (Rmax /Rmin) in the case of UV is higher than that in the UVH case. It means that corresponding to CH, honing pressure also has an inhabitation effect on cavitation effect of the grinding fluid under UVH, which can be seen from Fig. 6(a). Furthermore, the higher acoustic amplitude under UVH needs much greater the amplitude of each honing stone, to some extent. This not only puts forward requirements for the design of ultrasonic vibration system of UVH, but also is required to consider the energy consumption of the ultrasonic generator. Thus, in order to fit the application of honing, the maximum value of acoustic amplitude of honing stones is usually less than 2 MPa.

15

Fig.6. Effects of acoustic amplitude under UVH. (a) Normalized values of the bubble radius (R/R0) versus time (t). (b) Expansion-compression ratio of the bubble (Rmax/Rmin) versus acoustic amplitude (Pa) under UVH and VH.

4.3.

Effects of ultrasonic frequency

Fig. 7(a) shows the normalized values of the bubble radius (R/R0) versus time (t) under UVH for an initial radius of the bubble of 20 μm and acoustic amplitude of 0.8 MPa for various ultrasonic frequencies in the range of 18-22 kHz. Those ranges of values of ultrasonic frequencies are usually selected to design the device of UVH. It can be seen that as the ultrasonic frequency is increased, the maximum radius of the bubble (Rmax) is slightly reduced, and the oscillation interval is shortened. This trend indicates that the bubble growth is difficult to gain completely, while the bubble collapse is easy to perform, as increasing the ultrasonic frequency. Fig. 7(b) shows the expansion-compression ratio of the bubble versus ultrasonic frequency under UVH and VH, and the initial parameters are set as same as Fig. 7(a). As can be seen, with increasing the ultrasonic frequency, the ratio (Rmax /Rmin) is slightly decreased both in two cases (UVH and VH). This is mainly because that a higher ultrasonic frequency gives the bubble less time to expand, and furthermore it will results in weakening the bubble collapse. In addition, the ratio (Rmax /Rmin) in the case of UV is higher and complex than that in the UVH case. It also indicates that compared with the case in UV, the cavitation effect of the grinding fluid under UVH is restricted. During UVH, the ultrasonic frequency of the grinding fluid is transmitted from the honing stone and it mainly depends on the resonance state of the device of UVH. Moreover, the ultrasonic frequency may not be a fixed value strictly during honing, due to the probable phenomenon of frequency shift in the process of ultrasonic vibration system. Nevertheless, a relatively small range of frequency shift is can be accepted in machining of ultrasonic vibration system [42]. Thus, the influence of ultrasonic frequency on the dynamic behaviors of the bubble is the comprehensive results from the ultrasonic wave and the resonance state device of UVH. 16

Fig.7. Effects of ultrasonic frequency under UVH. (a) Normalized values of the bubble radius (R/R0) versus time (t). (b) Expansion-compression ratio of the bubble (Rmax/Rmin) versus ultrasonic frequency (f) under UVH and VH

4.4.

Experiment test

In order to seek a correlation between the ultrasonic driving parameters (ultrasonic frequency and acoustic amplitude) and the cavitation intensity of the grinding fluid in the case of UVH and UV, verification experiments should be carried out. However, it is difficult to measure the cavitation intensity of the grinding fluid in the process of honing, due to lack of the corresponding real-time monitoring equipment and method. In the present study, we mainly focus on the cavitation intensity of the grinding fluid during UV. The values of cavitation intensity in the grinding fluid under UV can be used to predict and control the cavitation of the grinding fluid under UVH. The range of magnitude of the cavitation intensity is especially of interest. Thus, the relationship of magnitude between those two cases under UVH and UV should be firstly discussed. The pressure generated by the pulsating bubble during an acoustic cycle can be described by the linear wave equation. If the time delay due to the finite velocity of acoustic wave propagation is ignored, the pressure pk radiated by the bubble can be expressed as [43]

pk 

 d( R 2 R ) s

dt



 s

  2 RR 2 ) (R2 R

where, s is the distance from the center of the bubble,

(22)

dots denote the time derivative.

From Eq. (12) and Eq. (22), the radiation pressure puvh produced by the bubble under UVH

can be approximately derives as follows

puvh 

4 R 1 R 1  R R R [(   )( 0 )3  ( 0 )3 ]  [3  ( 0 ) 2 ]  Zuvh [4  ( 0 )3 ] (23) s(1  k ) 3 R 3 R R s R 3s R pg 0

17

Zuvh 

1

3 [ pa sin t  p0  ph  pv ]  vh2  2

(24)

As can be seen from Eq. (23) and Eq. (24), the radiation pressure puv produced by a bubble under UV with neglecting ph and vh can be expressed as

puv 

4 R 1 R 1  R R R [(   )( 0 )3  ( 0 )3 ]  [3  ( 0 )2 ]  Zuv [4  ( 0 )3 ] (25) s(1  k ) 3 R 3 R R s R 3s R pg 0

Zuv 

1



[ pa sin t  p0  pv ]

(26)

Compared Eq. (23) with Eq. (25), a relative pressure equation to predict the interrelation between the pressure magnitude radiated by the bubble under UVH and UV can be obtained as follows

puvh  puvh  puh  (

R 3 R ph  vh2 ) [4  ( 0 ) 3 ]  2 3s R 1

(27)

From Eq. (27), it is indicated that honing pressure and velocity applied by honing machine is a major reason for weakened cavitation in the grinding fluid. The maximum pressure reduction rate can be described as (puvh ) max /( puh ) max . Thus, for the bubble with initial of 50 μm ( s  R0 , other parameters see Fig. 4), the maximum pressure reduction rate is 22.14 % at ph=0.3 MPa, but the maximum pressure can be reduced by 44.13% at ph=0.6 MPa. Furthermore, the maximum cavitation intensity from Eq. (17) and Eq. (27) can be decreased by 4.9% at ph=0.3 MPa, and 19.47% at ph=0.6 MPa. Thus, if the cavitation intensity of the grinding fluid under UV is obtained, we can carry out the theoretical cavitation intensity of that under UVH using Eq. (27) and (17). Thus, in the next section, we will focus on the cavitation intensity of the grinding fluid during UV. For experiments in research of cavitation intensity, there is not enough method of uniform quantitative from until now to describe. However, in many literatures, the cavitation intensity of liquids can be characterized by the following parameters such as temperature, voltage, acoustic pressure, acoustic intensity, and corrosion rate and so forth in some engineering applications [44-45]. In view of the feasibility of the operation, the average value of voltage was used to describe the cavitation intensity of the grinding fluid. The cavitation intensity I is related to the average value of voltage V provided by an acoustimeter as follows I  XV 2 , where X represents the correction parameter X=2). Therefore, one can take I  V .

The experimental apparatus of cavitation is described in Fig. 8. Before preparation, equipment of UVH with diameter of 47mm was fixed to MBA4215 semi-automatic vertical honing machine. The honing stone was immersed in the grinding fluid (kerosene) entirely. The ultrasonic frequency and power were adjusted by ultrasound generator H66MC. The voltage signal generated by the bubble oscillation in the grinding fluid was measured using 18

the acoustimeter YP0511C and exact values were interpreted by the GDS-1062 oscilloscope.

Fig.8. Schematic of experimental apparatus of cavitation.

Before measurement, the cavitation intensity of the grinding fluid in different positions near the honing stone should be considered to distinguish. Thus, a section of grinding fluids near the honing stone wall was divided equally into five areas, and each area was labeled A, B, C, D and E respectively. The voltage data of each area were collected by the detector bar connected with the acoustimeter. Half of peak-to-peak value (error range ± 0.1V) of the voltage signal from oscilloscope was last read to record the cavitation intensity of the grinding fluid. The measurement site of the honing stone wall versus cavitation intensity was shown in Fig. 9. From Fig. 9, it can be seen that the cavitation intensity of the two sides of the honing stone wall is weaker, such as area A and E, while that of the middle of the honing stone is the most violent, such as area C. The distribution of the cavitation intensity on the honing stone wall also fits the results of FEM of sound field analysis of UVH. Thus, in order to obtain and to deal with those data more efficient, a fixed location near the surface of honing stone, that is area C, is selected to measure the acoustic cavitation intensity. Fig. 10 gives the cavitation intensity versus ultrasonic frequency and acoustic amplitude. As can be noted, for small acoustic amplitude, the cavitation intensity of the grinding fluid is also relatively lower. As acoustic amplitude is increased, the cavitation intensity of the grinding fluid is gradually increased. Furthermore increasing acoustic amplitude, the increase of the cavitation intensity of the grinding fluid is slowing down. The experimental results are consistent with the numerical simulation analysis in Fig. 6. From Fig. 10, it is also found that the influence of ultrasonic frequency on the cavitation intensity of grinding fluids is rather complicated. As the device of UVH is in resonance, the cavitation intensity of grinding fluids can reach the highest. It means that the most violent cavitation of the grinding fluid can be obtained when the device is in an optimum resonance state. However, for other frequencies, that is the device of UVH is in the off-resonance, as the ultrasonic frequency increases, the cavitation intensity of the grinding fluid is gradually decreased. According to initial given 19

conditions of UVH, the resonant frequency of the device is 18.6 kHz. Thus, when ultrasonic frequency is close to the resonant frequency of the optimal model of UVH device, the most violent cavitation can be examined. When the ultrasonic frequency is deviated from the resonant frequency, the cavitation intensity of the grinding fluid can be weakened which can also be explained by Fig. 7. The ultrasonic frequency of the grinding fluid and the resonance frequency of honing device can be explained as follows.

Fig.9. Measurement site of the honing stone wall versus cavitation intensity.

Fig.10. Cavitation intensity versus ultrasonic frequency and acoustic amplitude.

In the honing process, without honing pressure and velocities, the cavitation effect in the grinding fluid is caused by ultrasonic vibration from the UVH device. The motion of the UVH device can be roughly regard as forced vibration with single degree of freedom and viscous damping caused by external excited force. 20

The equation for the vibration motion of the UVH device can be expressed as follows

mh yh  ch yh  kh yh  F (t )

(28)

where, y h is the displacement of the honing stone, and mh , ch , k h is the mass, viscous damping and stiffness of the UVH device, F (t ) is the harmonic excitation. Under the steady state solution of the Eq. (28), the resonant frequency  h of the UVH device is expressed as below

2  h

kh mh

(29)

On the basis of the theory of vibration modal analysis, the resonant frequency of the UVH device should meet   h or at least   h for achieving an excellent resonance performance (   2πf is the ultrasonic angular frequency). During honing, ultrasonic wave through grinding fluids has an obvious impact effect on the bubble dynamics and then can cause a change in the bubble oscillation. In order to identify the nonlinear oscillation of the bubble under UVH and UV, the bubble dynamic model of Eq. (9) was linearly dealt with in accordance with small amplitude changes of the bubble radius. Let us assume that R(t )  R0 [1  r (t )] , where r (t )  1. Then, one can obtain

d 2 r 4 1  r  r20 r  p 2 2 dt  R0  R02 uh 3 puh    vh2  ph  (k  1) p0  pa sin t 2

(30)

(31)

where, r 0  2f r 0 is the angular frequency of oscillation of a bubble in the grinding fluid under UVH, and f r 0 is the corresponding natural frequency, as follows

r20 

1 3 2 2 [ (k p0   pv ) ] 2 R0  R0  R0

(32)

In Eq. (30), the initial condition is defined by r (0)  0 , r (0)  0 , and the effect of viscosity is neglected, thus the analytical solution can be solved as

3 (1  cos r 0t )( vh2  ph  (1  k ) p0 ) 2 R(t )  R0  R0 [ ] r20 R02    honing disturbanes

  R0 [ 2 (sin t  sin r 0 t )] 2 2 (r 0   ) R0 r 0 pa

(33)

  ultrasonic vibration

where, the first term of the right side of the Eq. (33) is the initial radius of the bubble, and the second term of that is the bubble oscillation under honing disturbances, and the third term of that is the bubble oscillation under ultrasonic vibration. Thus, for UVH, the bubble oscillation can be determined by the full terms of the Eq. (33); while for CH, the bubble 21

oscillation should only be gained by the first two terms in the Eq. (33). From the definition of the natural frequency, it can be seen that r 0 is not related to honing disturbances, and is determined by the physical properties of grinding fluids. The optimal coupling state of the bubble in an ultrasonic wave can occur at   r 0 [46]. Therefore, combined Eq. (29) with Eq. (32), the optimum cavitation effect in the grinding fluid under UVH can be obtained, only when r 0    h or at least r 0    h . The formula can be used to estimate and evaluate the cavitation effect in the grinding fluid. Furthermore, the relationship between the ultrasonic frequency of the grinding fluid and the resonance frequency of honing device is highly complex and is looking forward to more in-depth study. However, according to our initial assumption, the experimental results are roughly in agreement with the theoretical analysis, and it can be provided with guidance opinions for recognition and utilization of the cavitation effect in honing process. Fig. 11 gives the results of comparative machining precision between UVH and CH. Several groups of cylinder liners made of 38CrMnA were honed to evaluate ultrasonic cavitation effect. The machined surface roughness Ra was measured by Roughness profiler JB-5C. The honing initial conditions are as same as Fig. 8 (pa=1.2 MPa, f=18.6 kHz), and others are as follows: p0 = 0.1 MPa, ph = 0.24 MPa, va = 0.05 m/s, n = 80-315 r/min. From Fig. 11(a), it can be seen that the Ra under UVH at 0.022-0.026μm was lower than that under CH at 0.04-0.05μm. The reason can be explained as below. For CH, pa=0 MPa, thus pa
Fig.11. Comparative machining precision between UVH and CH

22

5. Conclusions In this paper, cavitation and its generating bubbles in the grinding fluid under UVH were focused on by both theoretical analysis and experimental tests. Without ultrasonic vibration, the grinding fluid on the surface of the honing stone can form several groups of droplets. Those droplets under ultrasound begin to break down and further form many cavities, and eventually form several groups of araneose bubbles. The bubble under UVH exhibits the dynamic behaviors of growth, expansion, rapid implosion collapse and rebound. As the initial radius of the bubble increases, the maximum radius of the bubble is growing decreased and the oscillation interval is extended. However, the bubble under CH is compressed directly. As the initial radius of the bubble increases, the compression ratio of the bubble increases gradually, and the oscillation interval is extended. The oscillation of the bubble under UVH is more intense than the case under CH, and the maximum velocity of the bubble wall in the case under UVH is higher two magnitudes than the case under CH. For lower acoustic amplitude (pa
Acknowlegements The project was supported by the National Natural Science Foundation of China (51275490 and 50975265), the open foundation of Shanxi Key Laboratory of Advanced Manufacturing Technology (XJZZ201601-06), and the school fund of Taiyuan University of Technology (2016QNOZ).

23

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Highlights     

Cavitation bubble dynamics under different honing conditions were proposed. The cavitation bubbles of grinding fluids near honing stone wall under ultrasound were observed. Honing pressure has an inhabitation effect on cavitation effect of the grinding fluid. Ultrasound can improve the cavitation intensity in honing process. Effect of ultrasonic frequency on cavitation depends on the resonance state of honing device.

27