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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 169807, 11 pages

http://dx.doi.org/10.1155/2013/169807

## Modeling and Experimental Investigation of Pressure Field in the Grinding Zone with Nanoparticle Jet of MQL

School of Mechanical Engineering, Qingdao Technological University, Qingdao 266033, China

Received 31 March 2013; Revised 31 May 2013; Accepted 3 June 2013

Academic Editor: Guan Heng Yeoh

Copyright © 2013 C. H. Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*Solid nano*particles were added in minimum quantity lubrication (MQL) fluid medium to make nanofluids, that is, after the mixing and atomization of nanoparticle, lubricants and high pressure gas, to inject *solid nano*particle in the grinding zone with the form of jet flow. The mathematical model of two-phase flow pressure field of grinding zone with nanoparticle jet flow of MQL was established, and the simulation study was conducted. The results show that pressures in the grinding zone increased with the *acceleration* of grinding wheel, sharply decreased with the increased minimum clearance, and increased with the *acceleration* of jet flow. At three spraying angles of *nozzles*, when the *nozzle* angle was 15°, the pressure of grinding zone along the speed of grinding wheel was larger than the rest two angles. On the experimental platform built by KP-36 precision grinder and nanoparticle jet flow feed way, CY3018 pressure sensor was used to test the regularities of pressure field variations. The impact of the speed of grinding wheel, the gap between workpiece and grinding wheel, jet flow velocity, and spraying angles of *nozzles* on the pressure field of grinding zone was explored. The experimental result was generally consistent with the theoretical simulation, which verified the accuracy of the theoretical analysis.

#### 1. Introduction

Minimum quantity lubrication (MQL) refers to the minimum quantity of lubricants that enters the high temperature grinding zone after being mixed in high pressure gas and atomized with high pressure draft (4.0–6.5 bar). The traditional poured and debridged feed liquid of grinding fluid is 60 L/h for a unit of the width of grinding wheel, while the consumption of MQL grinding fluid is 30–100 mL/h for a unit of the width of the grinding wheel [1–8]. High pressure draft serves as cooling and chip removal. Lubricants are attached to the finished surface of the workpiece, forming a layer of protective film and serving as the lubrication. This technology integrates the advantages of poured and debridged grinding and dry grinding, presenting similar lubrication effects compared with traditional poured and debridged grinding. Lubricants adopt vegetable oil as alkyl ester of base oil, which shows features such as excellent biodegradability, lubricating properties, high viscosity index, low volatility, recycling, short production cycle, and insignificant environmental diffusion. The consumption of lubricants is only parts per thousand or a few hundredths of a percentage point compared with the traditional grinding approaches, which greatly improved the working environment. Thus, high pressure draft is an efficient low-carbon processing technology. However, studies show that cooling effect of high pressure draft is too limited to meet the needs of strengthened high temperature heat transfer of the grinding zone [8–12]. The processing quality of the workpiece and the grinding wheel life is worse than the traditional poured and debridged grinding, indicating that MQL technique requires further improvements.

According to strengthened heat transfer theory, the heat transfer ability of the solid greatly exceeds the liquid and gas. At room temperature, the coefficient of thermal conductivity of solid materials is greater than the fluid material by several orders of magnitude. It can be estimated that the coefficient of thermal conductivity of liquid with suspended metal, nonmetallic, or polymeric solid particles exceeded the pure liquid significantly. If solid particles are added in MQL medium, it is expected to greatly increase the coefficient of thermal conductivity of fluid medium so as to improve the convective heat transfer and offset the defects of insufficient cooling effects of MQL. In addition, nanoparticles (referring to ultrafine tiny solid particles with at least one dimension in the three-dimensional space, that is, in the nanoscale range (1–100 nm)) also present tribological features such as special antifriction and high carrying capacity in aspects of lubrication and tribology [13].

In this research, *solid nano*particles were added in MQL fluid medium to make nanofluids, that is, to inject *solid nano*particles after the mixing and atomization of nanoparticle, lubricants (oil or oil-water mixture) and high pressure gas in the grinding zone with the form of jet flow. Nanofluids refer to the new heat transfer working medium with nanoscale metal or metallic oxide particles added in fluids at a certain way and ratio. In effect, from the aspect of its compositions, it is the two-phase suspension liquid formed by liquid and nanoparticles and can be abbreviated as “nanofluids.” Due to the small size effect of nanoparticle, its behavior is similar with that of the liquid molecules; the intensive Brownian motion of nanoparticle maintains its stable suspension and keeps it from precipitation [5, 6].

There are few differences between Brownian motion of suspended particulates and the thermal motion of molecules in the true solution, and the most significant difference is the form of the thermal motion of molecules. The former involves the integrated effects of the thermal motion impact by many molecules while the latter involves the thermal motion of a single kind of molecules. Hence, in the research of three-phase flow (including compressed air, the grinding liquid, and nanoparticles), nanoparticles can be made suspending in the grinding liquid to form nanofluids, and transport parameters of nanofluids can be calculated based on related theories, which can thus be abbreviated into a study on two-phase flow.

When the grinding liquid was injected in the wedge-shaped zone between the grinding wheel and the workpiece surface, the fluid dynamic pressure of the grinding liquid was formed. Guo and Malkin [7] applied mass conservation equation and momentum conservation equation in the mathematical modeling, based on the consideration of the impact of the porosity of the grinding wheel. With theoretical calculation, the depth of the grinding liquid in the grinding wheel was obtained, indicating that the grinding wheel with pores has the function to pump the grinding liquid from the grinding zone. Chang [8] and others considered the impact from the porosity of the grinding wheel. According to conservation equation, mathematical model the dynamic pressure of grinding liquid during the gradual feeding was established, and the simulation results show that the larger the supply of grinding liquid is, the larger the dynamic pressure of grinding liquid will be. Ganesan et al. [9] applied Renolds equation and Laplace equation to establish the cooling liquid equation for the infinite narrow grinding wheel and provided the analytical solution for calculating the dynamic pressure of fluid. Furutani et al. [10] considered the impact of degree of permeability of the grinding wheel and established the cooling liquid equation for the infinite wide grinding wheel, so as to solve the lifting force from the fluid pressure and the dynamic pressure. Engineer and others measured the flow of the grinding liquid.

With experimental measurements, the flow in the grinding zone was identified, indicating the significant role of porosity of the grinding wheel and the location of nozzles on the flow. Gviniashvili et al. [11] measured the depth of the grinding liquid in the grinding wheel and identified the relationship between the depth and the maximum temperature of the grinding workpiece. Ebbrell et al. [12], Li et al. [13], and Ganesan et al. [14] considered the impact of inertia force. Based on two-dimensional steady incompressible fluid Navier-Stokes equation, the fluid equation in grinding zone was deducted in planar grinding, and the dynamic pressure of the fluid was simulated and solved, which was verified in experiments. Hryniewicz et al. [15, 16] considered the influence of the roughness and established a two-dimensional mathematical model. The regularities of distribution of the dynamic pressure were simulated and solved, which was verified in experiments. They identified the relationship between the dynamic pressure and the speed of grinding wheel as well as minimum clearance between the grinding wheel and the workpiece. Based on theoretical and experimental analysis, the following conclusions were drawn: with other conditions identical, the larger the roughness, the larger the dynamic pressure of fluid will be. Furthermore, when the grinding wheel left the grinding zone, not all the grinding liquid was thrown from the grinding wheel. Only a part of the liquid left the grinding wheel, and the rest moved with the grinding wheel. In the experiment, Hryniewicz observed the following phenomenon: the grinding liquid left the grinding zone sticking to the grinding wheel surface rather than to the workpiece. Kim [17] and Lee et al. [18] designed experimental apparatus to test the effective flow rate of the grinding liquid in the grinding zone via the feeding with nozzles. They acquired the conclusion that the porosity of the grinding wheel and the position of the nozzles imposed a significant impact on the effective flow rate, while the feeding velocity and grinding depth of the workpiece has little impact over it. Klocke et al. [19] assumed that the radius of the grinding wheel was infinite, and the width of the workpiece and the grinding wheel was finite. Based on the assumption, a two-dimensional mathematical model of pressure distribution in the grinding zone was established according to the Navier-Stokes equation so as to calculate infinite width of the grinding wheel. The normal applied force generated by the dynamic pressure of grinding liquid was defined as Coolant induced force [20]. With the simulating calculation, the larger the velocity of grinding wheel is, the larger the normal force will be. Hryniewicz et al. [15] applied two types of nozzles in the experiment of cooling system. The first was formed by two nozzles, and the main nozzle was used to the feeding of the grinding liquid, and the assistant nozzle was used to break through “airbond” of air flow around the grinding wheel. The second only involves one nozzle for the feeding of the grinding liquid. It can be concluded from comparing the experimental results that the feeding nozzle of two nozzles has lower than that of one nozzle. Klocke [19] studied the percentage experiment of the grinding liquid in the grinding zone that accounts for the entire grinding liquid and summed up that when the flow of the grinding liquid was increased, Coolant induced force was enlarged. Yet when the ratio of the grinding liquid in the grinding zone reached a certain value, it will increase with the increasing flow. Hryniewicz [15] conducted experiments of two grinding liquids (the oiliness grinding liquid and chemical synthetic fluids) and found that in the same experimental conditions, the maximum dynamic pressure generated by the oiliness of the grinding liquid was much larger than that from chemical synthetic fluids. In this research, the modeling and experimental investigation was conducted on nanoparticle jet flow of MQL grinding pressure field.

#### 2. Theoretical Modeling of Pressure Field in the Grinding Zone

Figure 1 shows the geometrical model. The three-dimensional system of coordinate was established, and the origin of coordinates was located at the workpiece surface between the grinding wheel and the minimum clearance. The direction of rotation of the workpiece surface along the grinding wheel was taken as axis, and the direction vertical to the workpiece surface was taken as axis, that along the width of the grinding wheel as axis.

##### 2.1. Modeling Conditions

(1)* Compressibility of Gas*. The room temperature was taken as , the peripheral velocity of grinding wheel as m/s, and it was obtained that sound velocity: m/s; Mach number: . As , the compressibility of gas can be excused from consideration in the fluid analysis.

(2)* Identification of Fluid State*. ; where —half width of outlet; —outlet velocity; —nanofluids dynamic viscosity. , so it is identified as turbulence flow. With the considerations of the following aspects (the fluid evenly flows in the grinding zone, the fluid is incompressible Newtonian flow, and the fluid in intervals is turbulence), for simplified calculation, the model was simplified as [21](i)to neglect the impact of temperature and pressure on fluid viscosity, or that of the inertial effect in the flow; (ii)to not consider the impact of the workpiece surface roughness and elastic deformation; (iii)to neglect the ratio of feeding velocity of the workpiece and the peripheral velocity of grinding wheel; (iv)to neglect the ratio of fluid inertia force, body force, and surface force in nanofluid film.

##### 2.2. The Establishment of Mathematical Model

According to the continuity equation, momentum conservation equation and energy conservation equation, of the hydromechanics, the mathematical model of the stress field of the grinding zone was established. (1)Continuity equation: (2)Momentum conservation equation [22]: where , —average velocity of nanofluids along and direction; —density of nanofluids; —Reynolds stress. (3)Energy conservation equation: where —total energy; —heat conductivity coefficient; —temperature; In the previous equation, the amount of unknown numbers exceeded equations. To this end, turbulence model equation was introduced. (4) turbulence model: (a) equation [23]: (b) equation: where shows the turbulence kinetic energy from the velocity gradient of laminar flow, is the turbulence kinetic energy from the buoyancy force, is the fluctuations from transitional diffusion in the compressible turbulence. , and are constants, and are the turbulence Prandtl numbers of equation and equation.(c)Turbulence velocity model: the turbulence velocity is determined by the following equation: where is a constant; constants of the model include , , , , .

#### 3. Simulation of Pressure Field in Grinding Zone

Figure 2 shows the pressure distribution of flow field of the grinding zone after the effects of compressed air continuous phase. It can be observed from the figure that the fluid pressure changes were only found at the entrance and exit of the wedge gap. There is a high pressure value, and the rapid pressure gradient occurs near the region where the gap between the grinding wheel and the work surface is minimal. The smaller the gap distance is, the higher the pressure gradient and the peak value pressure become. The pressure distribution is uniform in the direction of the width of the wheel except at the edge of wheel because of the side-leakage and becomes zero at the edge of the wheel, shown in Figure 3.

#### 4. The Simulation Results

##### 4.1. The Impact of the Peripheral Velocity of Grinding Wheel on the Pressure in Grinding Zone

By changing the peripheral velocity of grinding wheel, the pressure changes in the grinding zone can be obtained. The circumference velocity was taken as 45 m/s, 80 m/s, 120 m/s, and 160 m/s, and the corresponding changing curve was shown in Figure 4. In Figure 4, it can be seen that the pressure peak in direction increased with the peripheral velocity of the grinding wheel. There is a high pressure value, and the rapid pressure gradient which occurred near the region where the gap between the wheel and the work surface was minimal, as shown in Figure 4. Along the axis (the velocity of grinding wheel), the pressure gradually reached the maximum value from nothing, with the location close to the entrance of wedge gap. After this, it dropped sharply, even showing the negative pressure near minimum clearance. For *different velocities* of grinding wheel, two peak values of the pressure were almost at the same position, that is, close to the minimum clearance between the grinding wheel and the workpiece. Peak values of pressure were observed at the entrance near the wedge-shaped zone. The value was increased with rising velocity of grinding wheel, and the peak values of negative pressure were close to the exit of the wedge-shaped zone.

##### 4.2. The Impact of Minimum Clearance between the Grinding Wheel and the Workpiece on Pressure in the Grinding Zone

By changing the minimum clearance between the grinding wheel and the workpiece, pressure changes of the grinding zone were obtained, and minimum clearance was taken as 100 * μ*m, 80

*m, 50*

*μ**m, and 30*

*μ**m. The corresponding changing curve was shown in Figure 5.*

*μ*As can be seen from Figure 5, peak values of pressure in grinding zone sharply reduce along the increase of minimum clearance. The smaller the gap distance was the higher the pressure gradient and the peak value pressure attained. It can be inferred that the minimum clearance between the grinding wheel and the workpiece significantly influenced the pressure in the flow field of grinding zone.

##### 4.3. The Impact of Jet Flow Velocity on the Pressure of Grinding Zone

By changing the jet flow velocity, pressure changes of the grinding zone were obtained. The jet flow velocity was taken as 45 m/s, 60 m/s, 70 m/s, and 90 m/s. The corresponding changing curve was shown in Figure 6.

As can be seen from Figure 6, peak values of the pressure in grinding zone increase with increasing jet flow velocity, indicating that jet flow velocity influences the pressure in the flow field of grinding zone.

##### 4.4. The Impact of Positions and Angles of Nozzle on the Pressure in Grinding Zone

By changing the positions and angles of *nozzle*, pressure changes of the grinding zone were obtained. The positions and angles of *nozzle* were taken as the intersection between the workpiece surface as 0°, 15°, and 20°, and corresponding changing curve was shown in Figure 7.

It can be seen from Figure 7 that at 15° the pressure in grinding zone was larger than the rest two angles because at 15°, the sprayed nanofluids were over the boundary of the return flux, when nanofluids can easily enter the wedge gap for cooling and lubricating. Hence, in the grinding with nanoparticle jet flow of MQL, the position of nozzles should be located beyond the boundary of the return flux.

#### 5. The Experimental Study of Pressure Field in Grinding Zone

##### 5.1. Experimental Device

Numerical control precision surface grinding machine and minimum quantity nanoparticle jet flow feedway were used to establish minimum quantity grinding bench. The jet flow pressure field applied workpiece-embedded CY3018 pressure sensor to measure and collect data. The schematic diagram of the experimental device was shown in Figure 8, and the diagram of pressure field test system was shown in Figure 9. The machining system of the experiment is composed of a rotating grinding wheel and a work surface, and the gap between them is MQL filled in with grinding coolant by a nozzle. The varied parameters included the grinding wheel velocity, nozzle jet velocity, minimum clearance between the grinding wheel and the work surface, and different angles of *nozzle*. A reciprocating table grinder with variable speed was used for the experiments. The wheels used were all of diameter mm and width mm. Each work specimen was 300 mm in length along the grinding direction, 100 mm width, and 50 mm thickness. Parameters of nanoparticle jet flow of MQL are carbon nanotube particles with the average diameter of 10–20 nm; oil base (vegetable oil); volume fraction: 1%; the MQL flow rates: 615 mL/h.

In the measurement of parameters, the sensor and transmitter transferred the measured values to the tester. The data was uploaded to the host computer via the serial port. After the conversion, the data was displayed in the form of tables and curves. Each experiment was repeated three times for averaging.

In the experiment, the numerical control ultrasonic oscillator was used to prepare stable oil-based nanofluids grinding liquid. The procedures are as follows: with the example of the preparation of 300 mL of oil-based nanofluids, the volume fraction was 1%. Assume the volume of nanoparticle as and the volume of base fluid as . The volume fraction of nanoparticles of nanofluids is

According to the above equation, it can be calculated that the mass of nanoparticles should be 0.74 g, with the volume of vegetable oil as 279 mL, the proportion of the dispersing agent as 7% (28 g). With the combination of nanoparticle, base oil, and the dispersant, the ultrasonic vibration was used for the combination, with the vibration frequency as 70 Hz and the time as 15 min. After the mixture stabilized, the viscosity was measured.

#### 6. Analysis of Experimental Results

Four *different peripheral velocities* of grinding wheel were adopted for the experiment. Among them, the experimental results of two grinding wheel velocities were compared with the theoretical simulation as shown in Figure 10. The contrast of experimental result of the pressure in the grinding zone at two *different peripheral velocities* of grinding wheel was shown in Figure 11.

As shown in Figure 10, with lower the peripheral velocity of grinding wheel, the experimental result was relatively consistent with the theoretical simulation, when the velocity was 45 m/s; when the velocity was increased to 160 m/s, the experimental result at the entrance section of the wedge-shaped zone was lower than the theoretical simulation, which may be attributed to the increased difficulties of nanofluids breaking through the airbond with enlarged thickness. Figure 11 provides the contrast of experimental results of four *different peripheral velocities* of grinding wheel. The results show that the pressure in the grinding zone increased with the increases of the peripheral velocity of grinding wheel. With the velocity of 120 m/s, as the airbond layer prevented nanofluids from entering the grinding zone, the pressure change was close to the curve when the grinding wheel velocity was 80 m/s.

Four different jet flow velocities were adopted for the experiment. Among them, the experimental results of two jet flow velocities were compared with the theoretical simulation as shown in Figure 12. The contrast of experimental result of the pressure in the grinding zone from different jet flow velocities from the nozzles was shown in Figure 13.

As shown in Figure 12, with higher jet flow velocity, the experimental result was relatively consistent with the theoretical simulation, when the velocity was 90 m/s; when the velocity was reduced to 45 m/s, the experimental result of the pressure in the grinding zone was lower than the theoretical simulation, which may be attributed to the influence from the airbond around the grinding wheel. With lower jet flow velocity, the sprayed nanofluids were insufficient to break through the airbond and enter the grinding zone. Figure 13 provides the contrast of experimental results of four different jet flow velocities, indicating that the pressure in the grinding zone increases with the jet flow velocity, and its regularities are basically consistent with those in the simulation analyze.

Four different minimum clearances were adopted for the experiment. Among them, the experimental results of two minimum clearances were compared with the theoretical simulation as shown in Figure 14. The contrast of experimental result of the pressure in the grinding zone with different minimum clearances was shown in Figure 15.

It can be observed from Figure 14 that with larger minimum clearance, the experimental result was relatively consistent with the theoretical simulation, when the minimum clearance was 100 *μ*m; yet when the minimum clearance was gradually reduced to 30 *μ*m, the effective flow of nanofluids that enters the wedge gap was reduced, leading to lower experimental result of the pressure in the grinding zone than the theoretical simulation. Figure 15 shows the contrast of experimental curves with different minimum clearances. It can be found that the regularities are basically consistent with the finding in our simulation. In other words, the pressure increases as wedge gap narrows. Along the velocity direction of grinding wheel, the pressure gradually increases, almost reaching the entrance of the wedge gap and then showing the tendency of declining. The negative pressure with a certain value was observed close to the wedge gap.

Three different spraying angles of *nozzles* were adopted for the experiment. The intersection between *nozzle* and the workpiece surface was taken as 0°, 15°, and 20°, respectively. Among them, the experimental results of two spraying angles of *nozzle* were compared with the theoretical simulation as shown in Figure 16. The contrast of experimental result of the pressure in the grinding zone at different positions of nozzles was shown in Figure 17.

It can be observed from Figure 16 that when the spraying angle of *nozzles* was 15°, the experimental result was relatively consistent with the theoretical simulation; when the angle was 0°, the pressure in the grinding zone was lower than the theoretical simulation. It may be attributed to the lower spraying track of nanofluids at 0°. Figure 17 shows the contrast of experimental result of pressure at different spraying angles of *nozzles*. It can be observed that when the spraying angle of *nozzles* was 15°, the pressure was obviously higher than that at two different positions of nozzles, as the nanofluids were higher than the boundary of the return flux. At this angle, the nanofluids can easily enter the wedge-shaped zone.

#### 7. Conclusions

In this paper, the theoretical model of nanoparticle jet flow of MQL grinding zone pressure field was established for simulation and experiments. The results show the following. (1)With the velocity increase of grinding wheel, the pressure in the grinding zone gradually increases with a substantial range. For *different velocities* of grinding wheel, the peak values of the pressure were almost at the same position, that is, close to the minimum clearance between the grinding wheel and the workpiece. Peak values of pressure were observed at the entrance near the wedge-shaped zone. The value increases along rising velocity of grinding wheel. When the velocity was increased to 160 m/s, the experimental result at the entrance section of the wedge-shaped zone was lower than the theoretical simulation, which may be attributed to the increased difficulties of nanofluids breaking through the airbond with enlarged thickness.(2)Peak values of pressure in grinding zone sharply reduce along the increase of minimum clearance with a substantial range, indicating that the minimum clearance between the grinding wheel and the workpiece significantly influences the pressure at the wedge gap of the flow field in grinding zone. When the minimum clearance was gradually reduced to 30 *μ*m, the effective flow of nanofluids that enters the wedge gap was reduced, leading to lower experimental result of the pressure in the grinding zone than the theoretical simulation. (3)Peak values of the pressure in grinding zone increase with increasing jet flow velocity with a substantial range, indicating that jet flow velocity influences the pressure in the flow field of grinding zone to a certain degree. For *different velocities* of jet flow, the peak values of the pressure were almost at the same position, that is, close to the minimum clearance between the grinding wheel and the workpiece. When the velocity was reduced to 45 m/s, the experimental result of the pressure in the grinding zone was lower than the theoretical simulation, which may be attributed to the influence from the airbond around the grinding wheel. With lower jet flow velocity, the sprayed nanofluids were insufficient to break through the airbond and enter the grinding zone. (4)When the spraying angle of *nozzles* was 15°, the pressure at the wedge gap was obviously higher than that at two different positions of nozzles. When the spraying angles of *nozzles* were 0° and 20°, the spraying track of nanofluids was lower than the boundary of the return flux. In this way, the nanofluids would encounter great obstacles to enter the wedge-shaped zone. Thus, the pressure became lower than the simulation results.

#### Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (50875138; 51175276) and the Shandong Provincial Natural Science Foundation of China (Z2008F11; ZR2009FZ007).

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