Modeling and Numerical Simulation of the Grinding Temperature Field with Nanoparticle Jet of MQL

Abstract

In this research, the heat transfer model of surface grinding temperature field with nanoparticle jet flow of MQL as well as the proportionality coefficient model of energy input workpiece was established, respectively. The numerical simulation of surface grinding temperature field of three workpiece materials was conducted. The results present that, in the workpiece, the surface temperature was significantly higher than the subsurface temperature, presenting relatively large temperature gradient along the direction of workpiece thickness. The impact of the grinding depth on grinding temperature was significant. With the increase of the cut depth, peak values of the grinding temperature rocketed. Distribution rules of the temperature field of 2Cr13 in four cooling and lubrication approaches were the same. Based on the excellent heat transfer property of nanofluids, the output heat through the grinding medium acquired an increasingly high proportion, leading to the drop of the temperature in the grinding zone. For the same cooling and lubrication conditions, grinding temperature presented insignificant changes along the direction of grinding width. Yet, under different cooling conditions, the temperature variation was significant. MQL grinding conditions with additive nanoparticles demonstrated great impact on the weakening of temperature effect on the grinding zone.

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 flood cooling 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 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 flood cooling grinding and dry grinding, presenting similar lubrication effects compared with traditional flood cooling grinding. Lubricants adopt vegetable oil as alkyl ester of base oil, which shows features like as excellent biodegradability, lubricating properties, high viscosity index, low volatility, recycling, short production cycle and insignificant environmental diffusion, and so forth. 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 flood cooling grinding, indicating that MQL technique requires further improvements.

In order to improve the defects in cooling effect of MQL grinding, the Sanchez [12] team from Spain applied the low-temperature CO₂ to the MQL grinding, that is, to inject low-temperature CO₂ (238 K) and MQL medium with two nozzles in the grinding zone with the form of jet flow. Given the advantage of low-temperature heat transfer property of CO₂, the temperature of the grinding zone can be further reduced. Studies have shown that the consumption of CO₂ is remarkable (40 L/min), and two sets of feeding systems are needed. The costs are high and the rapid volatile property of CO₂ constrains its strengthened heat transfer in the grinding zone (low-temperature CO₂ MQL grinding ratio G = 4.5; flood cooling lubrication grinding ratio G = 4.22). Hence, the cooling effect of cryogenic gas on improving MQL subjects to certain restrictions.

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. In Table 1, we compared the coefficient of thermal conductivity of solid with liquid materials. It can be inferred 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. In this research, we added nanoscale solid particles in MQL fluid medium to produce nanofluids. Specifically, we injected nanoscale solid 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. Nanoparticle jet flow of MQL grinding provides an innovative grinding technology as well as the special equipment that integrates all advantages of MQL technology and presents better cooling effect as well as tribological features. This technology intends to effectively address the issue of grinding burn and to improve the workpiece surface completeness. It embodies important significance in the realization of efficient, environmentally friendly, resource-saving and low-carbon green production with low consumption.

Table 1:

The coefficient of thermal conductivity of matters.

Matters	Copper	Aluminum	Copper oxide	Aluminum oxide	Zinc oxide	Carbon nanotube	Diamond	Silicon	Water	Engine oil	Ethylene glycol

Thermal conductivity/W (m·K)⁻¹	401	237	19.6	40	100	3000	2300	148	0.613	0.145	0.253

The removed volume of unit materials during the grinding in the interface of the grinding wheel/workpiece generates a mass of energies. The introduction of MQL with insufficient cooling effect in the grinding is more challenging than other cutting methods. So far, only a few research groups conducted an exploratory study on MQL grinding technology. Xiu et al. explored the application prospect of MQL in the grinding from the aspect of environmental protection and ecology. The research demonstrated that, compared with the traditional flood cooling grinding, costs of MQL grinding fluid were reduced by 65%, and the investment of device was reduced by 22%. In addition, with the naturally degraded synthetic esters as lubricants, harms of the grinding fluid on the environment and human were minimized [13 –15]; Aurich et al. [16] studied the surface completeness of workpiece, specific energy, and abrasion contrast of the grinding wheel under different conditions including dry grinding, flood cooling wet grinding, and MQL. The results showed that, compared with the other two flood cooling methodology conditions, MQL provided effective lubrication, yet insufficient cooling effect. The completeness of the processed workpiece surface was deteriorated; Malkin and Guo [17] researched on the impact of grinding parameters on the workpiece surface quality in the flat grinder experiment. Compared with the flood cooling wet grinding, the workpiece surface quality as improved under the conditions of the optimization of grinding consumption and feed liquid parameters, with improved quality and reduced tangential grinding force and specific grinding energy; Huang and Liu [18] applied the precision surface grinder experiment to study the grinding power, grinding force, grinding temperature and surface roughness contrast of MQL grinding and flood cooling dry grinding. The results show that, with a suitable material removal rate, the grinding force and the grinding power of MQL were prior to that of flood cooling methodology. Yet, the roughness of the workpiece surface and residual stress was inferior to that of flood cooling methodology. Xu et al. [19] conducted the minimum cutting-in (5 μm) grinding contrast experiment on the precise DC grinder with the water droplets processing liquid attached by minimum quantity oil film, emulsion solution, soluble concentrates, minimum quantity spray and minimum quantity oil mist processing liquid. Furthermore, they measured the grinding force, surface roughness, the temperature of the grinding zone, and grinding ratio. Results showed that the cooling effect of the water droplets processing liquid attached by minimum quantity oil film as inferior to traditional processing liquid such as emulsion solution and soluble concentrates, yet presenting sound lubricating property [20 –23]. It also presented excellent advantages in regard of processing precision and the grinding wheel life. Yet, this method is applied for the grinding under the low grinding heat condition due to the limited heat transfer of minimum quantity water drops.

On account of the damages on environment and workers' health from the extensive use of grinding fluid in flood cooling methodology as well as the severely insufficient cooling effects of MQL grinding, nanoscale solid particles were injected in the grinding zone with the form of jet flow after the mixing and atomization of nanoparticle, lubricants (oil or oil-water mixture), and high-pressure gas because of the prior heat transfer of solid particles than liquid and gas. In this way, the defects of MQL cooling effect can be offset, which greatly improved the production environment, saving energy, and cost reduction and achieved low-carbon manufacturing. Furthermore, lubricants were injected in the grinding zone more effectively via breaking the airbond, improving effective flow rate of the grinding wheel/workpiece interface grinding medium. Compared with the wet grinding, the fluid dynamic pressure and introduction force generated by the grinding medium in the wedge-shaped contact area were reduced, as well as the deflection deformation of the principal axis of the grinding wheel [24 –27]. It also improved the precision of the workpiece processing. Furthermore, with the special lubricating property and tribological properties of nanoscale solid particles for jet flow, a nanoparticle shearing oil layer can be found on the interface of the grinding wheel/workpiece, which can enhance the improvement of lubricating property of MQL grinding and present practical meanings. In this research, the modeling and numerical simulation was conducted on nanoparticle jet flow of MQL grinding temperature field.

2. The Mathematical Model of Temperature Field

With the planar shallow-cut grinding as the study objective, Figure 1 shows heat source conduction of the grinding zone. Assume the grinding contact arc zone AA′B′B as the band-shape heat source, Y direction was regarded as infinitely long, and the intensity of heat source is q_m [J/m²·K·s]; the contact arc length is l_s, and the heat source AA′B′B is the set of countless linear heat sources d_xi. One linear heat source d_xi was taken with the intensity of q_md_xi, which moved along the X direction with the velocity of V.

Figure 1:

Planar heat source conduction.

The temperature rise equation of the point m(x, 0, z) from linear heat source q_mdx′d_t with the width of dx′:

d θ_{m} = \frac{q_{m}}{π λ} \exp [\frac{(x - x_{i}) v}{2 α}] k_{0} [\frac{v}{2 α} \sqrt{{(x - x_{i})}^{2} + z_{m}^{2}}] d x_{i} .

(1)

The temperature variation equation of the point m from the entire heat source belt is

θ_{(x, z)} = \frac{q_{m}}{2 π λ} \int_{- l}^{l} d x_{i} \int_{0}^{\infty} \frac{d t}{t} \exp {- \frac{{[x - x^{'} + v t]}^{2} + z^{2}}{4 α t}} = \frac{q_{m}}{2 π λ} \int_{- l}^{l} e^{(x_{i} - x) v / 2 α} K_{0} [\frac{v}{2 α} \sqrt{{(x_{i} - x)}^{2} + z^{2}}] d x_{i},

(2)

u = \frac{(x - x^{'}) v}{2 α}; X = \frac{v x}{2 α}; Z = \frac{v z}{2 α}; L = \frac{v l}{2 α} .

(3)

To substitute (3) in (2), we get the following equation:

θ_{(x, z)} = \frac{2 q_{m} α}{π λ v} \int_{X - L}^{X + L} e^{- u} K_{0} \sqrt{Z^{2} + u^{2}} d u,

(4)

where q_m is the surface heating source intensity of semi-infinite body, λ is the thermal conductivity of workpiece material W/(m·K), α is thermal diffusivity (cm²/s) $α = λ / ρ c_{p}$ , c_p is specific heat capacity (J/(kg·K)⁻¹, ρ is density (g/cm³), V is the movement velocity of heat source, and K₀(u) is zero-order-modified Bessel function of the second kind.

2.1. Energy Proportionality Coefficient

Assume the theoretical contact area and actual contact area of grinding wheel and the workpiece as S and S_e respectively; q_w was used to express the internal input energy in unit time to obtain

q_{w} = \frac{1}{2} (θ_{m} b) {[2 {(λ ρ c_{p})}_{w} v \frac{S_{e}}{S} l_{c}]}^{1 / 2} .

(5)

Input energy of the grinding wheel in unit time is

q_{s} = \frac{1}{2} (θ_{m} b) {[2 {(λ ρ c_{p})}_{s} v_{s} \frac{S_{e}}{S} l_{c}]}^{1 / 2} .

(6)

Output energy via nanofluids in unit time is

q_{f} = \frac{1}{2} (θ_{m} b) {[2 {(λ ρ c_{p})}_{f} v_{s} l_{c}]}^{1 / 2} .

(7)

The proportionality coefficient R_w of input energy is

R_{w} = \frac{q_{w}}{q_{s} + q_{f}}, = 1 \times (1 + \sqrt{{(λ ρ c_{p})}_{s} / {(λ ρ c_{p})}_{w} \times (S_{e} / S) v_{s} / v} {+ \sqrt{{(λ ρ c_{p})}_{f} / {(λ ρ c_{p})}_{w} \times v_{s} / v})}^{- 1},

(8)

where v_s, the speed of grinding wheel; b, grinding width; (λρc_p)_w, performance parameters of workpiece; (λρc_p)_s, performance parameters of grinding wheel; (λρc_p)_f, performance parameters of nanofluids.

Surface heating source intensity of the workpiece is

q_{m} = \frac{R_{w} F_{t} v_{s}}{l_{s} b} .

(9)

3. Numerical Simulation of Temperature Field

3.1. Simulation Conditions

The planar grinding process was regarded as the movement of planar heat source on the workpiece surface, and temperature field rules of 2Cr13, 45 Steel, and ZrO₂ at 25°C were studied. Material properties and grinding parameters are shown in Tables 2, 3, 4, 5, and 6 [28 –31].

Table 2:

Performance parameters of 2Cr13 material.

Temperature (°C)	25	100	200	300	400	500
Modulus of elasticity (GPa)	228	214	208	200	189	180
Coefficient of thermal conductivity (W/m·K)	23.8
Specific heat (J/Kg·K)	460
Coefficient of thermal expansion (10⁻⁵/K)	10.3
Density (Kg/m³)	7750
Poisson's ratio	0.29
Yield strength (MPa)	440

Table 3:

Performance parameters of 45 steel.

Temperature (°C)	25	100	200	300	400	500	600	700
Thermal conductivity (W/m·K)	41.7	43.4	43.2	41.4	39.1	36.7	34.1	32.0
Specific heat (J/Kg·K)	480	498	524	560	615	700	854	1064
Coefficient of thermal expansion (10⁻⁵/K)	—	1.159	1.232	1.309	1.371	1.418	1.467	1.498
Density (Kg/m³)	7850
Modulus of elasticity (GPa)	209
Poisson's ratio	0.296
Yield strength (MPa)	355

Table 4:

Performance parameters of ZrO₂.

Density (Kg/m³)	Coefficient of thermal conductivity (W/m·K)	Specific heat (J/Kg·K)	Coefficient of thermal expansion (10⁻⁵/K)	Modulus of elasticity (GPa)	Poisson's ratio	Breaking tenacity (Mpa)

5500	3.5	660	9.6	209	0.3	8.1

Table 5:

Technological parameters of grinding.

Speed of grinding wheel (ν_s)	Work speed (ν_w)	Grinding depth (a_P)	grinding width (b)

40 m/s	3 m/min	5 μm	16 mm

Table 6:

Performance parameters of cooling and lubrication approaches.

Cooling and lubrication approaches	Performance parameter

Flood cooling Methodology	Water-based grinding fluid, delivery value: 100 L/min
MQL	Pure oil base (35 mL/H)
Nanoparticle jet flow of MQL	Carbon nanotube particles with the diameter of 10–20 nm; oil base (vegetable oil); volume fraction: 1%; delivery value: 15 mL/min
Dry grinding	None

3.2. Finite Element Grid Division

In the finite element analogue simulation, grid division has a decisive effect on the precision of the calculation analysis. The less width of the grid division, the higher the corresponding computational accuracy, and the more computation time is needed. Hence, to improve the computational accuracy and efficiency, in this model, the DC3D8 mode of 8-node implicit linear heat conduction unit was adopted for the grid division of workpiece.

3.3. Thermal Loading

The mobile heat source model was discretized, that is, in the time of one analysis step, uniform and constant heat source was loaded to a certain area. In the next analysis step, the heat source was moved to another area. Meanwhile, the previous analysis results were used as the initiative conditions in the simulation so as to achieve the continuous moving loading of the heat source.

4. Result Analysis

4.1. Temperature Distribution along the Grinding Direction

In the planar grinding, with the constant feeding of the grinding wheel, the workpiece surface is influenced by the heat source effects, and its heat flux density and temperature field changed with the time. Rules of temperature variation at different positions are shown in Figure 2.

Figure 2:

Graph of temperature distribution at different points along the grinding direction.

As shown in Figure 2, along the feeding direction of the grinding wheel, 6 nodes on the finished surface were taken with equidistance successively to acquire the temperature-time diagram. It can be seen from the figure that the temperature variation tendency of the six nodes was much the same, progressing forward in the form of waves respectively. When the heat source moves to the grinding arc zone of nodes, the node temperature was rapidly increased and reached the peak value when the heat source was about to leave the grinding arc zone. When the position of heat source was removed from the grinding arc zone, energies of each node rapidly diffused with the temperature gradually getting stabilized. Furthermore, the nodes closer to the heat source will have higher equilibrium temperature at the steady state.

4.2. Temperature Distribution along the Workpiece Thickness Direction

Figure 3 shows the surface temperature field variation rules along the workpiece thickness direction of 45 Steel under the condition of nanoparticle jet flow of the MQL. It can be seen from the Figure 3 that in the grinding, the heat source had an extremely short effect time on the workpiece surface. In addition, due to the relatively small thermal conductivity of the workpiece material, the input heat on the workpiece surface from the heat source cannot be timely diffused, thus forming the local high temperature as shown in the Figure 3. Moreover, the workpiece surface temperature was much higher than the subsurface temperature of the workpiece, presenting a relatively large temperature gradient along the direction of workpiece thickness. The temperature variation of the workpiece along the direction of thickness is mainly related with the material properties of heat source and the workpiece. The coefficient of thermal conductivity of the workpiece imposes significant impacts on longitudinal temperature variation.

Figure 3:

Temperature distribution diagram of nodes along the direction of grinding depth.

As shown in Figure 3, four points with 0 mm, 0.2 mm, 0.5 mm, 1.0 mm, 1.8 mm, and 2.5 mm from the workpiece-finished surface along the workpiece thickness were taken, generating the time varying temperature diagram. It can be seen from the figure that the node with Z = 0 mm located on the surface of the grinding zone, and its maximum temperature, that is, the maximum temperature in the grinding zone, was about 280°C; with the node of Z = 0.5 mm, the maximum temperature of the node dropped to about 80°C. In addition, with the node of Z = 1.8 mm and Z = 2.5 mm, the temperature curve of the two nodes almost overlapped, and the maximum temperature at the steady state was about 50°C. It can be observed from the temperature curve of each node that in the planar grinding, from the temperature variation below the grinding surface, the node farther from the grinding surface will be less affected by the mobile heat source. When Z < – 1.5 mm, the temperature variation tendency of nodes along the direction of grinding depth.

4.3. Simulation Results of Grinding Temperature Field with Different Cut Depths

In order to research on the time-varying of temperature fields of the three kinds of materials, the analog simulation of these materials under working conditions of different grinding depths was conducted.

4.3.1. Analysis of Simulation Parameters

In the planar grinding, parameters were interrelated and mutually influenced. With the changes of grinding depths, other simulation technological parameters (such as grinding zone contact arc length, heat distribution coefficient, heat flux density of mobile heat source etc.) were changed. Analog simulation of temperature fields with different grinding depths was conducted. Firstly, parameters were calculated. Corresponding grinding technological parameters of three grinding depths were shown in Table 7.

Table 7:

Grinding technological parameters of 2Cr13.

Grinding depth a_p	Contact Arc length l_c	Heat distribution coefficient R_w	Grinding tangential force F_t	Heat flux density q_t

1 μm	0.45 mm	83%	28.4 N	8.57 W/mm²
5 μm	1 mm	90%	51.3 N	15.4 W/mm²
10 μm	1.41 mm	92%	51.3 N	20.8 W/mm²

Similarly, corresponding heat flux densities of 45 Steel with the grinding depth of 1 μm, 5 μm and 10 μm were respectively 17.8 W/mm², 21.6 W/mm², and 23.0 W/mm². Meanwhile, the corresponding heat flux densities of the ceramic material at three different grinding depths were 10.3 W/mm², 12.5 W/mm², and 14.5 W/mm².

4.3.2. Simulation Results

Figures 4–5 showed the time-varying temperature diagram of the stainless steel 2Cr13 and zirconia ceramics in nanometer size with the grinding depth of 1 μm, 5 μm, and 10 μm. It can be observed from the figure that, in the planar grinding, different grinding depths should be adopted for different workpiece materials, without changing the shape of time-dependent grinding temperature curve. The only change was the grinding temperature peak value. In other words, the larger the grinding depth is, the higher the grinding temperature is. With the gradual decrease of the cut depth, the temperature variation curve tended to be flat. With the consideration that the removal mechanism of ceramic material is brittle rupture, the grinding wheel squeezed with ceramic materials during the grinding so that ceramic materials produced a large sum of cracks, which kept on extending and eventually led to the brittle removal of abrasive dusts. Under the same grinding condition, brittle rupture removal materials only consumed relatively low specific energies. Hence, the temperature in the grinding zone was relatively lower. The two materials generated temperatures with remarkable gradients in the grinding zone. When the mobile heat source left the grinding zone, the temperature gradually decreased and tended to be stable. However, with different physical property parameters of the materials (such as thermal conductivity, specific heat and coefficient of thermal expansion etc.), the general tendency of temperature curves was similar but the temperature generated from the grinding zone was different.

Figure 4:

2Cr13 Temperature variation diagram.

Figure 5:

Time-varying diagram of ceramics temperature.

4.4. Simulation Analysis under Different Cooling and Lubrication Conditions

Figure 6 shows the simulation results of temperature field of 2Cr13 in four cooling and lubrication approaches. As shown in Figure 6, regularities of temperature field distribution are the same. Yet, due to different thermal ratios through grinding mediums, the temperatures of the grinding zone are different. However, based on excellent heat transfer property of nanofluids, the temperature of the grinding zone was greatly reduced. As shown in Figure 7, the location with the maximum temperature difference was in the grinding zone, indicating that only the injection of lubricants in the grinding zone and the maximum grinding temperature can be reduced to the most extent so as to prevent grinding burns and other issues during the grinding. Under the four cooling and lubrication conditions, the variations of grinding temperature along the grinding width were insignificant but temperature variations were significant. The addition of nanoparticle MQL in grinding remarkably weakened the temperature effect of the grinding zone.

Figure 6:

Temperature distribution along the grinding direction.

Figure 7:

Regularities of temperature distribution along the direction of grinding width.

Figure 8 shows the regularities of distribution of grinding temperature along the direction of workpiece thickness under four grinding conditions. Large temperature gradient can be observed from Figure 8. Besides, the temperature gradient of dry grinding obviously exceeded that of MQL. In addition, at the deep layer with Z = 2.8 mm, the internal grinding temperature was close to the initial temperature.

Figure 8:

Variation rules of grinding temperature along the direction of depth.

5. Conclusions

The heat transfer model of surface grinding temperature field with nanoparticle jet flow of MQL as well as the proportionality coefficient model of energy input workpiece was established, respectively. The numerical simulation of surface grinding temperature field of three workpiece materials was conducted, namely, 45 Steel, 2Cr13 and zirconia ceramics in nanometer size. In the grinding, the surface temperature of workpiece was the highest, with a large temperature gradient along the direction of workpiece thickness. Furthermore, the grinding depth greatly affected the grinding temperature. With the increase of the cut depth, the peak value of grinding temperature was rapidly elevated.

Distribution rules of the temperature field of 2Cr13 are the same in four cooling and lubrication approaches, namely, dry grinding, flood cooling methodology, MQL, and nanoparticle jet flow of MQL. Due to different thermal ratios from grinding medium, the temperature of the grinding zone was differed. Meanwhile, with the outstanding heat transfer property of nanofluids, the temperature in the grinding zone was greatly reduced. Under four cooling and lubrication conditions, little change of grinding temperature along the direction of grinding width was observed, however, with significant temperature variation. MQL with nanoparticle imposed the most significant impact on reducing the temperature effect of the grinding zone. During the grinding, only with the effective injection of grinding fluid in the grinding zone, the temperature of the grinding zone can be reduced to the most degree so as to prevent the grinding burn and improve the workpiece surface completeness.

Footnotes

Acknowledgment

This research was financially supported by the National Natural Science Foundation of China (50875138 and 51175276), the Shandong Provincial Natural Science Foundation of China (Z2008F11 and ZR2009FZ007), and the Specialized Construct Fund for Taishan Scholars.

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