- Email: [email protected]
Temperature measurement and heat flux characterization in grinding using thermography
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
journal homepage: www.elsevier.com/locate/jmatprotec
Temperature measurement and heat flux characterization in grinding using thermography A. Brosse ∗ , P. Naisson, H. Hamdi, J.M. Bergheau ´ Laboratoire de Tribologie et Dynamique des Syst`emes, Ecole Nationale d’Ing´enieurs de Saint-Etienne, 42023 Saint Etienne, France
a r t i c l e
i n f o
a b s t r a c t
Keywords:
The grinding process is commonly used to produce high-quality parts. A perfect control of
Grinding
this process is thus necessary to ensure correct final parts and limit damage. The expe-
Thermography
rience on this subject has shown that the main effects on ground surface are residual
Heat flux
stresses or metallurgical change, which are directly linked with the temperature and the
Inverse method
power absorbed during the process. Numerical simulations is a good mean to predict these effects in relation with the process parameters but the numerical models need input data such as the value and shape of the heat flux entering the workpiece. In order to estimate this flux, the temperature measurement is necessary but has shown its limits. Nowadays, a new method given by thermography seems promising for determination of temperature fields under the ground surface. This measurement combined with an inverse method allows the identification of the shape and value of the heat flux. This paper presents a new method for measuring the temperatures in grinding by means of thermography. The principle of measurement is proposed in combination with first results obtained from numerical simulations in order to obtain a new model of the heat flux entering the workpiece during the grinding process. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
The grinding process is one of the mostly used processes for parts machining. As soon as high precision parts are required manufacturers choose grinding. In this manner grinding is a high value added process and because it is often the last process of a part manufacturing caution has to be taken in order not to damage the workpiece. Previous work (Malkin, 1989; Marinescu et al., 2004; Hamdi et al., 2004) has shown that the grinding process implies great speed and temperature gradients in the workpiece which can lead to thermal damage on the ground surface. In order to avoid damage such as burns or residual stresses, we need to understand the way they appear in the workpiece and so the temperature reached in the workpiece.
∗
Corresponding author. Tel.: +33 477437538; fax: +33 477437539. E-mail address: [email protected] (A. Brosse). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.11.267
The first idea to determine this temperature and its effects is to model analytically the grinding process, but the work on this point (Guo and Malkin, 1992; Rowe et al., 1997; Warren, 1992) has shown the complexity of grinding and then the difficulty to obtain analytically the equation of the temperature below the ground surface. Another way that has shown great results is to perform numerical calculation instead of purely analytical formulation. Indeed, the improvement in development of numerical code allowed the simulation of many phenomena such as prediction of residual stresses induced by phase change (Mahdi and Zhang, 1997; Brosse et al., 2007). Nevertheless, even if the main characteristics of the numerical model are now quite easy to obtain (mesh, material properties, etc.), the main issue of simulation is the thermal load induced by grinding. Many
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
authors tried to model this heat flux in many ways. Usually, authors assume that the whole power is converted into heat and they estimate an energy partitioning ratio r between the wheel, workpiece, lubricant, chip, etc. to finally obtain the amount of heat entering the workpiece. Even if this method is still used nowadays there are many sources of errors including the estimation of r and the shape of the flux which is still unknown. That is why another method appeared based on the combination of an inverse method with a temperature measurement by thermocouple (Guo and Malkin, 1996). The critical point of this approach is the temperature measurement using thermocouples that has been revealed inappropriate for high temperature gradients (Hamdi et al., 2004; Thomas et al., 2006). Finally, it was shown that even if numerical simulation seems to be the best way to predict thermal damage and residual stresses with a very good precision, there is still a lack of knowledge about the grinding model. Indeed, the model of the heat flux entering the workpiece is the main issue today for the use of simulation with low error percentages. In this paper, a new method using thermography for the temperature distribution measurement in grinding is proposed, and the improvement for the modeling of grinding and its simulation are presented.
2. Temperature measurement using thermography 2.1.
Principle of thermography
Since the understanding of the radiation principles, it is well known that every body is submitted to the laws of radiation. In this way, each body at a temperature T emits a radiation with a wavelength inside the electromagnetic spectrum. The radiation emitted can be measured by a value called luminance and noted as L0 . The value of L0 is given analytically by the Planck’s law (Eq. (1)). L0 =
c1 −5 [exp(c2 / T) − 1]
(1)
where c1 is the first radiation constant: 3.741832 × 10−16 W m2 ; c2 the second radiation constant: 1.4388 × 10−2 m K; the wavelength [m]; T the absolute temperature [K] and L0 the energetic spectral luminance [W m−3 Sr−1 ]. Nevertheless, for a real body at the same temperature T, the luminance measured will not be equal to L0 but L = εL0 . Where ε is called emissivity of the material and takes values in the range [0,1]. The basic idea of thermography is then to measure the luminance of a body in a range of wavelength chosen to obtain the temperature of the body. Furthermore, inside the electromagnetic spectrum there are many kinds of radiation from the radio waves to the X and rays, the principle of infrared thermography is to measure the radiation in the infrared domain where the luminance reached maximum value. Finally, the thermography method gives very reliable measures with many advantages for grinding. Most of these advantages compared with thermocouples offer a better resolution (spatially and temporally) and also a whole window of
591
values instead of only one with a thermocouple. On the contrary, there are a few important parameters in thermography that authors have related (Thomas et al., 2006): the choosing of the spectral band of integration and the integration time for the camera, and also the determination of the emissivity of the workpiece, require a good knowledge about radiation.
2.2.
Experimental set-up
An experimental set-up is developed for the measure of temperature during the grinding process by thermography. An infrared camera is placed on the side of the workpiece. The wheel width is also taken wider than the workpiece in order to have a uniform and unilateral heat flux in all the workpiece. The workpiece is mounted on a dynamometer (Kistler 9257A) linked to an acquisition data system in order to measure also the loads during grinding. The camera is placed on a positioning system (2 translations, 2 rotations) in order to ensure the position of the optical axis with the workpiece. The camera and the workpiece are also mounted on the same plate with no relative movement during the grinding process to limit vibrations. In this way, the area measured by the camera is always the same and is chosen in the middle of the workpiece. With this method we limit the dispersion of the focal area between the surface and the sensor and ensure that the process is at steady state instantly with always the same material characteristics (same roughness and emissivity). Fig. 1 shows the final assembly used for the experiments. The camera is from the Flir system® company with a response time of about 2 ms in the spectral band from 3 to 5 m wavelength. In this band, the luminance has the advantage to be quite important in the range from 0 to 1000 ◦ C. Moreover, in this range the air is supposed to be transparent to infrared rays. Finally, the dimension of the measured window is an array of 320 × 255 pixels equivalent to a zone of 0.85 cm × 0.68 cm which gives us a spatial resolution of about 26 m per pixel.
2.3.
Experimental results
Many experiments have been carried out with the experimental device described in the previous part. An experiment design has been used with both alumina and cubic boron nitride (CBN) grinding wheels with depth of cut from 0.03 to
Fig. 1 – Thermography assembly.
592
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
Fig. 2 – Example of luminance field.
0.32 mm and a feed speed range from 6 to 18 m/min. Fig. 2 shows an example of the results obtained with a CBN wheel without lubrication with the machining conditions as follows: Material: 100C6 (AISI 52100); upgrinding condition; depth of cut Ap = 0.03 mm; feed speed Vf = 6.85 m/min and cutting speed Vc = 37.2 m/s. The thermal field observed is right after the instant of contact between the wheel and the workpiece. For this test the dynamometer gives a tangential load per unit length of 5 N per mm. This result is shown in Fig. 3 along with the other results of the experimental design. We can draw first remarks about the results obtained with the camera and the dynamometer. Firstly, it is important to note that even if the luminance field distribution seems to be in agreement with the literature, we need to treat the values and take into account the emissivity of our material. Secondly, it is noted that the evolution of the tangential load seems to be linear in relation with the depth of cut which means that doubling the depth of cut turns out to double the load. Finally, these results are quite interesting for the determination of the absorbed power.
2.4.
Post treatment
In order to obtain the real temperatures, a numerical integration of the Planck’s law is used in the range 3–5 m. Moreover, the emissivity of classic steel depends mainly on the temperature and has to be taken into account. The resolution of this non-linear system leads us to an iterative process for
Fig. 4 – Real experimental temperatures after treatment.
the determination of the real temperatures. This operation is performed using the calculation software MATLAB® . At the same time, a Gaussian filter is used to eliminate the noise and dithering in the measurement as well as a rotation. Fig. 4 shows the real temperature field after treatment. These temperatures are in agreement with the literature values on grinding. The innovation compared with previous work (Malkin, 1989; Rowe et al., 1997) is that now a distribution of temperature in a large zone under the wheel/workpiece contact can be known.
3.
Numerical simulations
3.1.
Principle
The numerical simulation of grinding turned out to be the most efficient way to determine the temperature and its effects (burns, residual stresses) on a ground surface (Hamdi et al., 2004; Mahdi and Zhang, 1995; Moulik et al., 2001). On the contrary, in order to obtain reliable results the numerical model of grinding is quite important. One of the most important parameters is the value and shape of the heat flux entering the workpiece. Today, it is commonly assumed that the shape of this flux is at least triangular (Malkin, 1989) or even exponential (Mahdi and Zhang, 1997). Then the flux value is usually found assuming that the whole absorbed power, calculated with the cutting speed and the measured tangential load, is converted into heat at the wheel/workpiece interface. This assumption is not valid without any consequences on the temperature and can involve errors for simulation. In this part, a numerical model for the simulation of grinding in the conditions of Section 2.3 based on the literature is presented. The model and calculated results are given and discussed.
3.2.
Fig. 3 – Tangential load Ft in relation with feed speed Vf and depth of cut Ap for a CBN wheel.
Numerical model
In order to simplify the simulation, the model is realized in plane grinding and consists of a moving heat source on a massive body. Because of the stationary of the process, a 2D
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
593
good results for the maximum temperatures reached in the workpiece, which are in agreement with experiments (Fig. 2). The results of calculation in Fig. 6b show that with a different equation for the heat flux, we can have more or less the same results on one point of the temperature map. Finally, these examples show that the shape of the heat flux is a very important parameter which has an influence not only on the maximum temperature reached in the workpiece but also on the distribution of this temperature. Since we have a new method for the measurement of a whole cartography of temperature, it could be interesting to find the best value and shape heat flux to minimize the error with experiment.
4.
Heat flux characterization
4.1.
Principle
Fig. 5 – Numerical model of grinding: mesh and load.
steady-state model is chosen that gives us only one step of calculation to perform. In this way, the model is equal to move along the workpiece with the heat source. Finally a model of 70 mm length × 15 mm width is meshed with 4-nodes bricks for a total number of nodes around 11,000 (Fig. 5). In this case, the heat flux was assumed to be triangular according to the literature (Malkin, 1989; Hamdi et al., 2004).
3.3.
Numerical results
In the conditions of grinding from Section 2.3, the tangential load per unit length is measured at 5 N/mm. Then, the value of the thermal load per unit length can be calculated as follows:
As shown in the previous part, numerical calculation is the best way to predict the apparition of residual stresses. The problem with a numerical model is to fit with the reality. Previous work is based upon the maximum temperature reached in the workpiece which leads to incomplete results. We propose to develop a method to determine the heat flux value and shape based on the whole surface of the temperature distribution. The basic idea of this inverse method is composed of an iterative process that optimizes the heat flux in order to obtain the desired convergence. This iterative process is solved using a standard Gauss-Newton method (Delalleau et al., in press) developed with the software MATLAB® .
4.2. P = Ft × Vc = 5 × 37.2 = 186 W mm−1
Results
(2)
The computation is performed with the finite element analysis software SYSWELD® . Fig. 6 shows the results of the simulation using material and conditions from Section 2.3. The contact length is obtained using the Malkin relation √ (Malkin, 1989): lc = (Ap d) = 2.7 mm. On the top (Fig. 6a), the heat flux is supposed to be triangular (Q = 50×) with a total power of 136 W mm−1 . Then, on the bottom (Fig. 6b) is shown another calculation with a heat flux assumed as Q = 17 + 20x so a power of 120 W. The results presented from the numerical simulations are very attractive for many reasons: The triangular heat flux assumption presented in the literature (Fig. 6a) gives very
The inverse method developed is used for the determination of the heat flux value and shape in the case of the experiment presented in Section 2.3. The input data are the temperature from Fig. 4 and an assumed heat flux expressed as the polynomial function: Q = A + Bx + Cx2
(3)
One can note that this equation allows to find a heat flux rectangular, triangular or polynomial depending on the value of A, B and C. Finally at the end of the calculation the optimization process converges to the following solution: A = 10; B = 23; C = 7.
Fig. 6 – Numerical simulations with 2 different thermal loads: (a) triangular heat flux Q = 50×; (b) rectangular + triangular heat flux Q = 17 + 20x.
594
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
Fig. 7 – Experimental and simulated maps of temperature.
Fig. 7 shows the comparison of the experimental map and the simulated map with the flux Q = 10 + 23x + 7x2 , and presents a comparison of the root mean square (RMS) errors obtained with both the old and the new models of heat flux. The results of the inverse method give very interesting results for the modeling of grinding. It is shown in Fig. 8 that even if an assumed triangular heat flux gives a quite good result it is not the optimized solution. The solution using a parabolic heat flux allows improving the model of grinding by decreasing the error. Nevertheless, we can note that there is still an error between experimental and simulated maps, which leads us to work on the improvement of the method on a few points: the improvement of the filtering of the experimental map in order to eliminate the noise created during the acquisition process (Fig. 7: experimental map). The characterization of the emissivity of our material, which comes for now from the literature, could be characterized more precisely. The amelioration of the inverse method in order to get a better and quicker solution could be realized by changing the optimization method. Anyway, this method is very promising and presents a great improvement for the characterization of the heat flux and the simulation of thermal damage due to grinding.
5.
Conclusion
The new coming out of thermography for temperature measurements in grinding brings a breakthrough in the modeling of the grinding process. Not only the results are a lot more accurate but also a whole thermal field is obtained on contrary with previous measurement using thermocouples. With this improvement the model of the heat flux entering the workpiece has been upgraded to fit with reality using an inverse method. With this method, it is shown that the current assumption of a triangular heat flux is not the most accurate result. Indeed, it seems that the heat flux entering the workpiece is given with a polynomial function of a second order. A test has been run for the determination of the heat flux using an experimental map, which confirms this model. The next step in the modeling of grinding is now to realize more characterization of the heat flux in other machining conditions and try to create a global law for the heat flux.
Acknowledgement The authors would like to thank Dr. A. Delalleau for his participation in this study and more specifically his help with the inverse methods.
references
Fig. 8 – Comparison of models.
Brosse, A., Hamdi, H., Bergheau, J.-M., 2007. Metallurgical effects during high speed grinding. In: Proc. HSM 2007, San Sebastian. Delalleau, A., Zahouani, H., Lagarde, J.M., Josse, G., Bergheau, J.M. Use of the Kalman Filters for the analysis of the mechanical properties of human skin in vivo. Inverse Problems Sci. Eng., accepted february 2007, to be published. Guo, C., Malkin, S., 1992. Heat transfer in grinding. J. Mater. Process. Manuf. Sci. 1, 16–27. Guo, C., Malkin, S., 1996. Inverse heat transfer of grinding part 2: applications. J. Eng. Ind. 118, 143–149.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
Hamdi, H., Zahouani, H., Bergheau, J.-M., 2004. Residual stresses computation in a grinding process. J. Mater. Process. Technol. 147, 277–285. Mahdi, M., Zhang, L., 1995. The finite element thermal analysis of grinding processes by Adina. Comput. Struct. 56,313–320. Mahdi, M., Zhang, L., 1997. Applied mechanics in grinding: 5 thermal residual stresses. Int. J. Mach. Tools Manufact. 37, 619–633. Malkin, S., 1989. Grinding Technology: Theory and Applications of Machining with Abrasives. Society of Manufacturing Engineers Editions, ISBN 0-87263-480-9. Marinescu, L.D., Rowe, W.-B. Dimitrov, B. Inasaki, I., 2004. Tribology of Abrasive Machining Processes, Andrew William Editions, ISBN 0-8155-1490-5.
595
Moulik, P.N., Yang, H.T.Y., Chandrasekar, S., 2001. Simulation of thermal stresses due to grinding. Int. J. Mech. Sci. 43, 831–851. Rowe, W.B., Black, S.C.E., Mills, B., Morgan, M.N., Qi, H.S., 1997. Grinding temperatures and energy partitioning. Proc. R. Soc. Lond. 453, 1083–1104. Thomas, G., Hamdi, H., Brosse, A., 2006. Grinding thermal fields measurements by infrared microscopy. In: Proc. AMPT 2006, Las Vegas. Warren, R.D., 1992. Analysis of Material Removal Processes. Springer-Verlag, Editions, ISBN 0-387-97728-7.
journal homepage: www.elsevier.com/locate/jmatprotec
Temperature measurement and heat flux characterization in grinding using thermography A. Brosse ∗ , P. Naisson, H. Hamdi, J.M. Bergheau ´ Laboratoire de Tribologie et Dynamique des Syst`emes, Ecole Nationale d’Ing´enieurs de Saint-Etienne, 42023 Saint Etienne, France
a r t i c l e
i n f o
a b s t r a c t
Keywords:
The grinding process is commonly used to produce high-quality parts. A perfect control of
Grinding
this process is thus necessary to ensure correct final parts and limit damage. The expe-
Thermography
rience on this subject has shown that the main effects on ground surface are residual
Heat flux
stresses or metallurgical change, which are directly linked with the temperature and the
Inverse method
power absorbed during the process. Numerical simulations is a good mean to predict these effects in relation with the process parameters but the numerical models need input data such as the value and shape of the heat flux entering the workpiece. In order to estimate this flux, the temperature measurement is necessary but has shown its limits. Nowadays, a new method given by thermography seems promising for determination of temperature fields under the ground surface. This measurement combined with an inverse method allows the identification of the shape and value of the heat flux. This paper presents a new method for measuring the temperatures in grinding by means of thermography. The principle of measurement is proposed in combination with first results obtained from numerical simulations in order to obtain a new model of the heat flux entering the workpiece during the grinding process. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
The grinding process is one of the mostly used processes for parts machining. As soon as high precision parts are required manufacturers choose grinding. In this manner grinding is a high value added process and because it is often the last process of a part manufacturing caution has to be taken in order not to damage the workpiece. Previous work (Malkin, 1989; Marinescu et al., 2004; Hamdi et al., 2004) has shown that the grinding process implies great speed and temperature gradients in the workpiece which can lead to thermal damage on the ground surface. In order to avoid damage such as burns or residual stresses, we need to understand the way they appear in the workpiece and so the temperature reached in the workpiece.
∗
Corresponding author. Tel.: +33 477437538; fax: +33 477437539. E-mail address: [email protected] (A. Brosse). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.11.267
The first idea to determine this temperature and its effects is to model analytically the grinding process, but the work on this point (Guo and Malkin, 1992; Rowe et al., 1997; Warren, 1992) has shown the complexity of grinding and then the difficulty to obtain analytically the equation of the temperature below the ground surface. Another way that has shown great results is to perform numerical calculation instead of purely analytical formulation. Indeed, the improvement in development of numerical code allowed the simulation of many phenomena such as prediction of residual stresses induced by phase change (Mahdi and Zhang, 1997; Brosse et al., 2007). Nevertheless, even if the main characteristics of the numerical model are now quite easy to obtain (mesh, material properties, etc.), the main issue of simulation is the thermal load induced by grinding. Many
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
authors tried to model this heat flux in many ways. Usually, authors assume that the whole power is converted into heat and they estimate an energy partitioning ratio r between the wheel, workpiece, lubricant, chip, etc. to finally obtain the amount of heat entering the workpiece. Even if this method is still used nowadays there are many sources of errors including the estimation of r and the shape of the flux which is still unknown. That is why another method appeared based on the combination of an inverse method with a temperature measurement by thermocouple (Guo and Malkin, 1996). The critical point of this approach is the temperature measurement using thermocouples that has been revealed inappropriate for high temperature gradients (Hamdi et al., 2004; Thomas et al., 2006). Finally, it was shown that even if numerical simulation seems to be the best way to predict thermal damage and residual stresses with a very good precision, there is still a lack of knowledge about the grinding model. Indeed, the model of the heat flux entering the workpiece is the main issue today for the use of simulation with low error percentages. In this paper, a new method using thermography for the temperature distribution measurement in grinding is proposed, and the improvement for the modeling of grinding and its simulation are presented.
2. Temperature measurement using thermography 2.1.
Principle of thermography
Since the understanding of the radiation principles, it is well known that every body is submitted to the laws of radiation. In this way, each body at a temperature T emits a radiation with a wavelength inside the electromagnetic spectrum. The radiation emitted can be measured by a value called luminance and noted as L0 . The value of L0 is given analytically by the Planck’s law (Eq. (1)). L0 =
c1 −5 [exp(c2 / T) − 1]
(1)
where c1 is the first radiation constant: 3.741832 × 10−16 W m2 ; c2 the second radiation constant: 1.4388 × 10−2 m K; the wavelength [m]; T the absolute temperature [K] and L0 the energetic spectral luminance [W m−3 Sr−1 ]. Nevertheless, for a real body at the same temperature T, the luminance measured will not be equal to L0 but L = εL0 . Where ε is called emissivity of the material and takes values in the range [0,1]. The basic idea of thermography is then to measure the luminance of a body in a range of wavelength chosen to obtain the temperature of the body. Furthermore, inside the electromagnetic spectrum there are many kinds of radiation from the radio waves to the X and rays, the principle of infrared thermography is to measure the radiation in the infrared domain where the luminance reached maximum value. Finally, the thermography method gives very reliable measures with many advantages for grinding. Most of these advantages compared with thermocouples offer a better resolution (spatially and temporally) and also a whole window of
591
values instead of only one with a thermocouple. On the contrary, there are a few important parameters in thermography that authors have related (Thomas et al., 2006): the choosing of the spectral band of integration and the integration time for the camera, and also the determination of the emissivity of the workpiece, require a good knowledge about radiation.
2.2.
Experimental set-up
An experimental set-up is developed for the measure of temperature during the grinding process by thermography. An infrared camera is placed on the side of the workpiece. The wheel width is also taken wider than the workpiece in order to have a uniform and unilateral heat flux in all the workpiece. The workpiece is mounted on a dynamometer (Kistler 9257A) linked to an acquisition data system in order to measure also the loads during grinding. The camera is placed on a positioning system (2 translations, 2 rotations) in order to ensure the position of the optical axis with the workpiece. The camera and the workpiece are also mounted on the same plate with no relative movement during the grinding process to limit vibrations. In this way, the area measured by the camera is always the same and is chosen in the middle of the workpiece. With this method we limit the dispersion of the focal area between the surface and the sensor and ensure that the process is at steady state instantly with always the same material characteristics (same roughness and emissivity). Fig. 1 shows the final assembly used for the experiments. The camera is from the Flir system® company with a response time of about 2 ms in the spectral band from 3 to 5 m wavelength. In this band, the luminance has the advantage to be quite important in the range from 0 to 1000 ◦ C. Moreover, in this range the air is supposed to be transparent to infrared rays. Finally, the dimension of the measured window is an array of 320 × 255 pixels equivalent to a zone of 0.85 cm × 0.68 cm which gives us a spatial resolution of about 26 m per pixel.
2.3.
Experimental results
Many experiments have been carried out with the experimental device described in the previous part. An experiment design has been used with both alumina and cubic boron nitride (CBN) grinding wheels with depth of cut from 0.03 to
Fig. 1 – Thermography assembly.
592
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
Fig. 2 – Example of luminance field.
0.32 mm and a feed speed range from 6 to 18 m/min. Fig. 2 shows an example of the results obtained with a CBN wheel without lubrication with the machining conditions as follows: Material: 100C6 (AISI 52100); upgrinding condition; depth of cut Ap = 0.03 mm; feed speed Vf = 6.85 m/min and cutting speed Vc = 37.2 m/s. The thermal field observed is right after the instant of contact between the wheel and the workpiece. For this test the dynamometer gives a tangential load per unit length of 5 N per mm. This result is shown in Fig. 3 along with the other results of the experimental design. We can draw first remarks about the results obtained with the camera and the dynamometer. Firstly, it is important to note that even if the luminance field distribution seems to be in agreement with the literature, we need to treat the values and take into account the emissivity of our material. Secondly, it is noted that the evolution of the tangential load seems to be linear in relation with the depth of cut which means that doubling the depth of cut turns out to double the load. Finally, these results are quite interesting for the determination of the absorbed power.
2.4.
Post treatment
In order to obtain the real temperatures, a numerical integration of the Planck’s law is used in the range 3–5 m. Moreover, the emissivity of classic steel depends mainly on the temperature and has to be taken into account. The resolution of this non-linear system leads us to an iterative process for
Fig. 4 – Real experimental temperatures after treatment.
the determination of the real temperatures. This operation is performed using the calculation software MATLAB® . At the same time, a Gaussian filter is used to eliminate the noise and dithering in the measurement as well as a rotation. Fig. 4 shows the real temperature field after treatment. These temperatures are in agreement with the literature values on grinding. The innovation compared with previous work (Malkin, 1989; Rowe et al., 1997) is that now a distribution of temperature in a large zone under the wheel/workpiece contact can be known.
3.
Numerical simulations
3.1.
Principle
The numerical simulation of grinding turned out to be the most efficient way to determine the temperature and its effects (burns, residual stresses) on a ground surface (Hamdi et al., 2004; Mahdi and Zhang, 1995; Moulik et al., 2001). On the contrary, in order to obtain reliable results the numerical model of grinding is quite important. One of the most important parameters is the value and shape of the heat flux entering the workpiece. Today, it is commonly assumed that the shape of this flux is at least triangular (Malkin, 1989) or even exponential (Mahdi and Zhang, 1997). Then the flux value is usually found assuming that the whole absorbed power, calculated with the cutting speed and the measured tangential load, is converted into heat at the wheel/workpiece interface. This assumption is not valid without any consequences on the temperature and can involve errors for simulation. In this part, a numerical model for the simulation of grinding in the conditions of Section 2.3 based on the literature is presented. The model and calculated results are given and discussed.
3.2.
Fig. 3 – Tangential load Ft in relation with feed speed Vf and depth of cut Ap for a CBN wheel.
Numerical model
In order to simplify the simulation, the model is realized in plane grinding and consists of a moving heat source on a massive body. Because of the stationary of the process, a 2D
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
593
good results for the maximum temperatures reached in the workpiece, which are in agreement with experiments (Fig. 2). The results of calculation in Fig. 6b show that with a different equation for the heat flux, we can have more or less the same results on one point of the temperature map. Finally, these examples show that the shape of the heat flux is a very important parameter which has an influence not only on the maximum temperature reached in the workpiece but also on the distribution of this temperature. Since we have a new method for the measurement of a whole cartography of temperature, it could be interesting to find the best value and shape heat flux to minimize the error with experiment.
4.
Heat flux characterization
4.1.
Principle
Fig. 5 – Numerical model of grinding: mesh and load.
steady-state model is chosen that gives us only one step of calculation to perform. In this way, the model is equal to move along the workpiece with the heat source. Finally a model of 70 mm length × 15 mm width is meshed with 4-nodes bricks for a total number of nodes around 11,000 (Fig. 5). In this case, the heat flux was assumed to be triangular according to the literature (Malkin, 1989; Hamdi et al., 2004).
3.3.
Numerical results
In the conditions of grinding from Section 2.3, the tangential load per unit length is measured at 5 N/mm. Then, the value of the thermal load per unit length can be calculated as follows:
As shown in the previous part, numerical calculation is the best way to predict the apparition of residual stresses. The problem with a numerical model is to fit with the reality. Previous work is based upon the maximum temperature reached in the workpiece which leads to incomplete results. We propose to develop a method to determine the heat flux value and shape based on the whole surface of the temperature distribution. The basic idea of this inverse method is composed of an iterative process that optimizes the heat flux in order to obtain the desired convergence. This iterative process is solved using a standard Gauss-Newton method (Delalleau et al., in press) developed with the software MATLAB® .
4.2. P = Ft × Vc = 5 × 37.2 = 186 W mm−1
Results
(2)
The computation is performed with the finite element analysis software SYSWELD® . Fig. 6 shows the results of the simulation using material and conditions from Section 2.3. The contact length is obtained using the Malkin relation √ (Malkin, 1989): lc = (Ap d) = 2.7 mm. On the top (Fig. 6a), the heat flux is supposed to be triangular (Q = 50×) with a total power of 136 W mm−1 . Then, on the bottom (Fig. 6b) is shown another calculation with a heat flux assumed as Q = 17 + 20x so a power of 120 W. The results presented from the numerical simulations are very attractive for many reasons: The triangular heat flux assumption presented in the literature (Fig. 6a) gives very
The inverse method developed is used for the determination of the heat flux value and shape in the case of the experiment presented in Section 2.3. The input data are the temperature from Fig. 4 and an assumed heat flux expressed as the polynomial function: Q = A + Bx + Cx2
(3)
One can note that this equation allows to find a heat flux rectangular, triangular or polynomial depending on the value of A, B and C. Finally at the end of the calculation the optimization process converges to the following solution: A = 10; B = 23; C = 7.
Fig. 6 – Numerical simulations with 2 different thermal loads: (a) triangular heat flux Q = 50×; (b) rectangular + triangular heat flux Q = 17 + 20x.
594
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 1 ( 2 0 0 8 ) 590–595
Fig. 7 – Experimental and simulated maps of temperature.
Fig. 7 shows the comparison of the experimental map and the simulated map with the flux Q = 10 + 23x + 7x2 , and presents a comparison of the root mean square (RMS) errors obtained with both the old and the new models of heat flux. The results of the inverse method give very interesting results for the modeling of grinding. It is shown in Fig. 8 that even if an assumed triangular heat flux gives a quite good result it is not the optimized solution. The solution using a parabolic heat flux allows improving the model of grinding by decreasing the error. Nevertheless, we can note that there is still an error between experimental and simulated maps, which leads us to work on the improvement of the method on a few points: the improvement of the filtering of the experimental map in order to eliminate the noise created during the acquisition process (Fig. 7: experimental map). The characterization of the emissivity of our material, which comes for now from the literature, could be characterized more precisely. The amelioration of the inverse method in order to get a better and quicker solution could be realized by changing the optimization method. Anyway, this method is very promising and presents a great improvement for the characterization of the heat flux and the simulation of thermal damage due to grinding.
5.
Conclusion
The new coming out of thermography for temperature measurements in grinding brings a breakthrough in the modeling of the grinding process. Not only the results are a lot more accurate but also a whole thermal field is obtained on contrary with previous measurement using thermocouples. With this improvement the model of the heat flux entering the workpiece has been upgraded to fit with reality using an inverse method. With this method, it is shown that the current assumption of a triangular heat flux is not the most accurate result. Indeed, it seems that the heat flux entering the workpiece is given with a polynomial function of a second order. A test has been run for the determination of the heat flux using an experimental map, which confirms this model. The next step in the modeling of grinding is now to realize more characterization of the heat flux in other machining conditions and try to create a global law for the heat flux.
Acknowledgement The authors would like to thank Dr. A. Delalleau for his participation in this study and more specifically his help with the inverse methods.
references
Fig. 8 – Comparison of models.
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