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Absorbed energy in laser truing of a small vitrified CBN grinding wheel
Journal of Materials Processing Technology 164–165 (2005) 1128–1133
Absorbed energy in laser truing of a small vitrified CBN grinding wheel X.Y. Wang a, ∗ , Y.B. Wu b , J. Wang c , W.J. Xu a , M. Kato b a
c
Key Laboratory for Precision and Non-traditional Machining of Ministry of Education, Dalian University of Technology, Dalian 116024, PR China b Department of Machine Intelligence and Systems Engineering, Faculty of Systems Science and Technology, Akita Profectural University, 84-4 Tsuchiya-Ebinokuchi, Honjo, Akita 015-0055, Japan School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology, GPO Box 2434, Brisbane 4001, Qld, Australia
Abstract Laser truing and dressing of abrasive grinding wheels has attracted great interest as a novel processing technique to complement conventional processing methods. Laser processes offer significant advantages over mechanical processes as lasers enable non-contact processing, and thus prevent tool wear. An energy balance model of energy absorption is presented that takes into account the space distribution of laser energy absorbed/scattered by the workpiece (circular profile). The models developed were used to predict various parameters, such as incident position, focal offset, and incident power, to compensate selective interaction during laser processing. Moreover, the incident angle for laser processing of small vitrified CBN grinding wheels was optimized. Further theoretical analysis and experiments determined the focal position of the incident beam with respect to the surface of the workpiece. Experiments were carried out using different processing parameters and grinding wheels to evaluate the effects of laser spatial properties on processing quality. The experimental results were shown to be in reasonable agreement with predicted results. © 2005 Elsevier B.V. All rights reserved. Keywords: Laser truing; Absorbed energy; Model; Vitrified CBN grinding wheel
1. Introduction Grinding with super-abrasive wheels offers many advantages, such as fine surface quality, dimensional stability and high efficiency, especially when used to machine tough and/or brittle material. However, preparation of a super-abrasive wheel, particularly the truing and dressing processes, presents several challenges: the limited ability to fabricate only ordered profiles/surfaces, long processing time and rapid wear of processing tools by conventional preparation methods. Also, the wheel wear and loading that inevitably occurs during grinding cannot be eliminated. Thus, it is difficult to achieve a satisfactory level of truing/dressing quality and efficiency by conventional processing technologies using singletip diamond dressers. For truing and dressing a small wheel, a highly efficient and fine processing method is much harder to develop. As a result, the potentials of grinding techniques ∗
Corresponding author. Tel.: +86 411 86929050; fax: +86 411 84708812. E-mail addresses: [email protected], [email protected] (X.Y. Wang). 0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.108
employing super-abrasive wheels have not yet been fully realized in most applications. To solve these problems, much research has been directed, by industrial practitioners and academic researchers alike, at exploring alternative highefficiency and high-precision truing and dressing techniques [1]. In the case of vitrified cubic boron nitride (CBN) wheels, single diamond dressers have been predominantly used to generate desired wheel surface profiles [1–3]. In some cases, the single diamond wears out quickly and a worn-out dresser cannot produce sufficient protrusion of the cutting grain edges, as verified by several researchers [2–4]. Laser truing and dressing for abrasive grinding wheels has attracted great interest as a novel processing technique to replace conventional processing methods. Laser dressing that removes the wheel materials through ablation of the bonding material (resin) to expose cutting grain edges has been tested for aluminum oxide wheels [5–7]. However, few studies have dealt with laser processing of the vitrified CBN wheel owing to its high temperature property of bond closed to abrasive [8]. There are also no reports on the usage of a laser beam
X.Y. Wang et al. / Journal of Materials Processing Technology 164–165 (2005) 1128–1133
Nomenclature A material’s absorption coefficient Cp specific heat (J/kg K) d diameter of the laser beam (mm) Dw wheel diameter (mm) eA (θ x ) absorbed energy (mJ) eR (θ x ) scattered energy (mJ) EA (θ x ) absorbed energy of revision (mJ) f focal length of the lens (mm) F focal length (mm) I charging current (A) kw structure coefficient k1 and k2 experimental coefficients K thermal conductivity (W/m K) N wheel rotation speed (rpm) Pr assisted oxygen pressure (kg/cm2 ) r laser beam radius (mm) R radius of spherical energy (mm) Rw radius of the wheel (mm) Sθ focal area (mm2 ) Sθ+z focal area of revision (mm2 ) t pulse width (ms) Tm melting point (◦ C) V beam traverse speed (mm/min) Greek letters α thermal diffusivity (106 m2 /s) center angle (◦ ) αa ν pulse frequency (Hz) θ incident angle (◦ ) ρ density (kg/m3 )
for preparation of small vitrified CBN wheels. Successful application of laser processing to truing/dressing of a small grinding wheel would enable high processing quality and high efficiency and help overcome shortcomings associated with mechanical processing, namely loading-induced deformation and shape distortion. The topic of beam-energy absorption/scattering during laser processing of all grinding wheels has received little coverage in the literature. Grinding wheels are cylindrical in this paper, and the position of laser irradiation greatly influences the amount of energy absorbed/scattered and is thus an important processing parameter. In a number of studies [9–11], the laser beam was applied vertically with respect to the surface of the workpiece (referred to as “vertical irradiation”), i.e. at an incident angle of zero. However, laser processing has been used in various applications and the incident angle is not always vertical. Different incident angles applied to the same area of the workpiece impart different levels of energy to the workpiece [9–11]. In the present study, energy absorption models
1129
were developed that take into account the space distribution of laser energy absorbed/scattered by the cylindrical surface of the workpiece. It was assumed that the laser energy is absorbed by the entire material in accordance with the energy balance equation. The models developed were used to compare selective interaction and improve processing quality during laser processing of grinding wheels. By varying parameters, such as incident power, incident angle, focal position and cutting speed, the optimal laser processing parameters were predicted for small vitrified CBN grinding wheels, and the novel processing technique developed was shown to be reliable.
2. Modeling of energy absorption The laser energy absorbed by the workpiece is converted into thermal energy, forming a temperature field throughout the workpiece, which is used in laser processing. Based on the principle of energy conservation, the total initial laser energy is equal to the sum of the absorbed and scattered energy. The scattered energy can be collected by the setup shown in Fig. 1. Based on the general shape of energy absorption curves obtained by metallography and existing data on energy scattering [11], a spherical model was proposed to characterize the space distribution of energy absorption and scattering during laser irradiation of a planar surface (Fig. 2). This geometric model was developed for the basic case of laser irradiation on the top surface of the wheels. In Fig. 2, O1 is the point at which the laser beam strikes the workpiece. O1 A represents the amount of absorbed energy in that direction eA (θ x ), while O1 B denotes the amount of scattered energy in that direction eR (θ x ). The following equations were derived based on the
Fig. 1. A setup for data collection of scattered energy.
Fig. 2. Principle schematic of absorbed energy on plane/0◦ .
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assumption that the radius of the laser beam is zero: eR (θx ) = R 1 − (1 − 2A)2 sin2 θx − (1 − 2A) R cos θx (1) eA (θx ) = R 1 − (1 − 2A)2 sin2 θx − (1 − 2A)R cos θx (2) Taking into consideration the effect of the laser beam radius, Eq. (2) was then revised to yield a model for practical application: EA (θx ) = R 1 − (1 − 2A)2 sin2 θx − (1 − 2A)R cos θx +kr sin θx
(3)
where eR (θ x ) is the scattered energy (mJ) in an arbitrary direction θ x and eA (θ x ) stands for absorbed energy (mJ) in an arbitrary direction θ x ; EA (θ x ) denotes the absorbed energy (mJ) in an arbitrary direction after revision for practical application θ x ; R is the radius of spherical energy (mm); A is the material’s absorption coefficient in relation to the laser. The kr sin θ x is the term for eA (θ x ) revision owing to the laser beam radius r (mm). So, Eq. (2) needs to be revised and k (effect factor) was determined by the following equation: k=
k1 fA (90◦ ) − k2 fA (0◦ ) k2 r
(4)
where k is a constant representing the focal point size of the laser beam; k1 and k2 are experimental coefficients associated, respectively, with scattered and absorbed energy. To obtain geometrical and mathematical relationships between the laser beam and grinding wheel with respect to incident position and incident angle, several irradiation conditions (vertical, parallel, and intermediate incident angles from 0◦ to 90◦ ) were selected to examine the effect of processing parameters. We can see in Fig. 3 that the reflected beam direction continuously varies between 0◦ and 90◦ with respect to the incident beam and it changes by 180◦ from y direction to −y direction, whereas the laser incident direction remains constant “direction −y”, shown in Fig. 3(b). Based on both theoretical and empirical methods, a space distribution was obtained, which was used for the selective processing of a vitrified CBN grinding wheel. Here, an oval formula that describes the focal area of an arbitrary point (irradiated position changed, but focal distance kept constant) is represented by the following equation: Sθ =
πd 2 4 cos(θ + αa )
(5)
where Sθ is the focal area (mm2 ); d the diameter of the laser beam (mm); αa the central angle with respect to the focal point on the wheel surface; and θ the incident angle (0–90◦ ), as illustrated in Fig. 3(a).
Fig. 3. Principle schematic of critical angle (a); interpreting results of energy distribution absorbed on circular surface (b).
For cases where laser processing conditions such as irradiation position and focal distance changed simultaneously, an oval formula that describes the focal area of an arbitrary point was derived: Sθ+z =
π(fθl + kw Rw (1 − cos θ))2 4 cos(θ + αa )
(6)
where Sθ+z is the focal area (mm2 ) incorporating the focal offset; f the focal length of the lens(mm); θ l the diffuse angle of laser; Rw the radius of the circular workpiece (mm); αa the central angle with respect to the irradiation focal point on the wheel surface which is inversely proportional to Rw ; θ the incident angle (0–90◦ ) and kw equals D/2f = 0.25, which varies depending on the particular laser beam (D is the diameter of the laser beam before focus). When substituting Eqs. (1)–(4) into Eqs. (5) and (6), geometrical relationships and the spatial distribution of absorbed energy on a cylindrical surface were obtained. A number of significant laser processing parameters could thus be predicted. These equations clearly reveal that the focal area on the cylindrical surface increases with incident angle, which means the energy density of laser irradiation decreases with incident angle.
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3. Results and discussions Calculations were made and the effects of incident angle/position, focal offset/processing parameters on energy absorption were plotted using Microsoft Excel and AutoCAD. In order to validate the governing equation, laser processing experiments were performed on small vitrified CBN grinding wheels. An LKS-250A pulse YAG laser was used with a maximum power of 400 W. The highest processing speed was 1500 mm/min, the pulse frequency was varied from 100 to 400 Hz, and the rotation speed of the wheel was maintained between 1000 and 2000 rpm. 3.1. Space distribution of absorbed energy at arbitrary point The space distributions were calculated and represented as shown in Fig. 3(b). The figure shows the effect of incident angle on absorbed energy at any position on the cylindrical surface. The curves represent the temperature field induced by laser irradiation. The temperature field has a spherical shape (circular in the figure) for vertical (0◦ ) laser irradiation of the surface. The isothermal curves are seen to be distorted due to the curvature of the surface. Changing the incident angle of laser irradiation from 0 to 90◦ results in a significant increase in the radii of curvature of the temperature profile, whereas, at a given position, its radii of curvature from left to right were gradually reduced along a temperature line. Thus, the relation between incident angle and absorbed energy should be modeled and used in optimization of laser processing parameters. Interpreting results of absorbed energy density on a cylindrical surface, Fig. 4(a) shows the theoretical prediction of the effects of incident angle on absorbed energy. The absorbed energy decreases rapidly with incident angle: it drops to 37.5% of its initial value in going from vertical irradiation (0◦ ) to an incident angle of 60◦ . As is clear from the figure, the increase in incident angle causes the focal area on the processing surface to expand, which in turn causes the laser density on the workpiece to decrease more sharply than the incident angle increases. Therefore, when a curved surface is laser-irradiated at close to 90◦ (parallel position), there exists a critical incident angle such that between θ c and 90◦ the irradiated area cannot be processed properly. If the laser-processing head does not move parallel to the axis of a wheel, laser focus offset may be generated. The focal offset would cause the laser focal area on the processing surface to expand. Consequently, the energy density of laser irradiation on the processing area would decrease. The relations are shown in detail in Fig. 4(b). The figure shows the calculated effect of focal offset on absorbed energy. Energy absorption is seen to decrease more sharply with laser focal offset than it does with incident angle. At a given area of laser irradiation, the absorbed energy drops to 15.6% of its value with offset (incident angle: 0◦ ). This is because the fo-
Fig. 4. Effect of incident angle on absorbed energy (two surfaces: linear and circular) (a); effect of focal offset on absorbed energy (D is the diameter of circular) (b).
cal area, in the presence of a focal offset, is effectively equal to the sum of the extra areas that both focal offset and incident angle yield above the original area under normal irradiation conditions. In general, every calculation (including experimental results) has a certain error associated with it. This needs to be considered as Fig. 4 shows that incident angle does not work when it reaches. Thus, further research will be conducted on laser processing of grinding wheels at this critical angle, thanks to which we expect to be able to report better optimized processing parameters in subsequent publications. In laser processing, the focal area changes with the radius of curvature of the wheel, i.e., the wheel size. Fig. 5 shows the absorbed energy as a function of wheel diameter. Thus, different processing parameters ought to be used when using different grinding wheel sizes to match the size of a particular workpiece. The effect of wheel diameter on absorbed energy is shown as well. To investigate the effect of circular workpiece diameter on absorbed energy, the focal distance was maintained constant during the measurement.
Fig. 5. Effect of wheel diameter/incident angle on absorbed energy.
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Table 1 Thermal properties of the particles and bonds Composition
Melting point, Tm (◦ C)
Density, ρ (kg/m3 )
Specific heat, Cp (J/kg K)
Thermal conductivity K (W/m K)
Thermal diffusivity, α (×106 m2 /s)
CBN Ceramic bond Al2 O3 Bronze/resin Diamond
3200 1000–1200 2050 831/350–400 3700–4000
3450
506 762–909 765 342/1591–1758 502
1300 20–30 36 25/0.25–0.35 146
744.7
3970 8760/1250–1300 3480–3560
Clearly, the absorbed energy decreases with both the diameter of circular workpiece and incident angle, more sharply with the latter. As such, the relation between the wheel size and absorbed energy should be modeled and taken into account during optimization of processing parameters. 3.2. Experimental versus calculated parameters for laser processing of grinding wheel The effects of laser processing parameters such as incident angle, focal offset, incident power, and traverse speed were tested by experiments. All these parameters were found to influence the absorbed energy and incident beam density. For example, the absorbed energy decreases with increasing incident angle (Fig. 4). The experimental results for incident angle were as follows: at an incident angle of 60, 70, and 80◦ ,the volume of material removal was 0.07, 0.04 and 0.02 mm, respectively. Calculated results showed a good agreement with experimental results. The laser processing is governed by the absorbed laser intensity at the target surface and by the thermal and optical properties of the target material. The properties of the materials composing diamond wheels are listed in Table 1. A principle schematic of laser truing of a grinding wheel is shown in Fig. 6(a), which is as well a basic setup for truing experiments. Therefore, a laser cutting experiment designed to simulate a single diamond dresser yielded the laser turning results revealed in the micrograph in Fig. 6(b). The processing parameters used were listed in Table 2, in which the constant parameters were: Dw = 5 mm, f = 40 mm, Pr = 3 kg/cm2 . The whole profile of a processed wheel is visible; it is seen to resemble a micro-thread.
11.9 8.34/0.088 82
to remove both diamonds and bond materials, but a little difference. The volume of material removed from vitrified CBN wheel surface increases with increasing of the laser power intensity and laser pulse width, but too larger laser power intensity and laser pulse width may cause damage to abrasive grains. According to calculation and experimental results, the processing parameters can be selected during laser truing both materials of vitrified bond and CBN as shown in Table 2. In these cases, the laser power intensities of irradiated spot on the vitrified bonded CBN wheel can reach the value of 7.5 × 104 to 1.125 × 105 W/cm2 . The wheel surface conditions compared with SEM micrographs (SEM: TOPCOM SM-200) have also been discussed to verify the material removal mechanism and the influence of laser irradiation on the wheel surface. Fig. 7(a) shows the micro-profile after mechanical preparation. A large number of CBN particles are observed. They are connected with vitrified bonds and there is porosity in between. Fig. 7(b) shows the wheel surface after laser processing. Unlike in mechanical processing, molten and re-solidified ceramic bonds have been found on the wheel surface
3.3. Parameter selection in laser truing of the small vitrified CBN wheel When truing vitrified CBN wheel, the incident angle, focal offset, laser power intensity, traverse speed, wheel rotation speed, and laser pulse parameter must be selected properly Table 2 Parameter selection in laser truing of small vitrified CBN wheels Truing mode
I (A)
V (mm/ min)
N (rpm)
t (ms)
θ (◦ )
ν (Hz)
Incident angle Focal offset
200–260 240–300
40–80 20–60
2000 1500
0.2–0.5 0.2–0.5
0–70 0–50
100–200 100–200
Fig. 6. Principle schematic of laser truing of a grinding wheel (a); wheel surface profile after laser beam turning (b).
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of molten ceramic exhibiting a different porous structure than the original wheel surface. An analysis of calculated and experimental results has provided an in-depth understanding of the relation between processing parameters and product quality, forming a knowledge base that will help improve techniques for laser truing and dressing of grinding wheels.
Acknowledgements The authors would like to thank Akita Prefectural University for providing the resources required to undertake this study and the university’s staff members and PhDs who assisted with the experimental setup and measurements. This study was supported in part by the NSFC Key Project (No. 59935110).
References Fig. 7. Wheel surface conditions (a) after mechanical preparation; (b) after laser processing.
following laser irradiation. Also, the protrusion of the actual cutting edges is reduced in laser processing. This will result in smoother, i.e., ground surfaces, i.e., better surface quality; however it will also reduce the grinding efficiency of the wheel.
4. Conclusions The model developed used the energy balance equation to calculate several parameters in laser processing of a small vitrified CBN grinding wheel. A new space distribution was obtained for the laser energy absorption at any position on a cylindrical surface between 0 and 90◦ . The present model predicted the effect of processing parameters such as incident angle (irradiation position) and focal offset on absorbed energy and the effect of incident power and processing speed on the volume of material removed. Characterization of the wheel surface after laser processing revealed re-solidification
[1] K. Syoji, Truing and dressing of super-abrasive wheels, Mach. Tools 2 (1989) 18–26. [2] N.M. Filho, Analysis of dressing performance using single crystal diamond dresser, Ind. Diamond Rev. 59 (1999) 133–142. [3] M. Hitchiner, Dressing of vitrified CBN wheels for production grinding, Finer Points 11 (1999) 18–25. [4] Y. Zhou, Wear and self-sharpening of vitrified bond diamond wheels during sapphire grinding, Wear 219 (1998) 42–45. [5] N.R. Babu, Investigations on laser dressing of grinding wheels. Part I. Preliminary study, ASME J. Eng. Ind. 111 (1989) 244–252. [6] N.R. Babu, Investigations on laser dressing of grinding wheels, ASME J. Eng. Ind. 111 (1989) 253–261. [7] X. Chen, I. Pashby, Comparison of laser cleaning of Al2 O3 and CBN grinding wheels, Key Eng. Mater. 257/258 (2004) 365–370. [8] C. Zhang, A novel laser-assisted truing and dressing technique for vitrified CBN wheels, Int. J. Mach. Tools Manuf. 42 (2002) 825–835. [9] J. Tadano, Y. Ito, Angular dependence of coupling between focused laser pulses and a transparent material studied by time-resolved imaging technique, in: Proceedings of Second International Conference on LEM21, Niigata, Japan, 2003. [10] X. Wang, J. Wang, An experimental study of laser 3D machining with variable processing parameters, in: Proceedings of the Second International Conference on LEM21, Niigata, Japan, 2003. [11] X. Wang, A numerical study of scattering phenomena in laser machining, in: Proceedings of the Sixth International Conference of ICFDM, Dalian, China, 2000.
Absorbed energy in laser truing of a small vitrified CBN grinding wheel X.Y. Wang a, ∗ , Y.B. Wu b , J. Wang c , W.J. Xu a , M. Kato b a
c
Key Laboratory for Precision and Non-traditional Machining of Ministry of Education, Dalian University of Technology, Dalian 116024, PR China b Department of Machine Intelligence and Systems Engineering, Faculty of Systems Science and Technology, Akita Profectural University, 84-4 Tsuchiya-Ebinokuchi, Honjo, Akita 015-0055, Japan School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology, GPO Box 2434, Brisbane 4001, Qld, Australia
Abstract Laser truing and dressing of abrasive grinding wheels has attracted great interest as a novel processing technique to complement conventional processing methods. Laser processes offer significant advantages over mechanical processes as lasers enable non-contact processing, and thus prevent tool wear. An energy balance model of energy absorption is presented that takes into account the space distribution of laser energy absorbed/scattered by the workpiece (circular profile). The models developed were used to predict various parameters, such as incident position, focal offset, and incident power, to compensate selective interaction during laser processing. Moreover, the incident angle for laser processing of small vitrified CBN grinding wheels was optimized. Further theoretical analysis and experiments determined the focal position of the incident beam with respect to the surface of the workpiece. Experiments were carried out using different processing parameters and grinding wheels to evaluate the effects of laser spatial properties on processing quality. The experimental results were shown to be in reasonable agreement with predicted results. © 2005 Elsevier B.V. All rights reserved. Keywords: Laser truing; Absorbed energy; Model; Vitrified CBN grinding wheel
1. Introduction Grinding with super-abrasive wheels offers many advantages, such as fine surface quality, dimensional stability and high efficiency, especially when used to machine tough and/or brittle material. However, preparation of a super-abrasive wheel, particularly the truing and dressing processes, presents several challenges: the limited ability to fabricate only ordered profiles/surfaces, long processing time and rapid wear of processing tools by conventional preparation methods. Also, the wheel wear and loading that inevitably occurs during grinding cannot be eliminated. Thus, it is difficult to achieve a satisfactory level of truing/dressing quality and efficiency by conventional processing technologies using singletip diamond dressers. For truing and dressing a small wheel, a highly efficient and fine processing method is much harder to develop. As a result, the potentials of grinding techniques ∗
Corresponding author. Tel.: +86 411 86929050; fax: +86 411 84708812. E-mail addresses: [email protected], [email protected] (X.Y. Wang). 0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.108
employing super-abrasive wheels have not yet been fully realized in most applications. To solve these problems, much research has been directed, by industrial practitioners and academic researchers alike, at exploring alternative highefficiency and high-precision truing and dressing techniques [1]. In the case of vitrified cubic boron nitride (CBN) wheels, single diamond dressers have been predominantly used to generate desired wheel surface profiles [1–3]. In some cases, the single diamond wears out quickly and a worn-out dresser cannot produce sufficient protrusion of the cutting grain edges, as verified by several researchers [2–4]. Laser truing and dressing for abrasive grinding wheels has attracted great interest as a novel processing technique to replace conventional processing methods. Laser dressing that removes the wheel materials through ablation of the bonding material (resin) to expose cutting grain edges has been tested for aluminum oxide wheels [5–7]. However, few studies have dealt with laser processing of the vitrified CBN wheel owing to its high temperature property of bond closed to abrasive [8]. There are also no reports on the usage of a laser beam
X.Y. Wang et al. / Journal of Materials Processing Technology 164–165 (2005) 1128–1133
Nomenclature A material’s absorption coefficient Cp specific heat (J/kg K) d diameter of the laser beam (mm) Dw wheel diameter (mm) eA (θ x ) absorbed energy (mJ) eR (θ x ) scattered energy (mJ) EA (θ x ) absorbed energy of revision (mJ) f focal length of the lens (mm) F focal length (mm) I charging current (A) kw structure coefficient k1 and k2 experimental coefficients K thermal conductivity (W/m K) N wheel rotation speed (rpm) Pr assisted oxygen pressure (kg/cm2 ) r laser beam radius (mm) R radius of spherical energy (mm) Rw radius of the wheel (mm) Sθ focal area (mm2 ) Sθ+z focal area of revision (mm2 ) t pulse width (ms) Tm melting point (◦ C) V beam traverse speed (mm/min) Greek letters α thermal diffusivity (106 m2 /s) center angle (◦ ) αa ν pulse frequency (Hz) θ incident angle (◦ ) ρ density (kg/m3 )
for preparation of small vitrified CBN wheels. Successful application of laser processing to truing/dressing of a small grinding wheel would enable high processing quality and high efficiency and help overcome shortcomings associated with mechanical processing, namely loading-induced deformation and shape distortion. The topic of beam-energy absorption/scattering during laser processing of all grinding wheels has received little coverage in the literature. Grinding wheels are cylindrical in this paper, and the position of laser irradiation greatly influences the amount of energy absorbed/scattered and is thus an important processing parameter. In a number of studies [9–11], the laser beam was applied vertically with respect to the surface of the workpiece (referred to as “vertical irradiation”), i.e. at an incident angle of zero. However, laser processing has been used in various applications and the incident angle is not always vertical. Different incident angles applied to the same area of the workpiece impart different levels of energy to the workpiece [9–11]. In the present study, energy absorption models
1129
were developed that take into account the space distribution of laser energy absorbed/scattered by the cylindrical surface of the workpiece. It was assumed that the laser energy is absorbed by the entire material in accordance with the energy balance equation. The models developed were used to compare selective interaction and improve processing quality during laser processing of grinding wheels. By varying parameters, such as incident power, incident angle, focal position and cutting speed, the optimal laser processing parameters were predicted for small vitrified CBN grinding wheels, and the novel processing technique developed was shown to be reliable.
2. Modeling of energy absorption The laser energy absorbed by the workpiece is converted into thermal energy, forming a temperature field throughout the workpiece, which is used in laser processing. Based on the principle of energy conservation, the total initial laser energy is equal to the sum of the absorbed and scattered energy. The scattered energy can be collected by the setup shown in Fig. 1. Based on the general shape of energy absorption curves obtained by metallography and existing data on energy scattering [11], a spherical model was proposed to characterize the space distribution of energy absorption and scattering during laser irradiation of a planar surface (Fig. 2). This geometric model was developed for the basic case of laser irradiation on the top surface of the wheels. In Fig. 2, O1 is the point at which the laser beam strikes the workpiece. O1 A represents the amount of absorbed energy in that direction eA (θ x ), while O1 B denotes the amount of scattered energy in that direction eR (θ x ). The following equations were derived based on the
Fig. 1. A setup for data collection of scattered energy.
Fig. 2. Principle schematic of absorbed energy on plane/0◦ .
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assumption that the radius of the laser beam is zero: eR (θx ) = R 1 − (1 − 2A)2 sin2 θx − (1 − 2A) R cos θx (1) eA (θx ) = R 1 − (1 − 2A)2 sin2 θx − (1 − 2A)R cos θx (2) Taking into consideration the effect of the laser beam radius, Eq. (2) was then revised to yield a model for practical application: EA (θx ) = R 1 − (1 − 2A)2 sin2 θx − (1 − 2A)R cos θx +kr sin θx
(3)
where eR (θ x ) is the scattered energy (mJ) in an arbitrary direction θ x and eA (θ x ) stands for absorbed energy (mJ) in an arbitrary direction θ x ; EA (θ x ) denotes the absorbed energy (mJ) in an arbitrary direction after revision for practical application θ x ; R is the radius of spherical energy (mm); A is the material’s absorption coefficient in relation to the laser. The kr sin θ x is the term for eA (θ x ) revision owing to the laser beam radius r (mm). So, Eq. (2) needs to be revised and k (effect factor) was determined by the following equation: k=
k1 fA (90◦ ) − k2 fA (0◦ ) k2 r
(4)
where k is a constant representing the focal point size of the laser beam; k1 and k2 are experimental coefficients associated, respectively, with scattered and absorbed energy. To obtain geometrical and mathematical relationships between the laser beam and grinding wheel with respect to incident position and incident angle, several irradiation conditions (vertical, parallel, and intermediate incident angles from 0◦ to 90◦ ) were selected to examine the effect of processing parameters. We can see in Fig. 3 that the reflected beam direction continuously varies between 0◦ and 90◦ with respect to the incident beam and it changes by 180◦ from y direction to −y direction, whereas the laser incident direction remains constant “direction −y”, shown in Fig. 3(b). Based on both theoretical and empirical methods, a space distribution was obtained, which was used for the selective processing of a vitrified CBN grinding wheel. Here, an oval formula that describes the focal area of an arbitrary point (irradiated position changed, but focal distance kept constant) is represented by the following equation: Sθ =
πd 2 4 cos(θ + αa )
(5)
where Sθ is the focal area (mm2 ); d the diameter of the laser beam (mm); αa the central angle with respect to the focal point on the wheel surface; and θ the incident angle (0–90◦ ), as illustrated in Fig. 3(a).
Fig. 3. Principle schematic of critical angle (a); interpreting results of energy distribution absorbed on circular surface (b).
For cases where laser processing conditions such as irradiation position and focal distance changed simultaneously, an oval formula that describes the focal area of an arbitrary point was derived: Sθ+z =
π(fθl + kw Rw (1 − cos θ))2 4 cos(θ + αa )
(6)
where Sθ+z is the focal area (mm2 ) incorporating the focal offset; f the focal length of the lens(mm); θ l the diffuse angle of laser; Rw the radius of the circular workpiece (mm); αa the central angle with respect to the irradiation focal point on the wheel surface which is inversely proportional to Rw ; θ the incident angle (0–90◦ ) and kw equals D/2f = 0.25, which varies depending on the particular laser beam (D is the diameter of the laser beam before focus). When substituting Eqs. (1)–(4) into Eqs. (5) and (6), geometrical relationships and the spatial distribution of absorbed energy on a cylindrical surface were obtained. A number of significant laser processing parameters could thus be predicted. These equations clearly reveal that the focal area on the cylindrical surface increases with incident angle, which means the energy density of laser irradiation decreases with incident angle.
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3. Results and discussions Calculations were made and the effects of incident angle/position, focal offset/processing parameters on energy absorption were plotted using Microsoft Excel and AutoCAD. In order to validate the governing equation, laser processing experiments were performed on small vitrified CBN grinding wheels. An LKS-250A pulse YAG laser was used with a maximum power of 400 W. The highest processing speed was 1500 mm/min, the pulse frequency was varied from 100 to 400 Hz, and the rotation speed of the wheel was maintained between 1000 and 2000 rpm. 3.1. Space distribution of absorbed energy at arbitrary point The space distributions were calculated and represented as shown in Fig. 3(b). The figure shows the effect of incident angle on absorbed energy at any position on the cylindrical surface. The curves represent the temperature field induced by laser irradiation. The temperature field has a spherical shape (circular in the figure) for vertical (0◦ ) laser irradiation of the surface. The isothermal curves are seen to be distorted due to the curvature of the surface. Changing the incident angle of laser irradiation from 0 to 90◦ results in a significant increase in the radii of curvature of the temperature profile, whereas, at a given position, its radii of curvature from left to right were gradually reduced along a temperature line. Thus, the relation between incident angle and absorbed energy should be modeled and used in optimization of laser processing parameters. Interpreting results of absorbed energy density on a cylindrical surface, Fig. 4(a) shows the theoretical prediction of the effects of incident angle on absorbed energy. The absorbed energy decreases rapidly with incident angle: it drops to 37.5% of its initial value in going from vertical irradiation (0◦ ) to an incident angle of 60◦ . As is clear from the figure, the increase in incident angle causes the focal area on the processing surface to expand, which in turn causes the laser density on the workpiece to decrease more sharply than the incident angle increases. Therefore, when a curved surface is laser-irradiated at close to 90◦ (parallel position), there exists a critical incident angle such that between θ c and 90◦ the irradiated area cannot be processed properly. If the laser-processing head does not move parallel to the axis of a wheel, laser focus offset may be generated. The focal offset would cause the laser focal area on the processing surface to expand. Consequently, the energy density of laser irradiation on the processing area would decrease. The relations are shown in detail in Fig. 4(b). The figure shows the calculated effect of focal offset on absorbed energy. Energy absorption is seen to decrease more sharply with laser focal offset than it does with incident angle. At a given area of laser irradiation, the absorbed energy drops to 15.6% of its value with offset (incident angle: 0◦ ). This is because the fo-
Fig. 4. Effect of incident angle on absorbed energy (two surfaces: linear and circular) (a); effect of focal offset on absorbed energy (D is the diameter of circular) (b).
cal area, in the presence of a focal offset, is effectively equal to the sum of the extra areas that both focal offset and incident angle yield above the original area under normal irradiation conditions. In general, every calculation (including experimental results) has a certain error associated with it. This needs to be considered as Fig. 4 shows that incident angle does not work when it reaches. Thus, further research will be conducted on laser processing of grinding wheels at this critical angle, thanks to which we expect to be able to report better optimized processing parameters in subsequent publications. In laser processing, the focal area changes with the radius of curvature of the wheel, i.e., the wheel size. Fig. 5 shows the absorbed energy as a function of wheel diameter. Thus, different processing parameters ought to be used when using different grinding wheel sizes to match the size of a particular workpiece. The effect of wheel diameter on absorbed energy is shown as well. To investigate the effect of circular workpiece diameter on absorbed energy, the focal distance was maintained constant during the measurement.
Fig. 5. Effect of wheel diameter/incident angle on absorbed energy.
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Table 1 Thermal properties of the particles and bonds Composition
Melting point, Tm (◦ C)
Density, ρ (kg/m3 )
Specific heat, Cp (J/kg K)
Thermal conductivity K (W/m K)
Thermal diffusivity, α (×106 m2 /s)
CBN Ceramic bond Al2 O3 Bronze/resin Diamond
3200 1000–1200 2050 831/350–400 3700–4000
3450
506 762–909 765 342/1591–1758 502
1300 20–30 36 25/0.25–0.35 146
744.7
3970 8760/1250–1300 3480–3560
Clearly, the absorbed energy decreases with both the diameter of circular workpiece and incident angle, more sharply with the latter. As such, the relation between the wheel size and absorbed energy should be modeled and taken into account during optimization of processing parameters. 3.2. Experimental versus calculated parameters for laser processing of grinding wheel The effects of laser processing parameters such as incident angle, focal offset, incident power, and traverse speed were tested by experiments. All these parameters were found to influence the absorbed energy and incident beam density. For example, the absorbed energy decreases with increasing incident angle (Fig. 4). The experimental results for incident angle were as follows: at an incident angle of 60, 70, and 80◦ ,the volume of material removal was 0.07, 0.04 and 0.02 mm, respectively. Calculated results showed a good agreement with experimental results. The laser processing is governed by the absorbed laser intensity at the target surface and by the thermal and optical properties of the target material. The properties of the materials composing diamond wheels are listed in Table 1. A principle schematic of laser truing of a grinding wheel is shown in Fig. 6(a), which is as well a basic setup for truing experiments. Therefore, a laser cutting experiment designed to simulate a single diamond dresser yielded the laser turning results revealed in the micrograph in Fig. 6(b). The processing parameters used were listed in Table 2, in which the constant parameters were: Dw = 5 mm, f = 40 mm, Pr = 3 kg/cm2 . The whole profile of a processed wheel is visible; it is seen to resemble a micro-thread.
11.9 8.34/0.088 82
to remove both diamonds and bond materials, but a little difference. The volume of material removed from vitrified CBN wheel surface increases with increasing of the laser power intensity and laser pulse width, but too larger laser power intensity and laser pulse width may cause damage to abrasive grains. According to calculation and experimental results, the processing parameters can be selected during laser truing both materials of vitrified bond and CBN as shown in Table 2. In these cases, the laser power intensities of irradiated spot on the vitrified bonded CBN wheel can reach the value of 7.5 × 104 to 1.125 × 105 W/cm2 . The wheel surface conditions compared with SEM micrographs (SEM: TOPCOM SM-200) have also been discussed to verify the material removal mechanism and the influence of laser irradiation on the wheel surface. Fig. 7(a) shows the micro-profile after mechanical preparation. A large number of CBN particles are observed. They are connected with vitrified bonds and there is porosity in between. Fig. 7(b) shows the wheel surface after laser processing. Unlike in mechanical processing, molten and re-solidified ceramic bonds have been found on the wheel surface
3.3. Parameter selection in laser truing of the small vitrified CBN wheel When truing vitrified CBN wheel, the incident angle, focal offset, laser power intensity, traverse speed, wheel rotation speed, and laser pulse parameter must be selected properly Table 2 Parameter selection in laser truing of small vitrified CBN wheels Truing mode
I (A)
V (mm/ min)
N (rpm)
t (ms)
θ (◦ )
ν (Hz)
Incident angle Focal offset
200–260 240–300
40–80 20–60
2000 1500
0.2–0.5 0.2–0.5
0–70 0–50
100–200 100–200
Fig. 6. Principle schematic of laser truing of a grinding wheel (a); wheel surface profile after laser beam turning (b).
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of molten ceramic exhibiting a different porous structure than the original wheel surface. An analysis of calculated and experimental results has provided an in-depth understanding of the relation between processing parameters and product quality, forming a knowledge base that will help improve techniques for laser truing and dressing of grinding wheels.
Acknowledgements The authors would like to thank Akita Prefectural University for providing the resources required to undertake this study and the university’s staff members and PhDs who assisted with the experimental setup and measurements. This study was supported in part by the NSFC Key Project (No. 59935110).
References Fig. 7. Wheel surface conditions (a) after mechanical preparation; (b) after laser processing.
following laser irradiation. Also, the protrusion of the actual cutting edges is reduced in laser processing. This will result in smoother, i.e., ground surfaces, i.e., better surface quality; however it will also reduce the grinding efficiency of the wheel.
4. Conclusions The model developed used the energy balance equation to calculate several parameters in laser processing of a small vitrified CBN grinding wheel. A new space distribution was obtained for the laser energy absorption at any position on a cylindrical surface between 0 and 90◦ . The present model predicted the effect of processing parameters such as incident angle (irradiation position) and focal offset on absorbed energy and the effect of incident power and processing speed on the volume of material removed. Characterization of the wheel surface after laser processing revealed re-solidification
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