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Dressing of resin-bonded superabrasive grinding wheels by means of acousto-optic Q-switched pulsed Nd:YAG laser
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Optics & Laser Technology 36 (2004) 409 – 419 www.elsevier.com/locate/optlastec
Dressing of resin-bonded superabrasive grinding wheels by means of acousto-optic Q-switched pulsed Nd:YAG laser X.-Z. Xie∗ , G.-Y. Chen, L.-J. Li Laser Institute of Hunan University, Changsha, Hunan 410082, PR China Received 4 August 2003; received in revised form 28 October 2003; accepted 7 November 2003
Abstract The preparation of the use of resin-bonded superabrasive grinding wheels remains a problem despite their availabilities on the market in the past years and possible technological advantages. In this paper, an acousto-optic Q-switched Nd:YAG pulsed laser is applied to dressing resin-bonded superabrasive wheels in orthogonal direction. The author proposes a systematical study on the mechanism of selective removal, crater ablated by single pulse and surface topography after dressing, and consequently presents a feasible method of selecting irradiation parameters and summarizes the dressing features and disciplines of dressing e;ects in
1. Introduction Diamond and cubic boron nitride (CBN) wheels, which are complementary to each other on adaptability, are generally called superabrasive grinding wheels. Grinding with superabrasive wheels o;ers a series of advantages such as long wheel life, high grinding eBciency, Cne surface quality, and Cne dimensional stability. Diamond wheels are applicable to grinding of hard and brittle non-ferrous metals, horniness alloys and hard and brittle non-metals like optical glasses, ceramics and gems while CBN wheels are to grinding of ultra hard and tough metals like chilled steels and thermal durable alloys. Due to their superior grinding performances, they are extensively applied to such Celds as aerospace, automobile, medicine, electronics and building materials, meanwhile they are what precision and super-precision grinding, high speed and eBciency grinding, hard-to-machine materials grinding, proCle grinding and grinding automation are based on.
∗ Corresponding author. Tel.: +86-731-8828265; fax: +86-731-4572613. E-mail address: [email protected] (X.-Z. Xie).
0030-3992/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2003.11.002
There are three types of bonds, namely resin bond, metal bond and vitriCed bond, generally used for superabrasive wheels, which have to be brought into dressing for grinding before their Crst uses or reaching the service life criterion. VitriCed-bonded superabrasive wheels can be dressed by means of conventional mechanical dressing methods on the interaction of force, while electrolytic methods are only applicable to metal-bonded wheels. Although mechanical dressing can be conducted on resin-bonded wheels, it can also cause deep cracks and undercuts, which may loosen chunks of grains causing the number of e;ective cutting edges to be reduced. Dressing tool is easy subjected to wear and the dressing tool geometry will be altered. It in
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necessary to Cnd an appropriate method for dressing these wheels. High-power laser are currently used as a non-contact micro-machining tool for a variety of manufacturing applications such as cutting, welding, drilling, scribing and controlled fracturing. Their salient characteristics such as high intensity, directionality and space coherence revolutionized the processing of hard and brittle materials are well known. The laser-induced thermal processing leads to spectacular e;ects involving phase change of the material such as melting, vaporization, and plasma production. Laser dressing is a promising dressing technology, which has the merits as extensive adaptability, small heat-a;ected zone (HAZ), non-contact machining, no dressing tool wear and non-pollution to environment. This has stimulated the idea of exploring the use of laser as a non-contact dressing tool. For these reasons, extensive investigations have been carried out on laser dressing in recent years. Babu and Phanindranath [5–9] Crstly used the conventional pulsed Nd:YAG laser to dress aluminum oxide wheel and predicted the groove geometry on laser-dressed grinding wheel surface. Then, the same wheel was dressed using continuous wave (CW) and Q-switched pulsed Nd:YAG laser by Nakajima et al. [10–12]. WestkPamper et al. [13,14] employed the conventional pulsed Nd:YAG laser to dress resin-bonded CBN wheel and proposed a method of dressing on wheels in orthogonal direction, while truing in tangential direction. Kang et al. [15,16] conducted a study of tangentially truing metal bonded diamond wheel by conventional pulsed Nd:YAG laser. Ho;meister and Timmer [17,18] made a review of various boned superabrasive wheels dressed by means of conventional pulsed Nd:YAG laser. Chen Genyu and Xie Xiaozhu [19] recommended the newly development of laser dressing and conducted a preliminary study on superabrasive wheels. Chen Ming et al. [20] presented the promising work on grinding wheel topography generation mechanism through the laser grooving and valuation by 3D laser scanning technology. Zuo Dunwen et al. [21] made a study of diamond plate dressed by CW CO2 laser. Zhang and Shin [22,23] developed a technique of CO2 laser-assisted truing and dressing for vitriCed CBN wheel. Moreover, dressing for porous cast-iron-bonded diamond grinding wheels using YAG–SHG laser with the wavelength of 532 nm was conducted by Kazuki et al. [24]. However, systematic study of dressing on resin-bonded superabrasive wheels by acousto-optic Q-switched pulsed Nd:YAG laser has not been reported for the moment. In this paper, acousto-optic Q-switched pulsed Nd:YAG laser is used to dress resin-bonded superabrasive wheels in orthogonal direction and the advantages and disadvantages among pulse laser, conventional mechanical and CW laser dressing on wheels are compared. The mechanism of selective removal, morphology of surface craters ablated by single pulse laser and topography of laser dressing on wheels is exhaustively analyzed. Experiments show that acousto-optic Q-switched pulsed Nd:YAG laser dressing is superior to
conventional mechanical and CW laser dressing and is suitable for dressing resin-bonded superabrasive wheels. 2. Experimental setup Fig. 1 shows the schematic illustration of dressing on superabrasive wheels by acousto-optic Q-switched pulsed Nd:YAG laser. The maxim continuous output power is 30 W, which is modiCed by current of krypton discharge source. There is an acousto-optic Q-switched device built in the resonant cavity whose frequency ranges from 1 to 10 kHz and therefore a pulse laser with pulse width (t0 ) from 150 to 500 ns and pulse repetition frequency (f) from 1 to 10 kHz can be secured. The output laser with a wavelength of 1:06 m is irradiated radially on the wheel from three positions (z = 0; 1:5; 3:0 mm). The focus lens is aberrationless hyperbolical with its focal length 60 mm. The gas is introduced coaxially to the laser beam through a nozzle and the gas
Fig. 1. Schematic illustration of dressing on superabrasive wheels by acousto-optic Q-switched pulsed YAG laser.
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419 Table 1 Dressing conditions
Grinding wheel Model of laser Mode Wavelength Emission wave Maximum output power Pulse width Full divergent angle Q-switched frequency Focal position Focus beam diameter Dressing speed Dressing passes Feed rate of laser beam
CBNII180B100, RVD180B10050×5 mm Nd:YAG laser Multi-mode 1:06 m Q-switched pulse Continuous wave wave 30 W 150 –500 ns 5 –20 mrad 1–10 kHz 0; 1:5; 3:0 mm 0:20 mm 0.18–2 m=s 2 0.08–0:8 mm rev of G.W
and RVD180B100, respectively) are prepared in small dimension (50 mm diameter × 5 mm width) which are convenient for observing under LM and SEM.
3. Results and discussion 3.1. Principles of selective removal An acousto-optic Q-switched pulsed Nd:YAG laser is used in this system. The Q-switched supply has a radio-frequency (RF) oscillator of 40 MHz and a modulation pulse generator of 1–10 kHz. When the RF oscillator works, the initial cavity losses caused by a beam of light passing through the cavity with an ultrasonic Celd will be greater than the ampliCer gain, therefore, no laser output is produced. The giant pulse output can be secured only when the RF oscillator stops oscillating suddenly, the cavity losses is reduced and a high Q-value cavity is produced. The giant pulse frequency is that of modulation pulse. Generally speaking, the giant pulse output possesses the merits of shorter pulse width (ns) and higher peak power (KW). When the laser irradiation is imposed upon the wheels, a part of the radiation is lost by re
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Table 2 shows the thermal–physical properties of abrasives and resin bond. The main contents of superabrasive wheels are resin bond, CBN, and diamond. Through calculation, the maximum thermal di;usion distance is 7 m, far less than the diameter of beam spot (0:2 mm). Thus, the assumption of laser processing can be explained by considering an even circular laser source with high power density acting upon a semi-inCnite half-space steadily. For this case, the temperature of wheel (T (z; t)) at di;erent depth and time is obtained as [25] √ z 2AP t ; (2) ierfc √ T (z; t) = K 4 t where the laser beam intensity (P) is P 0 ¡ t ¡ t0 P(t) = 0 t ¡ 0; t ¿ t0 ;
(3)
A is the material absorbance, and K is the thermal conductivity. When processing time (t) is up to pulse width (t0 ), the maximum surface temperature (Tmax ) of wheel is obtained as 2AP t0 : (4) Tmax = K Assuming t1 is pulse interval, the surface temperature on the front edge of next pulse decreases to √ 2AP √ T (0; t1 )t¿t0 = (5) t1 − t1 − t0 ; K where t1 ≈ 1=f. The relation between the above two temperatures is expressed as the quotient √ √ 2AP t1 − t0 ) T (0; t1 )t¿t0 K ( t1 − = Tmax t0 2AP K
=
t1 − t0
t1 − 1: t0
(6)
The smaller the duty cycle (t0 =t1 ), the lower the surface temperature. Due to acousto-optic Q-switched pulsed Nd:YAG laser with small pulse width (150 –500 ns) and high repetition frequency (1–10 kHz), the surface temperature on the front edge of next pulse is calculated as T (0; t1 ) = (0:002–0:01)Tmax :
(7)
It means that the surface temperature is so small that it can be neglected, even though the neighboring pulses are irradiated on the same region of the wheel. Each pulse individually heats up the material to melting points or vaporization, and then materials are removed. Small heat-a;ected zone ablated by acousto-optic Q-switched laser can maintain the integrity of wheel. For CBN and diamond abrasives, the temperature (Tmax ) used in Eq. (4) is decomposing temperature (Td ) instead of melting temperature (Tm ). That is because abrasives are
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Table 2 Thermal physical properties of resin bond and abrasives
Property
Resin (phenolic) ◦ C))
10−3
Thermal conductivity K=(W=(cm · SpeciCc heat c=(J=(g · ◦ C)) Thermal di;usivity =(cm2 · s−1 ) Melting temperature Tm =(◦ C) Decomposing temperature Td =(◦ C) Density =(g=cm3 )
(1:25–7:0) × 1.591–1.758 (1:15–3:06) × 10−3 200 – 400 200 – 400 1.25
Cubic boron nitride (CBN)
Diamond
13 2.224 1.680 3227 ¿ 1300 3.48
20 1.827 3.114 3700 – 4000 720 –800 3.515
Table 3 Pulse laser power density of resin bond and abrasives to be decomposed
Materials composing wheels
Resin (phenolic)
Cubic boron nitride (CBN)
Diamond
Absorbance at 1:06 m A Pulse laser power density required (when t0 = 150 ns) Pd (W=cm2 )
0.8 5 × 105
0.1 2:94 × 108
0.1 2:02 × 108
Table 4 The relationship between pulse repetition frequency and pulse width
Pulse repetition frequency f (kHz)
1
2
3
4
5
6
7
8
9
10
Pulse width t0 (ns)
150
200
250
300
350
400
450
500
500
500
easily subjected to oxidation above such temperature, and then would be damaged by high-intensity irradiation. Resin bond, which has no certain melting point, possesses the trait of sublimation. The power density levels necessary for abrasives removal is greater by a factor of two or three than that for resin bond (see Table 3). Appropriate pulse laser power density, which is lower than the decomposing power density for abrasives and higher than that for resin bond, can be selected by coordinating laser parameters. Thereby, resin bond is uniformly removed meanwhile grits are better protruded and not damaged, which indicates the achievement of selective removal, that is the essence of acousto-optic Q-switched pulsed laser dressing.
Defocus distance (z) is generally deCned as the distance perpendicular to the focus plane. When z is outside the wheel, it is positive. Conversely, it is negative. The beam diameter at z from the focus plane along the beam propagating is as follows: d(z) = db + 2z tan(=2);
where db is focus beam diameter, is full divergent angle. As defocus distance goes up, the beam diameter increases, which correspondingly results in the decrease of pulse laser power density. The beam power intensity attenuates sharply far from the focus plane, which is obtained as [26]
3.2. Pulse power density Supposing that the Gauss beam with rectangular pulse proCle is uniformly distributed within circular spot, the pulse laser power density is secured as 4Pm Pp = : (8) t0 fd2 The pulse laser power density increases in scale with the increase of average power (Pm ), while decreases with the increase of pulse repetition frequency (f) and beam diameter (d). Within the ranges of pulse repetition frequency, the pulse width is not Cxed, which mounts up with the increase of the frequency (see Table 4). Therefore, the in
(9)
P(x; y; z) =
8(x2 + y2 ) 8Pm exp − : d2 (z) d2 (z)
(10)
Thus, it is shown that the pulse laser power density mainly depends on the three parameters: average power, pulse repetition frequency, and defocus distance. The pulse power density at focus position can be obtained in Table 5 by calculating Eq. (8). For = 20 mrad, the ratio of beam diameter between z = 1:5 and 0 mm is 1.15 by calculating Eq. (9). Substituting the ratio value into Eq. (10), the ratio of pulse power density between z = 1:5 and 0 mm is 0.35. Thus, the corresponding power density at z = 1:5 mm is listed in Table 6. In the same way, the pulse power density at z = 3:0 mm can be deduced in Table 7.
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
413
Table 5 Pulse power densities Pp : 107 W=cm2 at z = 0:0 mm versus the combination of average power (Pm ) and pulse repetition frequency (f)
Pm (W )
3 5 10 15 20
f (kHz) 1
2
3
4
5
6
7
8
9
10
6.36 10.6 21.2 31.8 42.4
2.39 3.98 7.95 11.9 15.9
1.26 2.10 4.26 6.36 8.46
0.78 1.30 2.65 4.00 5.30
0.54 0.90 1.80 2.74 3.64
0.41 0.68 1.31 1.99 2.66
0.30 0.50 1.00 1.50 2.03
0.23 0.39 0.81 1.20 1.59
0.22 0.36 0.72 1.05 1.41
0.20 0.33 0.63 0.96 1.26
Table 6 Pulse power densities Pp : 107 W=cm2 at z = 1:5 mm versus the combination of average power (Pm ) and pulse repetition frequency (f)
Pm (W )
3 5 10 15 20
f (kHz) 1
2
3
4
5
6
7
8
9
10
2.22 3.71 7.42 11.13 14.84
0.83 1.39 2.78 4.17 5.56
0.44 0.73 1.46 2.19 2.92
0.27 0.45 0.90 1.35 1.80
0.18 0.31 0.62 0.93 1.24
0.14 0.23 0.46 0.69 0.92
0.10 0.17 0.34 0.51 0.68
0.08 0.13 0.26 0.39 0.52
0.07 0.12 0.24 0.36 0.48
0.06 0.11 0.22 0.33 0.44
Table 7 Pulse power densities Pp : 107 W=cm2 at z = 3:0 mm versus the combination of average power (Pm ) and pulse repetition frequency (f)
Pm (W )
3 5 10 15 20
f (kHz) 1
2
3
4
5
6
7
8
9
10
2.03 3.39 6.78 10.17 13.56
0.76 1.27 2.54 3.81 5.08
0.40 0.67 1.34 2.01 2.68
0.25 0.42 0.84 1.26 1.68
0.17 0.29 0.58 0.87 1.16
0.13 0.22 0.44 0.66 0.88
0.09 0.16 0.32 0.48 0.64
0.07 0.12 0.24 0.36 0.48
0.07 0.11 0.22 0.33 0.44
0.06 0.10 0.20 0.30 0.40
3.3. Single-pulse ablation on the wheels The crater is produced when single-pulse laser is irradiated on the wheel. Due to the higher peak power and shorter pulse width of acousto-optic Q-switched pulse laser, each pulse eliminates material at millimicron individually. When craters are arranged in sequence or overlapped, vast resin materials are removed and abrasives are well protruded, which means the achievement of laser dressing. Crater depth is usually applied to the measurement of material remove rate, which is determined by a certain pulse power density and in turn in
Fig. 2. Ablation crater depth on resin-bonded CBN wheel in
increasing of intensity. At the intensity of 5:5 × 105 W=cm2 , the crater depth is considerably small, so the beam intensity could be considered as a bottom limit for the dressing. As discussed above, the decomposing intensity for resin-bond
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
Fig. 3. Ablation crater depth on resin-bonded CBN wheel in
and CBN grain is 5:0 × 105 and 2:94 × 108 W=cm2 . An appropriate intensity, which is between the above two intensities, can be used for eBciently removing resin bond and protruding grain. By setting di;erent intensities, it is possible to adjust the ablation depth produced on the wheel when dressing to a value, which depends on the grain size and dressing pass for an optimum grain protrusion. Fig. 3 shows the ablation crater depth in
Fig. 4. Microscope photo of crater ablated on CBN wheel at (a) Pm = 3 W; f = 3 kHz; z = 0:0 mm; (b) Pm = 3 W; f = 8 kHz; z = 0:0 mm; (c) Pm = 3 W; f = 10 kHz; z = 0:0 mm.
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
415
Fig. 7. Ablation crater depth on resin-bonded diamond wheel in
Fig. 5. Section chart of crater ablated by single-pulse laser on (a) CBN wheel at Pm = 3 W; f = 3 kHz; z = 0:0 mm; (b) diamond wheel at Pm = 3 W; f = 3 kHz; z = 1:5 mm.
Fig. 6. SEM photo of crater on CBN wheel at Pm = 3 W; f = 3 kHz; z = 0:0 mm.
3.4. Acousto-optic Q-switched YAG laser dressing The diameter of 180# grain size for resin-bonded superabrasive wheel is approximate 65–90 m. Considering that the protruding proportion of grain is 20 –30% for the sake of obtaining satisfactory surface topography, the demanding protruding height is 15 –27 m. If the fulCllment
Fig. 8. Ablation crater depth on resin-bonded diamond wheel in
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
Fig. 9. Surface topography of dressing on resin-bonded CBN wheel at (a) before dressing, (b) Pm = 3 W; f = 2 kHz; z = 0:0 mm, (c) Pm = 3 W; f = 5 kHz; z = 0:0 mm, (d) Pm = 3 W; f = 9 kHz; z = 0:0 mm.
Fig. 10. ProCle traces of dressing on resin-bonded CBN wheel at Pm = 3 W; f = 5 kHz; z = 0:0 mm.
of dressing is in one dressing pass, the demanding pulse power density is so high that abrasives will be damaged. If the dressing passes are more than three, the dressing eBciency will be poor. Thus, the fulCllment of dressing should be within two dressing passes in view of improving dressing eBciency and not damaging the abrasives. The optimum ablation crater depth is of 11–13:5 m on condition that the overlap ratio is of 0.5. Then, the corresponding power density is 0.4 –1:2 × 107 W=cm2 selected from Figs. 2 and 7, which determines the corresponding combination of laser parameters: average power, pulse repetition frequency, and defocus distance from Tables 5–7. Hence, satisfactory surface topography of the wheels is obtained under these parameters, which is represented in Figs. 9(c) and 11(b)-(d).
Fig. 9 demonstrates a series of surface topography of dressing on resin-bonded CBN wheel dependent on pulse repetition frequency. After truing with a diamond roller, the topography is leveled, which is shown in Fig. 9(a). When the frequency is less than 2 kHz, long and deep slot is produced due to higher intensity (see in Fig. 9(b)). The grit particles are not anchored Crmly in the bond and, in some case, may shed o; as a result of a grinding operation. When the frequency rises to 5 kHz, better surface topography is obtained (see in Fig. 9(c)). The proCle trace of dressing on wheel also veriCes it (see Fig. 10). When the frequency rises above 8 kHz,
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
417
Fig. 11. Surface topography of dressing on resin-bonded diamond wheel at (a) Pm =13 W; f=1 kHz; z=0:0 mm; (b) Pm =13 W; f=7 kHz; z=0:0 mm; (c) Pm = 8 W; f = 3 kHz; z = 1:5 mm; (d) Pm = 13 W; f = 3 kHz; z = 3:0 mm.
Fig. 12. Comparison with corundum block dressing on (a) CBN and (b) diamond wheel.
Fig. 13. Comparison with CW laser dressing on (a) CBN wheel at Pm = 3 W; z = 0:0 mm and (b) diamond wheel at Pm = 13 W; z = 3:0 mm.
3.5. Comparison with other dressing methods For purpose of comparison, the corundum block and CW laser dressing are conducted on the wheels, shown in Figs. 12 and 13. For mechanical dressing, the grains be-
come chipped or rounded on the interaction of shear and extrusion force. The appearance of slots and insuBcient protrusion of grains is prone to produce. For CW laser dressing, some deep tunnels come into being around the grits due to the congregation of heat. While far from the grain,
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
the resin bond remove rates are suBcient. Thereby, both the two dressing methods cannot bring about better surface topography.
engineering, Hong Kong Polytechnic University, for performing the measurements. References
4. Conclusions In this paper acousto-optic Q-switched Nd:YAG pulse laser is used to dress resin-bonded superabrasive wheels in orthogonal direction and the advantages and disadvantages among pulse laser, conventional mechanical and CW laser dressing on superabrasive wheels are compared. This experiment deals with surface craters ablated by single-pulse laser and pulse laser dressing, advances a theoretical method of selecting laser irradiation parameters and summarizes the dressing features and disciplines of dressing e;ects in
[1] Heiji Yasui, Hiroshi Nakazono, Akira Hosokawa, Makoto Kurusu. A new eBcient dressing method of the resin bond CBN wheel. Int J Japan Soc Precis Eng 1991;25(2):98–9. [2] Syoji Katsuo, Piao Cheng Gao. Studies on truing of diamond vitriCed wheels (2nd report). Truing mechanism with cup-truer. Int J Japan Soc Precis Eng 1991;25(4):285–90. [3] Hirao Masatoshi, Izawa Masaki, Iguchi Nobuaki, Shirase Keiichi, Yasui Takeshi. Waterjet in-process dressing (1st Report)—dressing property and jet pressure. J Japan Soc Precis Eng 1998;64(9): 1335–9. [4] Yasushi Ikuse, Takeshi Nonokawa, Noriji Kawabata, Takehiko Kamo, Yoshihiko Yuzawa, Kuniaki Unno. Development of new ultrasonic dressing equipment. Int J Japan Soc Precis Eng 1995;61(7):986–90. [5] Ramesh Babu N, Radhakrishnan V, Murti YVGS. Investigation on laser dressing of grinding wheels—Part I: preliminary study. J Eng Ind Trans ASME 1989;111:244–52. [6] Ramesh Babu N, Radhakrishnan V. Investigation on laser dressing of grinding wheels—Part II: grinding performance of a laser dressed aluminum oxide wheel. J Eng Ind Trans ASME 1989;111: 253–61. [7] Ramesh Babu N, Radhakrishnan V. In
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419 [20] Chen Ming, Sun Fanghong, Liu Guoliang, Jian Xiaogang, Li Xiaotian. Theoretical and experimental research on generation mechanism of grinding wheel topography by laser dressing and 3D laser scanning. Key Eng Mater 2002;233–236(2): 497–502. [21] Zuo Dunwen, Kawano Yoshihiro, Yamashita Toshikazu, Wang Min. E;ect of CO2 pulsed laser scanning on diamond wheel pieces. Chinese J Mech Eng 1999;35(2):42–5. [22] Zhang C, Shin YC. A novel laser assisted truing and dressing technique for vitriCed CBN wheels. International J Mach Tools Manuf 2002;42:825–35.
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[23] Zhang C, Shin YC. Wear of diamond dresser in laser assisted truing and dressing of vitriCed CBN wheels. Int J Mach Tools Manuf 2003;43:41–9. [24] Hiroshi Funakoshi, Kazuki Jodan, Koji Matsumaru, Kozo Ishizaki. Laser dressing process of porous cast-iron bonded diamond grinding wheels for machining ceramics. Int Ceramic Rev 2001;50(6): 466–9. [25] Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. London: Oxford University Press; 1959. [26] Duley WW. CO2 laser e;ects and application. New York: Academic Press; 1976.
Optics & Laser Technology 36 (2004) 409 – 419 www.elsevier.com/locate/optlastec
Dressing of resin-bonded superabrasive grinding wheels by means of acousto-optic Q-switched pulsed Nd:YAG laser X.-Z. Xie∗ , G.-Y. Chen, L.-J. Li Laser Institute of Hunan University, Changsha, Hunan 410082, PR China Received 4 August 2003; received in revised form 28 October 2003; accepted 7 November 2003
Abstract The preparation of the use of resin-bonded superabrasive grinding wheels remains a problem despite their availabilities on the market in the past years and possible technological advantages. In this paper, an acousto-optic Q-switched Nd:YAG pulsed laser is applied to dressing resin-bonded superabrasive wheels in orthogonal direction. The author proposes a systematical study on the mechanism of selective removal, crater ablated by single pulse and surface topography after dressing, and consequently presents a feasible method of selecting irradiation parameters and summarizes the dressing features and disciplines of dressing e;ects in
1. Introduction Diamond and cubic boron nitride (CBN) wheels, which are complementary to each other on adaptability, are generally called superabrasive grinding wheels. Grinding with superabrasive wheels o;ers a series of advantages such as long wheel life, high grinding eBciency, Cne surface quality, and Cne dimensional stability. Diamond wheels are applicable to grinding of hard and brittle non-ferrous metals, horniness alloys and hard and brittle non-metals like optical glasses, ceramics and gems while CBN wheels are to grinding of ultra hard and tough metals like chilled steels and thermal durable alloys. Due to their superior grinding performances, they are extensively applied to such Celds as aerospace, automobile, medicine, electronics and building materials, meanwhile they are what precision and super-precision grinding, high speed and eBciency grinding, hard-to-machine materials grinding, proCle grinding and grinding automation are based on.
∗ Corresponding author. Tel.: +86-731-8828265; fax: +86-731-4572613. E-mail address: [email protected] (X.-Z. Xie).
0030-3992/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2003.11.002
There are three types of bonds, namely resin bond, metal bond and vitriCed bond, generally used for superabrasive wheels, which have to be brought into dressing for grinding before their Crst uses or reaching the service life criterion. VitriCed-bonded superabrasive wheels can be dressed by means of conventional mechanical dressing methods on the interaction of force, while electrolytic methods are only applicable to metal-bonded wheels. Although mechanical dressing can be conducted on resin-bonded wheels, it can also cause deep cracks and undercuts, which may loosen chunks of grains causing the number of e;ective cutting edges to be reduced. Dressing tool is easy subjected to wear and the dressing tool geometry will be altered. It in
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
necessary to Cnd an appropriate method for dressing these wheels. High-power laser are currently used as a non-contact micro-machining tool for a variety of manufacturing applications such as cutting, welding, drilling, scribing and controlled fracturing. Their salient characteristics such as high intensity, directionality and space coherence revolutionized the processing of hard and brittle materials are well known. The laser-induced thermal processing leads to spectacular e;ects involving phase change of the material such as melting, vaporization, and plasma production. Laser dressing is a promising dressing technology, which has the merits as extensive adaptability, small heat-a;ected zone (HAZ), non-contact machining, no dressing tool wear and non-pollution to environment. This has stimulated the idea of exploring the use of laser as a non-contact dressing tool. For these reasons, extensive investigations have been carried out on laser dressing in recent years. Babu and Phanindranath [5–9] Crstly used the conventional pulsed Nd:YAG laser to dress aluminum oxide wheel and predicted the groove geometry on laser-dressed grinding wheel surface. Then, the same wheel was dressed using continuous wave (CW) and Q-switched pulsed Nd:YAG laser by Nakajima et al. [10–12]. WestkPamper et al. [13,14] employed the conventional pulsed Nd:YAG laser to dress resin-bonded CBN wheel and proposed a method of dressing on wheels in orthogonal direction, while truing in tangential direction. Kang et al. [15,16] conducted a study of tangentially truing metal bonded diamond wheel by conventional pulsed Nd:YAG laser. Ho;meister and Timmer [17,18] made a review of various boned superabrasive wheels dressed by means of conventional pulsed Nd:YAG laser. Chen Genyu and Xie Xiaozhu [19] recommended the newly development of laser dressing and conducted a preliminary study on superabrasive wheels. Chen Ming et al. [20] presented the promising work on grinding wheel topography generation mechanism through the laser grooving and valuation by 3D laser scanning technology. Zuo Dunwen et al. [21] made a study of diamond plate dressed by CW CO2 laser. Zhang and Shin [22,23] developed a technique of CO2 laser-assisted truing and dressing for vitriCed CBN wheel. Moreover, dressing for porous cast-iron-bonded diamond grinding wheels using YAG–SHG laser with the wavelength of 532 nm was conducted by Kazuki et al. [24]. However, systematic study of dressing on resin-bonded superabrasive wheels by acousto-optic Q-switched pulsed Nd:YAG laser has not been reported for the moment. In this paper, acousto-optic Q-switched pulsed Nd:YAG laser is used to dress resin-bonded superabrasive wheels in orthogonal direction and the advantages and disadvantages among pulse laser, conventional mechanical and CW laser dressing on wheels are compared. The mechanism of selective removal, morphology of surface craters ablated by single pulse laser and topography of laser dressing on wheels is exhaustively analyzed. Experiments show that acousto-optic Q-switched pulsed Nd:YAG laser dressing is superior to
conventional mechanical and CW laser dressing and is suitable for dressing resin-bonded superabrasive wheels. 2. Experimental setup Fig. 1 shows the schematic illustration of dressing on superabrasive wheels by acousto-optic Q-switched pulsed Nd:YAG laser. The maxim continuous output power is 30 W, which is modiCed by current of krypton discharge source. There is an acousto-optic Q-switched device built in the resonant cavity whose frequency ranges from 1 to 10 kHz and therefore a pulse laser with pulse width (t0 ) from 150 to 500 ns and pulse repetition frequency (f) from 1 to 10 kHz can be secured. The output laser with a wavelength of 1:06 m is irradiated radially on the wheel from three positions (z = 0; 1:5; 3:0 mm). The focus lens is aberrationless hyperbolical with its focal length 60 mm. The gas is introduced coaxially to the laser beam through a nozzle and the gas
Fig. 1. Schematic illustration of dressing on superabrasive wheels by acousto-optic Q-switched pulsed YAG laser.
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419 Table 1 Dressing conditions
Grinding wheel Model of laser Mode Wavelength Emission wave Maximum output power Pulse width Full divergent angle Q-switched frequency Focal position Focus beam diameter Dressing speed Dressing passes Feed rate of laser beam
CBNII180B100, RVD180B10050×5 mm Nd:YAG laser Multi-mode 1:06 m Q-switched pulse Continuous wave wave 30 W 150 –500 ns 5 –20 mrad 1–10 kHz 0; 1:5; 3:0 mm 0:20 mm 0.18–2 m=s 2 0.08–0:8 mm rev of G.W
and RVD180B100, respectively) are prepared in small dimension (50 mm diameter × 5 mm width) which are convenient for observing under LM and SEM.
3. Results and discussion 3.1. Principles of selective removal An acousto-optic Q-switched pulsed Nd:YAG laser is used in this system. The Q-switched supply has a radio-frequency (RF) oscillator of 40 MHz and a modulation pulse generator of 1–10 kHz. When the RF oscillator works, the initial cavity losses caused by a beam of light passing through the cavity with an ultrasonic Celd will be greater than the ampliCer gain, therefore, no laser output is produced. The giant pulse output can be secured only when the RF oscillator stops oscillating suddenly, the cavity losses is reduced and a high Q-value cavity is produced. The giant pulse frequency is that of modulation pulse. Generally speaking, the giant pulse output possesses the merits of shorter pulse width (ns) and higher peak power (KW). When the laser irradiation is imposed upon the wheels, a part of the radiation is lost by re
411
Table 2 shows the thermal–physical properties of abrasives and resin bond. The main contents of superabrasive wheels are resin bond, CBN, and diamond. Through calculation, the maximum thermal di;usion distance is 7 m, far less than the diameter of beam spot (0:2 mm). Thus, the assumption of laser processing can be explained by considering an even circular laser source with high power density acting upon a semi-inCnite half-space steadily. For this case, the temperature of wheel (T (z; t)) at di;erent depth and time is obtained as [25] √ z 2AP t ; (2) ierfc √ T (z; t) = K 4 t where the laser beam intensity (P) is P 0 ¡ t ¡ t0 P(t) = 0 t ¡ 0; t ¿ t0 ;
(3)
A is the material absorbance, and K is the thermal conductivity. When processing time (t) is up to pulse width (t0 ), the maximum surface temperature (Tmax ) of wheel is obtained as 2AP t0 : (4) Tmax = K Assuming t1 is pulse interval, the surface temperature on the front edge of next pulse decreases to √ 2AP √ T (0; t1 )t¿t0 = (5) t1 − t1 − t0 ; K where t1 ≈ 1=f. The relation between the above two temperatures is expressed as the quotient √ √ 2AP t1 − t0 ) T (0; t1 )t¿t0 K ( t1 − = Tmax t0 2AP K
=
t1 − t0
t1 − 1: t0
(6)
The smaller the duty cycle (t0 =t1 ), the lower the surface temperature. Due to acousto-optic Q-switched pulsed Nd:YAG laser with small pulse width (150 –500 ns) and high repetition frequency (1–10 kHz), the surface temperature on the front edge of next pulse is calculated as T (0; t1 ) = (0:002–0:01)Tmax :
(7)
It means that the surface temperature is so small that it can be neglected, even though the neighboring pulses are irradiated on the same region of the wheel. Each pulse individually heats up the material to melting points or vaporization, and then materials are removed. Small heat-a;ected zone ablated by acousto-optic Q-switched laser can maintain the integrity of wheel. For CBN and diamond abrasives, the temperature (Tmax ) used in Eq. (4) is decomposing temperature (Td ) instead of melting temperature (Tm ). That is because abrasives are
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Table 2 Thermal physical properties of resin bond and abrasives
Property
Resin (phenolic) ◦ C))
10−3
Thermal conductivity K=(W=(cm · SpeciCc heat c=(J=(g · ◦ C)) Thermal di;usivity =(cm2 · s−1 ) Melting temperature Tm =(◦ C) Decomposing temperature Td =(◦ C) Density =(g=cm3 )
(1:25–7:0) × 1.591–1.758 (1:15–3:06) × 10−3 200 – 400 200 – 400 1.25
Cubic boron nitride (CBN)
Diamond
13 2.224 1.680 3227 ¿ 1300 3.48
20 1.827 3.114 3700 – 4000 720 –800 3.515
Table 3 Pulse laser power density of resin bond and abrasives to be decomposed
Materials composing wheels
Resin (phenolic)
Cubic boron nitride (CBN)
Diamond
Absorbance at 1:06 m A Pulse laser power density required (when t0 = 150 ns) Pd (W=cm2 )
0.8 5 × 105
0.1 2:94 × 108
0.1 2:02 × 108
Table 4 The relationship between pulse repetition frequency and pulse width
Pulse repetition frequency f (kHz)
1
2
3
4
5
6
7
8
9
10
Pulse width t0 (ns)
150
200
250
300
350
400
450
500
500
500
easily subjected to oxidation above such temperature, and then would be damaged by high-intensity irradiation. Resin bond, which has no certain melting point, possesses the trait of sublimation. The power density levels necessary for abrasives removal is greater by a factor of two or three than that for resin bond (see Table 3). Appropriate pulse laser power density, which is lower than the decomposing power density for abrasives and higher than that for resin bond, can be selected by coordinating laser parameters. Thereby, resin bond is uniformly removed meanwhile grits are better protruded and not damaged, which indicates the achievement of selective removal, that is the essence of acousto-optic Q-switched pulsed laser dressing.
Defocus distance (z) is generally deCned as the distance perpendicular to the focus plane. When z is outside the wheel, it is positive. Conversely, it is negative. The beam diameter at z from the focus plane along the beam propagating is as follows: d(z) = db + 2z tan(=2);
where db is focus beam diameter, is full divergent angle. As defocus distance goes up, the beam diameter increases, which correspondingly results in the decrease of pulse laser power density. The beam power intensity attenuates sharply far from the focus plane, which is obtained as [26]
3.2. Pulse power density Supposing that the Gauss beam with rectangular pulse proCle is uniformly distributed within circular spot, the pulse laser power density is secured as 4Pm Pp = : (8) t0 fd2 The pulse laser power density increases in scale with the increase of average power (Pm ), while decreases with the increase of pulse repetition frequency (f) and beam diameter (d). Within the ranges of pulse repetition frequency, the pulse width is not Cxed, which mounts up with the increase of the frequency (see Table 4). Therefore, the in
(9)
P(x; y; z) =
8(x2 + y2 ) 8Pm exp − : d2 (z) d2 (z)
(10)
Thus, it is shown that the pulse laser power density mainly depends on the three parameters: average power, pulse repetition frequency, and defocus distance. The pulse power density at focus position can be obtained in Table 5 by calculating Eq. (8). For = 20 mrad, the ratio of beam diameter between z = 1:5 and 0 mm is 1.15 by calculating Eq. (9). Substituting the ratio value into Eq. (10), the ratio of pulse power density between z = 1:5 and 0 mm is 0.35. Thus, the corresponding power density at z = 1:5 mm is listed in Table 6. In the same way, the pulse power density at z = 3:0 mm can be deduced in Table 7.
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
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Table 5 Pulse power densities Pp : 107 W=cm2 at z = 0:0 mm versus the combination of average power (Pm ) and pulse repetition frequency (f)
Pm (W )
3 5 10 15 20
f (kHz) 1
2
3
4
5
6
7
8
9
10
6.36 10.6 21.2 31.8 42.4
2.39 3.98 7.95 11.9 15.9
1.26 2.10 4.26 6.36 8.46
0.78 1.30 2.65 4.00 5.30
0.54 0.90 1.80 2.74 3.64
0.41 0.68 1.31 1.99 2.66
0.30 0.50 1.00 1.50 2.03
0.23 0.39 0.81 1.20 1.59
0.22 0.36 0.72 1.05 1.41
0.20 0.33 0.63 0.96 1.26
Table 6 Pulse power densities Pp : 107 W=cm2 at z = 1:5 mm versus the combination of average power (Pm ) and pulse repetition frequency (f)
Pm (W )
3 5 10 15 20
f (kHz) 1
2
3
4
5
6
7
8
9
10
2.22 3.71 7.42 11.13 14.84
0.83 1.39 2.78 4.17 5.56
0.44 0.73 1.46 2.19 2.92
0.27 0.45 0.90 1.35 1.80
0.18 0.31 0.62 0.93 1.24
0.14 0.23 0.46 0.69 0.92
0.10 0.17 0.34 0.51 0.68
0.08 0.13 0.26 0.39 0.52
0.07 0.12 0.24 0.36 0.48
0.06 0.11 0.22 0.33 0.44
Table 7 Pulse power densities Pp : 107 W=cm2 at z = 3:0 mm versus the combination of average power (Pm ) and pulse repetition frequency (f)
Pm (W )
3 5 10 15 20
f (kHz) 1
2
3
4
5
6
7
8
9
10
2.03 3.39 6.78 10.17 13.56
0.76 1.27 2.54 3.81 5.08
0.40 0.67 1.34 2.01 2.68
0.25 0.42 0.84 1.26 1.68
0.17 0.29 0.58 0.87 1.16
0.13 0.22 0.44 0.66 0.88
0.09 0.16 0.32 0.48 0.64
0.07 0.12 0.24 0.36 0.48
0.07 0.11 0.22 0.33 0.44
0.06 0.10 0.20 0.30 0.40
3.3. Single-pulse ablation on the wheels The crater is produced when single-pulse laser is irradiated on the wheel. Due to the higher peak power and shorter pulse width of acousto-optic Q-switched pulse laser, each pulse eliminates material at millimicron individually. When craters are arranged in sequence or overlapped, vast resin materials are removed and abrasives are well protruded, which means the achievement of laser dressing. Crater depth is usually applied to the measurement of material remove rate, which is determined by a certain pulse power density and in turn in
Fig. 2. Ablation crater depth on resin-bonded CBN wheel in
increasing of intensity. At the intensity of 5:5 × 105 W=cm2 , the crater depth is considerably small, so the beam intensity could be considered as a bottom limit for the dressing. As discussed above, the decomposing intensity for resin-bond
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
Fig. 3. Ablation crater depth on resin-bonded CBN wheel in
and CBN grain is 5:0 × 105 and 2:94 × 108 W=cm2 . An appropriate intensity, which is between the above two intensities, can be used for eBciently removing resin bond and protruding grain. By setting di;erent intensities, it is possible to adjust the ablation depth produced on the wheel when dressing to a value, which depends on the grain size and dressing pass for an optimum grain protrusion. Fig. 3 shows the ablation crater depth in
Fig. 4. Microscope photo of crater ablated on CBN wheel at (a) Pm = 3 W; f = 3 kHz; z = 0:0 mm; (b) Pm = 3 W; f = 8 kHz; z = 0:0 mm; (c) Pm = 3 W; f = 10 kHz; z = 0:0 mm.
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
415
Fig. 7. Ablation crater depth on resin-bonded diamond wheel in
Fig. 5. Section chart of crater ablated by single-pulse laser on (a) CBN wheel at Pm = 3 W; f = 3 kHz; z = 0:0 mm; (b) diamond wheel at Pm = 3 W; f = 3 kHz; z = 1:5 mm.
Fig. 6. SEM photo of crater on CBN wheel at Pm = 3 W; f = 3 kHz; z = 0:0 mm.
3.4. Acousto-optic Q-switched YAG laser dressing The diameter of 180# grain size for resin-bonded superabrasive wheel is approximate 65–90 m. Considering that the protruding proportion of grain is 20 –30% for the sake of obtaining satisfactory surface topography, the demanding protruding height is 15 –27 m. If the fulCllment
Fig. 8. Ablation crater depth on resin-bonded diamond wheel in
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
Fig. 9. Surface topography of dressing on resin-bonded CBN wheel at (a) before dressing, (b) Pm = 3 W; f = 2 kHz; z = 0:0 mm, (c) Pm = 3 W; f = 5 kHz; z = 0:0 mm, (d) Pm = 3 W; f = 9 kHz; z = 0:0 mm.
Fig. 10. ProCle traces of dressing on resin-bonded CBN wheel at Pm = 3 W; f = 5 kHz; z = 0:0 mm.
of dressing is in one dressing pass, the demanding pulse power density is so high that abrasives will be damaged. If the dressing passes are more than three, the dressing eBciency will be poor. Thus, the fulCllment of dressing should be within two dressing passes in view of improving dressing eBciency and not damaging the abrasives. The optimum ablation crater depth is of 11–13:5 m on condition that the overlap ratio is of 0.5. Then, the corresponding power density is 0.4 –1:2 × 107 W=cm2 selected from Figs. 2 and 7, which determines the corresponding combination of laser parameters: average power, pulse repetition frequency, and defocus distance from Tables 5–7. Hence, satisfactory surface topography of the wheels is obtained under these parameters, which is represented in Figs. 9(c) and 11(b)-(d).
Fig. 9 demonstrates a series of surface topography of dressing on resin-bonded CBN wheel dependent on pulse repetition frequency. After truing with a diamond roller, the topography is leveled, which is shown in Fig. 9(a). When the frequency is less than 2 kHz, long and deep slot is produced due to higher intensity (see in Fig. 9(b)). The grit particles are not anchored Crmly in the bond and, in some case, may shed o; as a result of a grinding operation. When the frequency rises to 5 kHz, better surface topography is obtained (see in Fig. 9(c)). The proCle trace of dressing on wheel also veriCes it (see Fig. 10). When the frequency rises above 8 kHz,
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
417
Fig. 11. Surface topography of dressing on resin-bonded diamond wheel at (a) Pm =13 W; f=1 kHz; z=0:0 mm; (b) Pm =13 W; f=7 kHz; z=0:0 mm; (c) Pm = 8 W; f = 3 kHz; z = 1:5 mm; (d) Pm = 13 W; f = 3 kHz; z = 3:0 mm.
Fig. 12. Comparison with corundum block dressing on (a) CBN and (b) diamond wheel.
Fig. 13. Comparison with CW laser dressing on (a) CBN wheel at Pm = 3 W; z = 0:0 mm and (b) diamond wheel at Pm = 13 W; z = 3:0 mm.
3.5. Comparison with other dressing methods For purpose of comparison, the corundum block and CW laser dressing are conducted on the wheels, shown in Figs. 12 and 13. For mechanical dressing, the grains be-
come chipped or rounded on the interaction of shear and extrusion force. The appearance of slots and insuBcient protrusion of grains is prone to produce. For CW laser dressing, some deep tunnels come into being around the grits due to the congregation of heat. While far from the grain,
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X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419
the resin bond remove rates are suBcient. Thereby, both the two dressing methods cannot bring about better surface topography.
engineering, Hong Kong Polytechnic University, for performing the measurements. References
4. Conclusions In this paper acousto-optic Q-switched Nd:YAG pulse laser is used to dress resin-bonded superabrasive wheels in orthogonal direction and the advantages and disadvantages among pulse laser, conventional mechanical and CW laser dressing on superabrasive wheels are compared. This experiment deals with surface craters ablated by single-pulse laser and pulse laser dressing, advances a theoretical method of selecting laser irradiation parameters and summarizes the dressing features and disciplines of dressing e;ects in
[1] Heiji Yasui, Hiroshi Nakazono, Akira Hosokawa, Makoto Kurusu. A new eBcient dressing method of the resin bond CBN wheel. Int J Japan Soc Precis Eng 1991;25(2):98–9. [2] Syoji Katsuo, Piao Cheng Gao. Studies on truing of diamond vitriCed wheels (2nd report). Truing mechanism with cup-truer. Int J Japan Soc Precis Eng 1991;25(4):285–90. [3] Hirao Masatoshi, Izawa Masaki, Iguchi Nobuaki, Shirase Keiichi, Yasui Takeshi. Waterjet in-process dressing (1st Report)—dressing property and jet pressure. J Japan Soc Precis Eng 1998;64(9): 1335–9. [4] Yasushi Ikuse, Takeshi Nonokawa, Noriji Kawabata, Takehiko Kamo, Yoshihiko Yuzawa, Kuniaki Unno. Development of new ultrasonic dressing equipment. Int J Japan Soc Precis Eng 1995;61(7):986–90. [5] Ramesh Babu N, Radhakrishnan V, Murti YVGS. Investigation on laser dressing of grinding wheels—Part I: preliminary study. J Eng Ind Trans ASME 1989;111:244–52. [6] Ramesh Babu N, Radhakrishnan V. Investigation on laser dressing of grinding wheels—Part II: grinding performance of a laser dressed aluminum oxide wheel. J Eng Ind Trans ASME 1989;111: 253–61. [7] Ramesh Babu N, Radhakrishnan V. In
X.-Z. Xie et al. / Optics & Laser Technology 36 (2004) 409 – 419 [20] Chen Ming, Sun Fanghong, Liu Guoliang, Jian Xiaogang, Li Xiaotian. Theoretical and experimental research on generation mechanism of grinding wheel topography by laser dressing and 3D laser scanning. Key Eng Mater 2002;233–236(2): 497–502. [21] Zuo Dunwen, Kawano Yoshihiro, Yamashita Toshikazu, Wang Min. E;ect of CO2 pulsed laser scanning on diamond wheel pieces. Chinese J Mech Eng 1999;35(2):42–5. [22] Zhang C, Shin YC. A novel laser assisted truing and dressing technique for vitriCed CBN wheels. International J Mach Tools Manuf 2002;42:825–35.
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[23] Zhang C, Shin YC. Wear of diamond dresser in laser assisted truing and dressing of vitriCed CBN wheels. Int J Mach Tools Manuf 2003;43:41–9. [24] Hiroshi Funakoshi, Kazuki Jodan, Koji Matsumaru, Kozo Ishizaki. Laser dressing process of porous cast-iron bonded diamond grinding wheels for machining ceramics. Int Ceramic Rev 2001;50(6): 466–9. [25] Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. London: Oxford University Press; 1959. [26] Duley WW. CO2 laser e;ects and application. New York: Academic Press; 1976.