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On-machine precision form truing of arc-shaped diamond wheels
Journal of Materials Processing Technology 223 (2015) 65–74
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
On-machine precision form truing of arc-shaped diamond wheels Bing Chen, Bing Guo ∗ , Qingliang Zhao Center for Precision Engineering, School of Mechatronics Engineering, Harbin Institute of Technology, PO Box 413, Harbin 150001, Heilongjiang, China
a r t i c l e
i n f o
Article history: Received 7 August 2014 Received in revised form 20 March 2015 Accepted 26 March 2015 Available online 6 April 2015 Keywords: On-machine truing Arc-shaped diamond wheel Rotary GC rod Truing performance Truing ratio
a b s t r a c t In order to realize the efficient and precision truing of arc-shaped diamond wheel for precision grinding of spherical, aspherical and free-form surfaces, a novel on-machine precision form truing of resin and metal bonded arc-shaped diamond wheels is proposed utilizing rotary green silicon carbon (GC) rod. Through this on-machine rotary GC rod (ORGCR) mutual-wear truing, any required radius of wheel arc profile could be formed by programmed truing paths, meanwhile, the vertical direction position error of the wheel center could be corrected after truing. Firstly, the principle of ORGCR mutual-wear truing for arc-shaped diamond wheel was introduced, and new evaluation methods of truing performance and truing ratio were provided. Then the truing performance and truing ratio were observed for different grains and bond of arc-shaped diamond wheels, the effects of ORGCR mutual-wear truing parameters on profile radius and form accuracy of wheels were investigated. Finally, the convex aspherical surface of single crystal silicon was ground by trued arc-shaped diamond wheel. The experimental results showed that the resin and metal bonded diamond wheels could be efficiently and precisely trued with high truing ratio. The form error of wheel arc profile reached 2.5–6 m/3 mm which decreased about 90% compared to pre-truing wheel. Besides, the diamond grains were well distributed on the wheel surface, and protruded out of the wheel bond after truing. The precision aspherical surface of single crystal silicon with the form accuracy PV of 507 nm and the average roughness Ra of 57.1 nm was achieved by parallel grinding with the trued D7 resin bonded wheel. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The development of advanced optoelectronic and astronomical devices highly demands for optical components and molds with spherical, aspherical and free-form surfaces with high profile accuracy and excellent surface finish. Most of these components and molds have to be machined by abrasive processes with diamond wheels due to their hard-brittle materials property, such as ceramics, cements, optical glasses and crystalline materials, as expounded by Brinksmeier et al. (2010). The arc-shaped diamond wheels with precision profile were usually adopted for ultra-precision grinding of spherical, aspherical and free-form surfaces. Saeki et al. (2001) investigated that the quality of aspherical opto-device surface ground by arc-shaped diamond wheels utilizing parallel grinding method was better than cross grinding method. Lin et al. (2014) applied arc-shaped diamond to grind BK7 glass with size of 430 × 430 × 27.5 mm using
∗ Corresponding author. Tel.: +0086 451 86402683; fax: +0086 451 86415244. E-mail addresses: [email protected] (B. Chen), [email protected] (B. Guo), [email protected] (Q. Zhao). http://dx.doi.org/10.1016/j.jmatprotec.2015.03.046 0924-0136/© 2015 Elsevier B.V. All rights reserved.
CNC envelope grinding on the surface grinder. Xie et al. (2010) demonstrated that CNC envelope grinding of free-form surface by arc-shaped diamond wheel permitted more grinding points around its torus-shaped working surface to take part in grinding process, and it decreased wears compared to a single grinding point when grinding large-size curve surface. Considering these grinding process of spherical, aspherical and free-form surfaces with arc-shaped wheel, the form accuracy of the ground surface was mainly determined by the profile accuracy of wheels. To improve the accuracy of the wheel profile, Wegener et al. (2011) introduced abundant truing methods proposed for formed diamond wheels. Wang et al. (2009) developed a cup truer with a cyclical arc swing mechanism to true arc-shaped wheels, and the form error of the wheel profile was ±5 m/17 mm after truing. Derkx et al. (2008) proposed a form crush dressing method to profile diamond grinding wheels, and the form crush dressing system concluded a lot of components, such as swiveling axis for truer, adjustment axis, motor housing, bearing housing and so on. Klocke et al. (2007) demonstrated that wire electro discharge (Wire-EDM) method which implemented on a conventional Wire-EDM machine was used to true and dress micro arc-shaped diamond wheels for grinding micro-arc array. Xie et al. (2010) showed that the fixed
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holding ability of the bond for some diamond grains is decreased so that the diamond grains like
,
,
fall off, and the diamond
, , are protruded out of the wheel bond. Meangrains like time, the similar removal mechanism emerges on the GC rod, the falls off, and the grains like , are protruded GC grain like out of the GC rod bond. The only difference is the GC grains may
Fig. 1. ORGCR truing mechanism (a) initial truing (b) truing process.
green silicon carbon (GC) stick CNC mutual-wear truing without any complex accessory was applied to true #180 metal bonded diamond grinding wheel. After truing, the form accuracy of trued diamond wheel was 18.2 m/10 mm. However, most of above truing methods need complicated attached devices, while the fixed GC stick CNC mutual-wear truing cannot confirm tool setting position of the wheel in the vertical direction after truing. Based on the above, a novel on-machine precision truing of resin and metal bonded arc-shaped diamond wheels is proposed utilizing mutual-wear between diamond wheel and GC rod without any complex accessory. In this ORGCR mutual-wear truing, the workpiece spindle on the machine was applied to drive GC rod to remove the wheel bond along the circular interpolation paths, and then the arc profile was formed gradually, while the vertical direction position error of wheel center would also be corrected automatically after truing. Firstly, the principle of ORGCR mutual-wear truing was introduced, and new evaluation methods of truing performance and truing ratio were provided. Then the truing ratio and truing performance were observed for different grains and bond of arcshaped diamond wheels. Next, the effects of ORGCR mutual-wear truing parameters on profile radius and form accuracy of wheels were investigated. Finally, the convex aspherical surface of single crystal silicon was ground by trued arc-shaped diamond wheel.
, be broken like because of mutual-strike with the diamond grains. Fig. 2 shows the ORGCR mutual-wear truing principle of arcshaped diamond wheel. In ORGCR mutual-wear truing, the GC rod is driven by the workpiece spindle on the machine with the wheel speed n to true diamond wheel with the wheel speed N along the circular interpolation paths circularly with the feed rate v in CNC grinding system as shown in Fig. 2(a), then a arc-shaped wheel may be gradually formed with the depth of cut ap through the CNC mutual-wear between the diamond wheel and GC rod dresser. Besides, the motion paths were designed to utilize more cylinder of GC rod to true the arc profile of diamond wheel as shown in Fig. 2(b). In the motion paths, when a circular interpolation path is completed, the diamond wheel is moved with the distance B along negative direction of Z axis, then the next circular interpolation movement is carried out, and keep the cycle going until the terminal of motion paths. After finishing the positive motion paths, the inverse movements are executed back to the beginning of motion paths. In short, the arc-shaped diamond wheel can be trued by rotary GC rod with circular interpolation paths and motion paths. The radius of interpolation arc a is described as Exp. (1). Any radius of wheel arc profile can be obtained for different requirements by changing the radius of interpolation arc. a=R+r
(1)
where R is the radius of GC rod which can be measured in truing process, and r is the expected radius of wheel arc profile, as shown in Fig. 2(a). In the truing process, however, the radius of GC rod is decreased unavoidably because of the mutual-wear. According to Exp. (1), the actual radius of wheel arc profile would be increased and deviate from the expected radius largely in truing process if the radius of interpolation arc remain the same. Therefore the radius of interpolation arc need be compensated by the radius of GC rod measured in truing process to guarantee the radius of arc profile wheel to meet the expected radius as follows:
2. ORGCR mutual-wear truing of arc-shaped diamond wheel
ai = r + Ri
Fig. 1 shows the ORGCR truing mechanism. In the truing process, the GC grains rub and remove the bond of diamond wheel, then the
where ai is the compensated radius of interpolation arc and Ri is the radius of GC rod measured in real-time.
Fig. 2. ORGCR mutual-wear truing mode of arc-shaped diamond wheel: (a)truing mode (b)truing motion paths.
(2)
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Fig. 3. On-machine measurement of trued arc-shaped diamond wheel (a) measuring process (b)adjustment of horizontal measure position.
Fig. 4. Volumetric removal mode in truing (a) diamond wheel (b) GC rod.
Considering the symmetry of the circular interpolation paths in XOY plane, the center position YP of wheel arc profile in vertical direction can be confirmed as follows: 1 YP = (Y1 + Y2 ) 2
(3)
where Y1 , Y2 is vertical direction coordinate of the interpolation arc beginning O1 and terminal O2 , as show in Fig. 2(a), then tool setting position of diamond wheel in the vertical direction is confirmed.
3. Evaluation of trued arc-shaped diamond wheel 3.1. On-machine measurement of trued arc-shaped diamond wheel In this paper, a direct measurement method was proposed to evaluate the wheel profile through a large amount of measured points collected by laser scan micrometer (LSM), as show in Fig. 3. Compared with the replication measurement methods, such as carbon replication as presented by Guo and Zhao (2015) and dental plastic replication as presented by Zhao and Guo (2015), this method is more direct and simpler. The LSM (KEYENCE LK-G5000) with a resolution of 0.1 m was adopted to measure the arc profile of diamond wheel. In measuring process, the LSM with sampling frequency f measured the rotary diamond wheel with speed N1 from the top surface to bottom surface of the wheel with the feed rate v1 . Note that the horizontal measure position of LSM with minimum extreme distance have to be found in order to reduce the measuring error, as shown in Fig. 3(b). After measurement, the truing performance can be evaluated on-machine by the data of arc profile wheel collected by LSM.
3.2. The calculation of arc profile radius and form accuracy of wheel The deviation of arc profile radius and the arc form error were generally used to evaluate the truing performance of arc-shaped wheel. In the actual grinding process, however, the grinding paths were generated according to the measured radius of the wheel, the deviation of arc profile radius cannot influence the grinding accuracy, while the form error of arc profile may be copied to the ground surface directly. Therefore, compared to the profile radius, the form accuracy is more important to be obtained in truing process. Crawford (1983) demonstrated that the least square method fitting algorithm was suitable to calculate arc profile radius and form accuracy trough the measured points. In the least square method fitting arc profile algorithm, the square error ıi defined as difference between the distance from the measured point (Xi , Yi ) to the theoretical profile radius and the theoretical radius is described as follows:
2
ıi = di2 − r 2 = Xi2 − A
+ Yi 2 − B
= Xi2 + Yi2 + aXi + bYi + c
2
− r2 (4)
where r is the theoretical radius, A, B is the center coordinate of arc. The arc profile radius r can be calculated through obtaining minimum ı2i :
r=
a2 + b2 − 4c 2
(5)
Besides, the arc form accuracy es defined as the difference between the maximum and minimum of the distance from the
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measured point to the theoretical radius profile is described as follows:
es =
max ıi −
min ıi
(6)
3.3. Truing ratio Fig. 4 exhibits the volumetric removal mode of wheel and GC rod in truing process. The removal volume of diamond wheel can be calculated by the difference value between the wheel volume before truing and after truing, as show in Fig. 4(a). The volume of diamond wheel V can be described as follows: V=
n−1
Sj × h
(7)
Fig. 5. ORGCR truing experimental setup.
Table 1 Truing conditions.
j
where n is the cycle number of LSM sampling spiral line around the periphery of diamond wheel, j is a certain cycle, Sj is the sectional areas of diamond wheel in j cycle, h is the distance between two adjacent cycles. In Exp. (7), Sj is described as follows: Sj =
k
X 2 +Y 2 + i
i
X 2 +Y 2 i+1
2
i+1
Machining tool
Three-axis ultra precision grinder
Diamond wheel
Resin bonded D3 (expected radius: 6 mm), D7 (expected radius: 4 mm) Metal bonded D15 (expected radius: 4 mm) Diameter: 75 mm, thickness: 6 mm, concentrations: 50%, initial radius: 3 mm #400,#800 for D3, D7, hardness: P #180 for D15, hardness: T Diameter: 20 mm, length: 110 mm Water-based, challenge 300-HT, concentrations: 2–3%, speed: 5 m/s, cross-sectional area of nozzle: 12.56 mm2 KEYENCE LK-G5000, sampling frequency: 50 KHz
2
× 2 ,where k is the total points
GC rod
i
of a cycle, k = 60f/N1 , i is a certain measured points, is the angle of two adjacent points, = 2/k. n is described as follows: n = Np /k, where NP is the total measured points of the wheel. h is described as follows: h = YNp − Y1 / (n − 1), where YNP is the Y coordinate of the last measured point and the Y1 is the Y coordinate of the first measured point of the wheel. Hence, the difference value between the wheel volume before truing and after truing Vw is described as follows: Vw = Vbe − Vaf
(8)
where Vbe is the volume of wheel before truing and Vaf is the volume of wheel before truing. Besides, the removal volume of GC rod VGC , as shown in Fig. 7(b), can be calculated as follows: VGC =
m1 − m2 GC
(9)
where GC is the average density of GC rod, and m1 , m2 is the weight of GC rod before and after grinding, respectively. Therefore the truing ratio can be defined as the ratio of wheel removal volume Vw to the GC rod removal volume VGC , as follows: =
Vw VGC
(10)
Coolant
LSM
4. Experimental setup 4.1. Precision truing of arc-shaped diamond wheel Fig. 5 shows the ORGCR mutual-wear truing experimental setup. The details of truing conditions and truing parameters are shown in Tables 1 and 2, respectively. The morphology of wheel surface was examined by a large scene depth laser microscope (LSDLM) and a scanning electron microscope (SEM). 4.2. Precision grinding of aspherical surface Fig. 6 shows the parallel grinding of aspherical surface with trued resin bonded D7 wheel and the on-machine measuring process. The morphology of aspherical surface was examined by SEM, while the surface roughness was measured in the vertical
Fig. 6. Aspherical surface grinding setup (a) grinding system (b) on-machine measurement system.
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Fig. 7. Truing performance of D3 wheel (a) Wheel profile before truing (b) Wheel profile after truing (c) Form deviation before truing (d) Form deviation after truing (e) Probability distributions of form deviation before truing (f) Probability distributions of form deviation after truing.
Table 2 Truing parameters. Wheel: D3, D7 No.
1 2 3 4 5 6 7 8 9 10 11 12
Wheel: D15 No.
n = 371 rpm Truing pass no.: 20 pass N (rpm) ap (m)
F (mm/min)
4000 5000 6000 7000 5000 5000 5000 5000 5000 5000 5000 5000
100 100 100 100 100 100 100 100 50 100 200 300
10 10 10 10 2 5 10 20 10 10 10 10
1 2 3 4 5 6 7 8 9 10 11 12
n = 571 rpm Truing pass no.20 pass N (rpm) ap (m)
F (mm/min)
4000 5000 6000 7000 5000 5000 5000 5000 5000 5000 5000 5000
160 160 160 160 160 160 160 160 80 120 160 200
9 9 9 9 3 6 9 12 9 9 9 9
Table 3 Aspherical surface grinding conditions. Wheel
D7 resin bonded wheel
Workpiece Grinding mode
Single crystal silicon, diameter: 20 mm, thickness:10 mm Parallel grinding
Aspheric equation
f (X) =
Rough grinding Semi-fine grinding Fine grinding Precision grinding
C × X2 /
1+
1 − (K + 1) × C × X 2
+
n i=1
Ci × Xi , convex surface
ap (m)
F (mm/min)
N (rpm)
N (rpm)
Pass
5 2 2 0
20 10 4 4
6000 6000 6000 6000
173 173 173 173
2 1 1 1
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grinding direction by a contact probe profilometer (Talysurf PGI 1240). Detailed grinding conditions are shown in Table 3. 5. Results and discussions A pre-experiment about truing ability of different GC grain size for different wheels was performed before above-experiments as shown in Table 4. The truing results showed that the GC rods of #180, #400, #800 with hardness of P hardly removed the D15 metal bonded wheel, while the #180 harder GC rod with hardness of T was applied to true the D15 wheel and obtained considerable removal ratio. For D3 and D7 resin bonded wheel, the truing accuracy of the wheel was unsatisfied with the #180 GC rod with hardness of P and T. It seems to be caused by extreme wear resistance of #180 GC rod compared with resin bonded diamond wheel, which resulted the run-error of GC rod was hard to reduce or eliminate. Hence, the #180 GC rod is not suitable to true resin bonded wheels. 5.1. Truing performance analysis Fig. 7 shows the truing performance of the D3 resin bonded wheel (#800 GC rod, N = 5000 rpm, ap = 5 m, n = 371 rpm, F = 100 mm/min). As shown in Fig. 7(a), before truing, many measured points were far away from and zigzagged around the fitting arc profile, while the measured points agreed well with the fitting profile arc after truing, and the wheel condition was improved significantly as shown in Fig. 7(b). The form deviations of the wheel profile before and after truing were obtained by removing their power values as shown in Fig. 7(c) and (d), and it could be observed intuitively that the form deviation and the run-out error was reduced significantly from 32 m to 2.3 m after truing, which was conducive to obtain precision surface in subsequent grinding process. Because of the optical collection principle, the irregular surface of diamond grains on the wheel profile surface may reflect the laser disorderly and generate noises inevitably in the LSM measuring process. Therefore the form deviation in the range of 99% probability of the measured points was considered as actual form error in this paper. As shown in Fig. 7(e) and (f), the form error of 2.5 m after truing decreased about 93% contrast of 35 m before truing. The similar truing performance also could be presented on the D7 and D15 wheels, and the optimal results of these three wheels in the experiment were displayed in Table 5. As a result, after truing, the radius of wheels was accurately close to the expected radius, the form errors and run-out errors of all wheels were reduced about 90% compared to before-truing. ORGCR mutual-wear truing can produce a precision truing accuracy of diamond arc-shaped wheel. 5.2. Truing ratio According to Exp. (10), the truing ratio versus GC rod granularity for different diamond wheels in ORGCR mutual-wear truing is shown in Fig. 8. The truing ratios of 0.7–6.7 were obtained in case of truing D3 and D7 diamond wheels by #400 and #800 GC rod. While the #800 GC rod exhibited lower truing ratio compared with #400 GC, it seems to be caused that #800 GC rod with smaller grains was easier to be worn when truing. Besides, the truing ratio when truing the D3 wheel was greater than truing the D7 wheel, it means that the D3 wheel is easier to be trued, it seems to be caused that the higher protrusion height of the D7 wheel diamond grains may remove more GC rod with the same truing conditions. For truing of metal bonded D15 wheel by #180 GC rod, the truing ratio was only 0.105, which was much smaller than truing resin bonded diamond wheels due to the harder wheel bond material and bigger grain size, it means that the metal bonded D15 wheel is harder to be trued. However, the precision radius and form accuracy of the
Fig. 8. Truing ratio.
D15 wheel still was formed through ORGCR mutual-wear truing method as shown in Table 5. Therefore, ORGCR mutual-wear truing can produce a remarkable truing ability of resin bonded D3 and D7 wheel and a reluctant truing ability of metal bonded D15 wheel. 5.3. Truing accuracy versus truing parameters Fig. 9 shows changes of truing accuracy in different truing parameters for D3 and D7 resin bonded wheels. The radius deviation after truing kept below 0.3 mm from expected radius. The radius after truing mainly ranged 5.7–5.9 mm for the D3 wheel (the expected radius is 6 mm) and 3.7–3.9 mm for the D7 wheel (the expected radius is 4 mm), and the wheel profile radius accuracy was affected weekly by truing parameters. In fact, the wheel profile radius accuracy is crucially affected by the compensated radius of interpolation arc, which corresponds to analysis of Section 2. Besides, the form error after truing with #800 GC rod was always smaller than #400 GC rod, and within 2.5–3.6 m/3 mm for the D3 wheel and 2.8–4.2 m/3 mm for the D7 wheel regardless of the truing parameters difference. Overall, the form error of wheel arc profile was increased with increased ap as shown in Fig. 9(d). In truing process, more material of wheel at edge of wheel profile may be removed at initial rub stage of interpolation movement because of high pressure with more depth of cut, with the progresses of interpolation movement, the material of GC rod was also removed, less material of wheel at center of wheel profile may be removed at middle rub stage of interpolation movement because of the decreased pressure, and more depth of cut increased the distance of wheel material removal quantity between edge and center of wheel profile so that the form error was increased. As shown in Fig. 9(e), the form error of wheel arc profile was also increased with increased arc interpolating speed, this seems to be caused that more arc interpolating speed makes the wheel cannot adequately contact, rub with and remove evenly GC rod. Besides, the wheel speed has little stable influence on the form error of wheel arc profile as shown in Fig. 9(f). Fig. 10 shows the changes of truing accuracy in different truing parameters for the D15 metal bonded wheel. The radius after truing mainly ranged 3.85–4.007 mm (the expected radius is 4 mm), the radius deviation was below 0.16 mm from the expected radius. The form error after truing was always within the scope of 3–6 m/3 mm. The influence of parameters on radius accuracy and form error of D15 wheel arc profile was similar with D3 and D7 wheel. However, when truing D15 metal bonded wheel with the wheel speed of 6000 rpm and 7000 rpm, the GC rod was blocked by the bronze bond of the wheel, as shown in Fig. 10(d). It seems to be caused that the bronze bond changes soft when the temperature rises up in high speed friction and fills the gap of GC grains.
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Table 4 truing ability of different GC rod grains. GC rod
D3 resin bonded wheel D7 resin bonded wheel D15 metal bonded wheel
#180 (hardness: P)
#400 (hardness: P)
#800 (hardness: P)
#180 (hardness: T)
ability
reason
ability
reason
Low wear Low wear Low removal
ability √ √
reason
× × ×
ability √ √
– – Low removal
× × √
Low wear Low wear –
×
reason – – Low removal
×
Table 5 Truing performance. Wheel
Truing parameters
Expected r
r before truing
r after truing
es before truing
es after truing
es quotient
D3 D7 D15
#800, N = 5000 rpm, ap = 5 m, n = 371 rpm, F = 100 mm/min #800, N = 5000 rpm, ap = 5 m, n = 371 rpm, F = 100 mm/min #180, N = 4000 rpm, ap = 9 m, n = 371 rpm, F = 160 mm/min
6 mm 4 mm 4 mm
3.093 mm 3.096 mm 3.818 mm
5.765 mm 3.867 mm 4.007 mm
35 m 26 m 33 m
2.5 m 2.8 m 3.2 m
14 9.3 10.3
Fig. 9. Truing accuracy of D3 and D7 versus truing parameters (a) radius versus ap (b) radius versus F (c) radius versus N (d) form error versus ap (e) form error versus F (f) form error versus N. Table 6 Optimal truing parameters. Wheel
GC
ap (m)
F (mm/min)
N (rpm)
D3 D7 D15
#800 #800 #180
5 5 6
100 50 80
5000 4000 4000
Finally, the optimal truing parameters could be acquired and listed in Table 6 for the least form error in base of Figs. 9 and 10.
5.4. Topography of diamond wheels after truing Fig. 11 shows the LSDLM photos of three wheels arc profile topography. The wheels were well trued as shown in Fig. 11(a), (d) and (g). Before truing, the arc profile topography transited wavily, and existed a lot of raised and foveate stripe on the wheel surface, as shown in Fig. 11(b), (e) and (h), which certainly reduced the form accuracy of the wheel profile. After truing, the formed arc profile topography was uniform and smooth, the truing traces could be observed clearly on the metal bonded wheel surface, as
shown in Fig. 11(c), (f) and (i). Therefore, the wheel performance was improved obviously in macroscopic view. Fig. 12 shows the SEM photos of wheel surface after truing, the diamond grains were well distributed on the wheel surface, protruded out of the wheel bond, and their cutting edges were also sharpened. This means that the ORGCR mutual-wear truing is not only valid to create high accuracy form of diamond wheels, but also could protrude the abrasive grains out of the wheel bond. 5.5. Aspherical surface grinding on single crystal silicon Fig. 13 shows the photo and SEM topography of single crystal silicon aspherical surface which ground by the D7 resin bonded diamond wheel with form accuracy of 3.1 m and arc radius of 3.867 mm in parallel grinding. The ground aspherical surface appeared the mirror effect as shown in Fig. 13(a). From the SEM topography of aspherical surface, it was mainly covered with ductile removal marks, and a little of cracks and deep grooves as shown in Fig. 13(b). Fig. 14 shows the aspherical surface with form accuracy PV of 507 nm measured by on-machine form accuracy measurement system and the average surface roughness Ra of 57.1 nm measured by Talysurf PGI 1240. It is indicate that the
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Fig. 10. Truing accuracy of D15 versus truing parameters (a) radius and form error versus ap (b) radius and form error versus F (c) radius and form error versus N (d) GC rod blocked.
Fig. 11. LSDLM photos of wheel arc profile topography (a) D3 resin bonded wheel (b) D3 wheel before grinding (c) D3 wheel after grinding (d) D7 resin bonded wheel (e) D7 wheel before grinding (f) D7 wheel after grinding (g) D15 metal bonded wheel (h) D15 wheel before grinding (i) D15 wheel after grinding.
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Fig. 12. SEM photos of wheel surface (a) D3 resin bonded wheel (b) D7 resin bonded wheel (c) D15 metal bonded wheel.
Fig. 13. Photos of single crystal silicon aspherical surface (a) photo (b) SEM topography.
Fig. 14. Aspherical surface quality of single crystal silicon (a) form accuracy (b) surface roughness.
wheel was trued with precision form accuracy of arc profile and well distribution of diamond grains, and the precision grinding of aspherical surface can be achieved with the arc-shaped diamond wheel trued by the ORGCR mutual-wear truing. 6. Conclusions A method of ORGCR mutual-wear truing was developed to precisely form resin and metal arc-shaped diamond wheels for
precision spherical, aspherical and free-form surfaces grinding. The detailed results are included as follows:
1. The ORGCR mutual-wear truing method is able to realize the precision truing of resin and metal bonded arc-shaped diamond wheels with any designed radius, and tool setting positon error of the wheel in the vertical direction can be corrected after truing. Besides, a direct and simple measurement method was proposed
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to evaluate truing performance and truing ratio through the measured points collected by LSM. 2. Compared with the #400 GC rod, the #800 GC rod was more suitable to obtain higher truing accuracy for the resin bonded diamond wheels, although the truing efficiency was lower. The truing ratios of #400 GC rod were 4.8–6.7, while the truing ratios of #800 GC rod were 0.7–2.0. By the increase of grain size and hardness of GC rod, the D15 metal bonded wheel was trued satisfactorily by the #180 GC rod with higher hardness of T with the truing ratio of 0.105. 3. Based on the parameters optimization, the D3 resin bonded wheel with from error of 2.5 m/3 mm, the D7 resin bonded wheel with from error of 2.8 m/3 mm and the D15 metal bonded wheel with from error of 3.2 m/3 mm were obtained, respectively. The radius deviation of these wheels was all below 0.3 mm from the expected radius of 4–6 mm. 4. In grinding experiment, the aspherical surface of single crystal silicon with the form accuracy PV of 507 nm and the average roughness Ra of 57.1 nm was achieved by parallel grinding with the trued D7 resin bonded wheel. Acknowledgments This work was supported by China Postdoctoral Science Foundation funded project [No. 2013M541361] and Heilongliang Postdoctoral Fund [No. LBH-Z13104].
References Brinksmeier, E., Mutlugünes, Y., Klocke, F., Aurich, J.C., Shore, P., Ohmori, H., 2010. Ultra-precision grinding. J. CIRP Ann. Manuf. Technol. 59 (2), 652– 671. Crawford, J.F., 1983. A non-iterative method for fitting circular arcs to measured points. J. Nucl. Instrum. Methods Phys. Res. 211 (1), 223–225. Derkx, J.M., Hoogstrate, A.M., Saurwalt, J.J., Karpuschewski, B., 2008. Form crush dressing of diamond grinding wheels. J. CIRP Ann. Manuf. Technol. 57 (1), 349–352. Guo, B., Zhao, Q., 2015. On-machine dry electric discharge truing of diamond wheels for micro-structured surfaces grinding. Int. J. Mach. Tool. Manu. 88, 62–70. Klocke, F., Brinksmeier, E., Riemer, O., Klink, A., Schulte, H., Sarikaya, H., 2007. Manufacturing structured tool inserts for precision glass moulding with a combination of diamond grinding and abrasive polishing. J. IDR 4, 65–69. Lin, X.H., Wang, Z.Z., Guo, Y.B., Peng, Y.F., Hu, C.L., 2014. Research on the error analysis and compensation for the precision grinding of large aspheric mirror surface. Int. J. Adv. Manuf. Technol. 71 (1–4), 233–239. Saeki, M., Kuriyagawa, T., Lee, J.S., Syoji, K., 2001. Machining of aspherical optodevice utilizing parallel grinding method. In: In The 16th ASPE Annual Meeting, USA, pp. 433–436, vol. 25. Wegener, K., Hoffmeister, H.W., Karpuschewski, B., Kuster, F., Hahmann, W.C., Rabiey, M., 2011. Conditioning and monitoring of grinding wheels. J. CIRP Ann. Manuf. Technol. 60 (2), 757–777. Wang, Z.Z., Guo, Y.B., Huang, H., He, L.Y., 2009. Development and application of cup truer in advanced optical grinding. J. Diamond Abrasives Eng. 1, 003. Xie, J., Zhou, R.M., Xu, J., Zhong, Y.G., 2010. Form-truing error compensation of diamond grinding wheel in CNC envelope grinding of free-form surface. Int. J. Adv. Manuf. Technol. 48 (9–12), 905–912. Zhao, Q., Guo, B., 2015. Ultra-precision grinding of optical glasses using mono-layer nickel electroplated coarse-grained diamond wheels. Part 2: Investigation of profile and surface grinding. Precis. Eng. 39, 67–78.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
On-machine precision form truing of arc-shaped diamond wheels Bing Chen, Bing Guo ∗ , Qingliang Zhao Center for Precision Engineering, School of Mechatronics Engineering, Harbin Institute of Technology, PO Box 413, Harbin 150001, Heilongjiang, China
a r t i c l e
i n f o
Article history: Received 7 August 2014 Received in revised form 20 March 2015 Accepted 26 March 2015 Available online 6 April 2015 Keywords: On-machine truing Arc-shaped diamond wheel Rotary GC rod Truing performance Truing ratio
a b s t r a c t In order to realize the efficient and precision truing of arc-shaped diamond wheel for precision grinding of spherical, aspherical and free-form surfaces, a novel on-machine precision form truing of resin and metal bonded arc-shaped diamond wheels is proposed utilizing rotary green silicon carbon (GC) rod. Through this on-machine rotary GC rod (ORGCR) mutual-wear truing, any required radius of wheel arc profile could be formed by programmed truing paths, meanwhile, the vertical direction position error of the wheel center could be corrected after truing. Firstly, the principle of ORGCR mutual-wear truing for arc-shaped diamond wheel was introduced, and new evaluation methods of truing performance and truing ratio were provided. Then the truing performance and truing ratio were observed for different grains and bond of arc-shaped diamond wheels, the effects of ORGCR mutual-wear truing parameters on profile radius and form accuracy of wheels were investigated. Finally, the convex aspherical surface of single crystal silicon was ground by trued arc-shaped diamond wheel. The experimental results showed that the resin and metal bonded diamond wheels could be efficiently and precisely trued with high truing ratio. The form error of wheel arc profile reached 2.5–6 m/3 mm which decreased about 90% compared to pre-truing wheel. Besides, the diamond grains were well distributed on the wheel surface, and protruded out of the wheel bond after truing. The precision aspherical surface of single crystal silicon with the form accuracy PV of 507 nm and the average roughness Ra of 57.1 nm was achieved by parallel grinding with the trued D7 resin bonded wheel. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The development of advanced optoelectronic and astronomical devices highly demands for optical components and molds with spherical, aspherical and free-form surfaces with high profile accuracy and excellent surface finish. Most of these components and molds have to be machined by abrasive processes with diamond wheels due to their hard-brittle materials property, such as ceramics, cements, optical glasses and crystalline materials, as expounded by Brinksmeier et al. (2010). The arc-shaped diamond wheels with precision profile were usually adopted for ultra-precision grinding of spherical, aspherical and free-form surfaces. Saeki et al. (2001) investigated that the quality of aspherical opto-device surface ground by arc-shaped diamond wheels utilizing parallel grinding method was better than cross grinding method. Lin et al. (2014) applied arc-shaped diamond to grind BK7 glass with size of 430 × 430 × 27.5 mm using
∗ Corresponding author. Tel.: +0086 451 86402683; fax: +0086 451 86415244. E-mail addresses: [email protected] (B. Chen), [email protected] (B. Guo), [email protected] (Q. Zhao). http://dx.doi.org/10.1016/j.jmatprotec.2015.03.046 0924-0136/© 2015 Elsevier B.V. All rights reserved.
CNC envelope grinding on the surface grinder. Xie et al. (2010) demonstrated that CNC envelope grinding of free-form surface by arc-shaped diamond wheel permitted more grinding points around its torus-shaped working surface to take part in grinding process, and it decreased wears compared to a single grinding point when grinding large-size curve surface. Considering these grinding process of spherical, aspherical and free-form surfaces with arc-shaped wheel, the form accuracy of the ground surface was mainly determined by the profile accuracy of wheels. To improve the accuracy of the wheel profile, Wegener et al. (2011) introduced abundant truing methods proposed for formed diamond wheels. Wang et al. (2009) developed a cup truer with a cyclical arc swing mechanism to true arc-shaped wheels, and the form error of the wheel profile was ±5 m/17 mm after truing. Derkx et al. (2008) proposed a form crush dressing method to profile diamond grinding wheels, and the form crush dressing system concluded a lot of components, such as swiveling axis for truer, adjustment axis, motor housing, bearing housing and so on. Klocke et al. (2007) demonstrated that wire electro discharge (Wire-EDM) method which implemented on a conventional Wire-EDM machine was used to true and dress micro arc-shaped diamond wheels for grinding micro-arc array. Xie et al. (2010) showed that the fixed
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holding ability of the bond for some diamond grains is decreased so that the diamond grains like
,
,
fall off, and the diamond
, , are protruded out of the wheel bond. Meangrains like time, the similar removal mechanism emerges on the GC rod, the falls off, and the grains like , are protruded GC grain like out of the GC rod bond. The only difference is the GC grains may
Fig. 1. ORGCR truing mechanism (a) initial truing (b) truing process.
green silicon carbon (GC) stick CNC mutual-wear truing without any complex accessory was applied to true #180 metal bonded diamond grinding wheel. After truing, the form accuracy of trued diamond wheel was 18.2 m/10 mm. However, most of above truing methods need complicated attached devices, while the fixed GC stick CNC mutual-wear truing cannot confirm tool setting position of the wheel in the vertical direction after truing. Based on the above, a novel on-machine precision truing of resin and metal bonded arc-shaped diamond wheels is proposed utilizing mutual-wear between diamond wheel and GC rod without any complex accessory. In this ORGCR mutual-wear truing, the workpiece spindle on the machine was applied to drive GC rod to remove the wheel bond along the circular interpolation paths, and then the arc profile was formed gradually, while the vertical direction position error of wheel center would also be corrected automatically after truing. Firstly, the principle of ORGCR mutual-wear truing was introduced, and new evaluation methods of truing performance and truing ratio were provided. Then the truing ratio and truing performance were observed for different grains and bond of arcshaped diamond wheels. Next, the effects of ORGCR mutual-wear truing parameters on profile radius and form accuracy of wheels were investigated. Finally, the convex aspherical surface of single crystal silicon was ground by trued arc-shaped diamond wheel.
, be broken like because of mutual-strike with the diamond grains. Fig. 2 shows the ORGCR mutual-wear truing principle of arcshaped diamond wheel. In ORGCR mutual-wear truing, the GC rod is driven by the workpiece spindle on the machine with the wheel speed n to true diamond wheel with the wheel speed N along the circular interpolation paths circularly with the feed rate v in CNC grinding system as shown in Fig. 2(a), then a arc-shaped wheel may be gradually formed with the depth of cut ap through the CNC mutual-wear between the diamond wheel and GC rod dresser. Besides, the motion paths were designed to utilize more cylinder of GC rod to true the arc profile of diamond wheel as shown in Fig. 2(b). In the motion paths, when a circular interpolation path is completed, the diamond wheel is moved with the distance B along negative direction of Z axis, then the next circular interpolation movement is carried out, and keep the cycle going until the terminal of motion paths. After finishing the positive motion paths, the inverse movements are executed back to the beginning of motion paths. In short, the arc-shaped diamond wheel can be trued by rotary GC rod with circular interpolation paths and motion paths. The radius of interpolation arc a is described as Exp. (1). Any radius of wheel arc profile can be obtained for different requirements by changing the radius of interpolation arc. a=R+r
(1)
where R is the radius of GC rod which can be measured in truing process, and r is the expected radius of wheel arc profile, as shown in Fig. 2(a). In the truing process, however, the radius of GC rod is decreased unavoidably because of the mutual-wear. According to Exp. (1), the actual radius of wheel arc profile would be increased and deviate from the expected radius largely in truing process if the radius of interpolation arc remain the same. Therefore the radius of interpolation arc need be compensated by the radius of GC rod measured in truing process to guarantee the radius of arc profile wheel to meet the expected radius as follows:
2. ORGCR mutual-wear truing of arc-shaped diamond wheel
ai = r + Ri
Fig. 1 shows the ORGCR truing mechanism. In the truing process, the GC grains rub and remove the bond of diamond wheel, then the
where ai is the compensated radius of interpolation arc and Ri is the radius of GC rod measured in real-time.
Fig. 2. ORGCR mutual-wear truing mode of arc-shaped diamond wheel: (a)truing mode (b)truing motion paths.
(2)
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Fig. 3. On-machine measurement of trued arc-shaped diamond wheel (a) measuring process (b)adjustment of horizontal measure position.
Fig. 4. Volumetric removal mode in truing (a) diamond wheel (b) GC rod.
Considering the symmetry of the circular interpolation paths in XOY plane, the center position YP of wheel arc profile in vertical direction can be confirmed as follows: 1 YP = (Y1 + Y2 ) 2
(3)
where Y1 , Y2 is vertical direction coordinate of the interpolation arc beginning O1 and terminal O2 , as show in Fig. 2(a), then tool setting position of diamond wheel in the vertical direction is confirmed.
3. Evaluation of trued arc-shaped diamond wheel 3.1. On-machine measurement of trued arc-shaped diamond wheel In this paper, a direct measurement method was proposed to evaluate the wheel profile through a large amount of measured points collected by laser scan micrometer (LSM), as show in Fig. 3. Compared with the replication measurement methods, such as carbon replication as presented by Guo and Zhao (2015) and dental plastic replication as presented by Zhao and Guo (2015), this method is more direct and simpler. The LSM (KEYENCE LK-G5000) with a resolution of 0.1 m was adopted to measure the arc profile of diamond wheel. In measuring process, the LSM with sampling frequency f measured the rotary diamond wheel with speed N1 from the top surface to bottom surface of the wheel with the feed rate v1 . Note that the horizontal measure position of LSM with minimum extreme distance have to be found in order to reduce the measuring error, as shown in Fig. 3(b). After measurement, the truing performance can be evaluated on-machine by the data of arc profile wheel collected by LSM.
3.2. The calculation of arc profile radius and form accuracy of wheel The deviation of arc profile radius and the arc form error were generally used to evaluate the truing performance of arc-shaped wheel. In the actual grinding process, however, the grinding paths were generated according to the measured radius of the wheel, the deviation of arc profile radius cannot influence the grinding accuracy, while the form error of arc profile may be copied to the ground surface directly. Therefore, compared to the profile radius, the form accuracy is more important to be obtained in truing process. Crawford (1983) demonstrated that the least square method fitting algorithm was suitable to calculate arc profile radius and form accuracy trough the measured points. In the least square method fitting arc profile algorithm, the square error ıi defined as difference between the distance from the measured point (Xi , Yi ) to the theoretical profile radius and the theoretical radius is described as follows:
2
ıi = di2 − r 2 = Xi2 − A
+ Yi 2 − B
= Xi2 + Yi2 + aXi + bYi + c
2
− r2 (4)
where r is the theoretical radius, A, B is the center coordinate of arc. The arc profile radius r can be calculated through obtaining minimum ı2i :
r=
a2 + b2 − 4c 2
(5)
Besides, the arc form accuracy es defined as the difference between the maximum and minimum of the distance from the
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measured point to the theoretical radius profile is described as follows:
es =
max ıi −
min ıi
(6)
3.3. Truing ratio Fig. 4 exhibits the volumetric removal mode of wheel and GC rod in truing process. The removal volume of diamond wheel can be calculated by the difference value between the wheel volume before truing and after truing, as show in Fig. 4(a). The volume of diamond wheel V can be described as follows: V=
n−1
Sj × h
(7)
Fig. 5. ORGCR truing experimental setup.
Table 1 Truing conditions.
j
where n is the cycle number of LSM sampling spiral line around the periphery of diamond wheel, j is a certain cycle, Sj is the sectional areas of diamond wheel in j cycle, h is the distance between two adjacent cycles. In Exp. (7), Sj is described as follows: Sj =
k
X 2 +Y 2 + i
i
X 2 +Y 2 i+1
2
i+1
Machining tool
Three-axis ultra precision grinder
Diamond wheel
Resin bonded D3 (expected radius: 6 mm), D7 (expected radius: 4 mm) Metal bonded D15 (expected radius: 4 mm) Diameter: 75 mm, thickness: 6 mm, concentrations: 50%, initial radius: 3 mm #400,#800 for D3, D7, hardness: P #180 for D15, hardness: T Diameter: 20 mm, length: 110 mm Water-based, challenge 300-HT, concentrations: 2–3%, speed: 5 m/s, cross-sectional area of nozzle: 12.56 mm2 KEYENCE LK-G5000, sampling frequency: 50 KHz
2
× 2 ,where k is the total points
GC rod
i
of a cycle, k = 60f/N1 , i is a certain measured points, is the angle of two adjacent points, = 2/k. n is described as follows: n = Np /k, where NP is the total measured points of the wheel. h is described as follows: h = YNp − Y1 / (n − 1), where YNP is the Y coordinate of the last measured point and the Y1 is the Y coordinate of the first measured point of the wheel. Hence, the difference value between the wheel volume before truing and after truing Vw is described as follows: Vw = Vbe − Vaf
(8)
where Vbe is the volume of wheel before truing and Vaf is the volume of wheel before truing. Besides, the removal volume of GC rod VGC , as shown in Fig. 7(b), can be calculated as follows: VGC =
m1 − m2 GC
(9)
where GC is the average density of GC rod, and m1 , m2 is the weight of GC rod before and after grinding, respectively. Therefore the truing ratio can be defined as the ratio of wheel removal volume Vw to the GC rod removal volume VGC , as follows: =
Vw VGC
(10)
Coolant
LSM
4. Experimental setup 4.1. Precision truing of arc-shaped diamond wheel Fig. 5 shows the ORGCR mutual-wear truing experimental setup. The details of truing conditions and truing parameters are shown in Tables 1 and 2, respectively. The morphology of wheel surface was examined by a large scene depth laser microscope (LSDLM) and a scanning electron microscope (SEM). 4.2. Precision grinding of aspherical surface Fig. 6 shows the parallel grinding of aspherical surface with trued resin bonded D7 wheel and the on-machine measuring process. The morphology of aspherical surface was examined by SEM, while the surface roughness was measured in the vertical
Fig. 6. Aspherical surface grinding setup (a) grinding system (b) on-machine measurement system.
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Fig. 7. Truing performance of D3 wheel (a) Wheel profile before truing (b) Wheel profile after truing (c) Form deviation before truing (d) Form deviation after truing (e) Probability distributions of form deviation before truing (f) Probability distributions of form deviation after truing.
Table 2 Truing parameters. Wheel: D3, D7 No.
1 2 3 4 5 6 7 8 9 10 11 12
Wheel: D15 No.
n = 371 rpm Truing pass no.: 20 pass N (rpm) ap (m)
F (mm/min)
4000 5000 6000 7000 5000 5000 5000 5000 5000 5000 5000 5000
100 100 100 100 100 100 100 100 50 100 200 300
10 10 10 10 2 5 10 20 10 10 10 10
1 2 3 4 5 6 7 8 9 10 11 12
n = 571 rpm Truing pass no.20 pass N (rpm) ap (m)
F (mm/min)
4000 5000 6000 7000 5000 5000 5000 5000 5000 5000 5000 5000
160 160 160 160 160 160 160 160 80 120 160 200
9 9 9 9 3 6 9 12 9 9 9 9
Table 3 Aspherical surface grinding conditions. Wheel
D7 resin bonded wheel
Workpiece Grinding mode
Single crystal silicon, diameter: 20 mm, thickness:10 mm Parallel grinding
Aspheric equation
f (X) =
Rough grinding Semi-fine grinding Fine grinding Precision grinding
C × X2 /
1+
1 − (K + 1) × C × X 2
+
n i=1
Ci × Xi , convex surface
ap (m)
F (mm/min)
N (rpm)
N (rpm)
Pass
5 2 2 0
20 10 4 4
6000 6000 6000 6000
173 173 173 173
2 1 1 1
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grinding direction by a contact probe profilometer (Talysurf PGI 1240). Detailed grinding conditions are shown in Table 3. 5. Results and discussions A pre-experiment about truing ability of different GC grain size for different wheels was performed before above-experiments as shown in Table 4. The truing results showed that the GC rods of #180, #400, #800 with hardness of P hardly removed the D15 metal bonded wheel, while the #180 harder GC rod with hardness of T was applied to true the D15 wheel and obtained considerable removal ratio. For D3 and D7 resin bonded wheel, the truing accuracy of the wheel was unsatisfied with the #180 GC rod with hardness of P and T. It seems to be caused by extreme wear resistance of #180 GC rod compared with resin bonded diamond wheel, which resulted the run-error of GC rod was hard to reduce or eliminate. Hence, the #180 GC rod is not suitable to true resin bonded wheels. 5.1. Truing performance analysis Fig. 7 shows the truing performance of the D3 resin bonded wheel (#800 GC rod, N = 5000 rpm, ap = 5 m, n = 371 rpm, F = 100 mm/min). As shown in Fig. 7(a), before truing, many measured points were far away from and zigzagged around the fitting arc profile, while the measured points agreed well with the fitting profile arc after truing, and the wheel condition was improved significantly as shown in Fig. 7(b). The form deviations of the wheel profile before and after truing were obtained by removing their power values as shown in Fig. 7(c) and (d), and it could be observed intuitively that the form deviation and the run-out error was reduced significantly from 32 m to 2.3 m after truing, which was conducive to obtain precision surface in subsequent grinding process. Because of the optical collection principle, the irregular surface of diamond grains on the wheel profile surface may reflect the laser disorderly and generate noises inevitably in the LSM measuring process. Therefore the form deviation in the range of 99% probability of the measured points was considered as actual form error in this paper. As shown in Fig. 7(e) and (f), the form error of 2.5 m after truing decreased about 93% contrast of 35 m before truing. The similar truing performance also could be presented on the D7 and D15 wheels, and the optimal results of these three wheels in the experiment were displayed in Table 5. As a result, after truing, the radius of wheels was accurately close to the expected radius, the form errors and run-out errors of all wheels were reduced about 90% compared to before-truing. ORGCR mutual-wear truing can produce a precision truing accuracy of diamond arc-shaped wheel. 5.2. Truing ratio According to Exp. (10), the truing ratio versus GC rod granularity for different diamond wheels in ORGCR mutual-wear truing is shown in Fig. 8. The truing ratios of 0.7–6.7 were obtained in case of truing D3 and D7 diamond wheels by #400 and #800 GC rod. While the #800 GC rod exhibited lower truing ratio compared with #400 GC, it seems to be caused that #800 GC rod with smaller grains was easier to be worn when truing. Besides, the truing ratio when truing the D3 wheel was greater than truing the D7 wheel, it means that the D3 wheel is easier to be trued, it seems to be caused that the higher protrusion height of the D7 wheel diamond grains may remove more GC rod with the same truing conditions. For truing of metal bonded D15 wheel by #180 GC rod, the truing ratio was only 0.105, which was much smaller than truing resin bonded diamond wheels due to the harder wheel bond material and bigger grain size, it means that the metal bonded D15 wheel is harder to be trued. However, the precision radius and form accuracy of the
Fig. 8. Truing ratio.
D15 wheel still was formed through ORGCR mutual-wear truing method as shown in Table 5. Therefore, ORGCR mutual-wear truing can produce a remarkable truing ability of resin bonded D3 and D7 wheel and a reluctant truing ability of metal bonded D15 wheel. 5.3. Truing accuracy versus truing parameters Fig. 9 shows changes of truing accuracy in different truing parameters for D3 and D7 resin bonded wheels. The radius deviation after truing kept below 0.3 mm from expected radius. The radius after truing mainly ranged 5.7–5.9 mm for the D3 wheel (the expected radius is 6 mm) and 3.7–3.9 mm for the D7 wheel (the expected radius is 4 mm), and the wheel profile radius accuracy was affected weekly by truing parameters. In fact, the wheel profile radius accuracy is crucially affected by the compensated radius of interpolation arc, which corresponds to analysis of Section 2. Besides, the form error after truing with #800 GC rod was always smaller than #400 GC rod, and within 2.5–3.6 m/3 mm for the D3 wheel and 2.8–4.2 m/3 mm for the D7 wheel regardless of the truing parameters difference. Overall, the form error of wheel arc profile was increased with increased ap as shown in Fig. 9(d). In truing process, more material of wheel at edge of wheel profile may be removed at initial rub stage of interpolation movement because of high pressure with more depth of cut, with the progresses of interpolation movement, the material of GC rod was also removed, less material of wheel at center of wheel profile may be removed at middle rub stage of interpolation movement because of the decreased pressure, and more depth of cut increased the distance of wheel material removal quantity between edge and center of wheel profile so that the form error was increased. As shown in Fig. 9(e), the form error of wheel arc profile was also increased with increased arc interpolating speed, this seems to be caused that more arc interpolating speed makes the wheel cannot adequately contact, rub with and remove evenly GC rod. Besides, the wheel speed has little stable influence on the form error of wheel arc profile as shown in Fig. 9(f). Fig. 10 shows the changes of truing accuracy in different truing parameters for the D15 metal bonded wheel. The radius after truing mainly ranged 3.85–4.007 mm (the expected radius is 4 mm), the radius deviation was below 0.16 mm from the expected radius. The form error after truing was always within the scope of 3–6 m/3 mm. The influence of parameters on radius accuracy and form error of D15 wheel arc profile was similar with D3 and D7 wheel. However, when truing D15 metal bonded wheel with the wheel speed of 6000 rpm and 7000 rpm, the GC rod was blocked by the bronze bond of the wheel, as shown in Fig. 10(d). It seems to be caused that the bronze bond changes soft when the temperature rises up in high speed friction and fills the gap of GC grains.
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Table 4 truing ability of different GC rod grains. GC rod
D3 resin bonded wheel D7 resin bonded wheel D15 metal bonded wheel
#180 (hardness: P)
#400 (hardness: P)
#800 (hardness: P)
#180 (hardness: T)
ability
reason
ability
reason
Low wear Low wear Low removal
ability √ √
reason
× × ×
ability √ √
– – Low removal
× × √
Low wear Low wear –
×
reason – – Low removal
×
Table 5 Truing performance. Wheel
Truing parameters
Expected r
r before truing
r after truing
es before truing
es after truing
es quotient
D3 D7 D15
#800, N = 5000 rpm, ap = 5 m, n = 371 rpm, F = 100 mm/min #800, N = 5000 rpm, ap = 5 m, n = 371 rpm, F = 100 mm/min #180, N = 4000 rpm, ap = 9 m, n = 371 rpm, F = 160 mm/min
6 mm 4 mm 4 mm
3.093 mm 3.096 mm 3.818 mm
5.765 mm 3.867 mm 4.007 mm
35 m 26 m 33 m
2.5 m 2.8 m 3.2 m
14 9.3 10.3
Fig. 9. Truing accuracy of D3 and D7 versus truing parameters (a) radius versus ap (b) radius versus F (c) radius versus N (d) form error versus ap (e) form error versus F (f) form error versus N. Table 6 Optimal truing parameters. Wheel
GC
ap (m)
F (mm/min)
N (rpm)
D3 D7 D15
#800 #800 #180
5 5 6
100 50 80
5000 4000 4000
Finally, the optimal truing parameters could be acquired and listed in Table 6 for the least form error in base of Figs. 9 and 10.
5.4. Topography of diamond wheels after truing Fig. 11 shows the LSDLM photos of three wheels arc profile topography. The wheels were well trued as shown in Fig. 11(a), (d) and (g). Before truing, the arc profile topography transited wavily, and existed a lot of raised and foveate stripe on the wheel surface, as shown in Fig. 11(b), (e) and (h), which certainly reduced the form accuracy of the wheel profile. After truing, the formed arc profile topography was uniform and smooth, the truing traces could be observed clearly on the metal bonded wheel surface, as
shown in Fig. 11(c), (f) and (i). Therefore, the wheel performance was improved obviously in macroscopic view. Fig. 12 shows the SEM photos of wheel surface after truing, the diamond grains were well distributed on the wheel surface, protruded out of the wheel bond, and their cutting edges were also sharpened. This means that the ORGCR mutual-wear truing is not only valid to create high accuracy form of diamond wheels, but also could protrude the abrasive grains out of the wheel bond. 5.5. Aspherical surface grinding on single crystal silicon Fig. 13 shows the photo and SEM topography of single crystal silicon aspherical surface which ground by the D7 resin bonded diamond wheel with form accuracy of 3.1 m and arc radius of 3.867 mm in parallel grinding. The ground aspherical surface appeared the mirror effect as shown in Fig. 13(a). From the SEM topography of aspherical surface, it was mainly covered with ductile removal marks, and a little of cracks and deep grooves as shown in Fig. 13(b). Fig. 14 shows the aspherical surface with form accuracy PV of 507 nm measured by on-machine form accuracy measurement system and the average surface roughness Ra of 57.1 nm measured by Talysurf PGI 1240. It is indicate that the
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Fig. 10. Truing accuracy of D15 versus truing parameters (a) radius and form error versus ap (b) radius and form error versus F (c) radius and form error versus N (d) GC rod blocked.
Fig. 11. LSDLM photos of wheel arc profile topography (a) D3 resin bonded wheel (b) D3 wheel before grinding (c) D3 wheel after grinding (d) D7 resin bonded wheel (e) D7 wheel before grinding (f) D7 wheel after grinding (g) D15 metal bonded wheel (h) D15 wheel before grinding (i) D15 wheel after grinding.
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Fig. 12. SEM photos of wheel surface (a) D3 resin bonded wheel (b) D7 resin bonded wheel (c) D15 metal bonded wheel.
Fig. 13. Photos of single crystal silicon aspherical surface (a) photo (b) SEM topography.
Fig. 14. Aspherical surface quality of single crystal silicon (a) form accuracy (b) surface roughness.
wheel was trued with precision form accuracy of arc profile and well distribution of diamond grains, and the precision grinding of aspherical surface can be achieved with the arc-shaped diamond wheel trued by the ORGCR mutual-wear truing. 6. Conclusions A method of ORGCR mutual-wear truing was developed to precisely form resin and metal arc-shaped diamond wheels for
precision spherical, aspherical and free-form surfaces grinding. The detailed results are included as follows:
1. The ORGCR mutual-wear truing method is able to realize the precision truing of resin and metal bonded arc-shaped diamond wheels with any designed radius, and tool setting positon error of the wheel in the vertical direction can be corrected after truing. Besides, a direct and simple measurement method was proposed
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to evaluate truing performance and truing ratio through the measured points collected by LSM. 2. Compared with the #400 GC rod, the #800 GC rod was more suitable to obtain higher truing accuracy for the resin bonded diamond wheels, although the truing efficiency was lower. The truing ratios of #400 GC rod were 4.8–6.7, while the truing ratios of #800 GC rod were 0.7–2.0. By the increase of grain size and hardness of GC rod, the D15 metal bonded wheel was trued satisfactorily by the #180 GC rod with higher hardness of T with the truing ratio of 0.105. 3. Based on the parameters optimization, the D3 resin bonded wheel with from error of 2.5 m/3 mm, the D7 resin bonded wheel with from error of 2.8 m/3 mm and the D15 metal bonded wheel with from error of 3.2 m/3 mm were obtained, respectively. The radius deviation of these wheels was all below 0.3 mm from the expected radius of 4–6 mm. 4. In grinding experiment, the aspherical surface of single crystal silicon with the form accuracy PV of 507 nm and the average roughness Ra of 57.1 nm was achieved by parallel grinding with the trued D7 resin bonded wheel. Acknowledgments This work was supported by China Postdoctoral Science Foundation funded project [No. 2013M541361] and Heilongliang Postdoctoral Fund [No. LBH-Z13104].
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