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An investigation into surface generation in ultra-precision raster milling
Journal of Materials Processing Technology 209 (2009) 4178–4185
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
An investigation into surface generation in ultra-precision raster milling L.B. Kong, C.F. Cheung ∗ , S. To, W.B. Lee Advanced Optics Manufacturing Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
a r t i c l e
i n f o
Article history: Received 14 November 2007 Received in revised form 27 October 2008 Accepted 1 November 2008 Keywords: Form error Freeform surfaces Surface generation Ultra-precision raster milling Optimization Tool wear
a b s t r a c t This paper presents a study of the factors that affect surface generation in ultra-precision raster milling. A series of experiments was conducted to study the effect of different factors on surface generation in ultra-precision raster milling. The results indicate that machining parameters, tool geometry, cutting strategy, and tool wear are the critical factors for achieving super mirror finish surfaces, while cutting strategies, tool path generation, and kinematic errors of the slides are vital to the form accuracy of freeform surfaces. The experimental results are useful for the diagnosis of systematic errors in machine tools, and the control of machining errors. Compensation strategies can be devised, and improvement can be made in the optimization of surface generation and hence the surface quality when using ultra-precision raster milling can be improved. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Optical freeform components are widely applied in laser scanners, digital cameras, automotive lighting systems, optical masks, etc., as discussed in the research of Lee et al. (2005). However, with the development of industry and of technology, conventional surfaces such as those that are spherical, aspherical and some other surfaces with rotational or symmetric axes no longer satisfy the growing demand for functional or special purpose surfaces. To meet this rising demand, freeform surfaces have been introduced and now they play an increasingly important role in various fields. This can be attributed to the fact that the optical freeform surface has more optical functions and other special features. The technology of freeform machining has become increasingly important. However, it is very difficult to manufacture high precision optical freeform surfaces because of their geometrical complexity. Current achievement of precise freeform surfaces usually depends on the experience of the operators, or on trialand-error machining, which is not only time-consuming but also expensive. Research into the factors affecting freeform surface generation has become one of the essential issues for surface error analysis. Lee and Chang (1996) presented an error analysis method for 5-axis machining, which is used to evaluate the
∗ Corresponding author. E-mail address: [email protected] (C.F. Cheung). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.11.002
cusp height between adjacent cutter locations. Control of the surface machining process and the optimization of the manufacturing strategy are important in order to produce high precision surface quality efficiently and inexpensively. Lim and Menq (1997) proposed a cutting-path-adaptive-feedrate strategy for improving the productivity of sculptured surface machining, and performed simulation studies on a two-dimensional curved surface. The factors affecting the surface quality in ultra-precision diamond turning and grinding have been studied by some researchers. Cheung and Lee (2000) studied the process factors and the material factors affecting the surface roughness in ultra-precision diamond turning, while Zhou and Ngoi (2003) investigated the effect of cutting tool conditions and tool set-up errors on surface distortion in the diamond turning of optical components. Lee and Baek (2007) conducted some research work on grinding aspheric surfaces for micro-lenses and the grinding conditions were optimized by designed experiments. Palanikumar and Karthikeyan (2007) investigated the relationships among the various factors involved, such as the effect of machining parameters on surface roughness in the turning process. However, the study of the factors affecting surface generation in ultra-precision raster milling of freeform surfaces has received relatively little attention. This paper presents an experimental study of the different factors that affect freeform surface generation in ultra-precision raster milling. The factors are discussed according to their contribution to surface finish and form generation. A series of experiments was conducted and the results were analyzed and discussed.
L.B. Kong et al. / Journal of Materials Processing Technology 209 (2009) 4178–4185
2. Surface generation in ultra-precision raster milling The cutting geometries for ultra-precision raster milling using horizontal and vertical cutting strategies are shown in Figs. 1 and 2, respectively. The diamond cutting tool is fixed onto the main spindle and rotates with the spindle. The cutting process involves two motions: feed motion and raster motion, based on which appropriate cutting strategies such as whether to cut horizontally or to cut vertically are decided upon. As shown in Fig. 1, horizontal cutting is carried out by the cutter feeding in a horizontal direction. After completing one profile of cutting, the diamond tool moves a step in the raster direction, and so in the way, the whole workpiece surface can be machined. In vertical cutting (see Fig. 2), the cutter feeds in a vertical direction while it moves a step in the horizontal direction. Irrespective of what strategy is used, a surface roughness profile of the machined surface is formed by the repetition of the tool tip making a cut at intervals according to the tool feed rate (c) and then moving a specified distance by steps (ε) under ideal cutting conditions. The feed direction is perpendicular to the raster direction, and both of the directions used in horizontal cutting are opposite to those used in vertical cutting. Walter (2003) described the generalized equation for the determination of theoretical arithmetic roughness for the different cutting strategies in ultra-precision precision raster milling as shown in Eq. (1)
Ra =
c2 ε2 + 24R1 24R2
(1)
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where R1 = R and R2 = r for horizontal cutting while R1 = r and R2 = R for vertical cutting; R is the swing distance and r is the tool nose radius. The selection of the appropriate cutting strategy depends on the surface topography and on the quality control of the form error and surface finish of the workpiece. As shown in Fig. 3, there are different tool path plans for raster milling. For example, one-direction cutting or bi-directional cutting, or a cutting path with tool retreat, or without retreat. The tool path plan can be selected according to the geometry and the quality of the surface of the workpiece. 3. Factors affecting surface generation in ultra-precision raster milling As shown in Fig. 4, the factors affecting surface generation in ultra-precision raster milling are related to the form generation and to surface roughness. The different factors are classified into three categories according to their main features which are the cutting mechanism, the tool path and the cutting process. The factors related to the cutting mechanism include the geometry of the diamond tool, tool wear, waviness of the tool edge, machining parameters and cutting strategy. Machine tool characteristics include slide motion errors, spindle error motions, and the relative vibration between the tool and the workpiece, which greatly affect the tool path and mainly contribute to the form errors of the surface generation. Relative displacement between the tool and the workpiece is involved in the cutting process and it is related to the surface
Fig. 1. Cutting geometry for ultra-precision raster milling using horizontal cutting strategy.
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Fig. 2. Cutting geometry for ultra-precision raster milling using vertical cutting strategy.
roughness. Machine dynamics plays an important role in the displacement between the tool and the workpiece. The dynamic characteristics of the machining system consist of a motor drive and a servo system, the machine tool structure, workpiece structure, as well as their interaction with each other. Motor drive and servo systems drive the motion of the slide tables and the spindle which contribute to the surface generation. Tool/holder deflection, spindle/chunk deflection from the machine tool structure, and workpiece deflection from the workpiece structure, all introduce dynamic errors because of the relative displacement between the tool and the workpiece. Surface generation by ultra-precision raster milling is a complex process. As discussed previously, it is a process which integrates the process of cutting with the mechanism itself, and the tool
path. In the present study, four important factors affecting surface generation in ultra-precision raster milling are studied experimentally. These factors are machining parameters, cutting strategy, slide motion errors and tool wear. 4. Experimental studies and discussion In this study, three groups of experiments have been conducted. They are experiments for studying the effect of machining parameters, as well as cutting strategy, tool wear, and slides errors, on surface generation. The diamond tool used in the experiments is made of natural single crystal diamond. It is a round cutting tool with a 0.1 mm tool-nose radius, 12.5◦ front clearance angle and 1◦ rake angle. The workpiece material used in the experiment is alu-
Fig. 3. Different tool path planning for ultra-precision raster milling.
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Fig. 4. Factors affecting surface generation in ultra-precision raster milling.
minum alloy (Al6061) with chemical composition in percentage of weight of Al: balance, Cu: 0.28, Si: 0.6, Mg: 1.0, and Cr: 0.20. 4.1. The effect of machining parameters and cutting strategy on the surface roughness The mechanism of surface generation by ultra-precision raster milling has been discussed in Section 2. The experiments conducted in the present study will further validate the effect of the machining parameters and cutting strategy on the surface roughness. As shown in Section 2, there are five main machining parameters for ultra-precision raster milling which are: spindle speed (S: rpm),
Fig. 5. Workpiece for studying the effect of machining parameters: (a) dimension of the workpiece design and (b) machined workpiece.
feed rate (f: mm/min), step distance (ε: m), tool nose radius (r: mm) and swing distance (R: mm). These five parameters are used for the convenience of machining setup, and some further parameters such as cutting speed (Vs , mm/s) and feed rate in mm/rev (c: mm/rev) can be derived from the above parameters, as follows: Vs = c=
S 2R = SR 60 30
f S
(2) (3)
Generally, the swing distance and tool nose radius are not changed very often. They are kept almost the same most of the time. The effects of spindle speed, feed rate and step distance on surface generation are investigated in the present study. Table 1 shows the machining parameters used in the experiments and the corresponding results. Fig. 5 shows the design of the workpiece used
Fig. 6. Effect of spindle speed on arithmetic roughness.
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Table 1 Summary of the effect of machining parameters on surface roughness. Spindle speed, S (rpm) H V
Ra (nm) Feed rate, f (mm/min)
H V
Ra (nm) Step distance, ε (m) Ra (nm)
H V
1000 15.70 13.57 20 9.41 9.85 10 14.11 14.19
2000 14.78 12.37 40 13.06 12.37 25 17.10 19.71
3000 14.38 13.41 60 14.11 14.19 50 31.05 22.11
4000 14.11 14.19 80 17.39 15.55 75 67.16 21.61
5000 13.86 13.91 100 17.70 16.00 100 221.58 31.12
f = 60 mm/min, ε=10 m, r = 2.54 mm, R = 23 mm, d = 3 m S = 4000 rpm, ε=10 m, r = 2.54 mm, R = 23 mm, d = 3 m f = 60 mm/min, S = 4000 rpm, r = 2.54 mm R = 23 mm, d = 3 m
Note: H: horizontal cutting; V: vertical cutting; and d: depth of cut.
Fig. 7. Effect of feed rate on arithmetic roughness.
Fig. 8. Effect of step distance on arithmetic roughness.
in the cutting test. Fig. 5(a) shows the dimensions of the workpiece. As shown in Fig. 5 (b), the sample consists of 30 flat surfaces which are grouped into two rows. The upper row of 15 flat surfaces is designed for use with a horizontal cutting strategy while the bottom row of 15 planar surfaces is designed for use with a vertical cutting strategy. Each row of surfaces is divided into 3 groups for
the study of the effect of spindle speed, feed rate and step distance on surface generation, respectively. After the workpiece was machined by ultra-precision raster milling machining system (Freeform 705G from Precitech Inc., USA), the surface data of the workpiece were measured by a Wyko NT8000 optical measurement system. Fig. 6 shows the
Fig. 9. Profile measurement of spherical surface machined by ultra-precision raster milling. (a) Profile of the spherical workpiece and (b) residual errors after form removal.
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effect of spindle speed while Fig. 7 shows the effect of feed rate on arithmetic surface roughness (Ra ), respectively. The effect of step distance on arithmetic surface roughness (Ra ) is shown in Fig. 8. From the experimental results in Figs. 6–8, it is interesting to note that the surface roughness decreases when spindle speed increases, while surface roughness increases when the feed rate and step distance increase. This implies that better surface finish can be obtained under a higher spindle speed, a finer feed rate and a smaller step distance in ultra-precision raster milling. In practice, the spindle speed has a certain limit due to the capability of the air bearing capability to run beyond the limit of stability. The spindle error motions (e.g. run-out, axial error motion) increase when the spindle speed increases. In addition, the feed rate and step distance should not be too small since this will affect machining efficiency. It is also interesting to note that the vertical cutting strategy produces a better surface finish than the horizontal cutting strategy. This can be explained by Eq. (1). In the raster milling process, the surface roughness is determined largely by the step distance, and the swing distance is also far bigger than the tool nose radius. In horizontal cutting, the step distance in the raster direction is determined by the tool nose radius; while, the step distance is determined by the swing distance in vertical cutting. So the vertical cutting strategy is preferred for achieving a better balance between surface quality and machining efficiency in practice. 4.2. The effect of tool wear on surface finish In fact, the process of surface generation is the replicating of the diamond tool profile on the workpiece. The tool wear inevitably affects the surface finish and form accuracy. A spherical surface workpiece was machined by a diamond tool. The profile of the workpiece was measured by a Form TalySurf PGI 1240 as shown in Fig. 9(a). The residual error after form removal is shown in Fig. 9(b), which indicates an obvious error variation from one side to the other side. In other words, the surface finish gets worse from the left to right. The diamond tool was then observed under a microscope as shown in Fig. 10 (Remark: please note that the image seen through the microscope is the reverse of the real cutter position). It is interesting to note that there are some wear regions (worn regions) found in the D-segment (see Fig. 10(b)) while the edge profile is clear and no worn region is found in the U-segment (see Fig. 10(c)). This implies that the residual errors of the spherical workpiece were caused by the tool wear (the edge was broken). As shown in Fig. 9(a), the Usegment profile of the cutter edge first engages in the cutting. After the engaged region passes the center of the edge profile, the D-segment of the edge then engages in cutting. However, the worn region of the cutter makes marks on the surface of the workpiece when this happens, due to wear in the D-segment of the cutter. This adversely affects the surface finish of the workpiece. This study is useful for diagnosis of the wear conditions of the diamond tool by measuring and analyzing the surface quality of the machined surfaces. This provides an indirect approach for the determination of the tool wear without the need for disassembling the cutting tool. The diagnosis of tool wear can prevent it from having an adverse effect on the surface generation in ultra-precision raster milling. 4.3. Effect of slide errors on form generation The slides of the machine have certain systematic errors such as straightness, roll, pitch and yaw errors, etc., which are due to errors
Fig. 10. Profile of the worn cutting edge of a raster milling cutter. (a) Complete profile of the cutter edge; (b) down profile of the cutter edge and (c) upper profile of the cutter edge.
in the manufacturing and installation of the motion slides. These slide motion errors affect the theoretical tool path and hence they introduce systematic form errors in the surface generation in ultraprecision raster milling. Fig. 11 shows the three motion errors for the X, Y and Z slides of the freeform machining system. The slide motion error data were provided by the machine tool manufacturer named Precitech Inc. in USA. Fig. 11 shows the slide motion errors in different directions. Fig. 11(a) shows the errors in the Z direction for the X slide and Y slide, Fig. 11(b) shows the errors in the Y direction for the X slide and Z slide while Fig. 11(c) shows the errors in the X direction for the Y slide and Z slide. It is interesting to note that slide motion errors vary in different regions. In other words, different regions of motion slides employed in the machining process would generate different form errors on the workpiece.
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Table 2 Effect of slide motion errors on form accuracy. Spherical surface Peak-to-valley height, St (m) F-theta Surface
Two experiments were conducted to verify the effect of slide errors on the form errors in raster milling. A spherical surface and a freeform surface (F-theta lenses used in laser scanner, etc.) were fabricated using the multi-axis freeform machining system. Fig. 12 shows the machined F-theta lens insert. The form error (peak-to-valley) of the spherical surface was measured by a Zygo interferometric profiler system while the freeform surface was measured by a Form Talysurf PGI 1240 measurement system and was characterized by an integrated form characterization method (IFCM) (Cheung et al., 2007) developed by the authors. Table 2 shows the formed errors which were predicted by the selection of certain segments of the slides for the fabrication of the two workpieces. The selection of the slide segments is made according to the shape of the workpiece shape, fixture design and machining coordinate setup, as well as the experience of the machine operators. It is interesting to note that the predicted errors agree well with the measured results. It is also found that the predicted form errors are less than the measured results. This may be due to the fact that the form errors are also affected by other factors such as
Predicted value Measured value Predicted value Measured value
0.642 0.674 3.008 4.729
Starting position of the slides: Slide X: 145.0 mm; Slide Y: 40.0 mm; Slide Z: 115.0 mm Starting position of the slides: Slide X: 225 mm; Slide Y: 47 mm; Slide Y: 77 mm
Fig. 12. F-theta lens inset.
the thermal effect and environmental factors. This study is not only useful for identifying the form errors of the surface caused by slide motion errors but also forms the basis for the compensation of the systematic errors or the selection of the best machining regions of each slides so as to minimize the form error of the surface being machined. 5. Conclusions Freeform surfaces are large-scale surface topologies with anamorphic shapes which generally possess non-rotational symmetry. Due to their geometrical complexity, they cannot be manufactured to a high degree of precision by conventional machining technology or magnetorheological finishing. Raster milling is an enabling approach to machine freeform optic surfaces with sub-micrometer form accuracy and nanometer surface finish. There are many factors affecting the surface generation including machining parameters, cutting strategy, tool path generation, machine tool stage interference, selection of motion slides, workpiece materials, environmental conditions, etc. This paper presents an experimental investigation of the effect of various factors that affect surface generation in ultra-precision raster milling. The critical factors for improving the surface finish include machining parameters, tool geometry, cutting strategy, relative vibration between tool and workpiece, material properties, and tool wear. The cutting strategies and machine slides motion errors are found to be the critical factors affecting the form accuracy in freeform surface generation. A series of experiments has been conducted and the results have been analyzed. The proposed research work contributes to the advancement of the manufacturing control process for ultra-precision raster milling and it also provides an important means to optimize the quality of optical freeform surfaces. Acknowledgements
Fig. 11. Slides motion errors of Freeform 705G. (a) Errors in Z direction for X-slide and Y-slide (Z-slide position: 0), (b) errors in Y direction for X-slide and Z-slide (Yslide position: 0) and (c) errors in X direction for Y-slide and Z-slide (X-slide position: 0).
The authors would like to express their sincere thanks to the Innovation and Technology Commission of the Government of the Hong Kong Special Administrative Region of the People’s Republic of China (project code: GHS/073/04) and the research committee
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of The Hong Kong Polytechnic University, for their support of the research work. References Cheung, C.F., Lee, W.B., 2000. Study of factors affecting the surface quality in ultra-precision diamond turning. Materials and Manufacturing Process 15 (4), 481–502. Cheung, C.F., Li, H.F., Lee, W.B., To, S., Kong, L.B., 2007. An integrated freeform characterization method for measuring ultra-precision freeform surfaces. International Journal of Machine Tools & Manufacture 47 (1), 81–91. Lee, E.-S., Baek, S.-Y., 2007. A study on optimum grinding factors for aspheric convex surface micro-lens using design of experiments. International Journal of Machine Tools & Manufacture 47, 509–520.
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Lee, Y.-S., Chang, T.-C., 1996. Machined surface error analysis for 5-axis machining. International Journal of Production Research 34 (1), 111–135. Lee, W.B., To, S., Cheung, C.F., 2005. Design and Advanced Manufacturing Technology for Freeform Optics. The Hong Kong Polytechnic University, Hong Kong. Lim, E.E.M., Menq, C.-H., 1997. Integrated planning for precision machining of complex surfaces. Part 1. Cutting-path and feedrate optimization. International Journal of Machine Tools & Manufacture 37 (1), 61–75. Palanikumar, K., Karthikeyan, R., 2007. Assessment of factors influencing surface roughness on the machining of Al/SiC particulate composites. Materials & Design 28, 1584–1591. Walter, M., 2003. Freeform Machining Training Guide. Precitech, Inc., USA. Zhou, M., Ngoi, B.K.A., 2003. Factors affecting form accuracy in diamond turning of optical components. Journal of Materials Processing Technology 138, 586–589.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
An investigation into surface generation in ultra-precision raster milling L.B. Kong, C.F. Cheung ∗ , S. To, W.B. Lee Advanced Optics Manufacturing Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
a r t i c l e
i n f o
Article history: Received 14 November 2007 Received in revised form 27 October 2008 Accepted 1 November 2008 Keywords: Form error Freeform surfaces Surface generation Ultra-precision raster milling Optimization Tool wear
a b s t r a c t This paper presents a study of the factors that affect surface generation in ultra-precision raster milling. A series of experiments was conducted to study the effect of different factors on surface generation in ultra-precision raster milling. The results indicate that machining parameters, tool geometry, cutting strategy, and tool wear are the critical factors for achieving super mirror finish surfaces, while cutting strategies, tool path generation, and kinematic errors of the slides are vital to the form accuracy of freeform surfaces. The experimental results are useful for the diagnosis of systematic errors in machine tools, and the control of machining errors. Compensation strategies can be devised, and improvement can be made in the optimization of surface generation and hence the surface quality when using ultra-precision raster milling can be improved. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Optical freeform components are widely applied in laser scanners, digital cameras, automotive lighting systems, optical masks, etc., as discussed in the research of Lee et al. (2005). However, with the development of industry and of technology, conventional surfaces such as those that are spherical, aspherical and some other surfaces with rotational or symmetric axes no longer satisfy the growing demand for functional or special purpose surfaces. To meet this rising demand, freeform surfaces have been introduced and now they play an increasingly important role in various fields. This can be attributed to the fact that the optical freeform surface has more optical functions and other special features. The technology of freeform machining has become increasingly important. However, it is very difficult to manufacture high precision optical freeform surfaces because of their geometrical complexity. Current achievement of precise freeform surfaces usually depends on the experience of the operators, or on trialand-error machining, which is not only time-consuming but also expensive. Research into the factors affecting freeform surface generation has become one of the essential issues for surface error analysis. Lee and Chang (1996) presented an error analysis method for 5-axis machining, which is used to evaluate the
∗ Corresponding author. E-mail address: [email protected] (C.F. Cheung). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.11.002
cusp height between adjacent cutter locations. Control of the surface machining process and the optimization of the manufacturing strategy are important in order to produce high precision surface quality efficiently and inexpensively. Lim and Menq (1997) proposed a cutting-path-adaptive-feedrate strategy for improving the productivity of sculptured surface machining, and performed simulation studies on a two-dimensional curved surface. The factors affecting the surface quality in ultra-precision diamond turning and grinding have been studied by some researchers. Cheung and Lee (2000) studied the process factors and the material factors affecting the surface roughness in ultra-precision diamond turning, while Zhou and Ngoi (2003) investigated the effect of cutting tool conditions and tool set-up errors on surface distortion in the diamond turning of optical components. Lee and Baek (2007) conducted some research work on grinding aspheric surfaces for micro-lenses and the grinding conditions were optimized by designed experiments. Palanikumar and Karthikeyan (2007) investigated the relationships among the various factors involved, such as the effect of machining parameters on surface roughness in the turning process. However, the study of the factors affecting surface generation in ultra-precision raster milling of freeform surfaces has received relatively little attention. This paper presents an experimental study of the different factors that affect freeform surface generation in ultra-precision raster milling. The factors are discussed according to their contribution to surface finish and form generation. A series of experiments was conducted and the results were analyzed and discussed.
L.B. Kong et al. / Journal of Materials Processing Technology 209 (2009) 4178–4185
2. Surface generation in ultra-precision raster milling The cutting geometries for ultra-precision raster milling using horizontal and vertical cutting strategies are shown in Figs. 1 and 2, respectively. The diamond cutting tool is fixed onto the main spindle and rotates with the spindle. The cutting process involves two motions: feed motion and raster motion, based on which appropriate cutting strategies such as whether to cut horizontally or to cut vertically are decided upon. As shown in Fig. 1, horizontal cutting is carried out by the cutter feeding in a horizontal direction. After completing one profile of cutting, the diamond tool moves a step in the raster direction, and so in the way, the whole workpiece surface can be machined. In vertical cutting (see Fig. 2), the cutter feeds in a vertical direction while it moves a step in the horizontal direction. Irrespective of what strategy is used, a surface roughness profile of the machined surface is formed by the repetition of the tool tip making a cut at intervals according to the tool feed rate (c) and then moving a specified distance by steps (ε) under ideal cutting conditions. The feed direction is perpendicular to the raster direction, and both of the directions used in horizontal cutting are opposite to those used in vertical cutting. Walter (2003) described the generalized equation for the determination of theoretical arithmetic roughness for the different cutting strategies in ultra-precision precision raster milling as shown in Eq. (1)
Ra =
c2 ε2 + 24R1 24R2
(1)
4179
where R1 = R and R2 = r for horizontal cutting while R1 = r and R2 = R for vertical cutting; R is the swing distance and r is the tool nose radius. The selection of the appropriate cutting strategy depends on the surface topography and on the quality control of the form error and surface finish of the workpiece. As shown in Fig. 3, there are different tool path plans for raster milling. For example, one-direction cutting or bi-directional cutting, or a cutting path with tool retreat, or without retreat. The tool path plan can be selected according to the geometry and the quality of the surface of the workpiece. 3. Factors affecting surface generation in ultra-precision raster milling As shown in Fig. 4, the factors affecting surface generation in ultra-precision raster milling are related to the form generation and to surface roughness. The different factors are classified into three categories according to their main features which are the cutting mechanism, the tool path and the cutting process. The factors related to the cutting mechanism include the geometry of the diamond tool, tool wear, waviness of the tool edge, machining parameters and cutting strategy. Machine tool characteristics include slide motion errors, spindle error motions, and the relative vibration between the tool and the workpiece, which greatly affect the tool path and mainly contribute to the form errors of the surface generation. Relative displacement between the tool and the workpiece is involved in the cutting process and it is related to the surface
Fig. 1. Cutting geometry for ultra-precision raster milling using horizontal cutting strategy.
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Fig. 2. Cutting geometry for ultra-precision raster milling using vertical cutting strategy.
roughness. Machine dynamics plays an important role in the displacement between the tool and the workpiece. The dynamic characteristics of the machining system consist of a motor drive and a servo system, the machine tool structure, workpiece structure, as well as their interaction with each other. Motor drive and servo systems drive the motion of the slide tables and the spindle which contribute to the surface generation. Tool/holder deflection, spindle/chunk deflection from the machine tool structure, and workpiece deflection from the workpiece structure, all introduce dynamic errors because of the relative displacement between the tool and the workpiece. Surface generation by ultra-precision raster milling is a complex process. As discussed previously, it is a process which integrates the process of cutting with the mechanism itself, and the tool
path. In the present study, four important factors affecting surface generation in ultra-precision raster milling are studied experimentally. These factors are machining parameters, cutting strategy, slide motion errors and tool wear. 4. Experimental studies and discussion In this study, three groups of experiments have been conducted. They are experiments for studying the effect of machining parameters, as well as cutting strategy, tool wear, and slides errors, on surface generation. The diamond tool used in the experiments is made of natural single crystal diamond. It is a round cutting tool with a 0.1 mm tool-nose radius, 12.5◦ front clearance angle and 1◦ rake angle. The workpiece material used in the experiment is alu-
Fig. 3. Different tool path planning for ultra-precision raster milling.
L.B. Kong et al. / Journal of Materials Processing Technology 209 (2009) 4178–4185
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Fig. 4. Factors affecting surface generation in ultra-precision raster milling.
minum alloy (Al6061) with chemical composition in percentage of weight of Al: balance, Cu: 0.28, Si: 0.6, Mg: 1.0, and Cr: 0.20. 4.1. The effect of machining parameters and cutting strategy on the surface roughness The mechanism of surface generation by ultra-precision raster milling has been discussed in Section 2. The experiments conducted in the present study will further validate the effect of the machining parameters and cutting strategy on the surface roughness. As shown in Section 2, there are five main machining parameters for ultra-precision raster milling which are: spindle speed (S: rpm),
Fig. 5. Workpiece for studying the effect of machining parameters: (a) dimension of the workpiece design and (b) machined workpiece.
feed rate (f: mm/min), step distance (ε: m), tool nose radius (r: mm) and swing distance (R: mm). These five parameters are used for the convenience of machining setup, and some further parameters such as cutting speed (Vs , mm/s) and feed rate in mm/rev (c: mm/rev) can be derived from the above parameters, as follows: Vs = c=
S 2R = SR 60 30
f S
(2) (3)
Generally, the swing distance and tool nose radius are not changed very often. They are kept almost the same most of the time. The effects of spindle speed, feed rate and step distance on surface generation are investigated in the present study. Table 1 shows the machining parameters used in the experiments and the corresponding results. Fig. 5 shows the design of the workpiece used
Fig. 6. Effect of spindle speed on arithmetic roughness.
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Table 1 Summary of the effect of machining parameters on surface roughness. Spindle speed, S (rpm) H V
Ra (nm) Feed rate, f (mm/min)
H V
Ra (nm) Step distance, ε (m) Ra (nm)
H V
1000 15.70 13.57 20 9.41 9.85 10 14.11 14.19
2000 14.78 12.37 40 13.06 12.37 25 17.10 19.71
3000 14.38 13.41 60 14.11 14.19 50 31.05 22.11
4000 14.11 14.19 80 17.39 15.55 75 67.16 21.61
5000 13.86 13.91 100 17.70 16.00 100 221.58 31.12
f = 60 mm/min, ε=10 m, r = 2.54 mm, R = 23 mm, d = 3 m S = 4000 rpm, ε=10 m, r = 2.54 mm, R = 23 mm, d = 3 m f = 60 mm/min, S = 4000 rpm, r = 2.54 mm R = 23 mm, d = 3 m
Note: H: horizontal cutting; V: vertical cutting; and d: depth of cut.
Fig. 7. Effect of feed rate on arithmetic roughness.
Fig. 8. Effect of step distance on arithmetic roughness.
in the cutting test. Fig. 5(a) shows the dimensions of the workpiece. As shown in Fig. 5 (b), the sample consists of 30 flat surfaces which are grouped into two rows. The upper row of 15 flat surfaces is designed for use with a horizontal cutting strategy while the bottom row of 15 planar surfaces is designed for use with a vertical cutting strategy. Each row of surfaces is divided into 3 groups for
the study of the effect of spindle speed, feed rate and step distance on surface generation, respectively. After the workpiece was machined by ultra-precision raster milling machining system (Freeform 705G from Precitech Inc., USA), the surface data of the workpiece were measured by a Wyko NT8000 optical measurement system. Fig. 6 shows the
Fig. 9. Profile measurement of spherical surface machined by ultra-precision raster milling. (a) Profile of the spherical workpiece and (b) residual errors after form removal.
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effect of spindle speed while Fig. 7 shows the effect of feed rate on arithmetic surface roughness (Ra ), respectively. The effect of step distance on arithmetic surface roughness (Ra ) is shown in Fig. 8. From the experimental results in Figs. 6–8, it is interesting to note that the surface roughness decreases when spindle speed increases, while surface roughness increases when the feed rate and step distance increase. This implies that better surface finish can be obtained under a higher spindle speed, a finer feed rate and a smaller step distance in ultra-precision raster milling. In practice, the spindle speed has a certain limit due to the capability of the air bearing capability to run beyond the limit of stability. The spindle error motions (e.g. run-out, axial error motion) increase when the spindle speed increases. In addition, the feed rate and step distance should not be too small since this will affect machining efficiency. It is also interesting to note that the vertical cutting strategy produces a better surface finish than the horizontal cutting strategy. This can be explained by Eq. (1). In the raster milling process, the surface roughness is determined largely by the step distance, and the swing distance is also far bigger than the tool nose radius. In horizontal cutting, the step distance in the raster direction is determined by the tool nose radius; while, the step distance is determined by the swing distance in vertical cutting. So the vertical cutting strategy is preferred for achieving a better balance between surface quality and machining efficiency in practice. 4.2. The effect of tool wear on surface finish In fact, the process of surface generation is the replicating of the diamond tool profile on the workpiece. The tool wear inevitably affects the surface finish and form accuracy. A spherical surface workpiece was machined by a diamond tool. The profile of the workpiece was measured by a Form TalySurf PGI 1240 as shown in Fig. 9(a). The residual error after form removal is shown in Fig. 9(b), which indicates an obvious error variation from one side to the other side. In other words, the surface finish gets worse from the left to right. The diamond tool was then observed under a microscope as shown in Fig. 10 (Remark: please note that the image seen through the microscope is the reverse of the real cutter position). It is interesting to note that there are some wear regions (worn regions) found in the D-segment (see Fig. 10(b)) while the edge profile is clear and no worn region is found in the U-segment (see Fig. 10(c)). This implies that the residual errors of the spherical workpiece were caused by the tool wear (the edge was broken). As shown in Fig. 9(a), the Usegment profile of the cutter edge first engages in the cutting. After the engaged region passes the center of the edge profile, the D-segment of the edge then engages in cutting. However, the worn region of the cutter makes marks on the surface of the workpiece when this happens, due to wear in the D-segment of the cutter. This adversely affects the surface finish of the workpiece. This study is useful for diagnosis of the wear conditions of the diamond tool by measuring and analyzing the surface quality of the machined surfaces. This provides an indirect approach for the determination of the tool wear without the need for disassembling the cutting tool. The diagnosis of tool wear can prevent it from having an adverse effect on the surface generation in ultra-precision raster milling. 4.3. Effect of slide errors on form generation The slides of the machine have certain systematic errors such as straightness, roll, pitch and yaw errors, etc., which are due to errors
Fig. 10. Profile of the worn cutting edge of a raster milling cutter. (a) Complete profile of the cutter edge; (b) down profile of the cutter edge and (c) upper profile of the cutter edge.
in the manufacturing and installation of the motion slides. These slide motion errors affect the theoretical tool path and hence they introduce systematic form errors in the surface generation in ultraprecision raster milling. Fig. 11 shows the three motion errors for the X, Y and Z slides of the freeform machining system. The slide motion error data were provided by the machine tool manufacturer named Precitech Inc. in USA. Fig. 11 shows the slide motion errors in different directions. Fig. 11(a) shows the errors in the Z direction for the X slide and Y slide, Fig. 11(b) shows the errors in the Y direction for the X slide and Z slide while Fig. 11(c) shows the errors in the X direction for the Y slide and Z slide. It is interesting to note that slide motion errors vary in different regions. In other words, different regions of motion slides employed in the machining process would generate different form errors on the workpiece.
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Table 2 Effect of slide motion errors on form accuracy. Spherical surface Peak-to-valley height, St (m) F-theta Surface
Two experiments were conducted to verify the effect of slide errors on the form errors in raster milling. A spherical surface and a freeform surface (F-theta lenses used in laser scanner, etc.) were fabricated using the multi-axis freeform machining system. Fig. 12 shows the machined F-theta lens insert. The form error (peak-to-valley) of the spherical surface was measured by a Zygo interferometric profiler system while the freeform surface was measured by a Form Talysurf PGI 1240 measurement system and was characterized by an integrated form characterization method (IFCM) (Cheung et al., 2007) developed by the authors. Table 2 shows the formed errors which were predicted by the selection of certain segments of the slides for the fabrication of the two workpieces. The selection of the slide segments is made according to the shape of the workpiece shape, fixture design and machining coordinate setup, as well as the experience of the machine operators. It is interesting to note that the predicted errors agree well with the measured results. It is also found that the predicted form errors are less than the measured results. This may be due to the fact that the form errors are also affected by other factors such as
Predicted value Measured value Predicted value Measured value
0.642 0.674 3.008 4.729
Starting position of the slides: Slide X: 145.0 mm; Slide Y: 40.0 mm; Slide Z: 115.0 mm Starting position of the slides: Slide X: 225 mm; Slide Y: 47 mm; Slide Y: 77 mm
Fig. 12. F-theta lens inset.
the thermal effect and environmental factors. This study is not only useful for identifying the form errors of the surface caused by slide motion errors but also forms the basis for the compensation of the systematic errors or the selection of the best machining regions of each slides so as to minimize the form error of the surface being machined. 5. Conclusions Freeform surfaces are large-scale surface topologies with anamorphic shapes which generally possess non-rotational symmetry. Due to their geometrical complexity, they cannot be manufactured to a high degree of precision by conventional machining technology or magnetorheological finishing. Raster milling is an enabling approach to machine freeform optic surfaces with sub-micrometer form accuracy and nanometer surface finish. There are many factors affecting the surface generation including machining parameters, cutting strategy, tool path generation, machine tool stage interference, selection of motion slides, workpiece materials, environmental conditions, etc. This paper presents an experimental investigation of the effect of various factors that affect surface generation in ultra-precision raster milling. The critical factors for improving the surface finish include machining parameters, tool geometry, cutting strategy, relative vibration between tool and workpiece, material properties, and tool wear. The cutting strategies and machine slides motion errors are found to be the critical factors affecting the form accuracy in freeform surface generation. A series of experiments has been conducted and the results have been analyzed. The proposed research work contributes to the advancement of the manufacturing control process for ultra-precision raster milling and it also provides an important means to optimize the quality of optical freeform surfaces. Acknowledgements
Fig. 11. Slides motion errors of Freeform 705G. (a) Errors in Z direction for X-slide and Y-slide (Z-slide position: 0), (b) errors in Y direction for X-slide and Z-slide (Yslide position: 0) and (c) errors in X direction for Y-slide and Z-slide (X-slide position: 0).
The authors would like to express their sincere thanks to the Innovation and Technology Commission of the Government of the Hong Kong Special Administrative Region of the People’s Republic of China (project code: GHS/073/04) and the research committee
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