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Characterization of closed-loop measurement accuracy in precision CNC milling
ARTICLE IN PRESS
Robotics and Computer-Integrated Manufacturing 22 (2006) 288–296 www.elsevier.com/locate/rcim
Characterization of closed-loop measurement accuracy in precision CNC milling Yongjin Kwona,, Tzu-Liang (Bill) Tsengb, Yalcin Ertekinc a
Applied Engineering Technology, Goodwin College of Professional Studies, Drexel University, Philadelphia, PA 19104, USA b Department of Mechanical and Industrial Engineering, The University of Texas at El Paso, El Paso, TX 79968, USA c Department of Engineering Technology, Tri-State University, Angola, IN 46703, USA Received 6 May 2005; received in revised form 2 June 2005; accepted 13 June 2005
Abstract This study investigates the closed-loop measurement error in computer numerical controlled (CNC) milling as they relate to the different inspection techniques. The on-line inspection of machining accuracy using a spindle probe has an inherent shortcoming because the same machine-produced parts are used for inspection. In order to use the spindle probe measurement as a means of correcting deviations in machining, the magnitude of measurement errors needs to be quantified. The empirical verification was made by conducting three sets of cutting experiments, followed by a design of experiment with three levels and three factors on a state-of-the-art CNC machining center. Three different material types and parameter settings were selected to simulate a diverse cutting condition. During the cutting, the cutting force and spindle vibration sensor signals were collected and a tool wear was recorded using a computer vision system. The bore tolerance was gauged by a spindle probe as well as a coordinate-measuring machine. The difference between the two measurements was defined as a closed-loop measurement error and the subsequent analysis was performed to determine the significant factors affecting the errors. The analysis results showed the potential of improving production efficiency and improved part quality. r 2005 Elsevier Ltd. All rights reserved. Keywords: On-line and off-line inspection; Touch probe; CNC machining
1. Introduction Discrete part manufacturing using computer numerical controlled (CNC) milling machines is common in modern manufacturing [1]. Depending on the accuracy and surface finish requirements, the machining parameters, which have a significant influence on part quality, need to be set properly [2,3]. Vibration in machining is particularly harmful in this regard [4], yet can be minimized through the use of computer simulation prior to the machining. The simulation can project the optimal range of cutting speeds and feed rates for a Corresponding author. Tel.: +1 215 895 0969; fax: +1 215 895 4988. E-mail address: [email protected] (Y. Kwon).
0736-5845/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2005.06.002
chatter-free machining, thereby producing less scrap and enhancing part quality. Since each machine tool exhibits disparate dynamic characteristics [5], the importance of pre-machining simulation is applied to each machine, especially when the machine is newly acquired. In this study, CutPros milling simulation software accompanied by a hammer test was used to generate a set of vibration free-cutting parameters. Equally important in machining is the confidence in the measuring instruments from which part quality characteristics are ascertained. Part dimensional accuracy check has been largely based on the post-process inspection such as a coordinate measuring machine (CMM). CMMs are widely used in the manufacturing industry for precision inspection and quality control [6,7], and recognized as reliable and flexible gauges suitable for assessing the
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acceptability of machined parts [8]. The downside of this technique is that non-conforming parts can be produced between inspections since there can be a significant delay between the production and completion of inspection [3]. To remedy the problem, a machine-mounted touch probe has started gaining popularity, which has the similar working principles of CMM [9]. The probe enables the measurement of machined parts while they are still fixed on the machine. By providing part size information directly into a CNC controller, a closedloop process control can be realized in the form of realtime automatic tool offset to correct deviations or prevent defects in machining [10]. This is particularly important for a modern, computer-controlled production environment, where very little human intervention is expected during the machining cycle. The accuracy of the probe, however, is affected by the machine tool’s positional accuracy and positioning system [10,11]. Since the same machine, which produces the parts is used for inspection, there is an inherent problem in the accuracy of probe inspection. Therefore, in order for the probe data to be used for real-time control, the capability of probe needs to be analyzed and the factors affecting the probe data need to be ascertained. This step is important since the discrete part manufacturing industry is shifting towards 100% part inspection for zero defect.
2. Cutting experiments To address the aforementioned problem, a newly acquired, state-of-the-art Cincinnati Arrow 750 CNC Vertical Machining Center was used to conduct the cutting experiments (see Fig. 1). Cutting experiments allow the production engineer to adjust the settings of
Fig. 1. Experimental setup showing the table mounted Kistler force dynamometer and the spindle housing mounted Kistler accelerometer.
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the machine in a systematic manner and to learn which factors and interaction effects have the greatest impact on the part quality before the machine is put to use for production. This step is necessary, because in metal cutting, most process control models are based on the empirical data and no universal mathematical models exist [12–15]. The impracticality of theoretical models for predicting quality characteristics is well known in metal cutting [16–18]. Three material types that are widely used in both automotive and aerospace industry (6061-T6 aluminum, 7075-T6 aluminum, and ANSI-4140 steel) were selected. One-inch diameter end mill was fixed in the spindle and the hammering on the tool was analyzed to determine frequency response function of the machine tool structure. The stability lobe graph generated by the CutPros software provided the combination of depth of cut and cutting speed for minimum chatter in machining. Consequently, the axial and radial depth of cut and cutting speed were tuned for a chatter-free machining. Each machined block has two stepped bores (65 and 50 mm diameter). The bores were selected as the critical quality characteristics because circularity and cylindricity of machined parts are regarded as the most fundamental geometric features in engineering [19]. To ensure the proper functioning of round parts, permissible deviations from the true circle are allowed in the form of tolerance zones bounded by two concentric circles [19], which dictate the desired dimensional and form accuracy [20]. The bores have a tolerance of 0.1 mm, corresponding to an ISO tolerance grade of IT10. Tolerances were measured using a spindle probe (a Renishaw MP 700 surface sensing wireless probe with 0.0000100 repeatability) and a newly calibrated Mitutoyo B403B CMM. Fig. 2 shows the sensors, the probe, and examples of machined blocks. The CNC mill was fitted with multiple sensors and data acquisition systems to collect cutting force measurements and spindle housing vibration/acceleration. Each measurement was further divided into components: x, y, z cutting force components (Fx, Fy, Fz) and x, y, z spindle housing vibrations (Ax, Ay, Az). Those components were filtered and processed for both time and frequency domain features. The arithmetic averages, Fv and Av, were also calculated. For aluminum parts, a high-speed steel (HSS), 2-flute, cobalt end mill cutter was used until the tool wore out. For steel, an uncoated, 2-flute, tungsten carbide cutter was assigned. All cuttings utilized coolant to minimize friction and overheating. After each block was machined, the tool was removed from the spindle and the wear on the cutting edges was measured using a computer vision system. A custom fixture was built to support the tool holder at a constant focal length. An integrated white LED light was used to illuminate the cutting edges. A DVT 540 CCD camera with 640 480 pixel resolution was connected to the
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Fig. 2. Spindle touch probe used to inspect the finished blocks (a) and three examples showing 6061 Al, 7075 Al, and 4140 Steel, from the left (b).
Ethernet and real-time images appeared on a PC contained the Framework Version 2.7.4 image analysis software. The exposure time was 2.5 ms and the LED was fired with a 250 ms interval controlled by the internal trigger. To prevent the glare due to the highly reflective surface of tool, an anti-blooming filter was applied to reduce the pixel saturation. The image contrast was improved by the Contrast Filter, and the slight image blurring was removed by the sharpen filter. After the preprocessing, the wear area was isolated from the rest of the image by applying the edge detection/ separation algorithms. The image showed a very good contrast for further processing. Once the edges were separated, the measurement region was selected as about 0.1500 from the tool end, corresponding to the depth of cut (see Fig. 3). The region was divided into 10 equally spaced intervals and each interval was measured to get the average. Since there are two cutting edges in the tool, this step was repeated. The system was calibrated using a high-grade Mitutoyo gage block and it was found that
Fig. 3. Preprocessed image of cutting edge (a) and the further processed image showing the wear width and the boundaries (b).
the pixel size at the specific focal length was 0.0002400 in pixel width (x) and 0.0002500 in pixel height (y). When compared with the wear measurements taken by the Mitutoyo tool maker’s microscope, the difference was less than 5%. The tool wear was defined as the average of the product of pixel numbers along y-direction and the pixel height: lðin:Þ ¼ n1
n X
0:00025ji ,
(1)
i¼1
where l is the average wear width along the measurement region, n ¼ 20 and fi is the number of pixels at interval i. The bores were measured at the end of the finishing cycle by the spindle probe. Then the block was removed from the machine and measured again by the Mitutoyo CMM. Before the experiments, the CMM was calibrated by a certified technician to ensure the accuracy. In addition, prior to utilizing the CMM, a process
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capability study was performed using a standard ball. The ball was measured by the same operator, using a series of processes that entailed measuring points along the circumference. Ten measurements were taken for each of the two established patterns of 4 and 8 points. The natural tolerance was determined by establishing the standard deviation for each point pattern, and then calculated to the 3-sigma value. The average was 0.00024800 . When it was compared to the manufacturer’s standard tolerance of 0.000300 , the CMM was considered operating within the proper tolerance parameters. The difference between the probe and CMM was defined in the form of: Di ¼ qCi qPi ,
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3. Closed-loop measurement error analysis The difference between the probe and CMM measurements provides the comparison between the in-process and the post-process inspection data. Many studies have been dedicated to improve machining accuracy based on feedback signals. It is an active research area and the examples are abundant: numerical analysis of machining feedback errors, CMM-based inspection modeling in machining operations, a numerical circular form error models in machining, spindle error compensation using a real-time feedback signal, and manufacturing data analysis of machine tool errors. However, there appears to be no research that investigated the measured difference between two methods [21–33]. Fig. 7 shows the variation in the difference according to the bore size and material type. For aluminum, the 50 mm bore has a smaller variation, while the steel block show a similar variation between the bore sizes. In this study, the CMM data are considered more reliable than those from the probe, hence the Di is used to analyze the feedback error. The arithmetic average of the difference for three material types was found using the following equation:
(2)
where Di is the difference (in), qCi is the CMM measurements, qPi is the probe measurements, and the index i the integer data number (iX1). The number of milled components for 6061-T6, 7075-T6 Al and AISI4140 steel were 20, 19 and 17, respectively. Figs. 4–6 represent the difference between the CMM and the probe measurements. The graphs show the random patterns, indicating no systematic errors involved in the measurement difference. The difference is mostly positive, meaning that the CMM measurements are usually larger than those of probe. The graphs also show that the difference is hardly affected by the number of workpiece.
mj ¼
n X Di i¼1
n
,
(3)
6061 Al: CMM-Probe Measurement 0.05000 0.04500 0.04000 0.03500 0.03000 0.02500
Inch
0.02000 0.01500 0.01000 0.00500 0.00000 -0.00500 -0.01000 -0.01500
CMM - Probe: 65 mm Bore CMM- Probe: 50 mm Bore
-0.02000 -0.02500 1
2
3
4
5
6
7
8
9
10 11 12 Workpiece No.
13
14
Fig. 4. Measured difference between CMM and Probe for 6061 Al.
15
16
17
18
19
20
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292
7075 Al: CMM - Probe Measurement 0.05000 0.04500 0.04000 0.03500 0.03000 0.02500
Inch
0.02000 0.01500 0.01000 0.00500 0.00000 -0.00500 -0.01000 -0.01500
CMM -Probe: 65 mm Bore CMM -Probe:50 mm Bore
-0.02000 -0.02500 1
2
3
4
5
6
7
8
9 10 11 Workpiece No.
12
13
14
15
16
17
18
19
Fig. 5. Measured difference between CMM and Probe for 7075 Al.
4140 Steel: CMM - Probe Measurement 0.05000 0.04500 0.04000 0.03500 0.03000 0.02500
Inch
0.02000 0.01500 0.01000 0.00500 0.00000 -0.00500 -0.01000 -0.01500 CMM - Probe: 65 mm Bore
-0.02000
CMM - Probe: 50 mm Bore
-0.02500 1
2
3
4
5
6
7
8 9 10 Workpiece No.
11
12
Fig. 6. Measured difference between CMM and Probe for 4140 Steel.
13
14
15
16
17
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as independent variables. Including two factor interaction effects and quadratic terms, the full model includes all possibilities:
Difference between CMM and Probe for Three Materials 0.06 0.05 0.04
EfYg ¼ b X ¼ b0 þ b1 TW þ b2 HD þ b3 F x þ b4 F y þ b5 F z þ b6 F v þ b7 Ax þ b8 Ax þ b9 Ay þ b10 Az
0.03 Inch
293
0.02
þ b11 Av þ b12 TW HD þ b13 TW F x
0.01 0.00
0
-0.01
þ b14 TW F y þ b15 TW F z þ b16 TW F v þ b17 TW Ax þ b18 TW Ay þ b19 TW Az þ b20 TW Av þ þ bn10 TW 2 þ bn9 HD2 þ bn8 F 2x þ bn7 F 2y þ bn6 F 2z þ bn5 F 2v þ bn4 A2x
50
5
þ bn3 A2x þ bn2 A2y þ bn1 A2z þ bn A2v .
41
41
40
40
St l:
St l:6
Al :5 0
70 75
Al :6 5
70 75
Al :5 0 60 61
60 61
Al :6 5
-0.02
Fig. 7. Distribution of measurement difference according to bore size and material type.
Table 1 Arithmetic average of difference and material hardness Material type
Rockwell hardness
mj
6061-T6-Al 7075-T6 Al 4140 Steel
43 85 92
0.0061 in/0.155 mm 0.0103 in/0.260 mm 0.0221 in/0.561 mm
ð4Þ
The explanatory variables have been reduced to six that have the highest degree of association with the dependable variable. Among those, HD2, Az and Av have stronger correlation with the Di and the tool wear found to be not correlated with the Di . The reduced form of fitted model with the least deviance for all three material types were found to be in the form of: Y^ i ¼ 0:0157 þ 106 HD2 þ 0:00452HD Az 2:64A2x 0:0218F y þ 0:00446F v 0:508Az þ 0:447Av . ð5Þ 2
where mj is the arithmetic average of difference (in), index j the material type, and n a number of workpiece. The mj was calculated and listed in Table 1. The amount of feedback (ci) for bore diameter correction needs to be examined under four different conditions given by the state of the four variables: the nominal bore diameter denoted as qN (in this case, either 50 or 65 mm), the probe measurement, the CMM measurement, and the mj. The conditions and the feedback (if the mj can be maintained) are in the form of:
Condition I: If qC4qP & qCoqN & Di40, then ci fqN ðqP þ mj Þg Condition II: If qC4qP & qCXqN & Di40, then ci fqN ðqP þ mj Þg Condition III: If qC4qP & qCoqN & Dio0, then ci qN qP þ m j Condition IV: If qC4qP & qCXqN & Dio0, then ci fqN ðqP þ mj Þg
¼
The coefficient of multiple determination (R ) between the responses Di and the fitted valuesY^ i was found to be 0.72. The reason that tool wear has no effect on the difference can be speculated that tool wear increases as cutting continues, affecting both probe and CMM measurements, while the difference has a random pattern throughout the cutting experiments. This phenomenon was observed earlier, illustrated in Figs. 4–6. Hardness, Fv and Av are in the equation, suggesting that increased material hardness and associated increase in cutting force and spindle housing vibration have an effect on the difference. Independent analysis for each material type, on the other hand, yielded much lower accuracy.
¼ 4. Design of experiment ¼ ¼
It should be noted that the amount of feedback has the same relationship between the nominal values, probe readings, and the average of difference, hence allowing the use of single equation for subsequent use. Forward elimination, multiple linear regression analysis was performed for all three material types using the Di as the dependable variable and the 10 measured parameters (HD as hardness, tool wear, Fx, Fy, Fx, Fv, Ax, Ay, Az, Av)
In industrial settings, a design of experiment (DOE) technique is used for product development to apply analysis of variance (ANOVA) principles. The primary goal is to extract the maximum amount of unbiased information regarding the factors that affect a production process from as few observations as possible to minimize the development cost. The fractional factorial design was implemented in this experiment to minimize the total number of runs, while ensuring that there is no significant impact on output [34]. A Full DOE design for this experiment would have consisted of three factors containing three levels each, as indicated in Table 2.
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In this setting, two replicates would have required 54 metal blocks (runs), whereas the fractional factorial formula reduced the time and costs involved by 33.3% by using: (331) (2 replicates) ¼ 18 runs. The actual Table 2 Factors and levels Level
Factors
Low (1) Center (0) Upper (+1)
Hardness
Speed
Feed
6061 aluminum 7075 aluminum 4041 steel
Slow Mid Fast
Slow Mid Fast
Table 3 Feed and speed levels Material
Feed
Speed
6061 6061 6061 7075 7075 7075 4140 4140 4140
127 mm/min (1) 254 mm/min (0) 381 mm/min (+1) 127 mm/min (1) 254 mm/min (0) 381 mm/min (+1) 50.8 mm/min (1) 127 mm/min (0) 254 mm/min (+1)
1250 rpm(1) 2500 rpm (0) 3750 rpm (+1) 1250 rpm (1) 2500 rpm (0) 3750 rpm (+1) 750 rpm (1) 1500 rpm (0) 2250 rpm (+1)
Al Al Al Al Al Al St St St
DOE design matrix was generated in Statisticas and in order to eliminate potential bias during the milling process, randomization of the run order was implemented. Two runs were selected for operating parameters for Statisticas to create two blocks. Blocking reduces the variability in the response due to other external factors that are not considered. The cutting tool Speed and Feed factors established using CutPros software is correlated with the appropriate material (as illustrated in Table 3). Figs. 8 and 9 show the measured difference between the CMM and the probe in DOE and the variation in measured difference according to material types and bore size. The similar pattern can be observed, however, the difference in Fig. 8 becomes larger after the workpiece number 12. This can be attributed to the increased tool wear as well as the machining of steel blocks. In DOE, the same statistical analysis technique was used to identify the significant explanatory variables. The best model (R2 ¼ 0:924) is in the form of: Y^ i ¼ 0:138 15:2Tw 5:57Ax 4:56Ay 3:22Az þ 7:37Av þ 0:0904F z .
ð6Þ
The DOE data show a contradicting result, having the tool wear as significant as well as all three components of vibration and z-directional force component. The material hardness turned out to be insignificant for DOE. Since the same tool is used to process the mixed
DOE: CMM - Probe Measurement 0.05500
0.04500
0.03500
Inch
0.02500
0.01500
0.00500
-0.00500
-0.01500
CMM -Probe: 65 mm Bore CMM- Probe: 50 mm Bore
-0.02500 1
2
3
4
5
6
7
8
9 10 11 Workpiece No.
12
13
Fig. 8. Measured difference between CMM and Probe in DOE.
14
15
16
17
18
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DOE: Difference between CMM and Probe Measurements 0.06 0.05 0.04
Inch
0.03 0.02
295
the capability of on-line measuring instruments. The future study can be envisioned that a development of error model encompassing machine tool thermal effects, a development of probing algorithms for better measurement accuracy, and a development of comprehensive feedback error control architecture that includes servo control errors.
0.01 0
0.00 -0.01
Acknowledgments 41 40 :5 0
65
D O E
41 40 :
50 D O E
70 75 :
65 D O E
70 75 :
50 D O E
60 61 :
D O E
D O E
60 61 :
65
-0.02
This study was supported by the National Science Foundation (NSF) Major Research Instrument (MRI) Grant No. 0116515. The authors are very grateful for their financial support.
Fig. 9. Distribution of measurement difference in DOE.
References materials of 18 blocks, it can be reasoned that the difference is affected by the tool wear and the associated vibration and z-cutting force. This may be attributed to the increasing magnitude in the difference as cutting continues. DOE model has a much better accuracy, suggesting that in a batch mode production, where a variety of materials produced on the same machine using different cutting parameters, this feedback error model has a high potential for shop-floor implementation.
5. Conclusions This study provides insights toward how two different measuring techniques affect the gauging of machine part dimensions. The randomness in difference represents that non-systematic errors exist between the two measurements. DOE, however, presents a systematic variation in setting up the experimental parameters, resulted in a much-improved accuracy in the regression equation. The comparative study on the CMM and probe readings presented in this study is useful for today’s manufacturing environment where diverse products are machined with ever decreasing lot size and minimal human intervention. The DOE conducted in this study simulated the batch mode manufacturing, using highly common industrial material types. Harder material (4140 steel) showed a much wider variation in the measurement difference between the CMM and the spindle probe, hence care must be exercised if a feedback signal is to be used for correcting part size. The error model for DOE has a very high accuracy, suggesting that the spindle probe reading can be used for real-time, closed-loop control of part size. This, however, stipulates a gauge study to verify the magnitude of errors and
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Robotics and Computer-Integrated Manufacturing 22 (2006) 288–296 www.elsevier.com/locate/rcim
Characterization of closed-loop measurement accuracy in precision CNC milling Yongjin Kwona,, Tzu-Liang (Bill) Tsengb, Yalcin Ertekinc a
Applied Engineering Technology, Goodwin College of Professional Studies, Drexel University, Philadelphia, PA 19104, USA b Department of Mechanical and Industrial Engineering, The University of Texas at El Paso, El Paso, TX 79968, USA c Department of Engineering Technology, Tri-State University, Angola, IN 46703, USA Received 6 May 2005; received in revised form 2 June 2005; accepted 13 June 2005
Abstract This study investigates the closed-loop measurement error in computer numerical controlled (CNC) milling as they relate to the different inspection techniques. The on-line inspection of machining accuracy using a spindle probe has an inherent shortcoming because the same machine-produced parts are used for inspection. In order to use the spindle probe measurement as a means of correcting deviations in machining, the magnitude of measurement errors needs to be quantified. The empirical verification was made by conducting three sets of cutting experiments, followed by a design of experiment with three levels and three factors on a state-of-the-art CNC machining center. Three different material types and parameter settings were selected to simulate a diverse cutting condition. During the cutting, the cutting force and spindle vibration sensor signals were collected and a tool wear was recorded using a computer vision system. The bore tolerance was gauged by a spindle probe as well as a coordinate-measuring machine. The difference between the two measurements was defined as a closed-loop measurement error and the subsequent analysis was performed to determine the significant factors affecting the errors. The analysis results showed the potential of improving production efficiency and improved part quality. r 2005 Elsevier Ltd. All rights reserved. Keywords: On-line and off-line inspection; Touch probe; CNC machining
1. Introduction Discrete part manufacturing using computer numerical controlled (CNC) milling machines is common in modern manufacturing [1]. Depending on the accuracy and surface finish requirements, the machining parameters, which have a significant influence on part quality, need to be set properly [2,3]. Vibration in machining is particularly harmful in this regard [4], yet can be minimized through the use of computer simulation prior to the machining. The simulation can project the optimal range of cutting speeds and feed rates for a Corresponding author. Tel.: +1 215 895 0969; fax: +1 215 895 4988. E-mail address: [email protected] (Y. Kwon).
0736-5845/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2005.06.002
chatter-free machining, thereby producing less scrap and enhancing part quality. Since each machine tool exhibits disparate dynamic characteristics [5], the importance of pre-machining simulation is applied to each machine, especially when the machine is newly acquired. In this study, CutPros milling simulation software accompanied by a hammer test was used to generate a set of vibration free-cutting parameters. Equally important in machining is the confidence in the measuring instruments from which part quality characteristics are ascertained. Part dimensional accuracy check has been largely based on the post-process inspection such as a coordinate measuring machine (CMM). CMMs are widely used in the manufacturing industry for precision inspection and quality control [6,7], and recognized as reliable and flexible gauges suitable for assessing the
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acceptability of machined parts [8]. The downside of this technique is that non-conforming parts can be produced between inspections since there can be a significant delay between the production and completion of inspection [3]. To remedy the problem, a machine-mounted touch probe has started gaining popularity, which has the similar working principles of CMM [9]. The probe enables the measurement of machined parts while they are still fixed on the machine. By providing part size information directly into a CNC controller, a closedloop process control can be realized in the form of realtime automatic tool offset to correct deviations or prevent defects in machining [10]. This is particularly important for a modern, computer-controlled production environment, where very little human intervention is expected during the machining cycle. The accuracy of the probe, however, is affected by the machine tool’s positional accuracy and positioning system [10,11]. Since the same machine, which produces the parts is used for inspection, there is an inherent problem in the accuracy of probe inspection. Therefore, in order for the probe data to be used for real-time control, the capability of probe needs to be analyzed and the factors affecting the probe data need to be ascertained. This step is important since the discrete part manufacturing industry is shifting towards 100% part inspection for zero defect.
2. Cutting experiments To address the aforementioned problem, a newly acquired, state-of-the-art Cincinnati Arrow 750 CNC Vertical Machining Center was used to conduct the cutting experiments (see Fig. 1). Cutting experiments allow the production engineer to adjust the settings of
Fig. 1. Experimental setup showing the table mounted Kistler force dynamometer and the spindle housing mounted Kistler accelerometer.
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the machine in a systematic manner and to learn which factors and interaction effects have the greatest impact on the part quality before the machine is put to use for production. This step is necessary, because in metal cutting, most process control models are based on the empirical data and no universal mathematical models exist [12–15]. The impracticality of theoretical models for predicting quality characteristics is well known in metal cutting [16–18]. Three material types that are widely used in both automotive and aerospace industry (6061-T6 aluminum, 7075-T6 aluminum, and ANSI-4140 steel) were selected. One-inch diameter end mill was fixed in the spindle and the hammering on the tool was analyzed to determine frequency response function of the machine tool structure. The stability lobe graph generated by the CutPros software provided the combination of depth of cut and cutting speed for minimum chatter in machining. Consequently, the axial and radial depth of cut and cutting speed were tuned for a chatter-free machining. Each machined block has two stepped bores (65 and 50 mm diameter). The bores were selected as the critical quality characteristics because circularity and cylindricity of machined parts are regarded as the most fundamental geometric features in engineering [19]. To ensure the proper functioning of round parts, permissible deviations from the true circle are allowed in the form of tolerance zones bounded by two concentric circles [19], which dictate the desired dimensional and form accuracy [20]. The bores have a tolerance of 0.1 mm, corresponding to an ISO tolerance grade of IT10. Tolerances were measured using a spindle probe (a Renishaw MP 700 surface sensing wireless probe with 0.0000100 repeatability) and a newly calibrated Mitutoyo B403B CMM. Fig. 2 shows the sensors, the probe, and examples of machined blocks. The CNC mill was fitted with multiple sensors and data acquisition systems to collect cutting force measurements and spindle housing vibration/acceleration. Each measurement was further divided into components: x, y, z cutting force components (Fx, Fy, Fz) and x, y, z spindle housing vibrations (Ax, Ay, Az). Those components were filtered and processed for both time and frequency domain features. The arithmetic averages, Fv and Av, were also calculated. For aluminum parts, a high-speed steel (HSS), 2-flute, cobalt end mill cutter was used until the tool wore out. For steel, an uncoated, 2-flute, tungsten carbide cutter was assigned. All cuttings utilized coolant to minimize friction and overheating. After each block was machined, the tool was removed from the spindle and the wear on the cutting edges was measured using a computer vision system. A custom fixture was built to support the tool holder at a constant focal length. An integrated white LED light was used to illuminate the cutting edges. A DVT 540 CCD camera with 640 480 pixel resolution was connected to the
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Fig. 2. Spindle touch probe used to inspect the finished blocks (a) and three examples showing 6061 Al, 7075 Al, and 4140 Steel, from the left (b).
Ethernet and real-time images appeared on a PC contained the Framework Version 2.7.4 image analysis software. The exposure time was 2.5 ms and the LED was fired with a 250 ms interval controlled by the internal trigger. To prevent the glare due to the highly reflective surface of tool, an anti-blooming filter was applied to reduce the pixel saturation. The image contrast was improved by the Contrast Filter, and the slight image blurring was removed by the sharpen filter. After the preprocessing, the wear area was isolated from the rest of the image by applying the edge detection/ separation algorithms. The image showed a very good contrast for further processing. Once the edges were separated, the measurement region was selected as about 0.1500 from the tool end, corresponding to the depth of cut (see Fig. 3). The region was divided into 10 equally spaced intervals and each interval was measured to get the average. Since there are two cutting edges in the tool, this step was repeated. The system was calibrated using a high-grade Mitutoyo gage block and it was found that
Fig. 3. Preprocessed image of cutting edge (a) and the further processed image showing the wear width and the boundaries (b).
the pixel size at the specific focal length was 0.0002400 in pixel width (x) and 0.0002500 in pixel height (y). When compared with the wear measurements taken by the Mitutoyo tool maker’s microscope, the difference was less than 5%. The tool wear was defined as the average of the product of pixel numbers along y-direction and the pixel height: lðin:Þ ¼ n1
n X
0:00025ji ,
(1)
i¼1
where l is the average wear width along the measurement region, n ¼ 20 and fi is the number of pixels at interval i. The bores were measured at the end of the finishing cycle by the spindle probe. Then the block was removed from the machine and measured again by the Mitutoyo CMM. Before the experiments, the CMM was calibrated by a certified technician to ensure the accuracy. In addition, prior to utilizing the CMM, a process
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capability study was performed using a standard ball. The ball was measured by the same operator, using a series of processes that entailed measuring points along the circumference. Ten measurements were taken for each of the two established patterns of 4 and 8 points. The natural tolerance was determined by establishing the standard deviation for each point pattern, and then calculated to the 3-sigma value. The average was 0.00024800 . When it was compared to the manufacturer’s standard tolerance of 0.000300 , the CMM was considered operating within the proper tolerance parameters. The difference between the probe and CMM was defined in the form of: Di ¼ qCi qPi ,
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3. Closed-loop measurement error analysis The difference between the probe and CMM measurements provides the comparison between the in-process and the post-process inspection data. Many studies have been dedicated to improve machining accuracy based on feedback signals. It is an active research area and the examples are abundant: numerical analysis of machining feedback errors, CMM-based inspection modeling in machining operations, a numerical circular form error models in machining, spindle error compensation using a real-time feedback signal, and manufacturing data analysis of machine tool errors. However, there appears to be no research that investigated the measured difference between two methods [21–33]. Fig. 7 shows the variation in the difference according to the bore size and material type. For aluminum, the 50 mm bore has a smaller variation, while the steel block show a similar variation between the bore sizes. In this study, the CMM data are considered more reliable than those from the probe, hence the Di is used to analyze the feedback error. The arithmetic average of the difference for three material types was found using the following equation:
(2)
where Di is the difference (in), qCi is the CMM measurements, qPi is the probe measurements, and the index i the integer data number (iX1). The number of milled components for 6061-T6, 7075-T6 Al and AISI4140 steel were 20, 19 and 17, respectively. Figs. 4–6 represent the difference between the CMM and the probe measurements. The graphs show the random patterns, indicating no systematic errors involved in the measurement difference. The difference is mostly positive, meaning that the CMM measurements are usually larger than those of probe. The graphs also show that the difference is hardly affected by the number of workpiece.
mj ¼
n X Di i¼1
n
,
(3)
6061 Al: CMM-Probe Measurement 0.05000 0.04500 0.04000 0.03500 0.03000 0.02500
Inch
0.02000 0.01500 0.01000 0.00500 0.00000 -0.00500 -0.01000 -0.01500
CMM - Probe: 65 mm Bore CMM- Probe: 50 mm Bore
-0.02000 -0.02500 1
2
3
4
5
6
7
8
9
10 11 12 Workpiece No.
13
14
Fig. 4. Measured difference between CMM and Probe for 6061 Al.
15
16
17
18
19
20
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7075 Al: CMM - Probe Measurement 0.05000 0.04500 0.04000 0.03500 0.03000 0.02500
Inch
0.02000 0.01500 0.01000 0.00500 0.00000 -0.00500 -0.01000 -0.01500
CMM -Probe: 65 mm Bore CMM -Probe:50 mm Bore
-0.02000 -0.02500 1
2
3
4
5
6
7
8
9 10 11 Workpiece No.
12
13
14
15
16
17
18
19
Fig. 5. Measured difference between CMM and Probe for 7075 Al.
4140 Steel: CMM - Probe Measurement 0.05000 0.04500 0.04000 0.03500 0.03000 0.02500
Inch
0.02000 0.01500 0.01000 0.00500 0.00000 -0.00500 -0.01000 -0.01500 CMM - Probe: 65 mm Bore
-0.02000
CMM - Probe: 50 mm Bore
-0.02500 1
2
3
4
5
6
7
8 9 10 Workpiece No.
11
12
Fig. 6. Measured difference between CMM and Probe for 4140 Steel.
13
14
15
16
17
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as independent variables. Including two factor interaction effects and quadratic terms, the full model includes all possibilities:
Difference between CMM and Probe for Three Materials 0.06 0.05 0.04
EfYg ¼ b X ¼ b0 þ b1 TW þ b2 HD þ b3 F x þ b4 F y þ b5 F z þ b6 F v þ b7 Ax þ b8 Ax þ b9 Ay þ b10 Az
0.03 Inch
293
0.02
þ b11 Av þ b12 TW HD þ b13 TW F x
0.01 0.00
0
-0.01
þ b14 TW F y þ b15 TW F z þ b16 TW F v þ b17 TW Ax þ b18 TW Ay þ b19 TW Az þ b20 TW Av þ þ bn10 TW 2 þ bn9 HD2 þ bn8 F 2x þ bn7 F 2y þ bn6 F 2z þ bn5 F 2v þ bn4 A2x
50
5
þ bn3 A2x þ bn2 A2y þ bn1 A2z þ bn A2v .
41
41
40
40
St l:
St l:6
Al :5 0
70 75
Al :6 5
70 75
Al :5 0 60 61
60 61
Al :6 5
-0.02
Fig. 7. Distribution of measurement difference according to bore size and material type.
Table 1 Arithmetic average of difference and material hardness Material type
Rockwell hardness
mj
6061-T6-Al 7075-T6 Al 4140 Steel
43 85 92
0.0061 in/0.155 mm 0.0103 in/0.260 mm 0.0221 in/0.561 mm
ð4Þ
The explanatory variables have been reduced to six that have the highest degree of association with the dependable variable. Among those, HD2, Az and Av have stronger correlation with the Di and the tool wear found to be not correlated with the Di . The reduced form of fitted model with the least deviance for all three material types were found to be in the form of: Y^ i ¼ 0:0157 þ 106 HD2 þ 0:00452HD Az 2:64A2x 0:0218F y þ 0:00446F v 0:508Az þ 0:447Av . ð5Þ 2
where mj is the arithmetic average of difference (in), index j the material type, and n a number of workpiece. The mj was calculated and listed in Table 1. The amount of feedback (ci) for bore diameter correction needs to be examined under four different conditions given by the state of the four variables: the nominal bore diameter denoted as qN (in this case, either 50 or 65 mm), the probe measurement, the CMM measurement, and the mj. The conditions and the feedback (if the mj can be maintained) are in the form of:
Condition I: If qC4qP & qCoqN & Di40, then ci fqN ðqP þ mj Þg Condition II: If qC4qP & qCXqN & Di40, then ci fqN ðqP þ mj Þg Condition III: If qC4qP & qCoqN & Dio0, then ci qN qP þ m j Condition IV: If qC4qP & qCXqN & Dio0, then ci fqN ðqP þ mj Þg
¼
The coefficient of multiple determination (R ) between the responses Di and the fitted valuesY^ i was found to be 0.72. The reason that tool wear has no effect on the difference can be speculated that tool wear increases as cutting continues, affecting both probe and CMM measurements, while the difference has a random pattern throughout the cutting experiments. This phenomenon was observed earlier, illustrated in Figs. 4–6. Hardness, Fv and Av are in the equation, suggesting that increased material hardness and associated increase in cutting force and spindle housing vibration have an effect on the difference. Independent analysis for each material type, on the other hand, yielded much lower accuracy.
¼ 4. Design of experiment ¼ ¼
It should be noted that the amount of feedback has the same relationship between the nominal values, probe readings, and the average of difference, hence allowing the use of single equation for subsequent use. Forward elimination, multiple linear regression analysis was performed for all three material types using the Di as the dependable variable and the 10 measured parameters (HD as hardness, tool wear, Fx, Fy, Fx, Fv, Ax, Ay, Az, Av)
In industrial settings, a design of experiment (DOE) technique is used for product development to apply analysis of variance (ANOVA) principles. The primary goal is to extract the maximum amount of unbiased information regarding the factors that affect a production process from as few observations as possible to minimize the development cost. The fractional factorial design was implemented in this experiment to minimize the total number of runs, while ensuring that there is no significant impact on output [34]. A Full DOE design for this experiment would have consisted of three factors containing three levels each, as indicated in Table 2.
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In this setting, two replicates would have required 54 metal blocks (runs), whereas the fractional factorial formula reduced the time and costs involved by 33.3% by using: (331) (2 replicates) ¼ 18 runs. The actual Table 2 Factors and levels Level
Factors
Low (1) Center (0) Upper (+1)
Hardness
Speed
Feed
6061 aluminum 7075 aluminum 4041 steel
Slow Mid Fast
Slow Mid Fast
Table 3 Feed and speed levels Material
Feed
Speed
6061 6061 6061 7075 7075 7075 4140 4140 4140
127 mm/min (1) 254 mm/min (0) 381 mm/min (+1) 127 mm/min (1) 254 mm/min (0) 381 mm/min (+1) 50.8 mm/min (1) 127 mm/min (0) 254 mm/min (+1)
1250 rpm(1) 2500 rpm (0) 3750 rpm (+1) 1250 rpm (1) 2500 rpm (0) 3750 rpm (+1) 750 rpm (1) 1500 rpm (0) 2250 rpm (+1)
Al Al Al Al Al Al St St St
DOE design matrix was generated in Statisticas and in order to eliminate potential bias during the milling process, randomization of the run order was implemented. Two runs were selected for operating parameters for Statisticas to create two blocks. Blocking reduces the variability in the response due to other external factors that are not considered. The cutting tool Speed and Feed factors established using CutPros software is correlated with the appropriate material (as illustrated in Table 3). Figs. 8 and 9 show the measured difference between the CMM and the probe in DOE and the variation in measured difference according to material types and bore size. The similar pattern can be observed, however, the difference in Fig. 8 becomes larger after the workpiece number 12. This can be attributed to the increased tool wear as well as the machining of steel blocks. In DOE, the same statistical analysis technique was used to identify the significant explanatory variables. The best model (R2 ¼ 0:924) is in the form of: Y^ i ¼ 0:138 15:2Tw 5:57Ax 4:56Ay 3:22Az þ 7:37Av þ 0:0904F z .
ð6Þ
The DOE data show a contradicting result, having the tool wear as significant as well as all three components of vibration and z-directional force component. The material hardness turned out to be insignificant for DOE. Since the same tool is used to process the mixed
DOE: CMM - Probe Measurement 0.05500
0.04500
0.03500
Inch
0.02500
0.01500
0.00500
-0.00500
-0.01500
CMM -Probe: 65 mm Bore CMM- Probe: 50 mm Bore
-0.02500 1
2
3
4
5
6
7
8
9 10 11 Workpiece No.
12
13
Fig. 8. Measured difference between CMM and Probe in DOE.
14
15
16
17
18
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DOE: Difference between CMM and Probe Measurements 0.06 0.05 0.04
Inch
0.03 0.02
295
the capability of on-line measuring instruments. The future study can be envisioned that a development of error model encompassing machine tool thermal effects, a development of probing algorithms for better measurement accuracy, and a development of comprehensive feedback error control architecture that includes servo control errors.
0.01 0
0.00 -0.01
Acknowledgments 41 40 :5 0
65
D O E
41 40 :
50 D O E
70 75 :
65 D O E
70 75 :
50 D O E
60 61 :
D O E
D O E
60 61 :
65
-0.02
This study was supported by the National Science Foundation (NSF) Major Research Instrument (MRI) Grant No. 0116515. The authors are very grateful for their financial support.
Fig. 9. Distribution of measurement difference in DOE.
References materials of 18 blocks, it can be reasoned that the difference is affected by the tool wear and the associated vibration and z-cutting force. This may be attributed to the increasing magnitude in the difference as cutting continues. DOE model has a much better accuracy, suggesting that in a batch mode production, where a variety of materials produced on the same machine using different cutting parameters, this feedback error model has a high potential for shop-floor implementation.
5. Conclusions This study provides insights toward how two different measuring techniques affect the gauging of machine part dimensions. The randomness in difference represents that non-systematic errors exist between the two measurements. DOE, however, presents a systematic variation in setting up the experimental parameters, resulted in a much-improved accuracy in the regression equation. The comparative study on the CMM and probe readings presented in this study is useful for today’s manufacturing environment where diverse products are machined with ever decreasing lot size and minimal human intervention. The DOE conducted in this study simulated the batch mode manufacturing, using highly common industrial material types. Harder material (4140 steel) showed a much wider variation in the measurement difference between the CMM and the spindle probe, hence care must be exercised if a feedback signal is to be used for correcting part size. The error model for DOE has a very high accuracy, suggesting that the spindle probe reading can be used for real-time, closed-loop control of part size. This, however, stipulates a gauge study to verify the magnitude of errors and
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