Qualifying Capacitive Sensing Hole Measurement System Technology for Performing Gage R&R Studies

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1 08AMT-0050 Qualifying Capacitive Sensing Hole Measurement System Technology for Performing Gage R&R Studies Copyright 2008 SAE International Robert Magee Capacitec, Inc. ABSTRACT The Capacitec CMS3 Reader, coupled with the CHP 48 sensor probe, achieves +/-3µm accuracy by mapping 24 diameters in high tolerance drill holes for the manufacture of composite or metal aircraft components. Gage repeatability and reproducibility (gage R&R) studies presented will show better than +/ inches (2.5µm) for this measurement technique. Using noncontact inspection for quality control is a way to perform this inspection more efficiently than traditional contact measuring instruments, while reducing sampling time compared to other methods. Gage repeatability is improved using non-contact methods because capacitive sensing at short distances has a linear and predictable correlation to displacement. Gage reproducibility is also better because different users introduce a different touch using bore gages and other contact measuring devices. In conclusion, using a probe that profiles 24 diameters at the click of a button using non-contact capacitance technology not only saves time but is a significant improvement to overall gage R&R. INTRODUCTION Gage R&R, repeatability and reproducibility can be very helpful when making a decision to choose bore gages or using the non-contact methods such as capacitive sensing like the CMS3 and CHP sensor probes to measure high precision hole diameters in aerospace components. High tolerance and precise holes are required for rivet and bolt holes on aircraft components to minimize ultimate fatigue and failure of components and structures. With aluminum and composite components making up most of the structures, many 1000 s of holes are drilled which require 100% inspection. A gage R&R study can show variability of the measurements obtained by a single operator using the same ring gage standard (repeatability) while also taking into account the variability of the measurement system caused by different operator behavior (reproducibility). A study was performed on the CMS3/ CHP probe to look at the superiority of the measurement device for this type of application. Most notably the time savings in hole profiling going through multiple structure times at the same time, which is an advantage using the 48 imbedded capacitive sensor probe. MAIN SECTION CAPACITANCE MEASUREMENT OVER CONTACT MEASUREMENT Capacitive Sensing Hole Measurement System Technology for quality control has many advantages over conventional split ball gages and calipers for hole dimensional inspection of precision holes. Capacitive technology allows for micro-inch accuracy in dimensional checks and utilizing a non-contact method the inspector can t influence the indicator reading. This allows for better in-process trend analysis of products with many holes to inspect. Further with the CMS3 Measuring system, 24 diameters are instantly recorded, profiling the hole in question compared to the single diameter which has to be physically moved to record more than one point. The CMS3 originally was designed as a system to measure aircraft fastener holes, but the concept should make it a valid process to measure all types of holes that also require tight tolerance. Typical flaws the CMS3 is designed to detect which affect cylindrical fastener holes are barreling, bell-mouthing and ovality as shown in Figure 1. Even with the best of technique by the technician, using split ball gages and other contact measurement methods, reproducibility is difficult to maintain between users. With capacitance non-contact methods, the operator will get repeatable data and less influence of variance between users because capacitance is independent of placement in hole.

2 Fasteners Proper Fit and Typical Flaws Good Hole Belmouthing The advantage of the CMS3 (figure 3) is it s superiority over other measuring methods for inspecting holes in aircraft assemblies because of the time savings and ability to pass the gage R&R studies. Gage R&R has two common methodologies. The first analysis method used is the Range & Average Method. It computes the total measurement system variability, and allows the variability to be separated into repeatability, reproducibility, and part variation. The second method used is the ANOVA (Analysis of Variation between Groups) method. ANOVA is the preferred method because it quantifies the interaction between the repeatability and reproducibility and is considered more accurate than the Range and Average method. Although the Range and Average method is easier, with computer software the added computations of the ANOVA method doesn t make it much more time consuming. GAGE R&R STUDY Range and Average Method Barreling Figure1. Ovality CMS3 and CHP Probe Background Information The concept of the CMS is based on the fact that electrical capacitance varies with the distance between opposing capacitor plates (i.e. sensor and conductive target) as given by the following formula C=e v KA/d Where: C=Capacitance, e v =Permittivity of Free Space A=Cross-Sectional Area, K=Dielectric of air or other material, d= distance between the plates The CHP sensor probe has 48 sensors positioned in 6 rows of 8 sensors spaced 45 degrees apart (see figure 2). The probes active elements spacing is determined by the components being bolted or riveted together in the assembly. The sensors are embedded into the probe body using a proprietary process, integrating layers of conductors and insulators. Probes have a nominal range of use of 100 to 200 microns. The CMS3 samples opposing sensor pairs, and adds the probe diameter, and provides a measurement to the user. Twenty four diameters are then sampled one at a time using a multiplexer in the CMS3 and exported using RS232 or wireless technology to collection software for data observation and processing. To quantify repeatability and reproducibility using range and average method, 10 samples, 3 appraisers, and 3 trials were used. With capacitive probes, the further the gap from the sensor to conductive target the more difficult measurement consistency is to achieve. Therefore.2525 in. (6.413mm) diameter hole was used to test the.2500(6.350mm) probe. The results can be seen in Table 1. Overall Gage R&R was 14.97%. A second set of data was created with the.2525 probe after the CMS3 electronics warmed up for 30 minutes and the probe handle was made remote using a flexible cable. The test data is shown in Table 2. The overall Gage R&R is 7.00%, which is within acceptable range of <10%. Although 14.97% is in the region which is acceptable because it is below the 30% required, by improving the process of taking readings under 10% could be obtained. Next we take a look at Cp and Cpk. Cp, Cpu, Cpl, and Cpk Cp is a simple and straight forward indicator of process capability when given within its natural variation. Cpk is a process capability index which indicates how a process whose average is acceptable is trending within the desired specification. How well it s centered in the sampling. Cp=(USL-LSL) /6 *sigma Cpu= (USL-Mean) /3 * sigma Cpl= (Mean-LSL) /3 * sigma Cpk=Min(Cpu or Cpl)

3 Process Capability index is taking account of offcenteredness. Effectively the Cp for a centered process producing a similar level of defects - the ratio between permissible deviation, measured from the mean value to the nearest specific limit of acceptability, and the actual one-sided 3 x sigma spread of the process. As a formula, Cpk = either (USL-Mean)/ (3 x sigma) or (Mean-LSL)/ (3 x sigma) whichever is the smaller (i.e. depending on whether the shift is up or down). This ignores the vanishingly small probability of defects at the opposite end of the tolerance range. Cpk measures not only the process variation with respect to the allowable specification, it also takes into account the location of the process average. This value is the smaller value of Cpl or Cpu. A Cpk of at least 1.33 is desired. In our testing the lowest value was 1.59, indicating that it s a well centered process. See Figure 4. Reviewing the data after the second run after the unit had been warmed up and using the remote cable, the lowest Cpk was 2.98 which indicate a very stable process. See figure 5. Figure 2. Figure 3.

4 Gage Repeatability and Reproducibility (R&R) Data Sheet (Long Method) Before warm-up Operator Operator 1 Operator 2 Operator 3 Trial Sample Range Range Range Totals First trial First trial First trial Third trial R Bar A Third trial R Bar B Third trial R Bar C Sum Sum Sum X Bar A X Bar B X Bar C R Bar A Select for equation at right Max X # Trials D4 R Bar B UCL r = Rbar*D4 Bar Min X R Bar C UCL r = Bar Sum Xdiff 5.1E-05 R Bar Analysis Repeatability- Equipment Variation (EV) % Tolerance Analysis EV=Rbar x (K1) Trials 2 3 Part Tol EV= K %EV=100 x EV/Tolerance %EV= Reproducibility - Appraiser Variation (AV) n=#of parts 10 %/AV=100 x AV/Tolerance AV=SQRT((XbarDiff * K2)sqd)-((EV)sqd/n*r)) r=#of trials 3 %AV= AV= Operator 2 3 K R&R=SQRT((EV Squared)+ (AV Squared)) %R&R=SQRT((%EVsquared)+(%AVsquared)) R&R= %R&R=

5 Table 1. Gage Repeatability and Reproducibility (R&R) Data Sheet (Long Method) After Warm Up and added Remote Sensor Operator Operator 1 Operator 2 Operator 3 Trial Sample Range Range Range Totals First trial First trial First trial Third trial R Bar A Third trial R Bar B Third trial R Bar C Sum Sum Sum X Bar A X Bar B X Bar C R Bar A Select for equation at right Max X # Trials D4 R Bar B UCL r = Rbar*D4 Bar R Bar C UCL r = Min X Bar Sum Xdiff 4.367E-05 R Bar 5.7E-05 Analysis Repeatability- Equipment Variation (EV) % Tolerance Analysis EV=Rbar x (K1) Trials 2 3 Part Tol EV= K %EV=100 x EV/Tolerance %EV= Reproducibility - Appraiser Variation (AV) n=#of parts 10 %/AV=100 x AV/Tolerance AV=SQRT((XbarDiff * K2)sqd)-((EV)sqd/n*r)) r=#of trials 3 %AV= AV= Operator 2 3 K R&R=SQRT((EV Squared)+ (AV Squared)) %R&R=SQRT((%EVsquared)+(%AVsquared)) R&R= %R&R=

6 Table 2. Cpk Calculation Before Warm-up PROBE OD Operator 1 RING GAGE DIAM 1 DIAM 2 DIAM 3 RANGE LEVEL 1 TOLERANCE USL LSL min max average std dev Cp Cpl Cpu Cpk Operator 2 Operator 3 DIAM 1 DIAM 2 DIAM 3 DIAM 1 DIAM 2 DIAM 3 LEVEL 1 LEVEL min min max max average average std dev std dev Cp Cp Cpl Cpl Cpu Cpu Cpk Cpk

7 Figure 3. Cpk Calculation of.2525 Ring Gage After Warm up and Adding Remote Sensor PROBE OD Operator 1 RING GAGE DIAM 1 DIAM 2 DIAM 3 RANGE LEVEL 1 TOLERANCE USL LSL min max average std dev Cp Cpl Cpu Cpk Operator 2 Operator 3 DIAM 1 DIAM 2 DIAM 3 DIAM 1 DIAM 2 DIAM 3 LEVEL 1 LEVEL min min max max average average std dev std dev Cp Cp Cpl Cpl Cpu Cpu Cpk Cpk Figure 4.

8 source of Variation ANOVA TABLE sum of SQ Deg of freedom appraiser mean sq Parts 9.59E-08 9 Interactio n E Gage Err 4.44E E-09 Total 6.21E F 2.21E E E Repeatability= Reproducibility= I= #NUM! #NUM! Figure 5. R&R= #NUM! source of Variation ANOVA TABLE sum of SQ Deg of freedom appraiser 3.04E-08 2 Parts 2.32E-08 9 Interaction 3.10E Gage Err 7.69E Total 1.61E mean sq F 1.5E E E E- 09 Repeatability= Reproducibility = I= E R&R=

9 Figure 6. Two Way ANOVA Method Using the Analysis of variance method (ANOVA) is the most accurate for determining Gage R&R for the CMS3. The ANOVA method also allows the variability of the interaction between appraisers and parts to be looked at. The ANOVA method should be similar in results but will be slightly different. The first Gage R&R with the ANOVA method the result was 15.5% which is slightly higher than the result from using the range and average method. When the data was taken after the ½ hour warm up time and added remote probe handle the result was 7.14% which is slightly higher than the range and average method. These results can be seen in Table 3 and 4. CONCLUSION The Capacitec CMS3 Reader, coupled with the CHP 48 sensor probe, achieves +/-3µm accuracy by mapping 24 diameters in high tolerance drill holes for the manufacture of composite or metal aircraft components. Gage repeatability and reproducibility (gage R&R) studies showed improvement of the measurement device with the.2525 probe after the CMS3 electronics warmed up for 30 minutes and the probe handle was made remote from the electronics. The Range and average method and the ANOVA methods plus looking at Process control indicators, Cp and Cpk showed that the CMS3 is a very reliable measuring device. The repeatability of the device improved because after a warm up period the electronics thermally stabilize and electronic components do not fluctuate as sometimes when the instrument is starting cold. The gage R&R reproducibility improved by adding the remote cable to the probe which, took out the variance between users out of the equation. All 3 users hold the instrument differently and when the button is selected to sample, push force is different between users. Gage R&R reduces as variance on push button force is now a removed variable from the measurement. The Cpk measurement can also be used to measure the trend of the data. Our results also show an improvement on staying within the specification with the introduction of a warm up time and remote probe from the electronics. The CMS3 and CHP hole probe provides a more advanced replacement inspection tool over conventional methods of inspection as proven by the statistical considerations as shown in the Gage R&R study. REFERENCES 1. The Capacitive Measuring System, October 21, Waxer, Charles, Process Capability (Cp, Cpk) and Process Performance (Pp, Cpk) what is the Difference? 3. Foster, R.L. Linear Capacitive Reactance Sensors for Industrial Applications, 40 th Annual Earth moving industry Conference CONTACT Robert Magee is Product Engineer for Capacitec, Inc. Capacitec is located in Ayer, MA Bob.magee@capacitec.com

10 APPENDIX Values of and Size of samples (n) # Samples (k) Duncan A. J (1986), Quality Control and Industrial Statistics Appendix D3

Cpk. X _ LSL 3s 3s USL _ X. Cpk = Min [ Specification Width Process Spread LSL USL

Cpk. X _ LSL 3s 3s USL _ X. Cpk = Min [ Specification Width Process Spread LSL USL Cpk A Guide to Using a Process Capability Index Cpk = Min [ USL _ X, X _ LSL ] 3s 3s Specification Width Process Spread LSL X USL The following information is provided by the Technology Issues Committee