The mechanical assembly dimensional measurements with the ...

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10670 J. Rejc et al. / Expert Systems with Applications 38 (2011) 10665–10675this distance is defined as 1.6 ± 0.05 mm. It directly influences theforce of bimetal pushing the toggle element.Due to the force exerted on the limit element, it slightly bendsand linear approximation of the upper edge is not suitable. Fig. 7demonstrates that the upper edge of the limit element lies onthe boundary where dimensions A and B connect. Therefore thedefinition of the boundary point is not possible. That is why thebottom limit element edge is mathematically defined, by using2nd order polynomial, marked with the line number 8. As next, thismathematically approximated polynomial is shifted upwards forthe fixed dimension E. This line represents the upper edge of thelimit element.Tests uncovered that the setting of the bimetal edge, markedwith the line number 2, is in most cases satisfactory only whenthe field of search rectangle is positioned upper-right. Therefore,we were forced to define the bimetal edge also on the left side ofthe set-screw, which is represented as line number 9. This searchprocedure is relative to the vertical line that defines the left edgeof the limit element hook and carried out in preset width. By combiningdata of the bimetal edge from Section 2 and 9, the bimetalbottom edge is most precisely defined.The calculations of the dimensions A and B are carried out in thecontact point of the set screw and the limit element. Since thispoint depends on the position of the set screw, it is impossible todetermine this point precisely. Most reasonable is that the pointof contact between the set screw and the limit element is takenin the middle of the set screw, as is defined in section 11. The middlepoint definition procedure uses the area from nearby right sideof the limit element hook vertical line and left rectangle side forlimit element edge search, letter E or line number 7. At this stepthe polynomial approximation of the upper limit element edge isshifted upwards for 0.04 mm. The algorithm first finds the blackarea of the set screw, the middle region represents the middle ofthe set-screw. Using this procedure the middle line of the set screwcan not be defined highly precise, but the tests demonstrated thatthe approach gives satisfactory results.A huge challenge was to define the toggle element edge, in Fig. 7numbered with line 12. Finding that edge was not trivial due to theshadows that can occasionally appear in the left bottom area of theimage. These shadows can appear from the limit element hookblocking the light. For successful definition of the toggle elementedge, a special algorithm was created. The algorithm is based on settingthe dynamic threshold of the image between the two presetthresholds. These two limits are set by the user, usually between10 and 100, with the lower and upper limits being 0 and 255. The dynamicadjustment step is 5. This dynamic approach was chosen toselect optimal value, i.e. when the threshold is increased the shadowslowly appears. The tests showed that there is a small white area betweenthe shadow and the toggle element edge, which is gettingsmaller with higher threshold values. When the threshold is high enoughthe white area disappears. This threshold is too high, thus previousvalue is used. Next, the mathematical approximation of theedge is carried out. The search is started from the short vertical linenumber 12 to the extreme right edge of the image, from bottom up.The last black pixel represents the eventual edge point. In this areadirt, shadows and part of the limit element hook can occur. That iswhy a moving average algorithm over the found edge points is used.This means that over the edge points a virtual window shifts fromleft to right, the step size is a pixel value. If the edge point in a windowis too far away from the last local mean value, then this pointgets the mean value. This algorithm does not catch the influence offar away points as in the case of direct use of the least mean squaremethod. Over the pool of edge binary points a linear approximationis defined, describing the toggle element edge.The last approximation line enables the calculation of dimensionsA and B, inFigs. 6 in Fig. 7 marked as lines number 13 and14. The calculation is performed by setting a line through the middleof the set screw perpendicular to the toggle element edge line.The intersections of approximated lines represent the dimensionsA and B.When the analysis is finished, the user is informed about themeasurement results and the program window displays dimensionsA, B, D, E and F. The user is also informed whether the dimensionsare in the predefined boundaries or not and the data is savedin the database.4.3. Calibration of the AVI systemEvery measuring instrument has to be calibrated before the use.For this purpose, our software offers also the calibration of themeasuring AVI system. For calibration purposes the user uses threecalibration protectors, with known dimensions A, B and E, in ourcase previously measured with the certified profile projector measuringsystem, type Mitutoyo PV500.The user has to manually insert the pre-measured dimensionvalues in the empty software fields, before the first calibration.The calibration procedure is the same as the measuring procedure,described in previous section. The main difference in calibrationprocedure is that dimensions are not calculated, but rather thenumber of pixels between intersection lines is defined. The numberof pixels between these edges is a decimal value number.By using the decimal pixel values the transformation betweennumber of pixels to metric units is performed. Because the opticsnonlinearities, the relationship between the pixels is not completelylinear. For this reason the user can select which approximationpolynomial order best transforms the number of pixels intometric units. The polynomial order can be selected from 1 to 6. Thispolynomial transformation is calculated by using the residuals andthe factor R 2 , called the coefficient of determination. This coefficienthas a value between 0 and 1, where higher value reflectsbetter approximation. An example of the transformation approximationcan be seen on Fig. 8, where polynomial of 4th order isused.R 2 was calculated using Eq. (6), where y is the measured value, yis the mean and ^y is the current calculated polynomial value.ResidualSS ¼ X ðy ^yÞ 2 ;TotalSS ¼ X ðy yÞ 2 ; ð6ÞR 2 ¼ 1ResidualSSTotalSS ;Fig. 8. User window for polynomial transformation from number of pixels intometric units.
J. Rejc et al. / Expert Systems with Applications 38 (2011) 10665–10675 10671For calibration purposes three normal protectors were chosenwith dimensions A, B and E being the most spread over the AVI systemmeasuring range. At this point it must be stated that also duringthe calibration procedure, the dimension E was fixed at value0.20 mm. This value is the same as measured by using calibratedprofile projector measuring system.5. Methodology5.1. Dimensional measurements of the calibration protectorsFor the calibration of the presented AVI system three objects areneeded. Their known dimensions A, B and E are pre-measured withan optical profile projector. It was also used to measure anotherfive protectors used as control samples for defining the measurementerror.On these eight protectors dimensions A, B and E were measured.Measurements were performed by the use of the profile projector,type Mitutoyo PV500. The resolution of this system is 1 lm withthe repeatability of 3 lm. The magnifying factor during the measurementswas set to 20. For more accurate protector positioningon the measurement board also a special magnifying glass with amagnifying factor of 10 was applied. Measurement uncertaintyof the profile projector is described by the publication EA-4/02(European Co-operation for Accreditation, 1999) and Eq. (7). Theresult and the measured distance L is expressed in lm.u ¼ 4 þ 5 10 6 L ; ð7ÞCalibration of the profile projector measuring system is performedevery 2 years. For the calibration special calibrating blocksand glass rulers are used. The procedure for the calibration of theprofile projector measuring system is not defined in detail by anyinternational standard. Therefore the calibration is performed byinternal calibration procedures, which are accredited by an externaljudge. In our case, by the Dutch independent, internationallyrecognized testing and certification institute, called NMi (NederlandsMeetinstituut). Every calibration protector was measuredonly once at room temperature (23 ± 1)°C.The measurement procedure is as following. The calibrationprotector is laid on the glass surface of the profile projector. Theprofile projector measuring system, by the use of lenses and mirrors,projects the image of the measured object on the glass surfaceequipped with coordinate system and ruler marks. By rotating themicrometers the coordinate system is moved to the preferred positionand orientation. In our case the X axis was levelled to thetoggle element and the Y axis to the middle of the set screw. Afterlevelling, the coordinate system was positioned at the bottom ofthe limit element still in the middle of the set screw. This wasthe position where the micrometers values were reset to zero. Thiscenter point was chosen as the most exposed part of the protectorwhen measured by a profile projector. The position of this centerpoint is not appropriate for measuring distances A and B, becausethe distance A is too short and distance B too long for 0.20 mm,as is the thickness of limit element material.This measurement procedure has a great subjective influence ofthe person who performs the measurements, because many edgesare difficult to define with great precision, although the use ofmagnification helps to achieve more accurate measurements.From all 8 reference protectors, three were defined as calibrationobjects to define the transformation of the number of pixelsinto metric units, in our case in millimeters. To describe the transformationa polynomial transformation of the 4th order was usedalongside the linear transformation function. The 4th order polynomialhad the highest R 2 value. The calibration protectors with sequencenumbers 2, 6 and 7 had their measured values A, B and Ethe most spread over the field of view of the AVI system. Other protectors,numbers 1, 3, 4, 5 and 8, had been used as control objectsfor defining measurement accuracy and repeatability of the AVIsystem. The measurements with the AVI system were performedat room temperature of 23 °C. Every protector was manually positionedinto the system bed. After a measurement was run, everyprotector was manually removed from the system bed. Numberof repeated measurements on each protector was 25.5.2. Dimensional measurements of the protectorsTo ensure that the manufactured protectors switch-off at theright temperatures, it is necessary to statistically test protectors ina laboratory. 72 protectors randomly taken from already sealedpackages presents a measurement set. Several sets are tested daily.Each protectors set is put into a special oven. Every protector in theoven is electrically connected to observe the state of the switch. Theoven is gradually heated. The inner temperature is measured with aPT-100 class A temperature sensor. Its measurement error is expressedby Eq. (8). The calculation temperature (T x ) is at 400 °C.DT ¼0:15 ð þ 0:002 T x Þ ¼ 0:95 C: ð8ÞThe heating of the oven proceeds until the last protector reachesits switch-off temperature. For safety reasons the maximum innertemperature is set to 480 °C, where the heaters are also switchedoff. After heating, the oven is passively cooled to the temperaturewhere the last protector switches back on. The switch-off andswitch-on temperature value of each protector are saved into acomputer database. The procedure is repeated three times in thelaboratory. As a measurement result, the average value of the secondand the third cycle is used. This measurement procedure in alaboratory is very slow and every set takes 6–9 h to complete. Inproduction facilities this slow procedure is performed only once.This is the main reason why a faster measurement would be verywelcome. The fastest method would be if the switch-off temperatureis in correlation to the dimension A. The presented AVI system needsless then a second to assess the dimensions A, B, D and F. Includingthe protector manipulation, the overall time is less than 2 s, whichis much less than manufacturing time cycle. Fast measurementsusing such a system would result in testing of each manufacturedprotector, as opposed to today’s statistical sampling methods.Until today no comparative measurement on a large set of protectorswas performed, where the dimension A could be directlycompared to the switch-off temperature. For measurement purposesa set of 220 protectors was chosen. All were fine calibratedduring their production. Furthermore, a second set of 220 protectorswas also chosen. They were only roughly calibrated at the set screwassembling. These are meant as non-calibrated. The reason to includealso non-calibrated protectors, was to verify if only rough calibrationwas enough for production. All protectors were numberedand than measured by the presented AVI system and also with thereference heat and cool oven procedure. During measurements withthe AVI system each protector was measured only once. In the oventhe standard procedure was repeated. In the set of calibrated protectors218 of them were successfully measured by the AVI system and217 of the non-calibrated set. The reason why some of the protectorswere not successfully measured originates from mechanical problemsof the pneumatic positioning system of the AVI system. Someof the ceramic protector housings were out of tolerances.6. Results6.1. Dimensional measurements of the calibration protectorsThe measurement results of dimensions A, B and E obtainedwhen using a certified profile projector are given in Table 1. All
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