1. Introduction
1.1Angle measurement
Prior to industrial revolution, accurate measurement of physical andgeometrical parameters remained as fashion; with the advent of nineteenthcentury, also marked as century of industrial revolutions changed this fashion intoa dire need. Man quest to approach and develop product with marked economicand technical efficiency were compelled to devise and develop new methods forthe measurement and produce authentic measurement reports reflecting the truevalues of the measurand. Now a day’s accurate and precise measurement is thebackbone of modern high tech systems.The decisions of rejected and accepted components are made based onmeasurement protocol. Accepted components are sent to assembly line andrejected components are sent to scrap yard based on measurement protocol. Thecomponents are measured and accepted/or rejected according to designspecifications. Here measurement plays a key role and slipping of rejected part toassembly line adversely affects the functionality of the whole system therebylower the technical efficiency; accordingly, slipping of qualified components toscrap yard lead to the increase of cost and wastage of time and materials leadingto decrease of economic efficiency.To produce authentic measurement results and increase both technical andeconomic efficiency, new measurement instruments were developed. Theseinstruments include (but not limited to) autocollimator, interferometers,microscope, co-ordinate measurement machine, roundness tester etc. Most of thepresent day measurement equipment is controlled through computers and performaccurate measurement.
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1.2Angle definition
There are two types of angles, known as solid angle and plane angle. Solidangle is the ratio of area to square of a length & measured in dimensionless unitscalled Steradian ( sr ) in international system of units (SI).Solid angle will not betreated in this dissertation. Plane angle is the ratio of two lengths and measured intwo types of systems, (1) sexagesimal system represented in degree, minute andsecond and (2) radian system, radian is the standard unit of angle measurement ininternational system of units (SI). In this dissertation, sexagesimal system will beused unless otherwise stated. In contact type angle measurement[2-4], accuracy of up to 0.1can beachieved using angle protractor; bevel gauges may swell the accuracy up to 0.01. Clinometers and pided circle[5]can measure angle up to third digit butsubjected to human errors.Non-contact angle measurement is the optical techniques and betteraccuracy can be achieved using non-contact type measurement. In non-contactangle measurement, various methods are used to measure angular parameters.Various instruments, for example, autocollimator[6-15], interferometer[16-22], andvarious methods, for example, using internal reflection method[23-24]and moirépattern[25]have been exploited successfully.
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2. Minimum zone plane determination based onMinimum Zone flatness evaluation method
2.1 Flatness –A critical parameter
According to ISO/TS 12781-1[43], flatness is defined as a condition of asurface having all features in one plane and flatness tolerance is defined as ameasured data of a plane feature bounded by two parallel planes within which thesurface may lie.International system of units (SI), is recommended to measure flatnesstolerance and measured in micrometer, however, for non-contact measurement,the wave length, of light source is used as unit of measurement. Recently, thewave length of He-Ne laser ( 632.8nm)is exploited in all optical measurementfor flatness.Flatness feature of a machine part surface is extremely critical to theperformance of parts and assemblies in terms of fitting and functionality. A planesurface may act as a datum surface for other geometrical tolerances or may act asa reference as a part of the measuring instrument; in both cases the measurementcan only be authentic and accurate as the reference.
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2.2 Flatness measurement approaches
The operation of flatness measurement includes partition, extraction,association and evaluation as shown in Figure 2.1[44]. In partition, a non-idealplane is extracted from non-ideal surface as shown in Figure 2.1(b). In extractionoperation, finite numbers of data points are extracted from surface as shown inFigure 2.1(c); extraction represents the true representation of the surface and datapoint should be extracted in some systematic fashion. ISO/TS 12781-2[45]providedata extraction strategy which include rectangular grid, polar grid, triangular grid,union jack , parallel profile, and point extraction strategy. Figure 2.2 showsschematic of rectangular grid strategy; rectangular grid strategy is exploited inexperimental work for flatness measurement. In association operation, ideal plane is developed from a non-idealextracted data points using some explicit rules, association operation are shown inFigure 2.1(c) and (d). Following association operation for flatness error andminimum zone plane development, ISO/TS 12781-1 explain two kinds ofreference planes and four kinds of parameters.
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3. Optimization techniques for flatness error and minimum zone plane ......27
3.1 Optimization Techniques..........27
3.2 Genetic algorithm flow ......29
3.3 Genetic algorithms for flatness error determination.....35
3.4 Verification of proposed algorithms.......37
3.5 Analysis of efficient genetic algorithms (EGA) ..........39
3.6 Applications of efficient genetic algorithms (EGA)....42
3.7 Programming language ......42
3.8 Summary ..............44
4. Uncertainty analysis of flatness of angular artifacts .....45
4.1 New generation geometrical product specification .....48
4.2 Experimental work......50
4.3 Mathematical model for uncertainty.......51
4.4 Flatness error and uncertainty analysis..........52
4.5 Summary ..............61
5. Novel angle measurement technique based on minimum zone.......63
5.1 Angular parameters definition .........65
5.2 Circle closure techniques ..........66
5.3 Measurement method.........68
5.4 Mathematical modeling .....70
5.5 Fixture design for experimental work.....73
5. Novel angle measurement technique based on minimumzone plane and uncertainty analysis using new generationGPS standard (GPS)
As stated in literature review, most of angle measurement methods areperformed using index table and autocollimator /or interferometers as ameasurement instruments. These measurement instruments in most of methodsremain the same, only the procedure varies; however, each procedure has theirown pros and cons. Indexing table is used for generating angles andautocollimator /or interferometer is use for small angle measurement deviations.Index table errors are well researched and index table errors can be quantifiedeasily but errors in autocollimator is difficult to quantify in convincing manner[36].For the same angular artifact measurement in same environmental conditions,different autocollimator shows different results[111,112],this shows the presence oferrors in the measurement instrument. The measurement can be compared amongdifferent autocollimators, but this is not clear which one is providing authenticresults.
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Conclusions
To perform accurate measurement, identification of errors sources and theirelimination by devising new methods or improving the existing methods is thesole option.Autocollimator succumb to a number of errors sources in measurementprocess. Most angle measuring methods are using autocollimator orinterferometer as a sole angle measurement instrument. Angle measurement usingautocollimator and interferometer have some sources of errors, among thesesources of errors are due to edge effect. A new method for angle measurementshas been devised which is based upon minimum zone plane and errors due toedge effect are eliminated, the contribution in reaching and addressing theproblem statement are:
1. The definition of angle between two planes is proposed based onminimum zone plane. The minimum zone plane is determined byminimum zone method which is standard techniques for measurementof many form tolerances and is the true representation of surface form.The definition is consistent with form tolerance.
2. To determine minimum zone plane, a genetic algorithms referred asEfficient genetic algorithm (EGA) were proposed, the method can alsobe used to determine flatness error, the subject algorithms has fastconverging rate, high precision and have marked repeatability.
3. Efficient genetic algorithm (EGA) is supported by a developedprocessing tool, an aide for handling of data and in determining flatness,minimum zone plane and angular error. Flatness error and differentangular parameters are determined and results are in good agreementfor flatness error and for new method of angle measurement.
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References (omitted)