International Conference 011 Trends ill ProductLifecycle, Modeling,

Simulation and SynthesisPLA/SS-JOII

Form Error Evaluation by Rapid Registration Method

S Ravishankar , H N V DurtSCientist. C-CADD, CSIR-National Aerospace Laboratories, )<vVTC Road, Bangalore. India.

Email: ravi@ccadd.cmmacs.emet.in, hnvdutt@ccadd.cnuuacs.emet.in.

B GUllUl10011hyProfessor. Department of Mechanical Engineering. Indian Institute of Science. Baugalore, India

Email: bgm@mecheng.iisc.ernet.ill

Abstract:TIle automated inspection to evaluate f0l111 error

on machined parts is an area of active research. In thispaper we develop a methodology for inspecting form errorbased on Least Square Plane Fitting and ModifiedIterative Closest Point (MICP) algorithm to quantify themanufacturing error'). In the current paper we useanalytically defined surfaces to validate our algorithm 50

that the additional error introduced due to tessellatedrepresentation of the geometry is eliminated. which is thecase for arbitrary machined parrs where the CADgeometry is represented by facets. The rigid registrationcarried out on inspected set of points with the nominalCAD points is described in two parts. The first part of thestudy deals with establishing manufacturing errors bygeneranug inspection data in a known reference systemcalled hard inspection on a Coordinate Measuring:-Iaclune (C:"ll\I). referred to a hard inspection. while the:econd part of the study deals with capturing the errors bygenerating inspection data from an unknown referencesystem called soft inspection. Both the results areevaluated and verified with experimental case studies. Theresults confirm the feasibility of the methodology andshow that the algorithm is effective and accurate andmakes this method attractive to carryout automatedinspection of machined components.Keywords: Soft inspection. hard inspection. softregistration. hard regi strati on. ouliue inspectiou. offiineinspection.Xomeuclature:

Nominal Part coordinate (Jx 1)

Four closest points in nominal partpoint dataset M~D vector of quarernions

Rotation Matrix

Pan Inspection coordinate

T

x.y.z.d

Translation vector..•t ,,{} f . ~ C), dJd tvectors or Xi • ~\i J- h P1'I t i J

respectively (n x l)

1 Introduction

The industrial products today demand large number offunctional features involving close tolerances to derivehigh levels of performance. This is becoming the order ofthe day ill many sectors such as aerospace. automobile and'white goods to name a few etc. with a marked increase inutilization of Class A surfaces. These feature and functionrich components have made the inspection a very complexprocess given the requirement of measuring dosetolerances at a fast rate with reliable results. The need toprovide the tolerance on dimensions defining the part in adrawing is due to the inherent inability of themanufacturing processes to achieve the dimensionsdictated i.n the drawings or in the CAD model. and theessence of manufacturing is to machine a part within thedefined tolerance limits. Deviations which affect the formand dimensions of the part. could be due to many reasonssuch as multiple operations and processes involved inachieving the desired dimensions on the finished pan.inbuilt machine tool error'> such as run our. position.perpendicularity. circularity among others. apart fromhuman errors. TIle acceptance of a part demands theconformance of dimensions to be within the allowabletolerances specified by standards and it is here that theinspection plays a crucial role in deciding whether the partmeets the agreed acceptance criteria or nor. One of theobjectives of manufacturing is also to carryout automatedinspection so as to reduce human interference and achievereliable and consistent quality with the manufactured pansatisfying the design intent. With the ever-increasingdemand to make inspection cost and time effective. it isbecoming necessary to automate the inspection procedure.In this paper we have adopted a combina tion of onhne and

Page '165 of 312

offline inspection processes. wherein the online inspectionstage captures the data and the offline inspection stagecarries out the data analysis and reporting. thus relievingthe C.:vl1v1to perform unhindered inspection therebyimproving its throughput and productivity. It is necessaryto note that the CWmodel could be represented by a setof curves such as B-Splllles or ~lTR.BS to define a wireframe geometry or by any of the modem surfacerepresentation techniques USl11ga set of points to definethe actual geometry. and any of these methods in principlewould introduce a geometrical error compared to ananalytically defined surface. However. within theengineering branch of knowledge. we know that thegeometric error could be reduced to any predefined levelsof accuracy at the expense of computational effort andresource requirements. In rhi - paper an effort is made togenerate analytically definable objects wherein the basicgeometric error is nullified along with the associatedcomputational effort. The geometric integrity facilitatesmea' uremeur of the manufacturing error using the hardinspection route by application of c~n\-l and comparingthe results obtained by soft inspection route through theapplication of Modified Iterative Closest Poi.nt CvIICP)algorithm. This paper proposes to present the results onvarious ca es involving application of least square planefit for inspection on planar features (flatness parameters)and Modified K'P on analytically defined objects. In eachof these cases the uuordered inspection datasets are inputmto our algorithm and the manufacturing deviations arecaptured. The components were inspected on CM~\!Lwhich is the defacto industry standard. whose tactilemethod of measurement eliminates the deficiencies causedby the presence of outliers. Further. the ability of theC\f~1 to measure an almost endless variety ofgeometrrcally complex components in a rapid andaccurate 'way has led to their widespread use in industry.The hard mspectiou results obtained from CIvL''vI arecompared against the soft inspection procedure adopted inthis paper and the results show good concurrence. Themethod is experimentally verified explicitly on planar.cylindrical. toroidal and spherical objects definedanalytically.

Establishment of proper correspondence between theinspection coordinate system used for measurement inC\L\I and that in the design coordinate system used forthe pan is necessary to determine the manufacturing errorand to verify it'>conformity to the tolerances specified onthe machined part in the drawing. Presently. thiscorrespondence is established a priori through the use ofhigh-precision markers and custom made jigs and industrypractices often adopt high precision fixture to locate thepart orientation [2]. This paper employs the ModifiedIterative Closest Point C\IICP) method [3] TO determinethe transformation relating the measured and nominalpoint set. a'> the registration of the two point sets enables

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establishing machining deviations 011the part with respectto its nominal geometry with the error distance definingthe manufacturing error. TIle paper also evaluates theapplication of Least Square Plane (LSP) fit method forfinding the deviation of parts having planar surfaces withrespect to its nominal form. The discrete measurementdata of a planar surface is obtained from C)'1\1 and therigid surface is fit to obtain an optimal solution. Theoptimal solution is compared with the dimensional resultsthat are obtained from hard inspection process. TIle LSPfit method was implemented on parallel bar and theinspection results are found to be very encouraging.

The reminder of this paper is organized as follows:Section 2 reviews the current stare of the art in theregistration of point data sets. An overview of the rapidregistration technique employed is described in Section 3.bringing out the importance of automatic registratron ofthe inspection daraset with the nominal data referencesystem. Section 4 describes the registration procedureadopted in detail. Section 5 presents the implementationand results of the proposed approach to actual machinedcomponents. Conclusions and suggestions for furtherwork are presented in Section 6.

2. Literature survey

The application of metrology equipments such asAdvanced crvl1vl"s. Laser Trackers. Scanners witharticulated arms ete. to carryout rapid and automaticinspection of complex components and assemblies is arecent approach and a subject of active research. The lastdecade has seen several effort in the areas of registrationof 3D point cloud data. These efforts have been primarilyrestricted to the areas of computer vision. imageprocessing. pattern recognition. reverse engineenng.texture mapping and so on.

The most popular approach to solving the registrationproblem is the class of algonthms based on the IterativeClosest Point (ICP) technique for pattern matchingbetween point set A and point set B suggested by Besl andMckay [4]. This algorithm is a general purposeregistration method for freeform curves and surfaceswherein it is assumed that the data pomt set IS a subset ofthe model point set and has seen many Implementationsover the years and by far provides the most accurateregistration results [2]. The ICP has three basic steps:1. Pair each point of the object dataset to the closest pointin the model dataset.2. Compute the motion that minimizes the mean squareerror between the paired point sets.3. Apply transformation to the object dataset and updatethe mean square error.

Zhang et al [5] highlight on the importance to considerthe source of error. which is related to the design of the

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1D scanner and the alignment between the inspection~oint cloud and the non~lal cad data. Tlus is subdividedinto error due to registration of multiple point clouds intoone C01111110ncoordinate frame and registration of theentire point cloud to the cad model. Rnsinkiewicz andLevoy [6] demonstrate an implementation of ICP where arough initial aliznmenr is always available and focuses onaligning a single pair of mesh. -The error metric used herei root mean square point to point distance between thecorresponding points i.n the two meshes. Lukacs er al r]address a problem ansing in the reverse engineering ofsolid models from depth maps and present a set ofmethods for the least squares fitting of spheres. cylinders.cones and tori to three dimensional datasets to identifyand fit surfaces of knO\\11 type, wherever there is a goodfit, Meuq er at [8] put forward a statistical sampling planto determine a suitable sample size to define the geometryaccurately with sufficient confidence. Narayanan et al. [9]proposes L, POI)110nual approximation for evaluation ofform errors of engineering surfaces with applicationsinvolvinz straightne~s, ~circularity. flatness andcylmdericiry. Roy [1OJ carries out tolerance analysis forcylindrical surface based on computational geometrytechniques and numerical analysis methods for computeraided inspection based on least squares. Shi and Xi [11]carrv out registration from a tessellated representation ofthe surface. ~'\s in inspection. the data from the inspectiondevice is a set of points. the daraser with whichcomparison need" to be done has to be either a smoothrepresentation of geometry or a sampling of points from it.A. tessellated representation of a surface cannot be used 111all case'> (including complex parts), as the inbuilttessellation error is not accounted for in these approaches,Nevertheless, this methodology is more suited to image-based registration applications rather than to the area ofcomputational metrology, Meuq. Yau and Lai [12] presenta method capable of determining actual measured pointsbv miuimizins the sum of the squared distances of themeasurement ~data from the surface of the part withrespect to parameters of a rigid body transformation wherethe tran formation matrix is determined by least squaremethod. The paper states that when the part deviationfrom its nominal position and orientation is small. thetransformation is recovered rapidly. while inca e of partswith large deviation where minimization problem ishizhlv n~nlineaI. a method to estimate the region ofconveraeuce is to be found. Weber et a/ [13]. introduces aunified~ linear approximation technique to evaluate theforms of srraizhtnes , flatness. circularity and cylindriciry.Non-linear equation for each form is' linearized usingTavlor expansion and then solved as a linear program.

'Gilbert et (1/ [15]. develops a methodology furinspecting the form of ally type of smooth surface bycollecting a sample of contact points and introduces aregression method derived from least square support

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Simulation and SynthesisPLMSS-]Oll

vector rezression that finds the deformation shape of suchsurfaces ~\\ith respect to their nominal form. Low andLastra [16], demonstrate that registration failures canOCClU' for several reasons such as insufficient overlapbetween the two surfaces. very large range measurementerrors. insufficient geometric constraints on the 3D rigidbody transformation between the two surfaces and largeclift~rellce in the initial relative pose between the twosurfaces, However. it is well knO\\11 that when the initialpose is closer. the ICP method provides a monotonicalconverzence to the local minima and this IS not the casealways- in practical conditions. The methods described inthe following section aims to address these limitations.

3. Automatic Inspection of Components

The traditional practice of carrying out inspection ofcomplex part . is through the usage of templates or gaugesthat define the acceptable surface geometry in localregions of the part (templates for example are defined atvarious sections of the part), Gauges are usually 11lpairs(e.g. go-nogo gauge) - one that checks if the dimension IS

within the prescribed lower limit of deviation and theother that checks if the dimension is within the higherlimit of deviation, thus capturing the range of acceptablesizes. The advent of C~fI\1 has brought in two scenarios.In the first case, the part to be scanned by the C~l~l IS

positioned in a well-defined manner using external jigs,fixtures or additional features that are built uno the partfor the specific purpose of locating it. In this scenario, thereference frame with respect to which the inspection datais obtained is well-defined enabling easy comparison withthe nominal data, We refer to this as hard registration ofinspection data and the inspection proce s is termed ashard inspection.

All alternative to the above is to scan and obtaininspection data from the part when it has been placed on a(,M1-1 III an arbitrary location without the use of anyfixtures or markers. In this case. the reference frame inwhich the inspection data has been obtained is to bematched with reference frame of nominal model. We referto this as soft registration of inspection data and theinspection process ~is termed as soft inspection, The softreaistratiou approach is clearly more desirable as it islower III cost (no invesrmeurs on complex and precisionjigs and fixtures). flexible (any part that can be mountedon the Cr.fI\1 bed can be inspecred) and quicker. :\11

additional advantage of thi process is that this processalso eliminates tile need for additional locatioualinformation such as tooling hole reference datum.position, perpendicularity and parallelism data of partsthat have to be trimmed after inspection. Further as thedata analysis and reporting activities are carried outoffline: the CrvIM can perform unhindered inspection thus

Page '167 of312

improving its productivity. A~ these processes eliminatethe need for much of the human intervention as requiredin tradi tioual inspection. the whole method lends itself to ahigh level of automation.

The first part of the study deals with evaluation offlatness adopting the Least Square Plane fit approach. TIleLSP fir assists in capturing the flatness of a planar surfaceand also define the parallelism between the two givenplanar surfaces. TIle scanned data points from CMi\l areused to tit the least square plane. The results obtained arevalidated by liar 1 inspection and compared against theLSP tit method. The results show good degree ofCOnCUlTeIlCe<me!any difference in results that may occurcould be attributed to different measurement techniques.algorithms. measuring environment. uncertainties clue tocalibration or human error:

The second pari of the study deals with evaluating theform errors ou analytically defined surfaces and tocarryout its inspection based on the modified iterativeclosest point algorithm as described in [3]. A variety ofalgorithms has been developed to evaluate the form erroron parts. Though the least square method is the commonlyused method in which the sum of the squares of thedeviation from the nominal surface is minimized. it doesnot provide the minimum zone result and often overestimates the tolerance zone resulting: in the rejection ofparts that are within the tolerance specifications. Eventhough a variety of techniques have been developed whichimprove upon the least squares method, many of 'whichprovide evaluation against the minimum tolerance zone.these are mathematically complex and oftencomputationally slow for cases where a large number ofdata points is to be evaluated [U].rhereiixe. we employMICP algorithm 10 evaluate the form error on analyticallydefined surfaces viz.. cylinder. sphere and tori. TIle sesurfaces are machined and the manufactured parts gothrough the procedure of hard and soft inspection. and theresults present close convergence.

·tRegistration methodology

The primary parameters that an ideal registrationalgorithm needs to satisfy [17] are: the algorithm shouldbe fast. ha'> to be accurate. where after successfulregistration. the distance between corresponding points inthe region of interest is less than O.Imm. which is thewell-known Target Registration Error iTREj parameterintroduced by Maurei er al [1 ][21]. In addition thealgorithm has 10 be robust. automatic and reliable. Thissection outlines the basic concepts of least square planefilling adopted tor evaluating the t0I111 error for planarsurfaces and then details the implementation of modifiediterative closest point for registration of analyticalsurfaces.

•

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4.1. Least Square Plane (I.SP) fit

Giveu a set ofpoints PER" . 'where 11=3 and P

= {Pi} for i:: 1..... N

representing the cartesian coordinate measurements.Given the equation of a plane as ax thy +cz =d.Let r, be the distance of point i i]:0111 the plane and

r, = ax i + by t + CZ i-cl = 0 (l )with

r,=((lX, + by, -r cz, =d )

Given a set ofN points (a point ihas coordinate x. y, z).

we wish to minimize, Q.

Q :::...±[(=, -j- b..•..i

+- c:- i _.d )2 ]I,,"l

(3)

From (3)

dQda

:-<:L[2x; ((1.\; + by, -I- C':'r - cl)] = 01",,1

(4)

dQde

N2:J2::j(axi +bl'l +cZ'r-d)]=O1",,[

(6)

dQdel

N:L[--2(oxi + 1~1';+ c: r -- d)] = 01",,1

Equation (7). noting that L(d)::: Nd can be rewritten as

cl :::: (IX 0 ·'l·in·o + cz c> •

\,•.hereAO ::::::Lx/N. yo:c:L: y/N. 70 :::::L: z,/N

Equation (8) shows that the best tit plane passes throughthe centre of mass. Subtracting the centre of mass from

Pane Isa of 3 12

each point and substirunng 111tOequations ~ - 6, we get aset of simultaneous equations which can be written as:

\VP=O (9)

We need to solve equation (9) to obtain LSP.

Equation (9) can always have a trivial solution for a = b=c= (I

To avoid tlus trivial solution we need to imposeconditions on the coefficients of the plane. The mostcommon condition beins.

il" - b~ - c2= 1 (l0)With the condition (l0). solution to (9) becomes aneigenvalue problem where

\\'E=YE (11 )

Where V =eigeuvalue and E =eigenvector and equation(11) \\111return three eigenvalues and 3 x 3 eigenvecror.

The eigeuvalues \n11 be the snm of the squares of thedistances and tile eigeuvector will provide the three sets (aset is a column of the matrix E) of a. b. c values.One then needs to choose the set a. band c associatedwith tile smallest of the eigeuvalues. It should be notedthat:

(a) The three sets of a, band c contained in Eare orthogonal to each other and representthe best. intermediate and worst planesrespectively.

(b) If the eigenvalues are similar or same withinthe margin of error. this suggests that thedata coordinates are either degenerate orsymmetric.

In summary, TO calculate LSP we need to get theeigenvalue and eigenvectors of W.

4,2. ~.Jodified Iterative Closest Point algorithmThe registration procedure adopted in this paper 15

based on the well kt10\\11 Iterative Closest Point (ICP)algorithm [4]. The ICP algorithm is based 011 determiningthe correspondence between points in two datasets. In the

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present approach we use the measured points from aCoordinate Measuring machine lCNn,,!) to represent theinspection point dataser. The nominal point daraserspecification of the pan is available from the analyticalgeometry and is used for both registration and comparisonand this allows the inspection task to be performedindependent of CAD system. TIle schema for automatedinspection is shO\\TI in fig. 1 where the part inspection dataset is obtained in the Inspection Coordinate System (ICS)and the nominal data set is obtained in the ModelCoordinate System (MCS) [3].

CNominal Part data .rr M3J1lJlil<.'l~sred part J-MCS_ J'. res

;- Rcgi>;lrntion.. "'I!Correspondence &-

Fig. 1- Schema tor automated component inspection

TIle regi stration procedure consists ofestablishing a matching between two sets of threedimensional point data sets called tile Part inspectiondataset P and the Nominal point data set ~1. where theirpoint elements are defined as

P = {Pi} for i = 1. ... Np and xr = {Mi } for 1 = 1. .

Nm where Pi and 1'-1;E R 11 • where n=3 and m> >p.

The spa tial translation between two sets is a linear

transformation vector in R 3 and is tile difference in thelocation of centre of gravity of both the sets. For therotational alignment of the two point sets we mequatemion algebra [19].

Here. the quarernion is a 4D vector denoted as q= [qo,qi. <12. q3] and is used to represent the 3D rotation whi eh isof practical importance TO us, TIle norm of a quaternion ~(q) is conventionally the sum of the squares of the tomcomponents. The 3x3 rotation matrix R generated by aunit quateruion is given as

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,q; +q; -q;-'1;R"< 2«1,'1, '-''1,<1,)

'.c('Lq, -<lA,)

:~(q,'l·I.-<j,<1,}Iq;,- q~ q.' -q;)clq,'1, +'10<1,)

.'.1'11,'1., .•. <1.'h I .]21'1,'1.," '1.'(,) (1)

, ..••• 2'1;; +q; -s; -e:

Theref re. the coordinate transformation which involvesthe rotation matrix R and the translation vector T fromthe part inspection coordinate system to the modelcoordinate system is solved using the quaterniou algebra.where

y1i =R;,P+ 1'1 (2)Here. Mi denotes the coordinates in the model frame andP denotes the coordinates in the part inspection frame. Anecessary condition for the current algorithm is that theinspection data set is assumed to be a small subset of thenominal point set which is represented by a large point setwithin the limits of available computer resources andacceptable accuracy ro achieve the desired tolerance.

The process of modified K'P can be classified in t'KOrages.

i) For every point in Wd iE [I, Np]. the closest point{M,}. i E I:L N,,,1 in the Nominal Point set is found.

A tilSI iterative method is adopted for establishing thecorrespondence with the closest points and \Vhl:.':11thecomponent region have large curvature. the input nominalpoint set need to be dense so as to define the geometryaccurately.ii i The transformation as given in equation (1) above isapplie I tor every point ill the inspection points set Pk Thetransformed inspection point set at say the /h step ofiteration i ' now closer to its corresponding points M illnominal point data set. The mean squared objectivefunction to be tninimized is the distance function givenby:

1 r.!'.l., i, 2d.> _·----"IIT R -M 11, L.. " I< I<

mK~l

The process enumerated 111iterative steps (i) and (ii) is

repeated lIS1l1gthe updated inspection point set p~until d,converges to a predefined threshold tolerance [20] orwhen a predetermined number of iterations is reached.

111 representing the nominal point data set in the currentwork. the point data set is generated as a topologicallyuniform rectangular grid in the parametric space (11. V).

The least square is calculated between points incorrespondence. The objective function minimized is thesum of squared distance" divided by the number of pointsin inspection data set. Since the points in the nominalpoint data are sampled. the actual error need not be tiledistance between the points in correspondence or theaverage of the square of this elTOLThe actual error that isof interest is the normal distance from pari inspection setto the nominal surface which is obviously not captured inthe procedures adopted rill now. We define the error as the

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distance between the. inspection point and the surface inthe vicinity of its corresponding point in the nominal pointdata set. TIle vicinity is defined by facets between fourpoints in close correspondence with the inspection point.The procedure'is illustrated in the iig.2 below.

Fig. 2 - Local quadnlateral facet

Here. Mj. M::\.M, and M, are the film closest points inthe Nominal Point data set 1v110 the part inspection pointsay PI which can be represented as four triangles ill 3Deach of which will define an analytical plane. Thelocalized region based approach captures the normaldistance of PI to each of these triangles. the minimum ofwhich establishes the closest deviation of themanufactured component to its native analyticalgeometry. This modified approach elimmates thepossibility of two in peciion points having the sameclosest point from the geometry 'et. It should be observedthat the least square norm to define the error acceptabilitycriteria fictitiously reduces the error to very low values.This becomes more pronounced when there are verylimited numbers of ourliers against a large number of wryclose marching points. This will lead to erroneouslyaccepting inspection points which otherwise are far awayfrom the acceptability criteria. The local quadrilateralfacet approach provides a practical technique i.n findingrhe absolute distance error a" the least square" methoddoes not necessarily define the accurate part tolerancedeviation as explained above. Computing the distancebetween the inspection point and the tangent plane at itscorresponding point will also nOI be the right measure forthe same reason that the corresponding point is obtainedfrom a sample and therefore may not he the actual closestpoint on the surface. Tangent plane at this point maytherefore not be the correct approximation of the surfacearound the closest point. This point wise distance could bewell above the acceptable tolerance. whereas tile leastsquare distance may be well below the permitted toleranceill the iterative scheme thereby leading ro a wrongconclusion of accepting: the erroneous (out of tolerance)component. Thus it is more appropriate to use the pointwise distance criterion to establish the manufacturingdeviation rather then the least square convergence

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criterion. This in a way ascertains the application ofL 'K

norm for minimizing the objective function rather than the

L" norm.

5. Implementation and results

The algorithm based OH Least. Square Plane fitand the Modified Iterative Closest Point was evaluated forestablishing the form error by carrying out inspection oninnltiple cases of components defined by analyticalgeometry. These included Cl parallel bar, cylinder. sphereand tori. The results obtained by inspecting thesecomponents are described below. The results demonstratethe performance of the above methods in a real worldinspection environment.

5.1 Iuspecriou of Parallel Bar by LSP methodThe inspection of the Parallel Bar was conducted on Cl

Cl\ll\c\ as shown in Fig.". The inspecuon points werecaptured randomly over the entire surface of the artifact toestablish the flatness error. Flatness tolerance which isdefined as zone between two parallel planes. within whicha surface must lie. is a fonu tolerance which does not needto be related to a datum. The inspection data genera redfrom the C]\I]\J for the parallel bar was applied toestablish the error by the least square plane fitmethodology as detailed in Section 4.1. The hardinspection result for the parallel bar was also obtainedfrom the c:vn\L Both the inspection results showed thatthe error varied from -0.008 mm to O.OI1:'illllU. thusdisplaying a incredible convergence of the inspectionresults from son inspection methodology followed m thispaper with the hard inspection results carried OUl OIlCJ\.EvL Fig.4 shows flatness error variation by the twomethods to be ill very .Qoodconformance.

Fig.J Inspection of Para lid Bar on CM.fvf

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O_L'I'l!:·

I xCMM 1"'f"'''I''''' I

O.f.J1f.l '" l.SP Mt..''"ihod ~x.

O!)!)!;"; ~ •• '" "r; " ".. "" ".s "(J.DDD ~ x~

"g J<"-W x

·'J.DD~; " "w." x

.{} 0"10 )t

~-0.D15

s 10 15 ::0 25 10 :)S

Fig:.4 Comparison of Hard and son inspection results forPlanar surface

5.1 Cyliader:A cylinder of 4011un diameter was machined 011 a

ruruing centre and the part was inspected on a CM.1vlasshown in fig 5. The graph comparing the inspectionresults carried out both by bard and soft inspection is inJig.6 'The hard inspection results show the machining errorrange from 24.4 micrometer to 35.6 micrometer while thesoft inspection results show the machining error rangefrom 1.3rllicrOlneler to 34 micrometer thus showing auexcellent conformance of the inspection method

Fig.vHard inspection of Machined Cylinder

[J03(:i ..

0.024·

E' [10;).:,

~ [)(J:11 ..

~~ 0.0;)0·

.5~ unza".•::ii [J026 ..

............MICP I,r',:'~>cbcnJ\~ult:u

fJ012 . ·····························_··1211 4D 60

'''Sp<:1:I;On points

Fig. 6 Comparison of Hard and SoH Inspection results forCylindrical surface

5.3 TorusA torus which is. a surface of revolution and

azimurhally symmetric about the t- axis. with major andminor radius of n..'i mm and .IOmm, thus having anaspect ratio of 2.75 with toroidal and poloidal angles of1 SOo re~pecti\-elywas machined on Vertical CNemachining centre. The machined ring torus wasinspected on a Cl\·Uvl as shown in fig 7. The graphcomparing the inspection results carried OlH by hard andsoft inspection is ,hO\\1\ in fig.8.The hard inspectionresults show the machining error range tJ-OIU .'i.7micrometer to 38.'\ micrometer while the son inspectionresults show the machining error range from 3.4micrometer to ,11.2 micrometer rhus showing an excellentconformance of the inspection method.

Fig 7. Hard inspection of Machined Torus

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, .....OH1 I tl MICP ~15~~!<,!iC<Jl r)11?e-Jo'li I companston of CMM vs MICPg,n.(~ •. GUM il1"Sp1!cticn fndt'.md for Torus

oc.oo ••.••••••••••••••••••••••~ 1.0. ••••••••••••. ! •••••••• • •••••• M•••

IUI)J:(l •.

1il 15 2U .c5 3D ~ 40 45 !·D ss !IDlnspection pomts

Fig.S Comparison of Hard and Soft Inspection results forTorus surface

5.4 SphereA reference sphere of 25ml1l diameter as shown in

fig. ') was taken for carrying out hard inspection on CM\{The hard inspection results showed that the error on thespherical artifact varied from 0 microns to a maximum of(1 micrometer 'while the soft inspection results showed theerror variation from 0 to 9.83 micrometer. thus showing avery good conformance of results. Fig. 10 shows thecomparison of results derived from the two methods.

Fig. 9 ITaI'd inspection of Spherical Artifact.

DIJJ:?·· ..·

O..:I:IQ·

e' 0.0,)9 ...sg D~(le .•.l~

" Q.Oi)4 ..'r:~ DGm·"

I>JDO·

·!}~o:?

I I

···················T····················1············· y •••••

:':0 3D ".~ :;0

Fig. 10. Comparison of Hard and Soil Inspection resultsfor Spherical Sm'11iCe

6 Conclusions

A form error evaluation method for different surfaceprofiles. which requires very little human interaction wasproposed and evaluated. TIle tolerance specifications asper the standards were made applicable for the variousanalytically defined shapes. The inspection plan based onboth online and offliue methodology was followed withdata registration carried out employing the LSP fit andmodified lCP algorithm. The soft inspection carried out011 the machined parts demonstrates their acceptabilitybased on the tolerance specifications. The soft inspectionresults were verified against the hard inspection carriedout using a Civil\.1and the results show close conformance.Validation of the inspection procedure by usinganalytically definable objects have showed that themethodology adopted was indeed capable of inspectingobjects of complex shapes represented by facetedgeometry and the future work would be to improve thegeneral applicability of the proposed approach. Further. iti well documented that when the initial pose is closer. theK'P algorithm provides Cl monoronical convergence to thelocal ml1l1111a.TIle method being sensitive to initialorientation. we propose to address this issue by the usageof a spherical gauge to cater to inspection conditionswhere the ICS and ivIes are far off. and this investigationwould be part of our upcoming research activities. -

Appendix A. Standard Mathematicaldefinition of tolerance zones [14J:

(i) Flatness. Flatness 15 the condition of a surface havinsall elements in one plane. A flatness tolerance specifies ~tolerance zone defined by two parallel planes betweenwhich the surface must lie. A flatness zone is a volume

consisting of all points P satisfying the condition

It. (P - A) 1~!..2

where

t = the direction vector of the parallel planes defining theflatness zone

A = a position vector locating the mid-plane of tile sizeof the flatne s zonet = the size of the flatness zone (the separation of theparallel planes)

(ii) Cvlindrtcity: A cyliudricity tolerance specifiesthat all points of the surface must lie in some zonebounded by two coaxial cylinders whose radii differ

International Conference 011 Trends ill ProductLifecycle, Modeling,

Simulation and SvuthestsPL\1SS-]OI1

by the specified tolerance. A cylindriciry zone is a volume

between rwo coaxial cylinders consisnng of all points Psatisfying the condition:

• - tIi T x (P - A) 1- r 1~-2

where

T = the direction vector of the cylindriciry axis

A = a position vector locating the cylindriciry axisr = the radial distance from the cylindricity axis to thecenter of the tolerance zonet = the size of the cylindriciry zone

(iii) Ctrcularitv (Roundness): Circularity is a conditionof a surface where:(a) for a feature other than a sphere. all points of thesurface intersected by any plane perpendicular to an axisare equidistant from that axis:(b) for a sphere. all points of the surface intersected byany plane passing through a common center areequidistant from that cenrerA circularity tolerance specifies a tolerance zone boundedby two concentric circles witlun which each circularelement of the surface must lie. and applies independentlyat any plane described in (a) and (b) above.A circularity zone at a given cross-section is an annular

area consisting of all points P satisfying then conditions:. -T· (P-A)=O

and- - t11(P - A) 1- r !~-

2where

T = for a cylinder or cone. a unit vector that is tangent to

the spine at A _ For a sphere. t is a unit vector that

points radially in all directions from A

A = a position vector locating a point on the spiner = a radial distance (which may vary between CIrcularelements) from the spine to the center of the circularityzone ( r > 0 for all CIrcular elements)r= the size of the circularity zone,

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