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DOI 10.1007/s00170-003-2004-4ORIGINAL ARTICLEInt J Adv Manuf Technol (2005) 26: 559564Patrick Martin Fabien Schneider Jean-Yves DantanOptimal adjustment of a machine tool for improvingthe geometrical quality of machined partsReceived: 28 July 2003 / Accepted: 24 October 2003 / Published online: 8 December 2004 Springer-Verlag London Limited 2004Abstract The manufacturing industry has to improve the qualityof its manufactured products. It is the reason why industry needstools and methods that make the control of that quality possible.In this paper, we propose a method that allows an optimal ad-justment of the machine tools in order to respect at best a set ofstandard functional requirements applied to a part. The require-ments have to use the maximal material requirement defined byISO standard.The proposed method works out a geometrical model. Inter-changeability boundaries enriched with adjustment parametersconstitute the basis of the model. Comparison between this ge-ometrical model and a first manufactured part allows us to ob-tain the variations of adjustment parameters. These variationsdirectly correct the machine tool being certain that the follow-ing parts respect at the very best the functional requirements.At least, this method brings the first step to statistically controla process.Keywords Adjustment Geometrical quality control Machining Tolerancing1 IntroductionNowadays the market fluctuation and the fashion ask for moreand more new and different patterns. As the batch size decreases,it is necessary to design and manufacture the best quality prod-ucts at lower cost while reducing delays. So the concept of con-current engineering 13 must be used, it is now well known inindustry as well as in academic areas. The design of the parts,the process planning, even the production system must be madesimultaneously.P. Martin (u) F. Schneider J.-Y. DantanLaboratoire de G enie Industriel et Production M ecanique (LGIPM),(Production Engineering and Mechanical Production Laboratory),ENSAM Metz, 4 rue Augustin Fresnel, 57078 Metz, FranceE-mail: patrick.martinmetz.ensam.frTel.: +33-3-87375465Fax: +33-3-87375470Figure 1 shows the different items involved in integrated de-sign and manufacturing. In manufacturing engineering, we seethe interactions between the product (or the workpiece), themanufacturing process (machining, forming, assembly, etc.) andthe manufacturing resources (machines, tools) in order to obtainthe manufacturing process, but also the manufacturable work-piece and even the manufacturing system. The aim of the productdesign consists of defining all the operations, resources and pro-cesses necessary for obtaining a real mechanism (set of assem-bled parts) that best fits functional requirements. This integrationmust answer to several objectives: quality of the product, duetime, production reactivity, etc., and constraints: cost, market,safety, laws, etc. In order to solve this wide problem, methods,models and tools can be used. Each of them must be represen-tative for each user (design office, manufacturing, marketing,production, etc.) and coherent along the several phases of theproduct life cycle.In this paper, we are focused on the geometrical quality ofmanufactured products. One way of improving product quality isin controlling the geometrical tolerancing by:- Either adjusting machine tools in order to respect at the verybestasetofstandardfunctionalrequirementsappliedtoapart.- Simulating the geometrical effect of manufacturing faultcauses and adjustment parameters in the respect of functionalrequirements.Therefore, we propose some tools and methods that allowus to solve this first point. We work in a manufacturing contextwhere mechanisms are mass-produced. The parts have commondimensions (a few hundred millimetres) and every type of part isproduced apart from each other. We suppose they are rigid con-cerning the local distortion and the global distortion. This is thereason why adjustment and tolerancing are able to control onlymanufacturing faults greater than the real distortion (a few hun-dredths of a millimetre at least). Moreover, we are able to link thevalue of adjustment parameters to the value offunctional require-ments, which are applied to a part of a mechanism. In this way,the aim is to control the adjustment parameters on the machinetool , which allows it to satisfy the functional requirements.560Fig.1. Reference diagram of our ap-proach2 Adjustment task compared with tolerancing taskTo understand the problems of adjustment, at first we have todefine the tolerancing task. Tolerancing task is a subset of thegeometrical definition of a mechanism.Limited to the geometrical point of view, design productsneed two studies (Fig. 2). A first one consists of choosing designed solutions andmanufacturing processes which will carry out a real mech-anism. The real mechanism is the answer to the functionalrequirements. The main aim of this study is to obtain a tech-nical drawing. The drawing takes finely into account allthe relations between parts and especially the manufacturinggenerations. The second study analyses and validates the result of the pre-vious study. Two aspects of the mechanism are studied at thesame time. A dimensioning that defines the nominal geometry. A tolerancing that takes aninterest inthe small deviationsbetween the real geometry and the nominal geometry.Thus, we are able to give now the aim of tolerancing accord-ing to the product design 4:The aim of tolerancing consists in controlling the small de-viations between the real geometry and the nominal geometry ofa mechanism in order to respect at the very best its functionalrequirements.If the problem is to control the effect of small deviationsbefore manufacturing, we have to solve a simulation in whichproduct drawings show the result.If the control of small deviations takes place during manufac-turing, we have to adjust machining-tools.Thus, adjustment is the practical and technical aspect of thegeneral tolerancing problem. Adjustment and tolerancing havethe same aim.3 Adjustment of machine tools3.1 Functional requirements and ISO languageRegarding the definition of adjustment, optimal adjustmentneeds a direct expression of functional requirements. Usually, as-sembly and positioning are two functional studied requirementshaving a geometrical expression.The concept of boundary cleverly translates the assemblycondition. A part of a mechanism fits all the other parts if none ofits manufactured points violate the interchangeability boundary.ISO standard 5 allows the use of the virtual condition with themaximum material requirement. This condition describes almostperfectly the concept of boundary and so the functional require-ment of assembly. A manufactured part fits for use if it is entirelyon the good side of the interchangeability boundary. A part is allthe better if its matter is near the boundary without violating it.Therefore, the deviation, and more exactly, the smallest devia-561Fig.2. Geometrical definition of mechamismtion between the part and the boundary evaluates numerically therespect of the function.On the other hand, the ISO standard language is not able totranslate correctly the functional requirement of positioning. Infact, the standard language is not able to take strictly into accountthe influence of variation of form or the influence of local dis-tortion. The principal effect is that good parts according to thetechnical drawing do not fit the other parts and good parts ac-cording to the function are refused 4. Thus, the product is notoptimal.Actually, no one is able to optimally adjust machine toolsaccording to the positioning condition expressed in ISO lan-guage. The ISO geometric model of tolerances takes into accountthe maximal form deviation of a feature but not the form faultdistribution in the tolerance zone. Thus, the position deviationbetween two parts in an assembly is not predicable with a realis-tic correlation. It is the reason why this paper proposes a methodtaking into account only the assembly condition. Moreover, theassembly condition must use the maximum material requirementand the virtual condition in order to tend towards optimum.Fig.3. Adjustment: quantities and uncertainties3.2 Manufacturing deviations, adjustment parameters andmeasurementFigure 3 shows the different quantities appearing in the ad-justment and uncertainties () disturbing adjustment for a partmachined.Adjusting a machine tool demands connecting the active partof the tool with the machined surface. This does not succeed thefirst time because there are a lot of errors or uncertainties dueto the adjustment operation and the machining process as wellas the static or dynamic behaviour of the machine tool (the toolor the workpiece). These uncertainties are the causes of manu-facturing deviations. To control the influence of some uncer-tainties as screw, displacement reversibility or slideway defects,machine-tool builders put some adjustment parameters into thenumerical control unit or adjustable stops on conventional ma-chine tool. The modification of these parameters allows move-ment of the uncertainty zone compared to its nominal position.The dimension of this displayed quantity (adjustment parameter)is the length.562In return, the dimension of the machined quantity is morecomplicated, it assures the respect of the functional requirement.So in practice, for adjustment corrections, these requirementsmust be translate into a dimension compatible with a length (di-mension of displayed quantity). Therefore, the aim of the meas-urement task is to evaluate the respect of the function and to givea measured quantity compatible with the adjustment parameters.The difference between displayed quantity and measured quan-tity gives the value of the adjustment parameter correction.3.3 Adjustment model for the determination of the correctionWe define a model built on a geometrical representation of the in-terchangeability boundary. Variation of some dimensions, whichcorrespond to adjustment parameters, allows us to distort themodel. For example, this allows us to fit the best adjustmentmodel to the geometry given by the measurement of the first(or a couple of) manufactured part on the coordinate measuringmachine. After moving and distorting the model, the variationsof dimension give the direct value of the corrections of the ad-justment parameters. Therefore, after having introduced thesecorrections, the following manufactured part has more chancesto fit the best interchangeability boundary and consequently thefunctional requirement.4 Geometricadjustment methodTo explain the proposed method, we use an application thatis representative of the industrial adjustment problem. The fol-lowing technical drawing (Fig. 4) defines a manufactured part(a cover) in accordance with the words of the ISO 2692 standard.Its first function is to respect an assembly condition: when thecover lies on the A plane and when a shaft goes through the Ccylinder, two screws have to fit with the part. The cover is manu-factured on a conventional machine tool, it lies on the A plane,a drilling tool drills both holes with a diameter of 12.5 mm.A boring tool finishes the diameter of 28 mm. Three adjustablelongitudinal stops put eachtool inits work position. The machinegives the other cross-position and the direction of drilling.There is no difference with a numerical machine tool; onlywe deal with numerical stops.Fig.4. Technical drawing of the cover4.1 Geometrical adjustment modelThe geometrical adjustment model is a construction of geomet-rical features based on the virtual condition. The features lay onexact positions. This model must include the feature (here the Ccylinder) defining a datum using a maximal material requirement(M). Minimal geometrical reduction elements and dimensionalcharacteristics represent each feature (point, vector, and radiusfor cylinders; point and vector for plan) (Table 1).Then the model is parameterised according to the adjust-ment possibilities of the machine tool. An L1 and L2 quantityparameterises the longitudinal hole positions. R1, R2 and R3parameterise hole diameters (Fig. 5). L1, L2, R1, R2, R3 arecharacteristics in harmony with ISO 17450-1, in other words,they are near key process parameter according to Boeings defin-ition BOI-00: O1O2 = L1 k , O1O3 = L2 k .4.2 Initial adjustment, drilling, and measurementFirst, the machine tool is initially adjusted according to thenominal dimensions of the part. Next, a first part is machined.A measurement by using a coordinate measuring machine ex-tracts points from the surface of the manufactured part. Now,a set of measured points Mi represents each feature (MiPl1,MiCy1, MiCy2, and MiCy3).4.3 Deviation between the adjustment modeland the extracted pointsWe search now for the best fit between the adjustment model andthe extracted points. We have to specify the deviation betweena measured point Mi and its own point I belonging to the adjust-ment model. For this purpose we use the principle of a mowingTable1. Geometrical features of the partFeatureMinimal geometrical reduction elementParamterPointVectorPl1O2?knoneCy1O1?kR1Cy2O2?kR2Cy3O3?kR3Fig.5. Geometrical adjustment model563of the initial adjustment model 5, but using the small displace-ment torsor defined by the moving ( Di) of point I (Fig. 6). Weuse a direct expression of the deviation (ei) between the meas-ured point and the nominal point of the moved model.This method presents the constraint to be able to determi-nate the nominal point of the moved model by the knowledge ofthe measured point and the geometrical properties of the nom-inal feature. However, this is always possible with the usualmachined feature (analytically defined geometric shapes): plan,cylinder, sphere, cone, parabola, gearwheel surface, etc.The knowledge of the minimal geometrical reduction elem-ents in their initial position defines the initial adjustment model.A small displacement torsor (SDT) (relation 1) expresses for-mally the moving of the initial reduction elements.?Ipd?=S / R?,DOS?uvwO,Rrelation 1This relation gives the displacement parameters at the pointO projected on the base R:- , and are the components of the small angular displace-ment of S in R base,- u, v and w are the components of the small displacement intranslation of point O belonging to S.This SDT can also be described by a 44 matrix (relation 2)in homogeneous coordinates.D =0u0 v0w0001S,Rrelation 2Fig.6. Adjustment principleFig.7. Deviations working outThese mathematical relation allows us to easily calculatedthe different models (nominal, moved, etc.) of each feature (de-fined by its geometrical reduction elements) and its particularparameters (characteristics) attached to the part definition.The moved reduction elements describe the adjustmentmodel. The deviation (ei) between the measured point (Mi) andthe nominal point (I) is formally evaluated from the moved re-duction elements. The original parameters of the initial modelallow its distortion by addition of a variation (equations 2):R1initial R1 = R1initial+R1L1initial L1 = L1initial+L1R2initial R2 = R2initial+R2L2initial L2 = L2initial+L2R3initial R3 = R3initial+R3equations 2Thus, for every shape (plane, cylinders), the deviation (ei)ex-presses itselffrom the reduction elements ofthe initial model, themeasured points, the unknowns (, , , u, v, w) of the small dis-placement torsor and the variations of the original parameters ofthe model (L1, l2, r1, r2, r3).Figure 7 shows the different operations that yield the devi-ation (ei) between each measured point (Mi) and its nominalpoint (I).The model represents the nominal part attached to the ma-chine tool, the original parameters correspond to the adjustmentparameter (corrections) of the machine tool, and each gap (ei)describes the deviation between the first part and the nominalpart.The unknowns (, , , u, v, w) allow us to fit the differ-ent datum of the machine tool and the coordinate measuringmachine.A variation of unknowns and parameters alters each devia-tion (ei).4.4 Working out the corrections of the adjustment parametersThe working out the corrections is equivalent to the resolutionof an optimisation problem under constraints. The target of theresolution is to find the moved and distorted model that best fitsthe measured points. Nevertheless, the measured points do notviolate the limits of the model.The mathematical description is:Targetbest fit between part and adjustment modelwe search the minimum of the maximal deviation:max(|ei|) minimum.564Fig.8. OptimisationFig.9. Best fitting of the adjustment model according to the partConstraint none of the measured points violate the limits of themodel i, ei?0, if the direction of normal vectorgoes out of the matter.Parameters unknowns of the SDT (,u,v,w) and its par-ticular parameters of the model (L1,l2,r1,r2,r3).The result of the optimisation under constraints directly givesthe values of it particular parameters (corrections) so that thefollowing part best fits the function requirement. Use of clas-sical solver software can solve this optimisation analytically ornumerically.Figure 8 shows the return of the improvement loop.The Fig. 9 shows the final relative position at the best fit be-tween the adjustment model and the first part.We have applied this method on some real machining. Wenote a consequent immediate improvement of the machine tooladjustment after the first part. Indeed, this procedure corrects theinitial static adjustment deviation but leaves a little fault corres-ponding to the machining deviation of the first part. Generally,the static adjustment fault is greater than the manufacturing fault.We have defined a strategy to improve the machine tool ad-justment and correct the residual machining fault, taking intoaccount the following parts. With simple cases, the correction cjof a parameter p after the jth part is equal to the opposite varia-tion of the parameter pjobtained with the jth part, divided by jcj= pjj.equation 35 Concluding remarksThe propose
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