MODELLING OF SYMMETRY MEASUREMENT UNCERTAINTY USING MONTE-CARLO METHOD

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1 8th International DAAAM altic Conference INDUSTRIAL ENGINEERING April 2012, Tallinn, Estonia MODELLING OF SYMMETRY MEASUREMENT UNCERTAINTY USING MONTE-CARLO METHOD Kulderknup, E Abstract: Symmetry deviation has importance for details which operating jointly as the moving parts of exact devices. The measurement of symmetry deviation has difficulties by main reason that there exist problems to present the datum surfaces for measurement. This paper presents measurement uncertainty estimation model for symmetry measurement. Novelty is, that the model takes account also production operation and simulation of uncertainty estimation is achieved using Monte-Carlo method. Key words: symmetry deviation, measurement, Monte-Carlo method 1. INTRODUCTION Symmetry deviation has importance for details which operating jointly as the moving parts of exact devices. The measurement of symmetry deviation has difficulties by main reason that there exist problems to present the datum surfaces for measurement. The real datum surfaces itself have geometrical deviation. Second problem is caused by circumstances that symmetry deviation depends on greatly from concrete production process. This paper presents measurement uncertainty estimation model for symmetry measurement. Novelty is, that model takes account also production operation and simulation of uncertainty estimation is achieved using Monte-Carlo method. For Monte-Carlo method is important to have exact model of combined measurement and production process as cumulative probability function F(x). Probability function F(x) is easy to bind to the measurement uncertainty, which can be found on the basis of uncertainty estimation model. Each correction in the model has its uncertainty and those shall to be estimated. Some of them can be found through practical experiments and some of them through calculation. Giving various values for those components depending on concrete operations can be found model Δ sym for various situations. Main tasks of this work were to have model suitable for use in practise This model allows to choose optimal production operation, to have higher accuracy of assemblies, to take account mate detail in use and to give some opinion which uncertainty components are representative and how they acting in practice. Above allows to have higher production and measurement capability. 2. MODEL OF SYMMETRY MEASUREMENT Symmetry deviation zone is limited by two parallel planes, a distance Δ sym apart,

2 symmetrically disposed about median plane with respect to the datum [1]. Measurement scheme is shown in Fig 1. Δ SYM a Fig. 1. Symmetry measurement schema On Fig. 1 line presents real details symmetry axes, the datum is symmetry axes for measure and a and c are measuring instruments for plane A and C. Main problem is to find the ideal symmetry axes for the measure by measurement procedure. This means that symmetry of the measuring instrument for plane a and c (Fig 1) shall be the same that symmetry axes for measure during movement across the detail. Symmetry deviation Δ SYM can be calculated initially through measuring instruments a and c indication by Equation: Δ SYM = max { + a i + c i } (1) where a i and c i are the measuring instrument indications and is the reference value. The symmetry measurement model can be expressed exactly taking account influence factors as follows: y = x MI SR MF SC + SCO + SA (2) ENV where x is the measurement value of measure Δ SYM, K MI is the correction from the measuring instruments calibrations, c K RE is the correction from the reading of indication, K DA is the correction from the datum deviations, K MF is the correction from measurement force, K SC is the ideal symmetry axes deviation for measuring instrument and K ENV is the correction from the measuring environment. For obtaining the real detail symmetry value huge importance has the production process which shall be added to the Equation 2 as separate correction K PROD. 3. UNCERTAINTY OF SYMMETRY MEASUREMENT 3.1 Uncertainty components The designer gives often high accuracy values for the tolerances for measures including for the symmetry deviation. To obtain realistic values in practice, tolerances should be optimised and uncertainty estimation would facilitate it. Uncertainty estimation allows prioritising the factors including producing, measurements and testing possibilities and measurement chain optimisation. During measurement of parameters, components having importance for uncertainty estimation are involved with various subparameters. Uncertainty of symmetry deviation Δ sym can be expressed through measurement model (2) giving concrete values for the influence components. For the batch of detail Δ sym shall be included summary uncertainty of production process. Combined uncertainty model u(δ sym ) for batch of details can be expressed as: u(δ sym ) = g(l meas, Δ meas, Δ prod, Δ meth, Δ bsurf, Δ var ), (3) where L meas is the measuring instrument indication, Δ meas is the measuring instrument indication correction on base of calibration, Δ prod is the correction from the production operations, Δ meth is the correction taking account measurement

3 method, Δ bsurf is the correction from datum surface determination and Δ var is correction from other various influence factors. 3.2 Uncertainty components values Uncertainty components presented in the general model (3) have next subcomponents from influence factors F i : - caused by measuring instrument: measuring instrument dimensional parameters; environment and its variation during the use of measuring instrument; calibration procedure of measuring instrument; measuring instrument specificity and its behaviour during measurement especially sensitivity and stability; - caused by production process: quality of the production and technological process, machining accuracy; - caused by measurement method: tolerances, object versus measuring instrument, measurement force, symmetry axes locating; - caused by measurement object: design, size, materials and chemical quantities and tolerances, surface roughness; - environment: humidity, temperature, vibrations, noise, altitude, interference fields, barometric pressure, pureness; - human factor, operator: sensitivity, competence, experience, commitment. Above factors that influence to the measurement can be shown as a structural scheme in Figure 2. This is fundamental for the further uncertainty estimation and has great similarity with circuit boards measurements handled in [2]. Parameters presented in Fig. 2 give components, which have influence to the uncertainty budget. The effect of some of these components may be little as long as they remain constant, but could affect measurement results when they start changing. For example, the variation of datum can be particularly important. 3.3 Uncertainty components values Combined uncertainty u is found through the estimation of standard uncertainties caused by individual factors F i. shown in art Operator Production process Measuring instrument Accuracy Design Calibration Visual acuity GPS Reading rounding Attentiveness Process quality Measurement probe Competence Machining accuracy Commitment dimensions and variation ehaviour during test Measurement of symmetry deviation Δ sym = f(f i ), where F i are factors Humidity Surface roughness Object vs. measuring instrument Vibration Size Stability Tempera- Design Measurement ture force Interference Tole- Datum fields rances location Pureness Material Probe tolerances Object Measurement method Fig. 2. Symmetry deviation influence factors scheme. Uncertainty tree Combined uncertainty u is calculated by next equation: uprod + uhf + umi + umet + u = (4) uec + uoj In the Equation (4) are given the main grouped factors accordingly to the model (2). Each uncertainty component has a concrete sensitivity coefficient. In equation (4) sensitivity coefficients are shown as 1, i.e. uncertainty components are estimated on the same influence level. In Table 1 is an example of uncertainty components values given in structural

4 scheme in Fig.2 for one measure value of object. The values are estimations collected during experience and measurements in the production process. Factor F Sub-uncertainty Uncertainty value u, μm u PROD Design 1 Process quality 1,5 Prod. accuracy 2 u HF Competence 1 Experience 1 u MI Dimensions of 1 probe Calibration 2 Stability/behaviour 1 u MET Datum locating 2 Measurement force 1 Stability 1 u ENV Vibration 0,5 Temperature 0,2 u OJ Material 0,5 Surface roughness 0,5 Table 1. Uncertainty components values by Δ sym = 0,020 mm, u(δ sym )= 0,005 mm 4. SIMULATION USING MONTE- CARLO METHOD 4.1 Cumulative probability function for symmetry measurement Symmetry deviation simulation can be presented using Monte-Carlo model as F(x) = P(x), where F(x) is cumulative probability function and P(x) is probability of symmetry deviation various values. Probability can be linked to the expanded uncertainty U, as P(x) = U(Δ sym ) and present as shown in Fig. 3. Dependence from some uncertainty components as P(x) = U(Δ sym ) can be shown presenting various curves 1, 2, 3 up to i as P(x) = U(Δ sym ; Δ i, factor ), where Δ i, factor is symmetry deviation individual component. Simulation of symmetry deviation measurement using Monte-Carlo method allows interpretation and optimisation of the production process and measurement method. This is important to achieve required statistical tolerances and process capability indices C p and C pk for batch of details. P(x) = U(Δ sym ) 1,0 1 0, ,0 Δ min Δ max Δ sym Fig. 3. Graph of dependence P(x)=Δ sym 5. CONCLUSION Symmetry deviation has problems by measurement caused by various influence factors. Measurement result can be exacted through uncertainty estimation. Simulation of symmetry deviation measurement is useful to carry out using Monte-Carlo method which allows interpretation and optimisation of the production process and measurement method. 6. REFERENCES [1] Humienny,Z and others. Geometrical product specifications. Warsaw University of Technology, Warsaw, [2] Kulderknup,E., Raba,K. Improvement of circuit boards testing set calibration. Proc. Of 7th Int.Conf. of DAAAM. Tallinn University of Technology. Tallinn, 2010, p ADDITIONAL DATA AOUT AUTHORS 1) Edi Kulderknup, PhD, associated professor, Institute of Mechatronics, Tallinn University of Technology, Ehitajate tee 5, Tallinn, edi.kulderknup@ttu.ee

5 4) Corresponding Author: Edi Kulderknup,

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