7188 FACTA UNIVERSITATIS Series:Mechanical Engineering https://doi.org/10.22190/FUME210507063M © 2020 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper ACCURACY ANALYSIS OF THE CURVED PROFILE MEASUREMENT WITH CMM: A CASE STUDY Tomasz Mazur1, Miroslaw Rucki1, Yuriy Gutsalenko2 1Kazimierz Pulaski University of Technology and Humanities in Radom, Poland 2National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine Abstract. In the paper, analysis of the curved profile measurement accuracy is described. Since there was no CAD model or other reference profile for the measured detail, the first step was to generate the reference contour of the cam using the technical drawing and tolerance requirements. The test campaign consisted of three experiments aimed at determining the effect of scanning velocity on the results of form deviation δ measurement, evaluation of deviation δ measurement uncertainty and the measurement repeatability. The scanning time was checked, too. The obtained results demonstrated feasibility of the chosen CMM and measurement strategy. It was found also that the measurement uncertainty did not depend on the scanning sampling step from 0.05 to 0.2 mm, and the true measurement time was for 30-40% longer than that expected from the nominal scanning velocity. Key Words: Curved Profile, Tolerance, Measurement, CMM, Uncertainty 1. INTRODUCTION Free-form surfaces and curved profiles are widely used in the design and manufacturing of details with high and strict precision requirements [1,2]. During the machining process, vibrations and other inaccuracies may affect the final state of the curved profile, which leads to the necessity of thorough dimensional and shape inspection to ensure its functionality. Thus, the characterization of free-form surfaces is an increasingly important area of metrology [3]. In particular, tolerance of the profile along with the position tolerance is a crucial feature in the design and manufacture of products with curved profiles. The contour of curved profiles can be detected either by sensing or by measuring, and measurement systems are generally based on mobile or stationary coordinate measurement Received May 07, 2021 / Accepted October 20, 2021 Corresponding author: Miroslaw Rucki Kazimierz Pulaski University of Technology and Humanities in Radom, Malczewskiego 29, 26-600 Radom, Poland E-mail: m.rucki@uthrad.pl 2 T. MAZUR, M. RUCKI, Y. GUTSALENKO systems with specific software and sensors [4]. The accuracy of the results from coordinate measurements depends on the accuracy of the measuring device, workpiece properties, environmental conditions, and especially on the operator and measurement procedures [5]. Appropriate planning of a measurement strategy for free-form surfaces is addressed in many publications. For example, it was proposed to establish the local geometric deviation, namely, the difference between each measurement point and the CAD model of the measured surface [6]. Other papers dealt with two key problems of surfaces and curves profile error measurement: (1) evaluation algorithm of profile error on the basis of minimum zone principle or maximum material condition; (2) computer aided arbitrament for minimum zone principle and maximum material condition [7]. For the measurement of freeform shaped workpieces, the distortions caused by the tip mechanical filtration have impact on measurement accuracy, so that correction is desired in order to restore to the real workpiece surface [8]. Menq and Chen noted that after measurement with a contact probe, the generated surface differed from the real one because of the radius compensation errors of the probe. Minimization of the compensation errors required that the probing directions of the CMM coincide with the normal vectors of the probed points. They emphasized unavailability of the normal vectors of data points when the CAD model of a new design did not exist [9]. Similarly, in 3D gear measurements, the influence of CMM geometric errors on the results is still unclear because the requirement for a gear measurement standard with ideal geometry cannot be fulfilled [10]. It should be noted that the laser-based measurement methods of curved profiles need compensation, too [11]. A significant share in the overall calculus of errors in scanning measurements performed on coordinate measuring machines (CMM) refers to dynamic errors [12]. Since the measurement time and cost increase proportionally as the increase of sampling points, it is essential to study a sampling method [13]. The volumetric probing uncertainty of a CMM is usually determined adding a component of the length measuring uncertainty, considering the distance between 25 points on the calibrating sphere, to get the overall point coordinate uncertainty of the CMM [14]. Evaluation of repeatability and reproducibility of the CMM equipment is necessary, too [15]. Prior to numerical characterization, filtering is done and it is also essential for extracting information needed to provide process feedback and establish functional correlation [16]. A study of roundness of different artifacts using different algorithm and filters demonstrated impact of filtering on the measurement results [17]. The number of CMM points in the measurement of each feature of a part has to enable achievement of a simulated feature-fit that results in a high-quality representation of the manufactured feature [18]. In order to simplify the calculation and simultaneously retain the accuracy of evaluation, the method was proposed, based on the extraction of key points from scanning data set [19]. Other authors emphasized, however, that the simulation of measurement became very complicated when the solution of the measuring task needed construction of elements using measured features [20]. Some authors emphasized that there are very few commercially available software systems that offer sweep scan path planning function. Moreover, newly proposed methods able to generate a viable sweep scan path automatically require significant user’s knowledge and involvement [21]. From that perspective, it is crucial to keep consistency in the measurement procedure. A dictionary definition of ‘consistency’ is ‘constant adherence to the same principles of thought or action’ [22]. Saunders and co-authors noted that this definition is intended to refer to a personal characteristic, but since many personal choices are made during Accuracy Analysis of the Curved Profile Measurement with CMM: a Case Study 3 programming, operating, and evaluating of the CMM measured points, the term also works well within the context of measurement [23]. According to the definition of the profile tolerance in ISO 1101 [24], the surface profile error can be defined by the minimum diameter covering all measured points of the cluster spheres whose centers lie on the design model. Profile tolerance may be related to a basic surface; then its orientation and position are dependent on the definition of bases and base-dependent coordinate system. Researchers have proposed various practical approaches towards evaluating form deviations of 2D contour profiles based on coordinate measurement data. For example, a 2D contour was divided into straight and curved parts [25]. There are reports in which extracted points of curved profile deviated from reference data within ±0.1 mm [26]. In the present paper, we focused on the statistical analysis of the results obtained for the curved 2D profile with no available CAD model. The measurement results appeared to be dependent on the scanning parameters, so that a balance between accuracy demands and measurement time had to be found. Also the problem of basic surface for measurements was challenged in order to keep consistence of the results. 2. MATERIALS AND METHODS In the research studies, a cam with complex 2D profile curvature was measured. Its dimensions and tolerances are shown in Fig. 1. Its form tolerance was 0.15 mm , and roughness of curved surface was limited to Ra = 1.25 μm and Rz = 6.3 μm. Using the data from Fig. 1, theoretical (reference) profile was generated as a file *.dxf using the program SolidWorks 2019. Fig. 1 Technical drawing of the measured cam 4 T. MAZUR, M. RUCKI, Y. GUTSALENKO The contour of the cam was generated using the technical drawing, and in form of *.dxf file was input to the CMM control program. In the file, 2829 theoretical (reference) points constituted the profile with coordinates x, y, z in the local coordinate system (LCS) defined according to the technical drawing. The points were located approximately uniformly 1 mm below the base surface of the cam, i.e. z = -1 mm for each point. The length of the contour was lc = 123,49 mm. The measurements were performed with the CMM Mitutoyo Crysta – Apex S 7106. It is a high-accuracy CNC coordinate measuring machine that guarantees a maximum permissible error defined by ISO 10360-2:2009 of E0,MPE = (1.7+3L/1000) μm at ambient temperature 20 ±2 °C. L stands for the selected measuring length in mm. The measuring range in three axis is x = 700; y = 1000; z = 600 mm, 3D acceleration a = 2309 mm/s2, and linear velocity in three directions x, y, z is v = 519 mm/s. Moreover, the CMM has temperature compensation function in the range of 16÷26 °C, which makes it suitable for working in the industrial conditions. The machine can be equipped with contact scanning probe, non-contact laser probe or vision probe [27]. Scanning mode makes it possible to perform measurement with 0.05-1.0 point-point step or distance between points, scanning speeds between 0.5 and 4 mm/s, and permissible probe deflection in the range from 0.15 to 0.4 mm. Fixation of the cam with defined LCS is shown in Fig 2. Fig. 3 presents the initial window of CMM for scanning of an outer closed contour with the set values described below in the text. Fig. 2 Fixation of the measured cam on the CMM table Accuracy Analysis of the Curved Profile Measurement with CMM: a Case Study 5 To perform the experiments, control software MCosmos was used. In this program, ready scripts are available for the measurement of all standardized geometrical tolerances, as well as the measurement of complex shapes in local coordinates. Before the measurement, a fixture was made so that the entire profile could be measured in one fixation with one probe. The probe was calibrated with the calibration sphere, and a local coordinate system (LCS) was defined according to the tolerance data provided in the drawing Fig 2. The LCS definition covered following elements: - base A as a head surface of the measured cam became the main surface of the LCS, it defined axes X and Y from 4 measuring points, - base B defined LCS center in the center of the hole ∅20, using 4 points of the circle, - base C as a line connecting three points, two of them lay in the bisector of the first smaller base hole and the third one was the center of the second smaller base hole; it was moved in parallel up to base B become axis Y, - remaining axes x and y are derived from the right-hand coordinate system. Fig. 3 Window of the MCosmos program for the measurement parameters During the measurement, the CMM program written for that specific purpose is collecting the coordinates of measuring points. According to the definition of the profile deviations, it registers maximal deviation value δmaxand shows its position in the profile. The number of collected points is dependent on the measurement step and only approximately corresponds to the profile length divided by step. Apart from deviation value δ, scanning time was registered directly by the CMM program. After the measurement is finished, the program records automatically the measurement report with the value of the largest registered deviation from the reference profile. Moreover, the program makes it possible to register all the measuring points from the scanning, in the respective file *.dxf. CNC Scanning Scanning Basic plane ---------- CNC parameters Step Clearance Velocity Deflection Start point ---- End point -- Start direction - End direction - Clean Help OK 6 T. MAZUR, M. RUCKI, Y. GUTSALENKO 3. TEST CAMPAIGN The test campaign consisted of three experiments aimed at determining the effect of scanning velocity on the results of form deviation δ measurement, evaluation of deviation δ measurement uncertainty and the measurement repeatability. During the profile scanning, three parameters could be set: - scanning velocity vs in the range between 0.5 and 4 mm/s, - permissible probe deflection pd in the range between 0.15 and 0.4 mm, and, - scanning step s between 0.05 and 1 mm. The respective values used in each measurement series are presented in the Table 1. Table 1 Parameters of experimental measurements Series No. vs [mm/s] pd [mm] s [mm] Number of repetitions n 1 1 0.15 0.2 5 2 1 0.2 0.2 5 3 1 0.3 0.2 5 4 1 0.4 0.2 5 5 2 0.15 0.2 5 6 2 0.2 0.2 5 7 2 0.3 0.2 5 8 2 0.4 0.2 5 9 3 0.15 0.2 50 (3×5+1×10+1×25) 10 3 0.2 0.2 5 11 3 0.3 0.2 5 12 3 0.4 0.2 5 13 4 0.15 0.2 5 14 4 0.2 0.2 5 15 4 0.3 0.2 5 16 4 0.4 0.2 5 17 3 0.15 0.2 50 18 3 0.15 0.05 50 The above-mentioned parameters were chosen in order to perform three different experiments, as explained below. 3.1 Effect of scanning velocity on results of the form deviation measurements In the first set of experiments, the goal was to determine the effect of different scanning velocities vs on the results of profile form deviation, considering the measurement time. In this set of measurements, the scanning step remained unchanged, s = 0.2 mm. As shown in the Table 1 above, the measurements were performed for 16 combinations of vs and pd settings. For each combination, the measurements were repeated 5 times. The number of measuring points differed in a small range from 645 up to 660. 3.2 Uncertainty evaluation It can be assumed that the factors having effect on the measurement uncertainty of a cam contour are similar to the ones typical for roundness measurement [28-29]. Uncertainty analysis was performed using the Type A approach [30] with 50 repetitions Accuracy Analysis of the Curved Profile Measurement with CMM: a Case Study 7 made in the repeatability conditions. Two series of measurements marked 17 and 18 in Table 1 had similar parameters vs = 3 mm/s and pd = 0.15 mm, but different sampling step. This experiment was to demonstrate how the uncertainty of form deviation is dependent on the number of probing points. In the series 17, at sampling step s = 0.2 mm, the number of probing points was ca. 650, while in the series 18 it was 2560-2590, close to the respective number in the reference file *.dxf. 3.3 Repeatability in short measurement series Considering a relatively long time of a single measurement, which can be as long as 200 s at scanning speed vs = 1 mm/s, it is reasonable to expect that 50 repetitions may not completely conform to the repeatability conditions requirement. To challenge this issue, the third experiment was performed. In the case of the series 9 (Table 1, vs = 3 mm/s, pd = 0.15 mm, s = 0.2 mm), the measurement was firstly performed three times with 5 repetitions each time, then with 10 repetitions, and finally with 25 repetitions. This procedure was described in Tab. 1 as 3×5+1×10+1×25. Thus, the strict repeatability conditions were kept only for each group of repetitions, but not only for the entire sample of 50 similar measurements. As a result, measurement repeatability for a smaller number of repetitions could be compared with the results for a larger number. All these measurements, as well as the ones described in Section 3.1, were performed on the same day, with no resetting the CMM. After calibration of the probe, the measured cam was not moved from its fixed position. The coordinate system once established was applied to each measurement due to the specially prepared software program. Moreover, to assure a higher level of repeatability, the initial position of the probe before each measurement was identical. The experiments described in Section 3.2, however, were performed several months later, and for each of them the CMM was started anew. In this way the obtained results in series 17 and 18 must be treated as two separate experiments, while the others are somewhat interconnected between each other through the same definition of the coordinate system and a relatively short time between the repetitions. 4. RESULTS AND DISCUSSION Overall number of the maximal deviation measurement results was 225. In order to determine normality of the results distribution, the Kolmogorov-Smirnov test was applied to each of tests with 50 repetitions, namely, series No. 9, 17 and 18, as described in the previous section. Respective D-values of the statistics were 0.1789, 0.14551 and 0.18754, while p-values were 0.07, 0.22 and 0.05, respectively. Hence the measurement results in the series did not differ significantly from Gaussian distribution, despite some differences in statistical parameters. Fig. 4 presents the respective histograms. 8 T. MAZUR, M. RUCKI, Y. GUTSALENKO Fig. 4 Histograms of the measurement results of 50 repetitions in the series No. 9, 17, and 18 Knowing that the distribution of form deviation δ measurement results is normal, it is possible to apply the Student-Fisher parameters to the smaller series of 5, 10 and 25 repetitions. Thus, confidence interval CI can be calculated as follows: CI = tα,n-1 ×Sn (1) where: tα,n-1 – Student-Fisher distribution quantile, n – number of the repetitions in series, Sn – standard deviation. Assuming confidence level P = 0.99, the respective quantile value for 5 repetitions is tα,n-1 = 4.604, for 10 repetitions tα,n-1 = 3.250, and for 25 repetitions tα,n-1 = 2.797 [31]. 4.1 Effect of scanning velocity on form deviation In Tables 2-5, there are collected measurement results for form deviation δ obtained at different scanning velocities vs and probe deflection pd, together with the time of measurement t. The series numbers correspond with the ones specified above in Table 1. Table 4 contains results for probe deflection pd = 0.15 mm only for one series with 5 repetitions. Table 2 Form deviation δ obtained at vs = 1 mm/s (series 1-4) pd= 0.15 mm pd= 0.2 mm pd= 0.3 mm pd= 0.4 mm Repetition No. δ [mm] t [s] δ [mm] t [s] δ [mm] t [s] δ[mm] t [s] 1 0.118 198 0.115 179 0.114 156 0.112 145 2 0.120 203 0.116 181 0.113 155 0.112 145 3 0.116 205 0.115 177 0.112 154 0.111 146 4 0.118 201 0.116 177 0.113 155 0.111 147 5 0.119 199 0.118 178 0.115 154 0.112 146 Mean value 0.118 201.2 0.116 178.4 0.113 154.8 0.112 145.8 Standard deviation Sn 0.001 2.864 0.001 1.673 0.001 0.837 0.001 0.837 Confidence interval 0.007 13.18 0.006 7.7 0.005 3.85 0.003 3.85 Accuracy Analysis of the Curved Profile Measurement with CMM: a Case Study 9 Table 3 Form deviation δ obtained at vs = 2 mm/s (series 5-8) pd= 0.15 mm pd= 0.2 mm pd= 0.3 mm pd= 0.4 mm Repetition No. δ [mm] t [s] δ [mm] t [s] δ [mm] t [s] δ[mm] t [s] 1 0.119 95 0.115 84 0.114 75 0.112 75 2 0.116 97 0.115 84 0.116 77 0.112 75 3 0.115 95 0.115 84 0.112 77 0.114 73 4 0.116 97 0.115 84 0.113 77 0.112 74 5 0.118 95 0.114 84 0.118 78 0.114 74 Mean value 0.117 95.8 0.115 84.0 0.115 76.8 0.113 74.2 Standard deviation Sn 0.002 1.095 0.000 0.000 0.002 1.095 0.001 0.837 Confidence interval 0.008 5.04 0.002 0.000 0.011 5.04 0.005 3.85 Table 4 Form deviation δ obtained at vs = 3 mm/s (series 9-12) pd= 0.15 mm pd= 0.2 mm pd= 0.3 mm pd= 0.4 mm Repetition No. δ [mm] t [s] δ [mm] t [s] δ [mm] t [s] δ[mm] t [s] 1 0.120 61 0.117 56 0.116 47 0.113 47 2 0.117 62 0.116 56 0.116 50 0.110 47 3 0.117 63 0.113 57 0.113 50 0.119 49 4 0.116 62 0.115 57 0.115 51 0.114 50 5 0.116 61 0.113 55 0.116 50 0.112 49 Mean value 0.117 61.8 0.115 56.2 0.115 49.6 0.114 48.4 Standard deviation Sn 0.002 0.837 0.002 0.837 0.001 1.517 0.003 1.342 Confidence interval 0.008 3.85 0.008 3.85 0.006 6.98 0.015 6.18 Table 5 Form deviation δ obtained at vs = 1 mm/s (series 1-4) pd= 0.15 mm pd= 0.2 mm pd= 0.3 mm pd= 0.4 mm Repetition No. δ [mm] t [s] δ [mm] t [s] δ [mm] t [s] δ[mm] t [s] 1 0.120 50 0.113 46 0.115 42 0.121 38 2 0.118 49 0.115 46 0.117 40 0.114 38 3 0.117 49 0.117 46 0.115 41 0.114 37 4 0.115 47 0.117 46 0.117 41 0.113 37 5 0.117 48 0.117 46 0.111 41 0.118 38 Mean value 0.117 48.6 0.116 46.0 0.115 41.0 0.116 37.6 Standard deviation Sn 0.002 1.140 0.002 0.000 0.002 0.707 0.003 0.548 Confidence interval 0.008 5.25 0.008 0.000 0.011 3.26 0.016 2.52 From the above results, it can be seen that larger permissible probe deflection pd enabled 22-28% shortening of the measurement time at each scanning speed. However, it caused distinguishable 1-6% reduction of the obtained result of form error δ. Graph in Fig.5 shows how this reduction differs for different scanning speed values vs. From Fig. 5 it can be concluded, that at higher scanning speeds, the influence of probe deflection is smaller. For pd≤ 0.2 mm, speed-dependent differences in obtained form deviations δ lay below E0,MPE = (1.7+3L/1000) μm for the used CMM. Notably, this range of the deflection values ensured insignificant effect of scanning speed vs on the form deviation results. For each pd = 0.15 and 0.2 mm, differences between obtained δ at various vs were 1 μm. Larger probe deflections led to widening of the results span, which indicated 10 T. MAZUR, M. RUCKI, Y. GUTSALENKO increased uncertainty of the measurement. Due to this observation, we are against application of pd> 0.2 mm for this sort of measurement. Fig. 5 Form deviation δ obtained at different scanning speeds vs and different probe deflections pd Calculations of true scanning velocity vs' revealed substantial differences between them and set values vs. Values of vs' were determined from the known length of measured contour lc and automatically registered time of each measurement. Table 6 presents the values and percentage differences between them. Table 6 True values of scanning speed vs' related to the nominal ones vs for different probe deflections pd (sampling step was 0.2 mm) pd= 0.15 mm pd= 0.2 mm pd= 0.3 mm pd= 0.4 mm vs [mm/s] vs' [mm/s] Percen- tage vs' [mm/s] Percen- tage vs' [mm/s] Percen- tage vs' [mm/s] Percen- tage 1 0.120 50 0.113 46 0.115 42 0.121 38 2 0.118 49 0.115 46 0.117 40 0.114 38 3 0.117 49 0.117 46 0.115 41 0.114 37 4 0.008 5.25 0.008 0.000 0.011 3.26 0.016 2.52 It should be noted that the true scanning speed never reached its nominal value, and smaller probe deflections reduced its value by almost 40%. Considering previous conclusion that the measurement should not be performed with pd> 0.2 mm, this finding becomes extremely important. In the case of 100% inspection of large lots of the cams similar to the one investigated, measurements will take 30-40% longer time than it would be expected from the nominal scanning speed. In the Flexible Manufacturing Systems working in the frames of Industry 4.0 concept [32], prolonged inspection time may become an issue. 4.2 Results of uncertainty evaluation In the Type A uncertainty evaluation, three series of the measurement results were used, 50 repetitions each. It can be assumed that the standard uncertainty is approximately equal to the standard deviation u(x) ≈Sn, and the coverage factor for the level of confidence Accuracy Analysis of the Curved Profile Measurement with CMM: a Case Study 11 p = 99% can be kp = 2.576 [28]. As described above, series No. 9 followed repeatability conditions, but not as strictly as series No. 17. On the other hand, series No. 18 had a larger number of probing points, close to that of the reference file derived from the technical drawing. Table 7 presents values of the calculated standard and expanded uncertainties. Examples of the measured profiles with emphasized δmax are shown in Figs 6 and 7. Table 7 Uncertainty estimation based on the series with 50 repetitions Series No. 9 17 18  [mm] 0.1151 0.1137 0.1152 Sn ≈ u(x) 0.00158 0.00195 0.00142 U0.99 = kp× u(x) 0.004 0.005 0.004 Fig. 6 Example of the measured profile with the result of δ = 0.113 mm; sampling step s = 0.2 mm, 660 probing points The results presented in Table 7 appear a little unexpected. A higher degree of conformity is between series No. 9 and 18 than between No. 17 and any of two others, despite its conditions were “in-between” (same number of probing points as No. 9 and time of experiment closer to No. 18). Nevertheless, it should be kept in mind that the differences between both mean values  and expanded uncertainties U0.99 for three series lay below E0,MPE. Hence, it may be stated that the influence of sampling is negligibly small when estimating the measurement uncertainty of CMM measurement of the cam profile. 12 T. MAZUR, M. RUCKI, Y. GUTSALENKO Fig. 7 View of the area with the largest identified form deviation: a) δmax = 0.113 mm after scanning with step s = 0.2 mm, b) δmax = 0.116 mm after scanning with step s = 0.05 mm This conclusion is confirmed by a detailed analysis of the maximal deviation localization on the cam profile. Irrespective of what sampling step, scanning velocity or probe deflection was applied ,δmax was identified in the same area. Moreover, it should be noted that a large number of probing points effects in increase of the processing time and, hence, the measurement lasts longer. Experimental evaluation of the uncertainty demonstrated that it is unnecessary, and the results with similar uncertainty may be obtained at a larger sampling step in a shorter time. 4.3 Repeatability in short measurement series Table 8 presents the results obtained subsequently for the series No. 9, as described in Section 3.3. The first column presents the number of each measurement in the series 9, while the second one is the number of a group, as follows: 5 repetitions in the 1st group, 5 in the 2nd and 3rd, respectively, 10 repetitions in the 4th group and 25 repetitions in the 5th group. For each group, respective standard deviations Sn and confidence intervals CI were calculated both for measured deviation δ and for measurement time t. In the last row, overall statistics is added for the entire series No. 9 for t0.01,49=2.6802. Fig. 8 shows the histograms of the results with approximated distribution curves for the group No. 5 and for overall statistics. Table 8 Statistics for form deviation δ and scanning time t obtained at vs = 3 mm/s with sampling step s = 0.2 mm and pd= 0.15 mm in short measurement groups Group No.  [mm] Sn CI t [s] Sn CI 1 0.1172 0.00164 0.0076 61.8 0.837 3.85 2 0.1150 0.00255 0.0117 65.2 0.447 2.06 3 0.1150 0.00173 0.0080 62.6 0.548 2.52 4 0.1153 0.00125 0.0041 60.4 1.35 4.39 5 0.1146 0.00115 0.0032 62.2 1.165 3.26 Overall 0.1151 0.00158 0.0042 62.2 1.646 4.41 Accuracy Analysis of the Curved Profile Measurement with CMM: a Case Study 13 Fig. 8 Distribution of the results in short measurement series: a) deviation δ and b) measurement time t Interestingly, the first three groups that would be expected to be similar, revealed the following statistics: mean values were similar for groups 2 and 3, with 2.2 μm higher for group 1, but the respective confidence intervals were similar for groups 1 and 3, with CI for the group 2 almost 50% wider. For the groups with 10 and 25 repetitions, confidence intervals reduced substantially, down to 0.0041 and 0.0032, respectively. Notably, mean value for group 4 was slightly higher than that for groups 2 and 3, while for group 5 it was slightly lower. The difference was smaller than 0.4 μm, significantly below the maximum permissible error E0,MPE = (1.7+3L/1000) μm for the CMM used in experiments. 5. CONCLUSIONS The results of the experimental research studies demonstrated that increased probe deflections pd reduced the values of measured form deviation. Additionally, pd higher than 0.2 mm increased the results dispersion. It was found also that the measurement uncertainty did not depend on the scanning sampling step from 0.05 to 0.2 mm, but it should be noted that a smaller step increased the measurement time.    14 T. MAZUR, M. RUCKI, Y. GUTSALENKO Noteworthy, the true measurement time was for 30-40% longer than that declared by nominal scanning velocity. These characteristics must be taken into consideration when projecting the batch inspection procedures, especially when 100% of parts must be measured. Moreover, there is no necessity in the increased number of repetitions since even a small number of repetitions gave similar mean results with differences close to the maximum permissible error of the CMM. The most important conclusion is that the highest value of form deviation was identified in the same location irrespective of the applied measurement parameters. Expanded uncertainty of form deviation measurement at the level of confidence p = 99% was U0.99 = 0.005 mm, less than 10% of the measured tolerance. This value proved that the chosen CMM as well as the inspection methodology were appropriate for the measurement of the given curved profile. 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