Estimating the uncertainty of measurements for various methods and 3D printed parts

Citation: Kozior, T.; Bochnia, J.; Bochenek, A.; Malara, D.; Nawotka, M.; Jansa, J.; Hajnys, J.; Wojtowicz, A.; Mesicek, J. Estimating the Uncertainty of Measurements for Various Methods and 3D Printed Parts. Appl. Sci. 2024, 14, 3506. https://doi.org/10.3390/ app14083506 Academic Editor: Giangiacomo Minak Received: 25 March 2024 Revised: 16 April 2024 Accepted: 17 April 2024 Published: 21 April 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). applied sciences Article Estimating the Uncertainty of Measurements for Various Methods and 3D Printed Parts Tomasz Kozior 1, Jerzy Bochnia 1,* , Aleksandra Bochenek 2, Dominik Malara 1,2 , Michal Nawotka 2, Jan Jansa 3, Jiri Hajnys 3, Adam Wojtowicz 2and Jakub Mesicek 3 1 Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, 25-314 Kielce, Poland; [email protected] (T.K.); [email protected] (D.M.) 2Central Office of Measures, Elektoralna 2, 00-139 Warsaw, Poland; [email protected].pl (A.B.); [email protected].pl (M.N.); [email protected].pl (A.W.) 3Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB–Technical University of Ostrava, 708 00 Ostrava, Czech Republic; [email protected] (J.J.); [email protected] (J.H.); [email protected] (J.M.) *Correspondence: [email protected] Abstract: This paper presents the results of a study on the dimensional accuracy analysis of models produced by 3D printing technology—Fused Filament Fabrication (FFF). Geometric measurements were conducted using a dial caliper, a 3D scanner and a coordinate measuring machine. In addition, a statistical analysis of the test results was carried out, considering the division into different numbers of test samples (3, 5, 10, 20, 30). The analysis of the test results made it possible to assess the influence of the measuring tools used and the number of samples tested on the final measurement result, as well as to determine the consequences associated with it. Keywords: FFF; PLA; 3D scanning; coordinate measuring machine; statistical analysis 1. Introduction Developing 3D printing technologies are increasingly competing with conventional manufacturing technologies. This is mainly due to the development of 3D printers, the increasing accuracy of the models produced, and the growing range of materials available. Nowadays, 3D printing is based on both plastic-based materials, metal powders, and ceramics. In the case of the 3D printing process, the dimensional and shape accuracy of the produced models depends on the technological parameters of the manufacturing process, which are variable depending on the 3D printing technology used. Studies of the dimensional and shape accuracy, and surface texture of models produced by 3D printing have been described in many scientific publications [ 1 – 5 ] and doctoral dissertations, but in many cases, the number of samples tested has been significantly limited. There are cases where studies aimed at determining the influence of technological parameters on the accuracy of 3D printing manufacturing have been carried out on only three or five manufactured samples. In such a situation, reporting the average value result alone is an incomplete representation of the actual result. Such situations may occur in the case of high production costs or a time-consuming process, but in the case of technologies such as FFF, they are unjustified. Therefore, in the present work, the study of the dimensional accuracy of models manufactured by 3D printing technologyFFF from the material based on pure PLA using three measuring tools, along with a comprehensive statistical analysis of the test results, was undertaken. This approach will make it possible to determine the influence of the measuring instrument used for testing and the number of samples evaluated on the value of the result. The results of metrological measurements of dimensional accuracy in many cases carry consequences regarding the decisions made on their basis, and therefore the information presented in this Appl. Sci. 2024,14, 3506. https://doi.org/10.3390/app14083506 https://www.mdpi.com/journal/applsci Appl. Sci. 2024,14, 3506 2 of 15 publication can be used by both 3D printing technologists and decision-makers responsible for the manufacture of prototypes. In the case of technologists, decisions made based on the dimensional accuracy testing performed can impinge on decisions regarding 3D printer service, calibration, component replacement, or the ability to manufacture a custom order. For scientists, knowledge of measurement methods, and their advantages and disadvantages, can contribute to the development of appropriate measurement methods, strategy [6], and improvement of the measurement processes for 3D printed models [7,8]. The rapid development of additive technologies observed in recent years requires the determination of the current dimensional and shape accuracy of the manufactured parts. Accordingly, research work is being carried out on the metrology of measurement of geometric quantities of models produced by 3D printing. Various measuring devices such as hand-held measuring instruments, coordinate measuring machines (CMM—coordinate measuring machine), 3D scanning (3DS), computer tomography (CT) [ 9 ], etc., are used for this purpose. In addition, there are publications where the authors also conduct a comparison of the accuracy of the mentioned systems. Ref. [ 10 ] presents the results of measurements for the three systems analyzed: coordinate measuring machine (CMM), 3D scanning, and computed tomography for samples produced using 3D printing technology: fused filament fabrication (FFF) and selective laser sintering (SLS). The results of the study indicate differences in measurement results for the different measurement systems and point to, among other things, equal measurement procedures and parameters as the reason. Very often, when describing the results of the tests, the issues of the number of samples on which they were conducted are overlooked. In the lack of information on the number of samples tested, it can be concluded that the tests were carried out on a single sample, which affects the reliability of the results obtained and is undoubtedly an inappropriate action [ 9 , 11 ]. The results of testing for a small number of samples in determining the type A standard uncertainty and for the expanded uncertainty are crucial and affect the final results [ 12 ]. The most common instruments for measuring geometric quantities such as shaft diameters are hand-held measuring instruments such as calipers and bore gages. These instruments usually have a measurement resolution of about 0.01 mm, and their accuracy is at a similar level. Measurements made with these devices are subject to numerous errors such as observer error and low-precision pressing force. In Ref. [ 13 ], the authors described the results of tests conducted using hand-held measuring instruments such as calipers and the errors associated with this type of measurement. The authors pointed out that upper limb motor skills (especially finger coordination) significantly affect the accuracy of measurement using a caliper. Coordinate measuring machines (CMMs) are another common method for measuring the geometry of 3D printed parts. Measurement using CMM for 3D printing involves the need for stable mounting of the test sample, proper selection of the diameter of the probe tip, and appropriate force of the probe tip on the test piece. In an article [ 9 ] on the measurement of 3D printed parts manufactured using fused deposition modeling/fused filament fabrication (FDM/FFF) technology on a CMM, the authors pointed out that the results obtained from the measurement of internal diameters were lower than the nominal diameters of these holes. On the other hand, the authors of Ref. [ 13 ], who conducted a study on the geometric accuracy of stationary 3D printers using a CMM, obtained similar results for internal diameters, where in each case the diameter had a value lower than the nominal one. However, when measuring external diameters for a nominal value of 20 mm, the diameter value was higher, and for a nominal value of 30 mm, the value was lower than expected. One of the popular methods of measuring the geometry and surface of a component is 3D scanning. It is distinguished by its remarkable measurement speed as well as technological intuitiveness. However, it has its limitations [ 14 ], such as the requirement for adequate illumination of the sample under examination; for example, if it has deep narrow holes, errors in the virtual model and inaccurate representation of the geometry are possible. Another important aspect of the scanning method is that it is a non-contact measurement, Appl. Sci. 2024,14, 3506 3 of 15 which prevents potential changes in the surface of the measured sample, although there may be larger deviations created in the intermediate stages and the performance of 3D model fitting [ 15 – 19 ]. Associated with the measurement of the geometry of parts manufactured by 3D printing technologies is the problem of estimating the uncertainty of the results of these measurements. Measurement uncertainty uis a parameter that allows one to determine the limits of the interval containing, with assumed probability, the unknown true value of the measured quantity. Measurement uncertainty is affected by a number of uncertainty components. Their determination can be made based on the evaluation of standard deviation estimators for the obtained scatter of the results of a series of measurements or, in the case of single measurements, by means of standard deviations determined on the basis of predicted probability distributions [20]. Ref. [ 21 ] proposed a general method for establishing a mathematical model of spatial uncertainty based on the measured geometry of microstructures created in the manufacturing of parts by 3D printing technology. Whereby, the spatial uncertainty was defined as the deviation between the planned and actual geometry of the model structure made by 3D printing. The dimensions of a part produced by an additive method often deviate from the nominal values of 3D model features due to factors such as printer resolution, printing parameters, printing technology, and measurement method. Using the example of a standard test artifact from the National Institute of Standards and Technology (NIST) containing a set of different features that can be used to characterize the performance of 3D printers, comparative tests were performed using different additive technologies [22]. The standard [ 23 ] for additive manufacturing recommends different shapes of master samples, for evaluating, among other things, the spatial uncertainty of parts that can be made using different 3D printing technologies. Achieving high dimensional accuracy in 3D printing technology, selecting a suitable measurement method for geometric dimensions, and estimating the uncertainty of measurement results is a considerable problem, as demonstrated in this work. In scientific research, a frequently used concept is measurement uncertainty, but in the presented work, the so-called production uncertainty was examined, which has been shown to be significantly influenced by the number of samples tested, and the final result varies depending on the measurement method used. The main purpose of the measurement is the diameter of the sample and the assessment of the impact of measurement accuracy on its values. Moreover, an additional goal of our research was to show how an accidental encounter of a seam by the operator of both the caliper and the coordinate measuring machine can be misinterpreted and falsify the result of the diameter, not the distance. We treat the seam as a defect that the operator taking the measurement is unaware of, because the seam may be scattered across the diameter and invisible at first view. 2. Materials and Methods 2.1. FDM/FFF Technology The FDM (fused filament fabrication) method, also known as FFF (fused filament fabrication), is one of the most popular 3D printing methods. These technologies have been included in the so-called group called MEX—material extrusion—for less than 3 years, according to the ISO/ASTM 52900:2021 standard [ 24 ]. In the presented article, due to the slow coming into use of the nomenclature mentioned in the standard, the widely used names FDM/FFF were used. In accordance with the above standard, the short name for the samples used in the article, describing the technology and material, is as follows: MEX-TRB/P/PLA, where TRB means thermal reaction bonding, and P-polymer material. It involves building the model layer by layer. The material, which is supplied in the form of a filament usually with a diameter of 1.75–3 mm to the printer’s extruder, is heated to a temperature slightly below the melting point of the material, and it is spread in the form of a thin filament, where during solidification it combines with another filament deployed by the device along a predefined trajectory [25]. Appl. Sci. 2024,14, 3506 4 of 15 2.1.1. Samples The sample model was designed using a 3D CAD program—SolidWorks 2024. The created model was cylindrical in shape with a diameter of 15 mm and a height of 15 mm, as shown in Figure 1. Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 16 of a thin filament, where during solidification it combines with another filament deployed by the device along a predefined trajectory [25]. 2.1.1. Samples The sample model was designed using a 3D CAD program—SolidWorks 2024. The created model was cylindrical in shape with a diameter of 15 mm and a height of 15 mm, as shown in Figure 1. Figure 1. 3D CAD model of the sample. The 3D CAD model was saved in STL form (Figure 2), which creates a solid model using a triangle mesh. The created model was approximated using 1440 triangles. The parameters of the STL file are: linear deviation—0.002 mm, and angle—1°. Figure 2. STL model of the sample. 2.1.2. PLA Material The samples were made from one of the most popular materials used in FDM/FFF technology, namely, PLA produced by MakerBot. Selected mechanical properties of the material used are shown below in Table 1. Table 1. Selected parameters of PLA material [26]. Mechanical Properties Standard Value and Unit Tensile Strength (X-Y) ISO 527 45~49 MPa Elongation at Break (X-Y) ISO 527 13.5~15.5% Figure 1. 3D CAD model of the sample. The 3D CAD model was saved in STL form (Figure 2), which creates a solid model using a triangle mesh. The created model was approximated using 1440 triangles. The parameters of the STL file are: linear deviation—0.002 mm, and angle—1◦. Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 16 of a thin filament, where during solidification it combines with another filament deployed by the device along a predefined trajectory [25]. 2.1.1. Samples The sample model was designed using a 3D CAD program—SolidWorks 2024. The created model was cylindrical in shape with a diameter of 15 mm and a height of 15 mm, as shown in Figure 1. Figure 1. 3D CAD model of the sample. The 3D CAD model was saved in STL form (Figure 2), which creates a solid model using a triangle mesh. The created model was approximated using 1440 triangles. The parameters of the STL file are: linear deviation—0.002 mm, and angle—1°. Figure 2. STL model of the sample. 2.1.2. PLA Material The samples were made from one of the most popular materials used in FDM/FFF technology, namely, PLA produced by MakerBot. Selected mechanical properties of the material used are shown below in Table 1. Table 1. Selected parameters of PLA material [26]. Mechanical Properties Standard Value and Unit Tensile Strength (X-Y) ISO 527 45~49 MPa Elongation at Break (X-Y) ISO 527 13.5~15.5% Figure 2. STL model of the sample. 2.1.2. PLA Material The samples were made from one of the most popular materials used in FDM/FFF technology, namely, PLA produced by MakerBot. Selected mechanical properties of the material used are shown below in Table 1. Table 1. Selected parameters of PLA material [26]. Mechanical Properties Standard Value and Unit Tensile Strength (X-Y) ISO 527 45~49 MPa Elongation at Break (X-Y) ISO 527 13.5~15.5% Modulus of Elasticity (X-Y) ISO 527 1000~1100 MPa Bending Strength (X-Y) ISO 178 69~75 MPa Izod Impact Strength (X-Y) ISO 180 4.5~5 KJ/m2 Appl. Sci. 2024,14, 3506 5 of 15 2.1.3. Samples Manufacturing The samples were printed using a MakerBot Sketch printer (MakerBot, New York, NY, USA) [ 27 ]. The digital models of the samples were placed on the virtual platform of the MakerBot Sketch printer and printed during one printing cycle in the amount of 30 pieces. Table 2, below, presents the most important printing parameters set in the MakerBot Print program. Table 2. MakerBot Sketch printer parameters for PLA. Printing Parameters Value and Unit Base layer Raft Extruder temperature 220 ◦C Infill density 20% Supported Materials MakerBot PLA Built plate temperature 50 ◦C Layer height 0.2 mm Figure 3below shows the layout (manufacturing paths) of the models on the work platform in MakerBot Print for the MakerBot Sketch printer. Appl. Sci. 2024, 14, x FOR PEER REVIEW 5 of 16 Modulus of Elasticity (X-Y) ISO 527 1000~1100 MPa Bending Strength (X-Y) ISO 178 69~75 MPa Izod Impact Strength (X-Y) ISO 180 4.5~5 KJ/m2 2.1.3. Samples Manufacturing The samples were printed using a MakerBot Sketch printer (MakerBot, New York, NY, USA) [27]. The digital models of the samples were placed on the virtual platform of the MakerBot Sketch printer and printed during one printing cycle in the amount of 30 pieces. Table 2, below, presents the most important printing parameters set in the MakerBot Print program. Table 2. MakerBot Sketch printer parameters for PLA. Printing Parameters Value and Unit Base layer Raft Extruder temperature 220 °C Infill density 20% Supported Materials MakerBot PLA Built plate temperature 50 °C Layer height 0.2 mm Figure 3 below shows the layout (manufacturing paths) of the models on the work platform in MakerBot Print for the MakerBot Sketch printer. Figure 3. Placement of sample models on the virtual 3D printer platform in MakerBot Print. Each of the printed samples had a seam [28], i.e., a place where the device began and ended the placement of the next layer of building material in each model. A seam is an unintentional defect on the surface resulting from the technological process of 3D printing, and there is only a possibility of its random scattering on the surface—in our case, a cylindrical surface. A seam is a defect similar to that found in machining—a burr that, if not removed, may cause error in the measurement. Moreover, it is possible to make the seam in one line, as shown in Figure 4c; this seam location is convenient for research purposes, and that is why it was chosen in the research. Figure 3. Placement of sample models on the virtual 3D printer platform in MakerBot Print. Each of the printed samples had a seam [ 28 ], i.e., a place where the device began and ended the placement of the next layer of building material in each model. A seam is an unintentional defect on the surface resulting from the technological process of 3D printing, and there is only a possibility of its random scattering on the surface—in our case, a cylindrical surface. A seam is a defect similar to that found in machining—a burr that, if not removed, may cause error in the measurement. Moreover, it is possible to make the seam in one line, as shown in Figure 4c; this seam location is convenient for research purposes, and that is why it was chosen in the research. 2.2. Measurement Methods One of the manufactured samples is shown in Figure 4, displaying the macrostructure of the surface in its various sections using different magnifications of the digital microscope. The macrostructure (shape) of the surface affects the results of geometric quantities depending on the measurement method used, as illustrated in Figure 5. Appl. Sci. 2024,14, 3506 6 of 15 Appl. Sci. 2024, 14, x FOR PEER REVIEW 6 of 16 (a) (b) (c) (d) (e) (f) Figure 4. Printed sample with characteristic spots observed under the microscope; (a)—view of the entire sample with marked observation spots, (b)—edge of the sample at observation spot 1, magnification 40×, (c)—seam of the sample, observation spot 2, magnification 60×, (d)—bottom part of the sample, contacting the printer working platform, observation spot 3, magnification 40×, (e)—top part of the sample, observation spot 4, magnification 240×, (f)—side surface of the sample, observation spot 5, magnification 125×. 2.2. Measurement Methods One of the manufactured samples is shown in Figure 4, displaying the macrostructure of the surface in its various sections using different magnifications of the digital microscope. The macrostructure (shape) of the surface affects the results of geometric quantities depending on the measurement method used, as illustrated in Figure 5. Figure 4. Printed sample with characteristic spots observed under the microscope; (a)—view of the entire sample with marked observation spots, (b)—edge of the sample at observation spot 1, magnification 40 × , (c)—seam of the sample, observation spot 2, magnification 60 × , (d)—bottom part of the sample, contacting the printer working platform, observation spot 3, magnification 40 × , (e)—top part of the sample, observation spot 4, magnification 240 × , (f)—side surface of the sample, observation spot 5, magnification 125×. Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 16 Figure 5. An example model of the effect of surface macrostructure on the result of measuring a geometric quantity, 1—the flat tip of a caliper or other contact sensor, 2—the blade of a caliper or other contact sensor, 3—the contact sensors of a measuring machine with a spherical blanket, 4— the light rays of a scanner, 5—the shadow effect from surface irregularities, 6—fragment of the sample. Figure 5 shows how the geometric structure (shape) of a printed sample can affect the measurement result. Different shapes of contact measurement sensors are used during measurements, and this has certain consequences, e.g., a flat tip (1) makes surface contact only with the tops of irregularities. On the other hand, blade-type (2) or ball-type (3) tips can plunge into the so-called “valleys” of irregularities, which affects the value of the final result of the measurement of a geometric quantity. The use of a scanner, which uses a light beam (4) is also not without disadvantages, as the so-called “shadow effect” (5) can be created, which affects the surface doping in the image processing on the basis of which the inspection of dimensions is carried out. When carrying out measurements using a dial caliper and a coordinate measuring machine, this phenomenon was considered and two types of measurements were made, the so-called diameter measurement with seam and the measurement without it. Each of the measuring tools had a different measurement strategy as described below, but in all cases, the values measured at three different heights were analyzed. It was decided to carry out the measurement with the diameter measurement omitted at the top surface due to a defect in the print in the form of excessive material flowing out, and the bottom surface due to the formation of a defect in the form of the socalled “Elephant foot”. Metrology tests were conducted using three pieces of equipment: - Dial Caliper, - Coordinate Measuring Machine, - 3D scanner. The INSIZE 1311-150A Dial Caliper (INSIZE Co., Ltd., Suzhou, China) was the first device used to make measurements. The resolution of the Dial Caliper used was 0.01 mm, according to the producer. According to the manufacturer, the accuracy of this caliper for a measuring range of 15 mm is equal ± 0.02 mm. The Dial Caliper had a valid calibration certificate at the time of measurement. The research involved measurement using a flat measuring tip (Figure 5—type 1) of a caliper in the place closest to the main body. The seamless measurement strategy involved taking four diameter measurements every 45° in the same cross-section (at the same height—Figure 6). The sample was measured in three different cross-sections at varying heights, resulting in a total of 12 measurements for each sample. The top surface of the sample was considered to be the face where the printing machine finished printing. Figure 5. An example model of the effect of surface macrostructure on the result of measuring a geometric quantity, 1—the flat tip of a caliper or other contact sensor, 2—the blade of a caliper or other contact sensor, 3—the contact sensors of a measuring machine with a spherical blanket, 4—the light rays of a scanner, 5—the shadow effect from surface irregularities, 6—fragment of the sample. Appl. Sci. 2024,14, 3506 7 of 15 Figure 5shows how the geometric structure (shape) of a printed sample can affect the measurement result. Different shapes of contact measurement sensors are used during measurements, and this has certain consequences, e.g., a flat tip (1) makes surface contact only with the tops of irregularities. On the other hand, blade-type (2) or ball-type (3) tips can plunge into the so-called “valleys” of irregularities, which affects the value of the final result of the measurement of a geometric quantity. The use of a scanner, which uses a light beam (4) is also not without disadvantages, as the so-called “shadow effect” (5) can be created, which affects the surface doping in the image processing on the basis of which the inspection of dimensions is carried out. When carrying out measurements using a dial caliper and a coordinate measuring machine, this phenomenon was considered and two types of measurements were made, the so-called diameter measurement with seam and the measurement without it. Each of the measuring tools had a different measurement strategy as described below, but in all cases, the values measured at three different heights were analyzed. It was decided to carry out the measurement with the diameter measurement omitted at the top surface due to a defect in the print in the form of excessive material flowing out, and the bottom surface due to the formation of a defect in the form of the so-called “Elephant foot”. Metrology tests were conducted using three pieces of equipment: - Dial Caliper, - Coordinate Measuring Machine, - 3D scanner. The INSIZE 1311-150A Dial Caliper (INSIZE Co., Ltd., Suzhou, China) was the first device used to make measurements. The resolution of the Dial Caliper used was 0.01 mm, according to the producer. According to the manufacturer, the accuracy of this caliper for a measuring range of 15 mm is equal ± 0.02 mm. The Dial Caliper had a valid calibration certificate at the time of measurement. The research involved measurement using a flat measuring tip (Figure 5—type 1) of a caliper in the place closest to the main body. The seamless measurement strategy involved taking four diameter measurements every 45 ◦ in the same cross-section (at the same height—Figure 6). The sample was measured in three different cross-sections at varying heights, resulting in a total of 12 measurements for each sample. The top surface of the sample was considered to be the face where the printing machine finished printing. Appl. Sci. 2024, 14, x FOR PEER REVIEW 8 of 16 Figure 6. Sample model with indication of measurement locations at three levels. The measurement strategy with a seam involved taking four diameter measurements at one location—the occurrence of a seam in the same cross-section—and at three different heights (a total of 12 measurements). Another measurement tool was a coordinate measuring machine (CMM), Optiv Reference 543 (Hexagon AB, Stockholm, Sweden), with metrological software PC-Dmis (https://hexagon.com/products/product-groups/measurement-inspection-software/metrology-software/pc-dmi (accessed on 16 April 2024)), equipped with the HP-S-X1 probing system. For this, machine length measurement error according to ISO10360-2 [29] is MPE_E(xy) = (0.8 + L/300) µm. The CMM measurement process is characterized by an uncertainty of 1.4 µm. A 5 mm diameter measuring tip with a force of 0.015 N was used during the measurements (Figure 7). The measurement strategy without seam involved the determination of a single diameter based on the measurement of 14 points (to avoid seam location) equally spaced around the circumference of the sample in the same section. In addition, the sample was measured in three different cross-sections at varying heights. The measurement strategy not excluding seam (with seam) involved the determination of a diameter using over 370 measurement points (few of them were in seam location) taken during a scan around the circumference of the sample in the same three cross-sections as in the point-to-point strategy. Figure 7. Sample clamping during CMM measurements. In this work for 3D scanning, a Creaform Handyscan Black mobile laser scanner (Canada, resolution: 0.025 mm, accuracy: 0.025 mm) was used. Scanning methods for measurement were obtained on the presented form. The scanned data were aligned using the Interactive Alignment function in GeomagicDesignX (2019) software. When carrying out the measurement using a 3D scanner, each sample was placed on the scanner platform with the flat surface of the sample, the base of the cylinder, i.e., in the same way as it was printed, as shown in Figure 3. Plane, vector, and point were used to align the polygon mesh. The plane was derived from the bottom surface of the sample, on which approximately 20 grid surface points were selected and intersected by the plane. For obtaining the axis of the cylinder, the Auto Segment function was used, which, based on the specified parameters and sensitivity, can find geometric shapes in the polygon network such as cylinder, plane, cone, etc. The Find Cylinder Axis method was used to create a center vector. The point was obtained by intersecting the plane and the vector. The alignment of the coordinate system using the Interactive Alignment function was performed to the Figure 6. Sample model with indication of measurement locations at three levels. The measurement strategy with a seam involved taking four diameter measurements at one location—the occurrence of a seam in the same cross-section—and at three different heights (a total of 12 measurements). Another measurement tool was a coordinate measuring machine (CMM), Optiv Reference 543 (Hexagon AB, Stockholm, Sweden), with metrological software PC-Dmis (https://hexagon. com/products/product-groups/measurement-inspection-software/metrology-software/pcdmi (accessed on 24 March 2024)), equipped with the HP-S-X1 probing system. For this, machine length measurement error according to ISO10360-2 [ 29 ] is MPE_E(xy) = (0.8 + L/300) µm . The CMM measurement process is characterized by an uncertainty of 1.4 µm. Appl. Sci. 2024,14, 3506 8 of 15 A 5 mm diameter measuring tip with a force of 0.015 N was used during the measurements (Figure 7). The measurement strategy without seam involved the determination of a single diameter based on the measurement of 14 points (to avoid seam location) equally spaced around the circumference of the sample in the same section. In addition, the sample was measured in three different cross-sections at varying heights. The measurement strategy not excluding seam (with seam) involved the determination of a diameter using over 370 measurement points (few of them were in seam location) taken during a scan around the circumference of the sample in the same three cross-sections as in the point-to-point strategy. Appl. Sci. 2024, 14, x FOR PEER REVIEW 8 of 16 Figure 6. Sample model with indication of measurement locations at three levels. The measurement strategy with a seam involved taking four diameter measurements at one location—the occurrence of a seam in the same cross-section—and at three different heights (a total of 12 measurements). Another measurement tool was a coordinate measuring machine (CMM), Optiv Reference 543 (Hexagon AB, Stockholm, Sweden), with metrological software PC-Dmis (https://hexagon.com/products/product-groups/measurement-inspection-software/metrology-software/pc-dmi (accessed on 16 April 2024)), equipped with the HP-S-X1 probing system. For this, machine length measurement error according to ISO10360-2 [29] is MPE_E(xy) = (0.8 + L/300) µm. The CMM measurement process is characterized by an uncertainty of 1.4 µm. A 5 mm diameter measuring tip with a force of 0.015 N was used during the measurements (Figure 7). The measurement strategy without seam involved the determination of a single diameter based on the measurement of 14 points (to avoid seam location) equally spaced around the circumference of the sample in the same section. In addition, the sample was measured in three different cross-sections at varying heights. The measurement strategy not excluding seam (with seam) involved the determination of a diameter using over 370 measurement points (few of them were in seam location) taken during a scan around the circumference of the sample in the same three cross-sections as in the point-to-point strategy. Figure 7. Sample clamping during CMM measurements. In this work for 3D scanning, a Creaform Handyscan Black mobile laser scanner (Canada, resolution: 0.025 mm, accuracy: 0.025 mm) was used. Scanning methods for measurement were obtained on the presented form. The scanned data were aligned using the Interactive Alignment function in GeomagicDesignX (2019) software. When carrying out the measurement using a 3D scanner, each sample was placed on the scanner platform with the flat surface of the sample, the base of the cylinder, i.e., in the same way as it was printed, as shown in Figure 3. Plane, vector, and point were used to align the polygon mesh. The plane was derived from the bottom surface of the sample, on which approximately 20 grid surface points were selected and intersected by the plane. For obtaining the axis of the cylinder, the Auto Segment function was used, which, based on the specified parameters and sensitivity, can find geometric shapes in the polygon network such as cylinder, plane, cone, etc. The Find Cylinder Axis method was used to create a center vector. The point was obtained by intersecting the plane and the vector. The alignment of the coordinate system using the Interactive Alignment function was performed to the Figure 7. Sample clamping during CMM measurements. In this work for 3D scanning, a Creaform Handyscan Black mobile laser scanner (Canada, resolution: 0.025 mm, accuracy: 0.025 mm) was used. Scanning methods for measurement were obtained on the presented form. The scanned data were aligned using the Interactive Alignment function in GeomagicDesignX (2019) software. When carrying out the measurement using a 3D scanner, each sample was placed on the scanner platform with the flat surface of the sample, the base of the cylinder, i.e., in the same way as it was printed, as shown in Figure 3. Plane, vector, and point were used to align the polygon mesh. The plane was derived from the bottom surface of the sample, on which approximately 20 grid surface points were selected and intersected by the plane. For obtaining the axis of the cylinder, the Auto Segment function was used, which, based on the specified parameters and sensitivity, can find geometric shapes in the polygon network such as cylinder, plane, cone, etc. The Find Cylinder Axis method was used to create a center vector. The point was obtained by intersecting the plane and the vector. The alignment of the coordinate system using the Interactive Alignment function was performed to the obtained point, where the Z-axis of the coordinate system is identical to the vector and the XY-axis lies in the created plane derived from the surface. To evaluate the diameter of the printed samples, a silhouette was created in six planes derived from the XY base plane at the intersection of the plane and the polygon mesh using the Mesh Sketch function. From the silhouette, a circle was derived using the Perimeter Circle function, which, based on three selected points from the silhouette, creates a circle in the sketch, as can be seen in Figure 8. Appl. Sci. 2024, 14, x FOR PEER REVIEW 9 of 16 obtained point, where the Z-axis of the coordinate system is identical to the vector and the XY-axis lies in the created plane derived from the surface. To evaluate the diameter of the printed samples, a silhouette was created in six planes derived from the XY base plane at the intersection of the plane and the polygon mesh using the Mesh Sketch function. From the silhouette, a circle was derived using the Perimeter Circle function, which, based on three selected points from the silhouette, creates a circle in the sketch, as can be seen in Figure 8. Figure 8. Final measured values from the printed cylinder with visible elephant foot in the lower part, and opposite effect in the upper part of the sample. 2.3. Statistical Analysis Statistical analysis is a key factor in the reliable presentation of measurement results, and also allows comparison of the results of different studies, so the calculation methodology used is presented [30]. The basic statistical parameter that allows further in-depth analysis is the standard deviation, which, in the presented test results, was calculated according to Equation (1) shown below. 𝑠=   ()∑(𝑥−𝑥  )   (1) where: 𝑛—number of samples, 𝑥—results of sample measurement, 𝑥—average value for series of measurements. Another parameter that makes it possible to assess the value of results in a much more precise way is the so-called standard uncertainty. The way of estimating the uncertainty is the criterion for its division into two types: − Type A uncertainties—determined by statistical methods, − Type B uncertainties—determined by other methods. Measurement results are subject to both type A and type B uncertainties, and they can have comparable values or significantly dominate each other. When the dominant uncertainty is: − Type A standard uncertainty specified as type A overall uncertainty, − Type B standard uncertainty shall be referred to as type B overall uncertainty. When the two uncertainties have comparable values, the total uncertainty will be the type AB uncertainty. The type A uncertainty for the study was calculated according to Formula (2), shown below. Figure 8. Final measured values from the printed cylinder with visible elephant foot in the lower part, and opposite effect in the upper part of the sample. Appl. Sci. 2024,14, 3506 9 of 15 2.3. Statistical Analysis Statistical analysis is a key factor in the reliable presentation of measurement results, and also allows comparison of the results of different studies, so the calculation methodology used is presented [ 30 ]. The basic statistical parameter that allows further in-depth analysis is the standard deviation, which, in the presented test results, was calculated according to Equation (1) shown below. s=s1 (n−1)∑n i=1(xi−x)2(1) where: n—number of samples, xi—results of sample measurement, x—average value for series of measurements. Another parameter that makes it possible to assess the value of results in a much more precise way is the so-called standard uncertainty. The way of estimating the uncertainty is the criterion for its division into two types: - Type A uncertainties—determined by statistical methods, - Type B uncertainties—determined by other methods. Measurement results are subject to both type A and type B uncertainties, and they can have comparable values or significantly dominate each other. When the dominant uncertainty is: - Type A standard uncertainty specified as type A overall uncertainty, - Type B standard uncertainty shall be referred to as type B overall uncertainty. When the two uncertainties have comparable values, the total uncertainty will be the type AB uncertainty. The type A uncertainty for the study was calculated according to Formula (2), shown below. uA=s1 n(n−1)∑n i=1(xi−x)2(2) The final statistical parameter that, for experimental studies, allows one to determine the result of a measurement that depends on the number of samples tested, is the Extended Uncertainty using Student’s t, or according to Gauss normal distribution. In the case of the presented research, Formula (3) was used, which takes into account an additional expansion factor—k p , the value of which in the following calculations is shown in Tables 3and 4 . The expanded uncertainty was calculated using the Student’s t-distribution because the size of the largest series of samples did not exceed the number 30. UCA =kpuA(3) where: kp —expansion factor for a series of measurements selected for a confidence level of 95%. There may be a situation where the measurement uncertainty calculated by the type A method is exceedingly small, which may be questionable. Therefore, it is necessary to refer to the limiting error of a single measurement. Table 3. Statistical analysis included statistical population size (number of samples) with seam. Measurement Tool Series n Coefficient kp Standard Deviation s, mm Standard Uncertainty, uA, mm Expanded Uncertainty UCA, mm Result x±UCA, mm Dial Caliper 3 4.3 0.012 0.007 0.029 15.11 ±0.029 5 2.78 0.023 0.010 0.029 15.10 ±0.029 10 2.26 0.023 0.007 0.016 15.09 ±0.016 20 2.09 0.023 0.005 0.011 15.08 ±0.011 30 2.05 0.022 0.004 0.008 15.08 ±0.008