Accuracy of FDM PLA Polymer 3D Printing Technology Based on Tolerance Fields

Abstract

Fused deposition modelling (FDM) 3D printers have the highest annual growth of 21.15% in the field of 3D printing. FDM desktop 3D printers account for 23.69% of FDM printers. The major drawback of FDM desktop printers is product accuracy, which is particularly pronounced when dimensionally inaccurate and multi-part printed products need to be fit together into a functional assembly. The research presented in this paper aims to determine the accuracy limits of FDM 3D printers when producing elements for assembly using a 3D printer in a tolerance-fit system. A novel method of computer-aided design (CAD) based on ISO 286 and the systematic calibration procedure of 3D printers were presented to achieve the dimensional accuracy of 3D printed parts. For this purpose, a set of nominal dimensions within the clearance fit was selected, and various CAD models were created according to the ISO 286 system of limits and fits. The CAD Slicer software–3D printer interaction was systematically examined for the best hardware and software features. It was found that the Horizontal Expansion parameter should be 0.0 mm and the Hole Horizontal Expansion parameter should be 0.13 mm. The Linear Advance factor was found to be 25. The measurement results showed that the desired tolerance ranges, system, and type of clearance fit could be achieved with a desktop 3D printer. The roundness tolerance for all clearance fits and shaft tolerance ranges in the hole base system was determined to join the parts into a clearance fit.

1. Introduction

The use of rapid prototyping techniques has greatly accelerated the process of developing new products, especially in the design phase, when it is necessary to create and test prototypes. Additive manufacturing (AM) is the latest technology employed for creating intricate and intricately constructed components across a range of uses. Fused deposition modelling (FDM) has received significant attention within the realms of development and manufacturing. The advantages of AM span various industries and applications. Its potential to create lightweight designs, reduce assembly requirements, and embrace a wide spectrum of materials—including metals, plastics, ceramics, and composites—further solidifies its role as a transformative force in manufacturing. As the world embraces digitalization, AM stands out as a method that enables on-demand production and customization, irrespective of geographical constraints [1,2]. Looking at the working environment in modern manufacturing processes, it is noticeable that 3D printing technologies, such as FDM, selective laser melting (SLM), stereolithography (SLA), etc., are widely used in addition to conventional processes, such as turning, milling, etc. The parts production using conventional processes is based on well-defined tolerances, international tolerance (IT) grades, fit types, and fit systems in which the parts are manufactured and assembled. Regarding FDM technology, it is known from the literature that FDM 3D printing can achieve the following IT grades: IT9, IT10, IT11, IT12, IT13, and IT14 [3], sometimes in single-axis directions and sometimes in all axis directions (IT11, IT12, and IT13) during printing. This also allows for a comparison of accuracy to that of conventional manufacturing technologies, but it is still worth investigating whether tighter tolerance zones can be achieved than those established by the ISO 286 system of limits and fits in all 3D printing directions. In addition, the volume in which a part can be printed potentially determines its geometry and how it is connected to other elements. Tiwary et al. [4] emphasize that dimensional accuracy and limited print volume are still important challenges that must be overcome with FDM 3D printers to make them more acceptable in industrial environments. They also point out that an acceptable method for joining parts produced with FDM 3D printers needs to be developed, as this is currently the biggest weakness of this technology. A potentially acceptable solution could be the application of the ISO 286-1:2010 system of limits and fits [5]. The application of the ISO 286-1:2010 system of limits and fits ensures the accuracy of parts, which in turn affects the accuracy of the connection of those parts. If a part is not manufactured according to the dimensions prescribed in the ISO 286-1:2010 limit and fit system, the accuracy of the assembled parts cannot be expected. This is also the most challenging part of rapid prototyping [6]. In the same paper, their results showed that FDM 3D printing can achieve an accuracy of, for example, 0.1128 mm in roundness tolerance, emphasizing that the orientation of the printed part and support material are important factors affecting the geometric accuracy of 3D-printed parts. Boschetto et al. focus on process parameters [7] and they state that the parts could not satisfy the design specifications nor assure the functionality of and the assembly fit with other components. The authors dealt with an anisotropic offset as a pre-processing virtual model applied to the surfaces, defined by a mathematical formulation, to compensate for dimensional deviations. The focus on methodology, accuracy, tolerances, process parameters, etc., was also highlighted in the following papers and their findings. Drozda et al. [8] propose that a thorough and systematic examination of native accuracy, tolerance, and repeatability is essential for FDM technology. Pombinha et al. [9] investigated how layer thickness and infill density impact the geometric tolerance of FDM-produced parts using benchmark parts for testing. Kacmarcik et al. [10] demonstrate that a relatively simple benchmark part can effectively assess various geometrical characteristics’ accuracy and reveal differences between two desktop 3D printers in terms of precision. Shortcomings such as joint clearances and geometric deviations that are dependent on machine-specific process parameters are highlighted in [11]. The current state of the art lacks suitable methods for addressing these issues, especially for 3D-printed mechanisms as shown in a statistical tolerance analysis. Zemicik et al. [12] underscore the complexity of the printing process, emphasizing the extensive range of parameters and limits, and advocate for the use of linear optimization methods. Their study concludes that linear programming is a functional approach for identifying optimal parameters in 3D printing. Luis-Perez et al. [13] investigated multiobjective parametric optimization and suggest maintaining the lowest values for the design of experiments (DOE) for the nozzle diameter, layer height, and temperature (0.4 mm, 0.1 mm, and 195 °C, respectively). Meanwhile, the print speed and extrusion multiplier should be set approximately at their central values (40 mm/s and 95%). Moradi et al. [14] investigated process parameters using response surface modelling optimization, and as a result, it was found that by increasing the number of contour layers from two to six, the maximum failure force increased by 42%. Increasing the contours, due to having a similar effect to that when increasing the infill density, increases the failure force and production time.

Alexopoulu et al. [15] emphasizes process parameters [15], but uses the ISO ASTM 5290-2021 standard with varying different hole diameters, printing speeds, and layer heights. The hole diameter measurements were obtained by a microscope and computer vision. An example of using computers, optical vision, and 3D digitisation was presented by Mendricky et al. [16]. Moreover, it has to be mentioned that the slicer software also affects the accuracy of printed parts. Šljivic et al. [17] presented a comparison of three different slicer software programmes and found that all three software programmes process objects in a unique way, concluding that the Cura slicer software and its printed parts are of good quality. In addition, the type of 3D printer can significantly affect the accuracy of the printed parts due to variations in the printing process, materials, and mechanisms involved. Different 3D printing technologies have unique characteristics that influence the final accuracy of the printed objects. For instance, SLA (stereolithography) and DLP (digital light processing) printers can achieve extremely fine layers, resulting in a higher accuracy and smoother surfaces. On the other hand, FDM printers typically have thicker layers, which might lead to visible layer lines and a slightly lower accuracy. Each 3D printing technology uses different materials with distinct properties. The choice of material can affect the dimensional stability, shrinkage, warping, and other factors that can impact the overall accuracy of the printed part.

The application of fits in additively manufactured parts can be seen in [18]. In their work, Schaechtl et al. perform an analysis of the non-assembly mechanism considering the fit clearance, and their results showed that the fit clearance has a greater influence than the part deviations. A similar work to this is [19], presented by Lieneke et al. In this work, the authors determined the tolerance values measured on models of a cube, cylinder, and sphere placed in nine different positions on the printer bed with respect to the x-y plane. As a result, the tolerance zones and achieved IT grades were given for a dimensional range from 3 mm to 400 mm. The grade of IT9 was achieved for a size of 315 mm for the x-axis only, and IT10-grade quality was achieved for dimensions of 120 mm for the x- and z-axis and 180 mm and 250 mm for the x-axis only. No study was found in the available literature that examined the geometric accuracy of a product and subsequently assembly manufactured it with dimensions specified according to the ISO 286-1:2010 system of limits and fits. When it comes to such dimensions in the form of, e.g., Ø50 ± 0.05 mm, it has not yet been shown how a 3D printer “understands” such a concept of tolerances and fits; however, this is not the job of a 3D printer, but the job of a slicer or of the person who models the object. Therefore, it was necessary to establish a systematic approach to accomplish this. How can a product be modelled with a computer to be manufactured with an FDM 3D printer within specified tolerance ranges? In line with the above studies, it is important to define the pre-processing parameters with which the parts will be printed, and a prerequisite for this is an appropriate 3D printer calibration, especially when it comes to desktop 3D printers.

So far, the approach taken in the literature has been to determine the product tolerances at the end of the FDM process without specifying them beforehand. The goal of this study is to propose a process for achieving specified tolerances with FDM 3D printing technology and define them in a way that is understandable to the 3D printer. The ISO 286-1:2010 system of limits and fits was used for CAD modelling, and the parts were manufactured to form a hole base system and a clearance fit. The upper and lower limits were defined for the nominal size achieved by the FDM 3D printer, and a comparison was made with those of the ISO 286-1:2010 system of limits and fits. A method for modelling a CAD model was proposed to ensure that the 3D printer produces the part within the allowable limits of the ISO 286-1:2010 system of limits and fits. Finally, the roundness tolerance was determined for each tolerance zone used. This research focused only on vertical 3D-printed holes and shafts.

In correlation with the previously reported studies, the findings in this work are based on the ISO 286 standard.

The professional and scientific contributions of this study are as follows:

• Outline the systematic calibration procedure of a 3D printer;
• Identify the influence of the size of the build plate;
• Present a novel approach for the CAD modelling of parts based on ISO 286 to 3D-print the parts within pre-set tolerance limits;
• Successfully apply the ISO 286 standard on a desktop 3D printer;
• Combine the Linear Advance and the Hole Horizontal Expansion factors and the ISO 286 standard to reduce the dimensional inaccuracy of the 3D-printed parts to a minimum and correlated them with, e.g., the clearance fit system.

2. Materials and Methods

For this study, a Creality 3D Ender-3 Pro FDM 3D printer (Figure 1) was used with a printing accuracy of ±0.1 mm according to the manufacturer’s specifications. PLA (polylactic acid, PLASTIKA TRČEK, Ljubljana, Slovenia, A grade—100% original, biodegradable and innocuous, white, 1.75 mm) material was used for 3D printing. Ultimaker Cura 5.1.1 slicer software was used for 3D printing preparation [20]. All models were printed with the parameters shown in

Table 1. General parameters used for 3D printing.

Parameter	Value
Temperature (°C)	200
Bed temperature (°C)	45
Layer height (mm)	0.2
PLA diameter (mm)	1.75
Infill (%)	100
Pattern	Lines
Printing speed (mm/s)	50
Fan settings (all layers) (%)	100
Layer orientation (°)	±45
Number of perimeters	1
Nozzle diameter (mm)	0.4

and are based on the default specifications of the material, 3D printer, and slicer software. A flow chart summarizing the procedure of this study is presented in Figure 2.

2.1. Hardware Properties

2.1.1. Extruder Calibration

The first step in calibration was to determine the extrusion flow rate (E-steps) to ensure that the printer was extruding filament at the correct rate and avoid under- or over-extrusion. The standard E-steps specified by the manufacturer were 93 steps/mm. To verify the flow rate, 50 mm of filament was extruded using the following procedure. The filament manufacturer recommended a temperature range of 195–225 °C, so it was set to 200 °C. The filament was marked at 50 mm from the extruder, measured from the flat side of the extruder as shown in Figure 3. On the 3D printer’s user interface, the extruder movement was set to 50. Extrusion was started, and once the filament stopped moving, the difference was measured. The distance between the mark and the extruder was measured and a new value was determined using the following formula:

$$E_{\mathrm{n}\mathrm{e}\mathrm{w}}=\frac{E_{\mathrm{o}\mathrm{l}\mathrm{d}}\times D_{\mathrm{S}}}{D_{\mathrm{m}}}$$

(1)

where

• $E_{\mathrm{n}\mathrm{e}\mathrm{w}}$—new extrusion E-steps, in steps/mm;
• $E_{\mathrm{o}\mathrm{l}\mathrm{d}}$—default extrusion E-steps, in steps/mm;
• $D_{\mathrm{s}}$—the distance to be extruded, in mm;
• $D_{\mathrm{m}}$—the measured distance between the markers, in mm;

Figure 3. The requested 50 mm of material to be extruded and the actual amount of the extrusion: under-extrusion.

Figure 3. The requested 50 mm of material to be extruded and the actual amount of the extrusion: under-extrusion.

The newly established E-steps were 125.67 steps/mm. The procedure was repeated, and the amount of the extrusion was checked and confirmed.

2.1.2. Bed Levelling

Next, the printer bed was calibrated, with the goal being to achieve a uniform distance between the nozzle tip and the bed surface across the entire printer bed. The bed is supported by four screws with cylindrical springs. By turning the screws, the bed can be moved away from or toward the nozzle. To achieve uniform spacing between the bed and nozzle, a 3 mm thick aluminium plate was used, and a test print was made with a 0.2 mm thick layer of material to ensure that the material was extruded evenly across the bed surface and that there were no gaps between the layers.

2.1.3. Axis Steps and Skew Checking

It was verified that the extruder performs the specified movement in the x and y direction. A 100 mm long part was modelled and printed in both directions (Figure 4) and measured. No irregularities were found. All measurements were made with an STALCO S-11115 0.02 mm calliper.

To ensure that the 3D-printed parts were not distorted in the x-y, x-z, and y-z directions, the method described in [21] was used to help with this step. The model shown in Figure 5a was printed in the x-y direction, while in Figure 5b, it was printed in the x-z and y-z directions, and the diagonal distances from the model vertices A-C and B-D were measured. No problems were found as the printed models had the correct dimensions and were not distorted in any direction (90° to the base) (Figure 5c,d).

2.1.4. Residual Pressure in the Nozzle (Oozing)

The Linear Advance (LA) parameter allows one to regulate the pressure that accumulates in the nozzle during material extrusion and retraction. The LA also pulls the material depending on the speed of the nozzle movement. Despite the speed of the nozzle movement (fast, slow, or paused), there is still residual pressure in the nozzle, which can lead to over-extrusion. To use LA, it must be activated in the slicer software and its factor must be set. According to [22], the LA calibration procedure was performed by printing several horizontal lines with different LA factors ranging from 0 to 100, in steps of 10, as shown in Figure 6. Since different printing speeds correspond to different LA factor sizes, some lines appeared thicker and others thinner, and the line width is not important. Therefore, a line that looks as even as possible should be considered as it indicates that the nozzle pressure is neither too high nor too low. Finally, the LA factor of 25 was chosen.

2.2. Software Properties

2.2.1. Dimensional Recognition in the Ultimaker 5.1.1 Slicer Software

After the CAD modelling in the Autodesk Inventor Professional 2023 Education License software, the object was imported into the Cura slicer software, and it was checked whether the software recognized the object with the exact dimensions of the CAD model. The menu in the slicer software shows the dimensions of the object along the x, y, and z axes differently from the CAD model. Specifically, for the measurement of Ø50 mm, the software displays 49.9965 mm along the x-axis and 49.9982 mm along the y-axis (Figure 7left). Using the uniform/snap (best choice for the user) scaling property, a correction was entered for both measurements and set to 50 mm (Figure 7right). This is important because each tolerance field defines how much the dimensions of the object may deviate from the defined target dimensions without being influenced by the slicer software or the transformation of the model CAD into the STL file. However, the snap scaling step is not always necessary. It depends on the CAD export parameters to STL.

The test print showed the correct measurement of 50.00 mm (Figure 8a). However, this option is only available if the dimensions of the object are external dimensions. Since both external and internal dimensions were taken into account, a hole with a diameter of 45 mm was added to the existing model (Figure 8b), to which this option cannot be applied. The test print showed inaccuracies in the internal dimensions of the object (44.80 mm), although the correct values were entered in the slicer software for the external dimensions, which were again printed accurately. Therefore, the next step was to perform a dimensional compensation.

2.2.2. Dimensional Compensation

The Horizontal Expansion (HE) parameter enables the size adjustment of 3D-printed parts in the x and y directions to compensate for the shrinkage of material as it cools. A positive HE value increases the outside dimensions of the printed part when it is smaller than expected due to shrinkage, while a negative value decreases the outside dimensions when the printed model is larger than expected. Initial Layer Horizontal Expansion (ILHE) is the same as HE, but it can only be applied to the first layer that is in contact with the build surface to reduce the “elephant foot” effect. Hole Horizontal Expansion (HHE) affects the inner dimensions of the printed part the same way that HE affects the outside dimensions. Therefore, to properly set these parameters, the same CAD model as that in Figure 5b was used, and the first 3D-printed part was measured with outer dimensions of Ø50 mm and inner dimensions of 44.80 mm. The “elephant foot” effect occurred on the first layer with dimensions of Ø50.64 mm. The negative difference of 0.2 mm in the x and y directions was divided by two, and the first HHE value was set to 0.1 mm. The iterations were performed for all three parameters, and the established values are shown in

Table 2. The established compensation values.

Parameter	Value
Horizontal Expansion (mm)	0.0
Initial Layer Horizontal Expansion (mm)	−0.2
Hole Horizontal Expansion (mm)	0.13

. It took five iterations to confirm the HHE value, as shown in

Table 3. Iteration steps for HHE value and Ø45 mm dimension.

Request, mm		Ø45
Iteration	Measurement (mm)	Difference (mm)	HHE Value (mm)
1.	Ø44.80	0.2	0.1
Adopted HHE value (mm)	0.1
2.	Ø44.94	0.06	0.03
Adopted HHE value (mm)		0.13
3.	Ø45	0	0.13
Adopted HHE value (mm)	0.13
4.	Ø45	0	0.13
Adopted HHE value (mm)		0.13
5.	Ø45	0	0.13
HHE value confirmed (mm)		0.13

. It has to be pointed out that the shrinkage depends on process parameter settings, as well as the dimension and geometry of the part. When transferring the printing settings from the calibration part to the functional part, the traditional shrinkage compensating methods follow a straightforward approach of scaling the input geometries based on developed models before the fabrication process. Once manufacturing is complete, the scaled CAD models undergo a shrinking effect, resulting in enhanced dimensional accuracy compared to that of a conventional fabrication workflow.

To check the accuracy of the set parameters, a test print of 5 models arranged on the build plate was carried out. This was to determine whether the 3D printer could print 5 models simultaneously at 5 different positions on the build plate, as shown in Figure 9, and whether there was a position where the model had inaccurate dimensions. For 2 of the models marked in Figure 9, deviations from the target dimensions were found in the x and y directions. Therefore, regardless of accuracy, 3D printing was performed exactly in the centre of the build plate.

2.3. ISO 286-1:2010 System of Limits and Fits

In practice, the hole basis system and the shaft basis system are applied, and preference should be given to the hole basis system to facilitate machining and measurements from the outside of the machine part [23]. Therefore, this paper investigates the possibility of joining printed parts that form the hole basis system. According to [3], the quality of FDM 3D printing starts at IT9 grade and goes up to IT14 grade. To produce a clearance fit, all available tolerance zones of the shaft from zone h (minimum clearance) to zone a (maximum clearance) were used. The MITCalc 2.02 software [24] was used to calculate and analyse the system of limits and fits. The nominal range used for the analysis was randomly set to 30–40 mm. The basic size to be used was calculated as follows:

$$D=\sqrt{D_1·D_2}$$

(2)

where

• D, in mm—geometrical mean value;
• D₁; D₂, in mm—lower and upper range values ($D_1=30$ mm; $D_2=40$ mm).

Therefore, D is equal to 34.64 mm, and it was rounded to 35 mm. This value was further used as the basic size, as shown in Figure 10. For the 35 mm dimension, the hole basis system, including a clearance fit and tolerance zones, starting with zone H9 for the hole and h9 for the shaft, was chosen as the first possible clearance fit.

Once the tolerance zones and qualities of the holes and shafts are defined, it is necessary to determine how to create a CAD model so that the 3D printer “understands” the tolerances. According to Table 3, for a hole with a measured diameter of Ø35H9, the lower deviation is EI = 0 mm and the upper deviation is ES = 0.062 mm, which means that the hole should be manufactured within these limits. So, how can we design the hole and the shaft so that the 3D printer makes the part within these limits? Normally a 3D printer has a nozzle diameter of 0.4 mm and the layer height can vary, but here, it is assumed to be 0.2 mm. In practice, it was assumed that the ideal layer width should be 20% wider than the nozzle diameter—in this case, 0.48 mm. Therefore, when a layer is printed on the 3D printer, the cross-sectional area of that layer has an elliptical shape, and when the printer makes a full circular nozzle move for a given diameter of 35 mm, the layer should look approximately as shown in Figure 11. This method was applied to all other hole and shaft sizes. Therefore, the CAD part of the hole (Figure 12a) and shaft (Figure 12b) was modelled as the arithmetic mean (rounded to 35 mm) of the minimum and maximum diameter allowed by the tolerance zone. For the case of Ø35H9, this is Ø35.031 mm. The CAD part of the hole has an arbitrarily chosen wall thickness of 3.2 mm. An example of analysed tolerances and fits for the tolerance zone H9 is shown below in

Table 4. Tolerances and clearance fit for the 35 mm basic size and tolerance zone H9.

Type of Fit	Tolerance Zones	Upper/Lower Deviation (mm)	Max/Min Diameter (mm)	Diameter to Be 3D Printed (mm)
Ø35H9/h9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35h9	0.000	Ø35.000	Ø34.969
		−0.062	Ø34.938
Ø35H9/g9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35g9	−0.009	Ø34.991	Ø34.960
		−0.071	Ø34.929
Ø35H9/f9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35f9	−0.025	Ø34.975	Ø34.944
		−0.087	Ø34.913
Ø35H9/e9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35e9	−0.050	Ø34.950	Ø34.919
		−0.112	Ø34.888
Ø35H9/d9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35d9	−0.080	Ø34.920	Ø34.889
		−0.142	Ø34.858
Ø35H9/c9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35c9	−0.120	Ø34.880	Ø34.849
		−0.182	Ø34.818
Ø35H9/b9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35b9	−0.170	Ø34.830	Ø34.799
		−0.232	Ø34.768
Ø35H9/a9	Ø35H9	0.062	Ø35.062	Ø35.031
		0.000	Ø35.000
	Ø35a9	−0.310	Ø34.690	Ø34.659
		−0.372	Ø34.628

, and to better understand Table 4, tolerance zone positions are presented in Figure 13.

2.4. Noncontact Measurement Procedure

After a specimen was 3D printed, it needed to be measured to determine its diameter. The specimens were measured using the pre-calibrated ON Diameter app [25] to avoid errors due to contact measurement with a sliding scale. To reduce the influence of measurement errors, each specimen was measured ten times. The measurement was carried out so that the top of each specimen was laid down on the screen of the mobile device to avoid the influence of the “elephant foot” on the results (Figure 14). It was obvious that in this phase, using a calliper was not an option. When tolerances and fits need to be analysed with precision, callipers are not a good measuring tool. It is better to use a more precise instrument, such as a micrometre or even a 3D measuring machine. However, here, a different approach was presented, and more importantly, noncontact measurement was used to avoid any influence on the accuracy in case of contact measurements since this is a thin-walled structure and it is very easy to deform it. The app accuracy is ±0.001 mm.

3. Results

All our measurements were analysed to determine the standard deviation, the minimum and maximum measured diameter values, the upper and lower deviation, and the roundness tolerance. The overall time of 3D printing was 1392 min. The total amount of printed parts was 54. It was checked whether the 3D printer could achieve the specified tolerance field. The mean value of the obtained measurement results was compared with the specified mean value of the CAD model. The results showed that all the tolerance zones for the holes and shafts were achieved, and thus, a clearance fit was achieved. When comparing the size of the tolerance zones according to ISO 286-1:2010, tighter tolerance zones than those prescribed were achieved for 3D printing (Figure 15), which means that the process of calibrating the 3D printer was carried out accurately.

The change in diameter due to the increase in the tolerance IT grade from IT9 to IT14 for both the hole (Figure 16a) and the shaft (Figure 16b) is presented. This shows that it is possible to guarantee the clearance between 3D-printed parts by combining the tolerance zones in a hole basis system and clearance fit. Finally, all the upper and lower deviations from the basic size of Ø35 mm were defined for all the tolerance zones that result in a clearance fit in the observed system (

Table 5. Tolerance zones and limits achieved by FDM 3D Printing.

Basic Dimension (mm)			Ø35	Tolerance Zones and Limits—3D Printing
H9	0.045	h9	−0.004	g9	−0.021	f9	−0.027	e9	−0.050	d9	−0.080	c9	−0.122	b9	−0.171	a9	−0.323
	0.002		−0.056		−0.071		−0.084		−0.095		−0.143		−0.176		−0.229		−0.370
H10	0.096	h10	−0.009	g10	−0.014	f10	−0.029	e10	−0.089	d10	−0.090	c10	−0.125	b10	−0.179	a10	−0.311
	0.008		−0.067		−0.080		−0.113		−0.142		−0.140		−0.210		−0.259		−0.401
H11	0.150	h11	−0.012	g11	−0.029	f11	−0.054	e11	−0.068	d11	−0.149	c11	−0.165	b11	−0.184	a11	−0.347
	0.077		−0.106		−0.109		−0.168		−0.200		−0.215		−0.212		−0.280		−0.470
H12	0.228	h12	−0.080	g12	−0.086	f12	−0.078	e12	−0.095	d12	−0.187	c12	−0.200	b12	−0.270	a12	−0.400
	0.127		−0.158		−0.155		−0.178		−0.210		−0.247		−0.274		−0.330		−0.491
H13	0.301	h13	−0.207	g13	−0.183	f13	−0.197	e13	−0.201	d13	−0.239	c13	−0.272	b13	−0.380	a13	−0.460
	0.188		−0.345		−0.336		−0.307		−0.323		−0.317		−0.377		−0.473		−0.580
H14	0.328	h14	−0.244	g14	−0.248	f14	−0.205	e14	−0.274	d14	−0.319	c14	−0.424	b14	−0.511	a14	−0.526
	0.249		−0.368		−0.365		−0.379		−0.413		−0.459		−0.639		−0.600		−0.671

). This also allows for an easy comparison with ISO 286:1-2010 tolerances and fits for the same basic size. Let us take the example of the fit Ø35H9/h9. For the tolerance zone H9, Ø35.031 mm (Dprinted) was used as the basic dimension for modelling the CAD model of the hole. Based on 10 measurements, to decrease measurement error, an average value of Ø35.026 (0.014) mm (Dmeasured) was obtained, with Ø35.002 mm as the smallest measured value and Ø35.045 mm as the largest (Figure 17a). Similarly, for the tolerance zone h9, a basic dimension of Ø34.969 mm (dprinted) was used to model the CAD model of the shaft. The measurement resulted in an average value of Ø34.972 (0.021) mm (dmeasured), with Ø34.944 mm as the smallest measured value and Ø34.996 mm as the largest (Figure 17b).

For each measured hole and shaft with different basic tolerance grades and tolerance zones, the roundness tolerance of the 3D printer was determined. The roundness tolerance is defined as the deviation bounded by two concentric circles at a distance of t. The distance t represents the difference between two concentric circles. Here, the distance t represents the difference between the minimum and maximum diameter measurements resulting from 10 readings of each 3D-printed object. The individual roundness tolerance values can be found in

Table 6. Roundness Tolerance t for the basic size Ø35 mm.

Basic Size (mm)			Ø35	Roundness Tolerance t (mm)
H9	0.043	h9	0.052	g9	0.050	f9	0.057	e9	0.045	d9	0.063	c9	0.054	b9	0.058	a9	0.047
H10	0.088	h10	0.058	g10	0.066	f10	0.084	e10	0.053	d10	0.050	c10	0.085	b10	0.080	a10	0.090
H11	0.073	h11	0.094	g11	0.080	f11	0.114	e11	0.132	d11	0.066	c11	0.047	b11	0.096	a11	0.123
H12	0.105	h12	0.078	g12	0.069	f12	0.100	e12	0.115	d12	0.060	c12	0.074	b12	0.060	a12	0.091
H13	0.113	h13	0.162	g13	0.153	f13	0.110	e13	0.122	d13	0.078	c13	0.105	b13	0.123	a13	0.120
H14	0.079	h14	0.124	g14	0.117	f14	0.174	e14	0.139	d14	0.140	c14	0.215	b14	0.151	a14	0.145

.

The presented CAD modelling method shown in Figure 10 was proven to be very simple and understandable. Placing the nozzle axis in the arithmetic mean of the upper and lower deviations for a nozzle diameter of 0.4 mm was successful. If we consider the empirical setting that the most acceptable layer width should be 20% wider than the nozzle width, which is 0.48 mm, it follows that for a CAD model diameter of Ø35.031 mm, the lower measurement would be Ø34.791 mm and the maximum would be Ø35.271 mm, which achieves a large deviation from the target dimension given by the H9 tolerance field. This can be affected by varying the layer height and nozzle diameter like in other studies, but this study has shown that this effect can be negligible with appropriate calibration and software parameters.

4. Discussion

Starting with CAD modelling, the user has to consider tolerances and fits in advance during the modelling time if it is necessary to create an assembly with high demand. This is the opposite of the study presented by Herbert Fritz et al. [3]. It turns out that if the tolerances and fits are not considered during the modelling time, the CAD modelling will become useless in terms of accuracy and 3D printing. This is comparable to the conventional turning process. If a technical drawing is not prepared using the tolerances and geometrical specifications of the part to be produced then how can we expect the worker at the turning machine to do his job accurately? A 3D printer will do its job no matter how accurately a model is prepared; the question is, how accurately can a part be prepared in advance? Therefore, the proposed approach suggests that the connection parts should be modelled using the arithmetic mean of the minimum and maximum values according to the used tolerance zone. Besides CAD modelling, slicer software can deal with the parameters that can affect accuracy. Studies reported by Ahmad et al. [1], Abdelrhman et al. [6], Boschetto et al. [7], and Pombinha et al. [9] have dealt with process parameters such as the layer thickness, deposition angle, temperature, etc., searching for a better accuracy. They have identified improvements. However, this study explores the parameters that are directly connected and can affect the geometry of the printed part, specifically the Horizontal Expansion parameter with its sub-parameters. The problem was with the internal dimensions; therefore, this parameter remained at 0.0 mm but the Hole Horizontal Expansion as a sub-parameter had to be changed to −0.13 mm. In our attempt to compare this result with other results, no study was found. When it came to the 3D printer, except for the extruder calibration procedure, no additional efforts or hardware changes were made.

5. Conclusions

The analyses presented in this paper proved that it is possible to produce objects with an FDM 3D printer within the permissible limits for the tolerance, fit, and type of fit. It is very important to perform a proper calibration of desktop FDM 3D printers because their manufacturing and assembly quality is questionable. It was shown that it is possible for a 3D printer to “understand” the tolerance dimension established with the ISO 286 tolerance system. This allows for a comparison with conventional manufacturing technologies such as turning, milling, drilling, etc., and also a comparison with the deviations defined in the ISO 286 system. A measure of the roundness tolerance is also provided. This approach can help to solve problems of inaccuracy in product manufacturing and the limitation of work volume in low-cost FDM 3D printers, which can increase their representation in the product development and manufacturing process. However, it is important to point out that additive technologies are not only used for manufacturing final products but also for making tools and moulds, prototypes, and parts that are difficult to manufacture using conventional methods, etc. Therefore, additive technologies still have great potential for applications in various industrial sectors. Among the problems that have not been successfully solved is the occurrence of “elephant feet” during the printing of the first layer, which causes each printed object to be outside the specified dimensions in its lower part near the build plate. Changing the printing temperature or printing speed of the first layers might be useful. In addition, when the printer’s nozzle completes a full circle, the beginning and end of the layer end up in the same place, resulting in a material build-up or a so-called seam. Measurements in this area of the objects were the subject of our analysis, as our focus was on what 3D printers can do without additional material post-processing.

It is necessary to express that this research was conducted on a desktop 3D printer, and the proposed parameters and factors must be re-considered on other types of 3D printers. Furthermore, the calibration procedure of each type of 3D printer is individual approach. Future works should consider using different types of FDM 3D printers, different types of materials such as PET-G, and case studies applying the clearance fit for the assembly of parts and functional analyses. Our future research will include calculations for and designs of parts that can be assembled into transition and interference fits based on the ISO 286 system. The same calibration process will be applied to other types of 3D printers, focusing on printers for metal 3D printing, and the differences will be analysed. Furthermore, future research should be conducted regarding 4D printing [26] and using materials such as poly vinyl chloride (PVC) [27].