Comparative study about dimensional accuracy and form errors of FFF printed spur gears using PLA and Nylon

Polymer Testing 117 (2023) 107862 Available online 5 November 2022 0142-9418/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Comparative study about dimensional accuracy and form errors of FFF printed spur gears using PLA and Nylon Irene Buj-Corral * , 1 , Enrique Ernesto Zayas-Figueras 1 Department of Mechanical Engineering, Barcelona School of Industrial Engineering (ETSEIB), Universtiat Polit` ecnica de Catalunya, Barcelona, Spain ARTICLE INFO Keywords: FDM 3D printing Dimensional accuracy Form error PLA Nylon ABSTRACT In the present paper the comparison of dimensional accuracy and form errors of FFF (Fused Filament Fabrication) 3D printed spur gears obtained in two different polymeric materials (PLA and Nylon-PA6) is presented. Two types of gears were designed and printed, having different module and teeth number. First, the gear modelling process is presented. The printing parameters were defined for both materials. Then, the measuring processes were described. Using the method of the sector span, the base circular thickness and the base pitch of the gears were determined. Additionally, the root and tip diameters were measured, and their roundness and concentricity errors were determined. The analysis of the results shows that, in general, PLA allows obtaining better dimensional accuracy than Nylon. Nylon parts, which were obtained with lower infill ratio than PLA parts showed lower from errors. 1. Introduction The use of plastic gears instead of metallic ones is a current trend with a widening area of applications. Their characteristics are being improved by new developments in both materials and processing technologies. For particular applications such as automotive and aerospace engineering, polymer gears have unique advantages over metal gears, such as: low cost of production, low density, low inertia, high efficiency, quietness of operation, capability to absorb shock and vibration as a result of elastic compliance, ability to operate with minimum or no lubrication, etc. In automobiles, they are used in the level of the gasoline tank, in windshield wiper systems, in the turbo, etc. They are also employed in toys such as moving dolls or remote-control cars; and in electronic component drives (electric toothbrushes, CD player doors) [1–3]. 3D printed gears can also be used in scale models in the field of engineering education. In particular, the gears that are presented here were designed for didactic models of mechanisms for teaching, where the gear transmissions have more of a kinematic type of operation than of high-power transmission [4]. On the other hand, the mechanical strength of the plastic gears is limited and depends greatly on the type of material chosen. In recent years, traditional plastic gear manufacturing processes, such as hobbing or injection moulding, have been complemented with Additive Manufacturing (AM) technologies. AM allow producing functional gears that are cheap if low-cost machines are employed. Some significant advantages of this technology are capability to handle complex gear shapes and to produce near net-shaped gears, resource efficiency and rapid product development. Gupta [1] outlines the four steps followed in AM processes to manufacture gears (Fig. 1): first, the design of the CAD (Computer Aided Design) model of the gear; second, the conversion of CAD model to STL (Standard Triangle Language) file, third, the transfer of the STL file to the machine and fourth, the building of the gear models. Some extensively used AM processes to manufacture gears of different sizes and shapes from plastics, metals, ceramics and composites are the following: Stereolithography (SLA) -liquid based, Fused Deposition Modelling (FDM) or Fused Filament Fabrication (FFF) -solid based, Selective Laser Sintering (SLS) -powder based. Finally, in the same work, the Polyjet printing and Ink-jet printing are explained, and some gears with a singular geometry are shown. On the other hand, Gibson [5] explains that most AM processes involve, to some degree at least, the following eight steps: 1) CAD modelling -all AM parts must start from a software model that fully describes the external geometry; 2) Conversion to STL - AM machine accepts the STL file format, which has become a de facto standard, 3) Transfer to AM Machine and STL File Manipulation -STL file must be transferred to the AM machine; there may be some general manipulation * Corresponding author. E-mail address: [email protected] (I. Buj-Corral). 1 Equal contribution of both authors. Contents lists available at ScienceDirect Polymer Testing journal homepage: www.elsevier.com/locate/polytest https://doi.org/10.1016/j.polymertesting.2022.107862 Received 2 August 2022; Received in revised form 16 October 2022; Accepted 4 November 2022 Polymer Testing 117 (2023) 107862 2 of this file so that it is the correct size, position, and orientation for building, 4) Machine setup -the AM machine must be properly set up prior to the build process, 5) Build -building the part is mainly an automated process and the machine can largely carry on without supervision, 6) Removal -once the AM machine has completed the build, the parts must be removed, 7) Post-process -once the parts has been removed from the machine, parts may require an amount of additional cleaning up before they are ready for use; and 8) Application -parts may now be ready to be used. Nevertheless, they may also require additional treatment before they are acceptable for use. For example, they may require priming and painting to give an acceptable surface texture and finish. Parts may also be required to be assembled together with other mechanical or electronic components to produce a final model or product. Different authors have 3D printed mechanical components such as connecting rods [3] or cams [4], mainly to be used as prototypes, by means of the FFF technology. As for gears, Zhang et al. [5] manufactured Nylon polymer gears using different materials, specifically: Nylon 618, Nylon 645, alloy 910 filaments (in a 3D Ultimaker 2 printer), together with Onyx and Markforged Nylon proprietary materials (in a Mark- Forged X7 3D printer). The best wear performance from a gear wear test rig was found for Nylon 618. It is hypothesised that the different mechanical performance among Nylon filaments was caused by differences in crystallinity. Moreover, SEM (Scanning Electron Microscopy) revealed dramatically different wear behaviour for the 3D printed gears when compared to literature reports for injection moulded gears (particularly for Nylon 66). The results showed that 3D printed Nylon 618 gears performed better than injection moulded Nylon 66 gears when low to medium torque was applied (torque below 12 N m). The authors also hypothesised that the better Nylon 618 friction and wear performance (when compared to other printed materials) essentially depends on the thermal behaviour and the level of sintering effect between layers. Different printing parameters influence the dimensional accuracy of FFF printed parts. Kechagias et al. [6] divide them into three groups: a) signal parameters effects, such as: part orientation, layer thickness, nozzle temperature and others; b) control parameters effects like the type of material, and c) noise parameters effects, which depend on the printed frame design and on the mechanical and electrical system. Gendviliene et al. [7] conclude that the parts printed with PLA/HAp (PLA with Hydroxyapatite) have equal or even better accuracy than the ones printed with PLA. On the other hand, they found that there were remarkable accuracy differences among 3D printers from different manufacturers. Zhang et al. [8] outlined the relevance of the appropriate selection of 3D printing parameters in the performance of 3D printed Nylon parts such as spur gears. Four 3D printing parameters were considered: printing temperature, print speed, printing bed temperature and infill percentage. A prediction model of 3D printed gears was carried out with three models, including an artificial neural network (ANN) model, a genetic algorithm (GA)-based ANN model and a leave-one cross validation-applied GA based model. A total of 100 spur gears were printed (50 matched pairs), and were later assembled on a gear wear test rig and subjected to life cycle with 10 N m torque. The tests included the recording of the wear occurring at the gear tooth until gear failure. Toe time from the beginning of the test run until the gear failure was considered as the fatigue time. The authors used the 3D printing parameters as input, and the corresponding gear life cycle data from test rig as an output to create the model. They employed a Gaussian process to perform multi-parameter regression to find out the approximate likelihood of the output accuracy. Their results suggest an optimised setting with the following parameters: printing temperature of 250 ◦C, print speed of 70 mm/s, bed temperature of 25 ◦C and infill percentage is 80%. Toe operational time of the printed gears was increased more than 3 times compared with the gears produced using the default print settings recommended by the manufacturer (printing temperature of 250 ◦C, print speed of 45 mm/s, bed temperature of 30 ◦C and infill percentage of 60%). The sensitivity analysis performed by means of the Garson’s algorithm indicated that infill percentage had the greatest influence on the performance of a 3D printed gear, and bed temperature had the lowest influence on the test result. Pisula et al. 3D printed gears in 3 different materials: ABS M-30; ULTEM 9085 and PEEK. They were subjected to a fatigue test. The gears made of PEEK showed lowest wear among the three materials studied [9]. Besnea et al. [10] present a comparative study regarding the wear of gearwheels of different thermoplastic materials such as: polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), carbon fibre-reinforced polyethylene terephthalate glycol (PETG) and Nylon. The authors designed and manufactured 8 gears using the same module and number of teeth for all the gears. They used a specialized gear measurement equipment to measure the geometry of the plastic gears, specifically a “double flank gear test”. The software provided the following geometric deviations of gearwheels: i) the double flank rolling deviation -that is, the difference between the maximum and minimum values of the working centre distance; ii) the double flank rolling tooth to tooth deviation – that is, the tooth radial composite deviation corresponding to one pitch, during one complete cycle of engagement of all the product gear teeth, and, iii) the radial runout -which represents the value of radial runout of the gear between the maximum and the minimum radial distance from the gear axis. The authors also designed and manufactured an experimental stand to check the wear of the printed gearwheels (checking the tooth profile, the bottom land and the state of the gear surfaces). The PLA gearwheels showed the smallest deviations from the nominal design dimensions. On the contrary, the biggest deviations correspond to the Nylon gearwheels. In addition, the most unaffected material is PLA, while ABS gearwheels showed the most important wear traces. Also, the surface of PETG and Nylon gearwheels had a noticeable change after testing. The authors highlight the viability of the temporary use of the gearwheels manufactured by FDM regarding both the precision of execution (tooth profile, tooth surface condition, etc.) and the advantage of its rapid low-cost manufacture, in industrial equipment requiring an uninterrupted cycle of operation, while the original worn metal gearwheel is being repaired, reconditioned or manufactured by conventional cutting methods. Vasilescu and Fleser [11] present a study about the dimensional generation and the technological parameters to consider to produce 3D printed spur and helical gears in PLA, ABS and PETG materials. The Fig. 1. Steps in Additive Manufacturing (AM) of gears (Adapted from Ref. [3]). I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 3 authors recommended to use PLA as first option, due to its better compressive strength and smaller elongation at break relative to the other two materials cited. The authors also made a comparison of compressive strength values among the above-mentioned plastic materials and aluminium -series 6028, 6063 and A380-. They concluded that there are great differences between plastic and metallic materials. In order to 3D print them, the authors recommended to use a pressure angle between 25◦and 35◦(to get a more underline base of the tooth), instead of the 15◦usually employed in injection-moulding or the 20◦ used in machining processes. The authors also suggest to use a standard module in the 3D modelling software to obtain a successful geometric correction, considering the shrinkage or expansion that may appear in the 3D printed gear. Shrinkage is much lower in the axial direction of the gears, that coincides with the vertical direction in which the gears are printed than in other directions. They use a mechanical part that consists of two gears of different dimensions coaxially assembled as a unique solid. Some recommendations relative to the settings of the layer generating program are made, for example: to activate the generation of a support area ensures a good adhesion of the gear wheel edges and a better geometry of the gear, the perimetral contours of the gear change from the first layer up to the last one, and the number of contours depends of the gear module used (a higher module requires more perimetral contours), so it is convenient to test and analyse different strategies of printing setting (e.g different values of linewidth, number of layers, etc.). The authors show that increasing the thickness of the peripheral lines will have good effects on the mechanical strength of the teeth. Also, some recommendations about the printing parameters are made, according to layers thickness (0.2 mm in the example given), being different for the perimetral layers than for the internal layers. For PLA, the printing temperature used was 210 ◦C and the printing bed temperature was 45 ◦C. According to Kechagias et al. [12] most influential parameters on mechanical strength in PLA parts are: raster deposition angle, nozzle temperature, printing speed and layer thickness. Using raster deposition angle of 0◦maximizes the mechanical strength of the parts. In addition, high nozzle temperature of 215 ◦C and low printing speed of 30 mm/s are recommended. For 100% dense parts, reducing layer thickness increases the mechanical strength of the parts, with a suggested layer thickness value of 0.1 mm. Regarding Polyamide, Vidakis et al. [13] found that raster angle of 0◦maximizes ultimate tensile strength and toughness of the parts, while raster angle of 45◦ optimizes theit Young’s modulus. Layer height of 0.25 mm optimizes the three responses. Nozzle temperature of 270 ◦C optimizes ultimate tensile strength and Young’s modulus, while nozzle temperature of 260 ◦C increases toughness. Regarding fatigue strength, Pandian et al. [14] compare the bending fatigue performance of spur gears manufactured with two types of Nylon by means of two different processes: selective laser sintering -SLS- (using Nylon 12) and the traditional process of plastic injection moulding -IM- (using Nylon 66). Single tooth bending fatigue tests were carried out in a custom-built test setup, applying cyclic pulsating loads on the tested gear. The results showed that SLS gears have higher bending fatigue life than IM gears, and this was remarkable in the high cycle fatigue region. On the contrary, this effect was not so important in the low cycle fatigue region. The reason of the above mentioned performance is that the fatigue strength of the SLS gears vary due to the different thermal behaviour at low cycle fatigue and high cycle fatigue regimes respectively. The crack path was undulating in SLS gears (where the layered structure of the gear helped in preventing the propagation of cracks) and smoother in IM gears. The same authors [15] found that layer orientation angle influences the bending fatigue strength. In that work, SLS gears were printed in on-edge configuration and the fatigue life was lower than that of the injection moulded gears. Cuesta and Mateos [16] created a computer application that allows the automatic programming of a Coordinate Measuring Machine (CMM) to measure cylindrical gears, both spur and helical gears. This application has two objectives: the first one, to identify an unknown gear (finding its construction parameters: such as the modulus, tooth number, tooth width, etc.) and the second one, to verify a known gear (calculating the profile errors, the base thickness error, the errors of flank distortion and the base pitch error). The basic terms and calculations on which the algorithm created by the authors is based correspond to the ISO 1328 Standard [17], related to the permissible errors in gears. Finally, the basic advantages of the combination of the use of the developed software together with the Coordinate Measuring Machine are presented. They are summarized in the following aspects: the measurement of the gear is automatic (CNC) and the entire calculation is carried out by the programme, so no specialized personnel is required; it is a fast process, as both measurement and calculation are carried out in the same machine and with only three teeth, saving an enormous amount of time compared to other systems that scan the entire profile, and the process involves a single measurement on a single machine, discouraging the combined use of different instruments, which introduces less uncertainty. Masovic et al. printed ABS and polyamide gears in both the horizontal and the vertical position. Highest dimensional accuracy was reported for ABS gears printed in the horizontal position [18]. In order to improve dimensional accuracy of 3D printed parts, Gao et al. propose two methods: auxiliary heating and polymer modification [19]. On the other hand, Fu et al. [20] highlighted that filament slippage with the feed gear can lead to dimensional error in FDM 3D printed parts. Few works are known about form errors of 3D printed gears. For example, Dennig et al. [21] reported that poor concentricity could increase pressure on the tool flank of the gears, thus increasing temperatures of the parts. The roundness error of the inner surface and the tooth profile error of the gears affect the radial clearance of the meshing pair [22]. Consequently, uneven load areas could appear. Dennig et al. [21] found roundness errors up to 0.674 mm for PA +CF (Polyamide with Carbon Fibre). In hemispherical 3D printed PLA parts, Luis et al. [23] reported roundness error values up to 0.297 mm and concentricity error up to 0.272 mm. Gaikwad et al. [24] reported average circularity error of 0.087 mm and average concentricity error of 0.026 mm. In the present paper, dimensional accuracy and form errors of spur gears printed in PLA and Nylon are presented. The gears work under the principle of conjugate profiles to obtain a constant transmission ratio. Achieving a good dimensional accuracy advantages a better contact between the teeth of the gears. Another important aspect is to maintain a distance between the centres of rotation of the wheels as exact as possible. This is also favoured by the dimensional accuracy of the wheels, for example, of their diameters. Thus, a good dimensional accuracy advantages an appropriate assembly and a good operation. Unlike other works, in the present work conventional measurement tools (gear tooth micrometres) are used to measure the sector span of the gears. From the measured data, intrinsic parameters of the gears like the base pitch and the base circular thickness were determined. Two different types of gears were studied, one of them having 17 teeth and module of 4 mm, and the second one, having 21 teeth and a module of 3 mm, both in PLA and in Nylon (PA 6). The sector span, the outer and root diameters were measured, and the circular pitch and the base circular thickness were calculated for each type of gears. In addition, roundness and concentricity of the outer and root circumferences were measured. 2. Materials and methods To achieve the goals of this work, a general methodology is proposed, consisting of 10 steps, outlined in Fig. 2, which are: 1) Selection of the type of gear and its basic parameters, taking into account three main factors: to use cylindrical gears, a standard module m and the number of teeth z to guarantee appropriate size and geometry of the gears; 2) Selection of the CAD modelling process by means of the use of SolidWorks software –choosing the modelling method that best generates the geometry of the gear; 3) Conversion of the CAD models to STL files, once gears have been modelled by means of the same CAD I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 4 software; 4) Selection of the polymeric materials for printing the gears –in this case PLA and Nylon have been used; 5) Selection of the printing parameters for the materials chosen; 6) Slicing process by means of the software BCN3D Cura version 3.2. –setting the right printing parameters and generating the G-Code files; 7) Transferring the G-Code files to the printing machine –this is made after these have been debugged; 8) Printing the desired gear models –by means of a BCN3D Sigma 19 printer; 9) Checking the printed gears –particularly checking the dimensions and form errors using a diversity of instruments and equipment, and 10) Discussion and conclusions of the results. Details of the above mentioned steps are explained in the following subsections. 2.1. Selection of the type of gear and its basic parameters As a start point, it is necessary to determine the type of gears to be modelled and printed. Three main selection factors were selected, which are: a) to use cylindrical gears (spur gears particularly) due to the fact that they have a more simple geometry than other types of gears and they are commonly used in practical applications, b) to use a standard module m of the metric system and c) to use a number of teeth z that favours an appropriate size and geometry of the gears. Two types of spur gears were selected: type A gear (with m =3 mm and z =21) and type B gear (with m =4 mm and z =17, which is the minimum number of teeth to avoid the undercutting in normal gears -without corrections [25]. The following subsection shows both the values of the geometrical parameters used for the modelling of the two types of gears and the comparative geometry of the tooth profiles generated by different modelling processes. 2.2. Selection of the CAD modelling process In this work, the CAD software used is SolidWorks® (SW) Education Edition (by Dassault Syst` emes). The gear models were obtained in two ways. The first one is using the Toolbox of SW, where once the desired standards are selected, and the type of gears are defined: module and number of teeth, pressure angle, etc., the 3D gear model is automatically generated. The second one consists of drawing a sketch of the tooth profile and extruding it. Fig. 3 a) shows a section of a normal gear and its geometrical parameters [26]: d is the reference diameter, d a is the tip diameter, d b is the base diameter, d f is the root diameter, h is the tooth depth, h a is the addendum, h f is the dedendum; S 1 is the tooth thickness, S 2 is the space width and r b is the fillet. Fig. 3 b) and c) show the Fig. 2. The general methodology of the work. Fig. 3. a) Geometrical parameters of a normal gear, b) Geometry of the teeth obtained by means of Toolbox library, b) Geometry of the teeth obtained by means of a sketch –more precise. I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 5 comparison between both types of gear tooth geometries. In this work, the last option was employed, since the tooth profile generated from the sketch (Fig. 3 c) shows a more precise tooth geometry, considering the radius of the tooth base and the continuity of the tooth profile. Fig. 4 shows the 3D models of type A and B gears respectively, which have been modelled according to the values of Table 1 and from which the gears have been 3D printed. 2.3. Conversion of the CAD model of the gear to STL file As the authors Gibson et al. [2] state, in the STL files the solid representation is approximated by a mesh of triangles and they only contain geometrical information. In this work, from the CAD models of the gears the STL files were created using SW. These files are necessary to set the appropriate parameters in the slicer software. 2.4. Selection of the polymeric materials for the gears The most commonly used polymeric materials for printing gears, according to the above mentioned references [5,11,16] are: Nylon, polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), polyethylene terephthalate glycol-modified (PETG). In this work, PLA and Nylon were selected, considering that the gearwheels are thought for low power applications where the motion transmission was required, for example to be used in didactic models. 2.5. Selection of the printing parameters Different printing parameters were selected for the two studied materials, PLA and Nylon (Table 2). For PLA, parameters were selected according to previous results [27], in order to favour low form and dimensional errors. For Nylon, preliminary tests were performed that suggested the use of printing temperature of 255 ◦C and a printing bed temperature of 90 ◦C. Low infill rate of 20% was used to minimize the warping effect, which is due to the high maximum shrinkage coefficient of Nylon of 1.50% [28], while maximum shrinkage coefficient for PLA is 0.50%. Fig. 5 depicts samples of the PLA and Nylon printed gears. Three samples were printed for each gear type. 2.6. Dimensional measurements In the present section the dimensional measurement procedures and the instruments used to measure the gears are explained. 2.6.1. Measurement of tooth thickness The measurement of tooth thickness of the gears was done by the method of the “Sector span W” (Fig. 6a), in this case using two different gear tooth micrometres (Fig. 6b), with range 0–25 mm and 25–50 mm respectively. Precision of both micrometres is 0.01 mm. Since the sector span method is one of the most common measurement methods for the gears manufactured by means of the hobbing process, here it is employed to measure the 3D printed gears [17]. The measurement procedure consists of placing the required number of teeth between the plates of he micrometre and measuring W (Equation (1)). Nipped Number of teeth is commonly called “Sector span of teeth z m ” (Equation (2)). Unlike other methods, a reference surface is not needed. This method allows determining the base pitch pb (Equation (3)) and the base circular thickness sb (Equation (4)) and using them it is possible to determine two intrinsic parameters of the gears: base diameter db (Equation (5)) and tooth thickness on the tip circle sa (Equation (6)) Fig. 4. 3D Models: a) Type A gear (m =3, z =21) and b) Type B gear (m =4, z =17). Table 1 Geometrical parameters of the two types of gears modelled. Geometrical parameters Type A gear Type B gear Module m [mm] 3 4 Number of teeth z 21 17 Pressure angle α [◦] 20 20 Circular pitch p [mm] 9.43 12.57 Tooth thickness s 1 [mm] 4.71 6.28 Space width s 2 [mm] 4.71 6.28 Fillet r b [mm] 0.79 1.05 Addendum h a [mm] 3 4 Dedendum h f [mm] 3.5 4.67 Tooth depth h [mm] 6.5 8.67 Reference diameter d [mm] 63 68 Root diameter d f [mm] 56 58.67 Tip diameter d a [mm] 69 76 Table 2 Printing parameters used for the PLA and Nylon materials. Printing parameters PLA Nylon Layer height [mm] 0.2 0.2 Wall thickness [mm] 1.2 1.2 Solid layer thickness [mm] 1.2 1.2 Print Bed temperature [◦] 60 90 Printing temperature [◦] 195 255 Print speed [mm/s] 40 50 Infill rate [%] 50 20 Upper/Lower pattern Zigzag Zigzag Infill pattern Triangular Triangular I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 6 [29]. In this case, for standard spur gears, the sector span W is calculated with Equation (1): W=m⋅cos( α )[ π (zm−0.5) + z⋅inv( α )] (Eq. 1) Where the sector span of teeth zm expression is (Equaton 2): zm= α ⋅z 180◦+0.5(Eq. 2) The approximation of the value of sector span of teeth zm is made using nearest integer. Table 3 shows the theoretical values of the sector span W of the gear, which are taken as reference values for the measurements. Fig. 5. Pictures of the 3D printed gears: a) Type A gear (m =3, z =21) in PLA, b) Type B gear (m =4, z =17) in PLA, c) Type A gear (m =3, z =21) in Nylon, d) Type B gear (m =4, z =17) in Nylon. Fig. 6. a) Diagram of the measurement of a sector span W and b) Example of a span measurement with a disk micrometre and Z m =2. I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 7 The base pitch pb and base circular thickness sb are calculated by means of the following expressions (Equation (3) and Equation (4)): pb=Wzm+1−Wzm(Eq. 3) sb=Wzm− (zm−1)⋅pb(Eq. 4) Hereby Wzm: Sector span corresponding to zm teeth, measured with the micrometre (mm). Wzm+1: Sector span corresponding to zm+1 teeth, measured with the micrometre (mm). α : Reference pressure angle (◦). m: Module (mm). z: Number of teeth of the gear. For the standard spur gears 3D printed in this work, a pressure angle α =20◦was used, Table 4 contains the theorical values corresponding to the above mentioned formulations for each gear type, taken as references for the measurements. The base diameter db and the tooth thickness on the tip circle sa (it is recommended that this value be greater than a fraction of the base modulus of the gear) are calculated by means of the following expressions (Equation (5) and Equation (6)): db=z⋅pb π (Eq. 5) sa≥0.3⋅pb π (Eq. 6) 2.6.2. Measurement of diameters, roundness and concentricity For the measurement of diameters, roundness and concentricity of the gears, a Mitutoyo Quick Vision 3D measuring machine was used. Given that the parts were printed in white colour, it was necessary to design and print a support in a dark colour (dark blue) for the gear to be measured. This machine allows capturing an image of the surface of the part, and a contrast between the areas of the part and the support is required (Fig. 7). From the image, the software allows calculating diameter and roundness of each circumference. It also allows determining the concentricity error between two circumferences. 3. Results and discussion 3.1. Sector span For each gear, chordal thickness (sector span W and sector span WZm+1) was measured. 3 measurements were performed in different sectors of the gears, in order to evaluate the variability. The results are shown in Table 4. The theoretical value of the sector span W for type A gears is 23.021 mm, and for type B is 18.663 mm. The theoretical WZm+1 values are 31.866 mm and 30.469 mm for type A and type B gears respectively. In Table 4 it is shown that the PLA gears have lower dimensional errors than the Nylon gears. Thus, the dimensions for the PLA gears are closer to the theorical values of the Sector span tha for the Nylon gears. The relative errors of the PLA gears are below 0.23% and the relative errors of the Nylon gears are below 2.3%. As for PLA, other authors have found relative error values of around 1.2% [30], while in the present work lower relative error values were reported. Regarding Nylon, for example Basavaraj and Vishwas [31] found a maximum relative error of 2.5%, which is similar to the values in the present study. Thus, the present results agree with those of other authors regarding dimensional accuracy in PLA and Nylon parts respectively. Table 5 contains the results for the base pitch pb and for the base circular thickness sb. Theoretical pb values are 8.845 mm and 11.806 mm for gears type A Table 3 Theoretical values of the Sector span W of the gear designed. Geometrical parameters Type A gear Type B gear Module m [mm] 3 4 Number of teeth z 21 17 Pressure angle α [◦] 20 20 Sector span W [mm] 23.021 18.663 Sector span of teeth zm (nearest integer) 2.83 ->3 2.38 ->2 Table 4 Dimensions of the Sector span WZm (zmTypeA =3 and zmTypeB =2) and WZm+1 (zm+1TypeA =4 and zm+1TypeB =3) of the gears. Gear type and replica number Values WZm [mm] Statistical parameters Values WZm+1 [mm] Statistical parameters Gear type Nr. 1 2 3 Mean of 3 measurements [mm] Mean of 3 parts [mm] Relative error (%) 1 2 3 Mean of 3 measurements [mm] Mean of 3 parts [mm] Relative error (%) Type A PLA 1 23.00 22.98 22.95 22.98 22.99 0.13 31.75 32.00 32.02 31.92 31.92 0.17 2 22.99 22.99 23.05 23.01 31.76 31.95 31.97 31.89 3 23.00 22.95 23.06 23.00 32.00 31.89 31.90 31.93 Type B PLA 1 18.65 18.65 18.68 18.66 18.67 0.04 30.39 30.36 30.35 30.37 30.40 0.23 2 18.66 18.64 18.63 18.64 30.37 30.47 30.44 30.43 3 18.69 18.71 18.69 18.69 30.41 30.42 30.41 30.41 Type A Nylon 1 22.72 22.69 22.74 22.72 22.70 1.41 31.20 31.29 31.27 31.25 31.30 1.77 2 22.74 22.68 22.64 22.69 31.36 31.33 31.25 31.31 3 22.69 22.73 22.68 22.70 31.33 31.33 31.34 31.33 Type B Nylon 1 18.28 18.28 18.31 18.29 18.30 1.95 29.78 29.79 29.74 29.77 29.78 2.26 2 18.32 18.37 18.34 18.34 29.70 29.80 29.83 29.78 3 18.27 18.25 18.26 18.26 29.77 29.83 29.78 29.79 Fig. 7. Mitutoyo Quick Vision measuring machine and a gear to be measured placed on a support. I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 8 and type B respectively. The values of pb follow the trend of smaller dimensional errors for PLA than for Nylon. Theoretical sb values are 5.331 mm and 6.857 mm for type A and type B gears respectively. For sb higher dimensional errors were obtained in type A than in type B gears respectively, regardless of the material considered. 3.2. – Diameter, roundness and concentricity In this section the diameters of the tip and root circumferences, their roundness and the concentricity error are presented. Table 6 contains the results for tip diameter and its roundness error. Theoretical da values are 69 mm and 76 mm for gears type A and type B respectively (see Table 1). Table 6 shows that lower relative errors for tip diameter were found for PLA than for Nylon. On the contrary, lower roundness errors were reported for Nylon than for PLA. This could be attributed to the fact that a lower infill rate was used for Nylon than for PLA (see Table 2). In this work, roundness values are lower than 0.25 mm, while Luis et al. [23] found roundness errors below 0.3 mm in PLA hemispherical parts. For both materials, Type A gears (module 3 mm and 21 teeth) show higher roundness error than Type B gears (module 4 mm and 17 teeth). This could be due to the lower dimensions of the teeth, and to the difficulty to reproduce the details of the geometry in small parts. Thus, it is not recommended to print gears with small teeth, because roundness errors could increase with respect to larger teeth. Table 7 shows the values of the root diameters, as well as their roundness values. Theoretical df values are 56 mm and 58.67 mm for gears type A and type B respectively (see Table 1). In Table 7 it can be observed that Nylon gears show higher relative error for the root diameter, than PLA ones. In addition, higher roundness errors were obtained for type A than for type B gears, especially in the root diameter. All roundness errors were lower than the maximum value of 0.674 mm reported by Dennig et al. [21]. Table 8 shows the concentricity errors between the tip and the root circumferences. Slightly lower concentricity errors were found for Nylon than for PLA. All concentricity errors are lower than those of 0.3 mm that were reported by Luis et al. for PLA hemispherical cups [23]. 4. Conclusions In this work, the comparison between PLA and Nylon 3D printed spur gears is presented. The main conclusions are the following: •Regarding dimensional accuracy, the method of sector span is applied. Relative errors for the sector span and for the root and tip diameters were higher for Nylon (up to 1.95%) than for PLA (up to 0.15%). PLA material, in general, allows obtaining dimensional values that are closer to their theoretical design value, compared to Nylon. •Roundness error was lower for Nylon gears (up to 0.177 mm) than for PLA gears (up to 0.254 mm). This could be attributed to the fact that the Nylon gears were printed with lower infill rate than the PLA ones. For both materials, Type A gears (module 3 mm and 21 teeth) show higher roundness error than Type B gears (module 4 mm and 17 teeth). This could be due to the lower dimensions of the teeth and, thus, to the difficulty to reproduce the details of the geometry is small parts. Further research is required in this field. •Slightly lower mean concentricity values were reported for Nylon than for PLA. According to the results of this study, as a general trend PLA is recommended to 3D print gears with respect to Nylon, in order to obtain lower dimensional error. Table 5 Mean and relative error values of the base pitch pb and of the base circular thickness sb Gear type and replica number Base pitch pb Base circular thickness sb Gear type Nr. WZm+1 [mm] WZm [mm] pb [mm] Mean Relative error (%) zm sb [mm] Mean [mm] Relative error (%) Type A PLA 1 31.92 22.98 8.94 8.92 0.85 3 5.09 5.16 3.21 2 31.89 23.01 8.88 3 5.24 3 31.93 23.00 8.93 3 5.14 Type B PLA 1 30.37 18.66 11.71 11.74 0.56 2 6.95 6.92 0.92 2 30.43 18.64 11.79 2 6.85 3 30.41 18.69 11.72 2 6.97 Type A Nylon 1 31.25 22.72 8.53 8.60 2.77 3 5.65 5.51 3.36 2 31.31 22.69 8.62 3 5.44 3 31.33 22.70 8.63 3 5.43 Type B Nylon 1 29.77 18.29 11.48 11.48 2.76 2 6.81 6.81 0.69 2 29.78 18.34 11.44 2 6.90 3 29.79 18.26 11.53 2 6.73 Table 6 Tip diameter and roundness. Gear type and replica number Gear type and replica number Gear type Nr. Tip Diameter d a [mm] Mean Diameter [mm] Relative Error of the Tip diameter (%) Roundness [mm] Mean Roundness [mm] Type A PLA 1 69.103 69.101 0.15 0.215 0.190 2 69.102 0.190 3 69.097 0.166 Type B PLA 1 75.990 76.015 0.02 0.100 0.113 2 76.068 0.108 3 75.988 0.130 Type A Nylon 1 68.773 68.811 0.27 0.095 0.088 2 68.838 0.101 3 68.821 0.067 Type B Nylon 1 75.834 75.776 0.29 0.036 0.061 2 75.720 0.004 3 75.775 0.143 I. Buj-Corral and E.E. Zayas-Figueras Polymer Testing 117 (2023) 107862 9 Author statement Conceptualization: E.Z.-F., I.B.-C. Methodology: I.B.-C. E.Z.-F. Software: E.Z.-F., I.B.-C. Validation: I.B.-C. E.Z.-F. Formal analysis: I.B.-C. E.Z.-F. Investigation: E.Z.-F., I.B.-C. Resources: I.B.-C. E.Z.-F. Data Curation: I.B.-C. E.Z.-F. Writing - Original Draft: E.Z.-F., I.B.-C. Writing - Review & Editing: I.B.-C. E.Z.-F. Visualization: E.Z.-F., I.B.-C. Supervision: I.B.-C. E.Z.-F. Project administration: I.B.-C. E.Z.-F. Funding acquisition. Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Irene Buj-Corral and Enrique Zayas-Figueras report a relationship with Polytechnic University of Catalonia that includes: employment and nonfinancial support. Data availability Data will be made available on request. Acknowledgements The authors would like to thank Alejandro Domínguez, Ram´ on Casado, Marc Sol` a and ` Oscar Garcia for their help with the experimental tests. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] K. Gupta, Recent developments in additive manufacturing of gears: a review, Adv. Transdiscipl. Eng. 8 (2018) 131–136. [2] Gibson, I.; Rosen, D.; Stucker, B. (Brent) Additive Manufacturing Technologies : 3D Printing, rapid prototyping, and direct digital manufacturing; ISBN 9781493921126. [3] N.K. Maurya, V. Rastogi, P. Singh, Fabrication of prototype connecting rod of PLA plastic material using FDM prototype technology, Indian J. Eng. Mater. Sci. 27 (2020) 333–343. [4] I. Buj-Corral, E. Zayas-Figueras, ` A. Monta˜ na-Faiget, Comparative study of flank cams manufactured by wedm and milling processes, Metals (2020) 10. [5] Y. Zhang, C. Purssell, K. Mao, S. Leigh, A physical investigation of wear and thermal characteristics of 3D printed nylon spur gears, Tribol. Int. (2020) 141. [6] J. Kechagias, D. Chaidas, N. Vidakis, K. Salonitis, N.M. Vaxevanidis, Key parameters controlling surface quality and dimensional accuracy: a critical review of FFF process, Mater. Manuf. Process. 37 (2022) 963–984. [7] I. Gendviliene, E. Simoliunas, S. Rekstyte, M. Malinauskas, L. Zaleckas, D. Jegelevicius, V. Bukelskiene, V. Rutkunas, Assessment of the morphology and dimensional accuracy of 3D printed PLA and PLA/HAp scaffolds, J. Mech. Behav. Biomed. Mater. 104 (2020), 103616. [8] Y. Zhang, K. Mao, S. Leigh, A. Shah, Z. Chao, G. Ma, A parametric study of 3D printed polymer gears, Int. J. Adv. Manuf. Technol. 107 (2020) 4481–4492. [9] J. Pisula, G. Budzik, P. Turek, M. Cieplak, An analysis of polymer gear wear in a spur gear train made using fdm and fff methods based on tooth surface topography assessment, Polymers 13 (2021). [10] D. Besnea, C. Rizescu, E. Moraru, E. Dinu, I. Panait, Comparative study regarding the wear of gearwheels manufactured through additive technologies, MATEC Web Conf 290 (2019), 08001. [11] M.D. Vasilescu, T. Fleser, Influence of technological parameters on the dimension of GEAR parts generated with PLA matherial by FDM 3D printing, Mater. Plast. 55 (2018) 247–251. [12] J.D. Kechagias, N. Vidakis, M. Petousis, N. Mountakis, A multi-parametric process evaluation of the mechanical response of PLA in FFF 3D printing, Mater. Manuf. Process. (2022), https://doi.org/10.1080/10426914.2022.2089895. [13] N. Vidakis, M. Petousis, J.D. Kechagias, Parameter effects and process modelling of Polyamide 12 3D-printed parts strength and toughness, Mater. Manuf. Process. 37 (2022) 1358–1369. Table 7 Root diameter and roundness. Gear type and replica number Root circumference Gear type Nr. Root Diameter d f [mm] Mean Diameter [mm] Relative Error of Root Diameter (%) Roundness [mm] Mean Roundness [mm] Type A PLA 1 56.099 56.061 0.11 0.344 0.254 2 56.052 0.209 3 56.032 0.208 Type B PLA 1 58.637 58.660 0.02 0.093 0.116 2 58.688 0.150 3 58.655 0.105 Type A Nylon 1 55.691 55.821 0.32 0.296 0.177 2 55.928 0.125 3 55.844 0.111 Type B Nylon 1 58.559 58.506 0.28 0.037 0.051 2 58.492 0.093 3 58.468 0.024 Table 8 Concentricity. Type of Gear Material No. Diameter of the tip circumference d a [mm] Diameter of the root circumference d f [mm] Concentricity [mm] Mean Concentricity [mm] Type A PLA 1 69.103 56.099 0.039 0.038 2 69.102 56.052 0.030 3 69.097 56.032 0.046 Type B PLA 1 75.990 58.637 0.023 0.032 2 76.068 58.688 0.030 3 75.988 58.655 0.044 Type A Nylon 1 68.773 55.691 0.007 0.026 2 68.838 55.928 0.029 3 68.821 55.844 0.054 Type B Nylon 1 75.834 58.559 0.038 0.030 2 75.720 58.492 0.021 3 75.775 58.468 0.018 I. Buj-Corral and E.E. Zayas-Figueras