Investigation of Optimal Temperature Parameters in ABS Additive Printing ^†

Abstract

This article presents an experimental study aimed at determining the optimal printing temperatures for the nozzle and the build plate when printing ABS by evaluating the geometric accuracy of the parts. The recommended printing temperatures were analyzed, and various operating temperature regimes were selected for the nozzle and the build plate. The experimental part is based on single-factor and two-factor experiments. An analysis of the manufacturing process was also performed. Despite the experimental determination of the optimal temperatures, the manufactured parts do not meet the specified tolerances. Further research is needed to determine the shrinkage coefficient and to make corrections to the initial model.

1. Introduction

Additive manufacturing by fused deposition modeling (FDM) has become a widely adopted route for producing functional polymer components with complex geometries, including rotating and sliding elements such as bushings and shafts. Acrylonitrile–butadiene–styrene (ABS) remains a common FDM material owing to its favorable balance of toughness, thermal resistance and processability; however, its relatively high shrinkage during cooling, coupled with complex thermal histories during deposition, makes it difficult to achieve tight dimensional tolerances, particularly on cylindrical inner and outer diameters (ID/OD).

A substantial body of work has shown that FDM dimensional accuracy is strongly governed by process parameters, especially layer height, print speed, infill, and thermal setpoints such as nozzle (extrusion) and build-plate (bed) temperatures. Several experimental and optimization studies on ABS have demonstrated that these parameters jointly affect both mechanical performance and geometric fidelity of printed parts, often in conflicting ways [1,2,3,4]. For example, Nathaphan and Trutassanawin analyzed six process parameters for standard cylindrical ABS compression specimens—nozzle temperature, bed temperature, number of shells, layer height, printing speed, and build orientation—and reported that high bed temperatures combined with low layer height, low speed and few shells maximized both compressive yield stress and dimensional accuracy [1]. Similarly, Tanoto et al. used a Taguchi L9 design with nozzle temperature, bed temperature and build orientation as factors, and multiresponse optimization (PCR–TOPSIS) including dimensional accuracy as one of the quality metrics; they found that bed temperature had a larger influence than nozzle temperature, and that a combination of relatively low nozzle temperature (230 °C) with high bed temperature (110 °C) and 90° orientation provided the best overall compromise between flexural strength, dimensional accuracy and processing time [2].

More focused investigations have examined the specific roles of nozzle and bed temperatures. Vaid et al. studied ABS cylindrical shafts printed by FDM and explicitly varied extrusion temperature and build-plate temperature, building an artificial-intelligence prediction model to identify temperature combinations that minimized dimensional variation of the shaft [5]. Although their work did not consider internal bores, it provides a direct demonstration that temperature alone—especially the combination of nozzle and bed setpoints—can be used as a primary control knob to reduce dimensional fluctuation in cylindrical ABS parts [5]. Ulkir et al., in a broader nozzle-temperature sweep (220–270 °C) on ABS tensile specimens, used ANOVA to show that nozzle temperature significantly affects both dimensional properties (length, width, thickness, mass) and mechanical strength, reinforcing the idea that melt temperature and viscosity changes translate into measurable dimensional shifts even when the bed temperature is held fixed [3].

At a more mechanistic level, Mosleh et al. combined COMSOL-based thermo-fluid simulations with experiments on single ABS strands to show that, while increasing nozzle temperature and layer thickness raise local temperatures near the nozzle, the build-platform temperature is the dominant determinant of the overall layer temperature for low layer thicknesses [6]. This finding supports the empirical observation from multiple studies that bed temperature exerts a strong influence on warpage, dimensional stability and circularity in thermoplastic FDM [1,2,4,7]. In composite systems, Hao et al. reported that increasing platform temperature improved interlayer adhesion, but excessive bed temperatures and printing temperatures could induce deformation; for ABS/carbon-fiber composites, they identified an optimum around 240 °C nozzle and 110 °C bed, with dimensional deviations on the order of 0.02–0.39 mm relative to nominal geometry [7]. Collectively, these works suggest that high bed temperatures near the upper end of the ABS processing window, combined with moderate nozzle temperatures, are often beneficial for dimensional control, provided that gross warpage is avoided.

Beyond ABS, related studies on PLA parts provide useful methodological guidance for quantifying cylindrical and circular features. Baraheni et al. investigated the effects of nozzle temperature, print speed and infill percentage on dimensional accuracy and surface quality of PLA components, explicitly quantifying inner and outer ovality as measures of deviation from perfect circularity; they found that increased nozzle temperature and infill, and reduced print speed, substantially improved both inner and outer ovality [8]. Alatefi et al. applied response surface methodology (RSM) and multivariate process capability indices to optimize extruder temperature, plate temperature, layer thickness and printing speed for cylindrical PLA compression specimens, jointly considering dimensional characteristics (length and diameter) and compressive properties [9]. Although these PLA studies are not directly transferable in terms of material behavior, they illustrate robust statistical frameworks and geometric metrics—ovalisation, circularity, and capability-based tolerance assessment—that are well suited to the analysis of bushing-like ABS parts.

Recent reviews of FDM process-parameter optimization further emphasize that, across a variety of materials and geometries, nozzle and bed temperatures consistently emerge as key determinants of dimensional accuracy, circularity and warpage, even when embedded in larger multi-parameter Taguchi or RSM designs [4]. Nevertheless, the existing ABS literature remains fragmented with respect to the specific problem of achieving tight ID/OD tolerances in bushing-like geometries: most studies either focus on solid cylinders [1,5], non-cylindrical specimens [3,10], composite materials [7], or multi-factor optimizations where nozzle and bed temperature effects are not isolated [1,2,4]. Moreover, explicit modeling of inner-diameter deviation, ovality and taper as functions of nozzle and bed temperatures is largely absent in ABS, with available circularity metrics developed primarily in PLA contexts [8,9]. This gap motivates a more targeted investigation of nozzle–bed temperature combinations for ABS bushings, under tightly controlled non-thermal parameters, using statistically rigorous design-of-experiments and response surface modeling to map and optimize ID/OD dimensional accuracy and tolerance achievement.

The present article details a study that is conducted with the objective of ascertaining the optimal printing temperatures for ABS in relation to geometric accuracy. The component selected for fabrication is of the bushing variety, and its manufacture is undertaken through the utilization of FDM additive printing technology. The experimental study is conducted in accordance with the methodology for a planned experiment. An investigation is conducted with the objective of an analysis of the technological process with regard to stability, capability and tunability.

2. Materials and Methods

• Used material

Acrylonitrile–butadiene–styrene (ABS) is a widely used engineering thermoplastic in fused filament fabrication because it offers a practical balance of stiffness and toughness, but printed parts are often anisotropic (weaker across layers than along rasters) due to interlayer interfaces and internal voids [11,12]. ABS is amorphous (no true melting point), and its printing behavior is strongly influenced by its glass transition temperature TgTg, which for common commercial filaments is typically around 110–115 °C; maintaining deposited material warm enough (near/above TgTg) helps interlayer bonding [13,14]. During printing, ABS melts are shear-thinning and viscoelastic, meaning flow depends strongly on temperature and shear rate and can vary by grade/formulation—this affects extrusion stability and bead geometry [15]. More generally, published work emphasizes that “ABS filament” is not a single material: differences in formulation (molecular weight, additives, pigment packages) can shift the processing window and help explain why “optimal” print parameters differ between studies and products [16]. The technical properties of ABS are shown in

Table 1. ASB properties [17].

Properties of 3D Printed Samples	ABS
Density [g/cm3]	1.04
Tensile Strength [MPa]	43
Elongation at break [%]	22
Flexural Strength [MPa]	66
Flexural Modulus [MPa]	1177
IZOD Impact Strength [kJ/m2]	29
Melt flow index [190 °C/2.16 kg]	12
Heat distortion temperature [°C]	78

. Recommended printing setting—

Table 2. Recommended printing settings [17].

Recommended Settings
Nozzle temperature	230–270 °C
Bed temperature	95–110 °C
Fan speed	100%
Printing speed	40–100 mm/s

.

• Printed detail

The component under consideration is of the bushing variety; its technical specifications permit the measurement of various parameters, including but not limited to height, bore, and shaft diameter. The component in question is straightforward to print—Figure 1, can be produced expeditiously, and requires only a modest amount of material.

• Additive manufacturing technology

The ISO/ASTM 52900 standard is a comprehensive categorization of the diverse range of 3D printing technologies [18]. The 3D printing technology that has been selected is FDM, as illustrated in Figure 2. This is an additive manufacturing method whereby layers of materials are fused together in a certain pattern to create a 3D object. FDM (Fused Deposition Modelling) is proven to be the most cost-effective method of producing custom parts and prototypes.

A wide variety of thermoplastic materials is available for the presented 3D printing technology, making them suitable for prototyping and functional applications [20]. A significant constraint of FDM is its comparatively poor resolution and dimensional accuracy in comparison with the other 3D printing technologies. The presence of visible lines on the produced parts requires subsequent treatment to achieve surfaces with lower roughness. Additionally, the adhesion between the layers renders the particles inherently anisotropic. This state of anisotropy weakens the particles in one direction, and makes them unsuitable for some applications.

• Used 3D printer

The components are fabricated using a Prusa MK4S 3D printer (Prusa Research, Prague, Czech Republic), which functions via the FDM technology delineated above. This is an open-source 3D printer that offers a high level of print speed, a high level of layer quality, and good geometric accuracy. Further information regarding the machine can be found on the website of the manufacturer.

• Design of experiment

The experimental design constitutes a fundamental element of empirical research, offering structured methodologies for investigating causal relationships while minimizing confounding and maximizing efficiency. In this domain, single-factor, two-factor, and factorial experimental designs are of particular importance. These designs offer progressively richer frameworks for evaluating main effects and interactions. The corpus of literature identified in this review emphasizes the theoretical underpinnings and methodological strategies associated with these designs, ranging from fundamental principles to advanced statistical innovations.

A significant proportion of the extant literature focuses on establishing the core principles that are essential to any experimental framework, namely randomization, replication, and blocking. It is evident that foundational texts, including Ireland’s fundamental concepts in the design of experiments [21] and Wu and Hamada’s experiments [22], provide comprehensive treatments of these concepts. In addition, they detail their implementation in single-factor and multi-factor settings. These works are complemented by broader resources such as Bowerman’s statistical design and analysis of experiments [23], which integrates inferential tools like ANOVA with design considerations for both fixed and random effects.

A number of references explore factorial designs in depth, offering theoretical and practical guidance on the structuring of experiments with multiple independent variables and the interpretation of interaction effects. Collins et al. [24] address the trade-offs between complete and fractional factorial designs, discussing power considerations, aliasing, and resource constraints. The scope of their work is expanded upon by Dziak et al. [25], who provide comprehensive guidance on factorial design strategies for behavioral science applications, encompassing multilevel and clustered factorial structures.

Fractional factorial designs, which are utilized to minimize the number of conditions in multi-factor experiments, have been the subject of extensive scrutiny in numerous sources. As Gunst and Mason [26] summarize, key statistical properties and design strategies are identified, while Hoshmand [27] and Voelkel [28] provide practical examples and techniques for constructing and analyzing such designs, including the implications of resolution and confounding. Bayesian approaches to fractional factorial design are explored by Toman [29], who derives Bayes-optimal designs in two- and three-level settings, highlighting the method’s utility in sparse-data conditions.

It is evident that advanced methodologies, including response surface methodology (RSM) and split-plot designs, are also represented. Chandra et al. [30] and Ryan [31] include RSM applications for continuous factor levels and process optimization, while Zhao [32] discusses clear-effect criteria in fractional factorial split-plot (FFSP) designs where randomization constraints exist between whole-plot and subplot factors.

Finally, domain-specific adaptations illustrate how these principles are applied and extended. Hoshmand [27] provides a detailed account of the utilization of single- and multi-factor designs in the context of agricultural research, while Singh and Chauhan [33] direct their attention to the subject of factorial optimization frameworks within the domain of pharmaceuticals. Across these applications, the link between statistical methodology and experimental structure remains a central concern.

Collectively, these references offer a comprehensive and methodologically sophisticated framework of theoretical and practical contributions to the design and analysis of single-factor, two-factor, and factorial experiments. It is evident from this body of literature that fundamental elements such as interaction analysis, efficient resource allocation, and statistical rigor are intricately interwoven within both the foundational theory and the evolving experimental practice.

Regression analysis constitutes a compulsory component of the DoE(Design of Experiment) application, as it facilitates the modeling and investigation of the relationship between linear dimensions and bed/nozzle temperatures in FDM. The primary function of the generated mathematical model is to provide a framework for analyzing the relationship between the variables under investigation, thereby facilitating a comprehensive examination of the resultant data. A significant application of this methodology is linear approximation, most often through the least squares approach (OLS). This provides further insight into the proximity of the obtained mathematical model to the experimental results under consideration. The linear regression equation constitutes the primary instrument employed in regression analysis [34]:

$$D\left(S\right)=a·t^1+b·t^0$$

(1)

• Statistical Process Control

Statistical Process Control (SPC) is a statistical framework for monitoring a process over time to distinguish in control (IC) behavior—variation due to common causes under a stable process distribution—from out of control (OOC) behavior, where special causes induce changes in the distribution (e.g., shifts in mean or increases in variability) [35]. The main tool is the control chart, which plots a process statistic against a center line representing the IC level and control limits that define the expected range of IC variation [35]. For a Shewhart X chart (subgroup size n), the classical limits are: UCL—Upper Control Limit and LCL—Lower Control Limit. When building a control chart, a central line must be calculated:

$$\overline{x}={\displaystyle \frac{x_1+x_2+\dots +x_n}{n}}$$

(2)

$$\overline{x}=\mathrm{CL}$$

(3)

After that UCL and LCL must be calculated:

$$UCL=CL+{z\sigma }_{\overline{x}}$$

(4)

$$LCL=CL-{z\sigma }_{\overline{x}}$$

(5)

where

• ${\sigma }_{\overline{x}}$—standard deviation, calculated by Formula (8);
• $\overline{x}$—sample average value;

z is the standard normal variable and it is equal to 2 for a 95.44% confidence level and to 3 for a 99.73% confidence level. In the current situation, a 3${\sigma }_{\overline{x}}$ is chosen, so our UCL and LCL will be calculated by Formulas (5) and (6).

$$UCL=CL+{3\sigma }_{\overline{x}}$$

(6)

$$LCL=CL-{3\sigma }_{\overline{x}}$$

(7)

$${\sigma }_{\overline{x}}={\displaystyle \frac{\sigma }{\sqrt{n}}}$$

(8)

where:

• σ—standard deviation of the process;
• n—number of tests in the samples.

The process capability ratio (C_p) is a metric employed to express the capability of a process. A plethora of options exist for the expression of capability. One such option is the utilization of the process capability ratio (PCR) C_p, which employs the upper specification limit (USL) and the lower specification limit (LSL) as quality characteristics.

$$C_P={\displaystyle \frac{USL-LSL}{6\sigma }}$$

(9)

The 6σ spread constitutes the fundamental definition of process capability. As previously stated, the value of σ is frequently unknown; consequently, it must be substituted with an estimate. The most common application of the symbol σ is as an estimated $\widehat{C_p}$. As demonstrated in the equation, the estimate of $C_p$ is denoted by s. As previously stated, the value of σ is frequently unknown; consequently, it must be substituted with an estimate. The most common application of the symbol σ is as an estimated $\widehat{C_p}$. The estimate of $C_p$ is denoted by s, as demonstrated in equation [36].

$$\widehat{\sigma }=s$$

(10)

According to the written above, we can calculate the precision factor $\widehat{C_p}$ by the formula:

$$\widehat{C_p}={\displaystyle \frac{USL-LSL}{6s}}$$

(11)

The process setup analysis is represented by the coefficient $C_{pk}$:

$$C_{pk}=\mathrm{m}\mathrm{i}\mathrm{n}(C_{pu},C_{pl})$$

(12)

$$C_{pup}={\displaystyle \frac{USL-\mu }{3\sigma }}$$

(13)

$$C_{plp}={\displaystyle \frac{\mu -LSL}{3\sigma }}$$

(14)

The value of σ can be replaced with (s), µ or c $\overline{\mathrm{x}}$, because σ is unknown in most of the times. According to the methodology presented by Douglas Montgomery, when calculating the C_pk coefficient, one-sided capability coefficients are used, which utilize half of the range of the normal distribution law—3 σ. In our case 3σ is replaced by 3 s, so C_pk will be calculated by formulas (15) and (16).

$$C_{pu}={\displaystyle \frac{USL-\mu }{3s}}$$

(15)

$$C_{pl}={\displaystyle \frac{\mu -LSL}{3s}}$$

(16)

The term ‘Statistical Process Control’ is employed to denote a fundamental statistical technique that is utilized for the assessment of the conformity of a product’s technical specifications. Even in the context of reliable technological processes, there exists the possibility of associating quality indicators with randomness, a phenomenon attributable to uncontrollable variables [37,38].

3. Results and Discussion

This section of the article presents the results obtained, which demonstrate the effect of nozzle temperature and bed temperature on the geometric accuracy of the parts. Following the methodology for a planned experiment, single-factor experiments were conducted to determine the optimal temperatures for the nozzle and the printer bed. A two-factor analysis is then performed to determine the optimal combination of bed and nozzle temperatures. Single-factor experiments are conducted to ascertain the optimal values for nozzle temperature and filament weight. In determining the optimal nozzle temperature, the recommended printing temperature specified by the selected filament manufacturer is chosen as the baseline, and the bed temperature is maintained at a constant level for all tests conducted. Subsequently, an incremental change in temperature is determined relative to the selected baseline.

The single-factor experiment for determining the bed temperature is designed using the same principle. In this manner, the impact of the two parameters on the geometric precision of the components is ascertained.

In the two-factor experiment, the optimal values for the nozzle and table temperatures are identified and adopted as the baseline. The temperature change increment is maintained at the level employed in the single-factor experiments. In this two-factor experiment, a variation of +/- 1 from the baseline levels is selected. This resulted in a combination of nine values for the selected parameters being produced and analyzed.

Subsequent to the production of the parts, they are measured, and the optimal printing temperature for the specific material and printing device is determined based on the results obtained. The measurement of external and internal dimensions is performed using micrometers, with the requisite range and a graduation value of i = 0.01 mm. Three dimensions were controlled: outer diameter (Dout), inner diameter (Din), and part height (H) (Figure 1). The measurement results are presented as the average value of each measurement. The data are presented in tabular and graphical form.

$$Din=f\left(t_b\right[\mathrm{℃}],t_n[\mathrm{℃}\left]\right)$$

(17)

where:

• Din—inner diameter of the controlled samples, t_b—printer bed temperature, t_n—nozzle temperature.

$$∆Din=Din\left(n\right)-Din\left(avg\right)$$

(18)

where:

• ΔDin—relative change in internal diameter of the controlled samples, Din(n)—nominal value of inner diameter, Din(avg)—average inner diameter value.

$$Dout=f\left(t_b\right[\mathrm{℃}],t_n[\mathrm{℃}\left]\right)$$

(19)

where:

• Dout—outer diameter of the controlled samples.

$$∆Dout=Dout\left(n\right)-Dout\left(avg\right)$$

(20)

where:

• ΔDout—relative change in the outer diameter of the controlled samples, Dout(n)—nominal value of outer diameter, Dout(avg)—average value of outer diameter.

Series 1—Single-factor experiments are conducted to determine the optimal nozzle temperature. An analysis of various ABS manufacturers is performed to establish the temperature range for the experiment. For this series, nozzle temperatures ranging from 215 to 290 °C are selected, with a 5 °C increment; the bed temperature is set to 110 °C, the results are presented in

Table 3. Series 1 results.

S1 Data, b Temp—110 °C
°C	Inner Diameter (Din), [mm];		Outer Diameter (Dout), [mm];		Height (h), mm
	Avg	Δ	Avg	Δ	Avg	Δ
215	29.79	0.21	39.60	0.40	10.03	−0.03
220	29.78	0.22	39.62	0.38	10.03	−0.03
225	29.79	0.21	39.60	0.40	10.02	−0.02
230	29.77	0.23	39.62	0.38	10.02	−0.02
235	29.80	0.20	39.58	0.42	10.01	−0.01
240	29.78	0.22	39.63	0.37	10.01	−0.01
245	29.78	0.22	39.61	0.39	10.00	0.00
250	29.79	0.21	39.63	0.37	10.02	−0.02
255	29.81	0.19	39.61	0.39	10.02	−0.02
260	29.82	0.18	39.66	0.34	10.16	−0.16
265	29.81	0.19	39.62	0.38	10.03	−0.03
270	29.83	0.17	39.67	0.33	10.01	−0.01
275	29.79	0.21	39.61	0.39	10.13	−0.13
280	29.76	0.24	39.60	0.40	10.04	−0.04
285	29.79	0.21	39.63	0.37	10.04	−0.04
290	29.78	0.22	39.62	0.38	10.03	−0.03

.

$$∆t_n=t_{n(k+1)}-t_{n\left(k\right)}=5°\mathrm{C}$$

(21)

where:

• Δtn—change in nozzle temperature, k—serial number of the test at a step of 5 °C.

$$∆t_b=t_{b(j+1)}-t_{b\left(j\right)}=5°\mathrm{C}$$

(22)

where:

• Δtb—change in bed temperature, j—sequential number of the experiment in step 5 °C.

The results presented show the smallest deviations from the nominal dimensions at a nozzle temperature of 270 °C. The dimensional deviations at the height of the bushings are similar, and no graphical representation of the results is provided. Based on the data presented in Table 3 and Figure 3, regression equations for Din and Dout have been derived. According to the results obtained, a nozzle temperature of 270 °C is selected for the prints of series 2.

y (S1 Dout) = −0.0014x + 0.3916

(23)

y (S1 Din) = −0.0004x + 0.2115

(24)

Series 2—investigation of the optimal bed temperature. Once again, the marked is analyzed, and it is determined a bed temperature range of 70 to 120 °C with a 5 °C increment. The maximum bed temperature of the printer is 120 °C, so there is no option to conduct experiments with temperatures higher than 120 °C. The results of the experiment are shown in

Table 4. Series 2 results.

S2 Data, n Temp—270 °C
°C	Inner Diameter (Din), [mm];		Outer Diameter (Dout), [mm];		Height (h), mm
	Avg	Δ	Avg	Δ	Avg	Δ
70	fail	fail	fail	fail	fail	fail
75	fail	fail	fail	fail	fail	fail
80	29.59	0.41	39.82	0.18	9.35	0.65
85	29.77	0.23	39.63	0.37	10.18	−0.18
90	29.77	0.23	39.65	0.35	10.02	−0.02
95	29.76	0.24	39.66	0.34	10.00	0.00
100	29.83	0.17	39.67	0.33	10.26	−0.26
105	29.80	0.20	39.64	0.36	10.03	−0.03
110	29.85	0.15	39.68	0.32	10.00	0.00
115	29.74	0.26	39.60	0.40	10.01	−0.01
120	29.76	0.24	39.62	0.38	9.99	0.01

and Figure 4.

The results presented show the smallest deviations from the nominal dimensions at a bed temperature of 110 °C. The dimensional deviations at the height of the bushings are similar, and no graphical representation of the results is provided. At lower temperature of the printer bed, there are some prints that failed to complete due to bad adhesion. Based on the data presented in Table 4 and Figure 4, regression equations for Din and Dout have been derived. According to the results obtained, a bed temperature of 110 °C and nozzle temperature of 270 °C are selected as a base for the prints of series 3.

y (S2 Dout) = 0.0353x + 0.0641

(25)

y (S2 Din) = 0.012x + 0.1227

(26)

Series 3—Two-factor experiment. The analysis of the single-factor experiments shows that the optimal values of the nozzle and bed are determined to be 270/110 °C. The values of the other temperatures are determined relative to the selected zero level. A single-factor experiment with levels ±1 from zero is selected, using a step of 5 °C for both factors. The results are presented in

Table 5. Series 3 results.

S3 Data
°C	Inner Diameter (Din), [mm];		Outer Diameter (Dout), [mm];		Height (h), mm
	Avg	Δ	Avg	Δ	Avg	Δ
265/105	29.78	0.22	39.61	0.39	10.05	−0.05
265/110	29.81	0.19	39.62	0.38	10.03	−0.03
265/115	29.77	0.23	39.59	0.41	10.06	−0.06
270/105	29.80	0.20	39.64	0.36	10.03	−0.03
270/110	29.85	0.15	39.68	0.32	10.00	0.00
270/115	29.74	0.26	39.60	0.40	10.01	−0.01
275/105	29.79	0.21	39.64	0.36	10.02	−0.02
275/110	29.79	0.21	39.61	0.39	10.13	−0.13
275/115	29.76	0.24	39.60	0.40	10.03	−0.03

and Figure 5.

The results presented show the smallest deviations in the average dimensions for the temperature combination of 270/110 °C. The regression equations for series 3 are:

y (S3 Dout) = 6 × 10⁻⁵x + 0.3782

(27)

y (S3 Din) = 0.0029x + 0.1975

(28)

Following the methodology described above, an analysis of the technological process is presented. The results are shown in

Table 6. Analysis of technological process data.

	Din	Dout
CL	29.79	39.62
s	0.0306866	0.02693
UCL	29.879	39.702
LCL	29.695	39.540
USL	30.13	40.00
LSL	30.00	39.9
Cp	0.7060631	0.61885
Cpu	3.717392	4.6849
Cpl	−2.3053	−3.447

and Figure 6 and Figure 7.

The results of the SPC analysis show that the Cp coefficients for the outer and inner diameters are less than 1.33. Cp values between 0.6 and 0.7 indicate that the manufacturing process does not meet the specified tolerances and requires intervention. According to the C_pk methodology, we select the minimum value of the coefficient. In the current situation, the C_pk(min) coefficients are negative for both diameters, which means that the process is off-center and does not meet the specified tolerances.

The results from Series 1 illustrate the deviation from the nominal dimensions of the manufactured parts. As demonstrated in Figure 3, the inner and outer diameters of the bushing demonstrate deviation from the nominal dimension, yet this deviation is not uniform between the two diameters. It is determined that a temperature of 270 °C is optimal for the series. At this temperature, the deviation for Din is 0.17 mm, and for Dout it is 0.33 mm. This represents a nearly twofold difference. A similar trend is observed at the other temperatures in the series. Further research is required to elucidate this trend.

The findings from series two demonstrate analogous behavior in the dimensional changes. In this series of tests, several failed prints are also observed at temperatures of 70 and 75 °C. This is attributable to inadequate adhesion between the print and the printer bed. The optimal temperature for this series is 110 °C.

A similar trend is also exhibited by two-factor experiments across the different temperature combinations. The optimal results for this experiment are achieved with a combination of 270 °C nozzle and 110 °C bed temperatures.

In all three series of experiments conducted, the behavior of the measured part heights is similar, and no significant deviations are observed.

Regression equations are derived for each planned experiment; these can be used to predict a correction factor in order to achieve the specified nominal dimensions. A study of this kind is planned for future work with this material.

A further study is conducted in order to facilitate a comparison between the results obtained and those from other studies on this topic. The retrieved literature provides substantial support for the view that nozzle and bed temperature are significant interacting drivers of dimensional outcomes in ABS FDM/FFF. However, the study also highlights a methodological gap: no study in this set effectively isolates nozzle/bed temperature (single- or two-factor) while reporting inner diameter (ID), outer diameter (OD), and height errors on the same cylindrical/ring artifact under otherwise fixed conditions [1,3,5,39,40].

4. Conclusions

This article presents a comprehensive experimental study to determine the nozzle and bed temperatures for ABS printing. Through single-factor experiments, the optimal values for the nozzle and bed temperatures were determined to be 270 °C and 110 °C, respectively. The two-factor experiment confirms that the optimal operating temperature is 270/110 °C. According to the presented results, none of the manufactured parts meet the specified tolerances. The analysis of the manufacturing process also shows that the manufactured parts do not meet the specified tolerances, and the manufacturing process is off-center. Further research is needed on the shrinkage coefficient of ABS. Future studies are planned to determine the shrinkage coefficient and introduce corrections to the initial model until the specified tolerances are achieved. The presented results can be used as a database for determining optimal printing parameters for various 3D printers and materials from different manufacturers by applying only the two-factor experiment. This can lead to a reduction in the time required to familiarize oneself with the system, lower material consumption, and the production of parts with higher geometric accuracy.