1. Introduction
In additive manufacturing (AM), a three-dimensional geometry is decomposed in bi-dimensional shapes and used to create solid parts that are built layer upon layer [
1]. This basic workflow is common to different manufacturing processes, like material jetting (MJT), material extrusion (MEX), and powder bed fusion (PBF) [
2]. The application of AM has evolved from prototypes to small-batches, but the objective of reaching mass production capabilities would require filling the gap between AM specification standards and the industrial needs [
3]. In fact, the achievable quality is still affecting the adoption rate of AM in the consumer market [
4].
Tolerance intervals (TI) are expected to be larger in AM than in traditional manufacturing processes [
5], and this lack of quality has been usually addressed by adding post-processing steps [
6]. Production planning in AM will require trustable information about the expected TI and the fulfillment of tolerance specifications to decide which machine or technology will be used beforehand [
7].
Those works investigating dimensional quality in the AM process are frequently focused on providing a quantification of dimensional quality [
8,
9,
10,
11,
12], analyzing the influence of different factors upon dimensional accuracy [
13,
14,
15,
16,
17], or proposing strategies to improve dimensional quality [
18,
19,
20,
21]. Boschetto [
13] modelled the dimensional deviation of parts manufactured in MEX machines as a function of the deposition angle and layer thickness. The model was verified for different materials and angles before being applied to a multi-feature case study. Huang [
18] used the deviations between the manufactured surface and the target one to compensate shrinkage in a stereolithography process. Lieneke [
14] used cuboids to analyze the achievable tolerances in a MEX machine, considering orientations along
X,
Y and
Z axes. Parts were manufactured in several positions, but the results were averaged and the possible influence of position upon results was not considered. Measured dimensions were found to be dependent on orientation and nominal size, and the authors provided an estimation of the correspondent TI amplitude and location.
Minetola proposed a reference multi-feature part that was used to evaluate the dimensional accuracy of AM systems [
8]. This researcher has also used the proposed test specimen to perform benchmarking comparisons between different MEX machines [
8,
9] and between different AM processes [
12]. In these works, the deviation of each measured feature from its nominal size was divided by the tolerance factor
i that corresponds to a range of basic sizes according to ISO 286-1:1988 [
22]. The results were later used to determine the maximum dimensional error expected for a specific feature size range, fitting it into a particular TI. Yap [
15] proposed a series of benchmark artifacts to investigate process capability and applied them to MJT. They analyzed the influence of process parameters upon dimensional quality, seeking for an optimal process configuration. Goguelin [
10] used a test artifact derived from the one proposed by NIST [
23] to evaluate the capabilities of a MEX equipment as part of their effort to develop a smart manufacturability assistant. Leirmo [
17] proposed a test artifact and an experimental strategy to evaluate dimensional and geometrical quality in PBF. This works paid attention to the differences in dimensional quality related to position and orientation of the part within the working space, but also to the variation related to consecutively manufactured trays. Their conclusions pointed to a negligible variation of measurements between builds, whereas a clear influence of the
x-
y position upon part dimensions was observed.
Benchmarking artefacts frequently use a multi-feature approach to provide a global perspective of the achievable quality in terms of machine or process comparison. Nevertheless, it is difficult for a designer to anticipate the achievable tolerance for a particular feature or dimension based on benchmarking results, especially due to the variability related to process configuration, and to part location and orientation. Moreover, there are also cases where the quality indicators are not relevant from an industrial point of view [
24,
25]. Consequently, designers still lack clear and trustable guidance regarding which would be the achievable TI for a particular geometry to be manufactured in a particular AM machine under certain processing conditions [
12].
Quality assessment in medium-to-large batches has been addressed in industrial practice by means of
machine performance,
process performance, and
process capability analysis. These types of analyses can be conducted under the guidance of the ISO 22514 series. According to ISO 22514-1 [
26], the purpose of a process is to “manufacture a product which satisfies a set of preset specifications”. Specifications can be defined for different characteristics of a product but, regarding performance or capability analysis, each characteristic must be considered independently. The analysis of machine performance or process capability has been applied to conventional processes like milling [
27,
28,
29], turning [
30], moulding [
31] or welding [
29].
Regarding AM processes, few works have applied the performance/capability approach to evaluate the quality of parts. Nevertheless, in recent years, several attempts to apply this type of analysis have been published. Singh [
32] investigated process capability in a MJT machine for different dimensional features corresponding to a single part, although the number of replicates in this analysis (16) was too low under the accepted conventions. Preißler [
33] conducted an attempt to perform a capability analysis for a MEX multi-feature specimen, but the experimental design was conducted with 25 replicas. This sample size was insufficient for a process capability study and even below the minimum of 30 replicas recommended for a machine performance analysis [
34]. No information was provided regarding the manufacturing sequence and the number of parts per tray. Günay [
35] conducted a capability analysis of MEX manufactured dog-bone test specimens. The significance of different process parameters upon quality was firstly analyzed. Thirty units were manufactured following a one part-per-tray sequence after determining the optimal configuration. A five-zones [
36] capability categorization (from “Inadequate” to “Super”) was applied, considering the process capable for values of
Cp and
Cpk above 1.00. This condition led to consider the process capable to achieve an IT10 for the length and the height of the test specimen, although the quality worsened to IT11 for the width of the specimen. Siraj [
37] also used a dog-bone test specimen to evaluate process capability in a low-cost MEX machine. Their results showed that the process was not in control, with an evident bias between measured sizes and target ones. Despite the fact that the specified tolerances were very large (1 mm and 2 mm ranges), the equipment was found to be not capable. Udroiu [
38] conducted a machine and process capability analysis for Material Jetting (MJT) manufactured cylinders. Control charts were used to evaluate if the process was in control before calculating capability indexes. This work established a ±0.1 mm TI to evaluate machine capability and a batch size of 50 units was manufactured simultaneously in a single tray. Measured values of the diameters followed a normal distribution and, comparing the result of the capability index with the capability target index (1.67), the machine was found to be capable of achieving the expected requirements for the diameter feature. Process capability was also evaluated using three trays (50 units each) and the process was also found to be capable. Zongo [
39] conducted a process capability analysis of tooling components manufactured in a laser power bed fusion (PBF) machine. This work considered the possible correlation between the position of the part in the chamber and the measured profile deviations. Although local differences were observed, they followed different patterns for consecutive trays, and capability analysis was conducted considering all manufactured parts from three different trays as a single batch.
Despite the experimental effort, machine performance or process capability studies still have to address some relevant circumstances. First, depending on the size of the part, the batch size and the available workspace, several parts could be manufactured within the same tray. This leads to the dilemma of considering AM processes as single-state [
40,
41] or multi-state processes [
40]. Nevertheless, this possibility has not been previously considered in the available literature, where parts have been manufactured under a “single state” assumption [
32,
38] or under a one part-per-tray strategy [
35]. Second, machine performance studies should be based on uninterrupted runs under normal operating conditions, which is a demanding condition in AM, where processes have frequently very slow cycle times, raw materials are provided in small volumes, and unavoidable critical operations (like warm-up or tray levelling) could violate repeatability conditions. Third, once the optimal process configuration has been employed in a performance analysis, there are limited possibilities of improving the results by means of a modification of such configuration.
Taking these circumstances into account, the present work proposes the application of a multi-state machine performance perspective to reduce the achievable tolerance intervals of features of linear size in material extrusion (MEX) processes. The main steps of the proposed quality improvement methodology (
Figure 1) are:
Statistical methods are used to analyse the dispersion and the location of the distribution of measured values between different states, to determine whether the production of a given geometrical feature should be treated as single-state or multi-state.
The results are used to determine the type of compensation that should be applied by means of a design for additive manufacturing strategy.
The 3D design files are modified to reduce deviations between manufactured values and theoretical values.
The variation in the achievable tolerance range, before and after the optimization of design, is evaluated by establishing a target machine performance index.
The method proposed in this work is encompassed in the “design optimization” stage of the optimization framework described in [
42]. More specifically, it could be applied as a previous step to a process capability analysis and serve as a guide for adjusting production to minimize the effect of machine-related inaccuracies. The objective of the proposed method is to reduce the achievable tolerance intervals in AM processes to make them a viable alternative to conventional processes. A feature of linear size (FoLS) [
43] consisting of the external surface of a hollow right circular cylinder, manufactured in a MEX machine was selected as a case study.
The paper is organized as follows:
Section 2 describes the proposed method and the experimental plan. The results of the case study are provided in
Section 3 and are discussed in
Section 4. Finally, the conclusions of this work are summarized in
Section 5.
4. Discussion
The proposed DfAM strategy allowed for a significant improvement in dimensional quality, according to the results, was provided in
Section 3. The minimum achievable tolerance interval required to fulfil the critical machine performance target was reduced from
to
. Considering the standard tolerance intervals [
43], the application of the proposed DfAM has resulted in a reduction of the achievable tolerance interval from IT14 to IT 11 [
43]. Even if the machine performance index is considered instead of the critical one and, consequently, the deviation between the mean value and the target specification is neglected, the achievable tolerance interval is equally reduced from
to
. Accordingly, considering the “potential” performance, the achievable tolerance interval would be reduced from IT12 to IT 10.
These results were obtained imposing an objective of 99.73% of the manufactured parts lying within specifications, and a minimum ratio of 1.67 between tolerance interval and results dispersion. Both results demonstrate that the proposed strategy can reduce the average deviation with respect to the target value while simultaneously narrowing down the associated dispersion.
The multi-state approach employed for machine performance calculation was key to this achievement since it has allowed to understand and address the relationship between the relative position of part within the tray and the expected quality results. Conversely, although the single-state strategy could be applied without violating repeatability conditions, as it was confirmed by the Barlett’s test, the F-test and the test for normality, this approach would lead to a misinterpretation of the causes behind the quality issues. In fact, this interpretation resulted on broader achievable tolerance intervals: from the perspective of machine performance, and from the perspective of the critical machine performance. The observed differences between both strategies are mainly related to the different ways of adjusting the results to the dispersion models. In the proposed cases study, extreme values were not stochastic in a rigorous sense but related to certain locations within the manufacturing tray. Nevertheless, when they were adjusted to a normal distribution under the single-state approach, they contributed to artificially enlarging the dispersion and, consequently, affecting the calculation of the standard deviation, worsening the estimation of the achievable tolerances. Conversely, under the multi-state approach, each location presented a relatively small associated dispersion. The achievable tolerance interval was affected by this dispersion as well as by the difference between extreme states locations (mean values), but the combined effect was still lower than that derived from a single-state perspective.
The consequences of the observed differences between both approaches have a relevant influence upon the DfAM strategy. Under the single-state approach, the samples were adjusted to a normal distribution model, with a mean value of 40.164 mm and the standard deviation of 0.0325 mm. Applying a compensation procedure to the design dimension could, in the best situation, center the results around the target (40.000 mm) but this would not have any significant effect upon the dispersion of results. Since a dimensional optimization based on the single-state approach would not affect the sources of variability, the optimized tolerance interval would not be expected to improve the value obtained with the original design and the potential machine performance index (
). On the other hand, under the multi-state approach, the position of the part within the tray was identified as a significant source of variability, and the DfAM strategy used this information to individually compensate the design size. This strategy reduced the inter-location variability (
Figure 12), resulting on an improvement of the achievable tolerance intervals.
The question of part location is not frequent in studies employing benchmarking artifacts [
10,
12,
51] because their objectives have more to do with comparison between different processes or machines or with the analysis of the influence of process parameters than with a general assessment of their capabilities. The use of the term “capability” in some works [
10] could lead to misunderstandings if the results obtained with a benchmark artifact are erroneously considered as a reference for the expected quality of a new production. In fact, the ISO 22514-1 [
26] establishes that capability or performance analysis should be conducted for each characteristic individually, as the non-fulfilment of a single specification could make the whole part to be rejected. Quality prediction would require of complex modelling because AM is subjected to multiple sources of variability. Conversely, running a performance or capability study is an adequate strategy to analyze and fix quality issues for medium-to-large production batches.
The rejection of S12 in the optimized trays was determined after checking its behavior as an outlier. The reasons for this anomalous behavior were found in the values of trays 5 and 6 that were used to calculate
Cj. Regarding S12, the difference between results in tray 5 and tray 6 (
Table 5) were the highest among all measured values (0.026 mm). This was also the case of the differences observed for S12 within the four original trays (
Table 2), which indicates that this specific location (0; −67.5) was subjected to a higher variability. Even when the Bartlett’s test did not consider this variability to be significantly different than the rest, this result could indicate that the compensation for S12 would require of more replicates to improve its accuracy. In any case, the multi-state approach allowed for the identification of such abnormal behavior and the adoption of further decisions on production arrangement.
The use of a sensibility coefficient
C was necessary to properly compensate the observed deviations. The first set of compensated trays (
Table 4) showed a significant reduction in the deviation between the absolute mean value of the manufactured set and the target one (from 0.164 mm to 0.040 mm), but this value was improved after the calculation of the
Cj and the manufacturing of the optimized trays (0.019 mm). It was observed that the relationship between the variation applied to the design diameter (input) and the measured variation of the manufactured diameters (output) was neither directly proportional nor independent from the state (location) of the part. This conclusion is also relevant for future works, since those DfAM strategies, based on modelling size deviations and applying a compensation to the CAD file, should also consider the possibility of the response being position-dependent. Moreover, although the result was very close to the target value, there was still room for further improvement. Even after recalculating the sensitivity coefficients, results obtained from optimization did not exactly match the target values. This fact points out that the calculation of those coefficients could be even more complex than expected. Considering the results, the obtained values pointed towards a non-linear behavior, which is also a question of interest for further research.
As it was discussed before, capability analyses are hardly comparable between different geometries, processes, or configurations [
35,
38,
39]. Nevertheless, once the production parameters have been set, attention should be drawn to those factors related to production decisions, with a special focus on the arrangement of parts within the manufacturing tray. Observations led to the conclusion that a multi-state perspective should be mandatory when analyzing machine performance in MEX AM processes. Moreover, since previous research studies have pointed out the relevance of the part position with respect to the reference axes in multiple AM processes [
17,
39], this finding should encourage other practitioners to adopt the multi-state perspective when working with those processes.
The proposed strategy could be applied in most industrial manufacturing facilities with a minimum adaptation effort. Nevertheless, it has to be noted that AM is not currently widespread in industry, but frequently restricted to companies that are specialized in AM. Those companies could lack the appropriate metrological equipment to conduct an optimization effort like the one described in this research. Additionally, certain technical skills regarding statistical and quality control analysis are also required, which could work as an obstacle for the adoption of the proposed strategy in small companies. Nevertheless, this should not be the case of well-stablished industrial manufacturers, accustomed to deal with quality issues, that incorporate AM to their manufacturing resources. Similarly, although the proposed strategy has been focused on MEX technologies, it could be adapted in the future to other AM processes, like PBF or MJT.
Additional future research will explore the possibilities of including process capability indexes as part of the quality improvement efforts. Since the method proposed in the present paper would allow for the approval of serial production under optimized quality conditions, long-term studies regarding process capability should be incorporated to achieve a continuous improvement of the achievable quality. The optimization effort could evolve into a progressive/iterative strategy, where each new set of parts provides an information that is incorporated to the previous results to keep the optimization parameters continuously updated. Another approach that should be explored in the future has to deal with the extension of the proposed method to a general model, encompassing a broad range of part dimensions. This multi-size approach would allow for the optimization of part dimensions even when a specific size has not been previously tested. Finally, an adaptation of this methodology to the case of geometrical tolerances is currently under development.