Determination of the Most Influential Factors on the Quality of Resin Gears Manufacturing

Abstract

The manufacture of industrial parts using silicone molds is becoming more frequent due to their versatility, durability, and precision, particularly in the production of complex components. One specific application is the manufacture of gears, which play a fundamental role in high-performance mechanical systems, where geometric accuracy is essential. Gears produced from resins offer several advantages such as efficient tribological performance, load resistance, noise reduction, and non-magnetic properties. The main goal of this paper is to determine the main factors affecting the final quality of resin gears by analyzing two principal gear quality parameters: teeth profile (ff$\alpha$) and helix deviation (ff$\beta$). This work includes a global analysis of all contributing factors influencing the final quality of gears manufactured. One of the main conclusions obtained is that gear quality depends on a combination of factors, such as mold properties, choice of resin, the manufacturing process, and the quality of the original model. As a result, two regression equations have been developed, relating all influencing factors to the two gear quality parameters (ff$\alpha$ and ff$\beta$). Different response surfaces have been obtained, enabling the definition of the required quality level of the model to achieve reproductions with certain ff$\alpha$ and ff$\beta$ values suitable for the intended application conditions.

1. Introduction

The manufacture of industrial parts using silicone molds is a practice that has gained traction in different industries due to its versatility, durability, and precision, particularly in the production of complex parts with intricate geometries [1]. This is attributable to the low molding shrinkage, good fluidity at high temperatures, and high thermal decomposition temperature [2]. The primary benefits of utilizing silicone molds for component fabrication include expedited manufacturing times, uncomplicated processes, and reduced production costs [3]. Conversely, drawbacks such as the necessity to create an entirely new mold for each component, leading to elevated costs and constrained scalability and profitability of the process, have been identified [4]. Additionally, the durability of silicone molds is a concern, as it impacts the longevity of molds in mass manufacturing processes [5]. This, in turn, raises questions about the efficiency and profitability of the process [6].

Advancements have been made in recent years in the field of silicone mold manufacturing for industrial components. These advancements pertain to various aspects, including mold design, resin composition, and manufacturing techniques. Advancements in manufacturing technologies, such as additive manufacturing, augmented by the integration of artificial intelligence and machine learning [7,8], have diversified the applications of silicone in mold fabrication across a wide spectrum of sectors, including the biomedical field [9,10]. The objective of these advancements is to optimize the production process and enhance the quality of molded parts. However, other advanced industrial sectors as those related to industrial components have not yet implemented this manufacturing process as their requirements in terms of dimensional accuracy and durability reach very high levels.

The fabrication and preparation of silicone molds is a meticulous process, necessitating a thorough examination of the geometry of the models. This ensures precision and accuracy in the replication processes, as evidenced in the research conducted by [11].

In pursuit of enhancing dimensional accuracy, surface finish, and durability of silicone molds, researchers have devoted efforts to identifying advanced silicone formulas characterized by heightened heat resistance, durability, and superior demolding properties. It is imperative to acknowledge that the initial preparation for silicone mold manufacturing is paramount to ensure the accuracy and precision of the final product [11], as well as the quality of the model utilized [12]. The utilization of silicone molds in the fabrication of industrial components encompasses a broad spectrum of applications, ranging from conventional molding processes such as vacuum casting and compression molding [13], to state-of-the-art technologies including 3D printing and hybrid machining methodologies. The adaptability, continuous improvement in precision, and cost-effectiveness of silicone molds have led to their increased utilization in industries that require the production of parts with complex geometries and specialized properties, such as gears. In the context of gear manufacturing, the quality of the molds is paramount and can vary depending on various factors that influence both the manufacturing process and the properties of the resin used. As articulated by [1], the precision, durability, and versatility of silicone molds are pivotal considerations in the manufacturing of gears, particularly given their intricate geometry. Gears play a pivotal role in high-performance mechanical systems, where geometric accuracy is paramount for their efficient operation, particularly in the context of modern industry, which demands components with enhanced durability and energy efficiency. The selection of gear material is instrumental in determining the final quality of the product. Cast iron, carbon steel, and alloy steel are renowned for their superior quality in comparison to other materials, resulting in enhanced durability. In addition to quality, the low costs associated with mass production and the good vibration damping properties of subsequently machined iron and steel gears make them a cost-effective option in gear systems [14]. Indeed, if magnetic gears are used in transmission systems, in addition to the advantages, noise and maintenance are reduced [15]. However, machined gears are susceptible to malfunction under heavy loads due to the complex dynamics present in planetary gearboxes [16] and buckling without adequate locking mechanisms in gear-based prostheses [17]. This underscores the necessity for exploring alternative materials, such as gears made from polymeric resins.

In the last five years, there have been notable advancements in the performance and characteristics of the resins utilized for gear manufacturing. Manufacturers have directed their efforts towards enhancing the mechanical strength, wear resistance, and thermal stability of the resins to meet the stringent requirements of diverse applications [6]. The most prevalent resins employed in gear manufacturing include polyurethane resin, glass fiber-reinforced polylactic acid (PLA), carbon fiber-reinforced PLA, and certain thermoplastics such as acrylonitrile butadiene styrene (ABS) and polyethylene terephthalate (PETG) [18]. These resins are primarily utilized due to their resistance to deformation, abrasion, and chemical agents (Martinez, 2018). Polyurethane resin is extensively employed for its versatility and durability in gear manufacturing processes, while glass fiber and carbon fiber reinforced PLA have gained popularity for their enhanced mechanical properties and, notably, for their abrasion resistance, which renders them suitable for applications necessitating high-performance gears [6]. In addition, the incorporation of thermoplastic polymer materials, such as PLA, ABS, and PETG, provides manufacturers with versatility in choosing the most suitable material to meet specific requirements [18]. As with silicone molds, new technologies are also being used to manufacture and improve resin gears. As demonstrated by [19], the employment of resin gears fabricated through rapid prototyping technology ensures high dimensional accuracy and commendable kinematic performance, underscoring the precision attainable with these components. Conversely, the employment of machine learning algorithms for the prediction of quality in injection molding processes ensures the consistency of the quality of resin gears, thereby underscoring the efficacy of advanced technologies in maintaining stringent standards [20]. In a similar vein, models and methodologies for fault prediction and detection serve as instrumental tools for ensuring the quality of gears. In [21], the application of deep learning tools to analyze pitting failures in gears using acoustic emission signals underscores the significance of predictive maintenance and condition monitoring in gear performance. Another notable example is the work of [22], which involves a comprehensive numerical and experimental analysis of the vibroacoustic behavior of an electric window regulator gear motor. This study underscores the intricate nature of controlling the factors that influence gear performance, such as electromagnetic forces and mechanical imbalance, within a numerical simulation.

A study of gears fabricated from resins reveals several advantages, including specialized mechanical properties, effective tribological performance, load resistance, and noise reduction. However, these materials have several limitations, which can be attributed to factors such as the deterioration of the silicone mold [23], the use of materials like epoxy resin, which can exhibit challenges related to abrasion resistance [6], and the variability in mechanical resistance [24].

The quality of resin gears manufactured in silicone molds is influenced by a combination of factors, including the properties of the molds, the choice of resin, the manufacturing process, and the quality control measures implemented [23]. By considering these factors and enhancing the optimization of production processes, it becomes feasible to manufacture high-quality gears with good dimensional accuracy, good surface finish, and high reliability [6].

Gears are essential components in the transmission of mechanical power. The precision of their geometry is a critical factor in determining the efficiency, reliability, and operational durability of the system. Geometric deviations in gears, such as irregularities in the shape of the profile, errors in the helix slope and eccentricity, can compromise system performance. These deviations can generate transmission inefficiencies, increased vibrations, and premature failures in the mechanical assembly. For each operating condition of the gears (speed, reduction ratio, friction coefficient), a certain quality of the gear teeth is required, usually specified in terms of Deviation from Profile Shape (ff$\alpha$) and Propeller Shape Deviation (ff$\beta$). Conventional inspection techniques, which have been superseded by advances in three-dimensional technology, were historically employed for gear inspection. The development of advanced verification methods has been driven by two factors: the increasing complexity of designs and the need to minimize failures in critical applications [25]. The integration of TCM and Quindos has enhanced the precision of dimensional verification, thereby reducing margins of error and optimizing manufacturing processes [26].

Considering the aforementioned challenges, adherence to international standards such as ISO 1328 [27] and ISO 21771 [28] is paramount. These standards establish stringent criteria concerning geometric tolerances, profile quality, and helix alignment. The employment of sophisticated metrology techniques is paramount for the identification and rectification of these defects, ensuring the optimal functionality of gears in high-precision environments, such as the aerospace and automotive industries and the fabrication of specialized machinery. Quindos is a state-of-the-art metrology software engineered to process data collected by the TCMs, enabling the assessment of critical parameters such as pitch, angular deviation, and topography of the gear teeth. Its integration with CAD models and reverse engineering algorithms enables the reconstruction of complex geometries, facilitating the detection of functional defects [29]. Furthermore, Quindos has positioned itself as one of the most suitable and accurate verification technologies in the field of gear verification, due to its ability to provide detailed analysis and its compatibility with various measurement configurations [30]. Recent studies have emphasized its applicability in the optimization of the design and validation of gears subjected to dynamic load conditions [26].

For these reasons, research has been conducted on the quality of gears manufactured in polymeric materials by casting in silicone molds. The influence of materials, the number of castings, and mold degradation on the final quality of the samples obtained was analyzed. To this end, two machined gears with different surface finishes were utilized as a reference, thereby enabling an analysis of the influence of the initial quality of the model on the final results. The quality of the resin gears was determined by using a coordinate measuring machine based on Quindos.

2. Materials and Methods

2.1. Materials

Two gears of different quality levels were selected to be used as models for the manufacturing of the silicone molds. Both gears have different superficial finishing and manufacturing process and their functional applications are also different.

The details of both specimens are shown in

Table 1. Models Gears characteristics.

	Q1-Gear (STANDARD)	Q2-Gear (MAXIMUM)
Dimensions	Z20-M3 (Press-Ang 20°)	Z20-M3 (Press-Ang 20°)
Finishing	Rack-cutter	Grinding
Application	Reducer (average speed)	Reducer (high speed)

.

Two different silicones were selected to manufacture the molds for both gears: Silicones Elastosil M4511 and Elastosil M4601 (Wacker Chemie AG, Munich, Germany). These materials were selected based on their different characteristics and suitability for specific applications following the supplier recommendations:

• SILICONE ELASTOSIL M4511: Condensation silicone for making flexible molds for casting polyester and polyurethane resins. High-strength two-component silicone casting material that vulcanizes at room temperature and undergoes condensation cross-linking. Has Excellent fluidity and self-deaeration, Low hardness (Shore A: approx. 12), Extremely high flexibility and elasticity, Excellent tear resistance and Outstanding mold durability thanks to its extraordinary resistance to unsaturated polyester resin and polyurethane resin. Universal high-performance molding material especially suitable for the reproduction of models with very pronounced details, when using polyester or polyurethane resin.
• SILICONE ELASTOSIL M4601: Addition silicone (non-shrinking) for the manufacture of molds in the manufacture of parts that have a lot of detail or that must maintain the dimensions of the copied part. On the molds made with Elastosil 4601, pieces of resin, concrete, wax, etc., can be made. It has a Shore hardness of 28, high elasticity, and very high mechanical resistance.

Table 2. Comparison of ELASTOSIL M4511 and M4601 properties.

Silicone Property	ELASTOSIL-M4511	ELASTOSIL-M4601
Processing time at 23 °C	60–90 min	90 min
Demoldable at 23 °C after	8–10 h	12 h
Demoldable at 70 °C after	-	20 min
Viscosity before vulcanization	25,000 (mPa·s)	20,000 (mPa·s)
Viscosity at 23 °C, in water	1.22 g/cm3	1.1 g/cm3
Hardness, Shore A	12	28
Tensile strength	3.5 N/mm2	3.0 N/mm2
Elongation at break	600%	>700%
Progressive tear resistance	>18 N/mm	>20 N/mm
Linear shrinkage	<0.4%	-
Linear thermal expansion coefficient	2.1 × 10−4 m/m·K	-

shows the properties of ELASTOSIL M4511 and ELASTOSIL M4601 silicones.

The materials selected to manufacture the gears reproduction were two different resins based on their properties. Elastic modulus, Impact resistance and hardness:

• RESIN RECAPOLI 2196: Polyester resin for transparent castings recommended for the production of transparent castings and encapsulations.
• RESIN PR 700: Polyurethane resin for making castings. High thermal resistance, good castability and low aggressiveness in molds, as well as good resistance to chemical aggression.

Table 3. Comparison of Recapoli 2196 and PR700 properties.

Resin Property	RECAPOLI 2196	PR700
Maximum water content	1000 ppm	-
Gel time from 25 to 35 °C	19–23 min	6-7 min
Curing time from 25 °C to exothermic peak	42–57 min	45 min
Maximum temperature 40–50 °C	40–50 °C	40–50 °C
Density at 23 °C	1100 kg/m3	1130 kg/m3
Tensile strength	56 MPa	80 MPa
Elastic modulus (tensile)	4.1 GPa	1800 MPa
Elongation at break	1.60%	1.30%
Flexural strength	-	130°C
Dimensional stability at heat (HDT)	55 °C	130 °C
Impact resistance	18 kJ/m2	60 kJ/m2
Barcol hardness	40–45	Shore 87
Volumetric shrinkage	-	(lineal: 2 mm/m)

shows the mechanical properties of both materials.

2.2. Experimentation Methodology

Figure 1 shows two gears of varying qualities (rack cutter and Grinding) were used as initial models to analyze the influence of the initial quality of the model on the quality of the reproductions.

The models were prepared in containers prior to the mixing of the silicone. The manufacture of the molds and the reproduction of the models were carried out in accordance with the recommendations of the supplier of the silicones and resin in each case. Both the silicone molds and the resin gears were manufactured under the conditions specified by the manufacturer, at temperatures ranging from 23 to 28 °C and relative humidity between 55% and 65%.

For the Elastosil M4601 silicone, the mixture was prepared at a ratio of 9:1 by weight at ambient temperature. Following homogenization, the mixture was transferred into containers. In the case of Elastosil M4511 silicone, the silicone was mixed at room temperature with 5% T21 hardener, and after homogenizing the mixture, it was poured into the containers. The containers of both silicones were demolded after 24 h and each mold was prepared and identified.

Figure 2 shows the front and rear parts of the silicone molds manufactured before demolding (a), the four molds made with Silicone Elastosil 4511 (b) and the four molds made with Elastosil 4601 (c).

To manufacture the resin reproductions with PR700 (Figure 3), it was imperative that the silicone molds underwent preliminary heating to 70 °C, with the isocyanate portion being meticulously weighed within the upper bowl, inclusive of the casting residue. Subsequently, the requisite quantity of the polyol component was introduced into the lower bowl, or mixing bowl, followed by the application of vacuum for a duration of 10 min. Subsequently, the isocyanate part was poured into the polyol part and mixed until the mixture was completely homogeneous (approximately 50 to 60 s). The mixture was then placed in molds that had previously been heated in an oven at 70 °C. After 20 min, the mixture was removed from the molds.

The process of producing reproductions with RECAPOLI 2196 (Resinas Castro S.L., Pontevedra, Spain) resin (Figure 4) is characterized by its simplicity, as it does not necessitate the application of heat to the molds or the establishment of a vacuum for a specific component. The required quantities of resin were meticulously measured, and a 2% catalyst was incorporated, employing the standard methyl ethyl ketone peroxide catalyst X-8 (Resinas Castro S.L., Pontevedra, Spain). Subsequent to the homogenization of the mixture, it was poured into the designated molds. Subsequent to a 30-min waiting period, the gears were removed from the molds.

Ten distinct casts were fabricated for each of the molds and resins. The results of the eight casts can be seen in Figure 5 as an example.

As a summary, Figure 6 shows the methodology used in the gear manufacturing process for this study. A preliminary quality control assessment on the gears was performed before measuring the various geometric deviations that may potentially compromise the performance of the system. A specific measurement was then conducted on the DEA Global Lite V19 (Hexagon AB, Stockholm, Sweden) coordinate measuring machine using PC Dmis V2022-1 Quindos Software 2020 R1 (Figure 7).

The measuring machine used belonging to ENPA ENGRANAJES, S.L. (Esquiroz, Navarra, Spain) is calibrated in accordance with regulations by a body accredited by the Spanish national accreditation entity (ENAC), obtaining a repeatability range of 2.1 micrometers. The measurement procedure used was as follows (Figure 8):

1.

Alignment and Fixing: Positioning of the gear on the CMM ensuring dimensional stability.

2.

Scanning and Data Acquisition: Capturing the three-dimensional topography of the gear using optical and tactile sensors.

3.

Processing and Evaluation: Analysis of geometric deviations through comparison with CAD models using Quindos.

4.

Correction and Validation: Determination of tolerances.

The parameters analyzed were:

• Deviation from Profile Shape (DPS): Discrepancy between the theoretical profile and the actual shape of the tooth. This deviation may be due to inaccuracies in machining or to deformations suffered during the operation. A high ff$\alpha$ value can induce uneven wear, loss of efficiency in the transmission of engine torque and variations in contact stiffness. To mitigate these effects, precision grinding and optimization of the tooth design using computer simulations are recommended.
• Propeller Shape Deviation (ff$\beta$): Impacts the helical geometry of the tooth, compromising the functionality of the gear.

In order to determine the appropriate number of gear specimens to be measured, a design of experiments (DOE) was performed to assess the durability of gears produced in the specified silicone molds. The DOE entailed the examination of various factors, including the type of silicone (4511 and 4601), the type of resin (RECAPOLI 2196 and PR700), the quality of the model gear (standard and maximum), and the casting number.

Table 4. List of experiments per casting.

Code	Silicone	Resin	Gear Quality
A	4511	RECA-2196	1 (Standard)
B	4511	RECA-2196	2 (Maximum)
C	4601	RECA-2196	1
D	4601	RECA-2196	2
E	4511	PR700	1
F	4511	PR700	2
G	4601	PR700	1
H	4601	PR700	2

illustrates the proposed tests, utilizing a $2^3$-factor design of experiments with ten replicates, corresponding to castings one through ten.

This approach enables the analysis of the influence that each factor (silicone, resin, model quality, and casting number) exerts on the dimensional adjustment of the gear manufactured, as depicted by the parameters ff$\alpha$ and ff$\beta$. To conduct this experiment, a total of 80 gears were manufactured and 48 elements were measured and included in the DOE analysis.

For each gear, four different teeth were checked on both the right and left flanks, obtaining eight data points per gear. The values included in the DOE experiment data were the main value.

3. Results and Discussion

A total of eight molds were manufactured, and ten resin gears were produced per mold, resulting in a total of 80 resin gears (40 per resin type). After a visual inspection, no deterioration was detected in the silicone molds, nor were any anomalies observed on the surface of the gears. This led to all pieces being considered valid for their study in the DOE.

Figure 9 shows the initial three castings of the pieces.

3.1. DOE Results

A reference measurement was conducted for both gear models. Four different teeth were checked on both the right and left flanks. The main values of these measurements are presented in

Table 5. Initial ff$\alpha$ and ff$\beta$ measurements.

Quality	ff$\mathit{\alpha }$	ff$\mathit{\beta }$
Q1-Standard	28.3	45
Q2-High	5.7	4.2

.

Subsequent to the fabrication of the gears, the requisite measurements were obtained using the DEA Gobal Lite V19 coordinate measuring machine, with the acquisition being facilitated by Quindos 2020 R1 software. A total of eight measurements of ff$\alpha$ and ff$\beta$ were obtained for each profile, with four measurements being recorded on the left side and another four on the right side of teeth 16, 11, 6, and 1, as illustrated in Figure 10 and Figure 11. The mean of these values was then entered into the Statgraphics Centurion 16.1 software, which was utilized for the DOE. The results of this process are presented in Table 6.

Table 6 below shows the results obtained for ff$\alpha$ and ff$\beta$ for each gear manufactured and checked according to the DOE. This table includes the code of the experiment (A, B,…., H), the resin used, the model quality, the silicone and the cast number.

Table 6. Gear measurements.

	Cast	ff$\mathit{\alpha }$	ff$\mathit{\beta }$		Cast	ff$\mathit{\alpha }$	ff$\mathit{\beta }$
A	1	21.13	119.00	E	1	17.74	36.92
	2	21.07	113.12		2	15.82	48.14
	3	23.68	113.38		3	18.71	37.16
	4	26.25	118.88		4	19.34	51.95
	5	24.38	133.57		5	19.42	46.25
	6	32.00	124.32		6	23.43	55.43
	7	32.05	142.01		7	29.24	50.96
	8	38.33	129.43		8	28.10	58.57
	9	41.74	160.88		9	29.46	51.98
	10	54.8	121.10		10	30.36	59.47
B	1	14.40	56.53	F	1	7.59	43.35
	2	18.09	66.16		2	8.98	21.68
	3	19.13	58.74		3	8.70	25.68
	4	19.79	70.15		4	9.03	23.71
	5	20.73	53.54		5	9.02	30.06
	6	22.07	73.80		6	9.65	25.41
	7	25.35	68.08		7	12.12	31.58
	8	24.93	77.13		8	10.85	26.78
	9	27.45	77.81		9	12.53	32.28
	10	29.72	78.31		10	13.70	33.53
C	1	25.92	58.20	G	1	14.90	29.63
	2	28.17	61.75		2	17.11	31.18
	3	27.63	61.47		3	17.15	41.11
	4	33.95	67.57		4	21.23	35.04
	5	41.62	65.32		5	17.53	44.73
	6	40.30	73.06		6	25.92	38.56
	7	48.50	62.29		7	26.26	46.14
	8	47.23	78.22		8	31.20	41.76
	9	49.43	67.38		9	40.80	55.52
	10	53.03	73.89		10	44.68	58.26
D	1	23.68	41.28	H	1	10.10	23.65
	2	23.82	37.97		2	8.90	27.90
	3	25.40	40.27		3	9.35	19.10
	4	26.12	42.01		4	9.55	29.98
	5	28.78	51.19		5	10.10	23.65
	6	28.00	45.72		6	10.77	31.72
	7	30.18	60.91		7	11.96	24.98
	8	32.46	49.10		8	12.57	33.14
	9	32.43	62.10		9	13.42	25.45
	10	39.30	62.58		10	14.14	23.70

Table 6. Gear measurements.

	Cast	ff$\mathit{\alpha }$	ff$\mathit{\beta }$		Cast	ff$\mathit{\alpha }$	ff$\mathit{\beta }$
A	1	21.13	119.00	E	1	17.74	36.92
	2	21.07	113.12		2	15.82	48.14
	3	23.68	113.38		3	18.71	37.16
	4	26.25	118.88		4	19.34	51.95
	5	24.38	133.57		5	19.42	46.25
	6	32.00	124.32		6	23.43	55.43
	7	32.05	142.01		7	29.24	50.96
	8	38.33	129.43		8	28.10	58.57
	9	41.74	160.88		9	29.46	51.98
	10	54.8	121.10		10	30.36	59.47
B	1	14.40	56.53	F	1	7.59	43.35
	2	18.09	66.16		2	8.98	21.68
	3	19.13	58.74		3	8.70	25.68
	4	19.79	70.15		4	9.03	23.71
	5	20.73	53.54		5	9.02	30.06
	6	22.07	73.80		6	9.65	25.41
	7	25.35	68.08		7	12.12	31.58
	8	24.93	77.13		8	10.85	26.78
	9	27.45	77.81		9	12.53	32.28
	10	29.72	78.31		10	13.70	33.53
C	1	25.92	58.20	G	1	14.90	29.63
	2	28.17	61.75		2	17.11	31.18
	3	27.63	61.47		3	17.15	41.11
	4	33.95	67.57		4	21.23	35.04
	5	41.62	65.32		5	17.53	44.73
	6	40.30	73.06		6	25.92	38.56
	7	48.50	62.29		7	26.26	46.14
	8	47.23	78.22		8	31.20	41.76
	9	49.43	67.38		9	40.80	55.52
	10	53.03	73.89		10	44.68	58.26
D	1	23.68	41.28	H	1	10.10	23.65
	2	23.82	37.97		2	8.90	27.90
	3	25.40	40.27		3	9.35	19.10
	4	26.12	42.01		4	9.55	29.98
	5	28.78	51.19		5	10.10	23.65
	6	28.00	45.72		6	10.77	31.72
	7	30.18	60.91		7	11.96	24.98
	8	32.46	49.10		8	12.57	33.14
	9	32.43	62.10		9	13.42	25.45
	10	39.30	62.58		10	14.14	23.70

3.2. ff$\alpha$ Analysis

After carrying out the DOE, the results for the ff$\alpha$ variable underwent analysis, yielding an adjusted R² value of 93.41%. Furthermore, the model exhibited a standard error of 3.2173 and a mean absolute error (MAE) of 2.02422. These values indicate an accurate fit of the model to the experimental data. In addition, the Durbin–Watson statistic was 2.37725 (p = 0.8334), confirming the absence of serial autocorrelation between the residuals at the 95% confidence level. The regression equation, delineated in Equation (1), demonstrates ff$\alpha$ as a function of all factors and their combinations.

$$\begin{array}{c}\hfill ff\alpha =16.0007+2.46154·\mathrm{Silicone}-1.30046·\mathrm{Resin}\\ \hfill -1.814·\mathrm{Quality}-4.70197·\mathrm{Cycle}\\ \hfill -1.43887·\mathrm{Silicone}·\mathrm{Resin}-0.71025·\mathrm{Silicone}·\mathrm{Quality}\\ \hfill +0.161174·\mathrm{Silicone}·\mathrm{Cycle}-1.90225·\mathrm{Resin}·\mathrm{Quality}\\ \hfill -0.430462·\mathrm{Resin}·\mathrm{Cycle}-1.82859·\mathrm{Quality}·\mathrm{Cycle}\end{array}$$

(1)

Figure 12 shows the Pareto diagram resulting from the analysis ff$\alpha$ variable.

As shown in Figure 12, the Pareto diagram obtained from the analysis reveals that the type of resin, the casting cycle, the initial quality of the model gear, and the silicone are significant variables in the study.

The most relevant factor is the type of resin. Specifically, analysing the results for the same quality level gear model, the type of resin that yields the lowest ff$\alpha$ (the desired outcome) is PR700 (series E, F, G, H), while the gears manufactured with the RECAPOLI 2196 resin exhibit the highest ff$\alpha$ parameter value, as can be seen in Figure 13a,b.

The analysis indicates a direct correlation between the number of casts and the resulting ff$\alpha$ value, suggesting that more casts lead to higher values. This is attributable to the deterioration of the silicone mold. The values obtained for the two last measurements corresponding to casts number nine and ten, show a high increase in the deviation from the first and second measurements. This deterioration of the molds is higher when silicon 4601 is used (Cases C,D,G,H). This effect could be seen on Figure 14 Analysis of the deterioration of molds as a function of the silicone used. Furthermore, in the figure it could be seen that the use of the resin R2196 aggravates the problem of mold deterioration in both silicones.

Furthermore, the analysis reveals that the quality of the gear model used to create the mold significantly impacts the outcome. Using a model of the highest possible quality is recommended for optimal results in this process. Nevertheless, the results confirm that this manufacturing process allows to reproduce a wide range of different quality levels, obtaining reliable results for each quality model. In the test carried out, the molds made from the model with the better quality suffered greater deterioration and the effect of the casting number became more important in both types of silicone.

Additionally, it has been determined that the molding silicone that yields the optimal ff$\alpha$ results is 4511, as shown in Figure 15.

Figure 16 shows the response surfaces obtained for ff$\alpha$ as a combination of each of the factors. These surfaces make it possible to determine the corresponding factor ff$\alpha$ to be reached for a specific casting number value as a function of the silicone, the quality of the original model and the resin used for the manufacture of the castings.

The analyses conducted on the molds and resin gears suggest a relationship between these factors and the Shore hardness of the materials used. Further experimentation is required to more accurately assess the influence of material hardness. This will enable the development of a response surface applicable to new materials through this index.

3.3. ff$\beta$ Analysis

For the study of the response variable ff$\beta$, the numerical analysis showed an adjusted $R^2$ of 92.7941%, a standard error of the model of 8.4411, and a mean absolute error (MAE) of 5.21406. These values indicate an accurate fit of the model to the experimental data. In addition, the Durbin–Watson statistic was 2.3619 (p = 0.89352), confirming the absence of serial autocorrelation between the residuals at the 95% confidence level. The regression equation, delineated in Equation (2), elucidates the relationship between ff$\alpha$ and the aggregate of all factors, along with their interplay.

$$\begin{array}{c}\hfill ff\beta =81.5257-28.5689·\mathrm{Silicone}-32.8566·\mathrm{Resin}\\ \hfill -22.864·\mathrm{Quality}+3.34302·\mathrm{Cycle}\\ \hfill +8.59962·\mathrm{Silicone}·\mathrm{Resin}+11.5883·\mathrm{Silicone}·\mathrm{Quality}\\ \hfill +0.0100682·\mathrm{Silicone}·\mathrm{Cycle}+10.2507·\mathrm{Resin}·\mathrm{Quality}\\ \hfill +0.553841·\mathrm{Resin}·\mathrm{Cycle}-0.992409·\mathrm{Quality}·\mathrm{Cycle}\end{array}$$

(2)

As illustrated in Figure 17, the Pareto diagram reveals that the type of resin is the most significant variable, followed by the initial quality of the model gear, the type of silicone, and the number of casting cycles.

As shown in Figure 18, and consistent with the ff$\alpha$ analysis, the PR700 resin yields optimal ff$\beta$ results. Experiments E, F, G, and H consistently outperformed A, B, C and D.

The initial quality of the model gear also aligns with the ff$\alpha$ findings, wherein ff$\beta$ results are optimal when employing the mold generated from the highest quality model gear. However, by analyzing the trends of the reproductions made to the models of the two qualities, it can be deduced that the technique of reproducing models using silicone molds can be used regardless of the initial quality of the model. The results obtained from the analysis of the influence of the initial quality of the model on the ff$\beta$ factor correspond to those obtained in the analysis of this factor on the ff$\alpha$.

However, when it comes to the silicone utilized in the mold, superior ff$\beta$ values are attained for the 4601. Figure 19 shows that experiments with silicone 4511 (A, B, F) deliver better results than silicone 4601 (Experiments C, D, F). Just in case of a standard quality model, and resin PR700 (Experiments E and G), the silicone used seems not to have a clear influence in the ff$\beta$ parameter obtained.

The results of the analysis of the ff$\beta$ parameter with respect to the most suitable type of silicone are in the opposite direction to those obtained in the analysis of the ff$\alpha$ parameter, so the relationship needs to be studied further. There is probably a third moderating variable of the relationship that has not yet been identified.

When analyzing the casting cycle, a detrimental influence on the ff$\beta$ value is observed, as evidenced by the ff$\alpha$ study except for PR700 and high quality model where the relationship is not clear. In Figure 20, which presents the analysis of mold deterioration as a function of ff$\beta$ measurements, the evolution of the difference between measurements (%) of the ff$\beta$ parameter can be seen. It is noteworthy that the value of this parameter deteriorates proportionally with the increase in the number of castings.

Finally, in Figure 21 the response surfaces obtained in the ff$\beta$ study can be seen, combining the factors two by two. These surfaces make it possible to determine the corresponding factor ff$\beta$ to be reached for a specific casting number value as a function of the silicone, the quality of the original model, and the resin used for the manufacture of the castings.

The analyses conducted on the molds and resin gears seem to relate these factors to the results obtained through the Shore hardness degree of the materials used. It has been found necessary to conduct new experiments to be able to analyze in more detail the influence of hardness. This will enable the development of a response surface applicable to new materials through this index.

The findings obtained for both parameters underscore the significance of the four factors examined (type of silicone, type of resin, quality of the model, and number of casts) in the geometric precision of the gears manufactured. In both studies, the type of resin (polyurethane versus polyester) emerged as the predominant factor, underscoring the pivotal role of the physicochemical and creep properties of the resin during the casting process in attaining a lower deviation from the shape (ff$\alpha$) and the tooth helix (ff$\beta$). Specifically, the PR700 polyurethane resin exhibited greater dimensional stability and a reduced propensity for surface defects in both studies. This is consistent with the findings of the study by [6], which highlighted the superior performance of polyurethane-based resins. This enhanced performance could be attributed to its superior mechanical behavior and reduced interaction with mold walls.

4. Conclusions

In this work, the manufacture of resin gears using silicone molds has been analyzed, with emphasis on the influence of the type of resin, the mold material, and the manufacturing conditions to obtain the highest possible quality gears.

Regarding the type of silicone utilized, which is paramount to attaining an adequate reproduction of the geometry, it is noteworthy that the study observed disparate behavior in the results. On one hand, Elastosil M4601 silicone, being an addition silicone, exhibits negligible shrinkage and high tear resistance, resulting in effective transmission of the tooth shape across the various casts. This observation is supported by the low ff$\alpha$ and ff$\beta$ values obtained in tests with M4601, even when successive casts were produced. Conversely, although M4511, a condensation silicone, exhibited good elasticity and performance in replicating complex geometries, a significant increase in deviations of the ff$\alpha$ but better results for ff$\beta$ parameters was observed. This apparent incongruence of the results obtained allows us to detect that there is a third moderating variable of the relationship that has not yet been identified, so it is necessary to study the relationship in greater depth by incorporating other materials with different mechanical properties necessary to clarify this relationship.

Additionally, the initial quality of the model gear was found to influence the measurements. Any defect in the original part tends to be replicated and, on occasions, amplified with successive casts. This is because each cycle subjects the silicone to thermal and mechanical stresses that generate micro-tears and/or loss of elasticity. This phenomenon has been evidenced by an increase in the values of ff$\alpha$ and ff$\beta$, particularly after multiple castings. This observation aligns with the findings reported by [23], who noted comparable trends in casting processes involving silicone molds and with the results obtained in [11,12] who emphasized the importance of a high-quality model to prevent the amplification of defects in successive reproductions. In fact, molds made from models with quality (Q2) suffered more pronounced degradation, indicating greater sensitivity to cumulative microdamage. The implications of these findings are particularly salient in the context of manufacturing gears for critical applications, where transmission precision and minimal noise or vibration levels are fundamental. It is important to note that the observed differences in the two parameters analyzed (ff$\alpha$ and ff$\beta$) can be attributed to the distinct mechanisms of tooth degradation. The tooth profile (ff$\alpha$) is primarily affected by minor contractions or localized defects, while the deviation of the helix (ff$\beta$) intensifies with the onset of global deformations in the mold or variations in the pouring of the resin. Consequently, the study and comparison of the results obtained for both measurements provides a comprehensive view of the dimensional behavior of the gear. Finally, the possibility of applying a maintenance or mold replacement strategy based on a defined number of casting cycles would reduce the negative effects of mold wear.

PR700 resin demonstrated superior performance in both parameters (ff$\alpha$ and ff$\beta$), which can be attributed to its higher impact resistance (60 kJ/m²) and superior thermal stability (HDT 130 °C) compared to RECAPOLI 2196. These data reinforce the findings of Kuo et al. [6], who associated better performance in polymer gears with polyurethane-based resins compared to polyesters, due to their lower volumetric shrinkage and less interaction with the mold walls.

Likewise, it has been shown that the casting cycle is a key factor, since greater use leads to mold degradation and therefore to greater geometric deviations, which highlights the need to create a mold replacement strategy.

Silicone molds were shown to reproduce the quality of the original model with high fidelity, and obtain parts with good replicability. The initial quality of the model used for mold manufacturing has a direct impact on the precision of the final gears as it reduces the propagation of defects. This reinforces the need to have reference models of the highest possible quality. Likewise, the response surfaces obtained enable the determination of the necessary model quality required to obtain reproductions with certain ff$\alpha$ and ff$\beta$ values that allow the silicon gears to be used in the foreseen conditions.

Regarding the different types of silicone molds analyzed, it was observed that ELASTOSIL M4601 silicone provides greater profile accuracy (ff$\alpha$), while ELASTOSIL M4511 minimizes helical deviations (ff$\beta$).

Finally, future research is thought to be directed towards the incorporation of reinforcing materials for silicone molds, with the aim of improving their durability and thus reducing the effects of degradation resulting from successive casting cycles.