Application of New Conformal Cooling Layouts to the Green Injection Molding of Complex Slender Polymeric Parts with High Dimensional Specifications

Eliminating warpage in injection molded polymeric parts is one of the most important problems in the injection molding industry today. This situation is critical in geometries that are particularly susceptible to warping due to their geometric features, and this occurs with topologies of great length and slenderness with high changes in thickness. These features are, in these special geometries, impossible to manufacture with traditional technologies to meet the dimensional and sustainable requirements of the industry. This paper presents an innovative green conformal cooling system that is specifically designed for parts with slender geometric shapes that are highly susceptible to warping. Additionally, the work presented by the authors investigates the importance of using highly conductive inserts made of steel alloys in combination with the use of additively manufactured conformal channels for reducing influential parameters, such as warpage, cooling time, and residual stresses in the complex manufacturing of long and slender parts. The results of this real industrial case study indicated that the use of conformal cooling layouts decreased the cycle time by 175.1 s—66% below the current cooling time; the temperature gradient by 78.5%—specifically, 18.16 °C; the residual stress by 39.78 MPa—or 81.88%; and the warpage by 6.9 mm—or 90.5%. In this way, it was possible to achieve a final warping in the complex geometry studied of 0.72 mm, which was under the maximum value required at the industrial level of 1 mm. The resulting values obtained by the researchers present a turning point from which the manufacturing and sustainability in the injection molding of said plastic geometries is possible, and they take into account that the geometric manufacturing features analyzed will present a great demand in the coming years in the auto parts manufacturing industry.


Introduction
The plastic manufacturing process of injection molding is currently considered one of the most widely used plastic transformation technologies worldwide [1]. It is estimated that 70% of consumer products incorporate components manufactured with this production process [2,3]. The global scope of the plastic injection molded market was estimated at USD 265.1 billion in the year 2020, and is expected to grow annually by 4.6% between 2021 and 2028 [4].
Although the demand for plastic components comes from various industrial fields, such as packaging, electrical, electronic products, and medical devices, the automotive industry is one of the areas that produces the largest number of plastic parts. The global injection molded plastics market size was valued at USD 265.1 billion in 2020 and is expected to expand at a compound annual growth rate(CAGR) of 4.6% from 2021 to 2028 [5]. The automobile requires the design of multiple plastic parts, such as wheel covers, cycle time in a range of 20 to 40%. Torres et al. [31] reduced cycle time by 13% in very complex optical parts with a high thickness ratio. Sayfullah and Masood [32] reduced the total cycle time by 35% as well as the maximum temperature by 30%, thus improving the differential shrinkage and, therefore, its warpage. Mazur et al. [33] obtained improvements of 5 • C in the maximum temperature, thus improving the shrinkage of the part as well as its warpage, and Smidt et al. [34] improved the cooling time by 32.7%, thus reducing the warpage by 28.2%.
Given the high influence of conformal cooling channels in reducing cycle time and improving part uniformity, different applications and designs have been proposed. Concerning the geometry of the layout, the spiral layout is one of the most used [34]. Unfortunately, these channels present sudden turns, which increase the pressure drop and slow down the flow, which results in weakening the effectiveness of the cooling process. To avoid these problems, other authors use layouts whose axes follow a zigzag [35,36] design. For highly complex geometries, it is possible to use cross-linked channel designs [37], porous [38], lattice [39,40], or vascularized [41] topologies. However, all these geometries [35][36][37][38][39][40][41] have the problem of requiring a connection between channels, so in the event of an obstruction caused by foreign elements, it could not be easily removed from the layout. Another way to cool complex cores is the use of inserts made of high thermal conductive materials, such as high conductive steel alloys. The high thermal conductivity of these materials helps in the process of reducing the cycle time while maintaining the corrosion and oxidation resistance of the mold [42].
Reducing the warpage of a plastic part to a minimum value is a highly significant factor, especially for complex optical parts where dimensional accuracy affects the functionality of the vehicle [43][44][45]. The current designs demanded in the industry, and especially in the automotive sector, increasingly complicate the manufacturing process by molding. The trends place increasing emphasis on the development of the visual or aesthetic appearance of the vehicle, which complicates the functional aspect of the molded parts. This fact increases if we take into account that, in addition to style, some of these pieces have to fulfill an optical function at the level of lighting or light signaling according to the standards. The style implemented today in the automotive industry highlights futuristic concepts that are characterized by large-format stylized details that incorporate new technologies, such as LEDs. These technologies require a marked precision in the dimensional aspect of the pieces, so it is necessary to look for designs that improve the current conception of the injection molding process. The procedures and tools used to date do not guarantee an optimal result in terms of the aesthetic or functional aspect of the part, nor do they ensure a competitive manufacturing process.
The use of long plastic parts with geometric slenderness, including areas with large thickness ratios, is becoming more common in the automotive field and, more specifically, in the area of optical plastic parts using LED technology. The upcoming lines of aesthetics and functionality that will come in the coming years for the car demand a type of lighting that is not only external, but also internal to the vehicle. These optical plastic parts require high aesthetic and dimensional specifications, and are also characterized by a great length and slenderness. These geometries cannot be manufactured with high quality using current production means. To avoid these problems, the use of conformal cooling layouts, together with high thermal conductivity materials, can help to obtain a uniform and balanced temperature map in these complex parts. Unfortunately, currently, the application of green conformal cooling channels for the cooling of injection molds is a complex procedure from initial design to the final manufacturing process of the mold. Despite previous literature and relevant review articles, unfortunately, there are still significant gaps in the research and application of conformal cooling layouts [22].
To avoid the problems raised so far, this paper proposes a new, industrially sustainable conformal cooling system that can reduce cycle times, longitudinal warpage, and residual stresses in the manufacturing of highly complex injection molded parts, which are characterized by their great length and slenderness, as well as by their thick points. Research has not yet been conducted at a scientific or industrial level on the application of conformal layouts to the manufacture of this type of plastic geometry that is impossible to manufacture while meeting the industry's requirements using traditional methods. The results obtained by the authors mark a turning point in the manufacture by molding of this type of topology, given that the geometric manufacturing features studied in this paper will present a very high demand in the coming years in the automotive industry [46,47]. The research results obtained show that the use of conformal cooling layouts in the cooling of injection molds makes it possible to manufacture parts that follow the high dimensional requirements demanded by current industries. Finally, the results presented by the authors are fully in line with the sustainability and energy-saving criteria demanded by the European Union and the rest of the world in terms of the manufacture of industrial plastic parts.

Geometric Analysis and Functional Description of the Plastic Part Manufactured via Injection Molding
The analysis and determination of the geometric, technological, and functional requirements of the plastic part directly influence the process of geometric design and the dimensioning of the main elements that make up the mechanical systems of the injection mold. Likewise, geometric aspects, such as the complexity of the surfaces, the distribution of the thickness map, general dimensions, and geometric tolerances, not only determine the final configuration of the injection mold, but also establish the technological parameters that control its correct manufacturing process. That is why, in this section, the main geometric features and parameters of the plastic part under study are described in detail, as well as the definition of its main application and functional requirements.
The plastic part object of study is defined as a chimsel. As shown in Figure 1, this real case study is an industrial part belonging to a LED-collimator lighting system, which is used in the automotive industry. The main function of this optical part is to collect the light coming from the LEDs using several collimating elements (see Figure 1) and project it onto a light output surface, which is geometrically composed of a large number of small squares with closed angle "Pillows" that are in charge of distributing the light according to the desired purpose (see Figure 1). In this way, the light generated by the LED lighting elements is directed along the plastic part according to the functionality and standards established by the automotive industry.
To avoid the problems raised so far, this paper proposes a new, industrially sustainable conformal cooling system that can reduce cycle times, longitudinal warpage, and residual stresses in the manufacturing of highly complex injection molded parts, which are characterized by their great length and slenderness, as well as by their thick points. Research has not yet been conducted at a scientific or industrial level on the application of conformal layouts to the manufacture of this type of plastic geometry that is impossible to manufacture while meeting the industry's requirements using traditional methods. The results obtained by the authors mark a turning point in the manufacture by molding of this type of topology, given that the geometric manufacturing features studied in this paper will present a very high demand in the coming years in the automotive industry [46,47]. The research results obtained show that the use of conformal cooling layouts in the cooling of injection molds makes it possible to manufacture parts that follow the high dimensional requirements demanded by current industries. Finally, the results presented by the authors are fully in line with the sustainability and energy-saving criteria demanded by the European Union and the rest of the world in terms of the manufacture of industrial plastic parts.

Geometric Analysis and Functional Description of the Plastic Part Manufactured via Injection Molding
The analysis and determination of the geometric, technological, and functional requirements of the plastic part directly influence the process of geometric design and the dimensioning of the main elements that make up the mechanical systems of the injection mold. Likewise, geometric aspects, such as the complexity of the surfaces, the distribution of the thickness map, general dimensions, and geometric tolerances, not only determine the final configuration of the injection mold, but also establish the technological parameters that control its correct manufacturing process. That is why, in this section, the main geometric features and parameters of the plastic part under study are described in detail, as well as the definition of its main application and functional requirements.
The plastic part object of study is defined as a chimsel. As shown in Figure 1, this real case study is an industrial part belonging to a LED-collimator lighting system, which is used in the automotive industry. The main function of this optical part is to collect the light coming from the LEDs using several collimating elements (see Figure 1) and project it onto a light output surface, which is geometrically composed of a large number of small squares with closed angle "Pillows" that are in charge of distributing the light according to the desired purpose (see Figure 1). In this way, the light generated by the LED lighting elements is directed along the plastic part according to the functionality and standards established by the automotive industry.  It should be noted that, as it is an optical part, the dimensional tolerances required to meet the requirements and standards of functionality and optical criteria are more demanding, relevant, and significant than for any other plastic part. In general, the final or resulting dimensional tolerances in plastic geometries are closely related to the design of the main components of the injection mold. This is especially true for the elements that make up the cooling system. Similarly, it is equally pertinent to establish the technological parameters that define the cooling phase within the cycle of manufacturing the plastic part. After manufacturing, warping can be generated due to physical concepts related to the cooling phase, including distribution of the cooling temperature gradients on the surface of the plastic part, residual stresses caused by a nonuniform cooling temperature, and the associated unbalanced volumetric shrinkage of the thermoplastic material. Therefore, an optimal design and dimensioning would favor the reduction of the final warpage of the plastic part, and, therefore, achieve its functional requirements.
During the cooling phase, the most relevant features and geometric parameters are the thickness map and the main part dimensions (width, length, height)-see Figures 2 and 3and the resulting variables are the time needed until the ejection temperature is reached, the distribution of volumetric shrinkage, and the warpage after the cooling phase. These parameters mainly determine the economic viability, the efficiency, and the sustainability of the manufacturing process, as well as the compliance with the dimensional tolerances and the functional requirements of the plastic part. Table 1 shows the magnitude of the main geometric parameters of the plastic part under study.
It should be noted that, as it is an optical part, the dimensional tolerances required to meet the requirements and standards of functionality and optical criteria are more demanding, relevant, and significant than for any other plastic part. In general, the final or resulting dimensional tolerances in plastic geometries are closely related to the design of the main components of the injection mold. This is especially true for the elements that make up the cooling system. Similarly, it is equally pertinent to establish the technological parameters that define the cooling phase within the cycle of manufacturing the plastic part. After manufacturing, warping can be generated due to physical concepts related to the cooling phase, including distribution of the cooling temperature gradients on the surface of the plastic part, residual stresses caused by a nonuniform cooling temperature, and the associated unbalanced volumetric shrinkage of the thermoplastic material. Therefore, an optimal design and dimensioning would favor the reduction of the final warpage of the plastic part, and, therefore, achieve its functional requirements.
During the cooling phase, the most relevant features and geometric parameters are the thickness map and the main part dimensions (width, length, height)-see Figure 2 and Figure 3-and the resulting variables are the time needed until the ejection temperature is reached, the distribution of volumetric shrinkage, and the warpage after the cooling phase. These parameters mainly determine the economic viability, the efficiency, and the sustainability of the manufacturing process, as well as the compliance with the dimensional tolerances and the functional requirements of the plastic part. Table 1 shows the magnitude of the main geometric parameters of the plastic part under study.    It should be noted that, as it is an optical part, the dimensional tolerances required to meet the requirements and standards of functionality and optical criteria are more demanding, relevant, and significant than for any other plastic part. In general, the final or resulting dimensional tolerances in plastic geometries are closely related to the design of the main components of the injection mold. This is especially true for the elements that make up the cooling system. Similarly, it is equally pertinent to establish the technological parameters that define the cooling phase within the cycle of manufacturing the plastic part. After manufacturing, warping can be generated due to physical concepts related to the cooling phase, including distribution of the cooling temperature gradients on the surface of the plastic part, residual stresses caused by a nonuniform cooling temperature, and the associated unbalanced volumetric shrinkage of the thermoplastic material. Therefore, an optimal design and dimensioning would favor the reduction of the final warpage of the plastic part, and, therefore, achieve its functional requirements.
During the cooling phase, the most relevant features and geometric parameters are the thickness map and the main part dimensions (width, length, height)-see Figure 2 and Figure 3-and the resulting variables are the time needed until the ejection temperature is reached, the distribution of volumetric shrinkage, and the warpage after the cooling phase. These parameters mainly determine the economic viability, the efficiency, and the sustainability of the manufacturing process, as well as the compliance with the dimensional tolerances and the functional requirements of the plastic part. Table 1 shows the magnitude of the main geometric parameters of the plastic part under study.     As can be seen in Table 1 and Figure 3, the plastic part has a particular topology, features, and geometric parameters, which differ from the usual standards in the plastics industry. The nominal length of the plastic part is 630 mm. The difference between the average and maximum thickness is 5.5 mm. This thickness variation is given by the need to include an upper wing and several collimating elements in order to project and direct the light beam coming from the LEDs towards the pillow elements (see Figure 1). The part is made up of a set of reinforcing elements of variable dimensions that greatly increase the thickness of the part in its lower area, which make it difficult to manufacture. These features and geometric parameters directly affect the design and manufacture of the main elements of the cooling system and its functionality.

Theoretical Background and Analytical Study of the Cooling Phase
The analytical study of the cooling phase of the plastic part under study focuses on the analysis of two technological parameters: the time to reach the ejection temperature and the longitudinal warpage. On the one hand, the evaluation of the current time that elapses until the plastic part reaches the ejection temperature facilitates the evaluation of the thermal performance associated with the design of the cooling system and the cooling phase of the plastic part. Meanwhile, the longitudinal warpage in a plastic part after cooling determines its compliance with dimensional tolerances and its functional requirements.

Time to Reach the Ejection Temperature
The manufacturing cycle of the plastic part is determined by different technological phases: filling, packing, cooling, and ejection. Among all of them, the cooling phase is the most important in the thermoplastic injection molding process and represents more than 70% of the total time invested in the manufacturing cycle, which gives it the greatest influence on energy consumption. The cooling phase begins with the solidification of the gate. This is followed by the solidification of the molten plastic front, which has completed the mold cavity, whereby it cools down until it reaches a sufficient and suitable temperature to go on to the ejection phase. The physical model used to determine the cooling time is established from the heat exchange by conduction that occurs between the thermoplastic material and the coolant flow. Consequently, the hypothesis is established that the thermal exchange by convection and the radiation between the main elements of the injection mold and the external environment are neglected, as they represent less than 5% of the total heat exchange. The heat flow by conduction is defined, according to Equation (1), using Fourier's differential equation, and is reduced to one dimension. Although this thermal analysis can be applied to the three main directions of space, the heat exchange flow between the thermoplastic material and the coolant flow is carried out in only one direction, the main direction of the thickness, so the unidirectional approach of the analysis is valid [5]. In this way, the one-dimensional heat flow or Fourier equation reduced to one dimension can be expressed as: where α p (m 2 /s) is the coefficient for the thermal diffusivity of the mold material, and which takes into account that, after the filling of the mold, the temperature of the molten plastic is constant, while the temperature of the surface of the mold changes until it reaches a value stationary. For these conditions, a solution of a particular type can be found (see Equation (2)) for Equation (1). At a belonging point to the mold cavity, it is possible to analyze the temperature of the molten plastic through the convergence of the Fourier series as indicated in Equation (1). When solving Equation (2) concerning the cooling time variable, the expression that determines the cooling time t cooling is defined in Equation (3): where T p (m) represents the maximum thickness of the plastic part, T melt ( • C) represents the temperature of the molten plastic front, T mold ( • C) represents the surface temperature of the injection mold cavity, and T eject ( • C) represents the recommended ejection temperature for the thermoplastic material (see Figure 4). At a belonging point to the mold cavity, it is possible to analyze the temperature of the molten plastic through the convergence of the Fourier series as indicated in Equation (1).
When solving Equation (2) concerning the cooling time variable, the expression that determines the cooling time tcooling is defined in Equation (3): where Tp (m) represents the maximum thickness of the plastic part, Tmelt (°C) represents the temperature of the molten plastic front, Tmold (°C) represents the surface temperature of the injection mold cavity, and Teject (°C) represents the recommended ejection temperature for the thermoplastic material (see Figure 4). In addition, it should be noted that the boundary conditions established to define Equation (3) are that the thickness of the plastic part is much less than the rest of its dimensions and that the direction of the heat flow, which is exchanged between the plastic part and the coolant, is perpendicular to the melt plastic flow direction [5].
Secondly, the magnitude of the main thermal variables that define Equation (3) are established and recommended by the manufacturer or supplier of the thermoplastic material. Also, Equation (3), determined by a physical model, establishes an analytical and approximate cooling time. In practice, the cooling time can be substantially longer if the mold maker considers that the plastic part requires more cooling time to achieve the required functional specifications and geometric tolerances. In addition, the definition of the magnitude of the surface temperature of the mold cavity Tmold (°C) (see Equation (3)) directly depends on the design and dimensioning of the main elements that make up the injection mold cooling system. Therefore, an optimized design adjusted to the features and geometric properties of the plastic part can significantly reduce the result of the cooling time, thus improving the sustainability of the process. In addition, it should be noted that the boundary conditions established to define Equation (3) are that the thickness of the plastic part is much less than the rest of its dimensions and that the direction of the heat flow, which is exchanged between the plastic part and the coolant, is perpendicular to the melt plastic flow direction [5].
Secondly, the magnitude of the main thermal variables that define Equation (3) are established and recommended by the manufacturer or supplier of the thermoplastic material. Also, Equation (3), determined by a physical model, establishes an analytical and approximate cooling time. In practice, the cooling time can be substantially longer if the mold maker considers that the plastic part requires more cooling time to achieve the required functional specifications and geometric tolerances. In addition, the definition of the magnitude of the surface temperature of the mold cavity T mold ( • C) (see Equation (3)) directly depends on the design and dimensioning of the main elements that make up the injection mold cooling system. Therefore, an optimized design adjusted to the features and geometric properties of the plastic part can significantly reduce the result of the cooling time, thus improving the sustainability of the process.

Warpage Analysis Process
The warpage map generated for the plastic part is a result of its manufacturing process. This map defines the final quality of the part according to its functional requirements and geometric tolerances. In general, the warpage map is related to the volumetric shrinkage that it undergoes during the different phases of the plastic injection cycle. In particular, the main physical effects that generate volumetric shrinkage in the plastic part are the pressure and temperature gradients that develop along its surface, especially after the cooling phase. According to [48], the differential volumetric shrinkage, which is caused by temperature gradients, stresses, and the geometry of the plastic part, causes longitudinal warpage outside its main plane (see Figure 5), and this can be expressed according to Equation (4): where W (m) represents the separation distance between the center of the plastic part and its outer contour, S edge represents the percentage of linear shrinkage that is obtained along the outer contour of the plastic part, and S center represents the percentage of linear shrinkage obtained in the central region of the plastic piece. Likewise, the volumetric shrinkage parameter is defined from the linear shrinkage experienced by the thermoplastic material in the three main directions of the space. In this way, if the hypothesis is established in which the thermoplastic material is considered to be isotropic, the linear shrinkage that it experiences in the three main directions of space is the same.

Warpage Analysis Process
The warpage map generated for the plastic part is a result of its manufacturing process. This map defines the final quality of the part according to its functional requirements and geometric tolerances. In general, the warpage map is related to the volumetric shrinkage that it undergoes during the different phases of the plastic injection cycle. In particular, the main physical effects that generate volumetric shrinkage in the plastic part are the pressure and temperature gradients that develop along its surface, especially after the cooling phase.
According to [48], the differential volumetric shrinkage, which is caused by temperature gradients, stresses, and the geometry of the plastic part, causes longitudinal warpage outside its main plane (see Figure 5), and this can be expressed according to Equation (4): Figure 5. Warpage due to differential shrinkage of temperature gradient.
where W (m) represents the separation distance between the center of the plastic part and its outer contour, Sedge represents the percentage of linear shrinkage that is obtained along the outer contour of the plastic part, and Scenter represents the percentage of linear shrinkage obtained in the central region of the plastic piece. Likewise, the volumetric shrinkage parameter is defined from the linear shrinkage experienced by the thermoplastic material in the three main directions of the space. In this way, if the hypothesis is established in which the thermoplastic material is considered to be isotropic, the linear shrinkage that it experiences in the three main directions of space is the same. As a result, the linear shrinkage experienced by the thermoplastic material can be expressed as a function of the magnitude of volumetric shrinkage according to Equation (5): where S represents the percentage of linear shrinkage of the thermoplastic material, and rv represents the percentage of volumetric shrinkage of the thermoplastic material. Finally, to complete the analytical study that determines the longitudinal warpages of the plastic part, Tait's double domain equations are used, which characterize the compressibility behavior of the thermoplastic material. From this analytical model, and as is shown in Equation (6), the specific volumes of the thermoplastic material can be defined from its temperature and pressure. As a result, the linear shrinkage experienced by the thermoplastic material can be expressed as a function of the magnitude of volumetric shrinkage according to Equation (5): where S represents the percentage of linear shrinkage of the thermoplastic material, and r v represents the percentage of volumetric shrinkage of the thermoplastic material. Finally, to complete the analytical study that determines the longitudinal warpages of the plastic part, Tait's double domain equations are used, which characterize the compressibility behavior of the thermoplastic material. From this analytical model, and as is shown in Equation (6), the specific volumes of the thermoplastic material can be defined from its temperature and pressure.
where υ 0 (m 3 /kg) represents the reference specific volume of the thermoplastic material for the analyzed temperature, β (Pa) represents the compressibility of the thermoplastic material for the analyzed temperature, and P (Pa) represents the analysis pressure of the thermoplastic material. Furthermore, this set of variables can be expressed according to Equations (7) and (8): where b 1 (m 3 /kg), b 2 (m 3 /kg), b 3 (Pa), b 4 (1/K), and b 5 (K) are technological parameters specific to the thermoplastic material, which are provided by its manufacturer and supplier. Finally, to define the longitudinal shrinkage (see Equation (4)) suffered by the plastic part, both in its outer contour and in its central region, the percentage of volumetric shrinkage of the thermoplastic material (see Equation (5)) is defined according to Equation (9). All these requirements, for temperature and pressure conditions between the instant before the beginning of the cooling phase, constitute the end of the manufacturing process.

Materials
In this item, we proceed to define the features and properties of the materials used during the research work, both for the main elements that make up the injection mold and for the thermoplastic material of the part under study. In this case, the polymer family used to manufacture the plastic geometry is polymethyl methacrylate (PMMA). This polymer is a highly transparent thermoplastic that is established by the polymerization of the methylmethacrylate monomer. In this way, thanks to its optical and aesthetic features, as well as its high surface strength, this thermoplastic material is used as a lightweight alternative to glass and polycarbonate (PC) when greater transparency, resistance to ultraviolet rays, and high mechanical performance against impacts are required. For this reason, the field of application of this thermoplastic material focuses on the automotive sector, especially for the manufacture of lighting components included in vehicle headlights. In particular, the trade name of the thermoplastic material used is Plexiglas 8N [49]. According to the physical models analyzed in this manuscript, Table 2 shows the mechanical, thermal, and rheological properties of this thermoplastic material according to the information provided by the supplier and manufacturer. Likewise, it should be noted that the manufacturing material can be subjected to a chemical recycling process. In other words, this material, in addition to encountering the requirements and specifications of the plastic part, is recyclable and maintains its original mechanical, thermal, and chemical properties without compromising the sustainability of the manufacturing process.
On the other hand, metallic materials have been defined as the main elements that make up the injection mold systems. For the main insert of the injection mold, a steel alloy called 1.2709 was used. The selection of this metallic material was justified due to the need to use a 3D additive manufacturing process, based on laser sintering (SLS) technology, which allowed for the optical fabrication of green conformal cooling channels. In addition, to optimize the cooling of the plastic part under study, it was proposed to use a high conductive steel alloy known as Fastcool-50 at 44 HRC for the auxiliary elements of the cooling system [50]. The high thermal capacities and performance of this material, together with the location and design of the auxiliary cooling elements, optimize the thermic exchange between the part and the mold, especially in those areas where the effectiveness of the cooling channels decreases, and the temperature gradients are greater. Tables 3 and 4 present several properties of the metallic materials used. The materials' properties have been provided by the plastic suppliers.

Cooling Channels Design
This section describes the design of the devices and channels of the traditional cooling layout that are currently used for the industrial optical part under study. It also presents the proposals for channels and elements of the cooling layout, based on the concept of green conformal cooling channels (GCCC) and Fastcool inserts, which allow for the optimization of the cooling phase, the technological parameters, and sustainability related to the manufacture of the complex part.
In the first place, the geometry and topology of the part have a direct influence on the main parameters of the process using injection molds, which include cycle time; the temperature map of the plastic part; the map of longitudinal warpage and residual stresses of the plastic part after the cooling phase; the thermal performance of the cooling system; and the uniformity in the thermal exchange between the plastic part and the coolant flow. Consequently, these parameters have great relevance to the surface and dimensional quality of the plastic part and contribute to the energy required for its manufacturing. As shown in Table 1 and Figure 2, the plastic piece under study has a maximum thickness in the collimator area of 9.6 mm, while the average thickness in the rest of the geometry is equal to 4.1 mm. That is, the thickness ratio is equal to 2.34:1. Therefore, the manufacture of a plastic part with this thickness variation is a challenge since, as the dimensions and thickness gradients in the plastic part increase, the residual stresses and longitudinal warpage similarly increase. In addition, the area of the part with greater thickness presents an increase in the accumulation of heat due to a slower cooling process. This variation in the temperature of the part generates an increase in the cooling time and, consequently, induces a non-uniform shrinkage process. Likewise, the topology of the plastic piece makes it difficult for the cooling channels to access the pillow region (see Figure 1) due to the reduced dimensions of the pillows. The use of traditional cooling channels in this area reduces the thermal exchange between the plastic material and the coolant flow, as well as their thermal performance.
On the other hand, the geometric design of the cooling system also determines the thermal and energy performance of the cooling phase of the plastic part. In particular, as is shown in Figure 6, the plastic part has a traditional injection mold design based on straight drilled channels. This traditional design must meet dimensional requirements that guarantee the structural integrity of the different elements and systems that make up the injection mold. These requirements are the distance between cooling channels, the distance between cooling channels and elements of the ejection system, and the distance between cooling channels and the surface of the mold cavity. The diameter of each of the cooling channels is 8 mm. The separation distance between the cooling channels themselves and the surface of the injection mold cavity or any other element thereof is 16 mm, that is, twice the value of the diameter of each of the cooling channels. In this way, the sizing and structural integrity criteria established by the industry are met, such that the minimum safety distance between elements of the injection mold is always greater than 10 mm. Figure 6 and Table 5 show the traditional design and magnitude of the geometric variables of the cooling system for the two cavities of the injection mold, whose manufacture is carried out using computerized numerical control (CNC) techniques.  Starting from the design and configuration of the straight drilled channels defined for the current cooling system of the plastic part under study and, taking into account the  Table 5. Geometric variables of the traditional cooling system design.

Description Units Value
Cooling channels diameter mm 8.0 Distance between cooling channels and injection mold cavity mm 16.0 Distance between cooling channels and ejection system mm 16.0 Starting from the design and configuration of the straight drilled channels defined for the current cooling system of the plastic part under study and, taking into account the thermal and rheological properties of the thermoplastic material associated with it, using Equations (3) and (4), a predictive analytical calculation can be made of the maximum longitudinal warpage obtained after the cooling phase and the total time that elapses during the cooling phase. Table 6 shows the results obtained for said analytical calculation. Table 6. Results obtained from the cooling phase analytical model for the cooling system traditional design.

Description Units Value
Analytical total warpage mm 7.1 Analytical cooling time s 271.5 As can be seen, the analytical results (see Table 6) show that the plastic part under study warped longitudinally by 7.1 mm with a time of the cooling phase equal to 271.5 s with a traditional cooling system. These analytical results do not meet the functional requirements, nor the geometric and dimensional tolerances established in the industrial sector for optical plastic parts used in vehicle lighting systems. According to the industrial sector, the maximum longitudinal warpage should not exceed 1 mm. Likewise, the resulting cooling time is very long, which implies an increase in cost and energy expenditure associated with the manufacturing process that is contrary to sustainable manufacturing. Therefore, the traditional tools, designs, and technologies for the manufacture and design of the injection mold cooling system are limited and sometimes do not allow the functional requirements and tolerances established by the industrial sector to be met. For this reason, in this manuscript, a new design of conformal cooling channels adapted to the geometry of the plastic part, along with the use of auxiliary cooling elements such as Fastcool inserts and the application of new SLS 3D additive manufacturing techniques, aim to optimize the cooling phase and the final quality of the plastic part, thus allowing the functional requirements and tolerances established for the plastic part under study to be achieved.

Green Conformal Cooling Channels Design
The design of the main elements that make up the cooling system of an injection mold focuses on optimizing the dissipation of the heat flow from the plastic part in a uniform manner in the shortest possible time until it reaches the temperature of ejection. However, this process presents great difficulties and inconveniences in plastic parts with complex surfaces, whose geometric and technological requirements, such as those in the case study, are impossible to solve with traditional cooling elements or systems.
The conformal cooling channels allow these drawbacks to be solved, since they are capable of optimizing the free volume between elements of the injection mold and, thanks to their SLS additive manufacturing process, can reduce the distance between the cooling channels and the surface of the plastic part in geometric areas of difficult access. Likewise, in this manuscript, to improve this problem, a novel design of conformal cooling channels has been proposed (see Figure 7), with a circular section, whose geometric arrangement allows for traversing of the upper and lower region of the plastic piece, as well as the concave area generated by the support, to place the pillows in the correct position to project the light coming from the collimators. On the other hand, although the application of conformal channels for this geometric area is appropriate, sometimes the separation between the channels and the surface of the mold cavity is not enough to dissipate all the heat flow from this region uniformly. As a solution to this design problem, the use of Fastcool inserts in combination with the use of conformal channels has been proposed (see Figures 8 and 9). Fastcool inserts are characterized by being associated with a metallic material with a high thermal transmission coefficient, which favors heat exchange in areas of the plastic part where high temperature gradients accumulate. However, during the cooling phase, the Fastcool insert exchanges a large amount of heat flow that it is not able to dissipate on its own. The use of conformal cooling channels, in these cases, can be very useful, not so much to directly cool the plastic part, but to cool the Fastcool insert itself.
capable of optimizing the free volume between elements of the injection mold and, thanks to their SLS additive manufacturing process, can reduce the distance between the cooling channels and the surface of the plastic part in geometric areas of difficult access. Likewise, in this manuscript, to improve this problem, a novel design of conformal cooling channels has been proposed (see Figure 7), with a circular section, whose geometric arrangement allows for traversing of the upper and lower region of the plastic piece, as well as the concave area generated by the support, to place the pillows in the correct position to project the light coming from the collimators. On the other hand, although the application of conformal channels for this geometric area is appropriate, sometimes the separation between the channels and the surface of the mold cavity is not enough to dissipate all the heat flow from this region uniformly. As a solution to this design problem, the use of Fastcool inserts in combination with the use of conformal channels has been proposed (see Figures 8 and 9). Fastcool inserts are characterized by being associated with a metallic material with a high thermal transmission coefficient, which favors heat exchange in areas of the plastic part where high temperature gradients accumulate. However, during the cooling phase, the Fastcool insert exchanges a large amount of heat flow that it is not able to dissipate on its own. The use of conformal cooling channels, in these cases, can be very useful, not so much to directly cool the plastic part, but to cool the Fastcool insert itself.  In this way, to evaluate the thermal performance of the application of conformal cooling channels and Fastcool inserts, three different cooling system designs have been proposed. These include a design defined solely by conformal cooling channels, (see Figure  7) and two hybrid designs that combine conformal cooling channels and Fastcool inserts of different lengths, as are shown in Figures 8 and 9. Table 7 shows the geometric features of the cooling elements used in the proposed cooling system designs. It should be noted that the geometric parameters that define the proposed cooling systems, conformal and hybrid, have been optimized and adapted to the requirements presented by its own 3D SLS additive manufacturing process, by the geometric features of the plastic part under study, and by the complexity of the real injection mold with which the present case study has been manufactured.  In this way, to evaluate the thermal performance of the application of conform ing channels and Fastcool inserts, three different cooling system designs have be posed. These include a design defined solely by conformal cooling channels, (see 7) and two hybrid designs that combine conformal cooling channels and Fastcool of different lengths, as are shown in Figures 8 and 9. Table 7 shows the geometric f of the cooling elements used in the proposed cooling system designs. It should be that the geometric parameters that define the proposed cooling systems, conform hybrid, have been optimized and adapted to the requirements presented by its o SLS additive manufacturing process, by the geometric features of the plastic part study, and by the complexity of the real injection mold with which the present cas has been manufactured.   In this way, to evaluate the thermal performance of the application of conformal cooling channels and Fastcool inserts, three different cooling system designs have been proposed. These include a design defined solely by conformal cooling channels, (see Figure 7) and two hybrid designs that combine conformal cooling channels and Fastcool inserts of different lengths, as are shown in Figures 8 and 9. Table 7 shows the geometric features of the cooling elements used in the proposed cooling system designs. It should be noted that the geometric parameters that define the proposed cooling systems, conformal and hybrid, have been optimized and adapted to the requirements presented by its own 3D SLS additive manufacturing process, by the geometric features of the plastic part under study, and by the complexity of the real injection mold with which the present case study has been manufactured. Table 7. Geometric variables of the traditional cooling system design.

Hybrid Cooling System Dashed Fastcool Bars
Cooling channels diameter 9.0 mm-6. Finally, by applying the methodology proposed in this manuscript that is unlike other cooling proposals, it is possible to minimize the cooling time and improve the surface quality of the plastic part under study, thus resulting in the sustainability of the manufacturing process using injection molds.

Numerical Simulations Definition for the Cooling System Thermal Modeling
In this section, the modeling process of the thermal and rheological numerical simulations, which were carried out to analyze the cooling phase of the plastic part for each of the proposed cooling system designs, is described. In this way, from the numerical results obtained, the thermal performance, and the thermal exchange produced between the elements of the cooling system and the plastic piece are evaluated, as well as the temperature gradients, longitudinal warpage, and resulting residual stresses obtained along the surface of the plastic part. All this is to verify whether the thermal performance of the proposed cooling system designs meets the technological, functional, and dimensional requirements established in the industrial sector for the optical plastic parts included in automobile lighting systems. To carry out the different numerical analyses that were carried out, the commercial simulation software of the CAE type Moldex3D (R21 version, CoreTech System Co., Ltd., Zhubei City, Taiwan) [50] was used.
The pre-processing and modeling phase of the numerical simulations began with the meshing operation and assignment of materials for the main computational domains of the injection mold: feeding system (Plexiglas 8N), coolant flow (water), plastic part (Plexiglas 8N), Fastcool cooling insert (Fastcool-50) and injection mold (steel alloy 1.2709). The CAE commercial software used in this manuscript has a meshing tool, Moldex Designer, from which the main features of the mesh are established, as well as the type and size of the element used in the discretization of the geometries. Table 8 shows the features and magnitude of the geometric parameters defined for the meshing process. Figures 10-12 show the typology of elements used to mesh the main computational domains of the injection mold. These finite elements were of the second-order tetrahedron type (SOLID 186) and had 10 control nodes, which allowed the resulting field of temperatures, stresses, and longitudinal warpage to be modeled with greater precision. In addition, to improve the calculation and modeling of the thermal exchange between computational domains, five layers of second-order prismatic elements (SOLID 186) of the "Boundary Layer Mesh" type with 15 control nodes were established. As are shown in Figures 10 and 12, these elements were located on the surfaces of the plastic part and the cooling channels that are in contact with the computational domain of the injection mold. The size of these elements was established by the offset ratio geometric parameter, which was defined as a percentage of the average size of the mesh element of each computational domain to which it belonged.        On the other hand, after the meshing phase, the magnitude of the thermal, r cal, and technological parameters of the boundary conditions was established. T nition of these parameters allowed for the simulation of each of the different p which the manufacturing cycle of the plastic part is divided. In this way, it was to model the path of the molten plastic front, along with the feeding system and mold cavity, the crystallization and solidification of the thermoplastic material, t ing process of the plastic part, and its subsequent cooling. Table 9 shows the ma of each of the defined parameters according to the specifications and recommen On the other hand, after the meshing phase, the magnitude of the thermal, rheological, and technological parameters of the boundary conditions was established. The definition of these parameters allowed for the simulation of each of the different phases in which the manufacturing cycle of the plastic part is divided. In this way, it was possible to model the path of the molten plastic front, along with the feeding system and injection mold cavity, the crystallization and solidification of the thermoplastic material, the packing process of the plastic part, and its subsequent cooling. Table 9 shows the magnitude of each of the defined parameters according to the specifications and recommendations established by the manufacturer and supplier of the thermoplastic material. Furthermore, these technological parameters established during the processing phase of the numerical simulations (see Table 9) were those that could be defined in the real injection machine. This, therefore, allowed us to generate a virtual manufacturing model of the plastic piece that was analogous to the plastic injection process through its corresponding injection mold. It should be noted that the magnitude of the flow inlet pressure to the cooling system was established to ensure that it developed in a turbulent flow, that is, that its Reynolds number was greater than 1.5 × 10 4 . In addition, to compare the numerical results obtained for each proposed cooling system design, the flow inlet pressure to the cooling system was dimensioned so that the Reynolds number was equal to 4.0 × 10 4 in each numerical simulation.
The phase aimed at the pre-processing and definition of the numerical simulations requires the establishment of the calculation or computation process to meet the following the criteria:

•
A transient cooling has been used to analyze the cooling of the plastic part over time; • An analysis model of the evolution of the dynamic, thermal, and physical properties in the cooling channels has been followed according to the configuration: "Run 3D Cooling Channels"; • A solver configuration methodology has been used for each analysis according to a maximum variation of the mold temperature, which establishes the values of 1 • C and 10 • C as a temperature difference parameter and maximum number of cycles; • For the turbulence model, it has been established using the roughness parameter in charge of defining the surface that interfaces between the cooling flow and the surface of the channels through which it circulates, with this value being 0.02 mm; • The effects of volumetric shrinkage of the mold, residual stress of the molten plastic front, volumetric shrinkage caused by temperature gradients, and longitudinal displacements caused by said gradients have been included.

Numerical Results and Discussion
After completing the pre-processing phase of the thermal and rheological simulations, we proceeded to present, evaluate, and compare the set of numerical results obtained for each of the cooling system designs proposed. From there, it was possible to determine the configuration of the cooling system that optimized the cooling phase of the plastic part under study and the one that improved the thermal performance and heat exchange between the plastic part and the coolant flow. First of all, Table 10 and Figures 13a,b and 14a,b show the magnitude and distribution along the surface of the plastic part of the resulting parameter "Max. Cooling Time" for each cooling system design analyzed. plastic part under study and the one that improved the thermal performance and heat exchange between the plastic part and the coolant flow. First of all, Table 10 and Figures  13a,b and 14a,b show the magnitude and distribution along the surface of the plastic part of the resulting parameter "Max. Cooling Time" for each cooling system design analyzed.     From the resulting parameter "Max. Cooling Time", which was obtained for the design of a traditional cooling system based on straight drilled channels, it was established that the analytical model used to determine the cooling time of the plastic part under study (see Table 6) was valid. According to the analytical model, the cooling time obtained was equal to 271.50 s, while the result obtained in the numerical simulations was equal to From the resulting parameter "Max. Cooling Time", which was obtained for the design of a traditional cooling system based on straight drilled channels, it was established that the analytical model used to determine the cooling time of the plastic part under study (see Table 6) was valid. According to the analytical model, the cooling time obtained was equal to 271.50 s, while the result obtained in the numerical simulations was equal to 262.55 s (see Table 9). In this way, the relative error associated with the calculation of the cooling time parameter (see Equation (3)), which was obtained through the analytical model presented, was equal to 3.40%, which took as reference the result obtained from the numerical simulations. Therefore, it was determined that the analytical and physical model, proposed in this manuscript to analyze the cooling phase of the plastic part, is admissible and validated, based on the resulting accuracy obtained. Likewise, as are shown in Figures 13A,B and 14A,B, the application of conformal cooling channels and auxiliary cooling elements, such as Fastcool inserts, optimized the cooling phase of the plastic part and significantly reduced the time associated with this phase. In particular, according to the results obtained, the application of the proposed cooling system designs improved the cooling time by 167.159 s (conformal channels and Fastcool full bars, see Figure 13A), 171.972 s (conformal channels and dashed Fastcool bars, see Figure 14A), and 175.123 s (conformal channels, see Figure 14B), when compared to the result obtained using the traditional cooling system design. This represents an improvement percentage of 63.668% (conformal channels and Fastcool full bars), 65.501% (conformal channels and dashed Fastcool bars), and 66.701% (conformal channels), respectively (see Table 10). In this way, the design based on conformal cooling channels minimized the magnitude of this variable when compared to the rest of the proposed designs, which in turn implies a significant decrease in the cost and energy expenditure associated with the manufacturing process of the plastic part. Next, Table 11 and Figures 15A,B and 16A,B, show the magnitude and distribution along the surface of the plastic part of the resulting parameter "Mold Temperature Difference" for each design of cooling analyzed.   Based on the results obtained, it was established that the designs of cooling systems with conformal channels and Fastcool inserts improved the uniformity and homogeneity of the temperature map and the geometry of the plastic part. In this line, the magnitude of the total temperature gradient was notably reduced, which made it possible to minimize the longitudinal warpage and residual stresses caused by the thermal effects. In particular, according to the results obtained, the application of the proposed cooling system designs improved the temperature gradient to 10,378 • C (conformal channels and Fastcool full bars, see Figure 15A), 12,467 • C (conformal channels and dashed Fastcool bars, see Figure 16A), and 18,163 • C (conformal channels, see Figure 16B), when compared to the result obtained with the traditional cooling system design. This represents an improvement percentage of 44.858% (conformal channels and Fastcool full bars), 53.888% (conformal channels and dashed Fastcool bars), and 78.509% (conformal channels), respectively (see Table 11). As can be seen, the design of the conformal channel cooling system optimized the uniformity of the temperature map and reduced the temperature gradient of the plastic part when compared to designs that include a Fastcool cooling insert. This is because Fastcool inserts, despite being cooled with conformal-type channels, do not exchange heat flow and dissipate it with the same effectiveness as a conformal cooling channel, despite being located closer to the surface of the plastic part (see   Table 7). In other words, in the first moments of the cooling phase, Fastcool inserts quickly exchange the heat flow with the plastic part, but they are not able to dissipate it through the injection mold and the conformal cooling channel, which increases its temperature and, therefore, decreases its thermal performance. In addition, according to the quality requirements established in the industrial sector of injection plastic molds, it is recommended that the parameter corresponding to the mold temperature difference should be equal to or less than 10 • C. As are shown in Figure 16A,B and Table 11, conformal channels and conformal channels with dashed Fastcool bars fulfilled this requirement. Tables 12 and 13 and Figures 17A,B, 18A,B, 19A,B and 20A,B show the magnitude and distribution along the surface of the plastic part of the resulting parameters "Total Warpage" and "Thermally Induced Residual Stress" for each cooling system design analyzed in this manuscript. Based on the results obtained, it was established that the designs of cooling systems with conformal channels and Fastcool inserts improved the uniformity and homogeneity of the temperature map and the geometry of the plastic part. In this line, the magnitude of the total temperature gradient was notably reduced, which made it possible to minimize the longitudinal warpage and residual stresses caused by the thermal effects. In particular, according to the results obtained, the application of the proposed cooling system designs improved the temperature gradient to 10,378 °C (conformal channels and Fastcool full bars, see Figure 15a), 12,467 °C (conformal channels and dashed Fastcool bars, see Figure 16a), and 18,163 °C (conformal channels, see Figure 16b), when compared to the result obtained with the traditional cooling system design. This represents an improvement percentage of 44.858% (conformal channels and Fastcool full bars), 53.888% (conformal channels and dashed Fastcool bars), and 78.509% (conformal channels), respectively (see Table 11). As can be seen, the design of the conformal channel cooling system optimized the uniformity of the temperature map and reduced the temperature gradient of the plastic part when compared to designs that include a Fastcool cooling insert. This is because Fastcool inserts, despite being cooled with conformal-type channels, do not exchange heat flow and dissipate it with the same effectiveness as a conformal cooling channel, despite being located closer to the surface of the plastic part (see Figures 7-9 and Table  7). In other words, in the first moments of the cooling phase, Fastcool inserts quickly exchange the heat flow with the plastic part, but they are not able to dissipate it through the injection mold and the conformal cooling channel, which increases its temperature and, therefore, decreases its thermal performance. In addition, according to the quality requirements established in the industrial sector of injection plastic molds, it is recommended that the parameter corresponding to the mold temperature difference should be equal to or less than 10 °C. As are shown in Figure 16a,b and Table 11, conformal channels and conformal channels with dashed Fastcool bars fulfilled this requirement. Tables 12 and 13 and Figures 17a,b, 18a,b, 19a,b and 20a,b show the magnitude and distribution along the surface of the plastic part of the resulting parameters "Total Warpage" and "Thermally Induced Residual Stress" for each cooling system design analyzed in this manuscript.          The results obtained for the "Total Warpage" and "Thermally Induced Residual Stress" parameters confirmed that the application of conformal cooling channels and Fastcool inserts improved the final quality of the plastic part under study. In particular, the resulting longitudinal warpage was reduced by a magnitude of 6.566 mm (conformal channels and Fastcool full bars, see Figure 17a), 6.569 mm (conformal channels and dashed Fastcool bars, see Figure 18a), and 6.911 mm (conformal channels, see Figure 18b), when compared to the result obtained with the traditional cooling system design. This represents an improvement percentage of 85.987% (conformal channels and Fastcool full bars),  The results obtained for the "Total Warpage" and "Thermally Induced Residual Stress" parameters confirmed that the application of conformal cooling channels and Fastcool inserts improved the final quality of the plastic part under study. In particular, the resulting longitudinal warpage was reduced by a magnitude of 6.566 mm (conformal channels and Fastcool full bars, see Figure 17a), 6.569 mm (conformal channels and dashed Fastcool bars, see Figure 18a), and 6.911 mm (conformal channels, see Figure 18b), when compared to the result obtained with the traditional cooling system design. This represents an improvement percentage of 85.987% (conformal channels and Fastcool full bars), 86.027% (conformal channels and dashed Fastcool bars), and 90.506% (conformal channels), respectively (see Table 12).
In addition, according to the quality requirements established in the industrial sector The results obtained for the "Total Warpage" and "Thermally Induced Residual Stress" parameters confirmed that the application of conformal cooling channels and Fastcool inserts improved the final quality of the plastic part under study. In particular, the resulting longitudinal warpage was reduced by a magnitude of 6.566 mm (conformal channels and Fastcool full bars, see Figure 17A), 6.569 mm (conformal channels and dashed Fastcool bars, see Figure 18A), and 6.911 mm (conformal channels, see Figure 18B), when compared to the result obtained with the traditional cooling system design. This represents an improvement percentage of 85.987% (conformal channels and Fastcool full bars), 86.027% (conformal channels and dashed Fastcool bars), and 90.506% (conformal channels), respectively (see Table 12).
In addition, according to the quality requirements established in the industrial sector of injection plastic molds, it is recommended that the parameter corresponding to the mold temperature difference should be equal to or less than 10 • C. As are shown in Figure 16A,B and Table 11, conformal channels and conformal channels with dashed Fastcool bars fulfilled this requirement.
On the other hand, the residual stresses derived from temperature differences on the surface of the plastic part were also significantly minimized to a magnitude of 35.844 MPa (conformal channels and Fastcool full bars, see Figure 19A), 38.368 MPa (conformal channels and dashed Fastcool bars, see Figure 20A), and 39.784 MPa (conformal channels, see Figure 20B), when compared to the result obtained with the traditional cooling system design. This represents an improvement percentage of 73.773% (conformal channels and Fastcool full bars), 78.968% (conformal channels and dashed Fastcool bars), and 81.882% (conformal channels), respectively (see Table 13). As can be seen, the conformal channel cooling system minimized longitudinal warpage and residual stresses of the plastic part after its manufacturing process. The magnitude of these variables comes, mainly, from the temperature differences along the plastic part. Additionally, as was previously defined, conformal cooling channels optimize the uniformity of the temperature map, minimize the temperature gradient of the plastic part, and maximize thermal efficiency during the cooling phase, when compared to designs that include a Fastcool insert.
Likewise, and analogously to the previously analyzed cooling time parameter, the longitudinal warpage obtained using the physical and analytical model presented (see Table 6) was close to the value obtained using numerical simulations for the design of a traditional cooling system. Specifically, based on the physical and analytical model presented, the longitudinal warpage obtained for the plastic part under study was equal to 7356 mm, while the result obtained from the numerical simulations was equal to 7.636 mm. In this way, the relative error associated with the calculation of the longitudinal warpage (see Equation (4)), obtained through the analytical model presented, is equal to 3.667%, which takes as a reference the result obtained from the numerical simulations. Therefore, it was determined that the analytical and physical model, proposed in this manuscript for the determination of the longitudinal warpage obtained after the manufacturing process of the plastic part, is admissible and validated, based on the resulting precision obtained.
Finally, it should be noted that the design of the cooling system with conformal channels is the only one that meets the functional requirements and the geometric and dimensional tolerances established by the industrial industry for optical plastic parts used in vehicle lighting systems. Additionally, the longitudinal warpage associated with this design was equal to 0.725 mm and does not exceed the limit value of 1 mm established by the industrial sector.

Conclusions
The manufacture of parts of great length, slenderness, and high thickness ratios for dimensional precision applications is practically impossible using traditional manufacturing means in injection molding processes while still respecting the precision and dimensional specifications of the current industry. The warpage in molded plastic parts depends fundamentally on the differential shrinkage caused by temperature gradients along their surface in the cooling process. This fact is accentuated to a greater extent in pieces of great length, since, in these cases, small temperature gradients can give rise to large longitudinal warpage located mainly at the ends of the piece. Warpage influences the number of rejected parts, which greatly impacts the sustainability of the production process. Injection molding is focused on large-scale industrial manufacturing, so a poor definition in the design of the tooling of a piece can lead to enormous economic and environmental losses.
The paper presents the use of conformal cooling layouts as a way to reduce cycle time, temperature gradients on the part surface, longitudinal warpage, and residual stresses in the manufacture of highly complex parts with high dimensional requirements. Likewise, the research carried out by the authors analyzed the influence of the use of Fastcool inserts in combination with conformal cooling layouts in reducing warpage in parts with geometry that is sensitive to this parameter. The results of the research indicate that the use of conformal cooling layouts reduced the cycle time by 175.1 s, which is 66% below the current cooling time used to manufacture the part through traditional cooling. With regard to the temperature gradient, it improved by 18.16 ºC, which is 78.5% better than the current temperature gradient. Finally, the proposal presented by the authors managed to reduce the warpage by 6.9 mm, or 90.5% of the current value, achieving a final warpage of 0.72 mm, which complies with the maximum warpage value required by the industry of 1 mm. The residual stresses decreased by 39.78 MPa, which are 81.88% below the current values obtained with traditional cooling. The results validate that the design of the cooling system with conformal channels improved the uniformity of the temperature map of the plastic part, reduced the temperature gradient along the surface, and improved the results of the production process when compared to the use of highly conductive inserts of the Fastcool type. This is because Fastcool inserts, despite being cooled with conformal channels, are not capable of exchanging and dissipating the heat flow generated with the same effectiveness as a conformal cooling channel, despite being located much closer to the surface of the plastic part.
Conformal cooling systems were presented as a valid and adequate proposal for the solution of current warpage problems in molded plastic parts where it is highly complex to obtain the dimensional requirements required by the industry. The geometric features for injection molding analyzed in the paper are especially important, given that growth in the demand for parts that include these features is estimated [46,47] in the coming years. The results obtained by the authors mark a turning point in the manufacture by molding of this type of highly complex plastic topology. The results, in terms of a decrease in the production cycle time, decrease in carbon emissions, reduction in the number of rejected parts, and reduction in energy expenditure, place the results of the authors totally in line with the criteria of industrial sustainability demanded by the European Union, as well as in the set of industrialized countries. Data Availability Statement: All data included in this study are available upon request through contact with the corresponding author.