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Article

Multi-Criteria Optimization of Yarn Guide Manufacturing Processes

Department of Manufacturing Technology and Automation, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(16), 9055; https://doi.org/10.3390/app15169055 (registering DOI)
Submission received: 13 July 2025 / Revised: 10 August 2025 / Accepted: 14 August 2025 / Published: 17 August 2025
(This article belongs to the Section Mechanical Engineering)

Abstract

Due to the insufficient durability (wear resistance) of guides made of 50SiCr4 steel tempered to a hardness of 400 HB, 14 variants of the yarn guide manufacturing process were developed. The ring spinner yarn guides were manufactured from three types of steel, from Al99.5% and its alloys, as well as from porcelain, Al2O3 sinter, and WC 94% + Co 6% tungsten carbide. The unit manufacturing cost and six manufacturing quality criteria were used as evaluation criteria: four parameters of the geometric structure of the surface and the maximum surface hardness, as well as the depth of hardening of the surface layer. The presented variants were then evaluated against the seven criteria, determining a set of optimal solutions in the Pareto sense. This set consisted of 12 variants. A distance function was then used to select the best manufacturing process variant, corresponding to the smallest value of the distance function. In this study, this is the process variant for which the semi-finished product is a drawn bar ø6 mm of C45 steel tempered to a hardness of 350 HB with a glazed porcelain insert. The alternative process, with a slightly higher distance function value, is the variant with the Al2O3 ceramic sinter insert.

1. Introduction

Multi-criteria decision optimization is a complex process that incorporates both quantitative and qualitative factors. It has wide application across many fields, including but not limited to engineering, construction, project and manufacturing management, safety and risk systems, energy systems, environmental and sustainable development, supply chain management, materials science, economics, quality management, medicine, social sciences, and machine learning, using a variety of methodological approaches [1,2,3]. The literature presents various case studies describing the areas of application of decision-supported algorithms, such as [4,5] engineering design (e.g., welded beam design problem, robot gripper optimization, or software engineering); scheduling optimization (e.g., combined economic emission dispatch problem or job-shop scheduling, airline crew rostering optimization); path planning (e.g., robot trajectory planning); resource optimization (e.g., water distribution network or wind farm layout optimization); transportation optimization (e.g., supply chain configuration, determination of the fastest path on logistics distribution). According to Lukic et al. [6], process planning is one of the most challenging tasks in product development, primarily due to the multitude of technical, technological, economic, and environmental criteria. Consequently, the selection of manufacturing processes appears as a complex multi-criteria decision-making problem, as it requires the evaluation of numerous alternative production processes besides a wide range of defined criteria. Manufacturing processes that do not meet the required thresholds based on established criteria such as material properties, production volume, productivity, dimensional accuracy, and surface finish are systematically eliminated according to predefined decision rules. Subsequently, a multi-criteria evaluation and classification of production processes is performed based on various factors, including production cycle time, process flexibility, material utilization, output quality, and operational cost.
The textile industry is facing increasing global competition, forcing manufacturers to innovate in product quality and process efficiency. Manufacturing processes are highly complex and multi-stage, involving numerous interdependent phases that require precise management at each stage. The decision space, defined by various process combinations and fluctuating production, is huge and stochastic due to numerous interacting factors influencing the manufacturing process. Since the relationship between process parameters and product properties remains unclear, decision-making occurs under significant uncertainty or risk [7]. Decision support systems optimize processes using various techniques: hybrid algorithms [8,9], fuzzy logic [10], and evolutionary algorithms [11]. However, these classical methods have become less effective with the development of artificial intelligence and rising manufacturing complexity. This is particularly evident as large-scale data and multi-dimensional decision spaces increasingly require multi-criteria assessment of production performance, rather than relying on a single standard [12,13].
In the case of surface treatment, the variety of means and methods creates a scenario where objects that are identical or similar in shape, dimensions, and accuracy are often made through different manufacturing processes. These processes differ in labor intensity and cost. Moreover, they provide different manufacturing qualities of the object, and consequently lead to better or worse performance [14,15]. Therefore, a complex multivariate task of designing and selecting the most rational type of material and form of semi-finished product arises, including heat-treated and thermo-chemical-treated steel materials [16,17]. In the case of semi-finished aluminum and its alloys, surface layers with special properties are produced by anodic oxidation [18]. In general, multi-variant design is carried out of the workpiece manufacturing process. In ring spinning machines, in the twisting zone, the yarn passes through a guide-eye (guide), which, in general cases, changes or maintains the direction of the yarn and produces the appropriate yarn tension [19]. In the interaction of the friction pair, yarn–guide, the guide generally remains stationary with respect to the yarn sliding on it. Its surface should meet the following conditions [19,20]:
  • Have a low coefficient of friction when interacting with the yarn, which mainly depends on the Surface Geometrical Structure (SGP) resulting from the treatment;
  • Not cause the formation of electrostatic charges and not transfer these charges to the yarn;
  • Be sufficiently resistant to wear.
Friction conditions decisively affect the efficiency of the process and the quality of the textile product. It is known that when the yarn slips over the guide, the amount of friction depends on the yarn tension, the geometric structure of the surface, and the physical properties of the bodies involved in the friction, as well as the external conditions under which this slippage occurs [19]. Information on the requirements that must be met by machine parts guiding yarn or thread, and guidelines for the selection of materials for guides, depending on the type of yarn, can be found in previous work [20]. The relationship between the kinetic coefficient of friction μk and the roughness parameter Ra of the steel guide for staple yarn of wool, cotton, and viscose silk is presented in previous works [15,20]. The influence of the arithmetic mean of the ordinates of the Ra profile of the guide surface, obtained by different treatments, on the kinetic coefficient of friction μk of a yarn that is a blend of 30% polyester, 60% wool, and 10% waste in the form of worsted tape is described in previous work [15]. An evaluation of the geometric structure of the surface of the oxide layer, including nine 2D surface roughness parameters, and their effect on the kinetic coefficient of friction µk of the yarn for AlCu4Mg1 alloys is provided in a previous paper [15]. On the other hand, the evaluation of the stereometric structure of the surface (3D geometric structure) of the oxide layer, produced on the AlCu4Mg1 alloy, and its effect on the kinetic coefficient of friction µk of the yarn, which is a blend of wool (70%) and polyester (30%) fibers, is presented in previous work [21].
Most previous work has generally recommended the use of two or more roughness parameters to analyze the geometric structure of the surfaces in contact with the yarn—for a more unambiguous assessment, see [15,22]. This allows a more accurate assessment of the influence of the type of material, type of heat treatment, thermo-chemical treatment, and surface treatment on the geometric structure of the surface. Very helpful in this evaluation is the linear correlation coefficient R of SGP parameters or 3D roughness parameters (topography) with the kinetic friction coefficient of the yarn µk [15,21].
The operating conditions of the guide (abrasion) require the material to be resistant to abrasion and thus to have high hardness occurring at a considerable depth. It is necessary, therefore, to take into account these physical properties of the surface layer when selecting the type of semi-finished material and heat, thermo-chemical, and surface treatment.
The issues of evaluating manufacturing processes using two and more criteria have been presented so far in a few works [15,21,23,24,25,26,27]. Methods for evaluating variants of manufacturing processes for parts in contact with the yarn of ring and spindleless spinning machines using subjective scoring criteria and fuzzy criteria with a Saaty matrix determining the weights of the individual criteria are presented in [15].
The Evolutionary Multi-Criteria Analysis System allows the determination of a few-element subset of representative solutions from a very large set of optimal solutions in the Pareto sense, and after considering the analysis in the space of decision variables, the identification of a single preferred solution is discussed in detail in [24,28]. A general method of multi-criteria optimization allowing decision-making (selection of the best option) based on three types of criteria, i.e., deterministic, probabilistic–statistical, and fuzzy, considering their importance, is provided in [25,26]. The implementation of this method involves three stages: determining the ratings of the individual options in light of the adopted criteria, determining the importance of the individual criteria in fuzzy form, and aggregating the ratings of the individual options considering the criteria weights.
A procedure for the evaluation and selection of the optimum manufacturing process variant for spindleless spinning machine rotors involves two steps: the optimum method in the Pareto sense and a distance function in view of four criteria: unit manufacturing cost, a coefficient for the ratio of durability to specific weight, a surface topography parameter, and maximum microhardness (treated as equally important), as discussed in [27].
The starting point for the evaluation and selection of the best solution is the determination of a set of acceptable variants of the manufacturing process of the considered object evaluated in light of certain criteria. Optimization criteria often treated in conventional models as deterministic—e.g., cost [29]—often have to be treated as non-deterministic in the design phase of the manufacturing process, and thus, for example, as subjective scoring [15,21] or fuzzy assessments [25]. However, in most cases, in the optimization of manufacturing processes of similar products, optimization criteria of a probabilistic–statistical nature, in order to simplify the procedure, are treated as deterministic, such as surface roughness parameters.
This study aims to select the best process variant for the manufacture of a yarn guide of a ring spinning frame due to multiple criteria using a two-stage optimization procedure.

2. Multi-Criteria Evaluation Method

In multi-criteria optimization, the concept of optimum in the Pareto sense plays a fundamental role. In less complex optimization problems, particularly when the number of evaluation criteria does not exceed three, the set of Pareto-optimal solutions may consist of only one element. In such cases, the procedure should be concluded at this stage, as the identified solution is optimal with respect to the evaluated criteria. Conversely, in highly complex problems involving a large set of variants and criteria, the set of Pareto-optimal solutions is almost never a singleton. It may even include nearly all or all available variants. Therefore, in the context of evaluating and selecting the most suitable manufacturing process variant under multiple criteria, a two-stage optimization procedure is often applied. This approach is characterized by its flexibility and universality. First, the set of optimal variants in the Pareto sense (the set of non-dominated solutions) is determined. Then, the best variant from this set is selected using a single criterion. In such cases, it becomes necessary to determine the value of the distance function for each variant, which enables their ranking. The best alternative is the one for which the distance function reaches the minimum value, while the worst is associated with the maximum value of this function [15,21].

2.1. Optimum Method in the Pareto Sense

The method of the optimum in the Pareto sense was used to evaluate and select the optimal variant of the ring spinning frame yarn guide manufacturing process considering multiple criteria. This method is based on determining the set of non-dominated variants or the set of optimal variants in the Pareto sense [15,23,24,30,31].
The procedure for determining the set of optimal variants in the Pareto sense can be formalized as an algorithm, presented in a block diagram in Figure 1.
The input data are defined as follows [15]:
  • The table of evaluations of variants of the manufacturing process of the yarn guide of the ring spinning frame with respect to deterministic criteria k j i d , where
    i = 1 , ,   n —the number of variants of the manufacturing process of the yarn guide;
    j = 1 , ,   m —the number of criteria;
  • The extremum direction vector K E X k e x j ( j = 1 , , m ) .
Each component of this vector indicates whether the corresponding criterion is subject to maximization or minimization. In particular, if the j-th criterion is to be minimized, the j-th component of the KEX vector is assigned a value of minus ( k e x j = 1 ) ; otherwise, it is assigned a value of k e x j = 1 .
The result of the procedure for determining optimal variants in the Pareto sense consists of the number of optimal variants LP, as well as the vector NR, whose subsequent coordinates represent the indices of the non-dominated variants [15].
The ideal process variant for manufacturing the yarn guide a i ( i d ) is one that simultaneously extremes each criterion.
In the case of minimization, a i ( i d ) is an ideal variant of the yarn guide manufacturing process if
a i A a i ( i d ) A k d ( a i i d ) k d ( a i )
where k d ( a i ) —vector of evaluations of the i-th variant of the yarn guide manufacturing process against each criterion.
Since these criteria tend to conflict, the ideal option in such a case does not exist.
The non-dominated variant a i ( n d ) (optimal in the Pareto sense) is a variant of the yarn guide manufacturing process for which no criterion can be improved without simultaneously worsening at least one of the others.
To determine the set of variants that are optimal in the Pareto sense of the yarn guide manufacturing process, the POLOPT.2 program was used. This program makes it possible to determine the set of variants that are optimal in the Pareto sense from an acceptable set consisting of up to 100 variants, evaluated for a maximum of 10 criteria each.

2.2. Selection of the Best Option from the Set of Optimal Solutions in the Pareto Sense

Distance function methods enable the determination of a single compromise evaluation, which typically leads to the determination of a single optimal variant in the Pareto sense. In order to avoid the influence of different units of each criterion, the normalization of evaluations provided in paper [27] was used. Taking into account that the set of criteria contains evaluations, some of which are to be minimized and others maximized, a distance function f d ( i ) was proposed using Euclid’s norm ||r|| = 2 without a component reflecting the decision-maker’s preference ωt:
f d ( i ) = j = 1 m [ c i j * c i d j * ] 2 m i n
where c i ( j ) * —normalized value j of the criterion for each variant, c i d ( j ) * —normalized value j of the criterion for the ideal point.
The best variant from the set of optimal variants in the Pareto sense is the one for which the distance function f d ( i ) reaches the minimum value.

3. An Example of the Selection of a Variant of the Optimal Yarn Guide Manufacturing Process in View of the Unit Manufacturing Cost and Manufacturing Quality Criteria

Previously, ring spinning yarn guides were made of 50SiCr4 steel and quenched to a hardness of approximately 400 HB. The fiber stream is a mixture of 30 ÷ 55% polyester fibers and 70 ÷ 45% wool fibers traveling at a speed of vw ≈ 30 m/min and with a maximum tension of up to approx. 30 cN, caused intensive wear on the guide mesh. To achieve increased wear resistance and thus significantly extend the service life of the guide, a suitable material had to be selected, followed by the development of a dedicated manufacturing process adapted to the specific properties of that material. For this purpose, a detailed analysis of the 2D surface geometrical properties and the physical characteristics of the surface layer of the guides was conducted. Based on the results, appropriate material types were selected, and corresponding manufacturing processes were developed. Subsequently, the optimal variant of the yarn guide manufacturing process was selected with respect to the adopted evaluation criteria. To select the best variant of the yarn guide manufacturing process, a two-stage optimization procedure was used, consisting of determining a set of variants that are optimal in the Pareto sense and selecting the best variant from this set using a distance function.

3.1. A Set of Acceptable Variants of the Yarn Guide Manufacturing Process

The attachment of the yarn guides on the ring spinning frame is shown in Figure 2. The basic dimensions of the width and height of the flap (item 3) are 60 mm; and its thickness, together with the nut (item 4) and the gap, is 18 mm. The guide (item 5) protrudes from the flap (item 3) by 25 mm. The diameter of the support tube (item 6) is 35 mm. The distance between the axis of the support tube (item 6) and the spindle axle is 100 mm.
In order to increase the durability of the yarn guides, 14 variants of the manufacturing process, differing mainly in the type of starting material, type of heat, thermo-chemical treatment, and surface treatment, were developed and analyzed. The yarn guiding devices of a ring spinning framer were made of three types of steels, Al99.5% and its alloys, porcelain, Al2O3 sinter, and tungsten carbide WC 94%/Co 6% (G10). The steel guides were subjected to the following heat and thermo-chemical treatments: guides made of 50SiCr4 steel were subjected to chromium plating, boron plating, and diffusion titanium plating, guides made of 41CrAlMo7 underwent nitriding and nitrosulfurization, while guides made of C45 underwent boronizing [16,17]. In another variant, a 100 ÷ 120 µm thick layer of Al2O3 ceramic powder with a grain size of 20 ÷ 40 µm was plasma sprayed onto the C45 steel guide. Guides made of Al99.5% and AlMg2 and AlCu4Mg1 aluminum alloys were subjected to hard anodic oxidation [18].
Regarding yarn guides made of porcelain, Al2O3 sinter, and tungsten carbide WC 94%/Co 6%, two possibilities were considered:
  • Selecting guides from the production range of companies engaged in such production and almost completely reconstructing their mounting on the ring spinning frame;
  • Aiming to leave the mounting of the guide unchanged, which involved developing a new shape of the guide from the aforementioned materials.
The ring spinning frame manufacturing company requested that the second solution be adopted, i.e., to not change the mounting of the guides on the spinning machine. Therefore, it was necessary to develop a new design of guides on the basis of existing guides with inserts made of porcelain, ceramic sinter Al2O3, or tungsten carbide WC 94%/Co 6%. So, guides made in this way could be used not only for the new generation of ring spinning machines but also for already manufactured spinning machines as spare parts. Therefore, a spiral shape of inserts (moldings) made of glazed porcelain, ceramic sinter, and tungsten carbide was developed. Subsequently, the shape of the guide-eyes, made of C45 steel in the form of a drawn rod with a diameter of ø6 mm, was adapted to embed the spiral inserts and fix them with Loctite adhesive [32].
The shape and dimensions of the guides made of steel, Al99.5%, and its alloys are shown in Figure 3a, while the guides made of C45 steel with embedded inserts made of porcelain, ceramic sinter, and tungsten carbide are shown in Figure 3b.
The variants of the yarn guide manufacturing process using the above-mentioned types of starting materials, heat and thermo-chemical treatment, and surface treatment by anodic oxidation, are shown with the help of a graph tree (Figure 5), and the content of operations is given in Table 1. Fourteen variants of the yarn guide manufacturing process were evaluated.

3.2. A Set of Criteria for Evaluating the Yarn Guide of Ring Spinning Frame

In order to assess the variants of the manufacturing process of the ring spinning machine yarn guide, the unit manufacturing cost and six manufacturing quality criteria were used:
  • Unit manufacturing cost Kw, PLN;
  • Mean square deviation of the profile Rq, µm;
  • Maximum profile elevation Rp, µm;
  • Mean square profile inclination RΔq, rad;
  • Mean radius of curvature of profile vertices rw, µm;
  • Maximum hardness at the surface of the surface layer HV0.1;
  • Depth of hardening of the surface layer gww, µm.
The calculation of unit manufacturing costs for different types of starting materials, heat and thermo-chemical treatments, and anodic oxide layers on yarn guides was based on the algorithm of multistage additive calculation according to station costs provided in previous works [33,34]. This method distinguishes cost centers, such as work centers and workstations, along with their related costs, including direct costs (e.g., depreciation, imputed interest, technological energy, facility maintenance) and indirect costs allocated through overheads. Figure 4 illustrates the cost allocation process.
Manufacturing costs consist of material, conversion, and development costs. Material costs are divided into direct and indirect components. Direct material costs represent costs directly assignable to cost drivers, while indirect material costs include activities like purchasing, transportation, storage, and warehouse management. Conversion costs cover direct pay (production workers’ remuneration with overheads), departmental costs (depreciation, imputed interest on fixed assets, energy, maintenance, and tooling), and indirect conversion costs, which are allocated through overheads (Nk*p). Adding indirect management and sales costs to a cost driver results in the prime cost [33,34].
To determine the unit manufacturing cost of yarn guide Kw, the annual production of two-sided ring spinning machines equal to 20 units was assumed. To equip each spinning machine, 2 ∙ 160 = 320 guides are necessary. Thus, for 20 spinning machines, the necessary number of guides is equal to 6400 pieces.
For the evaluation of SGP, the following four roughness parameters were adopted: Rq, Rp, RΔq, and rw [22,35,36,37], since the values of the calculated linear correlation coefficient R between these parameters and the kinetic friction coefficient μk of the yarn against the surface were the largest [15].
Recording and measuring the geometric structural parameters of the surface were carried out with a Talysurf 6 profilographometer from Rank Taylor Hobson, with a measuring tip of a conical shape and a rounding radius of the tip of the mapping blade ros = 2 μm. Measurements were made on the surfaces of the guides at a gauge pressure of 0.75 mN, a gauge blade travel speed of 0.5 mm/s, a discretization step of 0.20 µm, an elementary section of 0.4 mm, and a gauge section of 5 × 0.4 mm = 2.0 mm. At least three measurements spaced every 120° were taken on each guide, whereby the average radius of curvature of the profile vertices rw was determined by parabolic approximation of 10 selected representative profile vertices. Of all the local elevations of the profile, ten were selected for evaluation, with a typical profile shape, using the ability to graphically assess the quality of the approximation of selected sections of the profile. Measurements were carried out in a room with a temperature of T = 20 ± 1 °C.
To evaluate the physical properties of the surface layer, the following were adopted: the maximum hardness of the surface layer HV0.1 and the depth of hardening of the surface layer gww. As a result of several years of observation and research under industrial conditions, it was found that as the hardness increases on the surface and in the surface layer of the parts of ring and spindleless spinning machines in direct contact with the yarn, their wear decreases [15]. Measurements of the hardness distribution at the depth of the surface layer HV = f(gww) of the guides were carried out using the Vickers method, on oblique scrapes made at an angle of 1°30′ (0.026 rad), with an indenter load of 0.98 N, with a Leitz Wetzlar micro-hardness tester. Hardness measurements were taken at the locations where contact between the yarn and the surface of the yarn guide was expected. A minimum of threefold repeatability was used during the hardness measurements. All measurement results were checked for statistical homogeneity to eliminate coarse errors, using the Grubbs test. The critical value of the test function Tkr was read from Table 51 [38], depending on the number of trials np = 5 (only in the case of the radius of curvature of the profile vertices rwnp = 10), the number of repetitions np = 3, and the adopted significance level α = 0.05 (5%). Values greater than the critical value of the test function Tkr were eliminated from the measurements. After eliminating coarse errors, the average values for each evaluation criterion were calculated and are shown in Figure 5.

3.3. Selection of the Optimal Variant of the Yarn Guide Manufacturing Process in View of the Unit Manufacturing Cost and Manufacturing Quality Criteria

The values of the criteria ratings, obtained from calculations and measurements of the analyzed variants of the yarn guide manufacturing processes, are shown in Figure 5. All criteria were treated as equally important in the analysis and evaluation of the options. Next, the optimal set in the Pareto sense was determined for the analyzed set of acceptable variants, consisting of 14 variants of the yarn guide manufacturing process based on seven criteria using the POLOPT.2 program. In this example, the minimized criteria are the cost of producing one piece of yarn guide (Kw, in PLN), the mean square deviation of the profile (Rq, in μm), the maximum height of elevation of the profile (Rp), and the mean square inclination of the profile (RΔq, in rad). The maximizes criteria are the average radius of curvature of the profile tops (rw, in μm), the maximum hardness on the surface of the surface layer (HV0.1), and the depth of hardening of the surface layer (gww, in mm).
The optimal set in the Pareto sense due to the above-mentioned seven criteria consists of 12 variants. The variants that are optimal in the Pareto sense are a1, a2, a3, a4, a5, a6, a7, a8, a9, a12, a13, and a14.
In the next step, the values of the criteria evaluations, on the Pareto-optimal set, were normalized to the interval ≤0.1;0.9≥ using the function described by Equation (3).
c i j * = 0.1 + c i j min 1 i n ( c i j ) [ max 1 i n c i j min 1 i n ( c i j ) ] · 1.25
where cij—the values of the criteria of the considered variants relative to the individual criteria, i = 1, …, n; j = 1, …, m. n—the number of variants; m—the number of criteria.
The resulting normalized scores c*ij, according to Formula (3), are fractions in the range ≤0.1;0.9≥. This method of normalization excludes extreme ratings of 0 and 1. The values of the evaluation criteria after normalization for the set of variants that are optimal in the Pareto sense of the yarn guide manufacturing process are shown in Table 2.
The distance function defined by Equation (2) was used to select the best variant from the set of Pareto-optimal variants. For the seven criteria, the form of this function is as follows:
f d ( i ) = [ c i 1 * c i d 1 * ] 2 + [ c i 2 * c i d 2 * ] 2 + , , + [ c i 7 * c i d 7 * ] 2
From the definition of the ideal vector, we can see that it is determined by non-dominated solutions obtaining the smallest values of each criterion in minimization, or by the largest values of the criteria in maximization tasks [24]. Taking into account whether the criterion is to be minimized or maximized in the task, the coordinates of the ideal point (variant) were determined:
c i d ( j ) * = ( 0.1 ; 0.1 ; 0.1 ; 0.1 ; 0.9 ; 0.9 ; 0.9 )
The values of c i j * for the Pareto-optimal variants are shown in Table 2, while the values of the distance function f d ( i ) , i.e., the values of the distance from the ideal point (variant), for these 12 variants are shown in Table 3.
The best variant is the one for which the distance function f d ( i ) has the smallest value, meaning the shortest distance from the ideal point. In this case, the best variant is a12, in which the semi-finished product is a drawn bar (ø6 mm) of C45 steel subjected to a heat treatment operation (quenching and tempering to a hardness of 350 HB) with a spiral insert of glazed porcelain. The value of the distance function for this variant is f d = 0.8116 . For the optimal variant, the values of the criteria evaluations are as follows: Kw = 11.05 PLN/pcs.; Rq = 0.145 µm; Rp = 0.686 µm; RΔq = 0.0240 rad; rw = −0.200 µm; HV0.1 = 1130 i gww = 105 µm. A slightly inferior variant of the yarn guide manufacturing process is the a13 variant with an Al2O3 ceramic sinter insert, for which the value of the distance function is slightly higher: f d = 0.9083 .
In situations where accidental impact on the yarn guide with a porcelain insert may occur, such as with the spindle cap of a spinning machine, it is recommended to use guides with an Al2O3 sintered insert. Although the unit manufacturing cost of these guides is approximately 20% higher, their impact resistance is at least several times greater compared to guides with porcelain inserts.

4. Conclusions

Many methods can be applied in multi-criteria optimization or decision support for manufacturing processes. Not all of these methods always guarantee the correct solution, as can be seen when undertaking the task of selecting the best variant for a smaller set of permissible options due to no more than three evaluation criteria. In general, a frequently used solution to avoid this issue is to introduce weights for the evaluation criteria. These weights can be changed arbitrarily, and for each change, a Pareto-optimal set of variants is determined. The set of preferred solutions is formed by the variants that occur in each Pareto-optimal set. If the set of preferred solutions is not one element, which is almost always the case for several criteria greater than three, the next step is to select the best solution using one of the methods. The second approach to determining the weights of the criteria adopted for evaluation is for each expert to construct a matrix of evaluations of pairwise comparative importance of the criteria using Saaty’s method. For this method, experts with a broad knowledge of the field are necessary. In the absence of competent experts, the solution is to treat the criteria as equally valid.
Therefore, for the evaluation of variants of the yarn guide manufacturing process, a two-stage optimization procedure was adopted, treating the evaluation criteria as equally important, involving the following:
  • First stage, the determination of a set of optimal variants in the Pareto sense;
  • Second stage, the determination of the best variant from this set using a distance function.
The applied procedure is easy to implement and generally allows for the selection of the optimal solution.
As a result of research, measurements, and calculations, based on seven criteria, an optimal set in the Pareto sense was assigned, consisting of 12 variants of the yarn guide manufacturing process. The distance function values were then used to determine the best solutions:
  • Variant a12 ( f d = 0.8116 ) for which the semi-finished product is a drawn bar (ø6 mm) of C45 steel, quenched and tempered to a hardness of 350 HB, with a spiral insert made of glazed porcelain.
    The values of the criteria evaluations are Kw = 11.05 PLN/pcs.; Rq = 0.145 µm;
    Rp = 0.686 µm; RΔq = 0.0240 rad; rw = −0.200 µm; HV0.1 = 1130; and gww = 105 µm
  • Variant a13 ( f d = 0.9083 ) for which the value of the distance function is slightly higher, by 0.0967, is the variant with the Al2O3 ceramic sinter insert.
    The values of the criteria evaluations are Kw = 13.02 PLN/pcs.; Rq = 0.542 µm;
    Rp = 1.191 µm; RΔq = 0.0617 rad; rw = −0.137 µm; HV0.1 = 1450; and gww = 205 µm.
Taking into account the additional criterion of impact resistance, it is proposed to use guides with the Al2O3 ceramic sinter insert.

Author Contributions

Conceptualization, S.P.; methodology, S.P.; software, A.J. and P.Z.; validation, S.P., A.J., and P.Z.; formal analysis, S.P., A.J., and P.Z.; investigation, S.P. and P.Z.; resources, S.P.; data curation, S.P. and P.Z.; writing—original draft preparation, S.P. and A.J.; writing—review and editing, A.J.; visualization, A.J.; supervision, S.P. and P.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
SGPStructure of geometrical surfaces

References

  1. Emmerich, M.; Deutz, A. Multicriteria optimization and decision making: Principles, algorithms and case studies. arXiv 2024, arXiv:2407.00359. [Google Scholar] [CrossRef]
  2. Chong, E.K.; Lu, W.S.; Zak, S.H. An Introduction to Optimization: With Applications to Machine Learning; John Wiley & Sons: Hoboken, NJ, USA, 2023. [Google Scholar]
  3. Mardani, A.; Jusoh, A.; MDNor, K.; Khalifah, Z.; Zakwan, N.; Valipour, A. Multiple criteria decision-making techniques and their applications—A review of the literature from 2000 to 2014. Econ. Res.-Ekon. Istraživanja 2015, 28, 516–571. [Google Scholar] [CrossRef]
  4. Liang, J.; Ban, X.; Yu, K.; Qu, B.; Qiao, K.; Yue, C.; Chen, K.; Tan, K.C. A survey on evolutionary constrained multiobjective optimization. IEEE Trans. Evol. Comput. 2022, 27, 201–221. [Google Scholar] [CrossRef]
  5. Li, J.Y.; Zhan, Z.H.; Li, Y.; Zhang, J. Multiple tasks for multiple objectives: A new multiobjective optimization method via multitask optimization. IEEE Trans. Evol. Comput. 2023, 29, 172–186. [Google Scholar] [CrossRef]
  6. Lukic, D.; Milosevic, M.; Antic, A.; Borojevic, S.; Ficko, M. Multi-criteria selection of manufacturing processes in the conceptual process planning. Adv. Prod. Eng. Manag. 2017, 12, 151–162. [Google Scholar] [CrossRef]
  7. He, Z.; Tran, P.K.; Thomassey, S.; Zeng, X.; Xu, J.; Yi, C. A deep reinforcement learning based multi-criteria decision support system for optimizing textile chemical process. Comput. Ind. 2021, 125, 103373. [Google Scholar] [CrossRef]
  8. Das, S.; Ghosh, A.; Majumdar, A.; Banerjee, D. Yarn engineering using hybrid artificial neural network-genetic algorithm model. Fibers Polym. 2013, 14, 1220–1226. [Google Scholar] [CrossRef]
  9. Mwasiagi, J.I.; Huang, X.; Wang, X. The use of hybrid algorithms to improve the performance of yarn parameters prediction models. Fibers Polym. 2012, 13, 1201–1208. [Google Scholar] [CrossRef]
  10. Khan, M.K.; Khan, M.S.A.; Kamran; Popa, I.L. Intuitionistic hesitant fuzzy rough aggregation operator-based EDAS method and its application to multi-criteria decision-making problems. Axioms 2025, 14, 21. [Google Scholar] [CrossRef]
  11. Zhu, S.; Zeng, L.; Cui, M. Symmetrical generalized Pareto dominance and adjusted reference vector cooperative evolutionary algorithm for many-objective optimization. Symmetry 2024, 16, 1484. [Google Scholar] [CrossRef]
  12. He, Z.; Tran, K.P.; Thomassey, S.; Zeng, X.; Xu, J.; Yi, C. Multi-objective optimization of the textile manufacturing process using deep-Q-network based multi-agent reinforcement learning. J. Manuf. Syst. 2022, 62, 939–949. [Google Scholar] [CrossRef]
  13. Kaplan, S.; Araz, C.; Göktepe, Ö. A multicriteria decision aid approach on navel selection problem for rotor spinning. Text. Res. J. 2006, 76, 896–904. [Google Scholar] [CrossRef]
  14. Szadkowski, J. Artifical intelligence approach to structural and parametrical optimization of multi–tool–machinning processes. Gepgyartastechnologia 1992, 9–10, 359–366. [Google Scholar]
  15. Płonka, S. Metody Oceny i Wyboru Optymalnej Struktury Procesu Technologicznego [Methods of Assessing and Selecting the Optimal Structure of the Technological Process]; Wydawnictwo Politechniki Łódzkiej: Bielsko-Biała, Poland, 1998. [Google Scholar]
  16. Mittemeijer, E.J.; Somers, M. Thermochemical Surface Engineering of Steels; Woodhead Publishing: Cambridge, UK, 2015. [Google Scholar]
  17. Dobrzański, L.A.; Dobrzańska-Danikiewicz, A.D. Obróbka Powierzchni Materiałów Inżynierskich [Engineering Materials Surface Treatment]; International OCSCO World Press: Gliwice, Poland, 2011. [Google Scholar]
  18. Posmyk, A. Warstwy Powierzchniowe Aluminiowych Tworzyw Konstrukcyjnych [Surface Layers of Aluminium Engineering Materials]; Wydawnictwo Politechniki Śląskiej: Gliwice, Poland, 2010. [Google Scholar]
  19. Lawrence, C.A. Fundamentals of Spun Yarn Technology; CRC Press: Boca Raton, FL, USA, 2003. [Google Scholar]
  20. Rauschert GmbH. Ceramic Thread Guides Rapal® Catalogue. Available online: https://rauschert.com.pl/img/files/PDF/prowadnice/Rapal_Katalog_2013.pdf (accessed on 3 September 2024).
  21. Płonka, S. Wielokryterialna Optymalizacja Procesów Wytwarzania Części Maszyn [Multi-Criteria Optimization of Machine Parts Manufacturing Processes]; WNT: Warszawa, Poland, 2017. [Google Scholar]
  22. Nowicki, B.W. Struktura Geometryczna: Chropowatość i Falistość Powierzchni [Geometric Structure: Surface Roughness and Waviness]; WNT: Warszawa, Poland, 1991. [Google Scholar]
  23. Osyczka, A. Evolutionary Algorithms for Single and Multicriteria Design Optimization; Physica–Verlag: Heidelberg, Germany, 2002. [Google Scholar]
  24. Montusiewicz, J. Ewolucyjna Analiza Wielokryterialna w Zagadnieniach Technicznych. [Evolutionary Multi-Criteria Analysis in Technical Matters]. Postdoctoral Dissertation, Politechnika Lubelska (Lublin University of Technology), Lublin, Poland, 2004. Available online: https://rcin.org.pl/Content/9112/PDF/WA727_9272_57263-5-2004_Ewolucyjna-analiza.pdf (accessed on 3 September 2024).
  25. Breiing, A.; Knosala, R. Bewerten Technischer Systeme: Theoretische und Methodische Grundlagen Bewertungstechnischer Entscheidungshilfen [Evaluating Technical Systems: Theoretical and Methodological Foundations of Evaluation-Related Decision-Making Aids]; Springer: Berlin, Germany, 2013. [Google Scholar]
  26. Ganesan, T.; Elamvazuthi, I.; Vasant, P.; Shaari, K.Z.K. Multiobjective optimization of bioactive compound extraction process via evolutionary strategies. In Intelligent Information and Database Systems, Proceedings of the 7th Asian Conference, ACIIDS 2015, Bali, Indonesia, 23–25 March 2015; Nguyen, N., Trawiński, B., Kosala, R., Eds.; Lecture Notes in Computer Science; Springer: Cham, Switzerland, 2015; Volume 9012, pp. 13–21. [Google Scholar] [CrossRef]
  27. Płonka, S.; Postrożny, J.; Drobina, R. Methodology of optimum selection of material and semi-folded products for rotors of open-end spinning machine. Autex Res. J. 2021, 21, 393–402. [Google Scholar] [CrossRef]
  28. Montusiewicz, J. Wspomaganie Procesów Projektowania i Planowania Wytwarzania w Budowie i Eksploatacji Maszyn Metodami Analizy Wielokryterialnej [Assistance for Design and Manufacturing Planning Processes in the Construction and Operation of Machines Using Multi-Criteria Analysis]; Wydawnictwo Politechniki Lubelskiej: Lublin, Poland, 2012. [Google Scholar]
  29. H’mida, F.; Martin, P.; Vernadat, F. Cost estimation in mechanical production: The Cost Entity approach applied to integrated product engineering. Int. J. Prod. Econ. 2006, 103, 17–35. [Google Scholar] [CrossRef]
  30. Wang, Z.; Nabavi, S.R.; Rangaiah, G.P. Multi-criteria decision making in chemical and process engineering: Methods, progress, and potential. Processes 2024, 12, 2532. [Google Scholar] [CrossRef]
  31. Lindroth, P.; Patriksson, M.; Strömberg, A.-B. Approximating the Pareto optimal set using a reduced set of objective functions. Eur. J. Oper. Res. 2010, 207, 1519–1534. [Google Scholar] [CrossRef]
  32. Henkel Ltd. “Loctite® Maintenance, Repair & Overhaul. Solutions Guide & Product Selector”. Available online: https://airstart.com.au/pdf/LOCTITE-FULL_PRODUCT_CATALOGUE.pdf (accessed on 3 September 2024).
  33. Klimczak, K.M.; Mleczko, J.; Więcek, D. Działalność Gospodarcza Przedsiębiorstw w Warunkach Przemysłu 4.0 [Economic Activity of Enterprises in the Context of Industry 4.0]; Polskie Wydawnictwo Ekonomiczne: Warszawa, Poland, 2023. [Google Scholar]
  34. Więcek, D.; Więcek, D. Production costs of machine elements estimated in the design phase. In Intelligent Systems in Production Engineering and Maintenance—ISPEM 2017: Proceedings of the First International Conference on Intelligent Systems in Production Engineering and Maintenance, Wrocław, Poland, 28–29 September 2017; Springer International Publishing: Berlin/Heidelberg, Germany, 2017; pp. 380–391. [Google Scholar] [CrossRef]
  35. PN-EN ISO 21920-2; Specyfikacje Geometrii Wyrobów (GPS)—Struktura Geometryczna Powierzchni: Profil—Część 2: Terminy, Definicje i Parametry Struktury Geometrycznej Powierzchni. [Geometrical Product Specifications (GPS)—Surface Texture: Areal—Part 2: Terms, Definitions and Surface Texture Parameters]. Polish Committee for Standardization: Warszawa, Poland, 2022.
  36. Oczoś, K.E.; Liubimov, V. Struktura Geometryczna Powierzchni [Geometric Structure of the Surface]; Oficyna Wydawnicza Politechniki Rzeszowskiej: Rzeszów, Poland, 2003. [Google Scholar]
  37. Adamczak, S. Metrologia Geometryczna Powierzchni Technologicznych. Zarysy Kształtu—Falistość—Mikro- i Nanochropowatość [Geometric Metrology of Technological Surfaces: Outlines of Shape—Waviness—Micro- and Nanoroughness]; PWN: Warszawa, Poland, 2023. [Google Scholar]
  38. Zieliński, R.; Zieliński, W. Tablice Statystyczne [Statistical Tables]; PWN: Warszawa, Poland, 1990. [Google Scholar]
Figure 1. Algorithm for determining the set of optimal variants in the Pareto sense [15].
Figure 1. Algorithm for determining the set of optimal variants in the Pareto sense [15].
Applsci 15 09055 g001
Figure 2. Attachment of the yarn guide on the ring spinning frame: 1—upper part of the holder, 2—lower part of the holder, 3—flap, 4—nut, 5—guide, 6—support tube, 7—bolt, 8—pin, 9—jam screw [15].
Figure 2. Attachment of the yarn guide on the ring spinning frame: 1—upper part of the holder, 2—lower part of the holder, 3—flap, 4—nut, 5—guide, 6—support tube, 7—bolt, 8—pin, 9—jam screw [15].
Applsci 15 09055 g002
Figure 3. Shape and dimensions of guides: (a) made of steel, Al99.5%, and its alloys, (b) made of C45 steel with embedded inserts made of porcelain, ceramic sinter, and tungsten carbide (1—C45 steel; 2—insert; 3—adhesive).
Figure 3. Shape and dimensions of guides: (a) made of steel, Al99.5%, and its alloys, (b) made of C45 steel with embedded inserts made of porcelain, ceramic sinter, and tungsten carbide (1—C45 steel; 2—insert; 3—adhesive).
Applsci 15 09055 g003
Figure 4. Additional calculation according to cost centers [33].
Figure 4. Additional calculation according to cost centers [33].
Applsci 15 09055 g004
Figure 5. Graph tree of variants of the manufacturing process for the yarn guide of the ring spinning frame.
Figure 5. Graph tree of variants of the manufacturing process for the yarn guide of the ring spinning frame.
Applsci 15 09055 g005
Table 1. List of operations of variants of the yarn guide manufacturing process, including types of materials, heat treatment, thermo-chemical treatment, and surface treatment.
Table 1. List of operations of variants of the yarn guide manufacturing process, including types of materials, heat treatment, thermo-chemical treatment, and surface treatment.
Op.
No.
Name of OperationStation
10Cutting steel drawn rod ø4 to a length of 130 mm or rod ø6 mm to a length of 162 mmPHS-160 press
20Cutting an extrusion bar made of Al or its alloys ø4 mm to a length of 145 mmHand press
30Chamfering the ends of the steel bar ø4 mm or ø6 on both sides to 0.5 × 45°06-TSZ special grinder
40Chamfering the ends of the bar of Al or its alloys ø4 mm on both sides to 0.5 × 45°Belt grinder (abrasive cloth belt)
50Soft annealingPEC-90 electric stove
60Straightening, bending in the device according to the drawingLocksmith table + special instrument
70Milling the end of the guide of C45 steel with a diameter of ø6 mm to a dimension of 3 mm, keeping the dimension 2+0.1 (according to Figure 3b). Refracting the sharp edges to a dimension of 0.5 × 45°Precision milling machine
80 Hardening   of   the   guides   ( T = 850   ° C ,     τ = 0.25 h ) PEC-90 electric stove
90 Tempering   the   guides   from   50 SiCr 4   steel   to   a   hardness   of   400   HB   ( T = 350   ° C ,     τ = 1   h ) ,   and   from   41 CrAlMo 7   and   C 45   steel   to   a   hardness   of   350   HB   ( T = 400   ° C ,     τ = 1   h ) PEC-90 electric stove
100Removing scale by vibration“Bolton” vibratory smoothing machine
110BlackingBath: NaOH 100 g/L + NaNO3 130 g/L
120 Diffusion   chroming   and   hardening   ( T = 1000   ° C ,     τ = 10   h ) VFC furnace
130 Diffusion   boroning   and   hardening   ( T = 950   ° C ,     τ = 8   h ) VFC furnace
140 Diffusion   titanizing   and   hardening   ( T = 480   ° C ,     τ = 2.5   h ) VFC furnace
150 Diffusion   nitriding   ( T = 520   ° C ,     τ = 10   h ) Retort stove
160 Nitrosulfurization   ( T = 570   ° C ,     τ = 3   h ) Retort stove
170Plasma spraying with Al2O3 powderPLANCER device type PN-110
180 Hard   anodic   oxidation   ( electrolyte   temperature :   T = 6   ° C ,     τ = 1   h ) Bath: electrolyte in the form of sulfuric acid 6% + sulfosalicylic acid 3% + lactic acid 2% + glycerin 2%
190Preparing the porcelain paste according to the recipeMixer AG-015
200Pressing the porcelain mass in the moldHydraulic press
210Preparing the mass of aluminum powder Al2O3Mixer AG-015
220Pressing the mass of aluminum powder Al2O3 into a moldHydraulic press
230Preparing the mass from tungsten carbide powder WC 94%/Co 6% according to the recipeMixer
240Pressing in the form of a mass of powder WC 94%/Co 6%Hydraulic press
250Drying the porcelain molding at 120 °CChamber dryer
260Evaporating the molding with WC 94%/Co 6%SEL 13 dryer
270Burning the porcelain molding at 900 °CChamber gas stove
280Burning the Al2O3 molding at 1800 °CChamber gas stove
290Burning the molding with WC 94%/Co 6% at 1280 °CChamber gas stove
300Covering the porcelain molding with glazeBathtub with liquid glaze
310Burning the glazed porcelain molding at 1410 °CChamber gas stove
320Fitting the porcelain molding in the eyelet of the C45 steel guideLocksmith table + special grinder
330Embedding the porcelain molding with Loctite 3090 2K 10 g adhesive into the eyelet of the C45 steel guideLocksmith table
340Drying of the adhesive at 22 °C—about 5 hDryer
350Fitting the Al2O3 sintered molded part in the mesh of a C45 steel guidewayLocksmith table + special grinder
360Embedding the Al2O3 sintered molding on Loctite 3090 2K 10 g adhesive in the eyelet of the C45 steel guideLocksmith table
370Fitting the WC molding 94%/Co 6% into the eyelet of the C45 steel guideLocksmith table + special grinder
380Embedding the WC 94%/Co 6% molding on Loctite EA 3425 adhesive in the eyelet of the C45 steel guideLocksmith table
390Drying the adhesive at 22 °C—about 3 hDryer
400Final inspectionInspection stand
Table 2. Values of criteria after normalization for the set of variants optimal in the Pareto sense of the yarn guide manufacturing process.
Table 2. Values of criteria after normalization for the set of variants optimal in the Pareto sense of the yarn guide manufacturing process.
kj c i j * a1a2a3a4a5a6
k1 c i 1 * 0.10000.18220.18050.27130.19080.1942
k2 c i 2 * 0.21310.22500.37990.32340.41620.2689
k3 c i 3 * 0.20840.22030.63280.28540.55820.2076
k4 c i 4 * 0.34310.37450.32750.41760.46470.2624
k5 c i 5 * 0.50000.38240.16470.22350.28240.3588
k6 c i 6 * 0.10000.50000.63330.90000.41730.4200
k7 c i 7 * 0.22310.14100.30510.10000.21490.1410
kj c i j * a7a8a9a12a13a14
k1 c i 1 * 0.17880.61730.28930.52740.71160.9000
k2 c i 2 * 0.38620.90000.35830.10000.37710.3373
k3 c i 3 * 0.43870.90000.28620.10000.30050.3549
k4 c i 4 * 0.30860.90000.28820.10000.39570.4059
k5 c i 5 * 0.19410.10000.54710.90000.52940.2412
k6 c i 6 * 0.61730.57470.10480.40930.58000.5533
k7 c i 7 * 0.28460.46920.34620.40770.81790.9000
Table 3. The value of the distance function fd(i) for the 12 optimal variants in the Pareto sense.
Table 3. The value of the distance function fd(i) for the 12 optimal variants in the Pareto sense.
Variant Numbera1a2a3a4a5a6
Value of the distance function  f d ( i ) 1.15841.0493 1.17741.1455 1.2389 1.0838
Variant numbera7a8a9a12a13a14
Value of the distance function  f d ( i ) 1.0969 1.76611.1119 0.8116 0.9083 1.1870
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Jarco, A.; Płonka, S.; Zyzak, P. Multi-Criteria Optimization of Yarn Guide Manufacturing Processes. Appl. Sci. 2025, 15, 9055. https://doi.org/10.3390/app15169055

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Jarco A, Płonka S, Zyzak P. Multi-Criteria Optimization of Yarn Guide Manufacturing Processes. Applied Sciences. 2025; 15(16):9055. https://doi.org/10.3390/app15169055

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Jarco, Aleksandra, Stanisław Płonka, and Piotr Zyzak. 2025. "Multi-Criteria Optimization of Yarn Guide Manufacturing Processes" Applied Sciences 15, no. 16: 9055. https://doi.org/10.3390/app15169055

APA Style

Jarco, A., Płonka, S., & Zyzak, P. (2025). Multi-Criteria Optimization of Yarn Guide Manufacturing Processes. Applied Sciences, 15(16), 9055. https://doi.org/10.3390/app15169055

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