Investigation and analysis of the impact of fibre mixing on the strength of nonwoven fabrics produced using double-drum carding machines

Abstract

Viscose–polyester nonwovens are now widely used. The desired performance properties of these nonwovens, such as quality and strength, depend to a large extent on the carding process, in which homogenised layers of properly mixed fibres are formed. In this article, a comparative analysis of two different designs of modern, double-drum carders and their impact on the quality of fibre mixing and on the strength of the final nonwoven fabric is presented, based on research and tests carried out in an industrial production line. To this end, mathematical models were developed for the relevant indicators (fibre delay time and the average fibre circulation path length in the carding machine) that characterise the carding process. Based on numerical calculations, these indicators were determined for the actual geometry of the carding elements and the process parameters applied in the tests. A discussion is provided to interpret the values of these indicators and their correlation with the strength of the nonwoven fabric produced, taking into account the different design of the carders used in the tests. The results showed that the average fibre delay time ranged from 1.40 s to 1.99 s, while the corresponding fibre delay length varied between 4.42 m and 6.30 m. Moreover, the mean fibre circulation path length was greater in the second carding machine (20.5–26.4 m) than in the first (16.9–17.0 m), indicating more intensive longitudinal fibre mixing.

Introduction

Recent trends in the textile industry focus on producing spunlace nonwoven fabrics that maximise mechanical strength while minimising raw material use. Carding machine manufacturers are continuously introducing innovations to improve process efficiency and the quality of the nonwoven, particularly in terms of fibre homogeneity and web strength. Modern carding machines are complex, and effective operation requires skilled adjustment of process parameters.

The main task of a carding machine is to form a continuous, homogeneous stream of fibres called a fleece, separating fibre bunches into individual fibres and enabling intensive longitudinal mixing¹. Key factors affecting the mixing process include: (a) the type of cylinder and roller padding, which ensures fibre separation and combing; (b) the size of the main cylinders and worker-stripper systems, which influence fibre displacement, orientation, and binding; and (c) the method of maintaining fibre motion, with initial straightening followed by twisting to enhance bonding. Longer fibre residence times in the carding machine improve nonwoven strength but may reduce production efficiency, highlighting the need to balance mechanical quality with economic and technological constraints.

The transfer of fibres between carding-machine surfaces, analysed through the motion of a single fibre in an airflow, was originally investigated by Lee and Ockendon², demonstrating that aerodynamic forces strongly influence fibre pick-up and redeposition. Building on this, Gu et al.³, using CFD simulations, showed that reduced tooth depth on metallic card clothing produces more concentrated airflow near the tooth tips, increasing the probability of fibre capture by flat-top needles. Their “double-tooth” clothing design achieved approximately a 30% production increase in industrial trials. Similarly, the work of Yang and Gong⁴ showed that fibres experience significant acceleration and orientation changes in high-speed airflow channels, confirming that air-driven mechanisms are critical in fibre transport. Optimisation of card-clothing materials has also been shown to have a strong effect on fibre transfer efficiency. Gu et al.⁵ developed Nb-alloyed AISI 1090 steel card clothing with enhanced hardness and wear resistance, demonstrating that wall-shear stress distribution on clothing surfaces is a key determinant of stable fibre movement. These improvements support consistent fibre transfer across different fibre types such as cotton and terylene. Research on the structural behaviour of fibres within nonwoven processes provides deeper insight into fibre interactions originating during carding. Xie et al.⁶ developed a micro-scale finite-element modelling approach that reproduces realistic fibre geometry and entanglement based on Micro-CT data. Their findings show strong agreement between simulated and real fibre structures, helping to explain how fibre orientation and flow history influence web formation. At the machine level, Yeshzhanov⁷ demonstrated that increasing the rotation frequencies of key carding elements within realistic ranges does not deteriorate sliver quality and may reduce nep levels. This underscores that airflow, machine dynamics, and fibre transfer processes must be considered jointly when optimising carding performance.

The mechanical behaviour of the resulting nonwoven structures is closely linked to fibre mixing and orientation established during carding. Ivars et al.⁸ examined tensile and tear properties of nonwovens containing carbon fibres, confirming the crucial roles of fibre orientation and bond strength in defining mechanical performance. Broader reviews by Yilmaz et al.⁹, Venkataraman et al.¹⁰, and the book Advances in Technical Nonwovens (Kellie, 2016)¹¹ additionally show that while tensile properties of nonwovens are relatively well understood, the dynamic, bending, and damage behaviour, strongly influenced by fibre–fibre interactions, remain less explored.

The quality and mechanical properties of nonwoven fabrics largely depend on fibre type, orientation, and the strength of mutual bonds. While much literature focuses on needling, the preceding carding stage, where the fibre web is formed is equally critical. Modelling and analysis of carding have addressed various aspects of fibre transport and web formation. Classic approaches often consider a single-cylinder machine with one fibre collection and recycling system^12–15. For example, Russell¹⁵ describes a single-drum carding machine with a main cylinder and a worker-stripper/doffer system, detailing roller interactions and fibre stripping. Similarly Albrecht et al.¹² provides the mathematical foundations for roller carding, while^13,14 outline basic machine configurations and web randomisation.

Rust and Gutierrez¹⁶ developed a model for a single worker-stripper group, later extended to simulate a carding engine with six groups. A two-dimensional model considering longitudinal fibre transport and transverse diffusion was presented by Cherkassky¹⁷. Studies of fibre state changes in revolving-flats cards showed that while fibres are largely opened into single fibres at the taker-in, many tuftlets remain¹⁸. Lee PhD thesis¹⁹ explored fibre dynamics by modelling single-fibre motion, extraction from tufts, and interactions among entangled fibres, highlighting strong transfer forces between the taker-in and cylinder and weaker forces between cylinder and doffer. Whole-system dynamics have also been modelled. Paper²⁰ examined rational design approaches, while²¹ developed a simplified model with one degree of freedom. Nonwoven roller carding dynamics and web density control were investigated in²², analysing rotation angles, velocities, and time delays. Studies in²³ predicted transfer rate and web collection power based on roller motion, relative velocities, clothing tooth angles, and friction forces. Further work²⁴ incorporated auto-leveller effects on fabric layer thickness and input fibre quantity, providing a comprehensive view from fibre dynamics to final web formation.

In previous publications the main authors of this manuscript^25–27 analysed two different double-drum carding machine designs. In^25,26, they modelled a machine with a single intermediate drum between the main cylinders, while in paper²⁷ considered a machine with four intermediate drums. Both studies examined the dynamics of nonwoven web formation, focusing on fleece density homogeneity and mass balance of fibres. Numerical simulations explored the growth of fibre thickness over time in relation to the fibre collection factor and the number of worker-stripper systems. Furthermore²⁷, introduced a method to determine the fibre transfer coefficient, enabling derivation of relationships characterising the average fibre delay time during circulation in the carding process.

Consequently, the present research focuses on modelling solutions to improve the quality of mixing heterogeneous fibres^25–27 while simultaneously analysing their residence time in the carding machine. With an appropriate control system, both production efficiency and the transverse and longitudinal strength of the resulting nonwoven fabric can be optimised, achieving the desired areal density in the final product.

This article aims to verify the theoretical findings from^25–27 using experimental research carried out on two different double-drum carding machine configurations. The study evaluates the quality and strength of the produced nonwoven fabric and analyses the interdependent parameters of the carding process. A series of tests was performed on an industrial production line using a 40 gsm nonwoven made from an 80/20 polyester–viscose blend. The hypothesis is that fibre mixing quality depends on the average fibre circulation time and path length in the carding machine, which directly correlate with the longitudinal and transverse strength of the final nonwoven fabric.

Description and tests of the carding process

The actual process of producing nonwoven fabric, in an integrated technological line consisting of a power supply system, mixing, two carding machines, a water needle machine, a dryer and a winder, was tested. Attention was paid to the carding process, which is crucial for obtaining the desired physico-mechanical, qualitative and quantitative parameters of the nonwoven fabric produced. In the process studied, two different high-performance carding machines were installed, configured in a serial system in the nonwoven production line. This solution ensures that each carding machine can be operated separately or two of them at the same time. If two carding machines are used, they can be loaded in different proportions resulting from the set capacity of the production line. However, this requires in each case adjusting the parameters controlling the carding process.

A simplified diagram and a description of the geometry of carding machine 1 are presented in Figs. 1 and 2. A characteristic feature of carding machine 1 is its structure, consisting of two main cylinders and one fibre transfer drum between them. The carding process begins with bringing the fibre deck to the feed roller and take-in roller of the carding machine, marked with the symbol , which, together with the cleaning rollers, transfers all the fibres to the main cylinder 1 (tambour 1 – designated as ). On the circumference of the cylinder, 5 pairs of carding rollers are designed in a worker roller – stripper roller system (designation and ). Their task is to crush and mix the joined and twisted fibres, hereinafter referred to as tufts. The fleece is then transported by means of an intermediate cylinder (index ) to the master cylinder 2 (tambour 2 – designated as ). This is also equipped with a set of 5 pairs of carding rollers of the worker-stripper type which enables the further crumbling and mixing of fibres. The geometry of the drum 2 and the related arrangements of carding rollers is the same as for the drum 1. In the further course of the carding process, the fibre is pulled from the cylinder 2 by the doffer roller (marking ) and finally transferred, in the form of a homogeneous fibre web, to the transport conveyor by means of a condenser and take-off roller, marked and respectively. The red, in Fig. 1, indicates the flow of fibres in individual carding systems, starting from the entrance (left side – drum ) to the exit (right side – drum ). All the specified elements of the carding machine 1 were dimensioned using diameters and angles describing their location.

Fig. 1.

Geometry of all elements and the direction of the flow of the fibre, shown in red, in a double-drum carding machine (card1)²⁶.

Fig. 2.

Dynamics of the carding process in a double-drum carding machine (card 1)²⁶.

Figure 2 shows the linear velocities of individual elements of the carding machine (symbol ) and fibre collection coefficients () needed, in order to model the fibre flow in the carding process^25–27. The fibre collection coefficient determines the measure of the ability of fibres from one roller, to be taken over by another at the point of contact between these elements. Hence, it is defined as the probability of the fibre passing from one element to another while it is moving through the co-operation arc between these elements. This size depends on the type of padding, the gaps between the elements and their speed and is constant during regular production. Fibre collection factor is important for the model, as it determines the amount of fibre mixture that is collected from main cylinders and transferred to the cylinder through drum . In addition, we determine the coefficient of fibre collection from the collecting roller by the thickening roller and the coefficient of fibre collection for carders located on drum 1 and 2, assuming the same for all pairs of carding rollers with the same geometry. Appropriate configuration of carding machine 1 ensures the possibility of producing a variety of nonwoven fabric mixtures weighing from 25 to 80 gsm.

Figure 3 illustrates the real configuration of carding machine 1 that was investigated in this study. Figure 4 shows the diagram and geometry as well as the flow of the fibre mixture - shown in red - in the worker-stripper system. In this form, these systems are arranged around the perimeter of the master cylinders ( and ) in both carding machines tested; points marked A, B and C indicate the location of the minimum gap between the co-operating elements.

Fig. 3.

Actual construction of carding machine 1.

Fig. 4.

Geometry, dynamics of the carding process and direction of the fibre flow in the drum-worker-stripper system (shown in red)²⁷.

The diagram and description of the geometry of the carding machine 2 are shown in Figs. 5 and 6, respectively. The construction of this carding machine differs from carding machine 1, primarily by the arrangement of intermediate drums carrying fibres between the main cylinders marked and - in Fig. 5. This arrangement consists of two parallel sub-assemblies, i.e. shafts and as and . In addition in the case of carding machine 1 and carding machine 2, on each main cylinder, there are 5 worker-stripper systems. The fibre mixture (fleece) is transported in the same way as in the description shown in the example of the carding machine 1. Hence, in the mathematical model of carding dynamics for carding machine 2, we consider both the fibre collection coefficient for the rollers and carrying fibre to drum and the fibre collection coefficient for the rollers and transferring fibre to drum ¹⁷. In addition, we take into account the fibre collection coefficient for the carders located on drums and and the fibre collection coefficient of by the thickening roller from collecting roller . The configuration of carding machine 2 allows more fibres to be processed (in the same amount of working time) when compared to carding machine 1, i.e. in the range of 25 to 100 gsm.

Fig. 5.

Geometry of all elements and the direction of the flow of the fibre -shown in red in a double-drum carding machine (card 2)²⁷.

Fig. 6.

Dynamics of the carding process in a double-drum carding machine (card 2)²⁷.

Figure 7 illustrates the actual configuration of carding machine 2 investigated experimentally in this study. The different design of carding machines 1 (Fig. 3) and 2 (Fig. 7) also affects their process parameters, i.e. the speeds of individual main cylinders, the speeds of worker-stripper systems and other elements, such as the working rollers, in carding machines.

Fig. 7.

The actual construction of carding machine 2.

The research process, planned and carried out, consisted in producing a 40-gsm nonwoven fabric from a mixture of polyester (80%) and viscose (20%) in three different configurations of carding machines, i.e.:

1. Using only carding machine 1, fully loaded (test 1);

2. Using only carding machine 2, fully loaded (test 2);

3. simultaneously using carding machines 1 and 2, assuming a load of both carding machines at the level of 50% (test 3). The system of two carding machines working simultaneously was previously designed to achieve greater efficiency of the technological line.

Due to the stability of the research conducted, after initial tests, the linear speed of the process was unified to the level of 190 m/min, which was achieved and accepted for the three work cycles assumed. On the other hand, the speed levels of individually controllable elements of both carding machines were adjusted to obtain the best quality of fibre mixing in the optically observed deck of fibres, formed after leaving the carding machines and as based on long-term know-how. These speeds are summarised on Fig. 8a (carder 1, test 1 and 3) and Fig. 8b (carder 2, test 2 and 3). The designations of these values were adopted in accordance with the diagrams shown in Figs. 1 and 2 (carder 1) and Figs. 5 and 6 (carder 2). The indexation of the workers and the strippers applies to the main cylinders and respectively.

Fig. 8.

The linear speed settings and the density of the clothing teeth of the individual elements of: (a) Card 1 (Tests 1 and 3); (b) Card 2 (Tests 2 and 3).

During the experimental tests, a nonwoven fabric with a width of 3.2 m was produced, with a total length of 7900 rm (test 1), 5500 rm (test 2) and 4000 rm (test 3) and wound onto bales, Laboratory samples were taken at 5 locations on the last 500 running metres of the beam with the stabilised process. In each case, 7 samples (dimensions 50 × 200 mm) were taken for testing the longitudinal and transverse strength (in accordance with the standard ISO 9073-3: Nonwovens - Test methods – Part 3: Determination of tensile strength and elongation) and distributed homogeneously in relation to the width of the nonwoven fabric, from left to right. The strength tests were performed on an INSTRON testing machine. All measurements were performed under steady-state production conditions. To ensure representativeness of the analysed material, samples were collected only after the stabilization of the production process from the final section of the produced roll and distributed across the width of the nonwoven fabric to capture spatial variability of the material properties. Obtained results are summarised on Fig. 9a (longitudinal strength – MD) and Fig. 9b (transverse strength – CD) on which heatmaps are presented. On Fig. 9c current metre of sampling as a function of numbers of test sample is presented. The average and median values of MD and CD sizes, in relation to the width of the production line for individual tests, are presented in Fig. 10a, b. In addition, the average value and median of the dimensionless MD/CD coefficient were determined (Fig. 10c); this is commonly used in the textile industry to determine the strength of the final product. MD and CD values are expected to be as high as possible and close to each other at the same time.

Fig. 9.

Results of laboratory tests heatmaps of the spun-lace nonwoven: (a) MD - longitudinal tensile strength; (b) CD - transverse tensile strength; (c) Number of test sample (current metre of sampling).

Fig. 10.

Mean (solid line) and median (dashed line) values of: (a) MD - longitudinal tensile strength; (b) CD - transverse tensile strength; (c) MD/CD tensile strength ratios. (Card 1 – blue, Card 2 – red; Card 1 and 2 – green)

To evaluate whether the differences in tensile strength between the three production configurations are statistically significant, the measured MD and CD values were analysed using one-way analysis of variance (ANOVA). The analysis confirmed statistically significant differences between the analysed configurations (p < 0.05), with the highest strength values obtained for Test 3. These results support the interpretation that improved fibre circulation and mixing conditions in the carding process positively influence the mechanical properties of the produced nonwoven fabric. Based on the results obtained (Fig. 9a and b), it can noticed that both the longitudinal and transverse strength is the highest for Test 3, in which two carding machines with a load of 50% were used simultaneously. At the same time, the MD/CD coefficient takes the smallest value (Fig. 10c). In the case of only one carding machine, higher MD and CD parameters were obtained in Test 2, in which only carding machine 2 worked. The least favourable average values of longitudinal and transverse strength were obtained in Test 1, using only carding machine 1 (Fig. 10a and b).

Modelling the carding process

A mathematical model of the expected value of the lag time of a fibre, calculated in seconds and performing an average number of drum and scraper circuits in the carding process relative to a fibre that does not perform such circuits in the two carders described, is presented in works^25–27. This value is equal to

3.1

where are the times of rotation of drum , pick-up roller and the flow around the worker-stripper systems on drums 1 () and 2 (). These values are determined on the basis of the linear speed of individual drums and rollers and their sizes.

The rotation times of drums is calculated on the basis of the following formula

where is the radius of drum . The rotation time of doffer is equal to

for the radius of mm. The fibre flow times, between points, and in the drum-worker-stripper systems (Fig. 4) are calculated using the following formula

with index corresponding to drum and to drum . These quantities are determined based on the relations (Fig. 4)

for , where:

• , , are the radii of drum , and the worker and stripper respectively;

• , , are the linear speeds of rotation of drum, worker and stripper for i=1,2;

• is the angle of rotation of the worker from point to ;

• is the angle of rotation of the stripper from point to ;

• is the angle of rotation of the drum from point to .

The expected value of the sum of the number of carding cycles for the worker-stripper arrangement for the drum and the expected value of the number of drum carding cycles for (TT roller) for the scrapers under consideration, are calculated using the formula

3.2

where: is fibre collection coefficient; k₁ and k₂ are the number of worker–stripper pairs of rollers on drums T₁ and T₂ respectively.

Due to the differences in the construction of both carding machines, the expected value of the number of drum carding cycles for the drum and the expected value of the sum of the number of carding cycles, calculated taking into account the drum cyclicity for cylinder have a different form, depending on the carding machine under consideration; we then arrive at the following relations

3.3

for carding machine 1 and

3.4

for carding machine 2. The parameters define the fibre take-up rates of the individual rollers. The delay in units of length, calculated in metres, at a production speed of [m/min] is

3.5

A model describing the fibre collection ratio between the drum (cylinder) and the collection roller (doffer) is presented in¹⁷. If these work with linear velocities, marked by and , respectively, then we can determine using the relationship

3.6

where the constants are calculated as follows

Coefficient determines the friction between the fibre and the metal teeth of the roller padding. The parameters and are the sum of the working angle of the roll cover and the curvature of the roller surface in relation to the tangent at the base of the roll cover tooth, and are the magnitudes of determine the density of the teeth in the roll cover for the cylinder and the collecting roller, respectively. Tables 1 and 2 contain linear velocities and cover tooth densities of individual rollers for carding machines 1 and 2.

Table 1.

Fibre collection coefficients and delay time and length for Card 1 (cases: Test 1 and Test 3) and Card 2 (cases: Test 2 and Test 3).

Determined coefficients	Card 1		Card 2
	Test 3	Test 1	Test 3	Test 2
	0.4271	0.4179	0.1410	0.2075
	-	-	0.0884	0.1340
	0.7568	0.7568	0.7544	0.7548
	0.0859	0.0815	0.0651	0.0651
	0.1290	0.1290	0.1210	0.1234
[s]	1.9905	1.9396	1.9386	1.3969
[m]	6.3033	6.1420	6.1388	4.4234

Table 2.

The expected value of the number of drum and worker carding cycles in Card 1 (cases: Test 1 and Test 3) and Card 2 (cases: Test 2 and Test 3).

Determined coefficients	Card 1		Card 2
	Test 3	Test 1	Test 3	Test 2
	2.3414	2.3929	4.6099	3.1878
	1.1001	1.0616	1.6051	1.1099
	0.7405	0.7405	0.6883	0.7039
	1.3214	1.3214	1.3255	1.3249

Based on the above-described, expected values of the number of drum and worker cycles and the geometry of carding machines 1 and 2 (Figs. 1, 4 and 5), we can determine the average lengths of these cycles. Hence, the average length, calculated in metres, regarding how the fibre circulates in carding machines 1 and 2, can be expressed by the formula:

3.7

where and determines the path of the circulation of the fibre on drums and , and the length of the worker cycles, is the length of the drum cycle on the TT roller and the length of the drum-to-drum transition path . These values are calculated using the formula for the length of the circular arc, taking into account the geometry of individual rollers. In addition, in the case of carding machine 2, by modelling a double system of intermediate drums carrying fibres between the main cylinders and , the size was determined as a weighted average with weights respectively (path through the rollers and ) and (path through rollers and .

Numerical calculations

The input data for the numerical calculations, presented below, was obtained from the actual research process on a new technological line for the production of Spunlace nonwoven fabric, consisting of (among other things) two different carding machines characterised in this article. As part of the research, three tests were carried out as described in Chap. 2, for which process parameters were measured: the linear speed and tooth density of the covering of individual elements in the sub-assemblies responsible for transporting the fibre. The fibre collection coefficients were estimated using the formula (3.6), where the following values of coefficients and were adopted for all elements. The setting values of the linear speeds and the tooth density, resulting from the covering used for individual elements of carding machines 1 and 2 are presented on Fig. 8a and b. The expected value of the fibre delay time and the corresponding delay in length units were determined from equations (3.1) and (3.5). The obtained values for individual tests are summarised in Table 1 (for both carding machines: 1 and 2).

Table 2 present the expected values of the number of drum and carder carding cycles, calculated on the basis of formulas (3.2) - (3.4) for individual carding machines. Finally, the average length of the fibre of circulation path in carding machines was determined and given in Table 3, using the relationship (3.7).

Table 3.

The mean length of fibre circulation path on individual elements and in the entire for Card 1 (cases: Test 1 and Test 3) and Card 2 (cases: Test 2 and Test 3).

Mean length	Card 1		Card 2
	Test 3	Test 1	Test 3	Test 2
[m]	3.7919	3.7919	3.7919	3.7919
[m]	1.1242	1.1242	1.1242	1.1242
[m]	1.3407	1.3407	1.8117	1.8213
[m]	1.1242	1.1242	1.1242	1.1242
[m]	1.6748	1.6748	1.6116	1.6116
[m]	2.2192	2.2192	2.2192	2.2192
[m]	16.8955	17.0475	26.4234	20.5000

Based on the tests carried out, the following characteristics were observed:

• the average fibre delay time in carder 1 assumes comparable magnitudes in tests 1 and 3 (Table 1), which results from similar speed settings (Fig. 8a) on individual elements transferring fibres in the carding process;

• the average delay time of the fibre in carding machine 2 takes different values in tests 2 and 3 (Table 1), which results from different speed settings of the elements (Fig. 8b) in the system of transferring fibres from cylinder 1 to cylinder 2, in the process of carding;

• the average delay time of the fibre in the carding machine 1 and 2 (Table 1) in Test 3 assumes comparable magnitudes due to the degree of loading of both carders with the fibre input (50% each), which makes it possible to adjust/lower the speeds in the transmission system of carder 2;

• the average length of the fibre circulation path is longer in carding machine 2 compared to carding machine 1 (Table 3), which results from different values of the expected number of drum and carding cycles on cylinder 1 (Table 2).

• the average length of the fibre of circulation path in the carding machine 1 assumes comparable values in Tests 1 and 3 (Table 3), which results from similar values of the expected number of drum and carding cycles (Table 2);

• the average length of the fibre circulation path in the carding machine 2 takes a higher value in Test 3 than in Test 2 (Table 3), which results from different values of the expected number of drum and worker carding cycles on cylinder 1 (Table 2);

• in Test 3, the average length of the fibre circulation path in the carding machine 2 is definitely higher than in carding machine 1 (Table 3) despite the fact that the average delay time of fibre is similar; this is due to the speed settings of individual elements, which in turn suggests a better quality of the longitudinal mixing process.

Discussion

From the studies carried out and discussed in this thesis, it can be seen that a clear empirical correlation can be observed between the strength of the produced nonwoven fabric and the average time and distance travelled by fibres in the carding process. Although the present study does not constitute a fully controlled factorial experiment, the observed correlation is consistent with known physical mechanisms of fibre opening, mixing, and orientation during carding. Numerical calculations, based on the mathematical model^25–27 and the control parameters extracted from tests 1, 2 and 3 support the thesis of the influence of the fibre mixing quality on the strength of the nonwoven fabric. The quality of fibre mixing depends on the average length of the fibre path in the carder. A higher value of parameter positively impacts the fibre mixing process, which enhances fiber orientation and the homogeneity of the resulting pile. It is important to note that the value of parameter is related to the method of fibre transfer from cylinder 1 to cylinder 2 and the choice of the linear speed of cylinder 1 and the fibre transfer system to cylinder 2. It should be underlined that the proposed model represents a simplified probabilistic description of fibre circulation in the carding machine. The model assumes identical statistical behaviour of fibres and constant fibre transfer probabilities between machine elements under stable production conditions. While this approach allows analytical determination of key indicators describing fibre circulation, local disturbances and complex fibre–fibre interactions are not explicitly modelled. Nevertheless, the obtained results show good agreement with the experimentally observed mechanical properties of the produced nonwoven fabric.

As part of the research work, three tests were carried out on carding machines of different designs, assuming stable production and the same output. The resulting nonwoven fabric was subjected to strength tests while determining parameters from the mathematical model of the carding process. The results obtained confirmed the relationship between MD and CD values and the average path travelled by the fibre in the carder.

Conclusions

It can be concluded that the value of parameter effectively characterises the strength of the nonwoven fabric produced. This can be seen in the results described in this paper, where the best strength coincides with the highest value in Test 3. The design of carding machines and their control systems should aim to increase taking into account assumed production efficiency.

In technological terms, the operation of two carding machines and the uneven loading of them with a variety of fibres can lead to significant capital expenditure. This will be due to the cost of designing, constructing and building a complex production line. However, given the knowledge of the flow of heterogeneous fibres and the way in which they are mixed, namely, separately in the produced deck for each carder and during overlapping decks for both carders, it is possible to determine and then supervise the length of stay and consequently the mixing of the fed fibres with a view to achieving the expected strength of the nonwoven fabric produced. In the tests carried out, it was found that despite the uneven loading of the two carders, the production capacity of the nonwoven remained unchanged. This, in turn, makes it possible to conclude that the return on investment of the process line investigated will be significantly quicker than in the case of nonwoven fabric production in the classic solution using a single carding machine. In addition, by reducing the amount of fibre fed and increasing the degree of mixing in the individual carders, in the individual decks produced and then combining/overlapping the decks and reinforcing them with water needling, we can obtain a nonwoven fabric with a higher degree of strength. This is important in economic terms, viz., a reduction in raw material costs, energy costs and in ecological terms, viz., a reduction in artificial polymer fibres, a reduction in the disposal of waste from used nonwovens due to the reduction in weight and in social terms, namely a reduction in the purchase price of products made from a variety of nonwovens.

The aim of a subsequent study will be to further analyse the strength of the nonwoven fabric on the basis of tests that take into account a different mixture ratio of fed fibres and a different distribution of the raw material weight load of the two carders. By reducing the amount of fibres introduced into the nonwovens produced, while maintaining the same quality properties, it is possible to expand their use in various areas of social life, with a view to their use as an intermediate product by soaking in substances that aid hygiene and cleanliness.

Author contributions

Conceptualization: M.N., W.W. and M.S.; methodology: M.S., W.W. and M.N.; Software: M.N., K.U. O.O.; validation: M.S., W.W., M.N., K.U., O.O.; formal analysis: W.W., M.N. and M.S.; investigation: M.S., W.W. K.U., O.O. and M.N.; resources: M.S., W.W. and K.U.; writing—original draft preparation: M.N., M.S., W.W., O.O. and K.U.; writing—review and editing: M.S., W.W., O.O., K.U. and M.N.; visualization: M.N. and K.U; supervision: O.O., K.U. and M.N.

Funding

The research was carried out under partial financial support obtained from the research subsidy of the Bialystok University of Technology, grant No. WZ/WIZ-INZ/2/2025 (Olga Orynycz) and from a research subsidy from the Institute of Mechanical Engineering of the University of Zielona Góra. Kamil Urbanowicz declares that his contribution is financially supported by the Minister of Science under the ‘Regional Initiative of Excellence’ (RID) programme.

Data availability

All data generated or analysed during this study are included in this published article and its supplementary information file. The raw data are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.