Improvement in drying performance through sample movement change in tumble dryers

Abstract

To improve the drying performance of a tumble dryer, the movement of sample clothes as a function of the mechanical action of the dryer was analyzed. The movement of cotton shirts inside a tumble dryer, represented by sample movement patterns, occupancy, and velocity distribution, were quantitatively analyzed using sample movement indices. The differences in the sample movement and the subsequent drying performance were evaluated by varying the drum rotational speed and direction. A drum rotational speed of 50 rpm produced the best sample properties and a short drying period, as the samples actively moved primarily in the center of the drum. Changes in the direction of the drum rotation reduced the drying period and minimized wrinkles in the samples when the frequency of changes to the rotational direction was minimized; however, the change aggravated shrinkage and damaged the samples. The best drying performance was observed when the direction of the drum rotation was changed every 2 seconds. The correlation and regression analysis demonstrated that the sample movements occurred at the center of the drum and that the drying period decreased while the drying performance improved, as the samples were subjected to complex movements and the mixing between them increased.

Keywords

Tumble dryer sample movement drum rotational speed changing the drum rotational direction drying performance drying program

Drying clothes in a dryer is a process that evaporates and disperses the water they contain.¹ The removal of water is predominantly dependent on the temperature and humidity conditions in the drum, the airflow velocity, the drum rotational speed, and the drying load. These factors affect the drying performance and determine the efficiency of energy consumption by changing the movement of the fabric inside the tumble dryer.

Yadav et al.² used mathematical modeling to simulate and analyze the drying process. They evaluated it as an exchange of heat and mass between the fabric and tumble dryer, where the temperature and humidity of the drum and the airflow velocity were the main factors that improved the drying efficiency. As the temperature inside the drum increases, the drying rate accelerates due to the high thermal energy of the fabric, but shrinkage of the fabric also increases.^3,4 When the airflow velocity inside the drum increases, air circulation can reduce the energy consumption and wrinkle recovery is enhanced. Shrinkage occurs when hydrophilic knit fabric absorbs moisture. The diameter of the yarn affects the movement of the loop, and shrinkage occurs with the moving yarn position.^5,6 Wrinkling occurs when pressure is applied to a fabric, the hydrogen bonds that have been formed are broken, or molecules slide between molecules to form new hydrogen bonds.^7,8 Therefore, the mechanical movement of fabric unmistakably affects shrinkage and wrinkling. The mechanism of drying fabric is based on mechanical movement, including the stress applied to the fabric by mechanical force, tension due to bending of the fabric, and deformation due to compression, friction, and interference between fabrics.⁹ The drying process occurs as the moisture on the fabric surface between the yarns and on the fibers is diffused and desorbed and moves to the inside of the drum dryer.¹⁰

Yun and Park¹¹ correlated fabric movement to drum rotational speed. The drum rotation produces centrifugal and frictional forces, which are then transmitted to the fabrics, resulting in fabric movement. The fabrics exhibit repeated movement only at the bottom of the drum if the centrifugal force transmitted to them is small and the gravitational force due to fabric mass is large; they exhibit rotational movement with the drum wall only if the centrifugal force is sufficiently large. Park S et al.¹² investigated the movement and drying performance using fabrics with different mass, drape coefficient, friction coefficient, and thickness characteristics at specific values of drum rotational speed and airflow velocity, and found that the drum rotational speed has the biggest impact on the drying performance. The drying load affects the fabric movement by changing the occupied area in the drum. As the drying load increases, the energy consumption and drying time increase due to the reduction in the contact area between the fabrics and the hot air.^13,14

Since fabric movement directly affects the drying performance, it is important to appropriately adjust the forces applied to the fabric by controlling the drum rotational speed to ensure the effective movement of the fabrics. Therefore, a comprehensive understanding of the influence of the fabric movement on the drying performance is necessary to reduce the energy consumption and improve the fabric properties. Furthermore, shrinkage and wrinkle recovery, which are crucial factors affecting the drying performance, exhibit a trade-off relationship corresponding to the effect exerted by the drying conditions. As fabric moves to the center of the drum and folds and unfolds, the exposure to hot air increases and wrinkle recovery occurs, but the fabric is susceptible to shrinkage in this condition. Most previous studies focused only on enhancing either shrinkage or wrinkle recovery. Therefore, identification of the optimal conditions required to improve the drying performance of both the shrinkage and the wrinkle recovery is essential.

In this study, the movement of a sample was analyzed based on the drum rotational speed and direction to determine their effect on the drying performance. Casual dress shirts and T-shirts made of cotton were used as samples, and the drum rotational speed and direction were varied. The movement of the sample was represented by three-dimensional (3D) and two-dimensional (2D) patterns and movement indices. The drying period and the drying performance were evaluated as a function of shrinkage, wrinkles, and damage. The effect of the sample movement on the drying performance was analyzed by regression under different drying conditions. Based on these factors, we presented the optimal drying program to improve the overall drying performance, thereby reducing energy consumption by improving drying efficiency.

Experimental details

Materials and drying equipment

Knitted T-shirts and woven casual dress shirts made of 100% cotton were used as samples, and their characteristics are shown in Table 1. The samples were dyed in red using a pigment to observe their movement (PROCION® Mx Dye 030 Fire Engine Red). A drying load of 4 kg was made by combining one knit T-shirt (120 g), one woven dress shirt (290 g), and dummy loads of 15 pieces of pillowcases according to IEC 60456. Heat pump-type tumble dryers with a capacity of 16 kg (LG electronics, TS168VAKOR) were used in this experiment. One of the dryers was modified to be transparent when viewed from the front, right-hand side, and above to facilitate the observation of the sample movement, while another dryer used to evaluate drying performance was not modified.

Table 1.
Specifications of samples

Trait Description

Type T-shirts Casual dress shirt

Fiber content Cotton 100%

Weave type Knit Woven

Thickness (mm) 0.57 $\pm$ 0.02 0.36 $\pm$ 0.01

Conditioned mass per piece (g) 120.0 $\pm$ 3.0 289.9 $\pm$ 2.0

Drying conditions

One hundred percent knit T-shirts and woven casual dress shirts were used as the tracing samples, and IEC 60456 pillowcases were used as the dummy loads. One T-shirt, one casual dress shirt, and 15 dummy loads were combined for a total drying load of 4 kg. To easily observe the sample movement, tracing samples were dyed using a red reactive dye (Jacquard Procion MX Dye). The amount of initial moisture regain in the total drying loads, including the sample and the dummy loads, was adjusted to 60% using the pre-washing program of a top-loading washer (16 kg, TS168VAKOR, LG Electronics). A top-loading washer was used to wash the total drying loads without a detergent at 15°C for 4 min, and they were spin-dried for 26 min. Tap water at 15°C was supplied as the washing water. The water pick-up ratio of the overall sample was set to 60% before drying. The loads were dried at an airflow velocity of 0.2 m/min. The movement and the drying performance were analyzed while changing the drum rotational speed. Pre-tests were carried out at drum rotational speeds of 35, 50, and 65 rpm. The shrinkage intensified at 50 rpm, with other advantages, but was very low at 65 rpm, with other weaknesses. Therefore, we chose an intermediate drum rotational speed of 57.5 rpm for further testing. In addition, combining different drum rotational speeds or changing the direction of the drum rotation (clockwise/counter-clockwise) was evaluated from the moment when the amount of moisture regain dropped below 10% (Table 2).

Table 2.
The drying programs in the tumble dryer

Codes Drum rotation speed (rpm) The cycle of changing the drum rotational direction in 60 s The number of drum rotational direction changes in 60 s Schematic diagram

R 35 35 Clockwise 60 s 0

R 50 50

R 57.5 57.5

R 65 65

R50/57.5(0) 50 57.5 Clockwise 60 s 0

R50/57.5(1) 50 57.5 Clock-wise 30 s/counter-clockwise 30 s 1

R50/57.5(9) 50 57.5 Clock-wise 6 s/counter-clockwise 6 s 9

R50/57.5(29) 50 57.5 Clock-wise 2 s/counter-clockwise 2 s 29

Evaluation of the sample movements

Video capturing

The movement of the sample was analyzed for 1 min until the moisture regain of the total drying loads decreased to 3%. The movement of the sample was captured from the front and the right-hand side of the tumble dryer using two ultra-high-speed cameras (IDT NX3-S301-0117-1555, IDT X-Stream XS4). The videos captured at 5 frames per second were converted into video files (.avi) using Motion studio 32 (IDT Innovation in Motion, UK) software. Based on these video files, a total of 600 frames, including 300 frames each from the front and the right-hand side, were traced using TEMA motion (Image Systems Co., Ltd, Sweden) software. The average of the upper, lower, left, and right peak values of the traced fabric outline was set as the center coordinate of the tracing sample.

Analyzing the movement patterns of the sample

The center of the sample was determined as the average value of the upper, lower, left, and right outermost coordinates on the outline. The trajectory of the coordinates of the center of the sample was recorded into an Excel file (.csv), which was converted into a cylindrical diagram using the Washer Dynamics Analyzer software for 3D analysis of the sample movement.¹⁵ In Washer Dynamics Analyzer software, the movement path of the fabric was expressed by interpolating it with a smooth curve, providing insight into the fabric movement using the 3D trajectory function of the analysis system. In addition, the accumulated values of the sample occupancy were indicated by changes to the color spectrum, where the colors were red for high accumulation and blue for low accumulation.

Velocity distribution of the sample

The velocity can be expressed as the change in the coordinate of the sample center between two consecutive frames. The distance for the sample moved between frames was calculated through the change in the center (x, y), and the velocity was obtained using Equation (1). Here, U_x and U_y are the velocities of the sample in the x- and y-directions, respectively, and dx and dy are the displacements at time, t, along the x- and y-axes in the frame.

The total velocity, U_total, was calculated by combining the velocities in both the x- and y-directions using Equation (2), as shown below.^15,16 Higher velocities are expressed in red, while lower velocities are expressed in blue.
$U_{x} = \frac{x_{b} - x_{a}}{t_{b} - t_{a}} = \frac{d x}{d t^{'}}, U_{y} = \frac{y_{b} - y_{a}}{t_{b} - t_{a}} = \frac{d y}{d t}$
(1)

$U_{total} = \frac{\sqrt{{(x_{b} - x_{a})}^{2} + {(y_{b} - y_{a})}^{2}}}{t_{b} - t_{a}}$
(2)

x_b–x_a: x coordinate difference between two frames.

y_b–y_a: y coordinate difference between two frames.

t_b–t_a: time difference between two frames.

Analyzing the movement patterns of the total drying loads

The outlines formed by the total drying loads, including the sample and the dummy loads, were traced in two dimensions on the XY and YZ planes to analyze the spatial occupancy of the total drying loads inside the dryer.

Measurements of drying performance

Moisture regain

The moisture regain of the total drying loads was measured as follows
$Moisture regain (%) = (D - B) / B \times 100$
(3)
where D represents the mass of the total drying loads containing moisture and B represents the dry mass of the total drying loads. The dry mass was obtained by drying fabrics in an oven at 105 ± 3°C for 90 min, according to standard test method (ASTM D2495-07).¹⁷

Drying period and energy consumption

The drying period is defined as the time at which the initial moisture regain of the total drying loads, which was maintained at 60%, decreases to 3% after drying. The power consumption during drying was measured using a power meter (WT210, Yokogawa).

Shrinkage

The shrinkage of the sample T-shirt was evaluated in accordance with the AATCC test method 135.¹⁸ A 30 cm × 30 cm square was attached to the back of the sample, and the change in area was measured using Equation (4). For one sample, shrinkage was measured from three spots and the average of the three measurements was derived
$Dimensional shrinkage (%) = {(a c \times b d) - (a' c' \times b' d') / (a c \times b d)} \times 100$
(4)

Smoothness

To evaluate the wrinkles of the sample shirt after drying, the appearance smoothness grading of the sample shirt was evaluated by three experts using the AATCC smoothness appearance replica in accordance with the AATCC test method 124.¹⁹ The appearance smoothness was divided into grades from 1 to 5 (SA-1–SA-5), where a higher grade represents a surface with fewer wrinkles. The wrinkle evaluation was also performed for the 30 cm × 30 cm square drawn on the back of the sample shirt.

Damage

Damage was evaluated by attaching five-hole fabrics (MA 40, Test fabrics Inc., USA) to the samples. The degree of damage was evaluated by counting the number of unwound yarns in the warp/weft directions after drying.²⁰

Statistical analysis

IBM SPSS statistics 22.0 was used to analyze the correlation between the sample movement and the drying performance. The regression equations used to predict the drying performance were constructed by designing regression models, which used the significant movement indices as independent variables and the drying performance as a dependent variable.

Results and discussion

Effect of drum rotational speed on the sample movement

Movement patterns of the sample

Figure 1 shows the movement of the center of the tracing sample in 3D and 2D diagrams. This figure allows us to analyze the individual movement of the sample, which was mixed with the dummy loads inside the dryer. In the 3D diagram of Figure 1(a), the tracing sample remained mostly at the bottom of the drum at R 35 because the centrifugal force could not generate enough mixing or overcome the gravitational force exerted by the sample mass. When the drum rotational speed was increased to R 50, the sample actively moved toward the drum wall as the centrifugal force on the sample increased, initiating many instantaneous positional changes.

Figure 1.
Visualized movement pattern of the sample according to rotational speed. (a): three-dimensional diagram sample movement pattern, (b): two-dimensional (2D) diagram of the sample movement representing occupancy and (c): 2D diagram of the sample movement representing the velocity distribution.

In the case of R 57.5, the sample movement remained close to the drum wall as the centrifugal force further increased. However, when the drum rotational speed was R 65, the sample repeated only the rotational movement, constantly attaching to the drum wall, because the centrifugal force transmitted to the sample was too large, leading to the sample clinging to the drum at the same position without being mixed.²¹

Figure 1(b) shows a 2D diagram representing the accumulated occupancy of the tracing sample in the XY and YZ planes. In the XY plane, while the sample exhibited high occupancy at the bottom of the drum at R 35, it more evenly occupied the space in the drum at various positions at R 50. At R 57.5, the sample exhibited a higher occupancy at the positions close to the drum wall compared to lower rotational speeds. At R 65, the sample remained on the drum wall, residing at specific positions, thereby exhibiting high occupancy on the drum wall. The total drying load used in this study was 4 kg. Based on tracing of the sample movement, the difference in the movement along the YZ plane was minimal because the tracing samples could not actively move along the z-axis direction due to the presence of the other samples in the drying load.

Figure 1(c) shows the velocity of the tracing sample at each position along the XY plane. At R 35, the velocity of the sample center was rather low due to the short distance, as it could not be lifted high under the small centrifugal force, but it exhibited higher velocities in the area where it descended due to gravity. At R 50, the sample exhibited higher velocities due to the increase in the movement distance and the range as the centrifugal force acting on it further increased. At R 65, the sample showed the highest velocity, as it exhibited mainly rotational motion and moved along with the drum wall.

Movement patterns representing the outlines of the total drying loads

Figure 2 shows a 2D representation of the outline accumulation of the frames of the total drying load inside the drum. In the XY plane, the shape of a circle appears to have collapsed at R 35, and the drying load could not be lifted upward due to the small centrifugal force.²² At R 50, the diagram of the accumulated frames almost formed a complete circle, and the total drying load appears to have filled the internal space of the dryer. However, at R 65, the shape of a circle with a hole in the center was observed, indicating that the total drying load only moved along the drum wall without falling to the center of the drum.

Figure 2.
Visualized movement patterns representing the outlines of the total drying loads at various rotational speeds.

In the YZ plane, the movement of the total drying load was observed along the side of the dryer. The total drying load could not fill the inside of the drum at R 35, but completely filled the space when the drum rotational speed increased as the samples moved toward the drum wall.

Movement indices

Movement indices were developed based on the movement of the sample and total drying load. Specifically, the appearance of the area within the 1/2 drum radius, position factor, number of tumbling cycles, and appearance frequency were developed using the X and Y coordinates. These indices were quantified in the 1/2 drum radius area. The distance from the center of the drum, speed difference between the drum and the sample, angle change of the sample center between the frames, distance of the sample center between the frames, velocity of the sample center between the frames, and total distance moved were quantified using the X, Y, and Z coordinates.²³ For the movement of the total drying loads, the area determined by the outlines of the sample with the dummy loads was quantified in the XY and YZ planes. Table 3 presents the definition and the conceptual diagram of the movement indices.

Table 3.
Movement indices

The movement indices were examined for different drum rotational speeds (Figure 3). As the rotational speed increased, the average distance from the center of the drum and the angle change of the sample center between the frames increased, whereas the average distance from the drum wall decreased, indicating that the sample moved from the drum center toward the drum wall. We used the average change value, which refers to the average of the absolute value of the change, to demonstrate how much change occurred between the frames. The distance from the center of the drum (average change) and the distance from the drum wall (average change) were highest at R 50, followed by R 57.5, R 35, and R 65, indicating that the sample exhibited the most active movement at R 50 and only small changes were observed at R 65 due to its adherence to the drum wall during the rotation.^24,25 The speed difference between the drum and the sample (average, average change) was highest at R 50, followed by R 35, R 57.5, and R 65, indicating that the sample exhibited many changes in the position of the sample between frames at R 50. The total distance that the sample moved increased with the increase in the drum rotational speed. At R 35, the sample mainly stayed under the drum, but at R 50, it moved more actively, displaying a larger moving range. At R 65, the sample moved along the drum wall, exhibiting the maximum moving distance. The position factor was highest at R 50, indicating that the sample frequently appeared in the first quadrant, as its movement inside the tumble dryer was active. The appearance area within the 1/2 drum radius, the number of tumbling cycles, and the appearance frequency decreased in the order of R 65 < R 35 < R 57.5 < R 50. At R 50, the sample appeared most frequently in the center of the drum, and significant mixing occurred between the sample and dummy loads by a forward and backward motion in the drum. Considering the movement indices that represent changes in the outlines of the total drying loads, the average standard deviation among the frame and the average change in the occupied area ^XY and the occupied area ^YZ were highest at R 50, followed by R 57.5, R 65, and R 35. This result indicates that the sample moved actively throughout the drum space at R 50. For faster or slower rotations, the space in which the sample could move was limited.

Figure 3.
Movement indices according to drum rotational speed.

Figure 3.
Continued.

Effect on drying performance according to drum rotational speed

Drying period and energy consumption

As shown in Figure 4, the drying period and energy consumption required for complete drying were the shortest (105 min, 1409.6 Wh) for R 50, which exhibited the most active movement of the sample. The next shortest drying time was for R 57.5 (140 min, 1993.9 Wh), then R 35 (165 min, 2256.1 Wh), and the longest at R 65 (200 min, 2963.8 Wh). Drying was completed quickly at R 50 because the sample actively moved near the center of the drum without being agglomerated or clinging to the drum wall. This active movement is attributed to the sample moving mainly in the center of the drum, providing many opportunities for exposure to hot air, which is advantageous for reducing the moisture regain.²⁶ On the other hand, the drying period was longer at R 57.5 because the sample frequently moved along the drum wall and stayed at the center of the drum.

Figure 4.
Drying performance according to drum rotational speed.

Shrinkage

Shrinkage was observed as the moisture regain of the sample T-shirt decreased. Since the shrinkage of the woven fabric was less than that of the knit fabric, the latter was used to compare the change in shrinkage that occurred due to the change in movement regulated by the drum rotational speed. In particular, rapid shrinkage was observed when the moisture regain dropped below 10%. Cellulose has a high affinity for water molecules and exhibits high shrinkage during drying, as it contains several hydroxyl groups. When the fibers absorb the moisture and swell, the yarns form loops and move, thus increasing the curvature of the loop, reducing the space inside the yarn, and increasing the crimp.²⁷ The form of moisture adsorbed onto the fabric is classified into three types: bound water (alpha water), which is directly bonded to the hydrophilic group of the fiber polymer; free water (beta water), which is bonded to the alpha water; and capillary water, which can move to the fiber surface by capillary force through the pores of the fiber and the yarn. Accordingly, near the end of the drying period, the alpha water directly bonded to the fibers evaporates and causes de-swelling, thereby intensifying the shrinkage.²⁸

In addition, when the drum rotational speed was varied, R 50 exhibited the highest shrinkage at the completion of the drying process. At R 50, the increased exposure of the sample to hot air enhanced shrinkage due to the highly active movement; the sample exhibited many changes in its position between frames and frequently appeared in the center of the drum. Therefore, the sample dried very quickly before the swollen fibers returned to their original position.

Shrinkage was greater for the knitted shirt because the knitted sample was formed with loops, allowing the yarns in the knitted fabric to move more easily. Shrinkage occurs when a sample is dried while the curvature of the swollen yarns is largely deformed and the yarns are attached to each other.²⁹

Smoothness

As moisture regain of the casual dress shirt sample decreased, smoothness was observed. As for wrinkle recovery, wrinkles were not easily formed in the knit fabric, since the yarns moved easily; therefore, the woven fabric was chosen for wrinkle recovery comparison and identification. In addition, wrinkles rapidly and significantly recovered when the moisture regain dropped below 10%. Initially in a typical drying process, the samples are wrinkled with the swollen fibers, and the pores are filled by the swollen yarns or fibers due to the adsorption of moisture. During the drying procedure, the moisture is evaporated, thereby forming space between the fibers and causing the position to change by the thermal agitation of the dryer.³⁰ The molecular structures, which constitute the cotton fibers, maintain their shapes through their balance with each other based on van der Waals forces and hydrogen bonds. If external stress is applied at this instance, the balance between the forces that maintain the shape of the fibers is broken, and some bonds are disconnected. The disconnected bonds are rearranged in the direction of the stress, and new bonds are formed between the molecules at different positions. Specifically, external forces can easily change the position of hydrogen bonds when cotton fibers are bound by moisture. In this instance, the application of external forces, such as thermal flow and agitation, results in the recovery of the wrinkles in the sample because the rearrangement of the hydrogen bonds continues until a balance is reached.³¹ In addition, the moisture layer on the surface of wet samples induces cohesion between wet samples and agglomeration, making it difficult for hot air to pass through the samples, in contrast to dry samples. Therefore, as the sample movement increases, the cohesive forces between the samples are weakened. As the area of the sample exposed to hot air increases, thermal agitation actively occurs and wrinkle recovery ensues.³²

When the drum rotational speed was varied, the most significant wrinkle recovery was observed at R 50, and higher speeds were observed to be unfavorable for wrinkle recovery. At R 50, the sample had a greater possibility of exposure to hot air, staying near the center of the drum without being attached to the drum wall, and thus increasing the occurrence of rearrangement of hydrogen bonds.³³ Conversely, when the movement of the sample was not active under a small centrifugal force, as in the case of R 35, or when the sample repeatedly showed rotation close to the drum wall under a large centrifugal force, as in the case of R 65, there was no significant wrinkle recovery. This result may be attributed to fewer opportunities for the sample to change the position of the intermolecular bonds formed between or within the fibers due to less active movement.

Damage

The damage to the samples increased as the drying progressed. This is due to the continuous friction between the fibers or the samples due to the mechanical force during the drying process. When the drum rotational speed was varied, the highest damage was observed, interestingly, at R 35. The degree of damage gradually decreased as the rotational speed increased, presenting the lowest damage at R 65. At low speed, the sample and the dummy loads mainly stayed near the bottom of the drum without detaching from each other, and this appears to have caused significant damage by inducing friction between the samples.³⁴

Correlation between sample movement and drying performance

The correlation between the sample movement and the drying performance was analyzed to estimate the effect of the movement of the drying loads on the drying performance. The drying performance was derived through regression using the significant movement indices as independent variables from the Pearson correlation analysis (Supporting information), as shown in Equations (5)–(8) and in Table 4.

Table 4.
Statistical analysis results for regression equations

Standardized coefficient
t-value Significance probability

β

Drying period Constant – 7.105 0.000

Distance from the center of the drum (average change) –3.101 21.252 0.000

Occupied area ^XY (average change) –2.586 6.783 0.000

Occupied area ^YZ (average change) –2.146 2.625 0.015

Total distance moved .150 20.839 0.000

Shrinkage Constant – 1.115 0.275

Appearance area within the 1/2 drum radius 1.243 19.371 0.000

Occupied area ^XY (average change) .990 18.163 0.000

Position factor .750 11.622 0.000

Smoothness Constant – 1.166 0.211

Occupied area ^XY (average change) 2.620 15.161 0.000

Appearance area within the 1/2 drum radius .976 19.767 0.000

The number of tumbling .500 8.787 0.000

Occupied area ^YZ (average change) .413 8.302 0.000

Damage Constant – 1.017 0.225

Distance from the center of the drum (average change) 1.969 2.539 0.022

The number of tumbling .570 10.568 0.000

Appearance frequency .309 3.287 0.004

Speed difference between drum and sample (average change) .048 10.550 0.000

The primary movement indices affecting the drying period were identified as the distance from the center of the drum (average change), occupied area ^XY (average change), occupied area ^YZ (average change), and the total distance moved. The corresponding regression equation has an explanatory power of 97.9%. In particular, the distance from the center of the drum (average change) of the tracing sample was observed to have the highest impact on the drying period. This observation indicates that the drying can be completed in a short period when the entire drying load is spread out to ensure the maximum exposure of the samples to hot air.

The primary factors affecting the shrinkage were the appearance area within the 1/2 drum radius, the occupied area ^XY (average change), and the position factor. The corresponding regression equation has an explanatory power of 97.1%. In particular, the appearance area within the 1/2 drum radius was observed to have the highest impact on the shrinkage. This result indicates that the shrinkage increased with the increased movement of the sample at the center of the tumble dryer, increasing its exposure to the hot air and causing the sample to dry quickly before the yarns and fibers were rearranged to their original position.

The movement indices, which affect the wrinkle recovery, included the occupied area ^XY (average change), the appearance area within the 1/2 drum radius, the number of tumbling cycles, and the occupied area ^YZ (average change). The corresponding regression equation had an explanatory power of 84.6%. The occupied area ^XY (average change) significantly affected the wrinkle recovery, indicating that the spreading and expanding of the drying load, the increasing exposure to hot air, and the thermal agitation improved the wrinkle recovery. In particular, the increase in the number of tumbling cycles and the appearance area within the 1/2 drum radius are inferred to be favorable for wrinkle recovery because they increase the possibility of the folded or wrinkled parts being unfolded, which induces the rearrangement of the hydrogen bonds.³⁵

The movement indices that affect the damage were observed to be the distance from the center of the drum (average change), the number of tumbling cycles, appearance frequency, and speed difference between the drum and the sample (average change). The corresponding regression equation has an explanatory power of 81.5%. Specifically, the distance from the center of the drum (average change) and the appearance frequency had a significant effect, indicating that the damage intensified with the increase in the movement of the samples by changing the locations actively, and thus the mixing of the drying loads increased, inducing the sample friction
$\begin{matrix} • Drying period = - 3.101 x_{1} - 2.586 x_{2} - 2.146 x_{3} \\ + 0. 150 x_{4} (R^{2} = 0. 979) \end{matrix}$
(5)
where x₁ is the distance from the center of the drum (average change), x₂ is the occupied area ^XY (average change)_, x₃ is the occupied area ^YZ (average change), and x₄ is the total distance moved
$\begin{matrix} • Shrinkage = 1.243 x_{1} + 0. 990 x_{2} + 0. 750 x_{3} \\ (R^{2} = 0. 971) \end{matrix}$
(6)
where x₁ is the appearance area within the 1/2 drum radius, x₂ is the occupied area ^XY (average change), and x₃ is the position factor
$\begin{matrix} • Smoothness = 2.620 x_{1} + 0. 976 x_{2} + 0. 500 x_{3} \\ + 0. 413 x_{4} (R^{2} = 0. 846) \end{matrix}$
(7)
where x₁ is the occupied area ^XY (average change), x₂ is the appearance area within the 1/2 drum radius, x₃ is the number of tumbling cycles, and x₄ is the occupied area ^YZ (average change)
$\begin{matrix} • Damage = 1.969 x_{1} + 0. 570 x_{2} + 0. 309 x_{3} + 0.0 48 x_{4} \\ (R^{2} = 0. 815) \end{matrix}$
(8)
where x₁ is the distance from the center of the drum (average change), x₂ is the number of tumbling cycles, x₃ is the appearance frequency, and x₄ is the occupied area ^XY (average change).

Effect of changing the speed and direction of drum rotation on the sample movement

Through the regression analysis, the sample movement in the center of the drum was proven to be essential for drying time, shrinkage, and wrinkle recovery. In addition, the shrinkage rapidly increased and the wrinkles recovered when the moisture regain was less than 10%. To improve the properties of the sample, we combined two different drum rotational speeds and changed the number of drum rotational directions.

Movement patterns of the sample

The movement of the tracing sample and its occupancy inside the drum varied depending on the drum rotational speed. To efficiently dry the loads, the internal space of the dryer must be occupied as much as possible to increase the sample area, which is exposed to the hot air. Consequently, R 50 and R 57.5 were selected since active movement occurred near the center of the drum at these speeds, and the movement was analyzed for both the drum rotational speeds and directions. Figure 5(a) shows that the movement patterns for a combination of drum rotational speeds (R 50/57.5) that were similar to those at singular rotational speeds. However, when the rotational direction was changed along with the rotational speed, the movement of the drying loads increased with the increase in the frequency of the direction change (R 50/57.5(1) < R 50/57.5(9) < R 50/57.5(29)). Specifically, at R 50/57.5(29), the sample passed through various positions around the center of the drum.

Figure 5.
Visualized movement pattern of the sample at the combination of drum rotational speeds (R 50/57.5(0)) and at the combination of drum rotational speeds and direction (R 50/57.5(1), R 50/57.5(9), and R 50/57.5(29)): (a) three-dimensional diagram of the sample movement pattern; (b): two-dimensional (2D) diagram of the sample movement representing occupancy and (c): 2D diagram of the sample movement representing velocity.

Figure 5(b) shows the accumulated occupancy of the sample in the XY and YZ planes. When the rotational speeds were combined (R 50/57.5(0)), the sample was observed most frequently at the position where it was first located. However, as the number of changes in the drum rotational direction increased, the sample became positioned evenly throughout the inside of the drum instead of staying at a specific position.

Figure 5(c) shows the velocity of the sample at each position in the XY plane. At R 50/57.5(0) and R 50/57.5(1), the sample moved at a speed nearly equal to the drum rotational speed at the positions close to the drum wall due to the centrifugal force. However, in the case of R 50/57.5(9) and R 50/57.5(29), the sample did not continuously rotate along the drum wall and fell due to the change in the drum rotational direction, thereby passing through various positions.

Movement patterns representing the outlines of the total drying loads

Figure 6 shows a 2D representation of the outline accumulation of the frames of the total drying loads inside the drum, including the sample and the dummy loads. In the XY plane, the total drying loads filled the internal space of the dryer at R 50/57.5(0) and R 50/57.5(1). For frequent changes in the direction as in the case of R 50/57.5(9) and R 50/57.5(29), the total drying loads were observed to be actively mixed, and they were agglomerated or spread due to several changes in the outlines. When the drum temporarily stopped for a change in direction, we observed that the sample and the dummy loads agglomerated as they fell toward the bottom of the drum, and then they were spread out again by the centrifugal force when the rotation of the drum resumed.

Figure 6.
Visualized movement patterns representing the outlines of the total drying load at the combination of drum rotational speeds (R 50/57.5(0)) and at the combination of drum rotational speeds and direction (R 50/57.5(1), R 50/57.5(9), R 50/57.5(29)).

In the YZ plane, the outline of the total drying loads in the case of R 50/57.5(9) and R 50/57.5(29) fluctuated due to the frequent changes in direction. In particular, there was a clear difference in movement within all the samples; the total drying load fell to the bottom of the drum owing to gravity and spread by centrifugal force as the drum rotated, because the drum stopped temporarily when the direction was changed.

Movement indices

As shown in Figure 7, the varying combination of the drum rotational speeds and the frequent changes in the drum rotational direction resulted in a shorter distance of the sample from the drum center, longer distance from the drum wall, shorter movement distance of the sample center between the frames, and greater speed difference between the drum and the sample, indicating that the sample remained near the center of the drum. The position factor also increased with an increasing number of direction changes, indicating that the sample frequently appeared in the first quadrant, where the sample could ascend and descend, and thus it was frequently exposed to hot air. The appearance area within the 1/2 drum radius and the appearance frequency also increased with the increasing number of directional changes, which resulted in a more frequent appearance of the sample at the center of the drum caused by the forward and backward movement of the sample.

Figure 7.
Movement indices according to changing the speed and direction of drum rotation.

When the combination of different speeds and directions was applied, the appearance area within the 1/2 drum radius, the appearance frequency, the position factor, and the number of tumbling cycles values were higher than those for R 50. This result occurred because the sample appeared most frequently in the center of the drum due to changes to the drum rotational direction, and extensive mixing between the sample and dummy load was evident. Conversely, the occupied area ^XY (average) and the occupied area ^YZ (average) tended to decrease with the increase in the number of direction changes, which can be attributed to the interruption of the continuous movement of the total drying load.

Effect on drying performance according to changes in speed and direction of drum rotation

Drying period and energy consumption

As shown in Figure 8, when different drum rotational speeds were combined from the time at which the moisture regain was less than 10% (R 50/57.5(0)), the drying period was 133 min and energy consumption was 1722.9 Wh at the final stage (moisture regain 3%). When the direction was changed during the combination of drum rotational speeds, the drying period and energy consumption decreased with an increase in the frequency of changes to the rotational direction. In particular, at R 50/57.5(29), the drying period (110 min) and energy consumption (1512.7 Wh) were more than that of R 50 (1409.6 Wh). This increase in energy consumption can be attributed to a decrease in the distance of the sample to the drum when the rotational direction changed, presenting fewer opportunities for exposure to hot air.³⁶

Shrinkage

When two different rotational speeds were combined (R 50/57.5(0)), the shrinkage value demonstrated a synergic effect, shrinking 4.0% at the final stage, which was less than the average shrinkage value of 4.8% for R 57.5 and 11.1% for R 50. For R 50/57.5(0), the sample and dummy load had less possibility of deforming the loops by active movement or being exposed to hot air compared to R 50 because R 57.5 was introduced at the stage when shrinkage intensified. When the combination of different speeds and directions was applied, the shrinkage increased with the increase in the frequency of the rotational direction change in the following order: R 50/57.5(1) (5.9%) < R 50/57.5(9) (7.5%) < R 50/57.5(29) (7.6%). Shrinkage increased with the number of changes in rotational direction because the sample and the dummy loads could move actively by folding, unfolding, and thus deforming the loops, and the loads had greater exposure to hot air by the repeated detachment of the samples due to the directional change.³⁷

Figure 8.
Drying performance according to the change of speed and direction of drum rotation at 3% moisture regain.

Moreover, shrinkage values of the samples exposed to combined rotational speeds and directions were less than that of R 50 at 11.1% because of the mechanical forces that occurred near the end of the drying period. At that point in drying, the moisture in the fibers evaporates and causes de-swelling. To reduce shrinkage, a mechanical force applied to the sample is necessary.³³ However, the drum rotated only clockwise for the R 50, and therefore the mechanical force transmitted to the sample was less than that of the force incurred when the rotating drum changed direction.

Smoothness

At the combination of the rotational speeds (R 50/57.5(0)), relatively low wrinkle recovery was observed, similar to those at the singular drum rotational speeds. It is assumed that the wrinkle recovery was affected by the final rotational speed (R 57.5). In the case of the combined rotational direction and speed, the wrinkle recovery improved with an increase in the frequency of the change in the drum rotational direction. In particular, high wrinkle recovery was observed at R 50/57.5(9)(3.0 grade) and R 50/57.5(29)(4.2 grade) compared to R 50(3.7 grade), indicating that the positions of the hydrogen bonds in the fibers continuously changed through thermal agitation by inducing an increase in tumbling and the appearance frequency of the sample.

Damage

In the case of the combined rotational speeds and rotational direction, damage to the samples intensified as the frequency of changes in direction increased, producing the most damage at R 50/57.5(29). This damage is attributed to substantial friction and interference between the samples by frequent changes in direction.³⁸ Moreover, the combination of the drum rotational speeds and the frequent changes in the drum rotational direction resulted in a shorter distance of the sample from the drum center, thereby inducing the mixing between the samples.

Conclusion

In this study, fabric movement as a function of drying conditions was analyzed. Consequently, a drying program was proposed to improve the drying performance based on the movement of the samples exposed to the various conditions of our study. When the drum rotational speed was altered, the most active movement near the center of the drum was observed at 50 rpm, representing a short distance from the center of the drum, a large appearance area within the 1/2 drum radius, and a high position factor. The time required to finish drying the samples was shortest and the wrinkle recovery was excellent at this rotational speed, but these samples exhibited the highest shrinkage and damage. We also determined that these fabric properties, including shrinkage, began to change drastically when the moisture regain decreased to 10%. Through regression analysis, we identified the influential fabric movements affecting shrinkage, wrinkle recovery, and damage. New drying conditions were then suggested wherein the mechanical force transferred to the fabric was varied by changing the number of times that the drum rotational direction was reversed between clockwise and counter-clockwise. The drum rotational speed was then adjusted to 57.5 rpm when moisture regain was less than 10%. Subsequently, the direction in addition to the speed were altered in the region of the moisture regain below 10% to induce more active movement. Shrinkage was reduced by 32.4% and wrinkle recovery were improved by 13.5% when the drum rotating direction changed once every 2 s (R50/5.5(29)).

In the second stage of the research, the drying performance was derived through the regression analysis using significant movement indices as independent variables. Using this analysis method, we observed improved drying when the active movement near the center of the drum and the spreading or expanding of the drying loads within the drum space increased the possibility of exposing the sample to hot air, which changed the positions of the fibers or the yarns until the drying was completed. This study proposes a drying program that can enhance the comprehensive drying performance via active and diverse movements through a combination of rotational speed and directional changes. The results of this research can ultimately satisfy consumer needs and can be applied to sustainable industrial supply chains.

Further research is required to design a drying program to improve fabric drying performance and energy efficiency by analyzing the temperature and humidity in the drum during the total drying process. Thereafter, a more practical drying program should be developed by accelerating heat and mass transfer under the controlled temperature of the heater and varying airflow rate and velocity.

Trait	Description
Type	T-shirts	Casual dress shirt
Fiber content	Cotton 100%
Weave type	Knit	Woven
Thickness (mm)	0.57 $\pm$ 0.02	0.36 $\pm$ 0.01
Conditioned mass per piece (g)	120.0 $\pm$ 3.0	289.9 $\pm$ 2.0

Codes	Drum rotation speed (rpm)	The cycle of changing the drum rotational direction in 60 s	The number of drum rotational direction changes in 60 s	Schematic diagram
R 35	35	Clockwise 60 s	0
R 50	50
R 57.5	57.5
R 65	65
R50/57.5(0)	50	57.5	Clockwise 60 s	0
R50/57.5(1)	50	57.5	Clock-wise 30 s/counter-clockwise 30 s	1
R50/57.5(9)	50	57.5	Clock-wise 6 s/counter-clockwise 6 s	9
R50/57.5(29)	50	57.5	Clock-wise 2 s/counter-clockwise 2 s	29

		Standardized coefficient	t-value	Significance probability
Drying period	Constant	–	7.105	0.000
Distance from the center of the drum (average change)	–3.101	21.252	0.000
Occupied area ^XY (average change)	–2.586	6.783	0.000
Occupied area ^YZ (average change)	–2.146	2.625	0.015
Total distance moved	.150	20.839	0.000
Shrinkage	Constant	–	1.115	0.275
Appearance area within the 1/2 drum radius	1.243	19.371	0.000
Occupied area ^XY (average change)	.990	18.163	0.000
Position factor	.750	11.622	0.000
Smoothness	Constant	–	1.166	0.211
Occupied area ^XY (average change)	2.620	15.161	0.000
Appearance area within the 1/2 drum radius	.976	19.767	0.000
The number of tumbling	.500	8.787	0.000
Occupied area ^YZ (average change)	.413	8.302	0.000
Damage	Constant	–	1.017	0.225
Distance from the center of the drum (average change)	1.969	2.539	0.022
The number of tumbling	.570	10.568	0.000
Appearance frequency	.309	3.287	0.004
Speed difference between drum and sample (average change)	.048	10.550	0.000

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by LG Electronics Co., Ltd (grant number 350-20190050).

ORCID iDs

Sungmin Kim

Chung Hee Park

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