The effect of fabric movement on washing performance in a front-loading washer III: Focus on the optimized movement algorithm

Abstract

The objectives of this study were to investigate the correlation between fabric movement and washing efficiency in a front-loading washer and to make an algorithm for improving washing efficiency by optimizing fabric movements. A regression model between fabric movement and washing efficiency was made using 14 movement indexes. The angle change of the fabric gravity center, the speed difference between the drum and the fabric, and the shape factor were found to be determining factors for washing efficiency. Various kinds of wash spin speed were employed for making a complex movement algorithm, since it was found that turbulent or complex movement improves the washing efficiency. The optimal algorithm saved energy (25%) and time (27%), as well as achieving higher washing efficiency (4.8%).

Keywords

front-loading washer fabric movement fabric movement index washing efficiency complex movement

Mechanical action, chemical action, time, and temperature are four factors in the washing process that constitute the so-called as Sinner’s Circle, which was utilized to explain the basic principles of cleaning by Sinner. ^1–3 Among them, mechanical action is normally controlled by the washer through washing time, wash spin speed, and reversing rhythm. When the washer changes the mechanical actions, the fabric movement in the washer also changes, and the changed movements affect washing efficiency.^4,5

However, many studies were not focused on the mechanical actions within washing systems, and there is no enough understanding of the effects of fabric movement on washing efficiency. Thus, washing effects are considered difficult to explain exactly in respect of the mechanical washing mechanism, such as fabric movements, mechanical action by the washers, water flow dynamics, and so on. It eventually causes difficulties in explaining the overall washing mechanism, such as new washing methods,^6–9 washing evaluation methods,^10–14 and simulations on washing.^15–20 Therefore, there is a need for research on the effects of mechanical action, such as fabric movement on washing efficiency, for better understanding the overall washing mechanism.

In previous studies, Yun et al.²¹ and Yun and Park²² analyzed the force intervening in fabric movement in a front-loading washer, by changing the type of fabric, size of fabric, number of fabrics, and wash spin speed, in order to examine the effects of fabric movement on washing efficiency. Fabric movement in a front-loading washer was categorized as “sliding”, “falling”, and “rotating”. These categories were explained and were determined by the balance among centrifugal force received from the washer, frictional force of fabrics, and gravitational force. It was revealed that complex movement, which is comprised of various movements such as sliding, falling, and rotating, was advantageous for washing efficiency.

In this study, regression analysis was conducted on fabric movement that affected washing efficiency. Furthermore, by reflecting the results of the regression analysis, the final goal was to propose an algorithm for improving washing efficiency by finding conditions that could optimize fabric movement.

Experimental details

Specimens

Two types of polyester fabrics and two types of cotton fabrics that showed consistent behavior in fabric movement patterns in previous studies were used.^21,22 The characteristics of each specimen are shown in Table 1. The fabric sizes were differentiated as 20 cm × 40 cm, 40 cm × 40 cm, 40 cm × 80 cm, and 80 cm × 80 cm, and the number of fabrics was also set differently, as one, two, and eight pieces. Water contents were measured by the modified KS C IEC 60456 and coefficient of friction was measured by the Kawabata Evaluation System.^21–23
Table 1.
Characteristics of specimens

ID Characteristics P1 P2 C1 C2

Fiber content Polyester 100% Polyester 100% Cotton 100% Cotton 100%

Weave type Plain Waffle Honeycomb Oxford

Weight (g/m²) 38.7 186.7 141.2 289.1

Thickness (mm) 0.065 0.628 0.555 0.700

Water contents (%) 59.2 125.0 306.8 63.6

MIU (Coefficient of friction, –) 0.140 0.196 0.291 0.340

Washer

For easier observation of the fabric movement, the front/right-hand side/top of a front-loading washer (Samsung Electronics, WW-135UV; maximum capacity 13 kg) were converted to use. Programs to adjust the wash spin speed and the motor on/off time of the washer were received from Samsung Electronics.

Evaluation of fabric movements

Before observing movement, the specimens were soaked in water for 20 minutes to be similar in condition to washed fabrics. A total of 6.0 l of water was added for evaluating fabric movement.

Recording and analyzing the fabric movements

A high-speed camera, XS-4 (X-Stream™, IDT Co. Ltd), was used to record the fabric movement and it was recorded as the washer spun in the counter-clockwise direction. Each fabric movement was analyzed for 13 seconds, which was for 10 spins at 46 rpm. A total of five video recordings were taken for each sample, out of which the most typical video was selected from analysis by a panel of three independent evaluators, based on the types and frequency of fabric movements.

In order to analyze the fabric movement, the outlines of the fabric that appeared in the video, which was filmed with a high-speed camera, were traced using the outline-tracker functions of TEMA Motion (Image Systems Co., Ltd). Twenty frames per second and a total of 260 frames were tracked and analyzed for each sample.

For digitizing the fabric movement, the coordinate system shown on the right-hand side of Figure 1 was generated based on the center of the washer two points (Ref #1, #2) shown on the left-hand side of Figure 1. The center of the washer was set as the origin of the coordinate system, and two points where the length can be measured were used to convert length in the video. The center of gravity of the fabric was determined by connecting the outermost point of the up, down, left, and right points in the traced outline.
Figure 1.
Coordinate system for analysis of fabric movements.²¹

Fabric movement index

In order to analyze the correlation between fabric movement and washing efficiency, it was necessary to establish an index system for the various fabric movements. After supplementing the fabric movement indexes created in preceding studies,^21,23 they were utilized to analyze the correlation between fabric movement and washing efficiency.

The fabric movement index was categorized into three groups based on the center of gravity of the fabric, outline, and fabric movement. For a fabric movement index based on the center of gravity of the fabric, it included distance from the center of the drum, angle change of the fabric gravity center, speed difference between the drum and fabric, and total distance moved. Outline length, fabric area, shape factor, and number of unfolding were included in the movement index that was based on the outline. The number of sliding over the lifter, number of turnover, number of falling, number of rotating, position factor, and group index were included in the fabric movement index based on movement. The conceptual diagram and description for each fabric movement index is shown in Table 2.
Table 2.
Fabric movement indexes²¹

Name/description Concept map Name/description Concept map

1 Distance from the center of the drum 2 Angle change of the center of gravity

Distance between the center of the drum and the center of gravity of the fabric Changes in the angle of the fabric center of gravity between frames

3 Speed difference between drum and fabric 4 Total distance moved

Difference between the spinning speed of the drum and fabric moving speed Total length of the traces of the fabric center of gravity

5 Outline length 6 Fabric area

Outline length of the fabric Area created by the fabric outlines

7 Shape factor 8 Number of unfolding

Value of dividing the fabric area with the outline length Number of being folded (number of peaks in the graph for the fabric area)

9 Number of sliding 10 Number of turnover

Number of sliding from right to left of the lifter Number of being turned over by the lifter

11 Number of falling 12 Number of rotating

Number of being dropped by the lifter Number of rotating with the lifter

13 Position factor 14 Group index

Values from dividing the number of appearances of the fabric center of gravity in the second quadrant with the number of appearances in the fourth quadrant Time ratio of being divided into several groups

Evaluation of washing efficiency

Washing conditions

EMPA 106 was purchased from Testfabrics Inc. (415 Delaware Ave, West Pittston, PA 18643, USA) and cut into size of 5 cm × 10 cm. EMPA 106 was soiled with carbon black and mineral oil and could indicate mechanical effects well.²⁴

Tap water supplied to the lab was used after being set at 15℃, and the amount of water used at this time was 9.5 l.

“Persil” powder detergent by Henkel Company was used according to recommended usage (1.75 g/l). The detergent was completely dissolved prior to the test, at 15℃ and 0.5 l of water. The washing time for the washing efficiency evaluation was set at 30 minutes. EMPA swatches were rinsed lightly by hand three times, and then they were air-dried for 24 hours.

Measurement of reflectance

In order to evaluate washing efficiency, the spectrophotometer (MINOLTA, CM-2600d; Observer conditions – 10 degrees, Illuminant conditions – D65) and the analysis program (MINOLTA, Spectra Magic) were utilized to measure the reflectance. The reflectance of the soiled fabric was measured before and after washing.

Using the Kubelka–Munk equation in (1), the reflectance was converted to K/S values and the washing efficiency was calculated using formula (2):
$K / S = \frac{(1 - R) 2}{2 R}$
(1)
where R is reflectance, K is the absorption coefficient, and S is the scattering coefficient.
$D = \frac{(K / S) s - (K / S) w}{(K / S) s - (K / S) o} \times 100$
(2)
where D is washing efficiency, (K/S) _s is the K/S value of the soiled strip, (K/S) _w is the K/S value of the washed strip, and (K/S) _o is the K/S value of the unsoiled strip.

Tests for determining the washing efficiency were repeated three times for each test condition, and the mean value was used.

Measurement of power consumption

The power consumption during washing was measured using a powermeter (WT210, Yokogawa).

Statistical analysis

In order to analyze the correlation between fabric movement and washing efficiency, PASW Statistics 18 was used. Significant fabric movement indexes were chosen by stepwise regression analysis, and these were set as the independent variable, while washing efficiency was set as the dependent variable to make the regression analysis.

Results and discussion

Fabric movement index

Fourteen fabric movement indexes were examined with interchanging the fabric type, fabric size, number of fabrics, and wash spin speed, and the results for main fabric movement indexes are shown in Table 3. For several fabric movement indexes, in addition to the average and standard deviation, the average change was also used to examine the instantaneous changes that occurred in the fabric. The average change refers to the average of the absolute value of the change (Δy), and it can show how much change occurred between the neighboring frames.
Table 3.
Main fabric movement index values

Indexes Factors
Angle change of the center of gravity
Speed difference between drum and fabric
Shape factor

AVG
STD Change AVG STD Change AVG STD Change

Specimen Size No. of Sheets Wash spin speed [degree] [cm/s] [ratio]

P1 2040 1 46 0.1 4.7 3.9 99.6 18.6 17.9 0.152 0.040 0.029

4040 1 46 0.0 4.9 4.0 99.9 17.8 17.9 0.128 0.025 0.019

4080 1 32 0.2 5.6 4.5 59.2 21.6 14.2 0.115 0.025 0.012

4080 1 46 –0.1 4.8 4.1 100.3 15.7 15.8 0.118 0.023 0.014

4080 1 60 0.1 4.8 4.0 142.2 15.9 17.4 0.132 0.021 0.017

4080 2 46 0.1 5.2 4.3 101.4 18.3 17.9 0.071 0.009 0.006

4080 8 46 0.0 13.9 6.8 93.1 31.3 20.8 0.028 0.004 0.002

8080 1 46 0.1 4.8 4.1 102.5 15.5 15.7 0.103 0.010 0.007

P2 2040 1 46 0.1 4.2 3.5 104.0 15.3 14.4 0.207 0.038 0.027

4040 1 46 0.0 6.0 4.9 96.7 21.2 15.2 0.173 0.031 0.019

4080 1 32 2.9 17.1 10.0 33.6 20.3 14.7 0.148 0.032 0.012

4080 1 46 4.1 10.4 8.7 77.7 31.5 16.0 0.177 0.022 0.013

4080 1 60 12.2 14.3 15.7 73.7 41.5 15.0 0.168 0.037 0.014

4080 2 46 7.8 16.6 12.9 60.0 34.1 17.5 0.106 0.019 0.008

4080 8 46 2.9 22.1 12.9 78.9 23.9 14.7 0.045 0.006 0.003

8080 1 46 8.3 12.7 11.8 65.5 35.8 14.1 0.151 0.026 0.010

C1 2040 1 46 0.0 4.0 3.1 107.3 17.1 14.2 0.156 0.030 0.025

4040 1 46 4.2 9.6 7.8 79.4 34.5 18.2 0.135 0.027 0.016

4080 1 32 6.1 17.2 10.0 29.4 20.3 14.7 0.120 0.029 0.012

4080 1 46 10.2 9.4 12.0 54.1 33.1 15.2 0.134 0.021 0.012

4080 1 60 17.9 5.4 18.0 53.5 29.2 12.9 0.126 0.020 0.009

4080 2 46 8.5 14.2 11.8 62.0 32.5 16.8 0.079 0.012 0.005

4080 8 46 13.7 16.4 16.0 39.5 33.6 15.7 0.025 0.002 0.001

8080 1 46 10.1 13.5 12.7 53.9 31.2 14.9 0.109 0.014 0.007

C2 2040 1 46 6.9 11.0 9.8 68.7 34.3 16.0 0.199 0.044 0.021

4040 1 46 13.7 5.1 13.8 40.8 27.9 11.8 0.157 0.023 0.011

4080 1 32 8.5 14.9 11.1 30.6 19.7 13.1 0.154 0.039 0.013

4080 1 46 13.8 6.5 13.8 45.7 28.5 13.9 0.162 0.020 0.009

4080 1 60 17.9 3.0 18.0 12.1 14.7 8.9 0.144 0.017 0.007

4080 2 46 12.8 10.6 13.9 46.4 30.6 12.5 0.088 0.013 0.004

4080 8 46 5.7 18.2 13.6 81.6 28.5 19.0 0.036 0.007 0.003

8080 1 46 13.8 6.5 13.9 83.9 36.8 14.0 0.124 0.008 0.005

Angle change of fabric gravity center

The angle made by connecting the origin and the center of gravity for one frame and the next frame was named as “the angle change of fabric gravity center”. There was a small angle change resulting from sliding movement, while there was a large angle change resulting from rotating. Furthermore, a complex movement exhibited large values of the standard deviation and average change of the angle, where falling was the main movement mixed with minor movement of sliding and rotating. However, single movement of only sliding or rotating showed small values of the standard deviation and average change of the angle. This is because only one movement was repeated for single movement, while there were various changes of direction due to tumbling and falling in complex movement.

Speed difference between drum and fabric

Large values of standard deviation and average change of the speed difference between the drum and fabric mean complex movement. Sliding occurs only at one position regardless of drum rotation, and shows the largest speed difference. Rotating is the movement that moves together with the lifter and thus exhibits the lowest speed difference. However, as for the standard deviation of the speed difference, single movement where only sliding or rotating movement is repeated at a constant speed represented very low values of standard deviation. In complex movement conditions in which falling is the main movement with both sliding and rotating, the average change of speed differences were found to be the largest.

Shape factor

The shape factor was defined as the value of the fabric area divided with the outline length. In order to eliminate effects of fabric size and the number of fabrics, the shape factor was normalized so as for the completely unfolded fabric to have the value of “one”. The standard deviation of the shape factor increases when there is a lot of folding and unfolding movement, which occurs during the tumbling and turnover movements.

Correlation between fabric movement and washing efficiency

In order to examine the effects of fabric movement on washing efficiency, a regression model between fabric movement and washing efficiency was made, employing the values of the preceding study for washing efficiency.²²

When using washing efficiency as the dependent variable, the factors that could be used as independent variables were grouped into three levels. The first variables are the fabric absorption weight, friction coefficient, and wash spin speed, which are related to the centrifugal force, frictional force, and gravitational force, affecting the fabric movement in a front-loading washer.²² The second level is the value that expresses the fabric movement changed by the three forces. They are the angle change of fabric gravity center, moved distance, speed difference, distance from the center of the drum, outline length, and fabric area. The third variables are associated movements such as sliding, turnover, falling, rotating, and unfolding. When conducting the stepwise regression analysis by setting all of the variables of the three levels as independent variables, a regression model was made with independent variables in the second level. While the first level and the third level represent just one movement, angle change, moved distance, distance from the center of drum, outline length, and fabric area can represent all movements that occur in washing process, and they are assumed to be significant for washing efficiency.

Standard deviation of angle change of the fabric gravity center, standard deviation of speed difference between the drum and fabric, and average change/standard deviation/average of the shape factor were shown as the significant fabric movement indexes in the regression equation for washing efficiency. The results for model summary and coefficients of the regression analysis are shown in Table 4. The regression equation for the washing efficiency is as follows:
$Washingefficiency = 27.503 + 1.214 * x 1 + 0.205 * x 2 + 730.892 * x 3 - 551.579 * x 4 + 73.918 * x 5$
(3)
where x₁ is the angle change of the fabric gravity center (standard deviation), x₂ is the speed difference between the drum and fabric (standard deviation), x₃ is the shape factor (average change), x₄ is the shape factor (standard deviation), and x₅ is the shape factor (average) (adjusted R²= 0.743).
Table 4.
Regression analysis results for washing efficiency

(a) Model summary

Adjusted R square df1 df2 Sig. F change

.743
1 26 .013

(b) Coefficient

Unstandardized coefficient

Model
B Std. error t Sig.

(Constant) 27.503 3.199 8.597 .000

Angle change of the center of gravity (standard deviation) 1.214 .168 7.234 .000

Speed difference between drum and fabric (standard deviation) .205 .084 2.446 .022

Shape factor (average change) 730.892 182.684 4.001 .000

Shape factor (standard deviation) –551.579 148.429 –3.716 .001

Shape factor (average) 73.918 27.795 2.659 .013

The standard deviation of the angle change of the fabric gravity center, standard deviation of the speed difference between the drum and fabric, and the average change and average value of the shape factor had positive correlations with washing efficiency, while the standard deviation for shape factor had a negative correlation. As shown in Table 3, complex movement, which is comprised of various movements such as sliding, falling, and rotating, showed the high values of the standard deviation of the angle change of the fabric gravity center and the speed difference between the drum and fabric, which was therefore assumed to have a positive correlation with washing efficiency. It was judged that for the shape factor, all three values, average, standard deviation, and average change, affected washing efficiency, as can be seen in the regression equation. The sum of the three values reflecting the coefficient for the shape factor showed positive in all 32 test conditions and, therefore, it can be said that the shape factors also have a positive correlation with washing efficiency. Because shape factor expresses the folding or unfolding movement of fabrics and the change between them, large values for the shape factor mean various movements associated with more chances for flexing, and thus resulting in higher washing efficiency. When judging by the significance level of the t-value, the standard deviation of the angle change of the fabric gravity center and the average change of the shape factor were found to be the most influential variables. It was revealed that washing efficiency increased as there were greater changes in the angle change of the fabric gravity center and the shape factor when various fabric movements appeared. In order to improve washing efficiency by control of the fabric movement, therefore, it was necessary to make the fabric movement complex.

Improvement effects by complex movement algorithm

Complex movement algorithm

In order to improve the washing efficiency of existing algorithms that are susceptible to simple movement due to their makeup of just one reversing rhythm and wash spin speed, a washing efficiency improvement algorithm was proposed. The new algorithm had different motor on/off time and wash spin speed in CW1 (clockwise)→CCW1 (counter-clockwise)→CW2 →CCW2→CW3→CCW3. This was intended to achieve large values for the standard deviation of speed difference between the drum and fabrics, angle change of the fabric gravity center, and the shape factor, which are the influential variables in the regression equation. The conventional algorithm and proposed algorithm examples are shown in Figures 2 and 3.
Figure 2.
Conventional algorithm.

Figure 3.
Example of proposed algorithm for improving washing efficiency.

However, in the comparison test, the motor on/off time was set as 30 seconds on, 4 seconds off, like the conventional algorithm, so as to examine only the effects of complex movement on washing efficiency.

Based on 32, 46, and 60 rpm, which were confirmed to have an effect on fabric movement and washing efficiency,²² three sets of wash spin speed combinations were proposed. The three proposed combinations were: 42 – 46 – 50 rpm, 38 – 46 – 54 rpm, and 34 – 46 – 58 rpm. The conventional algorithm is comprised of the same wash spin speed: 46 – 46 – 46 rpm.

Washing efficiency of the proposed algorithm

In the case of a single movement, the fabric movement was limited and the position of the fabric where mechanical force was applied did not change, thus limiting the force that the fabric received from the washer. However, in the case of a complex movement, the movement of fabrics was diverse and the position of the fabric that received mechanical force also changed continuously, thus making washing efficiency higher.^21,22 The proposed algorithm made fabric movement complex with various wash spin speeds. The washing efficiency for the proposed algorithm is shown in Figure 4. It was assumed that the improved algorithm exhibited better washing efficiency possibly because complex movement occurred as the centrifugal force that the fabric received from the washer became more diverse. The algorithm of 34 – 46 – 58 rpm that combines the slowest and fastest spin speed and thus is expected to involve single movements, such as sliding or rotating movement, had the lowest washing efficiency among the improved algorithms.²²
Figure 4.
Comparison of washing efficiency between the conventional and proposed algorithm. (Number of sheets is eight: P1, two sheets, P2, two sheets, C1, two sheets, and C2, two sheets; fabric size: 40 cm × 80 cm.)

In the case of 38 – 46 – 54 rpm, the washing efficiency was 58.4%, showing an improved effect of washing efficiency of 4.8% (2.7%p) when compared with the conventional algorithm. Thus, it was concluded that the 38 – 46 – 54 rpm combination of wash spin speed was the optimal complex movement algorithm within this test condition.

Effectiveness verification of the proposed algorithm

In order to verify the effectiveness of the optimized movement algorithm under various conditions, the washing efficiency of the proposed algorithm and that of the conventional algorithm were compared using four fabrics that showed the different movements in the preceding studies.^21–23 As shown in Figure 5, the optimized movement algorithm exhibited higher washing efficiency than the conventional algorithm in all fabrics. It was proved that various kinds of wash spin speed employed for the proposed algorithm made the fabric movement more complex, and that the complex movement was advantageous for washing efficiency under various washing conditions.
Figure 5.
Verification of the proposed algorithm using four fabric samples. (Number of sheets is eight; fabric size: 40 cm × 80 cm.)

Effects on saving wash time and energy use

In order to examine the time and energy saving effect, the wash time of the complex movement algorithm was differentiated to 15/20/25/30 minutes. The results are shown in Figure 6.
Figure 6.
Washing efficiency of the optimal algorithm by wash time. (Number of sheet is eight: P1, two sheets, P2, two sheets, C1, two sheets, and C2, two sheets; fabric size; 40 cm × 80 cm.)

With the increase in washing time, washing efficiency also increased, but when wash time passed 25 minutes, the washing efficiency leveled off. The trend line and equation achieved from these results are shown in Figure 6. When calculating the wash time with the formula on the trend line, it needed 22 minutes for the optimal algorithm to have similar washing efficiency to the conventional algorithm. Therefore, using the optimal algorithm, washing was performed for 22 minutes, and then the washing efficiency, wash time, and power consumption were compared with the results of the conventional algorithm. The results for these are shown in Table 5.
Table 5.
Comparison of washing efficiency, wash time, and power consumption between the conventional and proposed algorithm. (Number of sheets is eight: P1, two sheets, P2, two sheets, C1, two sheets, and C2, two sheets; fabric size: 40 cm× 80 cm.)

Algorithm Measurement Conventional Proposed for

Efficiency Better performance

Wash time (min) 30 22 30

Washing efficiency (%) 55.7 56.0 58.4

Power consumption (Wh) 29.6 22.2 30.0

When washing for 22 minutes using the proposed optimal algorithm, washing efficiency was maintained at similar levels, while washing time was reduced by 8 minutes (27%) and energy consumption by 7.4 Wh (25%).

Conclusion

Effects of fabric movement on washing efficiency were examined using regression analysis. Through this, fabric movements causing high washing efficiency were found, and they were used to propose a washing efficiency improvement algorithm.

The angle change of the fabric gravity center, speed difference between the drum and fabrics, and shape factor were selected as the significant fabric movement indexes. The standard deviation of the angle change of the fabric gravity center and the average change of the shape factor were found to be influential independent variables for washing efficiency. Through the regression analysis, it was confirmed that the fabric movement had direct effects on washing efficiency.

An algorithm that combines a number of wash spin speeds was proposed to improve washing efficiency through diversifying fabric movement in the washer. The proposed complex movement algorithm showed higher washing efficiency when compared to the conventional algorithm, and the combination of wash spin speeds that showed the highest washing efficiency was 38 – 46 – 54 rpm, and it showed a washing efficiency improvement effect of 4.8%. The complex movement algorithm also exhibited a saving effect of 25% energy and 27% wash time, while achieving similar washing efficiency with the existing algorithm.

ID Characteristics	P1	P2	C1	C2
Fiber content	Polyester 100%	Polyester 100%	Cotton 100%	Cotton 100%
Weave type	Plain	Waffle	Honeycomb	Oxford
Weight (g/m²)	38.7	186.7	141.2	289.1
Thickness (mm)	0.065	0.628	0.555	0.700
Water contents (%)	59.2	125.0	306.8	63.6
MIU (Coefficient of friction, –)	0.140	0.196	0.291	0.340

Name/description	Concept map	Concept map
1	Distance from the center of the drum	2	Angle change of the center of gravity
Distance between the center of the drum and the center of gravity of the fabric	Changes in the angle of the fabric center of gravity between frames
3	Speed difference between drum and fabric	4	Total distance moved
Difference between the spinning speed of the drum and fabric moving speed	Total length of the traces of the fabric center of gravity
5	Outline length	6	Fabric area
Outline length of the fabric	Area created by the fabric outlines
7	Shape factor	8	Number of unfolding
Value of dividing the fabric area with the outline length	Number of being folded (number of peaks in the graph for the fabric area)
9	Number of sliding	10	Number of turnover
Number of sliding from right to left of the lifter	Number of being turned over by the lifter
11	Number of falling	12	Number of rotating
Number of being dropped by the lifter	Number of rotating with the lifter
13	Position factor	14	Group index
Values from dividing the number of appearances of the fabric center of gravity in the second quadrant with the number of appearances in the fourth quadrant	Time ratio of being divided into several groups

Indexes Factors	Angle change of the center of gravity	Speed difference between drum and fabric	Shape factor
P1	20*40	1	46	0.1	4.7	3.9	99.6	18.6	17.9	0.152	0.040	0.029
40*40	1	46	0.0	4.9	4.0	99.9	17.8	17.9	0.128	0.025	0.019
40*80	1	32	0.2	5.6	4.5	59.2	21.6	14.2	0.115	0.025	0.012
40*80	1	46	–0.1	4.8	4.1	100.3	15.7	15.8	0.118	0.023	0.014
40*80	1	60	0.1	4.8	4.0	142.2	15.9	17.4	0.132	0.021	0.017
40*80	2	46	0.1	5.2	4.3	101.4	18.3	17.9	0.071	0.009	0.006
40*80	8	46	0.0	13.9	6.8	93.1	31.3	20.8	0.028	0.004	0.002
80*80	1	46	0.1	4.8	4.1	102.5	15.5	15.7	0.103	0.010	0.007
P2	20*40	1	46	0.1	4.2	3.5	104.0	15.3	14.4	0.207	0.038	0.027
40*40	1	46	0.0	6.0	4.9	96.7	21.2	15.2	0.173	0.031	0.019
40*80	1	32	2.9	17.1	10.0	33.6	20.3	14.7	0.148	0.032	0.012
40*80	1	46	4.1	10.4	8.7	77.7	31.5	16.0	0.177	0.022	0.013
40*80	1	60	12.2	14.3	15.7	73.7	41.5	15.0	0.168	0.037	0.014
40*80	2	46	7.8	16.6	12.9	60.0	34.1	17.5	0.106	0.019	0.008
40*80	8	46	2.9	22.1	12.9	78.9	23.9	14.7	0.045	0.006	0.003
80*80	1	46	8.3	12.7	11.8	65.5	35.8	14.1	0.151	0.026	0.010
C1	20*40	1	46	0.0	4.0	3.1	107.3	17.1	14.2	0.156	0.030	0.025
40*40	1	46	4.2	9.6	7.8	79.4	34.5	18.2	0.135	0.027	0.016
40*80	1	32	6.1	17.2	10.0	29.4	20.3	14.7	0.120	0.029	0.012
40*80	1	46	10.2	9.4	12.0	54.1	33.1	15.2	0.134	0.021	0.012
40*80	1	60	17.9	5.4	18.0	53.5	29.2	12.9	0.126	0.020	0.009
40*80	2	46	8.5	14.2	11.8	62.0	32.5	16.8	0.079	0.012	0.005
40*80	8	46	13.7	16.4	16.0	39.5	33.6	15.7	0.025	0.002	0.001
80*80	1	46	10.1	13.5	12.7	53.9	31.2	14.9	0.109	0.014	0.007
C2	20*40	1	46	6.9	11.0	9.8	68.7	34.3	16.0	0.199	0.044	0.021
40*40	1	46	13.7	5.1	13.8	40.8	27.9	11.8	0.157	0.023	0.011
40*80	1	32	8.5	14.9	11.1	30.6	19.7	13.1	0.154	0.039	0.013
40*80	1	46	13.8	6.5	13.8	45.7	28.5	13.9	0.162	0.020	0.009
40*80	1	60	17.9	3.0	18.0	12.1	14.7	8.9	0.144	0.017	0.007
40*80	2	46	12.8	10.6	13.9	46.4	30.6	12.5	0.088	0.013	0.004
40*80	8	46	5.7	18.2	13.6	81.6	28.5	19.0	0.036	0.007	0.003
80*80	1	46	13.8	6.5	13.9	83.9	36.8	14.0	0.124	0.008	0.005

(a) Model summary
.743	1	26	.013
(b) Coefficient
	Unstandardized coefficient
Model	B	Std. error	t	Sig.
(Constant)	27.503	3.199	8.597	.000
Angle change of the center of gravity (standard deviation)	1.214	.168	7.234	.000
Speed difference between drum and fabric (standard deviation)	.205	.084	2.446	.022
Shape factor (average change)	730.892	182.684	4.001	.000
Shape factor (standard deviation)	–551.579	148.429	–3.716	.001
Shape factor (average)	73.918	27.795	2.659	.013

Algorithm Measurement	Conventional	Proposed for
Wash time (min)	30	22	30
Washing efficiency (%)	55.7	56.0	58.4
Power consumption (Wh)	29.6	22.2	30.0

Footnotes

Funding

This work was supported by the BK21 Plus project of the National Research Foundation of Korea Grant funded by the Korean Government and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.2015R1A2A2A03002760).

Declaration of conflicting interests

The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Indexes Factors				Angle change of the center of gravity			Speed difference between drum and fabric			Shape factor
Indexes Factors				AVG	STD	Change	AVG	STD	Change	AVG	STD	Change
Specimen	Size	No. of Sheets	Wash spin speed	[degree]			[cm/s]			[ratio]
P1	20*40	1	46	0.1	4.7	3.9	99.6	18.6	17.9	0.152	0.040	0.029
	40*40	1	46	0.0	4.9	4.0	99.9	17.8	17.9	0.128	0.025	0.019
	40*80	1	32	0.2	5.6	4.5	59.2	21.6	14.2	0.115	0.025	0.012
	40*80	1	46	–0.1	4.8	4.1	100.3	15.7	15.8	0.118	0.023	0.014
	40*80	1	60	0.1	4.8	4.0	142.2	15.9	17.4	0.132	0.021	0.017
	40*80	2	46	0.1	5.2	4.3	101.4	18.3	17.9	0.071	0.009	0.006
	40*80	8	46	0.0	13.9	6.8	93.1	31.3	20.8	0.028	0.004	0.002
	80*80	1	46	0.1	4.8	4.1	102.5	15.5	15.7	0.103	0.010	0.007
P2	20*40	1	46	0.1	4.2	3.5	104.0	15.3	14.4	0.207	0.038	0.027
	40*40	1	46	0.0	6.0	4.9	96.7	21.2	15.2	0.173	0.031	0.019
	40*80	1	32	2.9	17.1	10.0	33.6	20.3	14.7	0.148	0.032	0.012
	40*80	1	46	4.1	10.4	8.7	77.7	31.5	16.0	0.177	0.022	0.013
	40*80	1	60	12.2	14.3	15.7	73.7	41.5	15.0	0.168	0.037	0.014
	40*80	2	46	7.8	16.6	12.9	60.0	34.1	17.5	0.106	0.019	0.008
	40*80	8	46	2.9	22.1	12.9	78.9	23.9	14.7	0.045	0.006	0.003
	80*80	1	46	8.3	12.7	11.8	65.5	35.8	14.1	0.151	0.026	0.010
C1	20*40	1	46	0.0	4.0	3.1	107.3	17.1	14.2	0.156	0.030	0.025
	40*40	1	46	4.2	9.6	7.8	79.4	34.5	18.2	0.135	0.027	0.016
	40*80	1	32	6.1	17.2	10.0	29.4	20.3	14.7	0.120	0.029	0.012
	40*80	1	46	10.2	9.4	12.0	54.1	33.1	15.2	0.134	0.021	0.012
	40*80	1	60	17.9	5.4	18.0	53.5	29.2	12.9	0.126	0.020	0.009
	40*80	2	46	8.5	14.2	11.8	62.0	32.5	16.8	0.079	0.012	0.005
	40*80	8	46	13.7	16.4	16.0	39.5	33.6	15.7	0.025	0.002	0.001
	80*80	1	46	10.1	13.5	12.7	53.9	31.2	14.9	0.109	0.014	0.007
C2	20*40	1	46	6.9	11.0	9.8	68.7	34.3	16.0	0.199	0.044	0.021
	40*40	1	46	13.7	5.1	13.8	40.8	27.9	11.8	0.157	0.023	0.011
	40*80	1	32	8.5	14.9	11.1	30.6	19.7	13.1	0.154	0.039	0.013
	40*80	1	46	13.8	6.5	13.8	45.7	28.5	13.9	0.162	0.020	0.009
	40*80	1	60	17.9	3.0	18.0	12.1	14.7	8.9	0.144	0.017	0.007
	40*80	2	46	12.8	10.6	13.9	46.4	30.6	12.5	0.088	0.013	0.004
	40*80	8	46	5.7	18.2	13.6	81.6	28.5	19.0	0.036	0.007	0.003
	80*80	1	46	13.8	6.5	13.9	83.9	36.8	14.0	0.124	0.008	0.005

(a) Model summary
Adjusted R square		df1	df2	Sig. F change
.743		1	26	.013
(b) Coefficient
	Unstandardized coefficient
Model	B	Std. error	t	Sig.
(Constant)	27.503	3.199	8.597	.000
Angle change of the center of gravity (standard deviation)	1.214	.168	7.234	.000
Speed difference between drum and fabric (standard deviation)	.205	.084	2.446	.022
Shape factor (average change)	730.892	182.684	4.001	.000
Shape factor (standard deviation)	–551.579	148.429	–3.716	.001
Shape factor (average)	73.918	27.795	2.659	.013

Algorithm Measurement	Conventional	Proposed for
Algorithm Measurement	Conventional	Efficiency	Better performance
Wash time (min)	30	22	30
Washing efficiency (%)	55.7	56.0	58.4
Power consumption (Wh)	29.6	22.2	30.0