The effects of the fabric properties on fabric movement and the prediction of the fabric movements in a front-loading washer

Abstract

The purpose of this study is to determine the effects of the fabric properties on fabric movement and to suggest a prediction model for the fabric movements in a front-loading washer. During a wash cycle, the fabric moves in many different ways depending on the mechanical and physiochemical properties of the fabric. In this study, 14 different fabrics were measured for their mechanical and physiochemical properties by the Kawabata Evaluation System (KES) and the water absorption test. From the observation of the fabric movements in the washer, 13 movement indexes were derived, and the relationships between the fabric properties and fabric movements were studied. The critical fabric properties that affected the fabric movements were determined by the analysis of variance (one-way ANOVA) and the post hoc test using the Scheffe method. The major fabric properties that affected fabric movements were found to be fabric weight, drape coefficient, water content, shear recovery, compression linearity, and energy required for compression. These fabric properties were investigated for their relation with the fabric movement indexes. The predicting models for fabric movements were suggested by the multi-linear regression equations.

Keywords

Front-loading washer fabric properties fabric movements correlation analysis

The mechanical actions by the centrifugal force of a drum bath and the hydrodynamic flow make fabrics rotate, fall, and rub against each other, and these mechanical actions are one of the important factors of laundry performance. However, earlier studies have been focused more on the roles of physiochemical effects,^1–6 and the study of the roles of mechanical actions on washing efficiency are very limited. The previous research on the mechanical actions of washing machines included the effects of mechanical strength and the number of rotations for a whirlpool or an agitator-type washing machine.^7, ⁸ Yet, there are few studies on the mechanical washing mechanisms of a front-loading washer.

Fabric movements during washing are a combined result of fabric migration, fabric friction, fabric shape transformation, and restoration, which are influenced by the mechanical and physiochemical properties of fabrics. The mechanical properties of fabrics that are associated with fabric movement include tensile and shear properties, bending, compression, surface characteristics, stiffness, fabric weight, and thickness. The physiochemical properties of fabrics that are known to affect the mechanical actions during washing include the absorption property and the surface hydrophilicity. Various fabric movements, being dependent of fabric properties, can occur during washing, and these movements would result in different mechanical actions and washing efficiency. Therefore, in order to understand and predict the fabric movements and the washing performance during washing, it is required to understand the mechanical and physiochemical properties of the fabrics.

Among the previous studies^9, ¹⁰ on the roles of mechanical actions and their relationship to the washing efficiency, Lee et al.¹⁰ classified the types of mechanical actions into the hydrodynamic flow of detergent water, the flexing of a fabric, and the friction between the fabrics. A noteworthy observation from Lee’s study was that the types of soil can change the stiffness of the soiled fabric, which in turn affects the intensity of fabric movement and the folding characteristics. Also, the water absorption of a fabric during the immersion in the washing solution was observed to affect the folding action along with the hydrodynamic flow, enhancing washing efficiency. This study concluded that the fabric properties influenced the type and intensity of fabric movement during washing, thus affecting the washing efficiency.

Among a few studies that investigated the fabric movements in a front-loading washer,^11, ¹² Lee¹² analyzed the fabric movements and washing efficiency with an increased amount of laundry volume and evaluated the roles of mechanical actions in relation to the washing efficiency. However, the interpretations of multiple mechanical actions for the washing mechanism in the actual washing conditions need to be further clarified.

In this study, the significant fabric properties that influenced the fabric movements were identified using a statistical tool. Various types of fabrics were tested to include the wide range of fabric properties that can occur in real life laundry. Also an attempt was made to predict the fabric movements inside a front-loading washer from the fabric properties via linear regression models.

Experimental details

Specimens

The fabric samples used in this study were commercially available, and the characteristics of the samples are presented in Table 1. The selected samples were cotton, polyester, and nylon fabrics and were used after conditioning at 20℃ and 60 RH% for 24 hours.

Table 1.

Characteristics of specimens

Evaluation of fabric properties

In order to evaluate the properties of fabrics, the mechanical properties of the fabric sample were measured by the Kawabata Evaluation System (KES) (Kato Tech Co., Ltd., Japan) which included the KES_FB1 tensile and shear tester, the KES_FB3 compression tester, and the KES_FB4 surface tester.¹³ The drape coefficient was measured by the KS K 0115 method¹⁴ and the loop length was measured by the heart loop method.¹⁵ Sixteen different mechanical properties of the fabrics that were evaluated are given in Table 2.

Table 2.

Parameters describing mechanical and physicochemical properties of fabric

Properties		Characteristic value (Symbols)	Unit
Mechanical properties	Tensile	Linearity of load/extension curve (LT)	-
		Tensile energy (WT)	gf cm/cm²
		Tensile resilience (RT)	%
	Shear	Shear stiffness (G)	gf/cm·degree
		Hysteresis at Ψ = 0.5 of shear angle (2HG)	gf/cm
		Hysteresis at Ψ = 5 of shear angle (2HG5)	gf/cm
	Compression	Linearity of compression/thickness curve (LC)	-
		Compressional energy (WC)	gf cm/cm²
		Compressional resilience (RC)	%
	Surface	Coefficient of friction (MIU)	-
		Mean deviation of MIU (MMD)	-
		Geometrical roughness (SMD)	µm
	Drapability	Loop length	mm
	Drapability	Drape coefficient	-
	Weight	Weight	g/m²
	Thickness	Thickness	mm
Physicochemical Properties	Absorptiveness	Absorptivity	%
		Wet weight	g/m²
		Water content	g/m²
	Contact angle	Water contact angle (CA)	℃

The physiochemical properties of the fabric sample were evaluated by the water absorption and the surface hydrophilicity. Water absorption was measured by the modified KS C IEC 60456 method¹⁶ as follows: A sample of 20 cm × 20 cm was weighed in a dried condition, and then soaked in water at 20 ± 2℃for 20 minutes. After hanging the sample in ambient conditions for 2 minutes and 30 seconds, the sample was weighed in a wet condition. The absorptivity and water content were calculated using

Water content (g) = Weight in a wet condition (g) - Weight in a dry condition (g)

(1)

Absorptivity (%) = \frac{Water content (g)}{Weight in a dry condition (g)} \times 100 (%)

(2)

The weight was measured 10 times and the average value of absorptivity was used for the analysis. For the surface hydrophilicity, the contact angle between the sample surface and the water drop was measured one second after the water droplet was formed.

Recording and analyzing the fabric movements

The analysis of the fabric movements was performed as follows. A front-loading washer (Samsung WW-HF135UV, Korea) was modified for an easier observation of the fabric movements inside. Washing operation was run for 30 seconds at 46 rpm and stopped for 4 seconds with 6 L of water. A 40 cm × 80 cm sample was immersed for 20 minutes to simulate the actual washing process. Fabric movements during the washing cycle were recorded with a high speed camera XS-4 (X-Stream TM, IDT Inc., USA) at a speed of 200 frames per sec for 10 seconds. No detergent was used for easier observation of the fabric movement.

For the analysis of the recorded fabric movements, an action analysis program, TEMA Motion (Image Systems Co., Ltd, Sweden) outline-tracker, was used to track the outlines of the fabric. Each fabric movement was analyzed for 13 second, and 20 frames per second were tracked. The coordinate system of the program and the actual length were converted by means of the outlines and the center of gravity of the fabric and a certain position of the drum in order to digitize the fabric movements.

Statistical analysis

For the statistical analysis of the relationship of the fabric properties and the movements, PASW® Statistics 18 (Predictive Analytics Software, SPSS, Inc., USA) was utilized. Statistically significant factors of the fabric properties and the movement indexes were determined by the analysis of variance (one-way ANOVA) method. Multiple comparison tests using the Scheffe method were conducted as post hoc tests. Linear Regression analysis was performed to predict the fabric movement using the fabric properties.¹⁷

Results and discussion

Fabric properties

The fabric movements can be classified into four different patterns¹⁸ by the fabric movement diagrams as illustrated in Table 3.

Table 3.

Diagrams for fabric movement patterns.¹⁸

The mechanical action of the washer makes the various fabric movements, and those movements are also influenced by the fabric properties. In order to understand the relationship between the fabric properties and the fabric movements, the mechanical and physiochemical properties of fabrics shown in Table 2 were examined, and the fabric properties that were meaningful in affecting the fabric movements were determined by ANOVA. From the ANOVA test, 18 fabric properties out of a total of 20 examined fabric properties were found meaningful in differentiating the fabric movement pattern groups at a 95% confidence level (P value < 0.05). Among the 20 properties that were listed in Table 2, the two non-significant properties were water absorptivity and the mean deviation of the coefficient of friction (MIU) of the surface characteristics by KES_FB (MMD).

After excluding the non-significant property factors, the multiple comparison test was performed to examine how many pairs of movement pattern groups were significantly different for that specific fabric property (Table 4). A total of six multiple pairwise comparisons for four movement pattern groups were conducted for the variables of the fabric properties. If a certain fabric property is significantly different in every pair of groups, a total of six pairs would be significantly different for that specific fabric property. It can be assumed that the fabric property that makes more pairs of pattern groups significantly different is a more critical and influential property when related to fabric movement. There were no fabric properties that were significantly different in every pair of groups, indicating that only one fabric property many not sufficiently affect the fabric movement patterns, and that various fabric properties contribute to the fabric movements.

Table 4.

The results of the multiple comparison test for the fabric properties

Number of pairs that were significantly different	Fabric properties
4	Dry weight, Drape coefficient
3	Wet weight, Water content, Shear hysteresis (2HG5), Compression linearity (LC), Compression energy (WC)
2	Thickness, Loop length Tensile linearity (LT), Tensile energy (WT), Tensile resilience (RT) Shear rigidity (G), Shear hysteresis (2HG) Compression resilience (RC) Surface roughness (SMD)
1	Contact angle, Surface coefficient of friction (MIU)

(P value < 0.05).

The fabric properties that were significantly different in four pairs of groups were the dry weight and the drape coefficient. Those that were significantly different in three pairs of groups were weight in the wet condition, water content, shear hysteresis (2HG5), compression linearity (LC), and compression energy (WC). From this analysis, it was observed that the stiffness and dry weight were the most critical property factors that affected the fabric movement patterns. The other properties such as wet weight, shear hysteresis, compression linearity, and compression energy were the next critical property factors. Through ANOVA and the multiple comparison test, the main fabric properties that affected the fabric movements were able to be identified, by which the fabric movement patterns could be predicted.

The fabric properties are not completely independent. The six variables that were thought to affect the movement patterns most independently and to significantly affect the movement patterns were selected based both on the multiple comparison result and the researchers’ discretion such that: 1) the fabric property variables should represent both the mechanical and the physicochemical properties, 2) the fabric property variables should have a low correlation to each other. The selected variables are presented in Table 5.

Table 5.

Fabric properties classified as representative and subordinate properties

Subordinate properties	Representative fabric properties (selected one)
Physiochemical property	Wet weight, Water content	Wet weight
Mechanical property	Dry weight, Thickness	Wet weight
	Tensile: Linearity (LT), Energy (WT), Resilience (RT)	Tensile energy (WT)
	Shear: Rigidity (G), Hysteresis (2HG, 2HG5)	Shear hysteresis (2HG5)
	Compression: Linearity (LC), Energy (WC), Resilience (RC)	Compression resilience (RC)
	Surface: Geometrical roughness (SMD)	Surface geometrical roughness (SMD)
	Drapability: Drape coefficient, Loop length	Drape coefficient

Though surface roughness (SMD) and tensile energy (WT) were found as significant variables only for a few pairs of groups, those variables were included in the regression analysis as they were thought to affect the small-range partial movements, such as the friction in the local area and the number of turnovers to the lifter in addition to the macro movement patterns.

The selected six variables were used as independent variables for the regression analysis to predict the fabric movements.

The specimens C1, S1, and S2 which followed the movement pattern group A (Figure 1) had the lowest measurements for dry weight and thickness among the four groups. Though there were differences in hydrophilicity between cotton and synthetic fibers, all the specimens of pattern group A were the lightest, even in the wet condition. The shear hysteresis (2HG5) of pattern group A was relatively low due to the thin and flexible properties of the fabrics.

Figure 1.

The main mechanical and physicochemical properties of specimens.

The specimens S3 and S4 of pattern group B had a slightly heavier dry weight than those of pattern group A. However, their wet weight increased dramatically because of their high water absorptivity which comes from their weave structure. Also, their drape coefficient was higher, because of their higher stiffness, compared to the other three groups.

The specimens C2, S5, S6, and S7 of pattern group C had heavier weight both in dry and wet conditions when compared to both pattern groups A and B. Pattern group C had thick fabrics, and their higher wet weight was attributed to their bulky structure that allowed more water absorption.

The specimens C3, C4, C5, C6, and C7 of pattern group D were all cotton. Those specimens had heavy dry weights and had the heaviest wet weights. The drape property of this group in the dry condition was poor because of their high stiffness, while this group became more flexible when wet. The fabrics in this group had the highest values for shear hysteresis (2HG5) and the lowest values for compression resilience (RC).

Fabric movements

In order to analyze and distinguish the fabric movement types during the washing cycle, the movement indexes that represented fabric movements were established and digitized in the previous study by Yun et al.¹⁸ (Table 6).

Table 6.

Fabric movement index.¹⁸

The fabric movement indexes that explain the characteristics of patterns were determined by ANOVA. There were significant differences among the pattern groups for all fabric movement indexes (P value < 0.05). Multiple pairwise comparison tests were conducted to test how many pairs of pattern groups were significantly different from one another for the specific movement index (Table 7). From the pairwise comparisons, a total of six pairs of four pattern groups could be tested for significant difference by the movement indexes. It was assumed that the greater the number of pairs that were significantly different, the higher the effect of that fabric movement index on differentiating the movement pattern groups. The fabric movement indexes that were significantly different in every six pair of groups were ‘angle of changed of center of gravity,’ ‘vertical location,’ ‘speed difference between a drum and the fabric,’ ‘total distance moved,’ ‘number of falling,’ and ‘number of sliding.’ Those indexes were speculated to be associated with the macro movements such as: ‘how much the fabric went up along the drum wall’ or ‘how long it stayed at the bottom of the drum.’

Table 7.

The results of the multiple comparisons for the fabric movement indexes

Number of pairs that were significantly different	Fabric movement indexes
6	Angle of changed center of gravity
	Vertical location
	Speed difference between drum and fabric
	Total distance moved
	Number of falling
	Number of sliding
5	Position factor
4	Number of turnovers
3	Number of folding
2	Shape factor

(

P value < 0.05).

Fabric movement indexes such as ‘number of folding,’ ‘number of turnovers,’ and ‘shape factor’ appeared less significant as pattern-differentiating factors. This result is due to the fact that the movement patterns were classified mostly by the traces of the center of fabric gravity during the washing cycle, and local or small-range fabric movements were not considered as main criteria in classifying the fabric movement patterns. In other words, the macroscopic movement patterns may not capture all types of fabric movement including partial fabric shape changes, for example ‘number of folding/turnover’, and thus the influence of these fabric movement indexes on the washing efficiency could be underestimated.

From the study by Yun et al.,¹⁸ the main fabric movement indexes that were identified to affect the washing performance were: speed difference between drum and fabric, position factor, number of folding, and total distance moved. Those four fabric movement indexes (Table 8) were chosen as the dependent variables in the regression model.

Table 8.

The values of the main fabric movement index

Speed difference between drum and fabric (cm/s)	Position factor (ratio)	Number of folding	Total distance moved (cm)
C1	93.7	0.0	7	503.5
C2	54.1	18.8	7	1018.8
C3	42.3	45.8	0	1172.4
C4	44.0	40.0	0	1150.7
C5	45.6	33.9	3	1128.8
C6	43.1	51.1	1	1161.9
C7	49.2	43.4	10	1083.1
S1	100.3	0.0	5	417.6
S2	99.1	0.0	8	433.5
S3	73.8	4.9	6	762.5
S4	77.7	5.1	9	711.9
S5	58.7	12.4	7	959.6
S6	50.8	21.4	10	1061.9
S7	53.8	21.1	12	1026.0

Correlation between the fabric properties and the fabric movements

A linear regression analysis was conducted to test the assumption that the fabric movements during washing were influenced by the fabric properties (Table 9). By the regression model, the four selected fabric movement indexes (speed difference between the drum and fabric, position factor, number of folding, total distance moved) were predicted by the six fabric property variables that were identified in Table 5. The coefficients of independent variables are given in Table 9 to show the relation of the fabric properties to the fabric movement indexes. The modified R² shows how well the dependent variables, movement indexes, are predicted accurately by the regression models.

Table 9.

The linear regression analysis results for the fabric movement indexes

Dependent variable	Independent variables	Unstandardized coefficient		Multicollinearity		Modified R²
Dependent variable	Independent variables	B	Standard error	Tolerance	Variance inflation factor (VIF)	Modified R²
Speed difference between drum and fabric	constant	75.194	16.856	0.67
	wet weight	−.393	.403		.147	6.785
	drape coefficient	−30.210	13.812		.435	2.300
	SMD	−.457	.881		.302	3.312
	2HG5	−.046	.395		.382	2.620
	WT	−.278	.407		.636	1.572
	RC	.494	.205		.352	2.843
Position factor	constant	−26.861	10.905	0.82
	wet weight	.213	.261		.147	6.785
	drape coefficient	39.607	8.936		.435	2.300
	SMD	−.352	.570		.302	3.312
	2HG5	.594	.255		.382	2.620
	WT	1.214	.264		.636	1.572
	RC	−.029	.132		.352	2.843
Number of folding	constant	11.666	3.632	0.53
	wet weight	.130	.087		.147	6.785
	drape coefficient	−4.244	2.976		.435	2.300
	SMD	.305	.190		.302	3.312
	2HG5	−.110	.085		.382	2.620
	WT	−.480	.088		.636	1.572
	RC	−.024	.044		.352	2.843
Total distance moved	constant	743.531	219.216	0.67
	wet weight	5.130	5.244		.147	6.785
	drape coefficient	393.305	179.632		.435	2.300
	SMD	5.932	11.456		.302	3.312
	2HG5	.598	5.136		.382	2.620
	WT	3.604	5.297		.636	1.572
	RC	−6.415	2.660		.352	2.843

The test result for multicolinearity on the six fabric property variables are also given in Table 9. Hocking assumed that a multicolinearity value over 10 does not signify independence among the variables.¹⁹ From the test results, the multicolinearity value for each regression model was below 10, thus presenting the validity of the regression equation for the fabric movement indexes.

The regression equation for ‘speed difference between drum and fabric’ is as follows:

Regression model 1

Speed difference between drum and fabric = + 75.194 − 30.210(drape coefficient) + 0.494(RC) − 0.457(SMD) − 0.393(wet weight) − 0.278(WT) − 0.046(2HG5)

(P value < 0.01)

Regression model 1 shows the negative correlation between ‘speed difference between drum and fabric’ and ‘drape coefficient.’ This can be explained by the fact that a stiffer fabric moves with the drum rotation with a similar speed to the drum rotation; therefore, the speed difference between the drum movement and the fabric movement becomes less. The fabric with the highest measurements in thickness and fabric weight in pattern group D showed the lowest speed difference between the fabric movement and the drum rotation when compared to the other movement pattern groups. Also, as the fabric surface became rougher, the friction between the fabric and the drum wall increased, and this increase resulted in lowering the speed differences. The compression resilience (RC) showed a positive correlation with ‘speed difference between drum and fabric.’ When the fabric whose shape changed, because of a lifter or because of the hydrodynamic flow pressure, recovered its original shape, the speed difference increased.

The regression equation for ‘position factor’ is as follows:

Regression model 2

Position factor = − 26.861 + 39.607(drape coefficient) + 1.214(WT) + 0.594(2HG5) − 0.352(SMD) + 0.213(wet weight) − 0.029(RC)

(P value < 0.01)

Regression model 2 shows that ‘position factor’ had a positive correlation with the drape coefficient. The small value of ‘position factor’ can be because the softer fabrics stay longer at the bottom right of the drum and are not able to move up to the top of the drum because of their softness. From the high value of the modified R² (R²= 0.817) of regression model 2, the prediction model was assumed as appropriate in predicting the macro movements, such as ‘position factor’ and ‘total distance moved.’ It was concluded that the six selected variables of fabric properties are significantly associated with macro movements.

The regression equation for ‘number of folding’ is as follows:

Regression model 3

Number of Folding = + 11.666 − 4.244(drape coefficient) − 0.480(WT) + 0.350(SMD) + 0.130(wet weight) − 0.110(2HG5) − 0.024(RC)

(P value < 0.01)

Regression model 3 shows that ‘number of folding’ showed a negative correlation with the drape coefficient, which can be explained by the fact that a softer fabric with good drapery, with a lower drape coefficient, would have a larger “number of folding” value. When a fabric is flexible, the fabric easily spreads its folds by the hydrodynamic action or the centrifugal force of drum, leading to an increased ‘number of folding’ value.

The modified R² value was as low as 0.525, due to the following two cases where the stiff fabrics had high drape coefficients: 1) Stiff specimens C7, S6, and S7 showed frequent folding. The flexible fabrics were extended by the drum wall and were lifted when in the narrow lump shape, then got folded up again by the hydrodynamic flow. The stiff fabrics, such as S6, S7, and C7, rotated along the drum wall in a large round shape, and then fell down in spread state from the top to the bottom of a drum. According to our previous research,¹⁸ ‘number of folding’ was induced by a change of area greater than 60 cm². Therefore, those fallings of the specimens were counted in the ‘number of folding’ value. 2) The other exceptions were the specimens C4, C5, and S2 that had a high drape coefficient. When those specimens absorbed water, they became more flexible and were folded easily by the mechanical action, behaving in the same way as fabric of a low drape coefficient.

The regression equation for ‘total distance moved’ is as follows:

Regression model 4

Total distance moved = + 743.531 + 393.305(drape) − 6.415(RC) + 5.932(SMD) + 5.130(wet weight) + 3.604(WT) + 0.598(2HG5)

(P value < 0.01)

Regression model 4 shows the positive correlation between ‘total distance moved’ and ‘drape coefficient,’ and is a result of the fact that a stiffer fabric moves all-around the drum. When the fabric surface is rough, it increases the friction with the drum wall, and the fabric moves up to the top along the drum wall then falls to the bottom following the opposite side of drum wall. This action resulted in greater values of ‘total distance moved’ for the stiff fabrics in pattern groups C and D.

From the regression analysis, the effects of fabric properties on each fabric movement index were determined by the coefficient of the independent variables. The general finding was that the drape coefficient had a high correlation with the most of movement indexes. The other properties including surface roughness (SMD), tensile energy (WT), and compression recovery (RC) appeared to have less effect than the drape coefficient. The regression models in this study were based on the independency assumption of the independent variables, which may not be accurate. Most likely, heavier fabrics tend to be stiffer, which in turn affect the shear hysteresis and the tensile energy. This limitation of the research needs further study to clarify the independency assumptions of the variables by developing the experimental methods.

Conclusion

Fabrics were classified into four different groups according to their movement patterns, reflecting the fabric properties during the washing cycle. From the ANOVA results and the multiple comparison tests, it was verified that the major fabric properties that affect the fabric movements were dry weight, wet weight, drape coefficient, water content, shear hysteresis, compression energy, and compression linearity. The regression models to predict the four fabric movement indexes by the six independent fabric property variables were developed. The regression models showed an explanatory power of 53–82%.

The findings provided the fundamental information that could be used to develop a relevant washing program for a front-loading washer by using the prediction of the fabric movement that may lead to improved washing efficiency. It is recommended to further investigate the effect of a fabric weight on its interaction with fabric stiffness and fabric movements and to build a database that includes the fabric types with a wider range of properties.

Footnotes

Funding

This work was supported by Samsung Electronics Co., Ltd (grant number 350-20100041).

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