An experimental study on vibration isolation performance of weft-knitted spacer fabrics

Design of fabric structure

Due to the limited distance between two needle systems in a weft knitting machine, a special fabric structure was first suggested to fabricate thicker weft-knitted spacer fabrics by employing a longer linking distance of spacer monofilaments to knit the spacer layer and elastic yarns to knit the outer layers in this study. As shown in Figure 1(a), the suggested spacer structure is constructed of two outer layers knitted with elastic yarns in single jersey and a spacer layer knitted with tuck loops using monofilaments in an “X” shape. As the outer layers are knitted with elastic yarns, they will shrink after a steaming treatment, causing the inclined monofilaments to rotate to the thickness direction of the fabric structure and thus making the fabric thickness increase, as shown in Figure 1(b). If different linking distances of spacer monofilaments are adopted, spacer fabrics with different thicknesses can be easily realized. In fact, this design concept has been used in the development of spacer fabrics with negative stiffness. ²⁵ OPEN IN VIEWER

In order to obtain a spacer fabric that is as thick as possible, a linking distance of 20 needles, which is the maximum distance for a normal knitting process, was first selected after a series of preliminary trials, as shown in Figure 2(a). Beyond this distance, knitting becomes very difficult as needles for tucking could not catch the monofilaments well, causing knitting defects. On the other hand, in order to study the effect of the fabric thickness, the linking distance was reduced to 12 needles to obtain a thinner spacer fabric but still having sufficient thickness for good vibration isolation for comparison, as shown Figure 2(b). The two fabric structures were named Spacer-20h and Spacer-12h, where the number indicates the floating distance of each monofilament between two tucking points on the same needle bed, and “h” indicates only half numbers of needles knitting tuck stitches. From Figure 2, it can be seen that the tuck positions are evenly distributed. It should be pointed out that as the cross-over structure of the spacer monofilaments in the “X” shape along the course direction makes the fabric structure balanced under compression loads, the transverse shift along the courses of the fabric does not arise. It is possible to let all needles knit tuck stitches. However, twofold monofilaments limit the shrinkage of the outer layers during the steaming treatment, resulting in relatively low fabric thickness, which limits the range of displacement under vibration. Therefore, the structure with all needles knitting tuck stitches was not adopted in this study. OPEN IN VIEWER

Fabrication of fabric samples

The above proposed fabrics were knitted on a 14 gauge STOLL CMS 822 computerized flat knitting machine. While the two outer layers were knitted with single jersey structure using one 100D nylon multifilament yarn and one 30D Spandex/70D nylon covering yarn together, the spacer layer was knitted with 0.12 mm polyester monofilament. The NP value, which refers to cam setting, was set at 9.0 for knitting the spacer layer, and 11.0 for knitting the two outer layers. After knitting, fabric samples at their free state were subjected to a steaming treatment with a steam iron. The temperature of the steam iron was kept at around 50℃ to avoid possible yarn damages. Elastic yarns in the outer layers shrank during the steaming treatment, resulting in fabric thickening. After the steaming treatment, the fabric samples were further relaxed under an environmental condition of 20℃ and 65% relative humidity (RH) for one week. The characteristics of the two fabric samples Spacer-20h and Spacer-12h after relaxation are listed in Table 1. It can be seen that the loop densities of the two fabrics are similar, but Spacer-20h has greater areal mass and fabric thickness than Spacer-12h.

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Table 1.

The characteristics of the two weft-knitted spacer fabrics

Fabric code	Course density (wales/cm)	Wale density (courses/cm)	Areal mass (g/m2)	Thickness (mm)
Spacer-20h	7.15 (0.12)	26.10 (0.91)	1020.15 (21.99)	12.01 (0.17)
Spacer-12h	6.66 (0.06)	25.90 (0.42)	673.27 (31.33)	6.66 (0.18)

Figure 3 shows the cross-sectional views of the as-fabricated weft-knitted spacer fabrics. It can be found that the cross-sectional views along the course direction and the wale direction are different. Along the course direction, spacer monofilaments have a crossed structure. However, along the wale direction, spacer monofilaments have a curved shape. Moreover, linking points A and B of each monofilament with two outer layers are not located on the same vertical line. This dislocation between A and B should be taken into consideration when preparing the fabric samples for vibration testing. OPEN IN VIEWER

Fabric lamination

As mentioned before, all the monofilaments have a curved shape in the wale direction view. The formation of this shape mainly comes from the bending moments developed at the linking points by tuck loops. As shown in Figures 3(c) and (d), the linking points A and B for each monofilament are not located on the same vertical line in the fabric thickness direction. The main reason is that the courses where points A and B are located are not knitted simultaneously. As points A and B of each monofilament are not on the same vertical line, the transverse instability could take place along the wale direction when a single spacer fabric is subjected to a vibration test under a loaded mass. In order to circumvent the undesirable transverse shift along the wale direction of the spacer fabric structure during vibration tests, two identical spacer fabrics were bonded together using a double-sided adhesive tape, as shown in Figure 4(a). Thus, point A and point C are located on the same vertical line. In this case, the topmost layer and the base layer of the laminated fabric can maintain opposite to each other under the mass loaded, as shown in Figure 4(b). As two fabrics are bonded together, the relative slip between the two fabrics can be avoided. In this way, the transverse motion of the spacer fabric has no interference on the vertical motion of the mass-spacer fabric system. OPEN IN VIEWER

Typical transmissibility curve

The vibration isolation performance of the weft-knitted spacer fabrics was evaluated by the acceleration transmissibility T, which is defined as the ratio of the acceleration of the load mass to that of the shaker platform. As shown in Figure 7, a typical curve of T as a function of the excitation frequency obtained for Spacer-12h when tested under 0.3g excitation level and 2 kg load mass is selected as an example to explain the vibration isolation performance of this type of spacer fabrics. Although the tests were conducted from 4 to 500 Hz, all the acceleration transmissibility curves shown afterwards are only until 100 Hz to get a better demonstration. From Figure 7, it can be seen that under low excitation frequencies, the acceleration transmitted from the platform to the mass approximately equals the excitation level. However, with increasing the excitation frequency, the transmissibility rapidly increases until the resonance peak. The transmissibility reading above one unit ( T > 1 ) indicates that the vibration is amplified. At resonance frequency f_r (15.2 Hz), the transmissibility of the mass-spacer fabric system reaches the peak value T max (4.1). This means that acceleration is amplified by 4.1 times. Further elevating the excitation frequency above f_r, the transmissibility starts to decline. The frequency at which the transmissibility equals one unit ( T = 1 ) is called the cross-over frequency f_c (30.3 Hz), which defines the boundary between the amplification region and the isolation region. Vibration isolation ( T < 1 ) takes effect when the excitation frequency is larger than f_c. OPEN IN VIEWER

To achieve a wider isolation region, the resonance frequency f_r should be reduced. In a linear single-degree-of-freedom (SDOF) system, the curve shape near the resonance peak looks symmetric. In such a system, ³² f_r is related to the dynamic stiffness k_d and the load mass m, and is defined by equation f r = 1 2 π k d m . Observing the curve in Figure 7, it can be found that the curve shape near the resonance peak is asymmetric and bent to the left-hand side, indicating that the mass-spacer fabric system is a nonlinear one. Although in a nonlinear system, the calculation of f_r becomes more complicated, f_r is still affected by k_d and m. Besides, under a low excitation level, such a mass-spacer fabric system can be assumed as a linear one. The reduction of f_r implies either decreasing k_d or increasing the load mass. Since the load mass is predefined by the working condition, decreasing k_d should be the only approach to a better isolation performance.

Therefore, an ideal isolator should keep the dynamic stiffness as low as possible. However, due to the nonlinearity of weft-knitted spacer fabric, the value of k_d is affected by the load mass, the fabric thickness and the excitation level. For this reason, the following sections will discuss the effects of these factors on the isolation performance of the mass-spacer fabric system. For better comparison, two physical quantities, the resonance frequency f_r and the cross-over frequency f_c, are selected. Since the amplification region is to be avoided during the use, the peak transmissibility T max is not a concern in this study.

Effects of fabric thickness and load mass

Under the same excitation level, the effect of the fabric thickness on the vibration isolation performance also depends on the load mass due to nonlinear behaviors of spacer fabrics under both static and dynamic loading conditions. In other words, the spacer fabrics will be deformed at different compression strains and will have different stiffness when the load mass changes. In this regard, the effects of the fabric thickness and load mass are discussed together in this section. For ease of discussion, only the testing results for one excitation level of acceleration are presented here. The effect of the excitation level will be discussed in the next section.

Figures 8(a) and (b) respectively show the transmissibility curves of Spacer-20h and Spacer-12h with different load masses when the excitation level is kept at 0.1g. It can be seen that the resonance peaks of the transmissibility curves shift to the left-hand side when the load mass increases. This implicates that f_r and f_c decrease with the increase of the load mass (Figure 8(c)). However, as shown in Figure 8(a), an exceptional case is found for Spacer-20h when the load mass increases from 4 to 5 kg. In this case, the transmissibility curve with 5 kg load mass shifts back to the right-hand side instead of shifting to the left-hand side, resulting in a slight increase of f_r and f_c, as shown in Figure 8(c). When observing the effect of the fabric thickness, it can be found that f_r and f_c of Spacer-20h are smaller than those of Spacer-12h, indicating that f_r and f_c decrease with the increase of the fabric thickness. OPEN IN VIEWER

The above phenomena can be explained by stiffness changes of spacer fabrics when the load mass changes. As shown in Figure 9, the quasi-static compression curves of both laminated Spacer-20h and Spacer-12h are nonlinear, which indicates that their static stiffness k_s cannot be kept constant under different compression loads. It can be seen that although the compression curves of the two spacer fabrics are very different, the variation trends of their static stiffness k_s are very similar. This is that k_s first increases at the very beginning stage, then slightly decreases and finally rapidly increases due to the compaction of the fabric structure under high compression loads. However, the k_s values of the two fabrics are different. It should be pointed out that under the vibration condition, the dynamic stiffness k_d should be used to explain the vibration isolation performance of spacer fabrics. According to the quasi-static compression curves in Figure 9, it can be derived that the compression behavior of two weft-knitted spacer fabrics is similar to that of damping materials. Therefore, their dynamic stiffness k_d should be different from their static stiffness k_s due to history-dependent mechanical properties under vibration condition. In spite of the nonlinear compressive force–displacement relationship of spacer fabrics, under 0.1g excitation level, the vibration is so localized that the mass-spacer fabric system could be treated as linear. Using f r = 1 2 π k d m , the values of k_d for the two spacer fabrics with five load masses were calculated and are listed in Table 2. It can be seen that the k_d values of Spacer-20h are lower than those of Spacer-12h. This explains why f_r and f_c decrease with the increase of the fabric thickness and the thicker spacer fabric has better vibration isolation than the thinner fabric. OPEN IN VIEWER

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Table 2.

k_d values of the mass-spacer fabric system for a fixed excitation level at 0.1g

Load mass (kg)		1	2	3	4	5
kd (×104 N/m)	Spacer-20h	5.26	3.69	2.32	0.74	1.32
	Spacer-12h	7.03	4.96	3.65	2.62	2.40

The variation trends of k_d also explain why f_r and f_c decrease with the increase of the load mass, because the k_d values also decrease with the increase of the load mass. The exceptional case for Spacer-20h, in which f_r and f_c increases when the load mass increases from 4 to 5 kg, can be also explained by the k_d value change and static compression curve. As shown in Figure 9, when the load mass increases from 4 to 5 kg, Spacer-20h changes into the compaction stage with a rapid increase of stiffness. As the effect of the increase of stiffness is higher than that of the increase of load mass, f_r and f_c increase when the load mass increases from 4 to 5 kg. Table 2 also confirms that the k_d values increase when the load mass increases from 4 to 5 kg.

Effect of excitation level

The previous section discussed the effects of both the fabric thickness and load mass with a fixed excitation level. In this section, the effect of excitation level is discussed with a fixed load mass. Figures 10(a) and (b) respectively show the transmissibility curves of Spacer-20h and Spacer-12h with different excitation levels when the load mass is kept at 2 kg. It can be seen that the resonance peaks of the transmissibility curves shift to the left-hand side when the excitation level increases. This implicates that f_r and f_c decrease with the increase of the excitation level (Figure 10(c)). From Figures 10(a) and (b), it can be also found that the shapes of transmissibility curves at the resonance peaks become bent to the left-hand side when the excitation level increases, indicating that the mass-spacer fabric system becomes softened. As the increase of softening implicates a decrease of the dynamic stiffness k_d, f_r and f_c decrease with the increase of the excitation level. OPEN IN VIEWER

From Figure 10(c), it can also be found that the f_r and f_c values of Spacer-20h are lower than those of Spacer-12h for all the excitation levels, which confirms again that the thicker spacer fabric has better vibration isolation performance than the thinner spacer fabric. The result in Figure 10(c) also shows that the difference in f_r and f_c between the two spacer fabrics increase with the increase of excitation level. This may be explained by the fact that at low excitation level, the dynamic loads applied to the fabric are relatively smaller and the two fabrics work at their low deformation regions where the difference of their stiffness is not high. However, with increasing the excitation level, the dynamic loads applied to the fabric increase and the two fabrics will work in different deformation regions where their stiffness becomes more important. The detailed explanation needs a further theoretical analysis by considering the nonlinear softening of the mass-spacer fabric system, which is beyond the scope of this paper.