An experimental study on the vibration behavior and the physical properties of weft-knitted spacer fabrics manufactured using flat knitting technology

Abstract

Weft-knitted spacer fabrics, a kind of three-dimensional fabric structure, are potential substitutes for typical rubber sponges and polyurethane foams for the protection of human body from exposure to vibrations. To explore the capability and the designability of weft-knitted spacer fabrics as the functional material of personal protective equipment against vibration, such as anti-vibration gloves and car cushions, the vibration behavior and physical properties of weft-knitted spacer fabrics manufactured using flat knitting technology were studied. In the first part of the article, the vibration behavior of top-loaded weft-knitted spacer fabric under harmonic base excitation was analyzed. The effects of monofilament diameter, linking distance and excitation acceleration level on the transmissibility curve of the mass-spacer fabric were evaluated. It was shown that to broaden the frequency range for vibration isolation, spacer fabrics with smaller monofilament diameter and longer linking distance were preferred. In the second part of the article, the effects of monofilament type, monofilament diameter, and spacer structure on the physical properties of spacer fabric including fabric shrinkage coefficient, fabric thickness, fabric stitch densities, and fabric areal mass were analyzed. It was found that fabric thickness was increased by employing spacer structures with longer linking distance and lower filling density of spacer monofilament. In addition, in order to obtain an optimized high fabric thickness, nylon monofilament was preferred to polyester monofilament. On the other hand, monofilament diameter has a significant influence on stitch densities and fabric areal mass. Larger monofilament diameter resulted in lower stitch densities and heavier areal mass for spacer fabric.

Keywords

Computerized flat knitting weft-knitted spacer fabric fabric thickness vibration isolation frequency response curve

Knitted spacer fabrics are kinds of a three-dimensional (3D) textile structure consisting of two outer layers which are connected but kept apart by an inner layer of monofilaments. Due to the three-layer construction along the thickness direction, spacer fabrics are also named as sandwich structures.¹ Properties of high porosity, good compression resistance, and flexibility in structure and materials used make spacer fabrics very attractive in various applications including sound attenuation,^2–4 thermal insulation and moisture control,^5–7 cushion and medical products,^8–11 composite reinforcement,^12,13 intimate apparel,¹⁴ impact protection,^15–17 and so on.

Knitted spacer fabrics can be produced by both weft knitting and warp knitting technologies. So far, a considerable proportion of commercial knitted spacer fabric products^1,18–26 are produced by double needle-bar warp knitting machines due to a large range of variations in fabric structure and thickness¹³ and high production efficiency.²⁷ Comparatively, weft-knitted spacer fabrics^2,3,32–36 occupy relatively small portions in the technical market. Weft-knitted spacer fabrics can be produced with cylinder and dial weft knitting machines or computerized flat knitting machines. The thickness of a conventional weft-knitted spacer fabric is usually within 10 mm.^28–30 The weft knitting process is relatively simple and flexible, but low in production rate. The comparatively low speed of flat knitting machines conversely turns into an advantage when brittle and stiff yarns are used.³¹ Besides, weft-knitted spacer fabrics can be more competitive if texture effects such as color and jacquard pattern, or specified shapes, are needed.^28,32 The two-way stretch and the ability to conform to shape also make weft-knitted spacer fabrics very promising in lingerie industries³³ and for other next-to-skin applications such as medical bandages and knee braces.

The main focus of this study is on the vibration behavior of weft-knitted spacer fabrics, in order to promote their potential applications as vibration cushioning materials for the protection of the human body from harmful mechanical vibrations. For example, workers operating hand-held electrical or pneumatic powered rotary tools and drivers on bumpy roads are inevitably exposed to dangerous vibrations in specific frequency ranges, causing discomfort and even occupational diseases such as hand arm vibration syndrome (HAVS).³⁴ To effectively minimize these adverse vibrations, knitted spacer fabrics can be used to make into anti-vibration gloves and automotive seat cushions, which are advantageous over traditional typical rubber sponges and polyurethane foams due to their high breathability and thermo-physiological comfort.

Studies have been carried out to study the vibration properties of knitted spacer fabrics from different perspectives.^34–44 Frydrysiak and Pawliczak⁴¹ found that knitted spacer fabric has the advantage of having much lower thickness than typical sponges as vibration damping inserts in workplace seating. Krumm et al.⁴² found that warp-knitted spacer fabric is preferred to standard foam cushion as the seat backrest cushion based on a comparative study on the vertical seat transmissibility. Liu and Hu⁴³ found that thicker warp-knitted spacer fabrics were preferred to thinner ones for better vibration isolation performance. Chen et al.^34,44 have studied the nonlinearity in the frequency responses of weft-knitted spacer fabrics using experimental, theoretical and numerical methods.

Based on existing research, this study presents an experimental analysis on the vibration properties of weft-knitted spacer fabrics with different fabric design variables under forced harmonic excitation, aiming at laying a basis for specified application scenarios in the scope of vibration isolation in the future. Moreover, a systematic study on the design and fabrication of anti-vibration weft-knitted spacer fabrics having versatile physical properties will also be carried out, as the dimensional and physical properties such as fabric thickness, stitch densities and fabric areal mass are important for the wearing comfort when spacer fabric is made into personal protective equipment (PPE) against vibration.

Experimental method

Fabric structures and materials

The suggested weft-knitted spacer structure is constructed of two outer layers knitted with elastic yarns and an inner or spacer layer knitted with monofilaments in a cross-over structure. The structure and the materials for two outer layers are consistent for all types of weft-knitted spacer fabrics designed and manufactured herein. Namely, two elastic outer layers were knitted with single jersey structure using an untwisted ply yarn which contains one 100D nylon multifilament yarn and one 30D Spandex/70D nylon covering yarn (Shandong Hengtai Textile Co. Ltd, China). As this research focuses specifically on the vibration performance of spacer fabrics in its load bearing direction, for which the spacer structure and the monofilament properties will exert a greater influence, therefore weft-knitted spacer fabrics with varied spacer structures and varied monofilament types and diameters were designed accordingly.

Spacer structure

The knitting pattern and the corresponding spacer structure for one typical weft-knitted spacer fabric are illustrated in Figure 1(a) and (b). Two outer layers were knitted with plain stitches by two lines of elastic yarns on the respective needle bed, which was consistent for all spacer fabrics manufactured. Taking this specific spacer structure for example, each course in the spacer layer was made with tuck stitches alternately on the front and the rear needle beds by eight lines of spacer monofilament, forming into a cross-over or “X”-shaped structure. As shown in Figure 1(b), the linking distance is eight needles long for each continuous and zigzagged spacer monofilament. The linking distance is defined as the number of needles in the distance for one monofilament to link two adjacent tucking points on the same needle bed, which is an important variable for the spacer structure of weft-knitted spacer fabric.

Figure 1.

Drawings of (a) the knitting pattern and (b) the spacer structure for “S8f”, and (c) the knitting pattern and (d) the spacer structure for “S8h”.

Another important variable for the spacer structure of spacer fabric is the filling density of tucked monofilament, which describes the proportion of the total number of tuck stitches to the total number of needles. For example, as shown in Figure 1, although the linking distance for both spacer structures “S8f” and “S8h” is identical, their filling densities are however different. The former structure (“S8f”) employed full filling density of tucked monofilament, in comparison with the latter structure (“S8h”) which employed half filling density of tucked monofilament. Only 50% of needles were involved in making tuck stitches for the latter spacer structure (“S8h”). It is noted that for half filling density, tuck positions all through the fabric are still evenly distributed.

Considering three varieties of linking distance (eight, six, and four needles) and two varieties of filling density of tucked monofilament (full and half), six different spacer structures were designed in total, namely S8f, S6f, S4f, S8h, S6h, and S4h, in which the letter “S” stands for spacer structure, “f” indicates full filling density in which case all needles participate in making tuck stitches, and “h” indicates half filling density of tucked monofilament in which case only half numbers of needles participate in making tuck stitches.

Monofilament type and diameter

Two different types of monofilaments were used for constructing the spacer layer. Polyester (PET) monofilament is the most widely used for making spacer fabrics, while nylon (PA) monofilament exhibits lower modulus and provides better elastic recovery than polyester monofilament. To examine the effect of monofilament type on the physical properties of spacer fabrics, both polyester monofilament and nylon monofilament of an identical diameter 0.128 mm were selected. The as-made spacer fabrics are tagged as PET-D1 and PA-D1, respectively, in which the letter “D” stands for diameter. On the other hand, nylon monofilaments with diameters of 0.128 mm, 0.148 mm, 0.165 mm, and 0.185 mm were used, in order to examine the effect of monofilament fineness. The as-made spacer fabrics are tagged as PA-D1, PA-D2, PA-D3, and PA-D4, respectively. In total, five types of monofilaments were obtained. Their corresponding linear densities are 132.0D (PA-D1), 176.5D (PA-D2), 219.4D (PA-D3), 275.8D (PA-D4), and 159.8D (PET-D1). Polyester and nylon monofilaments were provided by Nantong Ntec Monofilament Technology Co. Ltd, China.

Spacer fabric type

As listed in Table 1, with a combination of six different spacer structures (S8f, S6f, S4f, S8h, S6h, and S4h) and five different monofilaments (PET-D1, PA-D1, PA-D2, PA-D3, and PA-D4), 30 types of weft-knitted spacer fabrics were produced in total. Taking spacer fabric S8f-PA-D1 for example, its fabric code means this type of spacer fabric uses nylon (PA) monofilament with a diameter of 0.128 mm (D1), and the spacer structure employs eight-needle linking distance of tucked monofilament with full filling density (S8f).

Table 1.

Fabric codes and photos for thirty types of weft-knitted spacer fabrics with varied spacer structure, monofilament type, and monofilament diameter

Fabric code	Monofilament type and diameter
	PET-D1	PA-D1	PA-D2	PA-D3	PA-D4
	0.128 mm	0.128 mm	0.148 mm	0.165 mm	0.185 mm
Spacer structure
S8f	S8f-PET-D1	S8f-PA-D1	S8f-PA-D2	S8f-PA-D3	S8f-PA-D4

S6f	S6f-PET-D1	S6f-PA-D1	S6f-PA-D2	S6f-PA-D3	S6f-PA-D4

S4f	S4f-PET-D1	S4f-PA-D1	S4f-PA-D2	S4f-PA-D3	S4f-PA-D4

S8h	S8h-PET-D1	S8h-PA-D1	S8h-PA-D2	S8h-PA-D3	S8h-PA-D4

S6h	S6h-PET-D1	S6h-PA-D1	S6h-PA-D2	S6h-PA-D3	S6h-PA-D4

S4h	S4h-PET-D1	S4h-PA-D1	S4h-PA-D2	S4h-PA-D3	S4h-PA-D4

Fabric fabrication

Spacer fabrics were knitted on a STOLL CMS 822 computerized flatbed knitting machine of gauge 14E (Karl Mayer Textilmaschinenfabrik GmbH, Germany). Figure 2(a) shows the knitting view of spacer fabric on the knitting machine. Two outer single jersey layers were knitted on the front and back needle beds of the knitting machine separately, and the spacer monofilaments made tuck stitches on these two needle beds by turns, thus integrating the two outer layers and the spacer layer into a unity. Proper setting of NP value, namely cam setting, one of the most important knitting parameters, is critical for obtaining spacer fabrics with good quality, as it directly influences loop length and fabric stitch densities. In general, the higher the NP value, the longer the loop length. In this study, NP values set at 9.0 for spacer layer and 11.0 for outer layers were found to give a good knitting effect.

Figure 2.

Photos of spacer fabric: (a) knitted on machine and (b) after full relaxation. Illustration of the coursewise shrinkage of spacer fabric and an increase in fabric thickness from: (c) on-machine knitting to (d) after steaming treatment.

After knitting, all fabric samples were subjected to a steaming treatment at a temperature of 50°C using a steam iron with a dwell time of 15 s. Due to the use of elastic yarns in two outer layers of spacer fabric, the shrinkage of two elastic face layers took place, accompanied by an increase in fabric thickness due to the rotation of the inclined monofilaments to the thickness direction of spacer fabric, as illustrated in Figure 2(c) and (d). Next, the fabric samples were further relaxed under a standard environmental condition of 20°C and 65% relative humidity for 24 h. During this period, fabric shrinkage continued, but at a lesser and slower extent. After full relaxation, spacer fabrics have stable dimensions as shown in Figure 2(b).

Vibration experiment

An electromagnetic vibration shaker (King Design Industrial Co. Ltd, Taiwan, China) was used to measure the vibration transmissibility curves of different weft-knitted spacer fabrics. As illustrated in Figure 3, the vibration shaker was equipped with a platform supporting the load mass-spacer fabric system. Spacer fabric having a flat area of 100 mm × 100 mm was placed on the center of the shaker platform and top-loaded with a 2.5 kg metallic mass having a surface size of 90 mm × 90 mm. The weight and the surface area of the load mass were selected with reference to the International Standard BS EN ISO 13753:2008, “Mechanical vibration and shock. Hand-arm vibration. Method for measuring the vibration transmissibility of resilient materials when loaded by the hand-arm system”.⁴⁵ The dimension of spacer fabric is larger than the load mass to avoid mass eccentricity during vibration. Two accelerometers were mounted on the vibration shaker platform (Accelerometer 1) and on the center of the load mass (Accelerometer 2), respectively. When the shaker platform was driven by the controller to vibrate at predefined frequencies and excitation levels, the acceleration signals of the load mass and the shaker platform were recorded by two accelerometers to measure the acceleration transmissibility of the mass-spacer fabric system. The shaker was excited by sinusoidal signals with frequencies sweeping from 4–500 Hz. During each sweep process, the excitation acceleration level was kept constant. The resulting excitation amplitude decreases as the driving frequency increases during one sweep event. In other words, excitation amplitude is large at low frequencies, while it becomes small at high frequencies. By this vibration sweep frequency response experiment, the acceleration transmissibility vs excitation frequency curve can be obtained for different spacer fabrics under different testing conditions.

Figure 3.

Schematic of the vibration testing setup for the mass-spacer fabric system.

Measurement of physical properties

To learn about how fabric design variables, namely spacer structure, monofilament diameter, and monofilament type, affect basic dimensional and physical quantities of spacer fabrics at full relaxation state, measurements were conducted on fabric thickness, fabric areal mass, stitch densities, and also coursewise shrinkage coefficient of the as-made 30 types of weft-knitted spacer fabrics.

Fabric thickness

Fabric thickness includes both the thickness of the spacer layer, which comprises the major portion of the total fabric thickness, and the thickness of the two thin outer layers. Using an Automatic Compression Tester KES FB-3A (Kato Tech Co. Ltd, Japan), force was applied on spacer fabric by a circular compressing board of 2 cm² attached with a sensor. Based on the obtained thickness-pressure curve, fabric thickness was measured under a pressure of 50 gf/cm² (4.90 kPa). The averaged value was calculated from 10 measurements for each sample type.

Fabric areal mass

Fabric areal mass is defined as the mass of spacer fabric per unit area, which was measured by weighing a square sample of 100 mm ×100 mm using an electronic balance. Three measurements were used for calculating the average value for each sample type.

Stitch densities

Stitch densities include the coursewise density, the walewise density, and the areal stitch density. The coursewise density (wales/cm) is the number of wales per unit length along the course direction. The walewise density (courses/cm) is the number of courses per unit length along the wale direction. The areal stitch density is the number of stitches per unit area of spacer fabric, which is calculated by multiplying the coursewise density with the walewise density. The averaged values of coursewise and walewise densities for each sample type were calculated from 10 measurements.

Coursewise shrinkage coefficient

Due to a fixed spacing between two needle beds, the as-made 30 types of spacer fabrics with varied spacer structure, monofilament diameter, and monofilament type had the same on-machine thickness in fact. However, their final thicknesses would become different, as a result of outer layer shrinkage of fabrics in the coursewise direction after a steaming treatment. Fabric shrinkage after the fabric is off-loom and after the steaming treatment will cause an evident increase in fabric thickness, due to the inherent structure of weft-knitted spacer fabric. Therefore, an analysis on the coursewise shrinkage coefficient of spacer fabric is necessary.

The coursewise shrinkage coefficient $ε$ for each type of spacer fabric sample has a relationship with the coursewise density as follows

ε = \frac{l_{o n} - l_{s t}}{l_{o n}} \times 100 % = 1 - \frac{l_{s t}}{l_{o n}} = 1 - \frac{ρ_{o n}}{ρ_{s t}}, ε > 0

(1)

where l_on is the on-machine fabric width in the course direction during knitting, l_st is the fabric width in the course direction after spacer fabric is stabilized,

ρ_{o n}

is the on-machine coursewise density during knitting, and

ρ_{s t}

is the coursewise density when the fabric is dimensionally stabilized. Due to the machine gauge of 14E, the on-machine coursewise density

ρ_{o n}

has a fixed value of 5.5 wales/cm for all fabrics. Therefore, the value of the coursewise shrinkage coefficient

ε

can be calculated based on the measured coursewise density

ρ_{s t}

when the fabric is finally dimensionally stabilized.

Results and discussion

The effects of monofilament diameter, the linking distance, and the excitation acceleration level on the acceleration transmissibility vs excitation frequency curve of the mass-spacer fabric system are presented in the next section on Fabric vibration properties. On the other hand, based on the as-made 30 types of weft-knitted spacer fabrics, the effects of different design variables, namely spacer structure, monofilament diameter, and monofilament type, on dimensional and physical properties of spacer fabric including fabric thickness, fabric areal mass, stitch densities, and fabric shrinkage coefficient are presented in the subsequent section on fabric physical properties.

Fabric vibration properties

To examine the effects of monofilament diameter, the linking distance, and the excitation acceleration level on the frequency response curve of the mass-spacer fabric system, three sets of vibration experiments were carried out, as shown in Table 2. The acceleration transmissibility vs excitation frequency curves for spacer fabrics with different monofilament diameters (D1, D2, D3, and D4) and linking distances (S8f, S6f, and S4f), and for different excitation acceleration levels (0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, and 0.6 g) were analyzed in this section, in which the letter g represents gravitational acceleration (9.81 m/s²).

Table 2.

Three sets of testing conditions to examine the effects of monofilament diameter, the linking distance, and excitation acceleration level on the frequency response curve of the mass-spacer fabric system

Testing condition	Testing item	Spacer fabric	Excitation acceleration level	Load mass (kg)
1	Monofilament diameter	S8f-PA-D1, S8f-PA-D2, S8f-PA-D3, S8f-PA-D4	0.5 g^a	2.5
2	The linking distance	S8f-PA-D1, S6f-PA-D1, S4f-PA-D1	0.5 g	2.5
3	Excitation acceleration level	Two stacked S8f-PA-D1	0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, 0.6 g	2.5

^aThe letter g represents gravitational acceleration (9.81 m/s²).

Effect of monofilament diameter

For a typical acceleration transmissibility vs excitation frequency curve as shown in Figure 4, taking spacer fabric S8f-PA-D1 for example, as the vibrational excitation was swept from low to high frequencies, the load mass-spacer fabric system experienced responses of a preceding vibration magnification and a following vibration isolation. First, under the lowest excitation frequencies, the response of the mass-spacer fabric system was nearly in phase with the vibration shaker platform. As a result, the acceleration transmissibility from the shaker platform to the load mass was equal to one. When the excitation frequency was elevated, the acceleration transmissibility increased gradually until the resonance peak emerged. At resonance, the vibration of the load mass reached the peak value, during which stage the response exhibited a 90° phase shift with the sinusoidal excitation from the shaker platform. Further elevating excitation frequencies above resonance, the acceleration transmissibility started to decline. When the excitation frequency stepped across a frequency threshold where the acceleration transmissibility was equal to one again, it divided the preceding vibration magnification region and the following vibration isolation region. As the acceleration transmissibility dropped below one, it indicated that the vibration level of the load mass began to be attenuated due to the use of spacer fabric as an anti-vibration material.

Figure 4.

The acceleration transmissibility vs excitation frequency curves for spacer fabrics S8f-PA-D1, S8f-PA-D2, S8f-PA-D3, S8f-PA-D4 under an excitation acceleration level of 0.5g.

To examine the effect of monofilament diameter on the vibration response of the mass-spacer fabric system, the acceleration transmissibility vs excitation frequency curves were obtained for spacer fabrics with different monofilament diameters, namely S8f-PA-D1, S8f-PA-D2, S8f-PA-D3, and S8f-PA-D4, under an excitation acceleration level of 0.5g, as shown in Figure 4. In the linear vibration theory, the resonance frequency $f_{r}$ is related to the dynamic stiffness $k_{d}$ and the load mass $m$ by this equation

f_{r} = \frac{1}{2 π} \sqrt{\frac{k_{d}}{m}}

(2)

Therefore, a higher dynamic stiffness $k_{d}$ will result in a larger resonance frequency $f_{r}$ . This agrees with the observation that as the monofilament diameter increased from D1 to D4, the resonance frequency increased, which was due to higher fabric stiffness for larger monofilament diameter. Besides, as monofilament diameter increased, the frequency threshold where vibration isolation started to take effect also increased, and the peak transmissibility decreased. In applications such as anti-vibration gloves made with weft-knitted spacer fabrics for protecting workers dealing with electrical or pneumatic powered rotary tools, dangerous vibrations emerge in specific frequency ranges, for instance, from 150–250 Hz. In this case, spacer fabric S8f-PA-D1 which has the smallest monofilament diameter, is preferable to the other three types as it gave the lowest transmissibility.

Effect of the linking distance

To examine the effect of the linking distance on the vibration response of the mass-spacer fabric system, the acceleration transmissibility vs excitation frequency curves were obtained for spacer fabrics with different linking distances, namely S8f-PA-D1, S6f-PA-D1, and S4f-PA-D1, under an excitation acceleration level of 0.5 g. As shown in Figure 5, when the linking distance decreased from eight to four needles, the peak transmissibility decreased while the resonance frequency increases. Besides, the frequency threshold where vibration isolation started to take effect also increased. The effect of decreasing the linking distance was similar with the effect of increasing the monofilament diameter.

Figure 5.

The acceleration transmissibility vs excitation frequency curves for spacer fabrics S8f-PA-D1, S6f-PA-D1, S4f-PA-D1 under an excitation acceleration level of 0.5g.

Effect of excitation level

To examine the effect of excitation acceleration level on the vibration response of the mass-spacer fabric system, the acceleration transmissibility vs excitation frequency curves were obtained for the stacked spacer fabric S8f-PA-D1 under excitation acceleration levels of 0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, and 0.6 g, as shown in Figure 6(a), in which case the frequency sweep direction was stepwise forward, namely from low to high frequencies. The reason for using two identical spacer fabrics stacked together as one sample instead of using one is due to the instability under relatively large excitations during vibration tests when using only one spacer fabric.

Figure 6.

The acceleration transmissibility vs excitation frequency curves during (a) forward (low to high) frequency sweep and (b) reverse (high to low) frequency sweep for the stacked spacer fabric S8f-PA-D1 under excitation acceleration levels of 0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, and 0.6 g.

Under a small excitation acceleration level, the mass-spacer fabric system can be treated as a linear mass-spring-damper vibration system, as shown in Figure 6(a). This explains the observation that when the excitation acceleration level was 0.1g, the resonance peak in the transmissibility curve behaved linearly. As the excitation acceleration level increased, the resonance peak started to lean to the left, which is indicative of a nonlinear mass-spacer fabric vibration system, giving rise to a nonlinear softening type of transmissibility curve. This tendency of nonlinear softening effect was more pronounced with the increase of excitation acceleration level, which was also accompanied by a decrease in the resonance frequency. The decrease in the resonance frequency $f_{r}$ was the result of a reduced dynamic stiffness $k_{d}$ caused by a higher excitation acceleration level in the nonlinear softening system, concerning Equation (2).

The jump phenomenon

When the excitation acceleration level became large enough, the “jump” phenomenon occurred, which is a phenomenon of sudden switch from one stable path to the other, as shown in the acceleration transmissibility vs excitation frequency curves during reverse (high to low) frequency sweeps under excitation acceleration levels of 0.4 g, 0.5 g, and 0.6 g in Figure 6(b). For these excitation conditions, frequency response curves obtained from reverse frequency sweeps were very different from those obtained from forward frequency sweeps.

In order to study the jump phenomenon, the acceleration transmissibility vs excitation frequency curve during the reverse frequency sweep event was superimposed on the other curve during the forward frequency sweep event for the stacked spacer fabric S8f-PA-D1 under the excitation acceleration level of 0.5g, as shown in Figure 7. Forward frequency sweep (from low to high frequencies) takes the lower (shown as the black full line) path, while reverse frequency sweep (from high to low frequencies) takes the upper (shown as the red dashed line) path. In regions away from resonance, for both relatively low and relatively high excitation frequencies in other words, two frequency response curves coincided with each other. However, around resonance, the path of the frequency response curve depends strongly on the frequency sweep direction. The region with bifurcated response is an indication of multiple theoretical solutions for the transmissibility, of which two stable solutions correspond to the lower and upper paths as shown in Figure 7, while the unstable solution cannot be observed experimentally. It is also noted that this “jump” phenomenon does not always take place in a nonlinear system.

Figure 7.

The nonlinear softening and jump phenomena in the acceleration transmissibility vs excitation frequency curves during forward frequency sweep (in the black full line) and reverse frequency sweep (in the red dashed line) for the stacked spacer fabric S8f-PA-D1 under an excitation acceleration level of 0.5g.

Fabric physical properties

Mean values and standard deviations of basic physical properties, namely stitch densities, coursewise shrinkage coefficient, fabric thickness, and fabric areal mass, for 30 types of weft-knitted spacer fabrics with varied spacer structure, monofilament type, and monofilament diameter are tabulated in Table 3.

Table 3.

Basic physical properties for 30 types of weft-knitted spacer fabrics with varied spacer structure, monofilament type, and monofilament diameter

Fabric code	Coursewise density (wales/cm)	Walewise density (courses/cm)	Coursewise shrinkage coefficient (%)	Fabric thickness (mm)	Fabric areal mass (×100 g/m²)
S8f-PA-D1	7.87 (0.18)	24.28 (0.26)	30.06 (1.56)	5.99 (0.06)	8.17 (0.03)
S8f-PA-D2	7.25 (0.05)	23.44 (0.30)	24.14 (0.52)	6.16 (0.20)	9.24 (0.10)
S8f-PA-D3	6.60 (0.00)	22.72 (0.44)	16.67 (0.00)	6.09 (0.12)	10.29 (0.02)
S8f-PA-D4	6.78 (0.04)	22.00 (0.25)	18.82 (0.42)	5.45 (0.13)	10.88 (0.10)
S6f-PA-D1	7.75 (0.05)	23.83 (0.35)	29.03 (0.46)	5.13 (0.15)	7.33 (0.24)
S6f-PA-D2	7.10 (0.07)	23.50 (0.41)	22.53 (0.77)	5.24 (0.15)	8.34 (0.03)
S6f-PA-D3	6.63 (0.04)	22.61 (0.60)	16.98 (0.44)	5.22 (0.10)	8.92 (0.13)
S6f-PA-D4	6.50 (0.00)	22.22 (0.26)	15.38 (0.00)	4.96 (0.13)	9.11 (0.03)
S4f-PA-D1	7.93 (0.06)	24.33 (0.25)	30.67 (0.50)	4.76 (0.15)	6.84 (0.06)
S4f-PA-D2	7.35 (0.07)	24.11 (0.22)	25.17 (0.72)	4.84 (0.20)	7.76 (0.06)
S4f-PA-D3	7.10 (0.10)	22.71 (0.27)	22.52 (1.09)	4.83 (0.18)	7.72 (0.06)
S4f-PA-D4	6.65 (0.14)	22.17 (0.35)	17.27 (1.76)	4.81 (0.30)	8.09 (0.01)
S8h-PA-D1	9.25 (0.35)	25.13 (0.23)	40.50 (2.27)	7.36 (0.22)	7.51 (0.04)
S8h-PA-D2	8.95 (0.07)	25.50 (0.35)	38.55 (0.49)	7.59 (0.16)	8.12 (0.04)
S8h-PA-D3	8.30 (0.07)	24.11 (0.42)	33.73 (0.56)	7.20 (0.26)	8.94 (0.04)
S8h-PA-D4	8.00 (0.10)	23.94 (0.39)	31.24 (0.86)	6.77 (0.14)	9.00 (0.03)
S6h-PA-D1	9.45 (0.13)	25.14 (0.24)	41.79 (0.81)	6.38 (0.26)	7.06 (0.18)
S6h-PA-D2	8.88 (0.04)	25.22 (0.26)	38.03 (0.25)	6.12 (0.18)	7.50 (0.06)
S6h-PA-D3	7.90 (0.35)	24.94 (0.30)	30.31 (3.12)	6.07 (0.18)	7.50 (0.04)
S6h-PA-D4	8.05 (0.05)	24.19 (0.46)	31.68 (0.42)	5.73 (0.19)	8.18 (0.05)
S4h-PA-D1	9.60 (0.00)	25.00 (0.35)	42.71 (0.00)	5.16 (0.15)	6.62 (0.07)
S4h-PA-D2	9.10 (0.14)	25.44 (0.30)	39.55 (0.94)	5.32 (0.11)	7.06 (0.06)
S4h-PA-D3	8.00 (0.07)	25.22 (0.36)	31.25 (0.61)	5.33 (0.14)	6.85 (0.16)
S4h-PA-D4	8.45 (0.05)	24.50 (0.32)	34.91 (0.39)	5.22 (0.18)	7.68 (0.01)
S8f-PET-D1	6.10 (0.00)	25.61 (0.22)	9.84 (0.00)	5.81 (0.16)	7.91 (0.06)
S6f-PET-D1	6.38 (0.04)	26.08 (0.20)	13.72 (0.48)	5.54 (0.17)	7.36 (0.10)
S4f-PET-D1	6.72 (0.03)	25.81 (0.46)	18.11 (0.35)	5.12 (0.22)	6.86 (0.06)
S8h-PET-D1	7.43 (0.04)	26.64 (0.24)	25.93 (0.35)	6.86 (0.24)	6.53 (0.08)
S6h-PET-D1	7.93 (0.06)	26.89 (0.33)	30.67 (0.50)	6.26 (0.23)	6.53 (0.08)
S4h-PET-D1	8.50 (0.20)	26.38 (0.23)	35.27 (1.52)	5.56 (0.29)	6.22 (0.02)

Standard deviations are given in parentheses.

The effects of monofilament diameter and spacer structure on the physical properties, namely stitch densities, fabric thickness, and fabric areal mass, of 24 types of spacer fabrics made with nylon monofilament are summarized in Figure 8. More specifically, the measurements of fabric stitch densities, including the coursewise density (wales/cm), the walewise density (courses/cm), and areal stitch density (stitches/cm²), are shown in Figure 8(a)–(c). Figure 8(d) gives the coursewise shrinkage coefficients of these spacer fabrics. Besides, the final fabric thickness and fabric areal mass values of spacer fabrics with structures of full filling density and half filling density of tucked monofilament are separately plotted in Figure 8(e) –(h).

Figure 8.

(a) Coursewise density; (b) walewise density; (c) areal stitch density; (d) coursewise shrinkage coefficients of spacer fabrics; fabric thickness for spacer structures having full filling density of tucked monofilament (e) and half filling density of tucked monofilament (f); fabric areal mass for spacer structures having full filling density of tucked monofilament (g) and half filling density of tucked monofilament (h).

Effect of monofilament diameter

Stitch densities

As shown in Figure 8(a)–(c), fabric stitch densities decreased with the increase of monofilament diameter in overall. The coursewise density is directly dependent on the coursewise shrinkage coefficient, as initially the coursewise densities were the same for all variants on the knitting machine, which agrees with the observations of the same variation tendencies in the coursewise density and the coursewise shrinkage coefficient with regard to varied fabric structural and material parameters, as shown in Figure 8(a) and (d). The coursewise shrinkage coefficient and the coursewise density exhibited nearly a linear decrease with the increase of monofilament diameter, due to larger monofilament diameter giving higher flexural rigidity, thus limiting the coursewise shrinkage of elastic yarns in the outer layers. However, it was an exception to this trend for the monofilament diameter of 0.185 mm (D4). It can be speculated that the walewise density and the coursewise density are interactive and interdependent, as the spacer monofilament exhibits a 3D curved shape in nature. Therefore, the decrease of the walewise density with the increase of monofilament diameter may account for the above-mentioned exceptional case.

Fabric thickness

The effect of monofilament diameter on fabric thickness was minor as compared with those of the linking distance and the filling density of tucked monofilament. As shown in Figure 8(e) and (f), when monofilament diameter increased from 0.148 mm (D2) to 0.185 mm (D4), fabric thickness decreased accordingly. This is coherent with the overall trend in the coursewise shrinkage coefficient, as larger monofilament diameter results in higher flexural rigidity, limiting the coursewise shrinkage and the improvement of fabric thickness. However, for spacer fabrics with longer linking distances, the effect of monofilament diameter on fabric thickness was non-monotonic. Fabric thickness first increased and then decreased with the increase of monofilament diameter. Taking spacer fabric S8h-PA-D1 for example, it uses nylon monofilament with a diameter of 0.128 mm, and the spacer structure employs eight-needle linking distance of tucked monofilament with half filling density. Due to the fact that the monofilament used in this type of spacer fabric is comparatively fine and thus has a relatively low rigidity, the monofilament segments tend to become curved during the shrinkage of outer layers of the spacer fabric, thus limiting the improvement of fabric thickness. As a result, spacer fabric S8h-PA-D1 exhibited a lower fabric thickness compared with spacer fabric S8h-PA-D2. This phenomenon was more pronounced for spacer fabrics with long linking distance, such as for fabric structures S8f and S8h.

In brief, the effect of monofilament deformation and the effect of fabric shrinkage are two competing factors in determining fabric thickness. For spacer fabrics using finer monofilament and longer linking distance, the former factor dominates, and hence fabric thickness increases with the increase of monofilament diameter. However, with further increase of monofilament diameter, the straight monofilament segment gets more rigid and more reluctant to be deformed into a curved shape during the shrinkage of outer layers of spacer fabric. In this case, the latter factor becomes dominant, resulting in a decrease of fabric thickness.

Fabric areal mass

Figure 8(g) and (h) display the effect of changing monofilament diameter on fabric areal mass. Overall, monofilament diameter exhibited a positive relationship with fabric areal mass. However, irregular results existed for two samples S4f-PA-D3 and S4h-PA-D3, which can be explained as follows. The trend of fabric areal mass is related with areal stitch density, monofilament linear density, face yarn linear density, and the length ratio of monofilament to face yarn. Since increasing monofilament diameter resulted in decreased areal stitch density as shown in Figure 8(c), then the result is an interplay of changing monofilament diameter and other physical properties of spacer fabric.

Effect of filling density of tucked monofilament

Stitch densities

The number of monofilament threads comprising one course of spacer fabric using full filling density (“f”) is doubled compared with that using half filling density (“h”), resulting in higher impedance against the shrinkage of elastic yarn in the outer layers of spacer fabric. Therefore, spacer fabrics knitted with half filling density (“h”) exhibited much higher stitch densities and coursewise shrinkage coefficients than those knitted with full filling density (“f”), as shown in Figure 8(a) –(d). In other words, fabric structures S8h, S6h, and S4h achieved much higher stitch densities and coursewise shrinkage coefficients compared with fabric structures S8f, S6f, and S4f.

Fabric thickness

Figure 8(e) and (f) shows that the thickness values of spacer fabrics with half filling density (“h”) were comparatively higher than those of spacer fabrics with full filling density (“f”). As was found earlier in Figure 8(d), fabric shrinkage coefficient was much higher for half filling density (“h”) than for full filling density (“f”). Higher coursewise shrinkage led to a greater extent of the rotation of monofilaments to the thickness direction, resulting in a higher fabric thickness. This explains why a higher fabric thickness can be obtained by employing fabric structure with half filling density (“h”) rather than with full filling density (“f”). On the other hand, however, a fabric structure with half filling density can also weaken the compression resistance of spacer fabric. In this case, a balance between adequate compression resistance and high thickness in spacer fabric should be made based on the requirements of end-users.

Fabric areal mass

As shown in Figure 8(g) and (h), spacer fabrics knitted with full filling density (“f”) weighed heavier than those knitted with half filling density (“h”). This is because the number of monofilaments forming one course in the former case are twice that in the latter case, although areal stitch densities of the former case were lower than those of the latter case.

Effect of linking distance

Stitch densities

As shown in Figure 8(a)–(d), the linking distance (eight, six, and four needles) has a minor effect on the coursewise shrinkage coefficient and stitch densities as compared with the other two fabric parameters, monofilament diameter and the filling density of tucked monofilament. Besides, the influencing rule of the linking distance was also not pronounced for spacer fabrics made of nylon monofilament. In general, the largest stitch densities and coursewise shrinkage coefficients mainly appeared in spacer fabrics having the shortest linking distance (spacer structures S4f and S4h). In some cases, longer linking distance resulted in lower coursewise shrinkage coefficient. This rule also applied to spacer fabrics made of polyester monofilament, as will be shown later in Figure 9(d). In some other cases, the linking distance exerted non-monotonic effects on stitch densities and coursewise shrinkage coefficients, which can be inferred to be caused by a complex interplay of opposed factors. On the one hand, a longer linking distance means employing more threads of monofilament in the construction of each course of the fabric, which impedes the coursewise shrinkage of spacer fabric. But on the other, the bending curvature of monofilaments at the tucking points in a spacer fabric with a longer linking distance was relatively smaller during knitting, and therefore these monofilaments were more ready to be further bent under the steaming treatment which causes fabric shrinkage.

Figure 9.

Schematic illustration of the change of inclination state from on-machine to finished for (a) monofilament segment M₁ having a length of l₁ in spacer fabric with a shorter linking distance and (b) monofilament segment M₂ having a length of l₂ in spacer fabric with a longer linking distance.

Fabric thickness

The linking distance of spacer monofilament is an important design variable for obtaining different fabric thicknesses. Figure 8(e) and (f) shows that spacer fabrics with longer linking distance achieved higher fabric thicknesses, which can be verified by a mathematic analysis as shown below.

Assuming the monofilament segment inside the spacer fabric keeps the shape of a straight line, the changes of inclination state from on-machine to finished for two different monofilament segments M₁ and M₂ are illustrated in Figure 10(a) and (b), respectively. Spacer fabric containing the monofilament segment M₁ adopted a shorter linking distance, and the other spacer fabric containing the monofilament segment M₂ adopted a longer linking distance. The monofilament segment M₁ maintains a length of l₁, and M₂ maintains a length of l₂. So, we have this relationship, l₂ > l₁.

Figure 10.

A comparison of: (a) coursewise density; (b) walewise density; (c) areal stitch density; (d) coursewise shrinkage coefficient; (e) fabric thickness and (f) fabric areal mass of spacer fabrics made with polyester monofilament and nylon monofilament.

Since the spacing between two needle beds is fixed, both monofilament segments had the same height h₀ during knitting on machine. Due to the shrinkage of elastic yarns in the outer layers, monofilament segments were inclined further, resulting in an increased height h₁ and h₂ for monofilament segment M₁ and M₂, respectively. The height of monofilament segment can be regarded as effectively the thickness of spacer fabric, since the thickness of outer layers of spacer fabric is relatively small. The following analysis will show that higher fabric thickness can be obtained by employing spacer fabric having longer linking distance, in other words, to prove that this inequation h₂ > h₁ is established, given that l₂ > l₁.

Let the coursewise shrinkage coefficient of spacer fabric containing monofilament segment M₁ and M₂ be $ε_{1}$ and $ε_{2}$ , respectively. Earlier analysis has already shown that the linking distance of spacer monofilament made a negligible impact on the coursewise shrinkage coefficient. It implicates that spacer fabrics with different linking distances have almost the same coursewise shrinkage coefficients. Then, we can assume $ε_{1} = ε_{2}$ .

Given that the height of monofilament segment in one spacer fabric at the stabilized state is h, the length of this monofilament segment is l, and the coursewise shrinkage coefficient of this spacer fabric is $ε$ , a geometrical analysis gives the following relationship

l^{2} = {(\frac{\sqrt{l^{2} - h_{0}^{2}}}{1 + ε})}^{2} + h^{2}, ε > 0 and 0 < h_{0} < l

(3)

From equation (3), the stabilized fabric thickness h is derived as

h = \frac{{[ε (2+ ε) l^{2} + h_{0}^{2}]}^{1 / 2}}{1 + ε}, ε > 0 and 0 < h_{0} < l

(4)

Since the coursewise shrinkage coefficient $ε$ and the on-machine fabric height h₀ are constant quantities with regard to different length l of monofilament segment, we can take the derivative of fabric thickness h with respect to l as

\frac{d h}{d l} = \frac{ε (2 + ε) l}{1 + ε} \cdot {[ε (2 + ε) l^{2} + h_{0}^{2}]}^{- 1 / 2} > 0

(5)

As this derivative is always positive, this indicates fabric thickness h is always positively correlated with the length l of monofilament segment, in other words, h₂ > h₁ if l₂ > l₁. Therefore, it is demonstrated that a longer linking distance results in higher fabric thickness.

Fabric areal mass

It is observed from Figure 8(g) and (h) that longer linking distance led to larger fabric areal mass. Since the variation in the linking distance of spacer monofilament caused insignificant changes in fabric stitch densities, we can assume the same stitch densities for spacer fabrics with varied linking distances. Under this condition, the larger areal mass for spacer fabric with longer linking distance can be deduced to have been caused by the longer total length of all the monofilament segments in such a spacer fabric.

Effect of monofilament type

Figure 9 compares basic physical properties of spacer fabrics made with polyester monofilament and nylon monofilament under an identical monofilament diameter (D1), based on which the influences of monofilament type on stitch densities, fabric thickness, and fabric areal mass of spacer fabrics are analyzed.

Stitch densities

As shown in Figure 9(a) and (d), for spacer fabrics knitted with polyester monofilaments, their coursewise densities and coursewise shrinkage coefficients were lower than those of spacer fabrics knitted with nylon monofilament. The reason lies in that polyester monofilament has a higher flexural modulus than nylon monofilament. As a result, polyester monofilament exhibited a higher level of resistance against the shrinkage of the outer layers during the steaming treatment. However, for the walewise density, spacer fabrics knitted with polyester monofilament showed higher values than those of spacer fabrics knitted with nylon monofilaments. The reason may lie in the fact that the stiffer polyester monofilament caused knitted stitches in the outer layers of spacer fabric to extend along the coursewise direction, making the stitches flat in shape so that the length of the loop pillar, the height of the stitch in other words, became short. As a result, the walewise density, which corresponds to the ratio of a specified distance along the wale direction to the height of the stitch, became accordingly high.

Fabric thickness

As shown in Figure 9(e), for longer linking distances, namely S8f and S8h, spacer fabrics made with nylon monofilament gave higher fabric thicknesses. On the contrary, for shorter linking distances, namely S4f and S4h, spacer fabrics made with polyester monofilament gave higher fabric thicknesses. Therefore, the influence of monofilament type on fabric thickness was also dependent on fabric structure. On the other hand, the degree of variation of fabric thickness with different linking distance (eight, six and four needles) was smaller for spacer fabrics made with polyester monofilament than for those made with nylon monofilament. This was attributed to higher flexural modulus of polyester monofilament than that of nylon monofilament.

Fabric areal mass

As shown in Figure 9(f) for fabric areal mass, although the linear density of polyester monofilament is higher than that of nylon monofilament, spacer fabrics knitted with polyester monofilament were lighter, which was related to their lower areal stitch densities, as shown in Figure 9(c).

Conclusions

The vibration behavior of top-loaded weft-knitted spacer fabric under harmonic base excitation was studied. The effects of monofilament diameter, the linking distance, and the excitation acceleration level on the acceleration transmissibility vs excitation frequency curve of the mass-spacer fabric system were evaluated. Furthermore, based on 30 different types of weft-knitted spacer fabrics manufactured by using flat knitting technology, the effects of different design variables, namely monofilament type, monofilament diameter, and spacer structure, on dimensional and physical properties of spacer fabric including stitch densities, fabric shrinkage coefficient, fabric thickness, and fabric areal mass were also analyzed. The following findings are discovered:

In applications using weft-knitted spacer fabrics as anti-vibration materials, spacer fabrics should be designed with proper materials and structures in order to avoid resonance and jump phenomena, especially for relatively high excitation acceleration level conditions.

In practice, the cushioning performance of an anti-vibration material is tool or excitation spectrum-specific. Thus, the frequency range in which dangerous vibrations emerge should be taken into consideration during fabric design or selection. For an example, in applications such as anti-vibration gloves for workers dealing with electrical or pneumatic powered rotary tools, the concerned frequencies can range from 150–250 Hz. In this condition, spacer fabric having the smallest monofilament diameter (D1) and the longest linking distance (S8f), for instance spacer fabric type S8f-PA-D1, exhibited the lowest vibration transmissibility. Therefore, it can be recommended for manufacturing.

To broaden the frequency range for vibration isolation, spacer fabrics with smaller monofilament diameter and longer linking distance were preferred since they gave relatively low fabric stiffness, leading to a relatively small resonance frequency. However, this was only effective for relatively high working frequencies. Besides, decreasing fabric stiffness in order to achieve smaller resonance frequency is not always realistic, because the spacer fabric is also required to possess an adequate static load-bearing capacity. Therefore, an optimal design of spacer fabric should result in a high-static-low-dynamic stiffness fabric in order to have a broadened frequency range for vibration isolation and to have enough static load-bearing capacity as the same time. On the other hand, for relatively low working frequencies, vibration may be unavoidably magnified as low-frequency vibration isolation is relatively difficult to achieve.

Fabric thickness depended mainly on the spacer structure of spacer fabric, namely the linking distance and the filling density of tucked monofilament. Higher linking distance and lower filling density contributed to improved fabric thickness. Nevertheless, higher linking distance also increased fabric areal mass, resulting in higher material costs. On the other hand, although lower filling density is beneficial to improved fabric thickness, it also unfavorably reduces the compression resistance of spacer fabric.

The relationships of the modulus and the diameter of spacer monofilament with fabric thickness were non-monotonic and complex. Besides, the influence of monofilament diameter on fabric thickness was not particularly significant. In addition, higher variability in fabric thickness was more readily realized by using a monofilament having a lower modulus. Therefore, nylon monofilament was preferred to polyester monofilament for obtaining an optimized high fabric thickness.

Fabric stitch densities and fabric areal mass were affected to a great extent by monofilament diameter. Larger monofilament diameter resulted in larger areal mass and lower stitch densities for spacer fabric. As lower stitch densities further relate to a higher porosity in the outer layers of spacer fabric, thus employing larger monofilament diameter is good for improving the air permeability of spacer fabric.

Footnotes

Acknowledgements

The authors greatly appreciate the valuable comments and suggestions received from the reviewers of this article.

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 Textile Vision Basic Research Program (Grant No. J202004), Shandong Province Key Research and Development Plan (Grant No. 2019JZZY010335) and Shandong Provincial Universities Youth Innovation Technology Plan Team (Grant No. 2020KJA013).

ORCID iD

Fuxing Chen

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