Knitted Heating Mats

Optimization of the construction of the mat was based on selecting the electrical and structural values in such a way that the temperatures of the mat fell within the limits of human physiological comfort.

Such considerations led to the selection of a strip made of 5 courses as the heating element. The measurement results for 5 courses are marked in red to distinguish the selected variant, although in some cases the strips with a different number of courses had slightly better results for the parameters tested.

Next, for basic research, a double faced fabric was produced consisting of six heating strips made of carbon yarn with a varying number of courses separated with ten courses made of cotton yarn (Fig. 5).

Fig. 5.

Measurements of the resistance, voltage and intensity of current flowing through the carbon strips in order to determine the power were started after 24 hours of fabric relaxation. Moreover, before the measurement, the samples were acclimatized and the tests were performed at a constant relative humidity of 40 % and temperature of 21 °C. As shown in Fig. 5, the width of the knitted fabric is non-uniform. Measurements of resistance R, using a multimeter, were performed for two variants of fabric width: non-uniform - after 24 hours of relaxation and constant - as a result of applying the sample onto a plexiglass frame with a width of 22 cm (Fig. 6).

Fig. 6.

Table 2 presents the results of resistance measurements of individual heating strips made of carbon yarn for different widths of the fabric.

The results from Table 2 are shown in graphical form in Fig. 7. As can be seen, the increase in the width of the fabric for the number of courses from 1 to 6 results in a decrease in the resistance value.

Fig. 7.

The specific structure of the knitted loop, whose top arc is in contact with the bottom half-arcs of the loop placed in the above course, leads to possible short-circuit points (Fig. 8). A short-circuit point means that the resistance of the conductor decreases while the intensity of the flowing current goes up.

Fig. 8.

With an increasing number of courses made of carbon yarns in a given strip, the area S of the conductor cross section increases, and at the same time the number of short-circuit points also grows, which results in a reduction in resistance of a single carbon strip. This phenomenon is confirmed by the formula for the conductor resistance: R=ρ∙l/S [Ω], where: ρ - specific resistance of the conductor material [(Ω∙mm²)/m], for carbon fibers at 20 °C ρ equals 15÷40 (Ω∙mm²)/m, l - conductor length [m], S - conductor cross-sectional area [mm²]. Subsequently, measurements were made of the current power flowing through the carbon yarns introduced into the fabric courses and of the temperature of the heating strips. If electrical current flows through a fabric strip of resistance R_i, it is accompanied by heat release according to Joule-Lenz’s law. The heat is equal to the work done by the current intensity I and voltage U at time t: W=U×I t or W= I² ·R_i t if, according to Ohm’s law, we substitute U = R_i I. The value of effective voltage or direct (alternating) current determines the thermal power of the current (the ratio of work to time), which is expressed by the formula: P_Q=W/t=I²·R_i=U²/R_i [W=J/s=V·A]. During the research, the current intensity I was measured for the variable values of voltage U in the range from 0 to 30 V, for six variants of carbon strips. The system was powered by a laboratory power supply type DF 1730SL10A. During the measurements, the voltage was changed every 0.5 V in order to obtain the specific current increase. For each voltage setting and current intensity measured with the ScanTemp 485 pyrometer, the temperature was read on the radiator strips. The results of the measurements are shown in the graphs (Fig. 9, 10 and 11).

Fig. 9.

Fig. 10.

Fig. 11.

The results of the studies conducted confirm the above formulated relations arising from Joule’s law, showing that thermal power increases with the increase of the applied voltage, which is higher for resistors with lower resistance. The dependence of the power increase as a function of the voltage is also described by a third order polynomial equation. The largest thermal power is observed in the case of the heating strip with a width of six courses. For the given range of voltage changes from 0 to 30 V, depending on the resistance of the courses made of carbon threads, the thermal power of the strips equals from 0 to 33.2 W. It should be noted that the power values presented are the product of the voltage and current intensity measured. The power calculated from the products (I²×R and U²/R) differs significantly from that determined from the relation I×U, as shown in Table 3 and in the graph (Fig. 10).

The differences result from the variability of the resistance R of the knitted fabric, caused by an increase in the temperature of the heating elements according to the relation: R = R_o (1 + α × T), where:

R_o - resistance at 0 ^oC, T - conductor temperature, α - temperature coefficient of conductor resistance. For the analyzed electrically conductive strips with a number of courses from 1 to 6, for the supply voltages most often applied: 12 V and 24 V, the power ranges from 0.6 to 4.1 W and from 2.6 to 19.0 W (Table 3). In the case of temperature changes on the surface of the heater, the highest temperature values can be observed for a fabric width of six courses (Fig. 11).

When analyzing the diagram, it can be seen that course 1 reaches the lowest temperature of about 54 °C for the highest supply voltage of 19 V. The highest temperature (70 °C) and, at the same time, the lowest voltage of 12 V are obtained for the strip with 6 courses.

Analysis of the results led to the selection of a strip with 5 courses made of carbon yarn. This variant was characterized by low resistance when supplied with a voltage of 12 V, optimum heating temperature, good efficiency and moderate power losses. As a result, the number of 5-course strips required for the design of the heating mat was calculated (Table 4).

In Table 4 (fifth column), the equivalent resistance R_iz for parallel connections was calculated based on Kirchhoff’s first law, i.e. Riz=∑ni=11Ri,$${R_{iz}} = \sum\nolimits_n^{i = 1} {{1 \over {{R_i}}}} ,$$ where n is the number of resistors (carbon strips connected in parallel).

The data presented show that the heating mat designed with eight up to ten heating strips made of carbon threads arranged in five courses generates a heating power of 16 to 20 W when supplied with a voltage of 12 V.

It should also be emphasized that thanks to the considerable elasticity of the knitted fabric, equal to e = 108 % when stretched along the courses (heating strips) there was no damage (breaking) to the knitted structure of the heater, and continuity of current flow through the carbon strips was maintained. Similarly, while stretching the fabric along the wales up to ε=56 %, no damage was done to the fabric structure or heating strips.

An innovative concept was developed for the construction of a highly flexible knitted heating mat (Fig. 12 a and b). The mat is constructed in the form of a composite (hybrid) ternary structure. The first element of the mat is the basic knitted fabric (1) characterized by high elasticity, whose relative elongation reaches several hundred percent.

Fig. 12.

Electrically conductive threads of varying resistance (2) are built in the base of the structure. One of the variants proposed are threads acting as heating elements. In the second variant it was assumed that electrically conductive threads with low resistance can serve as paths for transmitting electrical signals.

The third important element of the construction are the high- strength threads (3), whose task is to limit the maximum elongation of the knitted fabric, so that the functional electrically conductive threads are not broken during use or in the stretching process.

Fig. 12b shows the assumptions for the construction of a highly flexible heating mat. The basic knitted fabric is made of multi-guide warp-knitted stitches. Depending on the requirement, the structure may consist of two or three basic stitches, such as tricot or cord stitches with an underlap in opposition or a-jour structures with a small cover factor (for example pillar and weft stitches). The choice of warp-knitted stitches is not a random one. It results from the fact that they are characterized by greater flexibility than weft-knitted ones. The second important factor is that in the case of warp-knitted structures it is much easier to shape the cover factor of the fabric. However, most important is the possibility of introducing into the basic knitted fabric the electrically conductive threads, arranged in the configuration of wefts or other stitches in the longitudinal arrangement of the wales or transverse of the courses, as well as at any angle to the oriented axes of the courses and wales.

In order to ensure high elasticity of the structure, the basic knitted fabric is made of elastomeric threads and electrically conductive threads are introduced in a so-called zig-zag form. The geometry of the arrangement of these threads is characterized by the length l_ip of the elementary section AB and the angle α_np, which defines the position of the thread in relation to the horizontal arrangement of the courses. Parameters l_ip and α_np can also be indirectly described by the width s_w and the height h_w of the arrangement repeat of elementary thread AB.

When the fabric is stretched in the longitudinal direction towards the acting forces P, straightening of the electrically conductive threads takes place, which causes an increase in the angle α_np to the limit value π/2, an increase in h_w to the limit value l_ip, and a decrease in the value s_w (s_w≅0).

When the limit value of threads straightening is exceeded, i.e. when h_w > l_ip, elongation of the electrically conductive material takes place and the thread is broken.

From the geometrical model of the thread arrangement presented, it can be concluded, that larger elongation of the knitted structure, while maintaining the continuity (no damage - breaking) of the thread, can be obtained for the increased lengths of elementary sections l_iP and for small angles of thread inclination α_np.

In order to prevent the breaking of the electrically conductive thread, which would lead to the damage of the heater, so called protective threads were introduced into the knitted fabric. Their function is to ensure that in the extreme stretching conditions, the limit h_w,max = l_ip is not exceeded.

Just like the electrically conductive threads, the protective ones are arranged in the form of a zig-zag, with such geometric parameters that in the stretching process and during the final straightening, the limit value h_w satisfies the inequality: h_w,zab = l_iz < h_w,max Describing the function of protective threads, it can be said that in the stretching process they are vertically straightened and prevent the complete straightening of the zig-zag of electrically conductive filaments. To prevent damage to the knitted structure, the protective threads are characterized by high strength. It should be noted that the geometry of the thread arrangement can be programmed by means of the design and structural parameters of the fabric stitches.

A highly flexible warp-knitted fabric with electrically conductive threads was designed. The stitch is a weft three-guide structure. The basic knitted fabric is made up of a component pillar stitch with open loops (full threading) and a weft inlay with a lap along 2 t_u (Fig. 13). Elastomeric threads braided with polyamide with a linear density of 78 tex (Fig. 1) were selected for the basic fabric. The relative elongation of highly elastic threads of the gumitex type equals 234 %. The third component stitch of the knitted fabric is a weft stitch made of electrically conductive threads. This stitch is formed as a so called zigzag (red threads in Fig. 13). Height of stitch repeat R_w = 6 courses, repeat width R_h = 8 wales. To keep the diagram readable, only one thread was depicted. In two variants of the project, two types of electrically conductive threads were taken into account: variant W2.1 – double carbon threads with a linear density of 134 tex, variant W2.2 – threads PA6.6 coated with silver of the Shieldex type with a linear density of 11 tex (threads characteristics Fig. 1). The protective threads were neglected in the project.

Fig. 13.

The stitches of the two variants of the fabrics designed were made on a Karl Mayer Raschel knitting machine of the type RL5NF with a needle gauge E12. Knitted strips with a width of 50 mm (Fig. 14 and 15) were produced. One knitted strip was made of 56 warp threads with full threading of the guide bars of the first and second component stitch. Figures 15 a and b show two variants of the knitted fabrics with electrically conductive threads. In variant W 2.1, four carbon threads were introduced into the width of the strip, and in variant 2.2 - six threads of the Shieldex type were used.

Fig. 14.

Fig. 15.

After dry relaxation the fabric course density P_r equaled 120 courses/10 cm, and the wale density P_k = 112 wales/10 cm. Fig. 16 shows mechanical characteristics of the fabric in the stretching process. The longitudinal breaking force of the knitted strip equaled 738 N/50 mm (13.13 N/wale) and the relative elongation ε = 310 %.

Fig. 16.

The variants of the knitted fabrics obtained confirmed the correctness of the design assumptions and the effectiveness of the technology of knitting on warp knitting machines in the production process of highly flexible heating materials or structures transmitting electrical signals. The next stage of the research was to determine how much the loads affecting the heating strips in the stretching process influence the changes in the resistance parameters of the electrically conductive threads introduced.

In variant W 2.1, a system of 4 carbon threads with a linear resistance of 216 Ω/1 m of the thread was parallelly connected along the length of 100 mm. In variant W 2.2. six silver-coated threads with a resistance of 2 kΩ/1 m of the thread were joined.

The upper and lower parts of the strips were connected with a silver thread by sewing on a lockstitch sewing machine. Similarly prepared samples were acclimatized before measurements, and tests were performed at a constant relative air humidity of 40 % and temperature of 21 ^oC. The samples of knitted strips of a length of 100 mm were fixed in the grips of the Haunsfield testing machine of the type H50K-S, and stretched at a speed of V = 50 mm/min (Fig. 17). The stretching process was carried out in six stages for the specific elongation values of each stage. After stretching the sample and 5 minutes of relaxation, the resistances of the electrically conductive threads were read on the ohmmeter.

Fig. 17.

The selected stages of the stretching cycle of the knitted fabric are shown in Fig. 18, while the diagram in Fig. 19 presents the dependencies of changes in the thread resistance. The research presented shows that the resistance of electrically conductive elements increases together with the elongation of the highly elastic structure of the basic fabric. The nature of resistance increase R = f (Δl) takes the form of the fourth degree polynomial function (regression coefficient R² = 0.98).

Fig. 18.

Fig. 19.

For carbon threads in the elongation range ε= 210%, resistance R increased by 3.2 Ω, whose per unit growth of elongation ΔR/ε equals 0.0152 Ω/%. For silver-coated threads in the elongation range e = 270 %, the increase DR is 18.8 Ω and the resistance increase in relation to elongation equals 0.2218 Ω/%. Taking into account relative resistance changes in relation to elongation, i.e. (ΔR/R)/ε the increases are as follows: for carbon threads 3.7·10^-4, and for silver-coated threads 2.6·10^-3. In the interpretation of the results of resistance changes obtained, one should refer to similar behaviors of electrically conductive textiles. In our case, the electrically conductive threads introduced were to serve as heating elements, therefore it would be reasonable to analyze the changes in heating power (heat exchange balance) and temperature changes on the surface of the heater. Such analyzes will be made in the next study.