WO2015097219A1

WO2015097219A1 - Heating element with a layer of resistive material locally configured to obtain predetermined sheet resistance

Info

Publication number: WO2015097219A1
Application number: PCT/EP2014/079157
Authority: WO
Inventors: Thomas Wittkowski; Michael Olk
Original assignee: Iee International Electronics & Engineering S.A.
Priority date: 2013-12-23
Filing date: 2014-12-23
Publication date: 2015-07-02
Also published as: LU92345B1; DE112014005882T9; DE112014005882T5

Abstract

The invention concerns a heating element (1) for generating heat when connected to an electrical power source, comprising a substrate supporting first and second feedline (2, 2a) extending generally along opposite sides of the element (1), each feedline comprising an electrical contact point to the source, each feedline (2, 2a) distributing the power supply along it, an intermediate substrate part (3) sandwiched between the two feedlines (2, 2a) supporting a layer of resistive material, a current flowing from one feedline (2) to the other feedline (2a) in operation through the layer and dissipating heat. The layer is in the form of a pattern applied on the substrate part (3) and configured so that the sheet resistance thus locally obtained varies continuously over the intermediate substrate part (3) in correspondence to a respective predetermined sheet resistance in order to achieve a desired temperature distribution over the heating element (1).

Description

Heating Element with a Layer of Resistive Material Locally Configured to Obtain Predetermined Sheet Resistance

Technical field

[0001 ] The present invention generally relates to a heating element with a layer of resistive material locally configured to obtain a respective predetermined sheet resistance. As a preferential but non limitative application such a heating element may be used for heating surfaces in automotive vehicles, i.e. compartments of aviation, rail, and road vehicles with the aim of warming the occupants. A special focus is laid on heating of all kinds of surfaces such as door panels, steering wheels, arm rests, and several more in the cabin of automotive vehicles which are at least partially non planar surfaces.

Background Art

[0002] According to the state of the art, heating elements for generating heat when connected to an electrical power source comprise a substrate supporting a first feedline or first bus and a second feedline or second bus extending generally along opposite sides of the heating element. Each feedline comprises an electrical contact point to the electrical power source, each feedline distributing the electrical power supply along it. At least a layer of resistive material is arranged between and in electrical contact with the two feedlines. In operation an electrical current flows from the first feedline to the second feedline through the layer of resistive material and thereby dissipates heat when connected to the electrical power source.

[0003] One or a plurality of these heating elements may be grouped to form an electrically powered heater. These heating elements may be operated either in serial or in parallel by specific electrical supply circuits, thereby heating respective areas of an object to heat.

[0004] Individual heating elements as well as their feedlines may be applied on the substrate in some industrial deposition process such as printing, e.g., the substrate being a polymer film, a textile carrier or directly on the backside of the object to be heated. [0005] The adjustment of the temperature distribution in an electrically heated area is at the core of heater design. Today only crude approximations to the desired adjustment are possible. Reason is the use of only a small discrete number of heating elements characterized by their sheet resistance. Typically the same layer of resistive material, exhibiting a uniform sheet resistance for the whole layer is used. In consequence the temperature distribution in the heated area can hardly be adjusted. Only in certain special cases such as for small rectangular heated areas where the voltage drop is negligibly small, a certain uniformity of the temperature in such small area is achieved. However a defined, planar adjustment of the temperature is not possible today.

[0006] It is frequent to have electrically powered heater comprising more than one heating element as previously described. Such an electrically powered heater is operated either in serial or in parallel electrical circuits. Parallel electrical circuits can carry out planar heating.

[0007] A persisting challenge in these heaters is the creation of a defined temperature distribution within the heated area. The state of the art deals with this challenge by proposing various solutions.

[0008] In the majority of today's products the heating elements are chosen very small and of rectangular shape so that the voltage drop along the feedlines is negligibly small. In this way the heater is provided with small rectangular heating elements of constant temperature across the heated area. [0009] Another option to achieve a uniform temperature distribution is to take into account the voltage drop along an array of heating elements. Several heating elements of different geometric extensions or sheet resistances are operated so that the power density across the complete array of heating elements is quite uniform. However, this approach relies on a constant sheet resistance in each heating element.

[0010] In some products strong variations in the temperature distribution across the heater area are simply tolerated.

[001 1 ] None of the above mentioned solutions is able to adjust a non-uniform temperature distribution across the heated area in a well-defined manner or to adjust a uniform temperature distribution for heating elements, especially non- rectangular heating elements or for heating elements where the voltage drops significantly as a function of its length coordinate.

[0012] Consequently a heating element that compensates the deviations from rectangular geometry in a complex shaped area as well as the voltage drop in order to adjust the temperature distribution does not exist so far.

[0013] Furthermore heating elements for complex shaped areas are either small and rectangular in order to warrant a uniform temperature distribution over a small rectangular area or the complex shaped areas are submitted to a vastly nonuniform and non-adjustable heating temperature distribution.

Technical problem

[0014] An aim of the present invention is therefore to provide an improved heating element enabling the temperature distribution in the complete heated area to be adjusted.

General description of the invention [0015] This aim is achieved by a heating element for generating heat when connected to an electrical power source, comprising a substrate supporting a first feedline and a second feedline extending generally along opposite sides of the heating element. Each of said first and second feedline comprises an electrical contact point for connecting said feedline to an electrical power source, each feedline distributing an electrical power supplied along its extension. An intermediate substrate part between the two feedlines supports a layer of resistive material such that, in operation, an electrical current flows from the first feedline to the second feedline through the layer of resistive material and thereby dissipating heat. In accordance with the invention, the layer of resistive material is in the form of a microscopic pattern applied on the intermediate substrate part and configured so that the sheet resistance locally obtained for the applied pattern varies continuously over the intermediate substrate part in correspondence to a respective predetermined sheet resistance in order to achieve a desired temperature distribution over the heating element. [0016] In a preferred embodiment, the pattern is defined by the presence of microscopic exclusions in the resistive material wherein a distribution of exclusions of the pattern on the intermediate substrate part preferably follows a predetermined distribution, a random or a pseudo-random distribution in every unitary area element. It will be noted that in the context of the present invention, the expression exclusion is used to designate a microscopic area in the layer of resistive material in which no resistive material or a reduced amount of resistive material is present in the layer.

[0017] In accordance with the present invention, the heating area (between the two feedlines) of a heating element may be printed using a printable resistive material. The properties of the heating area are preferably not the same across the complete heating area. The resistive material is printed in a pattern such that the its sheet resistance of the heating area varies as a function of the lateral coordinates x, y, of the printed sheet so that Rsqp < Rsq(x,y) < °°. In addition Rsq(x,y) is preferably varied in a continuous manner, i.e. is doesn't change abruptly (in one step) between Rsqp and∞. [0018] The (continuous) variation of Rsq(x,y) is obtained by tiny exclusions in the pattern of the printing mesh. These exclusions should not be confused with Openings' or 'zones' or something alike. These exclusions are very small with respect to the dimension of the heater element. In accordance with a preferred embodiment, the exclusions may e.g. be circular and have a diameter between 20μηη and 300μηη, and preferably in the range of Ι ΟΟμιτι and 200μηη. Rsq(x,y) is adjusted continuously by adjusting the area density of such shaped exclusions n(x,y) as a function of the lateral coordinates x,y.

[0019] Preferably the area density of exclusions n(x,y) is a continuous function. In this way the sheet resistance, Rsq(x,y) is controlled by the local area density n(x,y) of exclusions. Rsqp is the minimum sheet resistance one obtains for n(x,y) = 0.

[0020] It is clear that in order to define a meaningful sheet resistance Rsq(x,y), the area for which Rsq is defined should be much greater than the area of a single exclusion. Note that the same requirement holds to determine a meaningful area density of exclusions. As a rule of thumb the unitary area element on which n(x,y) or Rsq(x,y) are defined exhibit lateral dimensions a factor of five and preferably a factor of ten greater than the lateral dimension of a single exclusion. [0021 ] In an embodiment where the diameter of an exclusion is 0.3 mm the area to define n(x,y) or Rsq(x,y) would be 3 x 3 mm². It is intuitively clear that the area of 3 x 3 mm² should be much smaller than the heating area. The heating area should be a factor of five and preferably a factor of ten greater than the area on which n(x,y) or Rsq(x,y) are defined. This means that the heating area is preferably 10⁴ d² times greater than the area of a single exclusion on the printing mesh.

[0022] In an embodiment, in which the intermediate substrate part comprises at least one opening, the influence of the opening on the local sheet resistance may be compensated by an appropriately adjusted area density of exclusions in the layer of resistive material on the intermediate substrate part in the surroundings of the opening. By an appropriate adjustment of the area density of exclusions, i.e. by a corresponding local adjustment of the sheet resistance, it is possible to deviate a heating current around the opening.

[0023] In a possible embodiment, the exclusions can be of different shape, at least two different shapes existing in an area element of the intermediate substrate part and, if the distribution of exclusions follows a predetermined distribution, each different shape of exclusions presents its own predetermined distribution.

[0024] In an embodiment of the invention, the intermediate substrate part extends substantially in two dimensions with coordinates x and y and only a single shape of exclusions in the layer of resistive material is present over the intermediate substrate part with no overlapping of these exclusions. The continuously adjusted sheet resistance Rsq(x,y) of the applied pattern with such exclusions is then defined in respect of the sheet resistance of a full pattern Rsqp by:

Rsq(x, y) = Rsqp^■ - -

1 - ₂ ^■ F - n(x, y)

with F being the area of an exclusion and n(x,y) being the area density of exclusions as a function of at least one of the coordinates x and y of the intermediate substrate part and with ai and a₂ being empirical factors that depend upon the exclusion's type (size and shape), the screen mesh, the ink viscosity and surface energy, the substrate surface energy, and the parameters of the printing process. In a possible embodiment, ai and a₂ may e.g. be equal to 1 . [0025] The first and the second feedlines may each have a wavelike form in phase with each other such that the width of the applied pattern on the intermediate substrate part alternates continuously between a reduced width and a larger width. In this case, the applied pattern of exclusions corresponding to a larger width preferably presents a lower sheet resistance than the pattern corresponding to a reduced width, thereby permitting a continuous variation of the sheet resistance over the intermediate substrate part with the pattern applied on it.

[0026] Preferably when the first and the second feedlines on opposite sides of the heating element are not parallel, i.e. divergent, the sheet resistance of the applied pattern diminishes continuously in function of the divergence of the feedlines.

[0027] Preferably when the feedlines are of variable width, starting from a lateral side of the heating element, the feedline width and the sheet resistance of the applied pattern vary respectively in function of the length coordinate of the heating element, starting from the said lateral side, according to the following equations:

wherein wfl(x) and Rsq(x) are respectively the feedline width and the adjusted sheet resistance Rsq(x,y) of the applied pattern at a length coordinate x of the heating element starting from the said lateral side, wflO and RsqO respectively the feedline width and the sheet resistance Rsq(x,y) of the applied pattern at the said lateral side, I the total length of the heating element, b and a respective coefficients with b different from zero.

[0028] Preferably a is a real value equal to or greater than zero, e.g. a is equal to 1 or 2, while coefficient b may adopt any real value greater than -1 which is different from zero.

[0029] Preferably if a is equal to 1 , the heating element presents a difference in electric potential, i.e. voltage u(x) function of the length coordinate of the heating element defined by:

uO being the voltage at the said lateral side, Rsqfl being the sheet resistance of the feedlines and Rsq the sheet resistance of the applied pattern. Rsq and wfl mean Rsq(x) and wfl(x) at x = 0, respectively.

[0030] If a is equal to 2, the heating element presents a voltage u(x) function of the length coordinate of the heating element defined by:

uO being the voltage at the said lateral side with electric contact points, Rsqfl being the sheet resistance of the feedlines and Rsq the sheet resistance of the applied pattern. Rsq and wfl mean Rsq(x) and wfl(x) at x = 0, respectively. [0031 ] It will be noted that the person skilled in the art can easily deduce the power density as a function of the length coordinate from the voltage.

[0032] Preferably the layer of resistive material is made of a material with a positive temperature coefficient of resistance.

Brief description of the drawings [0033] Preferred embodiments of the invention will now be described, by way of example, with reference of the accompanying drawings, wherein :

FIG.1 shows a part of a print pattern (of exclusions) continuously adjusted in the two dimensions of an intermediate substrate part of a heating element according to an embodiment of the present invention, the pattern presenting continuously adjusted sheet resistance in two dimensions;

Fig.2 shows a pattern applied on an intermediate substrate part of a heating element in accordance with another embodiment of the present invention, the pattern varying continuously between reduced width and larger width;

FIG.3 shows a pattern applied on an intermediate substrate part of a heating element in accordance with another embodiment of the present invention, the pattern is applied between diverging lateral sides and presents a continuously adjusted sheet resistance;

Fig.4 is a schematic top view of a heating element with respective parallel feedlines, the feedline widths and the resistive layer width being constant, this heating element being in accordance with the prior art;

FIG.5 shows a curve expressing the relative power density of the heating element shown in Fig.4 in function of the heating element length;

FIG.6 shows curves expressing the ratio of feedline width and sheet resistance to respective initial feedline width and initial sheet resistance in function of the ratio length to total length for a heating element in accordance with the preferred embodiment of the invention;

FIG.7 is a schematic top view of a heating element in accordance with the preferred embodiment of the invention with respective feedline and sheet resistance as a function of the length of the heating element, the width of the feedlines narrowing and the sheet resistance diminishing with increasing x l in the embodiment shown in this figure;

FIG.8 shows a zoomed view into a possible pattern of microscopic exclusions in an area element for application on an intermediate substrate part for the heating element in accordance with the preferred embodiment of the invention;

FIG.9 shows a curve expressing the relative power density of the heating element shown in Fig.7 in function of the heating element's length coordinate in accordance with a preferred embodiment of the invention.

Description of a preferred embodiment

[0034] In reference to Figs 4 and 7, a heating element 1 for generating heat when connected to an electrical power source in accordance of the present invention, comprises a substrate supporting a first feedline 2 and a second feedline 2a extending generally along opposite sides of the heating element 1 . Each feedline 2, 2a comprises an electrical contact point to the electrical power source and distributes the electrical power supply along it. [0035] An intermediate substrate part 3 which extends between the two feedlines 2, 2a supports a layer of resistive material. In operation an electrical current flows from the first feedline 2 to the second feedline 2a through the layer of resistive material and thereby dissipating heat. This intermediate substrate part 3 and the layer of resistive material applied thereon form the heating area of the heating element 1 .

[0036] According to the present invention and as shown in Fig. 8 which illustrates one embodiment of the present invention, the layer of resistive material is in the form of a pattern of microscopic exclusions applied on the intermediate substrate part 3 and configured so that the desired local sheet resistance is obtained.

[0037] The power density, i.e. the power per area unit, is adjusted in a continuous manner across the heating area of the heating element. At thermal equilibrium the power density is proportional to the temperature increase generated by the heating element. The continuous adjustment of power density is performed by a continuously adjusted sheet resistance of the heating area of the heating element. The continuous adjustment of the sheet resistance is performed by means of a continuously adjusted pattern of microscopic exclusions in the layer of resistive material applied on the intermediate substrate part 3.

[0038] It is important to note that continuous in the above sense means continuous in the application of the pattern on the intermediate substrate part 3 defined by spatial coordinates and not continuous in time. In practice the continuous adjustment of the print pattern may be approximated by a fine discretization of the printing plane in one or in two dimensions.

[0039] To obtain a continuously adjusted sheet resistance of the heating area of the heating element 1 , the heating area being formed by the intermediate substrate part 3 with the pattern applied on it, the applied pattern is defined by the presence of exclusions in the resistive material, wherein the expression "exclusion" is used to designate a microscopic area in the layer of resistive material in which no resistive material or a reduced amount of resistive material is present in the layer. The layer of resistive material applied on the intermediate substrate part 3 therefore may be provided with regions having a higher density of exclusions and corresponding to regions with a higher sheet resistance, while other regions having a lower density of exclusions form regions with a lower sheet resistance.

[0040] This continuously applied pattern adjustment permits to fully control continuously the temperature distribution on the heating area. [0041 ] From a technical point of view it may be important to mention that the printed sheet with sheet resistance Rsq at a certain position x,y looks different from an associated design of a printing mesh. The printing mesh in fact exhibits tiny circular exclusions of area density n(x,y). This microscopic design, however, is not transferred 1 :1 to the printing substrate in the printing process. Due to the smallness of the exclusions (of the order of the resolution of the printing process ) the shape of the exclusions will no longer be circular when transferred onto the substrate and their diameter will be smaller than for the print design. The shape of a 'printed' exclusion will be blurred or it may be that the 'printed' exclusion is no exclusion at all but is characterized by a locally reduced print thickness. So it should become clear that the print design shown in Fig. 8 will not be transferred 1 :1 onto the substrate in the printing process but may lead to a print whose average thickness is simply reduced compared to a design with n(x,y) = 0.

[0042] Fig. 1 schematically illustrates a first embodiment of a heating element in accordance with the present invention. This figure shows a continuously applied pattern adjustment in the two dimensions of an application plane of the pattern on the intermediate substrate part. Darker areas 4 indicate low sheet resistance (i.e. characterized by a low area density of microscopic exclusions) and lighter areas indicate high sheet resistance (i.e. characterized by a high area density of microscopic exclusions). The continuously varied sheet resistance in two dimensions is indicated by the continuous grey levels. The macroscopic pattern shown in Fig. 1 may be periodic in zero, in one or in two dimensions or in any suitable other form of distribution of the darker areas 4.

[0043] The darker areas 4, i.e. the low sheet resistance areas, provide an easier path for the electric current than the lighter areas. In this way, in dependence on the externally applied electrical field, the electric current is preferentially transported through the dark areas 4 of the adjusted resistance pattern. Since the power per unit area is proportional to the square of the current but depends only linearly on the resistance the two-dimensional power density and therefore the temperature distribution may be adjusted continuously in this manner. [0044] In this way the temperature distribution over the intermediate substrate part with the pattern applied on it may be adjusted to almost any specification. This kind of pattern may be advantageously used for:

• heating of free-form heated areas,

· compensation of voltage drop that can occur in feedlines of the heating element,

• patterning of the heating area to achieve special temperature distributions, i.e. periodicity in plane, etc .,

• highest homogeneity of temperature distribution in the heated area,

· channeling of current flow; in particular it is possible to cloak openings in the heating element such that the temperature distribution behind the opening (in direction of the current flow) is only slightly affected by the presence of the opening. An opening may be for example a door opener or a control panel in a door panel or in an arm rest, etc. [0045] Fig. 2 shows a second embodiment of a heating element in accordance with the present invention, wherein a continuous print pattern adjustment is performed for a heating element presenting wavy feedlines, the feedlines being not shown but delimiting the intermediate substrate part 3 with the pattern applied on it. The pattern applied on the intermediate substrate part 3 presents darker areas 4 corresponding to low sheet resistance . Lighter regions of the intermediate substrate part 3 correspond to high sheet resistance of the layer of resistive material.

[0046] In this embodiment, darker areas 4 correspond to a low sheet resistance and lighter areas to high sheet resistance, respectively. The sheet resistance is continuously adjusted by the print pattern, such that the sheet resistance is lower in those zones, in which the distance between the feedlines is high and such that the sheet resistance is higher in those zones, in which the distance between the feedlines is small.

[0047] This figure thus shows a continuous print pattern adjustment in x-direction, wherein i.e. the sheet resistance is a function of one coordinate only, i.e. the x coordinate. The feedlines that limit the intermediate substrate part 3 which forms the heating area extending from the top to the bottom in Fig. 2 are wavy in a particular manner. It is clear that feedlines do not necessarily need to be periodic and that details of this embodiment may look differently than illustrated in Fig.2. For example, the wavy feedines may have more periods, the feedlines being moreover parallel or not, etc. [0048] The continuous print pattern adjustment illustrated by the continuous grey levels warrants a uniform temperature distribution across the complete heated area. This is achieved by continuously adjusting the sheet resistance between the feedlines. Such a continuous print pattern adjustment is e.g. employed in steering wheel heating where a two-dimensional heater needs to be draped around a torus, i.e. the steering wheel.

[0049] Fig. 3 illustrates a third embodiment of the heating element in accordance with the present invention. This figure shows a continuous print pattern adjustment of a heating element with non-parallel feedlines 2, 2a.

[0050] Fig. 3 shows a continuous print pattern adjustment in a single coordinate direction, namely the x direction. In this embodiment, the feedlines 2, 2a that limit the intermediate substrate part 3 forming the heating area from the top to the bottom in Fig. 3 are not parallel. The intermediate substrate part 3 may form a trapezoid or, alternatively, almost any other compact shape. The continuous adjustment of the pattern on the intermediate substrate part 3 corresponds to different, continuously adjusted sheet resistance. The greyscale values in Fig.3 indicate the continuous variation of the sheet resistance over the intermediate substrate part 3 with the pattern applied on it, wherein darker areas 4 correspond to low sheet resistance and lighter areas to higher sheet resistance.

[0051 ] Such a continuous adjustment of the sheet resistance warrants a uniform temperature distribution across the intermediate substrate part 3 and consequently across the complete heating area. Such a continuous pattern adjustment may be employed in heaters where heating elements of that geometry are required. In this way it is possible to heat for instance narrow corners of a door panel or of an arm rest. [0052] In regard of all the embodiments illustrated in Figs. 1 to 3 and other embodiments in which the material sheet resistance may vary in function of two dimensions of the intermediate substrate part 3, when the sheet resistance of the layer of resistive material on the intermediate substrate part 3 is continuously adjusted by a continuous adjustment of the pattern applied on it, this continuous adjustment may be compared with the material sheet resistance obtained by the application of a full pattern. [0053] With the continuously adjusted sheet resistance in two dimensions x, y designated by Rsq(x,y) and the sheet resistance of a full pattern applied on the intermediate part of the substrate designated by Rsqp, the continuously adjusted sheet resistance writes:

Rsq(x, y) = Rsqp^■ - -

1 - ₂ ^■ F - n(x, y)

Eq. 1 with F being the area of a microscopic exclusion of the pattern and n(x,y) being the area density of exclusions as a function of at least one of the coordinates x and y of the intermediate substrate part 3. The factors ai and a2 are empirical factors that depend upon the exclusion's type (size and shape), the screen mesh, the ink viscosity and surface energy, the substrate surface energy, and the parameters of the printing process. In a possible embodiment, ai and 32 may e.g. be equal to 1 .

[0054] Equation 1 assumes that the area F of each microscopic exclusion of the pattern is the same and that these exclusions are not overlapping. It further assumes that the length dimension of each of these exclusions is of the order of the minimum structure size of the used application set-up. So if the application resolution is around 0.2 mm, e.g., then a typical diameter of an e.g. circular exclusion would also be of the order of 0.2 mm. It is self-understanding that such an exclusion is not required to be circular in shape. Neither is it mandatory that all of these exclusions exhibit the same shape or size. It is advantageous however to distribute the positions of the exclusions randomly or pseudo-randomly in an area element over the intermediate substrate part 3.

[0055] For purpose of illustration and comparison the topview of a heating element 1 shown in Fig. 4 depicts a classical heating element which is not subject of the invention. This heating element 1 is of rectangular shape and its power density as a function of the distance along its length axis is presented in Fig. 5. For Figs. 4 and 5 the geometrical and electrical parameters were chosen as follows: • Width of feedline, wfl = 0.014 m

• Sheet resistance of feedline, Rsqfl = 0.04 Ohm

• Width of the printed heating area of the heating element, w = 0.1 m

• Length of the printed heating area of the heating element, I = 0.4 m

· Sheet resistance of printed heating area, Rsq = 30 Ohm

• On board voltage, U0 = 13.5 V

[0056] In this embodiment according to the state of the art, the width of the applied heating area corresponding to the width wO of the intermediate substrate part between the points 0 and wO is constant along the length of the heating element 1 . The same applies for the width wflO of each feedline 2, 2a between respectively the points -wflO and 0 for the second feedline 2a and the points wO and wflO+wO for the first feedline 2.

[0057] These electrical parameters result in the targeted power density of approximately 600 W/m² at the contacted side of the heating element 1 and approximately 450 W/m² at the end of the heating element 1 , at x = I. Obviously the power density drops by roughly 25 % along the length axis of the heating element 1 which is unacceptable for efficient operation. It is thus desirable to be able to modify and adjust the power density as a function of the position along the heating element length axis. [0058] Opposite to the situation sketched in Figs. 4 and 5, the preferred embodiment of the present invention, illustrated in Figs 6 to 9 foresees to let the width of the feedlines wfl, as well as the material sheet resistance of the heating area, Rsq(x), vary in the same specified manner. Let the length coordinate of the heating element 1 be x. The heating element 1 is contacted at x = 0 while the length of the heating element 1 is I. In this example of the preferred embodiment the material sheet resistance Rsq(x) and the width of the feedlines wfl(x) both vary as a function of x: wfl(x) = wflO (l + b (y)")

and

Eq. 2 wflO and RsqO denote the feedline width and the material sheet resistance of the heating area at position x = 0, respectively. Exponent a may adopt real values equal to or greater than zero, coefficient b may adopt any real value greater than - 1 . For b = 0 the heating element 1 is unchanged compared to the one shown as an example in Fig. 4.

[0059] Fig. 6 shows how the ratios wfl/wflO and Rsq/RsqO vary according to Eq. 2 as a function of x/l for two arbitrary choices of coefficient b, i.e. b = 0.5 (dashdotted curves) and b = -0.3 (full curves). Values of exponent a are arbitrarily chosen 1 , 2, and 5. It can be seen that for positive b the feedlines widen and the material sheet resistance increases with growing x/l. Conversely for negative b the feedlines narrow and the material sheet resistance decreases with growing x/l.

[0060] Exponent a = 1 corresponds to a linear variation of wfl and Rsq in function of x/l. The variation of the voltages as a function of x is provided in Eqs. 3 and 4 for the technically most important cases a = 1 and a = 2.

6- Rsq wfl 6- Rsq wfl 6- Rsq wfl 6- Rsq wfl

Eq. 3 for a = 1 , and

Eq. 4 for a = 2. [0061 ] From these the power densities as a function of x can be calculated directly.

[0062] In this preferred embodiment it is desired to achieve a uniform power density corresponding to a uniform temperature distribution across the complete heating area of the heating element. At thermal equilibrium the temperature increase is proportional to the power density. [0063] As a starting point the same geometrical and resistance values are taken from the example shown in Figs. 4 and 5. For the preferred embodiment, it is desired to achieve a power density of approx. 600 W/m² over the complete area of the heating element at otherwise unchanged geometry of the heating area; i.e. the heating area is still 0.1 m wide and 0.4 m long.

[0064] It has been recognized that a satisfying temperature uniformity is achieved with:

• a = 1 corresponding to a linear variation of wfl and Rsq with x/l, and

• b = -0.42 corresponding to a narrowing of the width of the feedlines and a decrease in the sheet resistance Rsq with growing x/l.

[0065] Fig. 7 shows the schematic top view of a heating element 1 in accordance with the preferred embodiment of the present invention. The initial width of 1 .4 cm of the feedlines at x = 0 diminishes linearly down to 0.81 cm at the end of the heating element 1 , at x = I. Material sheet resistance diminishes accordingly from 30 Ohm at x = 0 down to 17.4 Ohm at x = I. As for the other preceding embodiments, a high material sheet resistance is shown in light grey and low material resistance is shown in dark grey, wherein a gradient of material sheet resistance is created along the length of the intermediate substrate part 3.

[0066] In order to obtain a material sheet resistance that varies linearly with x/l, the applied pattern of microscopic exclusions of the heating element 1 is generated according to Eq. 1 . The sheet resistance Rsq(x/I) is adjusted by excluding from application over the intermediate substrate part 3 a number of microscopic, pseudo-randomly distributed circular dots referenced 8 in Fig.8, each of diameter 0.3 mm. For the purpose of illustration Fig. 8 shows the applied pattern of exclusions in a tiny area element around position x = 0.125 m corresponding to x/l = 0.31 in Fig. 7. In this area element the area density of circular exclusions from the print, n(x/l = 0.31 ) = 470 cm^"2, and the sheet resistance is Rsq(x/I = 0.31 ) = 21 .7 Ohm.

[0067] The resulting power density of the heating area is shown as a function of a heating element length coordinate in Fig. 9. The power density exhibits a minimum at x/l « 0.2 and maxima at both ends of the heating element. The power density at x = 0 is still 600 W/m², the relative variations, however, amount to only ± 8 % across the length of the heating element. The generated distribution of the power density and consequently the temperature distribution meet much better the requirements with respect to magnitude, in average approximately 600 W/cm² and uniformity with a deviation smaller 10 % than the prior art shown in Figs. 4 and 5. [0068] Advantageously one or a plurality of these heating elements in accordance with the invention may form or may be grouped to form an electrically powered heater. These heating elements may be operated either in serial or in parallel by specific electrical supply circuits, thereby heating respective areas of an object to be heated. [0069] It is also possible to group one or more heating elements in accordance to the invention with one or more known heating elements in such a heater.

[0070] The present invention concerns also a method for producing such a heating element with the step of continuously adjusting the application of the pattern on the intermediate substrate part in function of at least one local coordinate of the intermediate substrate part so that the sheet resistance Rsq(x,y) thus obtained from the patterned layer of resistive material on the intermediate substrate part corresponds to a respective predetermined sheet resistance in order to achieve a desired temperature distribution over the heating element.

[0071 ] According to an embodiment of the method, when a voltage drop occurs along each feedline between the contact point and the most remote point of the feedline from this contact point, the voltage drop along the feedlines is compensated by the step of applying the pattern on the intermediate substrate part with a continuous adjustment of the area density of microscopic exclusions to correct the voltage drop. [0072] Advantageously, the heating element is produced by means of printing on a polymer film, this polymer film forming the substrate. The substrate can be made of PET, PEN, PU or silicone for example. However it is clear that other printing substrates such as fabrics or backside of some decor may be used as well. In an advantageous embodiment screen printing, i.e. flat bed or rotary, may be employed and a substrate of choice is a temperature stabilized polyester film of a preferred thickness between 50 and 125 micron. Optionally the surface of its printing side is pre-treated with some thin, adhesion promoting layer. [0073] The first step of the method for manufacturing a heating element is to carry out an application of the highly conductive layers on the substrate, advantageously by printing. The layers may consist of a polymer thick film (PTF) of typical thickness between 5 and 10 micron which contains silver flakes and a polymer binder. Alternatively an ink containing silver or copper nanoparticles as the electroconductive component may be employed. The wet print is dried in a conveyor belt oven for approximately 90 seconds at an air temperature of 145 °C.

[0074] The second step of the method is to prepare the low conductance layer on the substrate, advantageously by printing, this layer forming the pattern to be applied on an intermediate substrate part. The pattern may consist of a PTF of typical thickness between 5 and 10 micron. At the spot of a microscopic exclusion the print thickness is much thinner, down to zero micron. The layer may contain carbon black particles and a polymer binder. Alternatively an ink containing graphite, carbon nanotubes or graphene can be used. [0075] Of relevance is also the alternative use of an ink/print that exhibits a positive temperature coefficient of resistance (PTCR). Such an application of a material with a positive temperature coefficient of resistance helps to further homogenize the temperature distribution across the heating element and provides an additional safety in a hypothetical overheating scenario. As for the highly conductive print the wet low-conductance print is dried in a conveyer belt oven for approximately 90 seconds at an air temperature of 145 °C. The pattern is thus applied on the intermediate substrate part with continuous local adjustment in respect to a predetermined sheet resistance so that a desired temperature distribution over the heating element is realized. [0076] The third step may be the application of a dielectric protection layer with a typical thickness between 20 and 30 micron over the heating element. The dielectric may be a UV-reactive system that is cross-linked with a UV dose of approximately 1 J/cm².

[0077] Depending on the integration of the heating element into a heater it is often possible to apply a double-sided adhesive on the heating element which takes over the function of a protection layer and makes the dielectric layer obsolete. The double sided adhesive simultaneously ensures fixation of the heating element and its adhesion to a panel or to a decor to be heated.

[0078] The invention renders possible by a continuously adjusted pattern application over an intermediate substrate part to achieve defined temperature distributions in the heating area. This achievement is most valuable for high temperature uniformity, free-form heated areas and thermal cloaking in two dimensions.

[0079] A specific application of the present invention is for electrical heating objects in a compartment of a vehicle, for example vehicle seats but also doors, arm rests, steering wheel and many other interior surfaces in the compartment. Reason is the increase of occupant comfort due to additional heaters as well as the compliance of electrical heaters with hybrid or electric cars. Heating elements in accordance with the present invention enable almost any surface within the compartment to be heated up at a pre-determined temperature within a few ten seconds only and yield maximum heating power at a given area and for a given maximum surface temperature.

LEGEND

1 Heating element

2 Feedline

2a Feedline

3 Intermediate substrate part

4 Dark area

5 Circular exclusiona. Exponent coefficient

b Coefficient

I Total length

U0 Difference in electric potential, i.e. voltage, at the electric contact point

Rsq Layer of resistive material sheet resistance

Rsqfl Feedlines sheet resistance

w Layer of resistive material width

wO Initial layer of resistive material width

wfl Feedline width

wflO Initial feedline width

x Coordinate length

Claims

1 . Heating element (1 ) for generating heat when connected to an electrical power source, said heating element comprising a substrate supporting a first feedline (2) and a second feedline (2a) extending along opposite sides of the heating element (1 ), each of said first and second feedline (2, 2a) comprising an electrical contact point for connecting said feedline to an electrical power source, an intermediate substrate part (3) between the two feedlines (2, 2a) supporting a layer of resistive material, wherein, in operation, an electrical current flows from the first feedline (2) to the second feedline (2a) through the layer of resistive material, characterized in that the layer of resistive material is in the form of a pattern applied on the intermediate substrate part (3), said pattern being defined by the presence of microscopic exclusions in the resistive material, and in that a distribution of said microscopic exclusions of the pattern on the intermediate substrate part (3) follows a predetermined distribution such that the sheet resistance locally obtained for the applied pattern varies continuously over the intermediate substrate part (3).

2. Heating element (1 ) as claimed in claim 1 , wherein said predetermined distribution is a random or a pseudo-random distribution.

3. Heating element (1 ) as claimed in any one of claims 1 or 2, wherein the intermediate substrate part (3) extends substantially in two dimensions with coordinates x and y and wherein a dimension of said microscopic exclusions in x-direction or in y-direction is in the range between 20μηη and 30Όμηη, and preferably in the range of Ι ΟΌμιτι and 20Όμηη.

4. Heating element (1 ) as claimed in any one of claims 1 to 3, wherein the intermediate substrate part (3) extends substantially in two dimensions with coordinates x and y and wherein a dimension of said layer of resistive material x-direction or in y-direction is at least 100 times higher than a respective dimension of said microscopic exclusions.

5. Heating element (1 ) as claimed in any one of claims 1 to 4, wherein the intermediate substrate part (3) comprises at least one opening, and wherein the influence of the opening on the local sheet resistance is compensated by an appropriate local distribution of exclusions of the pattern on the intermediate substrate part (3).

Heating element (1 ) as claimed in any one of claims 1 to 5, wherein the exclusions can be of different shape, at least two different shapes existing over the intermediate substrate part (3) and if the distribution of exclusion follows a predetermined distribution mode, each different shape of exclusions presents its own predetermined distribution mode.

Heating element (1 ) as claimed in anyone of claims 1 to 6, wherein the intermediate substrate part (3) extends substantially in two dimensions with coordinates x and y, wherein the pattern comprises non-overlapping exclusions, and wherein the continuously adjusted sheet resistance Rsq(x,y) of the applied pattern with such zones is defined in respect of the sheet resistance of a full pattern Rsqp by:

. - ^αι

Rsq(x, y) = Rsqp^■ - -

1 - ₂ ^■ F - n(x, y)

with F being the area of an exclusion and n(x,y) being the area density of exclusions as a function of at least one of the coordinates x and y of the intermediate substrate part (3) and with ai and a₂ being empirical factors that depend upon the exclusion's type (size and shape), the screen mesh, the ink viscosity and surface energy, the substrate surface energy, and the parameters of the printing process.

Heating element (1 ) as claimed in anyone of the preceding claims, wherein said first and the second feedlines (2, 2a) each have a wavelike form in phase with each other such that the width of the applied pattern on the intermediate substrate part (3) alternates continuously between a reduced width and a larger width, and wherein the zone of the applied pattern corresponding to a larger width has a sheet resistance lower than the zone corresponding to a reduced width.

Heating element (1 ) as claimed in anyone of the preceding claims, wherein the first and the second feedlines (2, 2a) on opposite longitudinal sides of the heating element (1 ) are not parallel, and wherein the material resistance over the intermediate substrate part (3) with the pattern applied on it diminishes continuously in function of the divergence of the feedlines (2, 2a).

10. Heating element (1 ) as claimed in anyone of the preceding claims, wherein the feedlines (2, 2a) present a variable width (wfl) along their length, starting from a lateral side of the heating element (1 ) and wherein the feedline width (wfl) and the sheet resistance (Rsq) of the intermediate substrate part (3) with the pattern applied on it vary respectively in function of the length coordinate (x) of the heating element (1 ) according to the following equations:

wherein wfl(x) and Rsq(x) are respectively the feedline width and the adjusted sheet resistance Rsq(x) of the intermediate substrate part (3) with the pattern applied on it at a length coordinate x of the heating element (1 ) starting from the said lateral side, wflO and RsqO respectively the feedline width and the sheet resistance Rsq(x) of the intermediate substrate part (3) with the pattern applied on it at the said lateral side, I the total length of the heating element (1 ), b and a respective coefficients with b different from zero.

1 1 . Heating element (1 ) as claimed in claim 10, wherein a is a real value equal to or greater than zero, preferably a is equal to 1 or 2, while coefficient b may adopt any real value greater than -1 which is different from zero.

12. Heating element (1 ) as claimed in claim 10, wherein a is equal to 1 and wherein the heating element (1 ) exhibits a voltage u(x) in function of the length coordinate (x) of the heating element (1 ) defined by:

uO being the voltage at the said lateral side, Rsqfl being the sheet resistance of the feedlines (2, 2a) and Rsq the sheet resistance of the intermediate substrate part (3) with the pattern applied on it, Rsq and wfl meaning Rsq(x) and wfl(x) at x = 0, respectively.

13. Heating element (1 ) as claimed in claim 10, wherein a is equal to 2 and wherein the heating element (1 ) exhibits a voltage u(x) in function of the length coordinate (x) of the heating element (1 ) defined by:

uO being the voltage at the said lateral side with electric contact points, Rsqfl being the sheet resistance of the feedlines (2, 2a) and Rsq the sheet resistance of the intermediate substrate part (3) with the pattern applied on it, Rsq and wfl meaning Rsq(x) and wfl(x) at x = 0, respectively.

14. Heating element (1 ) as claimed in anyone of the preceding claims, wherein the pattern is made of a material with a positive temperature coefficient of resistance.