# Patent

## Title
Three dimensional sipe

## Abstract

Provided is a sipe extending into a tire tread, comprising an outer radial portion defined by a first waveform having a first amplitude, a first width, and a first wavelength, and an inner radial portion defined by a second waveform having a second amplitude, a second width, and a second wavelength. The first wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second amplitude may be more than 50% of the first wavelength or may be less than 10% of the first wavelength, or the second amplitude may be more than 50% of the second wavelength or may be less than 10% of the second wavelength.

## Background
TECHNICAL FIELD
Certain embodiments disclosed herein relate generally to a tire. More specifically, disclosed herein are embodiments relating to a tire sipe.
BACKGROUND
Tire performance is an important concern. Among manufacturers and developers of tires and vehicles that use tires, as well as others, tire characteristics and tire tread characteristics are of substantial interest.
One area of study is concerned with how tread features, such as lugs, grooves, gaps, sipes, convolutions, ribs, and/or flutes, may affect tread characteristics and/or tire performance.
It remains desirable to provide tread features, such as sipes, that affect tire performance.
SUMMARY
Provided is a sipe extending into a tire tread, comprising an outer radial portion defined by a first waveform having a first amplitude, a first width, and a first wavelength, and an inner radial portion defined by a second waveform having a second amplitude, a second width, and a second wavelength. The first wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second amplitude may be more than 50% of the first wavelength or may be less than 10% of the first wavelength, or the second amplitude may be more than 50% of the second wavelength or may be less than 10% of the second wavelength.
Further provided is a tire tread comprising at least one tread element comprising a waveform sipe therein. The waveform sipe has length, extends into the tire tread, and may comprise an outer radial portion and an inner radial portion. The outer radial portion may be defined by a first waveform having a first amplitude, a first width, and a first wavelength. The first waveform may be a sine or zig-zaged waveform. The inner radial portion may be defined by a second waveform having a second amplitude, a second width, and a second wavelength. The second waveform may be the same type of waveform as the first waveform. The first wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second amplitude may be more than 50% of the first wavelength or may be less than 10% of the first wavelength, or the second amplitude may be more than 50% of the second wavelength or may be less than 10% of the second wavelength.
Provided is a waveform sipe, the waveform sipe having length and width, the waveform sipe having depth defined by its extent into a tire tread. The waveform sipe may comprise an outer radial portion and an inner radial portion. The outer radial portion may be defined by a first waveform having a first amplitude, a first width, and a first wavelength. The first waveform may be a sine or zig-zaged waveform. The first width may be between 0 mm and 5 mm, inclusive. The first wavelength may be between 2 mm and 50 mm. The inner radial portion may be defined by a second waveform having a second amplitude, a second width, and a second wavelength. The second waveform may be the same type of waveform as the first waveform. The second width may be greater than the first width. The length of the sipe may be between 2 mm and 50 mm. The width of the sipe may be described by an opening function. The first wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second wavelength may be less than 5% of the length of the sipe or may be more than 100% of the length of the sipe, or the second amplitude may be more than 50% of the first wavelength or may be less than 10% of the first wavelength, or the second amplitude may be more than 50% of the second wavelength or may be less than 10% of the second wavelength.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a non-limiting embodiment of a tire;
FIG. 2 shows a non-limiting embodiment of a tire section;
FIG. 3 shows a non-limiting embodiment of a tread with sipes therein;
FIG. 4 shows some of the forms that a waveform sipe may take;
FIG. 5 shows a sinusoidal wave;
FIG. 6 shows a set of sinusoidal waves;
FIG. 7 shows a detailed view of one embodiment of a sipe;
FIG. 8 shows a close-up of a portion of a non-limiting tread;
FIG. 9 shows a close-up of a portion of a non-limiting tread;
FIG. 10 shows a close-up of a portion of a non-limiting tread;
FIG. 11 shows a close-up of a portion of a non-limiting tread;
FIG. 12 shows a close-up of a portion of a non-limiting tread;
FIG. 13 shows a close-up of a portion of a non-limiting tread;
FIG. 14 shows a close-up of a portion of a non-limiting tread;
FIG. 15 shows a close-up of a portion of a non-limiting tread; and
FIG. 16 shows a close-up of a portion of a non-limiting tread.



DETAILED DESCRIPTION
Reference will be made to the drawings, FIGS. 1-16, wherein the showings are only for purposes of illustrating certain embodiments of a three dimensional sipe.
FIG. 1 shows a non-limiting embodiment of a tire 100. As shown in FIG. 1, in some embodiment a tire comprises a tread 110. The tread 110 of a tire, or tire tread, comprises the circumferential surface of the tire 100. A tread 110 may comprise a tread pattern of grooves, sipes, ribs, blocks and other geometric elements. The grooves, sipes, ribs, blocks and other geometric elements of a tire tread 110 may promote the expulsion of water from the tire 100, affect tire noise, affect traction, or otherwise influence or affect tire performance.
FIG. 2 shows a non-limiting section of a tire 200. The tread area 210 of the non-limiting section of a tire 200 shown in FIG. 2 comprises a rib 220, a tread block 230, a groove 240, and a sipe 250. FIG. 3 shows a non-limiting example of a tread with several examples of a sipe 310 therein. A sipe 250 is a very narrow gap or thin cut in the tread. The width of a sipe 250 is typically, between 0 and 5 millimeters wide, inclusive. As will be disclosed further herebelow, the width of a sipe 250 may vary with depth or along the length of the sipe 250. A sipe having a width of 0 mm still comprises the sipe edges, length, depth, and a shape. Further, a sipe having a width of 0 mm may open or permit slip or motion between the faces of the sipe during operation of the tire in which they are made. A sipe 250 may have substantial depth, and may also be substantially elongated. The path of elongation described by a sipe 250 may take any of a large number of forms. A sipe 250 may comprise a straight shape, a curved shape, an arcuate shape, a waveform, or combinations thereof. FIG. 4 shows some of the forms that a waveform sipe may take: sine or sinusoidal 410, square 420, ramp 430, saw tooth 440, or triangular 450. As used herein, unless otherwise noted, the term “zig-zaged” will comprise the forms ramp 430, saw tooth 440, and triangular 450 as shown in FIG. 4. Without limitation, FIG. 3 shows several examples of a zig-zaged sipe 310. While the type of waveform may be important for performance and engineering reasons, including, but not limited to stress-concentration factors, the disclosures herein relate to all kinds of waveforms unless otherwise noted.
With reference to FIG. 5, and without limitation, a sinusoidal waveform 510 may be defined by an equation having the form:

y(x)=A·sin(ωx+φ)

Where:

    
    
        y(x) is displacement in a direction perpendicular to the x direction, the x-direction being the horizontal direction, (distance) in FIG. 5;
        A is the amplitude, the peak deviation of the function from its center position;
        ω is the angular frequency of the oscillations; and
        φ is the phase that specifies where in its cycle the oscillation begins.
    
    


The amplitude, A, the angular frequency, ω, and the phase, φ, each may be any real number. Square waveforms 420 and zig-zaged waveforms 430, 440, 450 and other waveforms may be defined or substantially approximated using a Fourier series. Accordingly, waveform sipes may be described in terms of their type of wave, their amplitude or “pitch width”, and their wavelength (λ) or “pitch length”.
With reference to FIGS. 4, 5, and 6, a waveform may be described in terms of the type of wave, the wavelength, and the amplitude. In the alternative, waveform may be described in terms of the type of wave, the frequency, and the amplitude. Shown in FIG. 6 are three sinusoidal waves. The top wave 610 has constant amplitude and a constant frequency. The middle wave 620 has a constant amplitude and a constant frequency slightly different from that of the top wave. The bottom wave 630 is the sum of the top and middle waves. The bottom wave 630 shows a beat; the amplitude of the wave 630 is variable along the path 635 of the wave. In general, waveforms can be formed by summing two of more other waveforms. As noted above, each of the square waveform 420 and the zig-zaged waveforms 430, 440, 450 shown in FIG. 4 can be formed or substantially approximated by a sum of sinusoidal waves. As noted above, some non-sinusoidal waveforms can be described in terms of a sum of sinusoidal waveforms or Fourier series.
With reference to non-limiting FIG. 7, and as noted above, a sipe 710 has depth. The depth of a sipe, whether parallel to the radial direction of the tire or not, may be described as a radial dimension, such that the sipe 710 has an outer radial portion 720 and an inner radial portion 730. The top of the sipe 740 is the radially outer most portion of the sipe and the bottom of the sipe 750 is the radially inner most portion of the sipe 710. The width or other characteristics of the sipe 710 may change with depth. In the non-limiting embodiment shown in FIG. 7, the width of the sipe is very narrow in the outer radial portion 720, the width increases dramatically with depth, and the inner radial portion 730 is very wide for a sipe. The sipe 710 shown in FIG. 7 may be referred to as a “keyhole sipe”. With continued reference to FIG. 7, in the embodiments shown, the outer radial portion 720 of the sipe is defined by a sinusoidal wave. The form of the inner radial portion 730 may be similar to the sinusoidal form of the outer radial portion 720 or it may differ therefrom; that is, the inner radial portion 730 may be straight, a similar waveform, a different waveform, or another geometry.
In embodiments in which the width of the sipe 710 changes with depth, the width of the sipe 710 may be a function of depth. A width that is a function of depth may be defined by an equation and may be linear, non-linear, continuous, or non-continuous. For example, and without limitation, in certain embodiments the width, w, of a sipe may be a linear function of depth, d, such that w(d)=A(d)+B; where A and B are constants. For example, and without limitation, in certain embodiments the width, w, of a sipe may be a quadratic function of depth, d, such that w(d)=A(d)^2+B(d)+C; where A, B, and C are constants. In certain embodiments the width of the sipe may be a non-continuous function of depth. For example, and without limitation, in certain embodiments the width, w, of a sipe may be a non-continuous function of depth, d, such that for 0=<d=<15 mm, w(d)=B; for 15<d, w(d)=A(d)+B; where A and B are constants. The latter non-continuous function describes a sipe having a constant width, B, for the outer 15 mm of depth and having a width that increases linearly over the portion of the depth deeper than 15 mm. A function that describes the width sipe that increases in width as depth increases will be referred to herein as an opening function.
Referring again to FIG. 6, a waveform may be constant in type, frequency or wavelength, and/or amplitude over its length, as shown in the top wave 610 and middle wave 620 of FIG. 6, or a waveform may vary in type, frequency or wavelength, and/or amplitude over its length, as shown in the bottom wave 630 of FIG. 6. Frequency, wavelength, and amplitude can all be variables that vary as a function of position. One way in which, frequency, wavelength, and amplitude can vary as a function of position is with position along the path of the waveform. As shown in FIG. 5, and without limitation, the path 520 of the waveform is parallel to the horizontal axis 530, distance, in the waveform shown in FIG. 5. Another way in which, frequency, wavelength, and amplitude can vary as a function of position is with depth. As shown in FIG. 5 and in FIGS. 7-9, and without limitation, the depth of the waveform corresponds to the dimension transverse to both the horizontal axis 530 and the vertical axis 540 of the waveform shown in FIG. 5; that is, depth is the dimension into or out of the page in FIG. 5. While the sipe itself may be angled or oblique with respect to the depth dimension, the sipe may still be referred to as having some depth.
The non-limiting embodiments in FIGS. 8, 9, and 10 show close-up sections of a tread. In some figures, the width of the sipe in the figure may be exaggerated for the purposes of improving visibility.
The non-limiting embodiments in FIGS. 8, 9, and 10 each show a sipe 810, 910, 1010 in which, in the region or area shown, the outer radial portion of the sipe 820, 920, 1020 is defined by a first waveform 830, 930, 1030 having a first wavelength, and the inner radial portion of the sipe 840, 940, 1040 is defined by a second waveform 850, 950, 1050 having a second wavelength. The region or area may be a particular geometric section of a tread, such as a block, or a rib, another finite region or area, or at least in the case of a waveform having variable properties, an infinitesimal region or area. The second waveform 850, 950, 1050 may be the same waveform as the first waveform 830, 930, 1030, as shown in FIGS. 8, 9, and 10, or it may be a different waveform. The second wavelength may be less than, equal to, or greater than, the first wavelength. The second amplitude may be less than, equal to, or greater than, the first amplitude.
In the non-limiting embodiment in FIG. 8 both the outer radial portion 820 and the inner radial portion 840 comprise a zig-zaged waveform 830, 850, the amplitude of the inner radial portion 840 waveform is substantially equal to the amplitude of the outer radial portion 820 waveform, and the wavelength of the inner radial portion 840 waveform is substantially equal to the wavelength of the outer radial portion 820 waveform.
The non-limiting embodiment in FIG. 9 shows a sipe having the same inner radial portion 940 waveform as that shown in FIG. 8, but the outer radial portion 920 waveform shown in FIG. 9 has a much smaller amplitude than does the outer radial portion 820 waveform of FIG. 8. The non-limiting embodiment in FIG. 9 shows both the outer radial portion 920 and the inner radial portion 940 comprise a waveform, the amplitude of inner radial portion 940 waveform is substantially greater than the amplitude of the outer radial portion 920 waveform, and the wavelength of the inner radial portion 940 waveform is substantially equal to the wavelength of the outer radial portion 920. In certain embodiments, both the outer radial portion and the inner radial portion comprise a waveform, and the amplitude of the inner radial portion waveform is more than 10% greater than the amplitude of the outer radial portion waveform, or is more than 20% greater than the amplitude of the outer radial portion waveform, or is even greater.
The non-limiting embodiment in FIG. 10 shows a sipe in which both the outer radial portion and the inner radial portion comprise a waveform, the wavelength of the inner radial portion 1040 waveform is slightly more than 50% greater than the wavelength of the outer radial portion 1020 waveform, and the amplitude of the inner radial portion 1040 waveform is substantially equal to the amplitude of the outer radial portion 1020. In certain embodiments, both the outer radial portion and the inner radial portion comprise a waveform, and the wavelength of the inner radial portion is more than 10% greater than the wavelength of the outer radial portion wavelength, is more than 50% greater than the outer radial portion amplitude, or even greater.
In all real world applications, the sipe will have a finite length, referred to herein as the sipe length. The ratio of the wavelength of waveform sipes to the sipe length may be relevant to performance. The ratio of the wavelength of a waveform sipe to the sipe length may range from nearly zero, for very short wavelengths in very long sipes, to nearly infinite for very long wavelengths in very short sipes.
In the non-limiting embodiment shown in FIG. 11, a close up of a tread element 1110 is shown comprising a waveform sipe 1120. The waveform sipe 1120 runs the full length of the tread element 1110 and consists of 26 wavelengths. Accordingly, the ratio of the wavelength of the waveform sipe 1120 in FIG. 11 to the sipe length of the waveform sipe 1120 is 1/26 or about 3.8%.
In the non-limiting embodiment shown in FIG. 12, a close-up of a tread element 1210 is shown comprising a waveform sipe 1220. The waveform sipe 1220 runs the full length of the tread element 1210 and consists of 5 wavelengths. Accordingly, the ratio of the wavelength of the waveform sipe 1220 in FIG. 12 to the sipe length of the waveform sipe 1220 is 1⁄5 or about 20%.
In the non-limiting embodiment shown in FIG. 13, a close-up of a tread element 1310 is shown comprising a waveform sipe 1320. The waveform sipe 1320 runs the full length of the tread element 1310 and consists of slightly less than 1 wavelength. Accordingly, the ratio of the wavelength of the waveform sipe 1320 in FIG. 13 to the sipe length of the waveform sipe 1320 is greater than 100%.
The ratio of the amplitude of a waveform sipe to the wavelength of the waveform sipe may be relevant to performance. The ratio of the amplitude of waveform sipes to the wavelength may range from nearly zero, for very low amplitudes in waveforms with very long wavelength, to nearly infinite for very high amplitudes in waveforms with very short wavelength.
In the non-limiting embodiment shown in FIG. 14, a close-up of a tread element 1410 is shown comprising a waveform sipe 1420. The waveform sipe 1420 runs the full length of the tread element 1410 and consists of 1 wavelength where the amplitude of the waveform sipe 1420 is approximately 1⁄4 the wavelength of waveform sipe 1420. Accordingly, the ratio of the amplitude of the waveform sipe 1420 to the wavelength of waveform sipe 1420 is about 25%.
In the non-limiting embodiment shown in FIG. 15, a close-up of tread element 1510 is shown comprising a waveform sipe 1520. The waveform sipe 1520 runs the full length of the tread element 1510 and consists of 1 wavelength where the amplitude of the waveform sipe 1520 is approximately 3⁄5 the wavelength of waveform sipe 1520. Accordingly, the ratio of the amplitude of the sipe in FIG. 15 to its wavelength is about 62.5%.
In the non-limiting embodiment shown in FIG. 16, a close-up of a tread element 1610 is shown comprising a waveform sipe 1620. The waveform sipe 1620 runs the full length of the tread element 1610 and consists of 1 wavelength where the amplitude of the waveform sipe 1620 is approximately 1/16 the wavelength of waveform sipe 1620. Accordingly, the ratio of the amplitude of the sipe in FIG. 16 to its wavelength is about 6.25%.
While the three dimensional sipe has been described above in connection with the certain embodiments, it is to be understood that other embodiments may be used or modifications and additions may be made to the described embodiments for performing the same function of the three dimensional sipe without deviating therefrom. Further, the three dimensional sipe may include embodiments disclosed but not described in exacting detail. Further, all embodiments disclosed are not necessarily in the alternative, as various embodiments may be combined to provide the desired characteristics. Variations can be made by one having ordinary skill in the art without departing from the spirit and scope of the three dimensional sipe. Therefore, the three dimensional sipe should not be limited to any single embodiment, but rather construed in breadth and scope in accordance with the recitation of the attached claims.

## Claims

1. A tire tread comprising at least one tread element comprising a waveform sipe therein,
said waveform sipe having a length, a width and a depth defined by its extent into the tire tread, said waveform sipe comprising:
an outer radial portion defined by a first waveform having a first amplitude, a first width, and a first wavelength; and,
an inner radial portion defined by a second waveform having a second amplitude, a second width, and a second wavelength;

wherein said second waveform is the same type of waveform as the first waveform;
wherein the second wavelength is different from the first wavelength;
wherein said first waveform is a sine waveform;
wherein the second amplitude is different from the first amplitude; and,
wherein the width of the sipe increases as the depth increases as a continuous linear function;

wherein said first wavelength is less than 5% of the length of the sipe;
wherein said second wavelength is less than 5% of the length of the sipe; and
wherein
the second amplitude is less than 10% of the first wavelength,
the second amplitude is less than 10% of the second wavelength,
the first width is between 0 mm and 5 mm, inclusive and
the length of the sipe is between 2 mm and 50 mm, inclusive.