JPH0323366B2 - - Google Patents

Description

[Detailed description of the invention]

FIELD OF THE INVENTION The present invention relates to tires, and relates to tires in which the noise generated is dispersed by means of a load-bearing element and its tread pattern. As the tire travels over the ground, air movement occurs and produces an audible sound. In every particular tread pattern, some amount of sound energy is produced. Although different types of tread patterns produce the same specific amount of sound energy, the noise produced by the tread patterns can have significantly different effects on people. Certain tire sounds are perceived as harsh and unpleasant, while other tire sounds are perceived as extremely pleasant. The difference between these types of sounds lies in their frequency spectrum or state of tonality. This tonality is a condition in which the sound produced is dominated by a single frequency and its harmonics.
That is, most of the generated sound is concentrated in an extremely small frequency range of the sound spectrum.
This tonality confuses the listener psychologically,
Makes you feel uncomfortable. Adding to the annoyance, calling a sound with such tonality a tonal sound means that tonal sounds can be heard over relatively long distances, and therefore cannot be compared to non-tonal sounds. In comparison, materials with better soundproofing properties are required. If the concentration of sound energy at a particular frequency could be spread out over a wider frequency range, it would reduce the tonal or undesirable sound conditions mentioned above. In the past, various methods have already been proposed to reduce the unpleasant noises generated by the impact of load-bearing elements on the road surface when tires are driven on the road by dispersing their frequencies. This is the circumferential length of the design cycle, which consists of the length of the load-bearing elements arranged along the circumference of the tire tread and one of the adjacent circumferential grooves, that is, the pitch of the load-bearing elements differs. pitching (referred to as pitching) to modulate the event or characteristic frequency generated by the load-bearing elements during rotation of the tire.
However, these known methods ignore the potential tonality in the low frequency range resulting from pitching itself. That is, as the distance between repeating design cycles changes, this can result in an unpleasant low frequency tonal sound that can take the form of a single low frequency repeat. This tonal sound is easily transmitted to the vehicle and, depending on the type of vehicle, can generate unpleasant noises. The main object of the present invention is to effectively reduce the tonal sound of the noise generated by the road running of a tire with radially protruding load-bearing elements generating audible noise by means of the design of the load-bearing elements. That's true. A second object of the present invention is to reduce tonality by effectively distributing the noisy event frequency energy generated by tires with load-bearing elements over a wide frequency band. A third object of the present invention is to provide different types of load-carrying elements, one on each arc of the circumference of the tread divided into different lengths, so that tonal sounds due to pitching of event frequency energy do not occur. It is an object of the present invention to provide a tire that disperses sound generated at an event frequency by a modulation frequency having a large amplitude and arranged to form two sine waves as a wavelength. The achievement of these and other objects, and the elimination of the disadvantages of the prior art, have been made possible by the present invention, as further detailed below. In the tire of the present invention, a design cycle consisting of one load-bearing element and a lateral groove adjacent to one side of the load-bearing element in the circumferential direction is continuously arranged on the circumference of the tire in a large number of repetitions, In addition, there are at least two types of different pitch lengths in the design cycle, and they are arranged on each harmonic progression arc where the circumference of the tread is divided into at least three or more arcs of different lengths. and each of the at least three or more harmonic progression arcs includes at least one load-carrying element of each type of the at least two different pitch lengths, and the maximum It is assumed that the wavelength of the modulation frequency having an amplitude matches the length of the harmonic progression arc, and the boundary between the harmonic progression arcs transitions from a pitch length longer than the shortest pitch length to the shortest pitch length. , the rounded approximate fractional values represented by the length-to-circumference ratios of at least three harmonic series arcs are the three in a group of the first nine harmonic series values starting from 1/1, respectively. There is no harmonic progression curve other than the three harmonic progression curves that has a magnitude greater than any of these harmonic progression curves, and the at least three harmonic progression curves correspond to two different values within the acoustic spectrum. Corresponding to different frequencies, the total number of harmonic progression arcs within the circumference is, NP is the number of design cycles, SP is the shortest pitch length,
When LP is the longest pitch length and B is a frequency modulation index in the range of 1.6 to 2.9, it has a tread in the range of NP x (LP - SP)/B x (LP + SP). The tires of the present invention are generally designed through the following steps. (1) A design placed along the circumference of the tire.
Step of selecting the maximum number of cycles, (2) Step of selecting the maximum pitch ratio, (3) Equation No. 1 NS = NP x (LP - SP) / B x (LP + SP) where NS is the required number of harmonic series arcuate , where NP is the number of design cycles, LP is the longest pitch length, SP is the shortest pitch length, B is the frequency modulation index, and the step of determining the appropriate number of harmonic progression arcs into which the tread circumference is divided according to (4 ) determining the dimensions of each harmonic progression bow and the number of design cycles within each harmonic progression bow; (5) the wavelength of the dominant modulation frequency, which is the modulation frequency that produces the maximum amplitude for each harmonic progression bow, is the length of the bow; Step of determining the arrangement of design cycles with different pitch lengths for each harmonic progression arc shape to match the . (6) Furthermore, in order to more appropriately distribute the generated noise, the present invention includes the steps of determining an appropriate arrangement order of harmonic progression terms for the arcuate harmonic progression and determining an optimal pitch ratio. include. Referring to FIG. 1, a tire 10 is shown having a tread portion 12 made in accordance with the present invention. The tread of the tire 10 extends circumferentially along the tire 10 and is segmented into a plurality of design cycles 14, including separation of load-bearing elements 11 and circumferentially adjacent load-bearing elements 11. One side of the adjacent groove 13 is included. The load-bearing element 11 is aligned on a plane P (not shown) perpendicular to the axis R, and the line of intersection of the periphery of the load-carrying element with said plane defines an arc, such as AR (not shown). Shortest design with longest design cycle length
The ratio to cycle length is called the "pitch ratio". These specific arrangements of different design cycles are called "pitch arrangements." Specific pitch alignment and pitch ratios are sometimes critical to the distribution of sound energy over a wide frequency range. The maximum number of design cycles used is
It depends on how short the cycle length can be made. It is also generally desirable that the length be as short as possible without creating physical distortions or unstable load-bearing elements that can cause irregular wear. Therefore, the first step in designing tread 12 is to determine the maximum number of design cycles 14 that can be used for the particular design contemplated. Currently, passenger car tires generally have a design cycle number of about 30 to about 100, preferably about 45 to 75 design cycles. but,
The present invention is not limited to such a number of design cycles. Once the maximum number of design cycles 14 has been selected, the maximum pitch ratio can be determined. design·
The maximum number of cycles is determined empirically by a skilled tire design engineer considering the tire profile, the rubber material used, the type of tire, etc. Based on the previously selected maximum number of design cycles, the pitch ratio is chosen as large as possible to optimize the effect of design cycle length. This selection is based entirely on practical performance characteristics. Currently, tires generally have up to
1.86 preferably has a pitch ratio of about 1.4 to 1.6. However, the present invention may have any desired pitch ratio. For the particular tread shown, the pitch ratio is 1.57. The circumference of the tread is then divided into the appropriate number of circumferential harmonic arcs 16 (FIG. 2) determined according to the following relationship: Formula No. 1 NS = NP x (LP - SP) / B x (LP + SP) Where, NS is the required number of harmonic progression arcs, NP is the number of design cycles, LP is the longest pitch length, SP is the shortest pitch length, B is the frequency modulation index. The above formula No. 1 is an experimental formula based on experiments conducted by the inventor. The at least three largest harmonic progression arcs of different lengths among the harmonic progression arc numbers determined by the above equation each correspond to a different frequency in the acoustic spectrum. In order to generate these different frequencies of the acoustic spectrum, the harmonic arc has a plurality of successive design cycles 14 of varying length, which design cycles further define the predominant frequency of each harmonic arc. The wavelength of the modulation frequency, ie the modulation frequency with the highest amplitude, is arranged such that it corresponds to the time-synchronized frequency corresponding to the length of the harmonic series arc during its rotation. This can be more clearly understood by referring to FIGS. 3 and 4. Formula No.
The calculated number of the harmonic progression arc 16 determined from 1 is rounded to the nearest integer since fractional arcs are undesirable. Furthermore, the number of harmonic progression arcs 16 should be chosen to be minimal. The smaller the number of harmonic series arcs 16, the more the tonal sound reduction effect is enhanced by the effect of modulation.
However, as the number of harmonic progression arcs 16 becomes smaller, the opportunities for introducing tonal sounds increase due to the succession of the same pitches in the design cycle. The minimum harmonic progression arcuate number that can be used for any particular size tire is determined according to the relationship below. Formula No. 2 fs=Nm×S/C However, fs is the lowest audible frequency, Nm is the minimum harmonic series arcuate number, S is the tire speed, and C is the tire circumference. The above formula No. 2 was obtained by the inventor based on experiments. When the tire noise is loud enough to be detected by the human ear, the speed is approximately 48.28 mph.
Km (30 miles). Substituting this value into Equation No. 2 above, we get the following relationship: Equation No. 3 fs = Nm x 48.28 Km/hr (30 miles)/C Frequencies less than 30 cycles per second usually
Although not audible to the human ear, it can be perceived as a beat sound. The hearing ability of the human ear varies depending on age; young people can hear up to 20 cycles of loud sounds, while older people can hear over 30 cycles. Therefore, it must be prevented. Now, by substituting fs=30 cycles, equation No. 3 is transformed into the following equation. Formula No. 4 Nm=30×C/48280×100cm/3600sec=30×C/1341.1
= C/44.704 However, C is expressed in cm. For passenger car tires with an outer diameter of approximately 64.8 cm,
The circumference is approximately equal to 203.2 cm. Substituting it into C, Nm=203.2/44.704=4.545 Therefore, the minimum number of arcuate harmonic series (Nm)
must be greater than 4.545. Since the harmonic progression arc 16 must be an integer, the number is rounded to the next whole number.
Therefore, the harmonic progression arcuate 1 for this particular tire
The number of six is at least five. Approximate value 5 of 4.545
0.50 or larger decimals are rounded to the next larger integer, and decimals smaller than 0.50 are rounded down (rounding). Also,
When replacing 30 cycles with 20 cycles, Nm=
20×203/1341≒3.02, and the minimum number of harmonic progression arcs is 3, which is the minimum harmonic progression arc number. Next, this number is NS calculated from formula No.1
compared to If Nm is larger than NS, the value of frequency modulation index (hereinafter referred to as modulation index) B is selected so that NS is larger than Nm. The basis for limiting and selecting the modulation index is determined empirically by the inventors based on experiments. If this cannot be corrected by changing B, change the original design reference value, eg NP, LP or SP. The modulation index B in Equation No. 1 is obtained by dividing the maximum frequency shift of the modulated wave at that time by using the modulation frequency when the tone changes as the numerator. This can be more clearly understood by referring to FIG. 3, where the maximum modulation frequency shift when the event frequency is modulated is indicated by the letter "A". Event frequency is the average number of times per second that a design cycle rotates and hits the road surface when the tire is traveling at a given speed. Therefore, 1
It is the number of tire revolutions per second multiplied by the number of design cycles around the tire's circumference. The modulation index determines the energy present in each sideband of the event frequency and the effect of pitching. With a modulation index smaller than 1, the modulation depth is shallow and there is little change in event frequency, so the effect of tire pitting is generally not produced, and a modulation index larger than 4 is generally not put into practical use. The reason for this is that in order to achieve a modulation index greater than 4, the pitch ratio must be increased, which requires a design with a large pitch that is too large and a design with a small pitch that is too small. manufacturing, the possibility of irregular wear, and the poor appearance of the tires. Examples of two good modulation indices for producing a pitching effect are approximately 1.6 and 2.9 based on the inventor's experiments. This is because, for this value of B, the fundamental wave and the next largest sideband have almost the same amplitude. Equation No. 1 is based on pure sine wave modulation. When the modulation is of a composite (ie, made up of several modulations) type, the modulation must be divided into multiple component parts. The amplitude of the modulating frequency fundamental, whose wavelength is the length of the arc, is the only one to be considered. As shown in FIGS. 5, 6, and 7, when the modulating wave is not purely sinusoidal, the shape factor must be considered in calculating NS. Shape factors can be used to help correct for non-sinusoidal types of design cycle sequences, but the use of shape factors is not necessary to practice the invention. In FIGS. 6, 7 and 8, the dotted lines indicate the fundamental frequency for the waveforms. The shape factor corrects for the fact that the amplitude of the fundamental frequency is smaller than the actual amplitude of the complex frequency modulation. Therefore, taking the shape factor into consideration, equation No. 1 is modified to the following equation. Equation No. 5 NS=NP×(LP-SP)/B×(LP+SP)×SF However, SF is a term for correcting this shape. Formula No. 5 was obtained based on the inventor's experiments. As an example, for illustrative purposes, 35 design cycle numbers, 3 design cycle lengths,
A passenger car tire having a long design cycle of 7.093 cm, a short design cycle of 4.518 cm, a modulation index of 1.6, and a shape factor of 1.1 that corrects for non-sinusoidal waveforms in a three design cycle arrangement is:
Calculated number of harmonic progression arcuate (5
(combined into an arcuate shape). This number is determined by formula no.
The minimum number Nm of the arcuate harmonic progression calculated based on 4
larger than Once the number NS of the harmonic series arc has been determined, the arc size is selected from the harmonic series, preferably a portion of the series represented by the series below. 1/1, 1/2, 1/3, 1/4...1/n The part of the harmonic sequence chosen has the same number of terms as the arc, and these terms are preferably in consecutive order. There is. That is, the inventor has empirically found through experimentation that the frequency components of the noise generated from the use of tires can be spread out to the maximum desirable range by using arcuate shapes corresponding to the terms of a harmonic series having a continuous order. . The above harmonic sequence, ie, 1/1, 1/2, 1/3, 1/4...1/n, is the only harmonic sequence handled by the inventor. The first nine terms were selected because the inventor was able to empirically determine through experiments that the first nine terms would yield a tire with desirable noise characteristics. For example, as shown in Figure 10, using the terms in the first nine terms tends to reduce the low frequency tonal sound and also allows the low frequency part to be spread out over many frequencies. Make it. The dimensions of each arc correspond to one of the terms of the harmonic series. For example, if a certain arc corresponds to 1/4,
Its arcuate dimension is equal to 1/4 of the tire circumference. It is desirable that the sum of the terms of the harmonic series be approximately equal to one. This is clear from the following example. For example, if six arcs are desired, six consecutive terms are selected from the harmonic series as follows. 1/4+1/5+1/6+1/7+1/8+
1/9 The sum of these terms is approximately equal to 0.996, which is very approximately equal to 1. This means allows each arcuate to accommodate a different low frequency modulation and effectively distributes the low frequency energy emitted by the design cycle over a wide band as illustrated in FIG. In the following, the dimensions of each arc have been obtained only approximately. The next step is to determine the actual dimensions of each bow. For each term in the harmonic series, the common divisor is determined by multiplying all the denominators of all terms. Each numerator of each term is then multiplied by all denominators of the other terms of the selected harmonic sequence. The numerators of each harmonic sequence term are then added together to change the common divisor. Generally, the sum of the numerator and the denominator are not the same. The sum of the numerators that results from adding all the numerators is then used as the denominator for each harmonic arcuate term. Using the numerator calculated for each term, the adjusted fractional portion of each term is determined. An example of this for a tread with six harmonic arcs is shown in Table 1.

【table】

Table: To determine the actual number of design cycles required for each bow, multiply the adjusted fraction of that bow by the total number of design cycles for the tire. Next, this number is rounded up or down to the nearest integer. Rounding up means including the decimal part in the first digit of an integer and rounding it up to the next larger integer.
Rounding down means cutting off the decimal part.
As used herein and in the claims, a rounded approximation value refers to a value obtained by normal rounding up or down as defined above. In some cases, the sum of design cycles included in each arc may not reach the required number of design cycles due to rounding up or down errors. The number of design cycles is then rounded up or down to the highest number in the direction required to modify the total number of design cycles. For example, as shown in Table 2.

【table】

[Table] It is possible that two arcs require the same number of design cycles. In such a case, 2
A larger harmonic progression arc is constructed with a larger number and longer design cycle than a smaller harmonic progression arc. Therefore, the harmonic progression bow shape should correspond to its design frequency. In any case, all specific harmonic series arcuate 1
6 must have an integer number of design cycles; fractional design cycles are not desired. Although the design cycle arrangement for each harmonic progression arc 16 is different from each other, each harmonic progression arc 16
should have a dominant modulation frequency that matches the fundamental frequency of its modulated number. As mentioned above,
The harmonic progression arc 16 is such that the dominant modulation frequency of the arc, ie the wavelength of the modulation frequency with maximum amplitude, matches the length of the arc. FIG. 9 shows a design cycle arrangement bow in which the dominant modulation frequency does not match the length of the bow. Preferably, the harmonic series arc is the fourth
As shown in the figure, by means of an arrangement of load-carrying elements which slowly vary the pitch length from one beginning to another, from where the adjacent arc begins again, in a virtually sinusoidal waveform only once in each arc. It can be configured as follows. FIG. 3 shows this sinusoidal waveform around the entire circumference of the tread. In the present invention, this modulation is accomplished by using three symmetrically arranged pitch lengths as shown in FIG. However, any desired number of different pitch lengths may be used. In the illustrated embodiment, the pitch length "2" between the longest pitch length "3" and the shortest pitch length "1" is the average of these. Table 3 below shows suggestions for a three-pitch tread design with a different design cycle for each arch. However, various other arrangements can be used to achieve the same results. In addition, the design cycle of the boundary from each harmonic progression arc to the next harmonic progression arc is arranged so as to transition from pitch lengths longer than the shortest pitch length to those with the shortest pitch length. Therefore, for each bow shape in Table 3, there is a transition from the "2" design cycle to the other "1" design cycle. Furthermore, in order to make the pitch arrangement on each arc sinusoidal, each arc must include at least one load carrying element of all types of pitch lengths used as shown in Table 3.

TABLE Each of these design cycle arrangements represents the design cycle modulation in terms of sinusoidal modulation cycles. Therefore, it is not desirable for each harmonic progression arc to have consecutive design cycles of the same length over 1/2 or more of its length. Also, the more types of pitch lengths that are used, the closer the waveform approaches a true sine waveform. In either case, at least two pitch lengths must be used. Figure 8 shows the use of multiple pitches. FIG. 7 shows an asymmetric design cycle arrangement using three pitch lengths. FIG. 5 shows the difference from basic sine wave modulation. In FIGS. 4-8, their dominant modulation frequencies correspond to frequencies whose period is the length of each arc. That is, if the illustrated waveform is divided into high-frequency components by Fourier analysis, the dominant modulation frequency (i.e., the frequency of maximum amplitude) is determined by the elapsed time of the length of the arc as the car rotates. The frequency will be The dimensions of the harmonic arc 16 are preferably made very close to the calculated values, but they may vary in length by up to 25%, preferably by less than 10%. A 25% variation in length is 1/4 of the modulation wavelength
corresponds to Variations beyond this limit will result in a different modulation than desired. For example, an ideal arcuate dimension produces a high frequency wave with a certain low frequency as shown in FIG. On the other hand, a variation of about 25% or more may cause not only the intended specific frequencies to be delivered with energy, but also an unacceptable amount of energy at the next lower or higher frequency, as shown in Figure 12. energy, resulting in an uneven frequency spectrum and an unpleasant tone. The amplitude of each modulation frequency within the arc can be checked by performing a Fourier analysis of the frequency modulation caused by the design cycle arrangement in the arc. The amplitude of the fundamental frequency of the modulated wave must be greater than any harmonic. In other words, the 12th
As shown in the figure, the amplitude at frequency n is greater than the amplitude at n+1 or n-1. The tread pattern can be further improved by proper placement of each harmonic arc. The order in which the arcuate shapes are arranged may result in cancellation or enhancement between each arcuate.
That is, depending on the order in which the bows are placed, the frequencies of some sounds will be higher, and the frequencies of some sounds will be softer. Therefore, it is desirable to keep the effects of each bow shape equal so that the low frequency spectrum is smooth and wide. Generally, this may be accomplished by distributing the arcuate so that the dimensions of the arcuate are asymmetric in order, ie, the dimensions are not arranged in a sequential order.
The following is an example of an arcuate sequence that has been found to be satisfactory for a tire with six arcs: Arcuate Number 6 1/4, 1/9, 1/6, 1/5, 1/8,
1/7 The following arcuate arrays (example only) were found to be satisfactory for tires with 4, 5 and 7 arcs. Arcuate number 4 1/3, 1/4, 1/6, 1/5 5 1/3, 1/7, 1/5, 1/6, 1/4 7 1/4, 1/6, 1/9 , 1/5, 1/7,
In order to fully utilize the 1/10 and 1/8 design cycle arrangement, the pitch ratio must be optimized.
Initially, the pitch ratio was chosen subjectively. However, for any particular tire design cycle arrangement, it is very likely that there will be a slightly lower pitch ratio that will result in a lower pitch tone. Whether a pitch ratio smaller than the originally selected pitch ratio exists is determined by performing two Fourier analyzes. This Fourier analysis is
It was well known before the present application was filed. One way to perform such Fourier analysis on tires was developed by William J.
"Designing Quiet Tire Spacing (1971)" by J.Vorih
Tread Spacings For Tires (1971)). Mr. Bory's design method involves inputting the pitch ratio and pitch arrangement into a computer as parameters, and then executing the Fourier expansion through a program on which the amplitude of each waveband is displayed on the screen as shown in Figure 14. The method is to disperse the peak amplitude portion by changing the pitch arrangement. A first analysis is performed using the initially selected maximum pitch ratio. A second Fourier analysis is performed by using a slightly smaller pitch ratio than the originally selected pitch ratio. That is, by plotting the amplitude of the highest tonal peak calculated for each analysis against the pitch ratio used, it can be determined whether a smaller optimal ratio is used. Now, in the stage of evaluating the pitch ratio of this example, we repurposed the Fourier expansion program used in Mr. Bory's design method and used the initially selected pitch ratio, for example, 1:1.6, and the pitch arrangement as the first analysis. input, output the amplitude of each sideband, and set the maximum amplitude value (peak value), for example, M ₁ , to the 13th
Plot as the corresponding value of the initial pitch ratio as shown in the figure. Next, enter a slightly smaller pitch ratio of 1:1.5 and plot the amplitude M ₁ ' in the sideband that showed the largest amplitude value in the first analysis. If this line slopes upward as pitch ratio increases, there may be a smaller optimal ratio at which the peaks are dispersed. Then, in the same way, plot the next highest amplitudes M ₂ and M ₂ ' occurring in both analyses. Next, connect these two points with a straight line. This procedure is repeated for the next two highest amplitudes M ₃ , M ₃ ′, M ₄ , M ₄ ′ found in both analyses. The optimum ratio of 1.53 can then be determined from the graph in which the difference between the amplitudes of all plotted lines is the minimum as shown in FIG. This procedure must be repeated between 1.53 and 1.6 to obtain the new optimum ratio, since the straight line method is only an approximation arithmetic. The procedure is stopped when the difference between the original pitch ratio and the calculated optimal ratio is less than about 2%. The design cycle array obtained by the above design has white noise or pink noise characteristics. For the purposes of this invention, white noise is defined as a sound whose intensity is equal across all frequencies in the audible spectrum, and pink noise is defined as a sound whose intensity is equal in intensity over every octave of the frequency spectrum. Defined as a sound that decreases in rate. The sound you hear when a shell is placed next to your ear is representative of white noise and pink noise, with pink noise not having as much high-frequency noise as white noise and more of a shushing sound. The sound is similar to white noise, except that it has . Although the invention has been described in detail above in connection with tire treads, the invention can be implemented generally in rotating devices having radially extending load-bearing elements. By way of example, a V-belt formed with triangularly extending notches for rotation along a small radius may be advantageously applied with the present invention by forming notches in the belt according to the principles as described above. . The invention can also be implemented on snowmobile tracks. Although some representative embodiments and their details have been shown for the purpose of illustrating the invention, various changes and other modifications may be made to the invention without departing from the spirit or scope of the invention. It will be obvious to those skilled in the art that such modifications may be made.

[Brief explanation of drawings]

FIG. 1 is a perspective view of a tire having a tread made in accordance with the present invention, FIG. 2 is a schematic diagram showing how the tread is divided into a plurality of arcuate harmonic progressions, and FIG. 3 is a diagram showing each harmonic progression. 4 is a schematic diagram showing the manner in which the frequency is modulated in each arc of the tortoise; FIG. 5 is a schematic diagram showing the manner in which the frequency is modulated in any one harmonic arc. 6 is a schematic diagram illustrating the format and phase shift with respect to FIG. 4; FIG. FIG. 7 is a schematic diagram illustrating another modified form in which the frequency is modulated in any one harmonic arc represented by three different pitch lengths with an asymmetric design cycle arrangement. FIG. 8 is a schematic diagram illustrating another modified form of modulation; FIG. The figures are schematic diagrams illustrating frequency modulation that does not conform to the principles of the present invention. In Figures 4 to 9, the units on the vertical axis roughly represent the pitch or the reciprocal of the relative frequency, and the units on the horizontal axis represent the beginning of an arc. FIG. 10 is a schematic diagram illustrating the manner in which the bows of the tread made according to the invention each correspond to a different frequency; FIG. FIG. 12 is a schematic diagram illustrating how a created arcuate shape of a specific size corresponds to a specific frequency, and FIG.
Figure 13 is a schematic diagram showing how frequencies other than the intended frequencies are supplied, by plotting the peak value of the amplitude of the tonality for each sideband against the pitch ratio. FIG. 14 is a graph showing the results obtained from the Fourier analysis performed, and FIG. 14 is a display of the amplitude of tire tread sound by sideband based on Fourier expansion by a computer. In the drawing, 10 is a pneumatic tire, 11 is a load-carrying element, 12 is a tread portion, 13 is an adjacent groove, 14 is a design cycle, R is an axis, and P is a plane perpendicular to axis R.

Claims (1)

[Scope of Claims] 1. A tire having a tread in which a plurality of load-bearing elements are arranged on the circumference, comprising one load-bearing element and a lateral groove adjacent to one of the load-bearing elements in the circumferential direction. A plurality of design cycles are successively arranged around the circumference of the tire in a large number of repetitions, and the design cycles have at least two different pitch lengths, which are arranged around the circumference of the tread. is at least 3
Each of the at least three harmonic progression arcs is arranged on each harmonic progression arc divided into three or more circular arcs of different lengths, and each of the at least three or more harmonic progression arcs is
said at least one load-carrying element of each type of at least two different pitch lengths, and for each harmonic progression arc, the wavelength of the modulation frequency having the maximum amplitude matches the length of the harmonic progression arc. and the boundary between the harmonic progression arcs transitions from a pitch length longer than the shortest pitch length to the shortest pitch length, and is determined by the ratio of the length of at least three harmonic progression arcs to the circumference. The rounded approximate fractional values represented as There is no harmonic arc having a magnitude greater than any of these harmonic arcs, and the at least three harmonic arcs correspond to different frequencies within the acoustic spectrum, and the at least three harmonic arcs correspond to different frequencies within the circumference of the harmonic arc. The total number of is NP×(LP−SP)/B×( A tire with a tread that falls within the range of LP+SP). 2. The design cycle of the treads in the three harmonic progression arcs is such that the arrangement of the different pitch lengths is one period of the sine wave pattern for each of the harmonic progression arcs, and one harmonic progression arc. 2. A tire according to claim 1, wherein the arcuate sine wave pattern is continuously connected to an adjacent harmonic progression arcuate sine wave pattern. 3 The three harmonic series arcs are the first, second and third.
The first harmonic progression arc is composed of a harmonic progression arc whose lengths on the tored circumference are within a difference of 10% or less corresponding to the first term among the three different harmonic progression terms. 1, and the second harmonic progression arc is 10% of the circumferential length of the tread corresponding to the second term among the three different harmonic progression terms.
The third harmonic progression arc has a second length that is within the difference of: having third lengths that are within a difference of 10% or less, each of the three harmonic progression arcs having consecutive design cycles of the same pitch length over 1/2 or more of its length; Claim No. 1
Tires listed in section. 4. A harmonic progression arc is one in which the treaded circumference is divided into at least four different lengths, and the rounding of the harmonic progression arcuate portions of at least four divided different lengths with respect to the treaded circumference length. The fractional value corresponds to four different terms in the group of the first nine terms of the harmonic progression starting from 1/1. tire. 5. A harmonic progression arc is one in which the treaded circumference is divided into at least five different lengths, and the harmonic progression arc is rounded to the treaded circumference of at least five divided different lengths. 4. The tire according to claim 1, wherein the fractional values correspond to five different terms of a group of first nine terms of a harmonic progression starting from 1/1. 6. Each of the three harmonic progression arcs has at least one design cycle for all types of different pitch lengths used in tires. The tire described in any one of the items. 7. Claims 1 to 7 in which each term of the harmonic series corresponding to each of all the harmonic series arcs is included in a group consisting of the first nine terms of the harmonic series essentially starting from 1/1. The tire according to any one of Item 6. 8. The trellis is divided into multiple harmonic series arcs, and the arcuate parts corresponding to the rounded fractional values of the circumference of the trellis are at least 90% of the circumference.
8. A tire according to claim 1, wherein the fractional part thereof corresponds to a value of the group consisting of the first nine terms of a harmonic progression starting from 1/1. 9. The tire according to any one of claims 1 to 8, wherein the arrangement order of the arcuate harmonic progression on the tire circumference is different from the arrangement order of the number sequences of the terms of the harmonic progression to which they correspond. 10. A tire according to any one of claims 1 to 9, in which only three different pitch length type design cycles are used.