JP2011255768A - Pneumatic tire and method for design of the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a pneumatic tire that can improve the feeling quality of the tire while maintaining the performance of the tire, and to provide its design method.SOLUTION: The pneumatic tire includes a tread, a sidewall and a bead. The sidewall has a pattern formed by extending to the circumferential direction of the surface, and the pattern is formed into a shape whose surface shape is varied in the circumferential direction on the basis of a 1/f fluctuation coefficient being a value which is varied by an order in a range that a fluctuation coefficient is not smaller than 0.5 and smaller than 2, and a difference between a maximum vale and a minimum value is not larger than 0.5, and in which an order range of a frequency with one cycle in the circumferential direction as primary is finite, thus solving the problem.

Description

  The present invention relates to a pneumatic tire mounted on a vehicle and a method for designing a pneumatic tire.

  There are various shapes of pneumatic tires attached to vehicles such as automobiles. For example, Patent Document 1 describes a pneumatic tire having a tread pattern in which n pattern elements forming a pattern constituent unit on the tread surface are arranged in the tire circumferential direction. In addition, the pneumatic tire includes a row of the pattern elements arranged in the tire circumferential direction, each pattern element as a unit pulse and one pattern element as a starting point in the arrangement order, and in the circumferential direction of each pattern element. The pitch length Li, which is the length, is replaced with a pulse train separated in the circumferential direction, and the amplitude of the Fourier series that can be calculated by a Fourier coefficient obtained by expanding the pulse train into a Fourier series satisfies a specific condition. Is formed. Patent Document 1 describes that the tread portion has the above-described shape, thereby imparting to the sound pressure of tire noise a fluctuation characteristic having a magnitude almost inversely proportional to the frequency, thereby reducing noise discomfort. .

Japanese Patent Laid-Open No. 7-186621

  Here, examples of the pneumatic tire include a tire in which serrations are formed on the surface of the sidewall portion. This serration is arranged in an easy-to-see part even when a pneumatic tire is mounted. Therefore, the texture of the tire can be improved by changing the shape of the serration. However, depending on the shape, the performance of the tire may deteriorate. Note that Patent Document 1 only reduces noise by the shape of the tread portion of the tire, and does not describe the shape of the sidewall portion.

  The present invention has been made in view of the above, and it is an object of the present invention to provide a pneumatic tire and a pneumatic tire design method capable of improving the sensitivity of the tire while maintaining the performance of the tire. To do.

  In order to solve the above-described problems and achieve the object, the present invention is a pneumatic tire including a tread portion, a sidewall portion, and a bead portion, wherein the sidewall portion is a circumferential direction of the surface. The pattern portion has a fluctuation coefficient of 0.5 or more and 2 or less, and the difference between the maximum value and the minimum value varies depending on the order within a range of 0.5 or less. And the shape of the surface is changed in the circumferential direction based on a 1 / f fluctuation function in which the order range of the frequency is limited to the first order in the circumferential direction. To do.

  Here, the 1 / f fluctuation function is a function in which the relationship between the frequency on the logarithmic axis and the spectral power density is inversely proportional (proportional to a decreasing direction) when the fluctuation coefficient is a constant value. It is preferable.

  The pattern portion is preferably a serration in which a plurality of protruding ridges extending along the tire radial direction are arranged side by side along the tire circumferential direction within a predetermined range in the tire radial direction.

  In the serration, it is preferable that at least one of the arrangement direction, the arrangement interval, the height, and the surface angle of the ridge is changed based on the 1 / f fluctuation function.

  The order range is preferably 1st order or more and 2000th order or less.

  The order range preferably includes at least three consecutive integer orders.

  The order range is preferably second order or higher.

  Moreover, it is preferable that the said fluctuation coefficient is the same value.

  In order to solve the above-described problems and achieve the object, the present invention is a pneumatic tire design method for determining a design of a sidewall portion, which extends in the circumferential direction of the surface of the sidewall portion. The change in shape in the circumferential direction of the formed pattern portion is a value that varies depending on the order within a range where the fluctuation coefficient is 0.5 or more and 2 or less, and the difference between the maximum value and the minimum value is 0.5 or less, And it determines based on the 1 / f fluctuation function that the order range of the frequency which makes 1 round of the circumferential direction the primary is finite.

  The 1 / f fluctuation function is preferably a function in which the relationship between the frequency on the logarithmic axis and the spectral power density is inversely proportional when the fluctuation coefficient is a constant value.

  Moreover, it is preferable to determine the shape of the serration in which a plurality of projecting ridges extending along the tire radial direction are arranged side by side along the tire circumferential direction as the pattern portion in a predetermined range in the tire radial direction.

  Further, it is preferable that at least one of the arrangement direction, the arrangement interval, the height, and the surface angle of the ridge is determined based on the 1 / f fluctuation function.

  Moreover, it is preferable that the range of the said order is 1 to 2000.

  The order range preferably includes at least three consecutive integer orders.

  The order range is preferably second order or higher.

  Moreover, it is preferable that the said fluctuation coefficient is the same value.

  INDUSTRIAL APPLICABILITY The pneumatic tire and the pneumatic tire design method according to the present invention have an effect that the sensitivity of the tire can be improved while maintaining the performance of the tire.

FIG. 1 is a side view of a pneumatic tire according to an embodiment of the present invention. FIG. 2 is a partially enlarged view of the pneumatic tire shown in FIG. FIG. 3 is an enlarged cross-sectional view showing a partial cross section of the serration portion. FIG. 4 is a flowchart showing an example of the design method of the present invention. FIG. 5A is a graph illustrating the relationship between frequency and spectrum power. FIG. 5-2 is a graph showing a fluctuation waveform generated based on the relationship shown in FIG. FIG. 6A is a cross-sectional view illustrating a cross section in which the serration portion is developed in the circumferential direction. FIG. 6B is an enlarged cross-sectional view showing a part of FIG. FIG. 7A is a graph illustrating a relationship between frequency and spectrum power. FIG. 7-2 is a graph showing a fluctuation waveform generated based on the relationship shown in FIG. FIG. 7C is a front view of the serration unit designed based on the calculation result illustrated in FIG. 7-4 is an enlarged cross-sectional view showing a partial cross-section of the serration portion shown in FIG. 7-3 developed in the circumferential direction. FIG. 8A is a graph illustrating the relationship between frequency and spectrum power. FIG. 8-2 is a graph showing a fluctuation waveform generated based on the relationship shown in FIG. FIG. 8C is a front view of the serration unit designed based on the calculation result illustrated in FIG. 8-4 is an enlarged cross-sectional view showing a partial cross-section of the serration portion shown in FIG. 8-3 developed in the circumferential direction. FIG. 9A is a graph illustrating the relationship between frequency and spectrum power. FIG. 9-2 is a graph showing a fluctuation waveform generated based on the relationship shown in FIG. FIG. 10A is a graph illustrating a relationship between frequency and spectrum power. FIG. 10B is a graph illustrating a fluctuation waveform generated based on the relationship illustrated in FIG. FIG. 11A is a graph illustrating the relationship between frequency and spectrum power. FIG. 11B is a graph illustrating a fluctuation waveform generated based on the relationship illustrated in FIG. FIG. 12 is a graph showing the relationship between frequency and spectrum power on a logarithmic axis. FIG. 13A is an enlarged cross-sectional view illustrating a partial cross section of the serration portion. 13-2 is an enlarged cross-sectional view showing a partial cross-section of the serration portion shown in FIG. 13-1 developed in the circumferential direction. FIG. 14A is an enlarged cross-sectional view illustrating a partial cross section of the serration portion. 14-2 is an enlarged cross-sectional view showing a partial cross-section of the serration portion shown in FIG. 14-1 developed in the circumferential direction.

  Embodiments of the present invention will be described below in detail with reference to the drawings. Note that the present invention is not limited to the embodiments. The constituent elements of this embodiment include those that can be easily replaced by those skilled in the art or those that are substantially the same. In addition, a plurality of modifications described in this embodiment can be arbitrarily combined within a range obvious to those skilled in the art.

  In the following description, the tire width direction refers to a direction parallel to the rotation axis (not shown) of the pneumatic tire 1, and the outer side in the tire width direction refers to a tire equator plane (tire equator line). The side away from). The tire circumferential direction is a circumferential direction with the rotation axis as the central axis. Further, the tire radial direction refers to a direction orthogonal to the rotation axis, the tire radial direction inner side means the side toward the rotation axis in the tire radial direction, and the tire radial direction outer side means the side away from the rotation axis in the tire radial direction. Say. The tire equatorial plane is a plane that is orthogonal to the rotation axis and passes through the center of the tire width of the pneumatic tire 1. The tire width is the width in the tire width direction between the portions located outside in the tire width direction, that is, the distance between the portions farthest from the tire equatorial plane in the tire width direction. Further, the tire equator line refers to a line on the tire equator surface along the circumferential direction of the pneumatic tire 1.

  Here, FIG. 1 is a side view of the pneumatic tire according to the embodiment of the present invention. FIG. 2 is a partially enlarged view of the pneumatic tire shown in FIG. FIG. 3 is an enlarged cross-sectional view showing a partial cross section of the serration portion. As will be described later, the ridge 51 shown in FIGS. 1 and 2 appears to be distorted, but this is due to the change in the surface shape. As shown in FIG. 1, the pneumatic tire 1 includes a tread portion 2 that is in contact with a road surface, and a side that can be visually recognized at the outermost side in the tire width direction when the pneumatic tire 1 is assembled on a rim 6 and mounted on a vehicle. The wall portion 3 and the bead portion 4 that fits with the rim 6 when assembled to the rim 6 are configured.

  As shown in FIGS. 1 and 2, the sidewall portion 3 has a serration portion 5 on its surface. The serration portion 5 is formed in an annular shape along the tire circumferential direction. The serration portion 5 has a plurality of protruding ridges 51 arranged in parallel along the tire circumferential direction while extending along the tire radial direction within a predetermined range in the tire radial direction. Further, the ridge 51 is formed with a continuous protrusion from one end to the other end in the tire radial direction within a predetermined range in the tire radial direction. One end of each of the plurality of ridges 51 is disposed along the outer ring 52 of the serration unit 5, and the other end is disposed along the inner ring 53 of the serration unit 5. The outer ring 52 is formed in an annular shape along the tire circumferential direction, and has an outer contour in the tire radial direction that is a predetermined range in the tire radial direction of the serration portion 5, and is formed in a protruding shape. The inner ring 53 is formed in an annular shape along the tire circumferential direction and forms a contour on the inner side in the tire radial direction that is a predetermined range in the tire radial direction of the serration portion 5, and is formed by a protrusion.

  Such a serration portion 5 is basically provided at the outermost position in the tire width direction, and the position of the end portion where the carcass (not shown) forming the skeleton of the pneumatic tire 1 is folded back by the bead portion 4. Is provided. For this reason, the serration portion 5 makes the appearance of the outermost side in the tire width direction (sidewall portion 3) look better due to the contrast of the ridge 51, and the bulge on the surface of the sidewall portion 3 due to the folded end portion of the carcass is less noticeable It can be made to.

  Here, as shown in FIG. 3, the ridges 51 constituting the serration unit 5 have different shapes one by one depending on positions. The ridge 51 has a height h, that is, a length in the tire width direction, which varies depending on the arrangement position in the circumferential direction, and an end surface (upper surface, an upper surface in FIG. 3) 54 in the tire width direction is an equatorial plane. It is inclined with respect to it. Here, the end face 54 of the ridge 51 of the serration portion 5 changes with a 1 / f fluctuation function with an arbitrary point in the circumferential direction as a base point and an average thickness as a reference plane (y = 0). The 1 / f fluctuation function is a fluctuation function in which the relationship between the spectrum power and the frequency is inversely proportional on the logarithmic axis.

  Hereinafter, the shape of the serration unit 5 will be described in detail together with the design method. Here, FIG. 4 is a flowchart showing an example of the design method of the present invention. FIG. 5A is a graph showing the relationship between frequency and spectrum power, and FIG. 5B is a graph showing the fluctuation waveform generated based on the relationship shown in FIG. FIG. 6A is a cross-sectional view showing a cross section of the serration portion developed in the circumferential direction, and FIG. 6B is an enlarged cross-sectional view showing a part of FIG. Here, in FIG. 5A, the horizontal axis represents frequency (f) and the vertical axis represents spectrum power (PSD). In FIG. 5B, the horizontal axis is the x coordinate, and the vertical axis is the y coordinate. Further, in FIGS. 6A and 6B, the horizontal axis is the length from the reference position, and the vertical axis is the height of the ridge. Here, the tire design can be designed by storing a program for executing the calculation described below in a calculation device such as a personal computer and executing the calculation by the calculation device.

  As shown in FIG. 4, the arithmetic device first determines a model as step S12. The model is a 1 / f fluctuation function used for calculation and parameters thereof. The 1 / f fluctuation function is a value that varies depending on the order in the range where the fluctuation coefficient is 0.5 or more and 2 or less, and the difference between the maximum value and the minimum value is 0.5 or less, and 1 in the circumferential direction. Various functions can be used as long as the 1 / f fluctuation function has a finite order range of the frequency whose circumference is the first order. However, in this embodiment, sin is expressed as shown in the following formula (1). A 1 / f fluctuation function using waves is used.

Here, in the formula (1), x is a rational number from 0 2 [pi, _{r n} is the uniform random number between 0 2 [pi. Further, f _n is an integer that satisfies f _n = n. The fluctuation coefficient is an arbitrary value between 0.5 and 2.0. From the above, in the 1 / f fluctuation function, one round in the circumferential direction is primary. That is, the 1 / f fluctuation function is a periodic function in which x = 0 and x = 2π have the same value. In addition, by being a uniform random number r _n, the respective values are different value at x = 0.

  After determining the 1 / f fluctuation function to be used, the arithmetic device further determines the order of the 1 / f fluctuation function. In the present embodiment, the order is set from the first order to the 2000th order, that is, 1 ≦ n ≦ 2000. Each parameter setting may be input by the user. In addition, the user may set a constraint condition, and the arithmetic device may determine based on the condition.

When the model is determined in step S12, the arithmetic unit generates a 1 / f fluctuation waveform in step S14. That is, the arithmetic device develops the model determined in step S12 in the range of 0 ≦ x <2π and calculates the relationship between the x value and the y value. As in the present embodiment, when the above equation (1) is used and the fluctuation coefficient is a value corresponding to the output shown in FIG. 5-1, the fluctuation waveform is calculated as a waveform as shown in FIG. Incidentally, since the uniform random number r _n, each time performing the calculation, the waveform changes.

  After generating (calculating) the 1 / f fluctuation waveform in step S14, the arithmetic unit performs fitting to the shape of the end surface (top surface) of the serration unit in step S16. Specifically, the coordinates of each position are assigned with an arbitrary point in the circumferential direction of the serration unit as the starting point, the circumferential direction as the x direction, and one round as 2π. The height direction of the ridge is defined as the y direction, y = 0 is defined as the average height of the ridge, and the maximum value of y is defined as the maximum height of the ridge. The arithmetic device calculates the shape as shown in FIGS. 6A and 6B by applying the calculation result shown in FIG. 5B to the shape of the end face 54 of the serration unit under the above conditions. 6A and 6B show the shape of the serration portion in the circumferential direction in a straight line. Therefore, both ends in the x direction (length L direction) are at the same position. The length L is a distance (distance in the circumferential direction) from an arbitrary position of the serration of the tire as described above.

  In the example shown in FIGS. 6A and 6B, a tire having a tire size of 215 / 65R16, that is, a tire width of 215 mm, a flatness ratio of 65%, a radial structure, and a rim diameter of 16 inches was used. Also, the circumferential length at the center of the serration is 1940 mm, the average height of the ridge is 0.5 mm, the maximum height is 1 mm, the minimum height is 0 mm, the ridge width is 0.5 mm, and the ridge spacing Was 0.5 mm. Specifically, as a fitting method, as shown in FIG. 6B, the 1 / f fluctuation function corresponding to both ends in the circumferential direction of each ridge (the portion surrounded by a dotted circle in FIG. 6B). The y coordinate was calculated, and the y coordinate was taken as the height of the edge of the ridge. The ridge end surface 54 is a surface obtained by connecting both ends calculated using a fluctuation function with a straight line.

  As described above, the shape of the end surface of the ridge is determined, and by setting the determined shape, the serration unit has the height of the ridge and the end surface depending on the position as shown in FIGS. 6-1 and 6-2. The shape is different in angle. In the graph shown in FIG. 6B, the black portion is a ridge.

  As described above, the pneumatic tire 1 can improve the texture of the appearance of the serration portion by changing the ridge of the serration portion according to the 1 / f fluctuation function. Quality can be improved. That is, by making the shape changed according to the 1 / f fluctuation function, it is possible to give a sense of comfort and comfort and to reduce the possibility of giving an uncomfortable feeling. In addition, by making one round in the circumferential direction the first order of the 1 / f fluctuation function, setting the fluctuation coefficient to 0.5 or more and 2.0 or less, and setting the difference between the maximum value and the minimum value to 0.5 or less. The uniformity of the tire can be made constant. That is, it is possible to reduce the influence of the change of the serration portion on the tire performance (running performance). Thereby, the pneumatic tire 1 can improve the sensitivity quality of a tire, maintaining the performance of a tire.

Also, as in the above embodiment, the addition of r _n of uniform random numbers to each order component of the 1 / f fluctuation function, the position in the circumferential direction, can be shifted position each order component becomes zero. Thereby, the 1 / f fluctuation function can be made into a more complicated shape and a left-right asymmetric shape, and the sensitivity quality of the tire can be improved.

  In the above embodiment, the 1 / f fluctuation function is in the range from the first order to the 2000th order, but the present invention is not limited to this. Here, FIG. 7-1 is a graph showing the relationship between the frequency and the spectral power, and FIG. 7-2 is a graph showing the fluctuation waveform generated based on the relationship shown in FIG. -3 is a front view showing a serration portion designed based on the calculation result shown in FIG. 7-2, and FIG. 7-4 is a partial cross-section of the serration portion shown in FIG. 7-3 developed in the circumferential direction. FIG. FIGS. 8-1 to 8-4 are diagrams illustrating calculation results when orders different from those in FIGS. 7-1 to 7-4 are used. The outline of each diagram is illustrated in FIGS. Each corresponds to FIG. In FIGS. 7-1 and 8-1, the horizontal axis represents frequency (f), and the vertical axis represents spectrum power (PSD). In FIGS. 7-2 and 8-2, the horizontal axis is the x coordinate, and the vertical axis is the y coordinate.

  Here, FIGS. 7-1 to 7-4 are the same except that the frequency order used for the 1 / f fluctuation function is changed from the first order to the 600th order (that is, 1 ≦ n ≦ 600 in the above equation (1)). This is a result calculated under conditions. FIGS. 8A to 8D show the same conditions except that the frequency order used for the 1 / f fluctuation function is changed from the first order to the 60th order (that is, 1 ≦ n ≦ 60 in the above formula (1)). It is the result calculated by.

  When the frequency order is changed from the first order to the 600th order, assuming that the fluctuation coefficient is a value corresponding to the output shown in FIG. 7A, the fluctuation waveform has the shape shown in FIG. On the other hand, when the frequency order is changed from the first order to the 60th order, if the fluctuation coefficient is a value corresponding to the output shown in FIG. 8-1, the fluctuation waveform has the shape shown in FIG. As shown in FIGS. 7-2 and 8-2, by changing the order of the 1 / f fluctuation function, the shape of the calculated fluctuation waveform also changes. Specifically, the fluctuation waveform becomes more complicated as the number of orders used is increased.

  Moreover, the shape of the serration part of the designed pneumatic tire based on each fluctuation waveform is the pneumatic tire 1a when the frequency order shown in FIGS. 7-3 and 7-4 is changed from the first order to the 600th order. The shape of the ridge 51b of the serration portion 5a of the pneumatic tire 1b is the shape of the ridge 51a of the serration portion 5a when the frequency order shown in FIGS. 8-3 and 8-4 is changed from the first order to the 60th order. Instead, the shape change becomes more complicated. That is, the difference in shape between the ridge and the adjacent ridge can be further increased. Thus, as a design method, the shape of various serration parts can be designed by appropriately designing the order to be used. Moreover, it can be set as the pneumatic tire which improved quality by various directions depending on the order of the frequency to be used.

  Here, the 1 / f fluctuation function preferably includes three or more consecutive integer order components, more preferably includes six or more integer order components, and includes twelve or more integer order components. Is more preferable. In this way, by setting the number of orders to be used to a certain number, it is possible to give appropriate fluctuations to the shape of the serration portion, and it is possible to give the above effect more suitably. Further, as described above, by increasing the order to be used, the shape of the serration portion can be made more complicated, the serration becomes a more unique shape, and the sensitivity quality can be maintained high.

  In addition, it is preferable to use an integer order component of second or higher order, that is, an integer order component of 2 ≦ n or more, for the 1 / f fluctuation function. In this way, by using an integer order component of the second or higher order in the 1 / f fluctuation function, that is, by not using the first order component, the balance of the serration portion of the tire is made more uniform, and the sensitivity quality is increased. Can be maintained.

  Here, FIG. 9A, FIG. 10A, and FIG. 11A are graphs showing the relationship between the frequency (f) and the spectrum power (PSD), respectively. 9-2 is based on the relationship shown in FIG. 9-1, FIG. 10-2 is based on the relationship shown in FIG. 10-1, and FIG. 11-2 is based on the relationship shown in FIG. It is a graph which shows the fluctuation waveform produced | generated, respectively. 9A and 9B use the third order to the fifth order (3 ≦ n ≦ 5) as the integer order component of the 1 / f fluctuation function, and FIGS. 3rd to 8th order (3 ≦ n ≦ 8) is used as the integer order component of the 1 / f fluctuation function, and FIGS. 11-1 and 11-2 illustrate the third order as the integer order component of the 1 / f fluctuation function. The fluctuation waveform was calculated using the 14th order (3 ≦ n ≦ 14).

  If the fluctuation coefficients are values corresponding to the outputs shown in FIGS. 9A, 10A, and 11A, the fluctuation waveforms are as shown in FIGS. 9-2, 10-2, and 11−. The shape shown in FIG. As shown in FIGS. 9-2 to 11-2, the fluctuation waveform can be made more complicated by increasing the integer order components to be used. By making the fluctuation waveform into a complicated shape, the shape of the serration can be made more complex, the serration becomes a more unique shape, and high sensitivity quality can be maintained. Moreover, as shown in FIGS. 9-2 to 11-2, by using the second order or higher order components, the left and right balance of the waveform can be improved, and the balance of the serration portion of the tire is made more uniform. , Sensitivity quality can be kept high.

  Here, FIG. 12 is a graph showing the relationship between frequency and spectrum power on a logarithmic axis. In FIG. 12, the horizontal axis represents frequency and the vertical axis represents power density. Both axes are logarithmic axes. As described above, by changing the fluctuation coefficient to 0.5 or more and 2 or less and having a difference between the maximum value and the minimum value within a range of 0.5 or less, the logarithm as shown in FIG. In the axis, the relationship between the frequency and the spectral power is included in the range of the gradient 2 / f to the gradient 0.5 / f. In addition, by setting the difference between the maximum value and the minimum value to be in a range of 0.5 or less, the inclination can be made substantially constant. Thereby, 1 / f fluctuation can be expressed suitably, and sensitivity quality can be made high.

  The fluctuation coefficient is preferably a constant value. That is, it is preferable that the fluctuation coefficient is a single value, and the relationship between the frequency and the spectrum power shown in FIG. 12 is a straight line with a slope of 2 / f, a straight line with 1 / f, and a straight line with 0.5 / f. In this way, by setting the fluctuation coefficient to a constant value, the 1 / f fluctuation can be suitably expressed, and the sensitivity quality can be improved.

  In the above embodiment, the fluctuation coefficient is an arbitrary value. However, the relationship between the fluctuation coefficient value and the order may be set as a function. Further, the low-order order fluctuation coefficient may be set lower than the high-order degree fluctuation coefficient. By reducing the low-order fluctuation coefficient, the tire mass balance can be made more uniform.

  Here, in any of the above embodiments, the height of the ridge and the angle of the surface (angle with respect to the equator plane) are changed in any case, but the present invention is not limited to this. Here, it is preferable that the ridge has a constant volume of each ridge, and only the surface angle and shape are changed depending on the position. Thus, by making the volume of the ridge constant, the mass balance of the tire can be made constant. Thereby, the performance of a tire can be maintained more reliably.

  Further, as the serration portion, in addition to or instead of the height of the ridge and the angle of the surface, at least one of the arrangement interval of the ridge, the width of the ridge, and the shape of the surface of the ridge according to the position in the circumferential direction. It may be changed. Further, although the case where only the ridge is formed in the serration portion has been described, a character, a symbol, or the like may be formed. In this case, only the ridge may be designed under the above conditions, or may be designed under the above conditions including those having other shapes such as characters and symbols.

  Moreover, although the case of the serration part of the side wall part was demonstrated in the said embodiment, it should just be formed over the circumferential direction of the side wall part, ie, the perimeter, and is not limited to a serration part. For example, the shape of the surface of the block formed in the side wall portion changes in the same manner depending on the order within the range where the fluctuation coefficient is 0.5 or more and 2 or less and the difference between the maximum value and the minimum value is 0.5 or less. Based on the 1 / f fluctuation function, the shape of the surface changes in the circumferential direction based on the 1 / f fluctuation function, which is a value to be used, and the order range of the frequency in which one round in the circumferential direction is primary, The same effect as described above can be obtained.

  Hereinafter, the pneumatic tire will be described in more detail using observation examples. Here, FIG. 13-1 is an enlarged cross-sectional view showing a part of the serration part in an enlarged manner, and FIG. 13-2 is a part of the serration part shown in FIG. 13-1 developed in the circumferential direction. It is an expanded sectional view showing a section. 14-1 is an enlarged cross-sectional view showing a part of the serration portion in an enlarged manner, and FIG. 14-2 is a partial cross-section of the serration portion shown in FIG. 14-1 developed in the circumferential direction. FIG. FIGS. 13-1 and 13-2 show a pneumatic tire 1c in which the serration ridge 51c is designed by the above-described method except that the order of the 1 / f fluctuation function is 3rd order to 600th order. is there. 14A and 14B show a pneumatic tire 1d having a serration in which a constant ridge 51d is formed in the circumferential direction as a comparative example.

  As seen from the comparison between FIG. 13-1 and FIG. 14-1, and from the comparison between FIG. 13-2 and FIG. 14-2, the example and the comparative example have different appearances of serrations. A sensory test was performed on the tire of this example and the tire of the comparative example under the following conditions. Questionnaire survey of 20 impressions of male and female adults (total of 40) with regard to the impressions received from the appearance of the tires of the tires of the example mounted on the vehicle and the tires of the comparative example mounted on the vehicle. did. As evaluation items, five items of “easy to stand out”, “fun”, “beauty”, “comfort”, and “luxury” were used. The higher the evaluation, the higher the score. In other words, a five-point evaluation is the best evaluation. The average value of 40 people for each evaluation item was calculated from the evaluation result of the questionnaire survey. The calculation results are shown in Table 1 below.

  As shown in Table 1, it can be seen that all of the items are higher in evaluation than the comparative example. In particular, the feeling of relaxation and visibility are high. From the above, it can be seen that the pneumatic tire of the present invention has high sensitivity quality.

  As described above, the pneumatic tire and the pneumatic tire design method according to the present invention are suitable for use as a pneumatic tire to be mounted on a vehicle and a design method thereof.

DESCRIPTION OF SYMBOLS 1 Pneumatic tire 2 Tread part 3 Side wall part 4 Bead part 5 Serration part 51 Ridge 52 Outer ring 53 Inner ring 54 End surface

Claims (16)

A pneumatic tire comprising a tread portion, a sidewall portion, and a bead portion,
The sidewall portion outer surface has a pattern portion formed extending in the circumferential direction of the surface,
The pattern portion has a fluctuation coefficient of 0.5 or more and 2 or less, and a value that varies depending on the order in a range where the difference between the maximum value and the minimum value is 0.5 or less. A pneumatic tire characterized in that the shape of the surface changes in the circumferential direction based on a 1 / f fluctuation function having a finite order range of frequencies.   2. The pneumatic according to claim 1, wherein the 1 / f fluctuation function is a function in which a relationship between a frequency on a logarithmic axis and a spectral power density is inversely proportional when the fluctuation coefficient is a constant value. tire.   2. The serration according to claim 1, wherein the pattern portion is a serration in which a plurality of protruding ridges extending along the tire radial direction are arranged in parallel along the tire circumferential direction within a predetermined range in the tire radial direction. 2. The pneumatic tire according to 2.   4. The air according to claim 3, wherein at least one of the arrangement direction, the arrangement interval, the height, and the surface angle of the ridge is changed based on the 1 / f fluctuation function. Enter tire.   The pneumatic tire according to any one of claims 1 to 4, wherein the order range is 1st to 2000th.   The pneumatic tire according to any one of claims 1 to 5, wherein the order range includes at least three consecutive integer orders.   The pneumatic tire according to any one of claims 1 to 6, wherein the order range is equal to or higher than the second order.   The pneumatic tire according to any one of claims 1 to 7, wherein the fluctuation coefficient has the same value. A pneumatic tire design method that determines the design of the sidewall part,
A change in shape in the circumferential direction of the pattern portion formed extending in the circumferential direction of the surface of the sidewall portion is a fluctuation coefficient of 0.5 or more and 2 or less, and a difference between the maximum value and the minimum value is 0. It is a value that varies depending on the order within a range of .5 or less, and is determined based on a 1 / f fluctuation function in which the order range of the frequency in which one round in the circumferential direction is the first order is finite. Pneumatic tire design method.   10. The pneumatic according to claim 9, wherein the 1 / f fluctuation function is a function in which the relationship between the frequency on the logarithmic axis and the spectral power density is inversely proportional when the fluctuation coefficient is a constant value. Tire design method.   The shape of a serration in which a plurality of protruding ridges extending along a tire radial direction are arranged in a predetermined range in the tire radial direction along the tire circumferential direction is determined as the pattern portion. Item 11. The pneumatic tire design method according to Item 9 or 10.   The pneumatic tire design method according to claim 11, wherein at least one of an arrangement direction, an arrangement interval, a height, and a surface angle of the ridges is determined based on the 1 / f fluctuation function. .   The method for designing a pneumatic tire according to any one of claims 9 to 12, wherein the order range is 1st to 2000th.   The pneumatic tire design method according to claim 9, wherein the order range includes at least three consecutive integer orders.   The method for designing a pneumatic tire according to any one of claims 9 to 14, wherein the order range is equal to or higher than the second order.   The pneumatic tire design method according to claim 9, wherein the fluctuation coefficients have the same value.

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