Tire noise reduction

Abstract

A tire has four circumferential grooves. Grooves are on the vehicle installation inner side of the tire, and on the vehicle installation outer side of the tire. Grooves which are on the vehicle installation inner side each have a plurality of fences in the groove arranged alternately along the groove next to each side wall of the groove. Grooves which are on the vehicle installation outer side do not have fences. The fences increase the path length of sound due to pipe resonance and delay the sound in comparison to grooves on the vehicle installation outer side of the tire. This directs the sound towards the inner side of the tire and reduces the noise on the outer side.

Claims

1. A tire having a vehicle installation outer side and a vehicle installation inner side, at least two circumferential grooves, and a midpoint which is halfway between two circumferential grooves which are outermost in the tire width direction, at least one of the at least two circumferential grooves, which is on the vehicle installation inner side with respect to the midpoint, having a plurality of protrusions in the groove arranged alternately along the groove next to each side wall of the groove, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}>0$ where: k denotes a groove on the vehicle installation inner side with respect to the midpoint; n is the number of grooves on the vehicle installation inner side with respect to the midpoint; l denotes a groove on the vehicle installation outer side with respect to the midpoint; m is the number of grooves on the on the vehicle installation outer side with respect to the midpoint; Ak and Bl is the area of the protrusion when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; and AGk and BGl is the total area of the groove when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; and wherein two of the circumferential grooves, which are on the vehicle installation inner side with respect to the midpoint, each have a plurality of protrusions in the groove arranged alternately along the groove next to each side wall of the groove, and two of the circumferential grooves, which are on the vehicle installation outer side with respect to the midpoint, do not have any protrusions.

2. The tire according to claim 1, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}>0.20.$

3. The tire according to claim 1, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\mathrm{Ek}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\mathrm{Fl}\frac{\mathrm{Bl}}{\mathrm{BGl}}>1.20$ where: Ek and Fl is the protrusion density ratio, the protrusion density being the number of protrusions in a certain length of groove, and the protrusion density ratio being the ratio of the protrusion density in the groove to the protrusion density in the groove with the lowest protrusion density.

4. The tire according to claim 1, wherein, for any of the circumferential grooves, which is on the vehicle installation inner side with respect to the midpoint, the following inequality is met: $\frac{\mathrm{Ak}}{\mathrm{AGk}}>0.2.$

5. The tire according to claim 1, wherein the at least one of the circumferential grooves which is on the vehicle installation inner side with respect to the midpoint and which has the protrusions is substantially parallel to the tire circumferential direction.

6. A tire having a vehicle installation outer side and a vehicle installation inner side, at least two circumferential grooves, and a midpoint which is halfway between two circumferential grooves which are outermost in the tire width direction, at least one of the circumferential grooves, which is on the vehicle installation inner side with respect to the midpoint, having a plurality of protrusions in the groove arranged alternately along the groove next to each side wall of the groove, and having a plurality of recesses, each recess being provided in a side wall of the groove opposite to a different protrusion, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}+\frac{\mathrm{Ck}}{\mathrm{CGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{BL}}{\mathrm{BGl}}+\frac{\mathrm{Dl}}{\mathrm{DGl}}>0$ where: k denotes a groove on the vehicle installation inner side with respect to the midpoint; n is the number of grooves on the vehicle installation inner side with respect to the midpoint; l denotes a groove on the vehicle installation outer side with respect to the midpoint; m is the number of grooves on the on the vehicle installation outer side with respect to the midpoint; Ak and Bl is the area of the protrusion when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; AGk and BGl is the total area of the groove when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; Ck and Dl is the area of the recess when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; CGk and DGl is the total area of the groove when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; and wherein two of the circumferential grooves, which are on the vehicle installation inner side with respect to the midpoint, each have a plurality of protrusions in the groove arranged alternately along the groove next to each side wall of the groove, and a plurality of recesses, each recess being provided in a side wall of the groove opposite to a different protrusion, and two of the circumferential grooves, which are on the vehicle installation outer side with respect to the midpoint, do not have any protrusions or any recesses.

7. The tire according to claim 6, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ck}}{\mathrm{CGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Dl}}{\mathrm{DGl}}>0.$

8. The tire according to claim 6, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}>0.$

9. The tire according to claim 6, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}+\frac{\mathrm{Ck}}{\mathrm{CGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}+\frac{\mathrm{Dl}}{\mathrm{DGl}}>0.90.$

10. The tire according to claim 6, wherein the following inequality is met: $\underset{k=1}{\overset{n}{.Math.}}\mathrm{Ek}\frac{\mathrm{Ak}}{\mathrm{AGk}}+\mathrm{Gk}\frac{\mathrm{Ck}}{\mathrm{CGk}}-\underset{l=1}{\overset{m}{.Math.}}\mathrm{Fl}\frac{\mathrm{Bl}}{\mathrm{BGl}}+\mathrm{Hl}\frac{\mathrm{Dl}}{\mathrm{DGl}}>1.1$ where: Ek and Fl is the protrusion density ratio, the protrusion density being the number of protrusions in a certain length of groove, and the protrusion density ratio being the ratio of the protrusion density in the groove to the protrusion density in the groove with the lowest protrusion density; and Gk and Hl is the recess density ratio, the recess density being the number of recesses in a certain length of groove, and the recess density ratio being the ratio of the recess density in the groove to the recess density in the groove with the lowest recess density.

11. The tire according to claim 6, wherein the at least one of the circumferential grooves which is on the vehicle installation inner side with respect to the midpoint and which has the protrusions and recesses is substantially parallel to the tire circumferential direction.

Description

(1) Preferred embodiments of the present disclosure will now be described, purely as examples, with reference to the drawings in which:

(2) FIG. 1 is a schematic perspective view of four circumferential grooves showing the fence distribution of a tire according to a first embodiment;

(3) FIG. 2 is an enlarged fragmentary plan view of one circumferential groove of the embodiment of FIG. 1;

(4) FIG. 3 is a graph of overall noise reduction vs rotation for tires with only two out of four circumferential grooves with fences;

(5) FIG. 4 is three graphs showing the sound pressures detected by three microphones positioned around a tire;

(6) FIG. 5 is a schematic perspective view of four circumferential grooves showing the fence distribution of a tire according to a second embodiment;

(7) FIG. 6 is a graph of overall noise reduction vs rotation for tires with four out of four circumferential grooves with fences;

(8) FIG. 7 is an elevation view of a tire along the tire circumferential direction showing four circumferential grooves;

(9) FIG. 8 is, on the left, a front view of the tire of FIG. 7, and, on the right, a perspective view of the tire of FIG. 7, both showing the positions of microphones, and graphs showing the sound pressures detected by two of the microphones;

(10) FIGS. 9 to 11 are graphs for tires with four out of four circumferential grooves with fences;

(11) FIG. 12 is graphs for tires with four out of four circumferential grooves with fences where different grooves have different widths;

(12) FIG. 13 is graphs for tires with only two out of four grooves with fences;

(13) FIG. 14 is a schematic perspective view of four circumferential grooves showing the fence and void distribution of a tire according to a third embodiment;

(14) FIG. 15 is a plan view of the embodiment of FIG. 14;

(15) FIG. 16 is graphs for tires with only two out of four grooves with fences and voids.

(16) Referring to FIG. 1, four grooves 10, 12, 14 and 16 are shown, which represent the circumferential grooves of a tire 1 of the first embodiment. It should be noted that the grey bars in FIG. 1 show the grooves and not ribs. In the present embodiment, the grooves 10, 12, 14 and 16 are parallel. Grooves 10 and 12 are on the vehicle installation inner side of the tire 1, and grooves 14 and 16 are on the vehicle installation outer side of the tire 1. In the present embodiment, the grooves 10, 12, 14 and 16 are equidistant from each other. A midpoint which is halfway between the two circumferential grooves 10 and 16 which are outermost in the tire width direction is shown by dashed line 20.

(17) In the present embodiment, two of the grooves (namely, grooves 10 and 12) which are on the vehicle installation inner side with respect to the midpoint each have a plurality of protrusions in the form of fences 30, 32 in the groove 10, 12 arranged alternately along the groove 10, 12 next to each side wall of the groove 10, 12. Grooves 14 and 16 do not have fences. The fences 30, 32 increase the path length of sound due to pipe resonance and delay the sound in comparison to grooves 14 and 16. This directs the sound towards the inner side of the tire 1 and reduces the noise on the outer side.

(18) FIG. 2 shows an enlarged fragmentary view of the embodiment of FIG. 1, and in particular the groove 12. FIG. 2 shows the path of sound S as it travels along the groove 12. The sound S follows a sinuous path. When the sound, travelling in the groove longitudinal direction, encounters a fence 32 it is diverted towards the opposite side of the groove 12. It travels backwards and forwards in this way as it travels down the groove 12. Thus the path length is longer than had the sound simply traveled straight along the groove longitudinal direction.

(19) In the present embodiment, the fence density, which is the number fences in a certain length of groove, is larger in groove 10 than in groove 12. However, this is not essential.

(20) The fence density ratio in groove 12 is 25/25=1. The fence density ratio in groove 10 is 39/25=1.6. Here, 25 and 39 are the number of fences per 100 mm.

(21) In the present embodiment, fences 30 in groove 10 are each 4 mm in height and 4.5 mm in length (measured in the groove width direction) giving a fence area of 18 mm.sup.2. Fences 32 in groove 12 are each 2.2 mm in height and 3.8 mm in length giving a fence area of 8.4 mm.sup.2. The thickness is 1 mm (measured in the groove longitudinal direction).

(22) The grooves 10 and 12 are each 5 mm in height and 10 mm in width giving a total area of 50 mm.sup.2.

(23) When the following inequality is met, the noise will be rotated inwards:

(24) $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}>0$ where: k denotes a groove on the vehicle installation inner side with respect to the midpoint; n is the number of grooves on the vehicle installation inner side with respect to the midpoint; l denotes a groove on the vehicle installation outer side with respect to the midpoint; m is the number of grooves on the on the vehicle installation outer side with respect to the midpoint; Ak and Bl is the area of the protrusion (and optionally the area of the void) when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove; and AGk and BGl is the total area of the groove when the groove is viewed in cross-section perpendicular to the longitudinal direction of the groove.

(25) In the present embodiment, the term:

(26) $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}$
is calculated for grooves 10 and 12 as 18/50+8.4/50=0.53.

(27) In the present embodiment, the term:

(28) $\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}$
is calculated as for grooves 14 and 16 and is calculated as 0/50+0/50=0.

(29) Therefore, the comparison is 0.53−0=0.53. This is greater than 0 as required for rotation inwards. Simulations of the present embodiment gave a rotation of −0.48 dB and an overall noise reduction of −0.18.

(30) FIG. 3 is a graph of the results of simulations with the configuration shown in FIG. 1 but with the height and width of the fences varied. The fence densities were not varied. It can be seen that all data points show a negative rotation because the fences are only provided on the vehicle installation inner side. Some data points also show an overall noise increase rather than reduction, with a trend for larger rotations to give larger noise reductions.

(31) It can be seen that for rotations less than −0.3 dB, the overall noise reduction is positive (i.e. the overall noise actually increases). However, as the rotation increases, the overall noise level is reduced, and above a certain rotation (−0.4 dB), all simulations showed an overall noise reduction.

(32) FIG. 4 shows the simulated microphone outputs for a microphone on the left (inner) side, the right (outer) side and the centre of the tire 1. The line labelled “131” is output for the configuration of grooves according to FIG. 1 as described above. The line labelled “Reference” is for a tire without any protrusions in grooves 10, 12, 14 and 16.

(33) Pipe resonance occurs in the frequency range 900-1200 Hz. The outputs are integrated over this range. Then, for the left microphone, the reference output (which has no fences) is subtracted from the result for the configuration with the fences, and the same is done for the right microphone. Typically, the results of the subtractions will be negative. The result for the left microphone is then subtracted from the result for the right, to give the rotation. For example, if the result for the left is −1.5 dB and for the right is −2.9 dB: −2.9-−1.5=−1.4 dB rotation. For the results shown in FIG. 3, since all the protrusions are on the left (inner) side of the tire 1, all the rotations are negative.

(34) The overall noise reduction is then calculated. As the rotations are all negative, the calculation only involves the centre and right microphone outputs. Specifically, for the centre microphone, the reference output (which has no fences) is subtracted from the result for the configuration with the fences. This is then added to the subtraction result done earlier for the right microphone. The result gives the overall noise reduction. This can be summarised as follows:

(35) Rotation:

(36) (Output right—reference output right)—(output left—reference output left).

(37) Overall noise reduction: If rotation negative: (output centre—reference output centre)+(output right—reference output right) If rotation positive: (output centre—reference output centre)+(output left—reference output left)

(38) FIG. 5 shows configuration of grooves of a tire 40 of a second embodiment. The configuration is similar to that of FIG. 1 and the first embodiment except that all the grooves have fences. In detail, the grooves 50, 52, 54 and 56 are the same as grooves 10, 12, 14 and 16 of FIG. 1 except that grooves 54 and 56 have fences 74 and 76 whereas grooves 14 and 16 do not. The midpoint is shown by dashed line 60.

(39) FIG. 6, similarly to FIG. 3, is a graph of the results of simulations with the configuration shown in FIG. 5 but with the height and width of the fences varied. The fence densities were not varied. In this case, in contrast to FIG. 3, not all data points show a negative rotation because the fences are provided on both the vehicle installation inner and outer sides. Again, some data points also show an overall noise increase rather than reduction, with a trend for larger rotations to give larger noise reductions.

(40) In FIG. 6 unlike FIG. 3, the actual values of some data points are shown. The values of “Z” given are the total volumes of the fences in the grooves. These are calculated by multiplying the fence area by the fence density ratio for each groove and summing the results to give the total for all the grooves. The fence density is the number of fences in a certain length of groove, and the fence density ratio is the ratio of the fence density in the groove to the fence density in the groove with the lowest fence density. The fence densities used in calculating the values of “Z” were 4.9, 3.1, 1.9, 1 for grooves 50, 52, 54, 56 (inner side to outer side). These values of 4.9, 3.1, 1.9, 1 are calculated by dividing the number of fences in 100 mm of the groove (39, 25, 15 and 8, respectively) by 8 (which is the fence density in the groove with the lowest fence density).

(41) For example, in the configuration which gave the data point on the far left with X: −0.3991, Y: −0.1138 and Z: 136.5, the fences had the dimensions given in Table 1 below. The table also gives the fence volumes for each groove which are added to give the total volume of the fences in the grooves. All fences are 1 mm thick.

(42) TABLE-US-00001 TABLE 1 Groove of FIG. 5 50 52 54 56 Fence Length 3.8 3.9 1.9 4.0 (mm) Fence Height 4.3 2.9 2 3.6 (mm) Fence Area 16.3 11.3 3.8 14.4 (mm.sup.2) Fence Density 39/8 = 4.9 25/8 = 3.1 15/8 = 1.9 8/8 = 1 Ratio Volume of Fences 79.7 35.3 7.1 14.4 Total Volume 136.5 of Fences

(43) The configuration of FIG. 1 was found to be better than that of FIG. 5 in terms of providing a good balance of rotation and water drainage. The water drainage is better because grooves 14 and 16 in FIG. 1 do not have fences (in contrast to grooves 54 and 56 of FIG. 5).

(44) To confirm the effects, experiments were also undertaken on actual tires with fences installed in their circumferential grooves in the tire tread. FIG. 7 shows such a tire 80. The fences are provided on an insert which is inserted into the circumferential groove. Grooves 90 and 92 are on the vehicle installation inner side, and grooves 94 and 96 are on the vehicle installation outer side. All four grooves 90, 92, 94, 96 have fences, with lengths, respectively, of 2.1 mm, 6.0 mm, 3.3 mm and 2.4 mm (left to right in FIG. 7). The heights of the fences 90, 92, 94, 96 are, respectively, 3.8 mm, 3.0 mm, 3.0 mm and 3.8 mm (left to right in FIG. 7).

(45) FIG. 8 shows how the experiment was set up for the tire shown in FIG. 7. The tire was run at 80 kph with a load of 5.14 kN. Microphones 1-5 were placed in an arc around the tire, with “MIC1” being on the outer side, and “MIC5” being on the inner side. The graphs for MIC1 and MIC5 show a larger noise reduction (−2.9 dB) on the outer side than on the inner side (−1.5 dB). The difference of −1.4 dB shows a rotation inwards.

(46) The results of the microphone test were also confirmed using a sound camera map. The visual outputs showed louder sounds on the inner side than the outer side. Also, the special averages were taken of the sound recorded on the inner and outer sides and compared. These showed a good correlation with the microphone test. The spatial averages were then integrated over the range 900-1200 Hz and compared as with the microphone test. The tire was run at 50 kph. The results showed a noise reduction of −4.0 dB on the outer side vs −2.5 dB on the inner side. The difference of −1.5 dB shows a rotation inwards.

(47) Simulations (referred to as “first simulations” above) were run according to the general configuration shown in FIG. 5 but in which the fence areas were varied while maintaining a constant fence density. The simulations gave data for rotation and overall noise reduction. FIG. 9A is a graph showing the rotation plotted against fence area comparison. The fence area comparison is calculated using the formula:

(48) $\underset{k=1}{\overset{n}{.Math.}}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\frac{\mathrm{Bl}}{\mathrm{BGl}}=\mathrm{fence}\mathrm{area}\mathrm{comparison}$

(49) Table 2 below shows calculations for the same configuration of fences in Table 1. The fence area comparison result of 0.19 and rotation of −0.3991 is shown as one of the data points in FIG. 9A.

(50) TABLE-US-00002 TABLE 2 Groove of FIG. 5 50 52 54 56 Fence Length 3.8 3.9 1.9 4.0 (mm) Fence Height 4.3 2.9 2 3.6 (mm) Fence Area 16.3 11.3 3.8 14.4 (mm.sup.2) Groove Area 50 50 50 50 (mm.sup.2) Fence 0.33 0.23 0.08 0.29 Area/Groove Area (Ak/AGk) Fence Area (0.33 + 0.23) − Comparison (0.08 + 0.29) = 0.19

(51) From FIG. 9A, the correlation between the fence area comparison result and the rotation inwards is clear, where, as the fence area comparison result increases, so does the rotation inwards.

(52) FIG. 9B is a graph of rotation against subtracted fence volume proportion comparison for the same simulations as FIG. 9A. The subtracted fence volume proportion comparison is calculated using the formula:

(53) $\underset{k=1}{\overset{n}{.Math.}}\mathrm{Ek}\frac{\mathrm{Ak}}{\mathrm{AGk}}-\underset{l=1}{\overset{m}{.Math.}}\mathrm{Fl}\frac{\mathrm{Bl}}{\mathrm{BGl}}=\mathrm{subtracted}\mathrm{fence}\mathrm{volume}\mathrm{proportion}\mathrm{comparison}$
where: Ek and Fl is the protrusion density ratio, the protrusion density being the number of protrusions in a certain length of groove, and the protrusion density ratio being the ratio of the protrusion density in the groove to the protrusion density in the groove with the lowest protrusion density. For example, if the protrusion density in the groove in question is 40 protrusions per 100 mm and the protrusion density in the groove with the lowest protrusion density is 8 protrusions per 100 mm, the ratio will be 40/8=5. Hence this comparison also takes into account the protrusion density.

(54) It can be seen from FIG. 9B that there is a trend for larger fence volume comparison results to have a more negative (i.e. inward) rotation. The larger the comparison result, the more fence volume on the tire inner side compared to the outer side. All simulations with a comparison result of >1.15 give a rotation inwards.

(55) FIG. 10 is a graph of noise reduction against fence area comparison for the same simulations as FIG. 9. The fence area comparison is calculated using the above formula. It can be seen that where the comparison is >0.35, there is an overall noise reduction (the noise reduction becomes negative).

(56) FIG. 11 is a graph of noise reduction against subtracted fence volume proportion comparison for the same simulations as FIG. 9A. The subtracted fence volume proportion comparison is calculated using the formula mentioned above in connection with FIG. 9B.

(57) According to the FIG. 11, there seems to be a trend from low values of the subtracted fence volume comparison result towards values around 1.00, the noise reduction becomes more positive (which is undesirable) but as the values increase from 1.00 there seems to be a trend for more negative noise reduction (which is desirable). It can be seen that above 1.90 for the comparison result, all noise reduction values are negative, that is there is an overall noise reduction.

(58) Simulations (referred to as “second simulations” above) were run for the same general configuration shown in FIG. 5 except that the two grooves next to the midpoint were wider than the other two grooves. Specifically, the groove next to the midpoint were 16.5 mm in width, whereas the other two grooves were 10.2 mm in width. The results are shown in FIG. 12 where similar trends can be seen to those of FIGS. 9-11.

(59) Next, simulations were run for the general configuration shown in FIG. 1 where protrusions are provided only on the inner side. In these simulations, the fence areas were varied while maintaining a constant fence density. The simulations gave data for rotation and overall noise reduction. FIG. 13 shows graphs produced from data from those simulations, and corresponding to the graphs shown in FIGS. 9-12.

(60) FIGS. 14 and 15 show a configuration of grooves of a tire 100 of a third embodiment. The configuration is similar to that of FIG. 1 and the first embodiment except that the grooves with fences also have recesses in the form of voids. In detail, the grooves 101, 103, 105 and 107 are the same as grooves 10, 12, 14 and 16 of FIG. 1 except that grooves 101 and 103 have fences 111 and 113 and voids 115 and 117. The midpoint is shown by dashed line 120.

(61) Each void 115 is provided in a side wall of the groove 101 opposite to a different protrusion 111, and the same is true for voids 117 and protrusions 113. In this embodiment, each void 115 and 117 (or, more specifically, its centre in the groove longitudinal direction) is provided at the same position in the groove longitudinal direction as its opposite protrusion 111 and 113 (or, more specifically, the protrusion's centre in the groove longitudinal direction). This was found to give the best rotation and overall noise reduction.

(62) Each protrusion 111 has the same dimensions as void 115, and each protrusion 113 has the same dimensions as void 117.

(63) Simulations were run for the general configuration shown in FIGS. 14 and 15 where protrusions and voids are provided only on the inner side. In these simulations, the fence and void areas were varied while maintaining a constant fence density. The simulations gave data for rotation and overall noise reduction. FIG. 16 shows graphs produced from data from those simulations, and corresponding to the graphs shown in FIGS. 9-12. Here, like the FIG. 1 embodiment, the fence density ratios of grooves 101 and 103 are 1.6 and 1, respectively. Also, the recess density ratios of grooves 101 and 103 are 1.6 and 1, respectively.

(64) In all embodiments described, the fence density increases from the vehicle installation outer side towards the inner side, and where there are four grooves with fences, each groove has greater fence density than its outer adjacent groove. However, this is not essential, and the fence density could be the same for each groove, for example.

(65) In addition, each fence extends at a right angle to the groove sidewall, but that is not essential and the fence may extend at smaller angle, for example.

(66) Preferred embodiments of the present disclosure have been described purely by way of example, and various modifications, additions and/or omissions will present themselves to one skilled in the art, all of which form part of the present disclosure, together with their equivalents.