JP2005121555A - Method for estimating high-speed uniformity of tire and method for sorting tire - Google Patents
Method for estimating high-speed uniformity of tire and method for sorting tire Download PDFInfo
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Abstract
Description
本発明は、タイヤの高速ユニフォミティ推定方法及びタイヤの選別方法に関する。より詳細には、実用域の速度でのタイヤのＴＦＶ（タンジェンシャルフォースバリエイション）のフーリエ解析による１次周期成分（高速ＴＦＶ１次成分）の大きさをタイヤの他の測定データから推定する方法、及び、この推定値に基づいて高速ＴＦＶ１次成分の小さいタイヤを選別する方法に関するものである。 The present invention relates to a tire high-speed uniformity estimation method and a tire sorting method. More specifically, a method of estimating the magnitude of a primary period component (high-speed TFV primary component) by Fourier analysis of TFV (tangential force variation) of a tire at a speed in a practical range from other measurement data of the tire, and The present invention relates to a method for selecting a tire having a small primary TFV primary component based on the estimated value.
一般に、空気入りタイヤにおいては、１回転する間にタイヤ軸にユニフォミティと言われる力変動が発生する。タイヤは、高速走行時においては約１０〜３０回／秒で回転するため、高速走行時におけるユニフォミティの１次成分の周波数は１０〜３０Ｈｚである。一方、車両のサスペンションのばね下共振周波数は通常１０〜１８Ｈｚにあるため、高速走行時、ユニフォミティの一次成分の周波数と合致したときにボディ振動やステアリング振動を発生させる。 Generally, in a pneumatic tire, a force fluctuation called uniformity is generated on a tire shaft during one rotation. Since the tire rotates at a speed of about 10 to 30 times / second during high speed traveling, the frequency of the primary component of uniformity during high speed traveling is 10 to 30 Hz. On the other hand, since the unsprung resonance frequency of the suspension of a vehicle is normally 10 to 18 Hz, body vibration and steering vibration are generated when the frequency coincides with the frequency of the primary component of uniformity during high speed traveling.
上記振動の中で、ステアリング振動に関しては、従来より前後方向の力変動であるＴＦＶが影響することが知られている。 Among the above vibrations, it is known that TFV, which is a force fluctuation in the front-rear direction, affects steering vibrations.
しかし、実走状態でのＴＦＶを計測するには、下記特許文献１や特許文献２にあるような特別な試験機が必要であり、タイヤ全数を計測することは困難である。
However, in order to measure the TFV in the actual running state, a special testing machine as described in
そこで、実走状態での高速ＴＦＶをタイヤの他の測定データから推定することが求められ、例えば、高速ＴＦＶを低速（１回／秒）でのＴＦＶで代用することが考えられるが、ＴＦＶは低速ではほとんど発生しないため、低速データによる管理は不可能である。 Therefore, it is required to estimate the high speed TFV in the actual running state from other measurement data of the tire. For example, it is conceivable to substitute the high speed TFV with the low speed (one time / second) TFV. Since it hardly occurs at low speed, management by low speed data is impossible.
下記特許文献３には、バランスと低速ユニフォミティデータを用いたタイヤのユニフォミティの予測方法が開示されており、高速ＴＦＶの１次成分を推定する方法についても記載されているが、高速ＲＲＯ１次成分と静アンバランスから高速ＴＦＶ１次成分を精度良く推定できるという本発明の特徴については開示されていない。
また、下記非特許文献１，２には、高速ＴＦＶが、その一要因であるタイヤ径変動（ＲＲＯ：ラジアルランアウト）と相関があると紹介されているが、実際には相関がない場合も多く、実用可能な推定精度を有していないのが実情である。
本発明は、以上の点に鑑みてなされたものであり、高速ＴＦＶ１次成分の推定を可能にして、高速ＴＦＶ１次成分を新たに計測することなくタイヤを選別することを目的とする。 The present invention has been made in view of the above points, and an object of the present invention is to enable estimation of a high-speed TFV primary component and to select a tire without newly measuring the high-speed TFV primary component.
本発明者は、タイヤの高速ＴＦＶがその速度での高速ＲＲＯと静アンバランスにより発生すると考え、更にそのときにＴＦＶの大きくなる位置が高速ＲＲＯ１次成分より９０°位相進みの位置であり、また静アンバランスより９０°位相遅れの位置であることを見い出した。そこで、これらの関係を求めることで高速ＴＦＶ１次成分を新たに計測することなく推定できると考え、本発明を完成するに至った。 The present inventor considers that the high-speed TFV of the tire is generated by the high-speed RRO and static unbalance at that speed, and the position where the TFV increases at that time is a position that is 90 ° phase advance from the high-speed RRO primary component. It was found that the position was 90 ° behind the static unbalance. Accordingly, it is considered that the high-speed TFV primary component can be estimated without newly measuring by obtaining these relationships, and the present invention has been completed.
すなわち、本発明は、第１に、ある品種のタイヤについて高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスを測定して、高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスとの関係を求めておき、高速ＴＦＶ１次成分が未知の同種のタイヤについて、高速ＲＲＯ１次成分と静アンバランスを測定し、その測定結果と前記関係から、そのタイヤの高速ＴＦＶ１次成分の推定値を算出することを特徴とするタイヤの高速ユニフォミティ推定方法を提供するものである。 That is, according to the present invention, first, a high-speed TFV primary component, a high-speed RRO primary component, and a static unbalance are measured for a certain type of tire, and the relationship between the high-speed TFV primary component, the high-speed RRO primary component, and the static unbalance is measured. Obtain a high-speed RRO primary component and static unbalance for the same type of tire whose unknown high-speed TFV primary component is known, and calculate an estimated value of the high-speed TFV primary component of the tire from the measurement result and the relationship. The high-speed uniformity estimation method of the tire characterized by these is provided.
本発明は、第２に、ある品種のタイヤについて高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と低速ＲＲＯ１次成分と静アンバランスを測定して、高速ＲＲＯ１次成分と低速ＲＲＯ１次成分と静アンバランスとの第１の関係を求めるとともに、高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスとの第２の関係を求めておき、高速ＴＦＶ１次成分が未知の同種のタイヤについて、低速ＲＲＯ１次成分と静アンバランスを測定して、前記第１の関係から高速ＲＲＯ１次成分の推定値を算出し、この高速ＲＲＯ１次成分の推定値と静アンバランスから前記第２の関係に基づき、そのタイヤの高速ＴＦＶ１次成分の推定値を算出することを特徴とするタイヤの高速ユニフォミティ推定方法を提供するものである。 Secondly, the present invention measures high-speed TFV primary component, high-speed RRO primary component, low-speed RRO primary component, and static unbalance for a certain type of tire, and provides high-speed RRO primary component, low-speed RRO primary component, and static unbalance. And a second relationship between the high-speed TFV primary component, the high-speed RRO primary component, and the static unbalance, and for the same type of tire whose high-speed TFV primary component is unknown, the low-speed RRO primary component and The static unbalance is measured, an estimated value of the high-speed RRO primary component is calculated from the first relationship, and the tire high-speed is calculated based on the second relationship from the estimated value of the high-speed RRO primary component and the static unbalance. The present invention provides a high-speed uniformity estimation method for a tire characterized by calculating an estimated value of a TFV primary component.
この場合、上記第２の関係は、第１の関係で推定した高速ＲＲＯ１次成分の推定値と、実際に測定した高速ＴＦＶ１次成分及び静アンバランスの測定値を用いて導出されたものであることが、より高い推定精度を得る上でより好ましい。 In this case, the second relationship is derived using the estimated value of the fast RRO primary component estimated in the first relationship, the actually measured fast TFV primary component and the measured value of the static unbalance. It is more preferable to obtain higher estimation accuracy.
ここで、「低速」とは、静アンバランスに基づく遠心力によってタイヤに新たな径変動を発生させない程度のタイヤ回転数をいい、通常１回／秒である。また、「高速」とは、それよりも速い回転数であり、通常８回／秒以上の回転数、より詳細には１０〜３０回／秒の範囲内で適宜に決定されるものである。 Here, “low speed” refers to the number of rotations of the tire that does not cause a new diameter variation in the tire due to the centrifugal force based on the static unbalance, and is usually 1 time / second. The “high speed” is a rotational speed faster than that, and is appropriately determined within a range of usually 8 rotational speeds / second or more, more specifically 10-30 rotational speeds / second.
上記第１の発明における関係と第２の発明における第２の関係において、高速ＴＦＶ１次成分は、高速ＲＲＯ１次成分をタイヤ回転方向前方に５０〜１３０°進めたベクトルと、静アンバランスをタイヤ回転方向後方に５０〜１３０°遅らせたベクトルとを合成したものとして表されることが好ましい。なお、本発明において、位相の「遅れ」は、タイヤ回転方向の後方にずれることを意味し、位相の「進み」は、タイヤ回転方向の前方にずれることを意味する。 In the relationship in the first invention and the second relationship in the second invention, the high-speed TFV primary component is a vector in which the high-speed RRO primary component is advanced by 50 to 130 ° forward in the tire rotation direction, and the static unbalance is rotated by the tire. It is preferably expressed as a combination of vectors delayed by 50 to 130 ° in the rearward direction. In the present invention, the “lag” of the phase means shifting backward in the tire rotation direction, and the “advance” of the phase means shifting forward in the tire rotation direction.
上記第１の発明における関係と第２の発明における第２の関係は、より具体的には、下記式で表されることが好ましい。 More specifically, the relationship in the first invention and the second relationship in the second invention are preferably represented by the following formulas.
Ｔ＝ａ１＋ｂ１・Ｈｙ−ｃ１・Ｓｙ＋（ａ２−ｂ２・Ｈｘ＋ｃ２・Ｓｘ）・ｊ
式中、Ｔは高速ＴＦＶ１次成分、Ｈｘは高速ＲＲＯ１次成分の実数部、Ｈｙは高速ＲＲＯ１次成分の虚数部、Ｓｘは静アンバランスの実数部、Ｓｙは静アンバランスの虚数部、ａ１、ａ２、ｂ１、ｂ２、ｃ１、ｃ２はタイヤの品種に応じて定められる係数であり、ｊ２＝−１である。
T = a 1 + b 1 · H y −c 1 · S y + (a 2 −b 2 · H x + c 2 · S x ) · j
Where T is the fast TFV primary component, H x is the real part of the fast RRO primary component, H y is the imaginary part of the fast RRO primary component, S x is the static unbalance real part, and S y is the static unbalance imaginary number. , A 1 , a 2 , b 1 , b 2 , c 1 , c 2 are coefficients determined according to the tire type, and j 2 = −1.
本発明のタイヤの選別方法は、上記方法で算出した高速ＴＦＶ１次成分の推定値と、高速ＴＦＶ１次成分の規格値とを比較してタイヤを選別するものである。ここで、規格値とは、タイヤに応じて予め定められた出荷できる上限値である。 The tire sorting method of the present invention sorts tires by comparing the estimated value of the high-speed TFV primary component calculated by the above method with the standard value of the high-speed TFV primary component. Here, the standard value is an upper limit value that can be shipped in advance according to the tire.
本発明であると、高速ユニフォミティマシンによらずに高速ＴＦＶ１次成分を推定することができるので、この推定値と高速ＴＦＶ１次成分の規格値とを比較して、規格値以下のタイヤを選別することにより、高速ＴＦＶ１次成分が規格値を超えるタイヤの出荷を防止することができる。 According to the present invention, the high-speed TFV primary component can be estimated without using a high-speed uniformity machine, and the estimated value and the standard value of the high-speed TFV primary component are compared to select tires that are less than the standard value. Accordingly, it is possible to prevent the shipment of tires in which the high-speed TFV primary component exceeds the standard value.
また、特に上記した第２の発明によれば、低速ＲＲＯ１次成分と静アンバランスの測定結果から高速ＴＦＶ１次成分の大きさを推定することができるので、通常計測している低速ユニフォミティマシンとバランサーのデータより高速ＴＦＶ１次成分を推定することができる。 In particular, according to the second invention described above, since the magnitude of the high-speed TFV primary component can be estimated from the measurement result of the low-speed RRO primary component and the static unbalance, the low-speed uniformity machine and the balancer that are normally measured The high-speed TFV first order component can be estimated from the above data.
１．高速ＴＦＶ１次成分と高速ＲＲＯ１次成分との関係
ＴＦＶの発生メカニズムについて、上記非特許文献１に提案された図３に示すモデルを考える。このモデルは、トレッドリングとホイールが回転方向にそれぞれ独立自由度を持った２自由度系モデルであり、その運動方程式は以下のようになる。
θｔ＝θｗ …（５）
であり、従って、式（２）（３）（５）より、
θ t = θ w (5)
Therefore, from the equations (2), (3), and (5),
このことを確認するため、タイヤサイズ＝１７５／８０Ｒ１４のタイヤについて、リムサイズ＝１４×５−Ｊ、空気圧＝１９３ｋＰａ、荷重＝３９６０Ｎ、回転数＝１５．６回／秒とし、質量が変化しないように径変動を加えてＴＦＶ１次成分とＲＲＯ１次成分を測定した。径変動の付与は、より詳細には、タイヤの踏面部の１／４周分をバフ掛けにより削ってＲＲＯを変化させ、バフ掛けにより減少した質量分のゴムパッチをバフ掛け位置のタイヤ内周面に貼り付けた。その結果、ＲＲＯ１次成分が増加（０．３ｍｍ）した位置に対して８６°進みの位置にＴＦＶ１次成分が３２Ｎ発生した。これにより、高速ＴＦＶ１次成分は高速ＲＲＯ１次成分のほぼ９０°進みで発生することが確認された。 In order to confirm this, for tires with tire size = 175 / 80R14, rim size = 14 × 5-J, air pressure = 193 kPa, load = 3960 N, rotation speed = 15.6 times / second so that the mass does not change. The TFV primary component and the RRO primary component were measured by adding diameter variation. More specifically, the diameter variation is applied by cutting the quarter of the tread surface of the tire by buffing to change the RRO, and the rubber patch corresponding to the mass reduced by the buffing is applied to the tire inner circumferential surface at the buffing position. Pasted on. As a result, 32N of TFV primary component was generated at a position advanced by 86 ° with respect to the position where the RRO primary component increased (0.3 mm). As a result, it was confirmed that the high-speed TFV primary component is generated approximately 90 ° ahead of the high-speed RRO primary component.
２．高速ＴＦＶ１次成分と静アンバランスとの関係
タイヤに質量アンバランスがあると、その質量の遠心力の前後方向成分がＴＦＶに寄与すると考え、高速ＴＦＶ１次成分と静アンバランスとの関係を求めた。
2. Relationship between high-speed TFV primary component and static unbalance When the tire has mass unbalance, the longitudinal component of the centrifugal force of the mass contributes to TFV, and the relationship between high-speed TFV primary component and static unbalance was obtained. .
具体的には、タイヤサイズ＝１７５／８０Ｒ１４のタイヤについて、リムサイズ＝１４×５−Ｊ、空気圧１９３ｋＰａ、荷重＝３９６０Ｎ、回転数＝１５．６回／秒とし、タイヤに質量を付与して高速ＴＦＶ１次成分を測定したところ、図４に示すように、質量１０ｇ付与時（ａ）で質量付与位置に対して９０°遅れの位置に大きさ１８ＮのＴＦＶ１次成分が発生し、質量２０ｇ付与時（ｂ）で質量付与位置に対して８５°遅れの位置に大きさ３７ＮのＴＦＶ１次成分が発生し、質量３０ｇ付与時（ｃ）で質量付与位置に対して９４°遅れの位置に大きさ５６ＮのＴＦＶ１次成分が発生した。 Specifically, for a tire with a tire size = 175 / 80R14, a rim size = 14 × 5-J, an air pressure of 193 kPa, a load = 3960 N, a rotation speed = 15.6 times / second, a mass is given to the tire, and a high speed TFV1 When the next component was measured, as shown in FIG. 4, when a mass of 10 g was applied (a), a TFV primary component having a size of 18 N was generated at a position 90 ° behind the mass application position, and when a mass of 20 g was applied ( In b), a TFV primary component with a size of 37 N is generated at a position delayed by 85 ° relative to the mass application position. A TFV primary component was generated.
このことから、タイヤに質量変動を加えると、高速ＴＦＶ１次成分が変化し、そのピーク位置は質量の約９０°遅れの位置に発生することが確認された。これは、質量が踏面部を越えて後方にきた時にＴＦＶ１次成分が最大になるためと考えられる。 From this, it was confirmed that when mass variation was applied to the tire, the high-speed TFV primary component was changed, and the peak position occurred at a position about 90 ° behind the mass. This is presumably because the primary component of TFV is maximized when the mass moves backward beyond the tread surface.
３．高速ＴＦＶ１次成分の推定式
上記１．及び２．の関係を考慮すると、高速ＲＲＯ１次成分のデータより位相をタイヤ回転方向前方に９０°進めたデータと、静アンバランスのデータより位相をタイヤ回転方向後方に９０°遅らせたデータを用い、これらのデータを合成することにより高速ＴＦＶ１次成分を表されるものと考えられる。この関係を図示したのが図１である。図１に示すように、高速ＴＦＶ１次成分Ｔは、高速ＲＲＯ１次成分Ｈをφｒ＝９０°進めたベクトルＨｔと、静アンバランスＳをφｓ＝９０°遅らせたベクトルＳｔとを用いて（なお、ユニフォミティの表現では通常遅れを正で表現する。）、これらのベクトル和として求められ、誤差も考慮すると下記式（７）で表される。
3. Estimation formula of fast TFV primary component And 2. In consideration of the relationship, the data obtained by moving the phase 90 ° forward in the tire rotation direction from the data of the high-speed RRO primary component and the data obtained by delaying the phase 90 ° rearward in the tire rotation direction from the static unbalance data are used. It is considered that the high-speed TFV primary component is represented by combining the data. FIG. 1 illustrates this relationship. As shown in FIG. 1, the fast TFV primary component T uses a vector Ht obtained by advancing the fast RRO primary component H by φ r = 90 ° and a vector St obtained by delaying the static unbalance S by φ s = 90 ° ( In the expression of uniformity, the delay is usually expressed as a positive value.) This is obtained as a vector sum of these, and is expressed by the following equation (7) when an error is taken into consideration.
Ｔ＝ａ＋ｂ・Ｈｔ＋ｃ・Ｓｔ ……（７）
ここで、ａ、ｂ、ｃはタイヤの種類に応じて定められる係数である。
T = a + b · Ht + c · St (7)
Here, a, b, and c are coefficients determined according to the type of tire.
図１に示すように、タイヤ赤道面上にｘ−ｙの直交座標を定義したとき、静アンバランスＳは、大きさＳｍと基準位置からのタイヤ周方向における位置、即ち位相θｓとを有するベクトルであり、高速ＲＲＯ１次成分Ｈも、大きさＨｍと位相θｒとを有するベクトルである。そのため、上記した変換後のベクトルＨｔ及びＳｔは下記式（８）、（９）により表される。
そして、ベクトルＨｔは、上記ｘ−ｙの直交座標上のｘ成分とｙ成分に分解して（Ｈｔｘ，Ｈｔｙ）で表され、またベクトルＳｔもｘ成分とｙ成分に分解して（Ｓｔｘ，Ｓｔｙ）で表され、更に高速ＴＦＶ１次成分Ｔも、大きさＴｍと位相θｔとを有するベクトルであり、ｘ成分とｙ成分に分解して（Ｔｘ，Ｔｙ）で表される。このように、Ｔ、Ｈｔ及びＳｔはいずれも大きさだけでなく位相成分も含み、上記ｘ成分を実数部、ｙ成分を虚数部とする複素数である。従って、式（７）は、下記式（１０）に書き換えられる。その際、実数部と虚数部はそれぞれ独立なので、式（１１−１）および（１１−２）により別々に重回帰分析し、これらを合成することで式（１０）が得られる。 The vector Ht is expressed by (Ht x , Ht y ) after being decomposed into an x component and a y component on the xy orthogonal coordinates, and the vector St is also decomposed into an x component and a y component (St x , St y ), and the fast TFV first-order component T is also a vector having a magnitude Tm and a phase θ t and is decomposed into an x component and a y component and expressed by (T x , T y ). The As described above, T, Ht, and St are complex numbers that include not only the magnitude but also the phase component, and the x component is a real part and the y component is an imaginary part. Therefore, Expression (7) can be rewritten to the following Expression (10). At that time, since the real part and the imaginary part are independent of each other, the multiple regression analysis is separately performed by Expressions (11-1) and (11-2), and these are combined to obtain Expression (10).
Ｔ＝ａ１＋ｂ１・Ｈｔｘ＋ｃ１・Ｓｔｘ
＋（ａ２＋ｂ２・Ｈｔｙ＋ｃ２・Ｓｔｙ）・ｊ …（１０）
（実数部）Ｔｘ＝ａ１＋ｂ１・Ｈｔｘ＋ｃ１・Ｓｔｘ …（１１−１）
（虚数部）Ｔｙ＝ａ２＋ｂ２・Ｈｔｙ＋ｃ２・Ｓｔｙ …（１１−２）
ここで、ａ１、ａ２、ｂ１、ｂ２、ｃ１、ｃ２はタイヤの品種に応じて定められる係数であり、タイヤの種類毎に重回帰分析して当てはめることができる。なお、ｊ２＝−１である。
T = a 1 + b 1 · Ht x + c 1 · St x
+ (A 2 + b 2 · Ht y + c 2 · St y ) · j (10)
(Real part) T x = a 1 + b 1 · Ht x + c 1 · St x (11-1)
(Imaginary part) T y = a 2 + b 2 · Ht y + c 2 · St y (11-2)
Here, a 1 , a 2 , b 1 , b 2 , c 1 , c 2 are coefficients determined according to the tire type, and can be applied by multiple regression analysis for each tire type. Note that j 2 = −1.
このように、式（８）〜（１０）により高速ＴＦＶ１次成分Ｔを高速ＲＲＯ１次成分Ｈと静アンバランスＳを用いて表すことができるので、高速ＴＦＶ１次成分Ｔが未知のタイヤについて高速ＲＲＯ１次成分Ｈと静アンバランスＳを測定し、その測定結果から式（８）〜（１０）を用いて高速ＴＦＶ１次成分Ｔの大きさを推定することができる。 Thus, since the high-speed TFV primary component T can be expressed by using the high-speed RRO primary component H and the static unbalance S according to the equations (8) to (10), the high-speed RRO1 for tires for which the high-speed TFV primary component T is unknown. The secondary component H and the static unbalance S are measured, and the magnitude of the fast TFV primary component T can be estimated from the measurement results using equations (8) to (10).
なお、より詳細には、高速ＴＦＶ１次成分の大きさＴｍは下記式（１２）により与えられる。
ところで、上記変換角度がφｒ＝９０°およびφｓ＝９０°である場合、図２に示すように、上記ベクトルＨｔ及びＳｔは下記式（１３）、（１４）により表される。 By the way, when the conversion angles are φ r = 90 ° and φ s = 90 °, the vectors Ht and St are expressed by the following equations (13) and (14) as shown in FIG.
Ｈｔ＝Ｈｙ−Ｈｘ・ｊ …（１３）
Ｓｔ＝−Ｓｙ＋Ｓｘ・ｊ …（１４）
ここで、Ｈｘは高速ＲＲＯ１次成分Ｈの実数部、Ｈｙは高速ＲＲＯ１次成分Ｈの虚数部、Ｓｘは静アンバランスＳの実数部、Ｓｙは静アンバランスＳの虚数部である。
Ht = H y −H x · j (13)
St = −S y + S x · j (14)
Here, H x is the real part of the fast RRO primary component H, H y is the imaginary part of the fast RRO primary component H, S x is the real part of the static unbalance S, and S y is the imaginary part of the static unbalance S. .
従って、この場合、式（１０）は下記式（１５）となり、
Ｔ＝ａ１＋ｂ１・Ｈｙ−ｃ１・Ｓｙ
＋（ａ２−ｂ２・Ｈｘ＋ｃ２・Ｓｘ）・ｊ …（１５）
よって、高速ＴＦＶ１次成分Ｔが未知のタイヤについて、高速ＲＲＯ１次成分Ｈと静アンバランスＳを測定し、その測定結果から式（１５）を用いて高速ＴＦＶ１次成分Ｔの大きさＴｍを推定することができる。この大きさＴｍは、より詳細には、下記式（１６）により与えられる
T = a 1 + b 1 · H y −c 1 · S y
+ (A 2 −b 2 · H x + c 2 · S x ) · j (15)
Therefore, the high-speed RRO primary component H and the static unbalance S are measured for tires for which the high-speed TFV primary component T is unknown, and the magnitude Tm of the high-speed TFV primary component T is estimated from the measurement result using Equation (15). be able to. More specifically, this size Tm is given by the following equation (16).
なお、上記変換角度φｒおよびφｓはともに９０°であることが、推定精度の点から好ましい。但し、高速ＲＲＯ１次成分Ｈの変換角度φｒ＝９０°±４０°（５０°〜１３０°）、静アンバランスＳの変換角度φｓ＝９０°±４０°（５０°〜１３０°）の場合でも、ある程度の推定精度を確保することができるので使用可能である。該変換角度φｒおよびφｓのより好ましい範囲はφｒ＝９０°±２５°（６５°〜１１５°）、φｓ＝９０°±２５°（６５°〜１１５°）である。 Note that both the conversion angles φ r and φ s are preferably 90 ° from the viewpoint of estimation accuracy. However, when the conversion angle φ r of the high-speed RRO primary component H is 90 ° ± 40 ° (50 ° to 130 °) and the conversion angle φ s of the static unbalance S is 90 ° ± 40 ° (50 ° to 130 °). However, it can be used because a certain degree of estimation accuracy can be ensured. More preferable ranges of the conversion angles φ r and φ s are φ r = 90 ° ± 25 ° (65 ° to 115 °) and φ s = 90 ° ± 25 ° (65 ° to 115 °).
例えば、後述する実施例１の場合、相関係数は、φｒ，φｓ＝９０°の場合で０．９３６、φｒ，φｓ＝９０°±２５°の場合で０．８９６、φｒ，φｓ＝９０°±３５°の場合で０．７６８、φｒ，φｓ＝９０°±４０°の場合で０．７０５、φｒ，φｓ＝９０°±４５°の場合で０．６４３、φｒ，φｓ＝９０°±６５°の場合で０．４７０であり、φｒ，φｓ＝９０°±４０°でも相関係数０．７以上を確保することができた。 For example, in the case of Example 1 described later, the correlation coefficient, phi r, 0.936 in the case of φ s = 90 °, φ r , φ s = 90 ° in the case of ± 25 ° 0.896, φ r , Φ s = 90 ° ± 35 °, 0.768, φ r , φ s = 90 ° ± 40 °, 0.705, φ r , φ s = 90 ° ± 45 °, 0. In the case of 643, φ r , φ s = 90 ° ± 65 °, it is 0.470, and even when φ r , φ s = 90 ° ± 40 °, a correlation coefficient of 0.7 or more can be secured.
４．高速ＲＲＯ１次成分の推定式
高速ＲＲＯ１次成分は、高速ユニフォミティマシンがなくても計測可能（例えば、タイヤを装着して高速回転させることが可能な装置に設けたレーザー式変位計により計測可）であるが、下記（Ａ）及び（Ｂ）の方法により、低速ＲＲＯ１次成分と静アンバランスより推定可能であり、そのため、通常計測している低速ユニフォミティマシン（低速ＲＲＯ１次成分を計測可）とバランサーのデータより推定することができる。
4). High-speed RRO primary component estimation formula High-speed RRO primary component can be measured without a high-speed uniformity machine (for example, it can be measured with a laser displacement meter mounted on a device that can be rotated at high speed by wearing a tire) However, it can be estimated from the low-speed RRO primary component and the static unbalance by the following methods (A) and (B). Therefore, the low-speed uniformity machine (low-speed RRO primary component can be measured) and the balancer that are normally measured It can be estimated from the data.
（Ａ）タイヤのある部分に質量アンバランスがあると、高速回転時にその部分が遠心力により膨らむことにより、タイヤに新たな径変動が生じる。そのため、高速ＲＲＯ１次成分は、低速ＲＲＯ１次成分に、静アンバランスに起因する新たなＲＲＯ１次成分を合成したものであると考えられる。そのため、高速ＲＲＯ１次成分Ｈは、低速ＲＲＯ１次成分Ｌと、静アンバランスＳを用いて、これらのベクトル和として求められ、誤差成分を考慮すると、下記式（１７）で表される。 (A) If there is a mass imbalance in a portion of the tire, the portion will swell due to centrifugal force during high-speed rotation, resulting in new diameter fluctuations in the tire. Therefore, it is considered that the high-speed RRO primary component is a combination of a new RRO primary component resulting from static unbalance with the low-speed RRO primary component. Therefore, the high-speed RRO primary component H is obtained as a vector sum of these using the low-speed RRO primary component L and the static unbalance S, and is expressed by the following equation (17) in consideration of the error component.
Ｈ＝ｐ＋ｑ・Ｌ＋ｒ・Ｓ …（１７）
ここで、ｐ、ｑ、ｒはタイヤの品種に応じて定められる係数である。
H = p + q · L + r · S (17)
Here, p, q, and r are coefficients determined according to the tire type.
詳細には、これらＨ、Ｌ及びＳはいずれも大きさだけでなく位相成分も含む複素数であるため、式（１７）は、下記式（１８）に書き換えられる。その際、実数部と虚数部はそれぞれ独立なので、式（１９−１）および（１９−２）により別々に重回帰分析し、これらを合成することで式（１８）が得られる。 Specifically, since these H, L, and S are all complex numbers that include not only the magnitude but also the phase component, Expression (17) can be rewritten as Expression (18) below. At that time, since the real part and the imaginary part are independent from each other, the multiple regression analysis is separately performed by Expressions (19-1) and (19-2), and these are combined to obtain Expression (18).
Ｈ＝ｐ１＋ｑ１・Ｌｘ＋ｒ１・Ｓｘ
＋（ｐ２＋ｑ２・Ｌｙ＋ｒ２・Ｓｙ）・ｊ …（１８）
（実数部）Ｈｘ＝ｐ１＋ｑ１・Ｌｘ＋ｒ１・Ｓｘ …（１９−１）
（虚数部）Ｈｙ＝ｐ２＋ｑ２・Ｌｙ＋ｒ２・Ｓｙ …（１９−２）
ここで、Ｌｘは低速ＲＲＯ１次成分Ｌの実数部、Ｌｙは低速ＲＲＯ１次成分Ｌの虚数部、ｐ１、ｑ１、ｒ１、ｐ２、ｑ２、ｒ２はタイヤの品種に応じて定められる係数であり、タイヤの種類毎に重回帰分析して当てはめることができる。なお、ｊ２＝−１である。
H = p 1 + q 1 · L x + r 1 · S x
+ (P 2 + q 2 · L y + r 2 · S y ) · j (18)
(Real part) H x = p 1 + q 1 · L x + r 1 · S x (19-1)
(Imaginary part) H y = p 2 + q 2 · L y + r 2 · S y (19-2)
Here, L x is the real part of the low-speed RRO primary component L, L y is the imaginary part of the low-speed RRO primary component L, and p 1 , q 1 , r 1 , p 2 , q 2 , and r 2 depend on the tire type. This coefficient is determined by multiple regression analysis for each tire type. Note that j 2 = −1.
このようにして式（１８）を求めておけば、高速ＲＲＯ１次成分Ｈが未知の同種のタイヤについて低速ＲＲＯ１次成分Ｌと静アンバランスＳを測定し、その測定結果から式（１８）を用いて高速ＲＲＯ１次成分Ｈを推定することができる。 If formula (18) is obtained in this way, low speed RRO primary component L and static unbalance S are measured for the same type of tire whose unknown high speed RRO primary component H is used, and formula (18) is used from the measurement result. Thus, the fast RRO primary component H can be estimated.
（Ｂ）上記のように、タイヤのある部分に質量アンバランスがあると、高速回転時にその部分が遠心力により膨らむことにより、タイヤに新たな径変動が生じる。そのため、下記式（２０）により、高速ＲＲＯ１次成分Ｈのデータから低速ＲＲＯ１次成分Ｌのデータを位相も考慮して引くことで求めたＲＲＯ１次成分の速度変化Ｄは、静アンバランスに基づくものであって、これが遠心力により大きくなる分に相当する。 (B) As described above, if there is a mass imbalance in a portion of the tire, the portion swells due to centrifugal force during high-speed rotation, resulting in a new diameter variation in the tire. Therefore, the velocity change D of the RRO primary component obtained by subtracting the data of the low-speed RRO primary component L from the data of the high-speed RRO primary component H in consideration of the phase according to the following equation (20) is based on the static unbalance. In this case, this corresponds to an increase due to the centrifugal force.
Ｄ＝Ｈ−Ｌ …（２０）
各速度での、単位静アンバランス当たりのＲＲＯ１次成分の変化量の比は下記式（２１）により求められ、この比を用いて、高速ＲＲＯ１次成分Ｈは、下記式（２２）のように表される。即ち、高速ＲＲＯ１次成分Ｈは、低速ＲＲＯ１次成分Ｌに上記単位静アンバランスＳ当たりのＲＲＯ変化量Ｄを静アンバランスＳの位相にて加えることにより求められる。
D = H−L (20)
The ratio of the change amount of the RRO primary component per unit static unbalance at each speed is obtained by the following equation (21). Using this ratio, the high-speed RRO primary component H is expressed by the following equation (22). expressed. That is, the high-speed RRO primary component H is obtained by adding the RRO change amount D per unit static unbalance S to the low-speed RRO primary component L in the phase of the static unbalance S.
比＝mean（abs（Ｄ））／（mean（abs（Ｓ））・（速度）２ ）…（２１）
（式中、meanは平均、absは絶対値を意味する。）
Ｈ＝Ｌ＋Ｓ・（速度）２・比 …（２２）
このようにして式（２２）を求めておけば、高速ＲＲＯ１次成分Ｈが未知の同種のタイヤについて低速ＲＲＯ１次成分Ｌと静アンバランスＳを測定することにより、その測定結果から式（２２）を用いて高速ＲＲＯ１次成分Ｈを推定することができる。
Ratio = mean (abs (D)) / (mean (abs (S)) · (speed) 2 ) (21)
(In the formula, mean means average and abs means absolute value.)
H = L + S · (speed) 2 · ratio (22)
If the equation (22) is obtained in this way, the low-speed RRO primary component L and the static unbalance S are measured for the same type of tire whose high-speed RRO primary component H is unknown, and the equation (22) is obtained from the measurement result. Can be used to estimate the fast RRO primary component H.
５．タイヤの選別方法１
（i）高速ＴＦＶ１次成分の推定式の導出
タイヤの選別に先立って、高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスとの関係を求める。
5).
(I) Derivation of estimation formula for high-speed TFV primary component Prior to tire selection, the relationship between the high-speed TFV primary component, the high-speed RRO primary component, and the static unbalance is obtained.
詳細には、ある品種のタイヤについて、公知の高速ユニフォミティマシン及びバランサーを用いて、高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスを所定本数（例えば２０〜３０本）測定する。そして、その測定結果を上記式（１０）又は（１５）に当てはめ、重回帰分析して各係数を求める。なお、高速ＴＦＶ及び高速ＲＲＯを測定する際の回転数は、下記（iii）で推定しようとする高速ＴＦＶの回転数と同一速度とする。 Specifically, a predetermined number (for example, 20 to 30) of high-speed TFV primary component, high-speed RRO primary component, and static unbalance are measured for a certain type of tire using a known high-speed uniformity machine and balancer. Then, the measurement result is applied to the above equation (10) or (15), and multiple regression analysis is performed to obtain each coefficient. Note that the rotation speed when measuring the high-speed TFV and the high-speed RRO is the same as the rotation speed of the high-speed TFV to be estimated in the following (iii).
（ii）高速ＲＲＯ１次成分と静アンバランスの測定
高速ＴＦＶ１次成分が未知である上記と同品種のタイヤについて、高速ＲＲＯ１次成分と静アンバランスを測定する。その際、静アンバランスについては、公知のバランサーにより測定することができる。また、高速ＲＲＯ１次成分については、タイヤを高速回転可能な装置に設けたレーザー変位計により測定することができる。このようなタイヤを高速回転可能な装置としては、タイヤ回転軸が固定されている装置であれば使用可能であり、高速ユニフォミティマシンのような力検出部が不要であるため、容易に製作することができる。
(Ii) Measurement of high-speed RRO primary component and static unbalance The high-speed RRO primary component and static unbalance are measured for tires of the same type as the above in which the high-speed TFV primary component is unknown. At that time, the static unbalance can be measured by a known balancer. Moreover, about a high-speed RRO primary component, it can measure with the laser displacement meter provided in the apparatus which can rotate a tire at high speed. As a device capable of rotating such a tire at high speed, it can be used as long as the tire rotation shaft is fixed, and a force detection unit such as a high-speed uniformity machine is unnecessary, so that it can be easily manufactured. Can do.
（iii）高速ＴＦＶ１次成分の推定
上記（ii）の測定結果を上記（i）で求めた推定式に当てはめて、そのタイヤの高速ＴＦＶ１次成分の推定値を算出する。
(Iii) Estimation of high-speed TFV primary component The measurement result of (ii) above is applied to the estimation formula obtained in (i) above, and the estimated value of the high-speed TFV primary component of the tire is calculated.
（iv）タイヤの選別
上記（iii）で算出した高速ＴＦＶ１次成分の推定値と、その品種のタイヤについて予め定められた高速ＴＦＶ１次成分の規格値とを比較し、推定値が規格値以下のタイヤを選別し、規格値を超えるタイヤを取り除く。
(Iv) Tire selection The estimated value of the high-speed TFV primary component calculated in (iii) above is compared with the standard value of the high-speed TFV primary component predetermined for the tire of that type, and the estimated value is less than the standard value. Sort tires and remove tires that exceed standard values.
これにより、高速ＴＦＶを実際に計測することなく、規格値を超えたタイヤの出荷を防止することができる。 Thereby, the shipment of tires exceeding the standard value can be prevented without actually measuring the high-speed TFV.
６．タイヤの選別方法２
（i）高速ＴＦＶ１次成分の推定式の導出
タイヤの選別に先立って、高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と低速ＲＲＯ１次成分と静アンバランスとの関係を求める。
6).
(I) Derivation of estimation formula for high-speed TFV primary component Prior to tire selection, the relationship between the high-speed TFV primary component, the high-speed RRO primary component, the low-speed RRO primary component, and the static unbalance is obtained.
詳細には、ある品種のタイヤについて、公知の高速ユニフォミティマシン、低速ユニフォミティマシン及びバランサーを用いて、高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と低速ＲＲＯ１次成分と静アンバランスを所定本数（例えば２０〜３０本）測定する。そして、その測定結果から上記式（１８）又は（２２）に示す第１の関係を求めるとともに、上記式（１０）又は（１５）に示す第２の関係を求める。この第２の関係を求めるに際しては、第１の関係により推定した高速ＲＲＯ１次成分の推定値と、実際に測定した高速ＴＦＶ１次成分及び静アンバランスの測定値を用いて導出してもよく、あるいはまた、実際に測定した高速ＴＦＶ１次成分、高速ＲＲＯ１次成分及び静アンバランスの測定値を用いて導出してもよい。なお、高速ＴＦＶ及び高速ＲＲＯを測定する際の回転数は、下記（iii）で推定しようとする高速ＴＦＶの回転数と同一速度とし、低速ＲＲＯを測定する際のタイヤ回転数は、下記（ii）で低速ＲＲＯを測定する際と同一速度とする。 Specifically, with respect to a certain type of tire, a known number of high-speed TFV primary components, high-speed RRO primary components, low-speed RRO primary components, and static unbalances using a known high-speed uniformity machine, low-speed uniformity machine and balancer (for example, 20 to 30) Measure. And while calculating | requiring the 1st relationship shown to the said Formula (18) or (22) from the measurement result, the 2nd relationship shown to the said Formula (10) or (15) is calculated | required. In obtaining this second relationship, it may be derived using the estimated value of the fast RRO primary component estimated by the first relationship and the measured value of the fast TFV primary component and static unbalance actually measured, Or you may derive | lead-out using the measured value of the high-speed TFV primary component, high-speed RRO primary component, and static imbalance which were actually measured. The rotational speed when measuring the high speed TFV and the high speed RRO is the same as the rotational speed of the high speed TFV to be estimated in the following (iii), and the tire rotational speed when measuring the low speed RRO is the following (ii) ) To the same speed as when the low speed RRO is measured.
（ii）低速ＲＲＯ１次成分と静アンバランスの測定
高速ＴＦＶ１次成分が未知である上記と同品種のタイヤについて、低速ＲＲＯ１次成分と静アンバランスを測定する。低速ＲＲＯ１次成分については公知の低速ユニフォミティマシンにより、静アンバランスについては公知のバランサーにより測定する。
(Ii) Measurement of low-speed RRO primary component and static unbalance The low-speed RRO primary component and static unbalance are measured for tires of the same type as the above in which the high-speed TFV primary component is unknown. The low-speed RRO primary component is measured by a known low-speed uniformity machine, and the static unbalance is measured by a known balancer.
（iii）高速ＴＦＶ１次成分の推定
上記（ii）の測定結果を上記（i）で求めた第１の関係の推定式に当てはめて、そのタイヤの高速ＲＲＯ１次成分の推定値を算出する。そして、この高速ＲＲＯ１次成分の推定値と静アンバランスの測定値を上記（i）で求めた第２の関係の推定式に当てはめて、そのタイヤの高速ＴＦＶ１次成分の推定値を算出する。
(Iii) Estimation of high-speed TFV primary component The measurement result of (ii) above is applied to the estimation equation of the first relationship obtained in (i) above, and the estimated value of the high-speed RRO primary component of the tire is calculated. Then, the estimated value of the high-speed RRO primary component and the measured value of the static unbalance are applied to the estimation equation of the second relationship obtained in (i) above, and the estimated value of the high-speed TFV primary component of the tire is calculated.
（iv）タイヤの選別
上記（iii）で算出した高速ＴＦＶ１次成分の推定値と、その品種のタイヤについて予め定められた高速ＴＦＶ１次成分の規格値とを比較し、推定値が規格値以下のタイヤを選別し、規格値を超えるタイヤを取り除く。
(Iv) Tire selection The estimated value of the high-speed TFV primary component calculated in (iii) above is compared with the standard value of the high-speed TFV primary component predetermined for the tire of that type, and the estimated value is less than the standard value. Sort tires and remove tires that exceed standard values.
これにより、高速ＴＦＶを実際に計測することなく、通常計測している低速ユニフォミティマシンとバランサーのデータより高速ＴＦＶ１次成分を推定して、規格値を超えたタイヤの出荷を防止することができる。 Thus, without actually measuring the high-speed TFV, it is possible to estimate the high-speed TFV primary component from the data of the low-speed uniformity machine and balancer that are normally measured, and to prevent the shipment of tires exceeding the standard value.
（実施例１）
タイヤサイズ＝２３５／６０Ｒ１６ １００Ｈのタイヤを１８本用い、リムサイズ＝１６×７−ＪＪ、空気圧＝１９６ｋＰａ、荷重＝５，８８４Ｎとして、高速ＴＦＶ１次成分、高速ＲＲＯ１次成分、低速ＲＲＯ１次成分、低速ＲＦＶ１次成分および静アンバランスを測定した。高速ＴＦＶ及び高速ＲＲＯの測定におけるタイヤ回転数は１８．６回／秒（１４０ｋｍ／ｈ）とし、低速ＲＲＯ及び低速ＲＦＶの測定におけるタイヤ回転数は１．０回／秒＝７ｋｍ／ｈ）とした。
(Example 1)
Tire size = 235 / 60R16 Using 18 tires of 100H, rim size = 16 × 7-JJ, air pressure = 196 kPa, load = 5,884N, high-speed TFV primary component, high-speed RRO primary component, low-speed RRO primary component, low-speed RFV1 The next component and static imbalance were measured. The tire rotation speed in the measurement of high-speed TFV and high-speed RRO was 18.6 times / second (140 km / h), and the tire rotation speed in the measurement of low-speed RRO and low-speed RFV was 1.0 rotation / second = 7 km / h). .
図５（ａ）に、低速ＲＲＯ１次成分の大きさと高速ＴＦＶ１次成分の大きさとの関係を示した。両者の相関係数はＲ＝０．４５６であった。また、図５（ｂ）に、低速ＲＦＶ１次成分の大きさと高速ＴＦＶ１次成分の大きさとの関係を示した。両者の相関係数は、Ｒ＝０．４１１であった。 FIG. 5A shows the relationship between the magnitude of the low-speed RRO primary component and the magnitude of the fast TFV primary component. The correlation coefficient between them was R = 0.456. FIG. 5B shows the relationship between the magnitude of the low-speed RFV primary component and the magnitude of the fast TFV primary component. The correlation coefficient between them was R = 0.411.
上記で測定した高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスの測定値を用いて、上記式（１５）に当てはめ、重回帰分析して下記式（１５−１）を得た。 Using the measured values of the high-speed TFV primary component, the high-speed RRO primary component and the static unbalance measured above, the above equation (15) was applied, and multiple regression analysis was performed to obtain the following equation (15-1).
Ｔ＝−2.1＋236542・Ｈｙ−315・Ｓｙ
＋（20.8−244653・Ｈｘ＋121・Ｓｘ）・ｊ …（１５−１）
図６に、式（１５−１）による推定値と実際の測定値との関係を示した。両者の相関係数はＲ＝０．９３６であり、低速ＲＲＯ１次成分の大きさや低速ＲＦＶ１次成分の大きさから高速ＴＦＶ１次成分を推定する場合に比べて、より正確に高速ＴＦＶ１次成分の大きさを推定できることが確認された。
T = −2.1 + 236542 ・ H y −315 ・ S y
+ (20.8−244653 · H x + 121 · S x ) · j (15-1)
In FIG. 6, the relationship between the estimated value by Formula (15-1) and an actual measured value was shown. The correlation coefficient between them is R = 0.936, and the magnitude of the high-speed TFV primary component is more accurately compared to the case where the high-speed TFV primary component is estimated from the magnitude of the low-speed RRO primary component and the magnitude of the low-speed RFV primary component. It was confirmed that the thickness could be estimated.
（実施例２）
上記実施例１で測定した高速ＲＲＯ１次成分と低速ＲＲＯ１次成分と静アンバランスの測定値を用いて、上記式（１８）に当てはめ、重回帰分析して下記式（１８−１）を得た。
(Example 2)
Using the measured values of the high-speed RRO primary component, the low-speed RRO primary component and the static unbalance measured in Example 1, the above equation (18) was applied, and multiple regression analysis was performed to obtain the following equation (18-1). .
Ｈ＝0＋0.953・Ｌｘ＋0.0188・Ｓｘ
＋（0＋0.878・Ｌｙ＋0.0150・Ｓｙ）・ｊ …（１８−１）
図７に、式（１８−１）による推定値と実際の測定値との関係を示した。両者の相関係数はＲ＝０．９６７であった。
H = 0 + 0.953 · L x + 0.0188 · S x
+ (0 + 0.878 · L y + 0.0150 · S y ) · j (18-1)
FIG. 7 shows the relationship between the estimated value based on Equation (18-1) and the actual measured value. The correlation coefficient between them was R = 0.967.
次いで、式（１８−１）により推定した高速ＲＲＯ１次成分の推定値と、上記実施例１で測定したＴＦＶ１次成分及び静アンバランスの測定値を用いて、上記式（１５）に当てはめ、重回帰分析して下記式（１５−２）を得た。 Next, using the estimated value of the high-speed RRO primary component estimated by the equation (18-1), the measured value of the TFV primary component and the static unbalance measured in Example 1, the above equation (15) is applied, Regression analysis was performed to obtain the following formula (15-2).
Ｔ＝6.9＋206926・Ｈｙ−739・Ｓｙ
＋（21.8−232126・Ｈｘ−45・Ｓｘ）・ｊ …（１５−２）
図８に、式（１５−２）による推定値と実際の測定値との関係を示した。両者の相関係数はＲ＝０．８９７であり、実施例１よりも劣るものの、低速ＲＲＯ１次成分の大きさや低速ＲＦＶ１次成分の大きさから高速ＴＦＶ１次成分を推定する場合に比べて、より正確に高速ＴＦＶ１次成分の大きさを推定できることが確認された。
T = 6.9 + 206926 ・ H y -739 ・ S y
+ (21.8-232126 · H x -45 · S x ) · j (15-2)
In FIG. 8, the relationship between the estimated value by Formula (15-2) and an actual measured value was shown. The correlation coefficient between the two is R = 0.897, which is inferior to that of the first embodiment, but is higher than that in the case where the fast TFV primary component is estimated from the magnitude of the slow RRO primary component and the magnitude of the slow RFV primary component. It was confirmed that the magnitude of the fast TFV primary component can be estimated accurately.
（実施例３）
タイヤサイズ＝２１５／７０Ｒ１６ ９９Ｓのタイヤを１２本用い、リムサイズ＝１６×６1/2−ＪＪ、空気圧＝１９６ｋＰａ、荷重＝５，７８６Ｎとして、高速ＴＦＶ１次成分、高速ＲＲＯ１次成分、低速ＲＲＯ１次成分、低速ＲＦＶ１次成分および静アンバランスを測定した。高速ＴＦＶ及び高速ＲＲＯの測定におけるタイヤ回転数は１８．１回／秒（１４０ｋｍ／ｈ）とし、低速ＲＲＯ及び低速ＲＦＶの測定におけるタイヤ回転数は１．０回／秒＝８ｋｍ／ｈ）とした。
(Example 3)
Tire size = 215 / 70R16 Using 99S tires, rim size = 16 × 61 / 2-JJ, air pressure = 196 kPa, load = 5,786 N, high-speed TFV primary component, high-speed RRO primary component, low-speed RRO primary component, Slow RFV primary components and static imbalance were measured. The tire rotation speed in the measurement of high-speed TFV and high-speed RRO was 18.1 times / second (140 km / h), and the tire rotation speed in the measurement of low-speed RRO and low-speed RFV was 1.0 rotation / second = 8 km / h). .
図９（ａ）に、低速ＲＲＯ１次成分の大きさと高速ＴＦＶ１次成分の大きさとの関係を示した。両者の相関係数はＲ＝−０．１２１であった。また、図９（ｂ）に、低速ＲＦＶ１次成分の大きさと高速ＴＦＶ１次成分の大きさとの関係を示した。両者の相関係数は、Ｒ＝０．８２２であった。 FIG. 9A shows the relationship between the magnitude of the low-speed RRO primary component and the magnitude of the fast TFV primary component. The correlation coefficient between them was R = −0.121. FIG. 9B shows the relationship between the magnitude of the low-speed RFV primary component and the magnitude of the fast TFV primary component. The correlation coefficient between them was R = 0.822.
上記で測定した高速ＴＦＶ１次成分と高速ＲＲＯ１次成分と静アンバランスの測定値を用いて、上記式（１５）に当てはめ、重回帰分析して下記式（１５−３）を得た。 Using the measured values of the high-speed TFV primary component, the high-speed RRO primary component and the static unbalance measured above, the above equation (15) was applied, and multiple regression analysis was performed to obtain the following equation (15-3).
Ｔ＝−9.4＋225974・Ｈｙ−3550・Ｓｙ
＋（6.4−197990・Ｈｘ＋2208・Ｓｘ）・ｊ …（１５−３）
図１０に、式（１５−３）による推定値と実際の測定値との関係を示した。両者の相関係数はＲ＝０．９８０であり、低速ＲＲＯ１次成分の大きさや低速ＲＦＶ１次成分の大きさから高速ＴＦＶ１次成分を推定する場合に比べて、より正確に高速ＴＦＶ１次成分の大きさを推定できることが確認された。
T = -9.4 + 225974 ・ H y -3550 ・ S y
+ (6.4−197990 · H x + 2208 · S x ) · j (15-3)
In FIG. 10, the relationship between the estimated value by Formula (15-3) and an actual measured value was shown. The correlation coefficient between the two is R = 0.980, and the magnitude of the fast TFV primary component is more accurately compared to the case where the fast TFV primary component is estimated from the magnitude of the slow RRO primary component and the magnitude of the slow RFV primary component. It was confirmed that the thickness could be estimated.
（実施例４）
上記実施例３で測定した高速ＲＲＯ１次成分と低速ＲＲＯ１次成分と静アンバランスの測定値を用いて、上記式（１８）に当てはめ、重回帰分析して下記式（１８−２）を得た。
Example 4
Using the measured values of the high-speed RRO primary component, the low-speed RRO primary component and the static unbalance measured in Example 3 above, the above equation (18) was applied, and multiple regression analysis was performed to obtain the following equation (18-2). .
Ｈ＝0＋0.958・Ｌｘ＋0.0477・Ｓｘ
＋（0＋0.995・Ｌｙ＋0.0456・Ｓｙ）・ｊ …（１８−２）
図１１に、式（１８−２）による推定値と実際の測定値との関係を示した。両者の相関係数はＲ＝０．９７４であった。
H = 0 + 0.958 · L x + 0.0477 · S x
+ (0 + 0.995 · L y + 0.0456 · S y ) · j (18-2)
In FIG. 11, the relationship between the estimated value by Formula (18-2) and an actual measured value was shown. The correlation coefficient between them was R = 0.974.
次いで、式（１８−２）により推定した高速ＲＲＯ１次成分の推定値と、上記実施例３で測定したＴＦＶ１次成分及び静アンバランスの測定値を用いて、上記式（１５）に当てはめ、重回帰分析して下記式（１５−４）を得た。 Next, using the estimated value of the high-speed RRO primary component estimated by the equation (18-2) and the measured value of the TFV primary component and the static unbalance measured in Example 3, the above equation (15) is applied, Regression analysis was performed to obtain the following formula (15-4).
Ｔ＝−11.3＋224452・Ｈｙ−3429・Ｓｙ
＋（7.7−186436・Ｈｘ＋1140・Ｓｘ）・ｊ …（１５−４）
図１２に、式（１５−４）による推定値と実際の測定値との関係を示した。両者の相関係数はＲ＝０．９３４であり、実施例３よりも劣るものの、低速ＲＲＯ１次成分の大きさや低速ＲＦＶ１次成分の大きさから高速ＴＦＶ１次成分を推定する場合に比べて、より正確に高速ＴＦＶ１次成分の大きさを推定できることが確認された。
T = -11.3 + 2244452 ・ H y -3429 ・ S y
+ (7.7−186436 · H x + 1140 · S x ) · j (15-4)
In FIG. 12, the relationship between the estimated value by Formula (15-4) and an actual measured value was shown. The correlation coefficient between the two is R = 0.934, which is inferior to that of the third embodiment. However, compared with the case where the fast TFV primary component is estimated from the magnitude of the slow RRO primary component and the magnitude of the slow RFV primary component. It was confirmed that the magnitude of the fast TFV primary component can be estimated accurately.
本発明は、高速ユニフォミティマシンによらずに高速ＴＦＶ１次成分の推定を可能にするものであり、製造したタイヤの性能を評価する際に、また、製造したタイヤを選別する際に効果的に利用することができる。 The present invention enables estimation of a high-speed TFV primary component without using a high-speed uniformity machine, and is used effectively when evaluating the performance of manufactured tires and when selecting manufactured tires. can do.
Ｔ……高速ＴＦＶ１次成分
Ｈ……高速ＲＲＯ１次成分
Ｈｔ……高速ＲＲＯ１次成分の位相を進ませたベクトル
Ｓ……静アンバランス
Ｓｔ……静アンバランスの位相を遅らせたベクトル
T: High-speed TFV primary component H: High-speed RRO primary component Ht: Vector with the phase of the high-speed RRO primary component advanced S: Static unbalance St: Vector with the phase of static unbalance delayed
Claims (8)
高速ＴＦＶ１次成分が未知の同種のタイヤについて、高速ＲＲＯ１次成分と静アンバランスを測定し、その測定結果と前記関係から、そのタイヤの高速ＴＦＶ１次成分の推定値を算出することを特徴とするタイヤの高速ユニフォミティ推定方法。 The high-speed TFV primary component, the high-speed RRO primary component, and the static unbalance are measured for a certain type of tire, and the relationship between the high-speed TFV primary component, the high-speed RRO primary component, and the static unbalance is obtained.
For the same type of tire whose unknown high-speed TFV primary component, the high-speed RRO primary component and static unbalance are measured, and the estimated value of the high-speed TFV primary component of the tire is calculated from the measurement result and the relationship. High-speed tire uniformity estimation method.
Ｔ＝ａ１＋ｂ１・Ｈｙ−ｃ１・Ｓｙ＋（ａ２−ｂ２・Ｈｘ＋ｃ２・Ｓｘ）・ｊ
（式中、Ｔは高速ＴＦＶ１次成分、Ｈｘは高速ＲＲＯ１次成分の実数部、Ｈｙは高速ＲＲＯ１次成分の虚数部、Ｓｘは静アンバランスの実数部、Ｓｙは静アンバランスの虚数部、ａ１、ａ２、ｂ１、ｂ２、ｃ１、ｃ２はタイヤの品種に応じて定められる係数であり、ｊ２＝−１である。） The fast uniformity estimation method according to claim 1, wherein the relationship is expressed by the following equation.
T = a 1 + b 1 · H y −c 1 · S y + (a 2 −b 2 · H x + c 2 · S x ) · j
(Where T is the fast TFV primary component, H x is the real part of the fast RRO primary component, H y is the imaginary part of the fast RRO primary component, S x is the real part of the static unbalance, and S y is the static unbalance. (The imaginary part, a 1 , a 2 , b 1 , b 2 , c 1 , c 2 are coefficients determined according to the tire type, and j 2 = −1.)
高速ＴＦＶ１次成分が未知の同種のタイヤについて、低速ＲＲＯ１次成分と静アンバランスを測定して、前記第１の関係から高速ＲＲＯ１次成分の推定値を算出し、この高速ＲＲＯ１次成分の推定値と静アンバランスから前記第２の関係に基づき、そのタイヤの高速ＴＦＶ１次成分の推定値を算出することを特徴とするタイヤの高速ユニフォミティ推定方法。 While measuring the high-speed TFV primary component, the high-speed RRO primary component, the low-speed RRO primary component, and the static unbalance for a certain type of tire, the first relationship between the high-speed RRO primary component, the low-speed RRO primary component, and the static unbalance is obtained. The second relationship among the high-speed TFV primary component, the high-speed RRO primary component, and the static unbalance is obtained,
For a tire of the same type whose high-speed TFV primary component is unknown, the low-speed RRO primary component and the static unbalance are measured, an estimated value of the high-speed RRO primary component is calculated from the first relationship, and the estimated value of the high-speed RRO primary component A high-speed uniformity estimation method for a tire, wherein an estimated value of a high-speed TFV primary component of the tire is calculated based on the second relationship from the static unbalance.
Ｔ＝ａ１＋ｂ１・Ｈｙ−ｃ１・Ｓｙ＋（ａ２−ｂ２・Ｈｘ＋ｃ２・Ｓｘ）・ｊ
（式中、Ｔは高速ＴＦＶ１次成分、Ｈｘは高速ＲＲＯ１次成分の実数部、Ｈｙは高速ＲＲＯ１次成分の虚数部、Ｓｘは静アンバランスの実数部、Ｓｙは静アンバランスの虚数部、ａ１、ａ２、ｂ１、ｂ２、ｃ１、ｃ２はタイヤの品種に応じて定められる係数であり、ｊ２＝−１である。） The fast uniformity estimation method according to claim 5 or 6, wherein the second relation is expressed by the following equation.
T = a 1 + b 1 · H y −c 1 · S y + (a 2 −b 2 · H x + c 2 · S x ) · j
(Where T is the fast TFV primary component, H x is the real part of the fast RRO primary component, H y is the imaginary part of the fast RRO primary component, S x is the real part of the static unbalance, and S y is the static unbalance. (The imaginary part, a 1 , a 2 , b 1 , b 2 , c 1 , c 2 are coefficients determined according to the tire type, and j 2 = −1.)
ことを特徴とするタイヤの選別方法。 A tire is selected by comparing the estimated value of the high-speed TFV primary component calculated by the method according to any one of claims 1 to 7 with a standard value of the high-speed TFV primary component. Method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2003358560A JP4113088B2 (en) | 2003-10-17 | 2003-10-17 | High-speed tire uniformity estimation method and tire selection method |
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Cited By (4)
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| JP2009008506A (en) * | 2007-06-27 | 2009-01-15 | Sumitomo Rubber Ind Ltd | Method for estimating high-speed uniformity of tire |
| JP2011051371A (en) * | 2009-08-31 | 2011-03-17 | Yokohama Rubber Co Ltd:The | Tire noise reducing device, and pneumatic tire having the same |
| US9823153B2 (en) | 2013-06-18 | 2017-11-21 | Compagnie Generale Des Etablissements Michelin | Tire uniformity improvement through identification of process harmonics from static balance measurements |
| JP2020052019A (en) * | 2018-09-28 | 2020-04-02 | 住友ゴム工業株式会社 | Method for estimating high-rate uniformity of tire |
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| JP2009008506A (en) * | 2007-06-27 | 2009-01-15 | Sumitomo Rubber Ind Ltd | Method for estimating high-speed uniformity of tire |
| JP2011051371A (en) * | 2009-08-31 | 2011-03-17 | Yokohama Rubber Co Ltd:The | Tire noise reducing device, and pneumatic tire having the same |
| US9823153B2 (en) | 2013-06-18 | 2017-11-21 | Compagnie Generale Des Etablissements Michelin | Tire uniformity improvement through identification of process harmonics from static balance measurements |
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| JP7077900B2 (en) | 2018-09-28 | 2022-05-31 | 住友ゴム工業株式会社 | How to estimate high-speed uniformity of tires |
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