Prediction of Vertical Spindle Force due to Loaded and Rolling Tire

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㸨1Ph. D. student, Department of mechanical engineering, Doshisha University, Kyoto Telephone: +81-774-65-6488, Fax: +81-774-65-6488, E-mail :etl1303@mail4.doshisha.ac.jp

㸨2Department of mechanical engineering, Doshisha University, Kyoto

ࡣࡌࡵ࡟

஌⏝㌴⏝ࢱ࢖ࣖࡢᡥᖹ໬࠾ࡼࡧࢧࢫ࣌ࣥࢩࣙࣥࡢ㧗

๛ᛶ໬࡟క࠸㸪㌴ᐊෆ㦁㡢࡟࠾࠸࡚ࢱ࢖ࣖ᣺ື⮬యࡀ ධຊ※࡜࡞ࡿ300Hz௨ୗࡢ࣮ࣟࢻࣀ࢖ࢬࡀ㢧ⴭ࡜࡞ࡗ

࡚࠸ࡿ ¹⁾㸬࣮ࣟࢻࣀ࢖ࢬࡣ㊰㠃ࡢพฝ࡟ࡼࡾࢱ࢖ࣖࡀ

᣺ືࡋ㸪ࡑࡢ᣺ືࡀ㌴㍈ࢆ㏻ࡋ࡚㌴ᐊෆ࡬ఏ㐩ࡍࡿ㦁㡢ࡢࡇ࡜࡛࠶ࡿ㸬ࡑࡢࡓࡵ㸪㌴㍈᣺ື࡜㌴ᐊෆ㦁㡢ࡢ 㛵ಀゎ᫂࡟㛵ࡍࡿ◊✲ࡀ⾜ࢃࢀ࡚࠾ࡾ㸪≉࡟ୖୗ㌴㍈

᣺ື㸦௨ୗ㸪㌴㍈᣺ື㸧 ࡟ࡘ࠸࡚ࡣᙳ㡪ࡀ኱ࡁ࠸ࡇ

࡜ࡀሗ࿌ࡉࢀ࡚࠸ࡿ²⁾㸬

㌴యࡢ㒊ศᵓ㐀࡜ࡋ࡚㸪ࢱ࢖ࣖ㌿ື᫬ࡢ㌴㍈᣺ືࢆ

ண ࡍࡿࡇ࡜ࡀ࡛ࡁࢀࡤ㸪ຠ⋡ⓗ࡞࣮ࣟࢻࣀ࢖ࢬࡢప ῶ㸪ࡉࡽ࡟ࡣ㛤Ⓨ᫬㛫ࡢ▷⦰࡟ࡘ࡞ࡀࡿ ³⁾㸬ࡇࡢ࡜ࡁ㸪

㌴㍈᣺ືࡢண ⢭ᗘ࡟㛵ࢃࡿ㔜せ࡞ၥ㢟ࡀ㸪㌿ື᫬ࡢ

ࣔࢹࣝ໬࡜ࢩ࣑࣮ࣗࣞࢩࣙࣥࣔࢹࣝ࡬ࡢධຊ᮲௳࡛࠶

ࡿ㸬ࡑࡢࡓࡵ㸪ࢱ࢖ࣖࡢࣔࢹࣝ໬ࢆྵࡵ㊰㠃ධຊࢆᢕ ᥱࡍࡿࡇ࡜ࡀ㔜せ࡞ၥ㢟ࡢ୍ࡘ࡜࡞ࡗ࡚࠸ࡿ㸬ࡇࢀࡲ

࡛ᵝࠎ࡞ᡭἲࢆ⏝࠸࡚㊰㠃ධຊࡢྠᐃࡀ⾜ࢃࢀ࡚ࡁࡓ ࡀ㸪ࢱ࢖ࣖ᣺ື≉ᛶࡢᙳ㡪ࢆཷࡅࡿࡓࡵ᮲௳㐪࠸࡟ࡼ

ࡾᐇ㦂࣭ゎᯒࡀᚲせ࡜࡞ࡿ㸬ᮏ◊✲ࡣ㌿ື᫬ࡢࢱ࢖ࣖ

᣺ື≉ᛶཬࡧᚤᑠ✺㉳࡟ࡼࡿࢱ࢖ࣖ᣺ືఏ㐩≉ᛶࢆ᫂

ࡽ࠿࡟ࡋࡓୖ࡛㸪1⮬⏤ᗘࢱ࢖ࣖࣔࢹࣝࢆᥦ᱌ࡋ㸪㌴

Prediction of Vertical Spindle Force due to Loaded and Rolling Tire

Masami MATSUBARA^*1, Takayuki KOIZUMI^*2, Nobutaka TSUJIUCHI^*2 (Received April 6, 2013)

It is important to predict the interior noise of a passenger car for evaluation of performance of NVH. There are many sound sources including engine, power train, and tire in the passenger car. In particular, the dynamic force transmission of rolling tires from the road surface to the spindle is a critical factor in interior noise of the passenger car. We focus on structure-borne noise transferred through the spindle. It is necessary for effort of the effective tire/road noise reduction to predict spindle force excited by tire/road contact. The important issues for predicting spindle forces are tire model and how to input on the model because tire vibration characteristic change generated by rolling and contact. In this paper, we suggest the simple prediction of vertical spindle force that affect the interior noise clearly.

First, we measures the spindle force generated by a projection and multiple projections. And we check the linearity of spindle force. It is found that we can predict the spindle force generated by optional projections based on the spindle force excited by a basic projection. Second, based that first mode of tire don’t change generated by rolling, one degree model of a rolling tire is built up. Road force is identified from spindle force using this tire model. Finally, an estimation method of spindle force for any tire-rolling speed and height of cleat is proposed based on the identified road force.

.HUZRUG: tire, vertical spindle force, estimation of road input, road noise

࣮࣮࢟࣡ࢻ: ࢱ࢖ࣖ㸪ୖୗ㌴㍈᣺ື㸪㊰㠃ධຊ᥎ᐃ㸪࣮ࣟࢻࣀ࢖ࢬ

ࢱ࢖ࣖ᥋ᆅ࣭㌿ື᫬࡟࠾ࡅࡿୖୗ㌴㍈᣺ືண

ᯇཎ ┿ᕫ㸪ᑠἨ Ꮥஅ㸪㎷ෆ ఙዲ

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㍈᣺ື࠿ࡽ㊰㠃ධຊࢆྠᐃࡍࡿ㸬ࡑࡢྠᐃ⤖ᯝࢆඖ࡟㸪

⡆᫆࡟௵ព᮲௳ୗࡢ㌴㍈᣺ືࢆண ࡍࡿ᪉ἲࢆᥦ᱌ࡍ

ࡿ㸬

✺㉳஌ࡾ㉺ࡋヨ㦂᪉ἲ ࣮ࣟࢻࣀ࢖ࢬ㊰㠃ࡢᚤᑠ✺㉳ᙧ≧ࣔࢹࣝ໬

ࢩ࣑࣮ࣗࣞࢩࣙࣥ᫬࡟࠾࠸࡚௵ព㊰㠃ࢆ࡝ࡢࡼ࠺࡟

⡆᫆࡟ࣔࢹࣝ໬ࡍࡿ࠿ࡣၥ㢟࡛࠶ࡿ㸬ᒣ⏣ ⁴⁾ࡣ㊰㠃ࡢ พฝࢆ༢୍✺㉳ࡢ㞟ྜయ࡛⾲⌧ࡋ㸪༢୍✺㉳஌ࡾ㉺ࡋ

᫬࡟Ⓨ⏕ࡍࡿ㌴㍈᣺ືࢆ㔜ࡡྜࢃࡏࡿࡇ࡜࡛㸪௵ព㊰

㠃㉮⾜᫬ࡢ㌴㍈᣺ືࢆண ࡍࡿ᪉ἲࢆᥦ᱌ࡋ࡚࠸ࡿ㸬

Fig. 1ࡣࡑࡢᴫせᅗ࡛࠶ࡿ㸬ᮏᡭἲ࡟࠾ࡅࡿ༢୍✺㉳

ᙧ≧ࡣ෇⟄ᙧ≧✺㉳ࢆ᥇⏝ࡋ࡚࠸ࡿࡇ࡜࠿ࡽ㸪ᮏ◊✲

࡟࠾࠸࡚ࡶྠᵝ࡟෇⟄ᙧ≧✺㉳㸦௨ୗ㸪✺㉳㸧ࢆ᥇⏝

ࡍࡿࡶࡢ࡜ࡍࡿ㸬✺㉳ࡣ┤ᚄ 10 mm㸪㧗ࡉ 1.5mm㸪

3.0mm㸪4.5mm㸪6.0mmࡢࡶࡢࢆ౑⏝ࡋࡓ㸬

Fig. 1. Characterization of road.

ヨ㦂ᴫせ

Fig. 2 ࡟ヨ㦂ࢱ࢖ࣖࢆ♧ࡍ㸬ࢱ࢖ࣖࢧ࢖ࢬࡣ

195/65/R15㸪୺⁁ࢆ᭷ࡋࡓࣛࢪ࢔ࣝࢱ࢖ࣖࢆ౑⏝ࡋࡓ㸬

ヨ㦂ᴫ␎ᅗࢆFig. 3࡟♧ࡍ㸬ࢱ࢖ࣖ༢యࢻ࣒ࣛヨ㦂ᶵ ࡢࢻ࣒ࣛ࡟ᑐࡋ࡚ࢱ࢖ࣖࢆᢲࡋ௜ࡅ㸪ࢻ࣒ࣛࢆᅇ㌿ࡉ ࡏࡿࡇ࡜࡛ࢱ࢖ࣖࢆ㐃ࢀᅇࡾࡉࡏࡿ㸬ࡇࡢ࡜ࡁ㸪ࢻࣛ

࣒⾲㠃ୖ࡟ྲྀࡾ௜ࡅࡓ✺㉳࡟ࡼࡾບ㉳ࡉࢀࡓ㌴㍈᣺ື

ࢆィ ࡍࡿ㸬✺㉳᥋ゐ఩⨨㸦௨ୗ㸪ධຊ఩⨨㸧ࡣ Fig.

3ࡢྛࢺࣞࢵࢻࣜࣈ㒊ࡢ୍Ⅼ࡜ࡋ㸪༢✺㉳᫬㸪ከ✺㉳

᫬࡛ヨ㦂ࢆ⾜ࡗࡓ㸬㌴㍈Ⲵ㔜ࡣ4200N㸪ࢱ࢖ࣖෆᅽࡣ 230kPa࡜ࡋࡓ㸬

Fig. 2. Test tire.

Fig. 3. Test setup.

✺㉳஌ࡾ㉺ࡋ᫬ࡢୖୗ㌴㍈᣺ື≉ᛶ ㌿ື㏿ᗘ㐪࠸࡟࠾ࡅࡿ㌴㍈᣺ື≉ᛶ

ධຊ఩⨨ࢆࢭࣥࢱ࣮㒊࡜ࡋ㸪✺㉳஌ࡾ㉺ࡋヨ㦂ࢆᐇ

᪋ࡋࡓ㸬Fig. 4(a)࡟㌿ື㏿ᗘ30km/h᫬ࡢ㌴㍈᣺ືࢆ♧

ࡍ㸬✺㉳㧗ࡉࡣ1.5mm࡜ࡋࡓ㸬Fig. 4(b)࡟㌿ື㏿ᗘ30,

50km/h ᫬ࡢ㌴㍈᣺ືࡢࣃ࣮࣡ࢫ࣌ࢡࢺࣝᐦᗘ㛵ᩘࢆ

♧ࡍ㸬✺㉳஌ࡾ㉺ࡋ≉ᛶࡢ≉ᚩࡣ㸪㊰㠃ධຊࡢ࿘Ἴᩘ

≉ᛶ࡜ࢱ࢖ࣖ᣺ື≉ᛶࡀ᭷ࡍࡿඹ᣺࿘Ἴᩘࡀ⤌ࡳྜࢃ

ࡉࢀࡿ⤖ᯝ㸪1ḟඹ᣺ࡢPeak to Peak್ࡀ㏿ᗘ࡟౫Ꮡࡍ

ࡿࡇ࡜࡛࠶ࡿ㸬ୖୗ㌴㍈᣺ື1ḟඹ᣺࡟ᐤ୚ࡍࡿࢱ࢖

ࣖ᣺ື࣮ࣔࢻࡣᅇ㌿ຠᯝࡢᙳ㡪㸪᥋ᆅ࡟ࡼࡿቃ⏺᮲௳

ࡢኚ໬ࡢᙳ㡪ࢆ↓ど࡛ࡁࡿࡇ࡜࠿ࡽ⁵⁾㸪Fig. 4(b)࡟࠶ࡿ

ࡼ࠺࡟㌿ື㏿ᗘ࡟ࡼࡽࡎ 80Hz௜㏆࡟༟㉺ࡋࡓඹ᣺࿘

Ἴᩘࡀ࠶ࡿࡶࡢ࡜⪃࠼ࡽࢀࡿ㸬

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Fig. 4(a). Vertical spindle force due to cylindrical cleat.

Fig. 4(b). Power spectrum density of spindle force.

✺㉳㧗ࡉ㐪࠸࡟࠾ࡅࡿ㌴㍈᣺ື≉ᛶ

ධຊ఩⨨ࢆࢭࣥࢱ࣮㒊࡜ࡍࡿ✺㉳஌ࡾ㉺ࡋヨ㦂ࢆᐇ

᪋ࡋ㸪㌿ື㏿ᗘ 30km/hࢆ୍ᐃ࡜ࡋ㸪✺㉳㧗ࡉ㐪࠸࡟

ࡼࡿ㌴㍈᣺ືࡢኚ໬ࢆᢕᥱࡋࡓ㸬✺㉳㧗ࡉࢆ1.5mm㸪 3.0mm㸪4.5mm㸪6.0mm࡜ࡋࡓ࡜ࡁࡢ㌴㍈᣺ືࢆ Fig.

5(a)࡟♧ࡍ㸬ྛ㌴㍈᣺ື࠿ࡽ㸪✺㉳㧗ࡉ࡟ࡼࡽࡎᛂ⟅

Ἴᙧࡢഴྥࡣྠࡌ࡛࠶ࡿ㸬ࡲࡓ㸪Fig. 5(b)࡟㌴㍈᣺ື

ࡢ Peak to Peak್ࢆ♧ࡍ㸬✺㉳㧗ࡉ࡟ᛂࡌ࡚ᛂ⟅ࣞ࣋

ࣝࡀ኱ࡁࡃ࡞ࡗ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

ከ✺㉳࡟࠾ࡅࡿ㌴㍈᣺ື

ᖜ᪉ྥ࡟✺㉳㧗ࡉ 1.5mmࡢ✺㉳ࢆ」ᩘಶ஌ࡾ㉺ࡋ ࡓ࡜ࡁࡢ㌴㍈᣺ື࡟ࡘ࠸࡚⪃࠼ࡿ㸬Fig. 6ࡣࢩࣙࣝࢲ

࣮㒊࡜ࢭࣥࢱ࣮㒊ࡢ஧Ⅼධຊ㸪Fig. 7ࡣࢩࣙࣝࢲ࣮㒊㸪

࣑ࢹ࢕࢚࢖ࢺ㒊࡜ࢭࣥࢱ࣮㒊ࡢ୕Ⅼධຊ࡟࠾ࡅࡿ㌴㍈

᣺ື࡛࠶ࡿ㸬ࡲࡓ㸪ྛධຊ఩⨨࡟࠾ࡅࡿ༢✺㉳஌ࡾ㉺

ࡋ᫬ࡢ㌴㍈᣺ືࢆ㔜ࡡྜࢃࡏࡓἼᙧࢆేࡏ࡚ᅗ♧ࡋࡓ㸬

ྠᵝ࡟๓ᚋ᪉ྥ࡟✺㉳ࢆ」ᩘಶ஌ࡾ㉺ࡋࡓ࡜ࡁࡢ㌴

㍈᣺ືࢆ⪃࠼ࡿ Fig. 8࡟㸰ࡘࡢ✺㉳ࢆࢭࣥࢱ࣮㒊๓ᚋ

᪉ྥ࡟㓄⨨ࡋࡓ࡜ࡁࡢ㌴㍈᣺ືࢆ♧ࡍ㸬࡞࠾㸪๓ᚋ᪉

ྥࡢ✺㉳㛫㊥㞳ࢆ 50 mm࡜ࡋࡓ㸬᥋ゐ㛤ጞ᫬㛫ࢆ⪃

៖ࡋ㸪༢✺㉳஌ࡾ㉺ࡋ᫬ࡢ㌴㍈᣺ືࢆ㔜ࡡྜࢃࡏࡓἼ ᙧࢆేࡏ࡚ᅗ♧ࡋࡓ㸬

Fig. 6-8ࡢ⤖ᯝ࠿ࡽ㸪ᖜ᪉ྥ࠾ࡼࡧ๓ᚋ᪉ྥࡢ✺㉳࡟

ࡼࡿ」ᩘධຊ࡟ᑐࡋ࡚㸪ྛධຊ࡟ᑐᛂࡍࡿ༢✺㉳஌ࡾ

㉺ࡋ᫬ࡢ㌴㍈᣺ືࡀࢃ࠿ࢀࡤ⥺ᙧ࿴࡜ࡋ࡚ண ࡛ࡁࡿ

ࡇ࡜ࡀࢃ࠿ࡗࡓ㸬

Fig. 5(a). Vertical spindle force at height of cleat (30km/h).

Fig. 5(b). Vertical spindle force at height of cleat (30km/h).

Fig. 6. Spindle force due to shoulder and center cleats.

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Fig. 7. Spindle force due to shoulder, mediate and center cleats.

Fig. 8. Spindle force due to center cleats.

ୖୗ㌴㍈᣺ື࡟㉳ᅉࡍࡿࢱ࢖ࣖ᣺ື

ࢱ࢖ࣖ㌴㍈㛫ࡢ᣺ືఏ㐩≉ᛶ

᣺ືఏ㐩≉ᛶࢆᢕᥱࡍࡿࡓࡵ㸪᭷㝈せ⣲ࣔࢹࣝࢆ

⏝࠸࡚㠀᥋ᆅ࣭㌿ື᫬࡟࠾ࡅࡿ࿘Ἴᩘᛂ⟅ゎᯒࢆᐇ᪋

ࡋࡓ㸬Fig. 9࡟ゎᯒ⤖ᯝ࡜୺࡞᣺ືᙧ≧ࢆ♧ࡍ㸬ධຊ

ࡣࢭࣥࢱ࣮㒊ἲ⥺᪉ྥ㸪ᛂ⟅ࡣධຊ᪉ྥࡢ㌴㍈᣺ື࡜

ࡋࡓ㸬ࡇࡢ⤖ᯝ࠿ࡽ㸪ୖୗ㌴㍈᣺ື࡟࠾࠸࡚ࡣ㸪࿘᪉

ྥ࣮ࣔࢻࡢ1ḟࡀᨭ㓄ⓗ࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬2ḟ௨ 㝆ࡣ᣺ືᙧ≧ࡀ㍈ᑐ㇟࡛࠶ࡿࡓࡵ㸪㌴㍈᣺ືࡀບ㉳ࡉ

ࢀ࡟ࡃ࠸ࡇ࡜ࡀࢃ࠿ࡿ㸬

Fig. 9. Frequency response function and main vibration shape.

ࢱ࢖ࣖ ⮬⏤ᗘࣔࢹࣝ

᥋ᆅ࣭㌿ື᫬ࡢࢱ࢖ࣖ᣺ື≉ᛶࡣ᥋ᆅ㠃࡟ࡼࡿቃ⏺

᮲௳ࡢᙳ㡪㸪ᅇ㌿ຠᯝࡢᙳ㡪㸪ࢦ࣒ᮦᩱ≉ᛶࡢᙳ㡪ࢆ

ཷࡅࡿࡓࡵ㸪㠀᥋ᆅ࣭㠀㌿ື᫬ࡢࢱ࢖ࣖ᣺ື≉ᛶ࠿ࡽ

ኚ໬ࡍࡿ㸬ࡑࡢࡓࡵ㸪✺㉳஌ࡾ㉺ࡋ᫬ࡢࢱ࢖ࣖࢆ࡝ࡢ

ࡼ࠺࡟ࣔࢹࣝ໬ࡍࡿ࠿ࢆ⪃࠼ࡿᚲせࡀ࠶ࡿ㸬

➹⪅ࡽࡣඛ⾜◊✲࡜ࡋ࡚㸪࿘᪉ྥ1ḟ࣮ࣔࢻ࡟ࡘ࠸

࡚ᐇ㦂࣭ゎᯒࢆ⾜ࡗࡓ ^5-6)㸬ࡑࡢ⤖ᯝࡼࡾ㸪᥋ᆅ࣭㌿

ື᫬࡟࠾ࡅࡿቃ⏺᮲௳ࡢᙳ㡪㸪ᅇ㌿ຠᯝࡢᙳ㡪ࡣ↓ど

࡛ࡁ㸪1ḟ࣮ࣔࢻࡣᐃᅾⓗ࡟ບ㉳ࡉࢀࡿ㸬ࡉࡽ࡟㸪ࢦ

࣒ᮦᩱ≉ᛶࡢᙳ㡪࡟ࡼࡾ㌴㍈Ⲵ㔜࡟౫Ꮡࡋ࡚ࢱ࢖ࣖ๛

ᛶࡀపୗࡍࡿࡇ࡜᫂ࡽ࠿࡟ࡋࡓ㸬ࡲࡓ㸪ࢱ࢖ࣖ๛ᛶࡣ

㏿ᗘ౫Ꮡࡼࡾࡶ㸪㌿ືࡍࡿࡇ࡜࡟ࡼࡾ㢧ⴭ࡟పୗࡍࡿ㸬 ࡑࡢⅭ㸪ࢱ࢖ࣖ࿘᪉ྥ1ḟ࣮ࣔࢻࡣ༢⣧࡞1⮬⏤ᗘ᣺

ື⣔࡛⾲⌧ྍ⬟࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡗࡓ㸬

Fig. 10࡟ࢱ࢖ࣖ᣺ືࣔࢹࣝࢆ♧ࡍ㸬࣍࢖࣮ࣝ㸫㌴㍈

⣔ࡣࢱ࢖ࣖ࡟ᑐࡋ࡚㧗๛ᛶ࡛࠶ࡿ࡜⪃࠼㸪๛య࡜ࡋ࡚

ྲྀࡾᢅ࠸㸪㌴㍈᣺ືࢆ᣺ືບ㉳ຊ࡟ᑐࡍࡿఏ㐩ຊ࡜⪃

࠼ࡿ㸬

m

^{ࡣ㌿ື᫬ࡢ} 1ḟ࣮ࣔࢻ㉁㔞㸪

c

_rot^ࡣ㌿ື᫬

ࡢ1ḟῶᩘᐃᩘ㸪

k

_rot^{ࡣ㌿ື᫬ࡢ}1ḟ࣮ࣔࢻ๛ᛶࢆ♧

ࡍ㸬ࡇࡢ࡜ࡁࡢ㐠ື᪉⛬ᘧ࡜㌴㍈᣺ືࡣḟᘧࡢࡼ࠺࡟

⾲ࡉࢀࡿ㸬

t f z dt k c dz dt

z

md ₂ _rot _rot

2 (1)

z dt k c dz

f_spindle _rot _rot (2)

(5)

ࡇࡢ࡜ࡁ㸪ධຊࢆ࢖ࣥࣃࣝࢫධຊ࡜ࡋࡓሙྜ㸪㌴㍈᣺

ືࡣḟᘧࡢࡼ࠺࡟ᘧኚᙧ࡛ࡁࡿ㸬

^e ^t

^I ^t ^e ^t

t t I

t m e

t k I t m e

t I c t f

d t d n d

t

d t d rot d t d rot

spindle

n n

Z Z Z Z

9 9

Z Z Z Z

9Z 9Z

sin 1 sin

2

sin sin

2 2

' w

w

'

¸¸¹

·

¨¨©

§ ' w

w

(3)

I

ࡣ࢖ࣥࣃࣝࢫࡢ኱ࡁࡉ㸪

' t

^{ࡣ༢୍࢖ࣥࣃࣝࢫධຊ}

ࡢస⏝᫬㛫㸦ཪࡣ㞳ᩓ᫬㛫㸧࡟┦ᙜࡍࡿ㸬ᘧ(3)ࡼࡾ㸪

㌿ື᫬ࡢᅛ᭷ゅ᣺ືᩘZ_n㸪ῶ⾶ẚ] ࡢࡳ࡛㌴㍈ᛂ⟅

ゎᯒࢆ⾜࠺ࡇ࡜ࡀ࡛ࡁࡿ㸬௵ពධຊ࡟ᑐࡋ࡚࢖ࣥࣃࣝ

ࢫධຊ࡛㞳ᩓ໬ࡋ㸪␚ࡳ㎸ࡳ✚ศ࡟ࡼࡾ㌴㍈᣺ືࢆィ

⟬ࡍࡿ㸬ᮏ◊✲࡛ࡣ㸪1ḟඹ᣺ࡀ༟㉺ࡋ࡚ບ㉳ࡉࢀ࡚

࠸ࡿ㌿ື㏿ᗘ30 km/hࡢ㌴㍈᣺ື࡟ᑐࡋ࡚㸪ධຊࢆ࢖

ࣥࣃࣝࢫධຊ࡜௬ᐃࡍࡿࡇ࡜್࡛༙ᖜἲࢆ㐺⏝ࡍࡿࡇ

࡜࡛㌿ື᫬ࡢᅛ᭷᣺ືᩘ࡜ῶ⾶ẚࢆྠᐃࡋࡓ㸬

ୖୗ㌴㍈᣺ືண ㊰㠃ධຊྠᐃ

ᐇ ࡋࡓ༢✺㉳஌ࡾ㉺ࡋ᫬ࡢ㌴㍈᣺ື࠿ࡽ㞳ᩓ໬࢖

ࣥࣃࣝࢫධຊࢆྠᐃࡍࡿ㸬㞳ᩓ໬࢖ࣥࣃࣝࢫධຊࢆḟ ࡢࡼ࠺࡟ᐃ⩏ࡍࡿ㸬

>

n

@

input I I I

I ₁, ₂,, (4)

ホ౯㛵ᩘࢆ㌴㍈᣺ືࡢᐇ㦂್࡜ゎᯒ್ࡢ㸰஌ࣀ࣒ࣝ

࡜ࡋ㸪ホ౯㛵ᩘࡀ᭱ᑠ್࡜࡞ࡿࡼ࠺࡟㞳ᩓ໬࢖ࣥࣃࣝ

ࢫධຊࢆ᭱㐺໬ࡍࡿ㸬ホ౯㛵ᩘࡣḟᘧࡢࡼ࠺࡟࡞ࡿ㸬

^

f_spindle f_estimation I1,I2, ,I_n

`

²

Error (5)

᥎ᐃ࡟ࡣ᭱㐺໬ࢶ࣮࡛ࣝ࠶ࡿMode frontierࡢ↝ࡁ࡞ࡲ

ࡋἲࢆ⏝࠸ࡓ㸬㌿ື㏿ᗘ30 km/h㸪✺㉳㧗ࡉ1.5 mm࡟

࠾ࡅࡿ᭱㐺໬ࡢ⤖ᯝࢆFig. 11࡟♧ࡍ㸬Fig. 11(a)ࡣ᭱㐺

໬ࡋࡓ㞳ᩓ໬࢖ࣥࣃࣝࢫධຊ㸪Fig. 11(b)ࡣࡑࡢ࡜ࡁࡢ

㌴㍈᣺ືࢆ♧ࡍ㸬

㌿ື㏿ᗘ㐪࠸࡟࠾ࡅࡿ㌴㍈᣺ື᥎ᐃ

㌿ື㏿ᗘ㐪࠸࡟࠾ࡅࡿ㌴㍈᣺ືࡢኚ໬ࡣධຊ≉ᛶኚ

໬ࡀ୺ᅉ࡜⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪㌿ື㏿ᗘ࡟౫Ꮡࡏࡎ᥋ ᆅ㠃ෆᅽຊศᕸࡣ୍ᐃ࡛࠶ࡿࡇ࡜࠿ࡽ⁷⁾㸪ධຊศᕸࡢ

Fig. 10. tire model for prediction of vertical spindle force.

Fig. 11(a). Identification of road force due to 1.5 mm cleat at rolling speed 30 km/h.

Fig. 11(b). Comparison of spindle force between estimation and experiment.

኱ࡁࡉࡣኚࢃࡽࡎ㸪ධຊ᫬㛫ࡀኚ໬ࡋࡓࡶࡢ࡜᥎ᐹࡉ

ࢀࡿ㸬ࡑࡇ࡛㸪ࡍ࡛࡟ྠᐃࡋࡓ㞳ᩓ໬࢖ࣥࣃࣝࢫධຊ

ࢆ⏝࠸࡚㸪௵ព㌿ື㏿ᗘ࡟࠾ࡅࡿ㌴㍈᣺ືࢆ᥎ᐃࡍࡿ

᪉ἲࢆ⪃࠼ࡿ㸬

㌿ື㏿ᗘV₁࡟࠾࠸࡚ධຊࢆྠᐃࡍࡿ㸬ྠᐃࡋࡓ㞳 ᩓ໬࢖ࣥࣃࣝࢫධຊࡢ኱ࡁࡉࢆI_input㸪༢୍࢖ࣥࣃࣝ

ࢫධຊࡢస⏝᫬㛫't₁࡜ࡍࡿ㸬ࡇࡢ࡜ࡁ㸪ධຊస⏝᫬

(6)

㛫

t

₁࡜ࡍࡿ㸬ࡇࡢ࡜ࡁ㸪ධຊస⏝᫬㛫

t

₁^{ࡣḟࡢࡼ࠺}

࡟࡞ࡿ㸬

1

1 n t

t ' (6)

ࡇࡇ࡛㸪nࡣ࢖ࣥࣃࣝࢫධຊᩘࢆ⾲ࡍ㸬ࡍ࡞ࢃࡕ㸪

input

I ࡢࢹ࣮ࢱᩘ࡟ᑐᛂࡍࡿ㸬㌿ື㏿ᗘV₂ࡢධຊࡢ࢖

ࣥࣃࣝࢫධຊᩘࡀྠࡌ࡜ࡍࡿ㸬ࡇࡢ࡜ࡁ㸪ධຊస⏝᫬

㛫t₂ࡣḟᘧ࡜࡞ࡿ㸬

2

2 n t

t ' (7)

ධຊస⏝᫬㛫ࡣ✺㉳ࡀ᥋ᆅ㠃ෆ࡟࠶ࡿ᫬㛫࡟┦ᙜࡍ

ࡿࡇ࡜࠿ࡽ㸪ḟᘧࡀᡂࡾ❧ࡘ㸬

2 2 1

1V n tV t

n' ' ₁

2

2 1 t

V

t V '

'

(8)

㌿ື㏿ᗘ30 km/h㸪✺㉳㧗ࡉ1.5 mm㸪ࢭࣥࢱ࣮㒊࡟ධ

ຊࡋࡓሙྜࡢධຊࢆ⏝࠸࡚㸪㌿ື㏿ᗘ 50 km/h࡟࠾ࡅ

ࡿධຊࢆ᥎ᐃࡋࡓ㸬᥎ᐃࡋࡓධຊࢆFig. 12(a)࡟♧ࡍ㸬 ᥎ᐃࡋࡓධຊࢆ⏝࠸࡚ண ࡋࡓ㌴㍈᣺ືࢆFig. 12(b)࡟

♧ࡍ㸬ࡇࡢ⤖ᯝ࠿ࡽ㸪㌴㍈᣺ືࡣⰋዲ࡟୍⮴ࡋ࡚࠸ࡿ

ࡇ࡜࠿ࡽ㸪㌿ື㏿ᗘ㐪࠸࡟࠾ࡅࡿ㌴㍈ࢆண ྍ⬟࡛࠶

ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

✺㉳㧗ࡉ㐪࠸࡟࠾ࡅࡿ㌴㍈᣺ື᥎ᐃ

࣊ࣝࢶࡢ᥋ゐ⌮ㄽ࡟ࡼࡾ㸪ᚤᑠ✺㉳஌ࡾ㉺ࡋ᫬ࡢධ ຊࡢ኱ࡁࡉࡣ㸪ࡑࡢᚤᑠ✺㉳ࡢ௦⾲༙ᚄࡢ 3/2஌࡟ẚ

౛ࡍࡿࡇ࡜ࡀሗ࿌ࡉࢀ࡚࠸ࡿ ⁸⁾㸬ࡑࡇ࡛㸪௦⾲༙ᚄ࡟

✺㉳㧗ࡉࡀẚ౛ࡍࡿࡶࡢ࡜ࡋ࡚㸪✺㉳㧗ࡉ㐪࠸࡟࠾ࡅ

ࡿධຊࡢ኱ࡁࡉࢆ᥎ᐃࡍࡿ㸬

࣊ࣝࢶࡢ᥋ゐ⌮ㄽࡀᡂࡾ❧ࡘ࡜ࡍࡿ࡜㸪✺㉳㧗ࡉ

h1࡟ᑐࡍࡿ࢖ࣥࣃࣝࢫධຊࡢ኱ࡁࡉI_n_,₁࡟㛵ࡋ࡚ḟ ᘧࡀᡂࡾ❧ࡘ㸬

2 3 1 1

, C h

I_n _n (9)

ࡇࡇ࡛㸪ῧ࠼Ꮠࡢnࡣn␒┠ࡢ㞳ᩓ໬࢖ࣥࣃࣝࢫධຊ

ࢆ⾲ࡍ㸬ྠᵝ࡟✺㉳㧗ࡉh₂࡟ᑐࡍࡿ࢖ࣥࣃࣝࢫධຊ ࡢ኱ࡁࡉI_n_,₂࡟㛵ࡋ࡚ࡶḟᘧࡀᡂࡾ❧ࡘ㸬

2 3 2 2

, C h

In n (10)

ࡇࡇ࡛㸪ᘧ(9)㸪(10)ࡼࡾ㸪ḟᘧࡀᡂࡾ❧ࡘ㸬

1 , 2 3

1 2 2 2 ,

3 2 2 3 1 2 ,

1 ,

n n

n n n

n I

h I h h

C h C I I

¸¸¹

·

¨¨©

§ (11)

ᘧ(11)ࡣ࠶ࡿ✺㉳㧗ࡉ࡟ᑐࡍࡿධຊࢆྠᐃࡍࡿࡇ࡜ࡀ

࡛ࡁࢀࡤ㸪௵ពࡢ✺㉳㧗ࡉ࡟ᑐࡍࡿධຊࢆ᥎ᐃࡍࡿࡇ

Fig. 12(a). Estimation of road force due to 1.5 mm cleat at rolling speed 50 km/h.

Fig. 13(a). Estimation of road force due to 3.0 mm cleat at rolling speed 30 km/h.

(7)

࡜ࡀ࡛ࡁࡿࡇ࡜ࢆព࿡ࡍࡿ㸬㌿ື㏿ᗘ 30 km/h㸪✺㉳

㧗ࡉ 1.5 mm㸪ධຊ఩⨨ࢭࣥࢱ࣮㒊ࡢ᮲௳࡟࠾࠸࡚ྠ

ᐃࡋࡓධຊࢆ⏝࠸࡚㸪✺㉳㧗ࡉ 3.0 mm࡟࠾ࡅࡿධຊ

ࢆ᥎ᐃࡋࡓ㸬᥎ᐃࡋࡓධຊࡢ⤖ᯝࢆFig. 13(a)࡟♧ࡍ㸬

ࡲࡓ㸪᥎ᐃࡋࡓධຊࢆ⏝࠸࡚ண ࡋࡓ㌴㍈᣺ືࢆ Fig.

13(b)࡟♧ࡍ㸬ࡇࡢ⤖ᯝ࠿ࡽ㸪㌴㍈᣺ືࡣⰋዲ࡟୍⮴ࡋ

࡚࠸ࡿࡇ࡜࠿ࡽ㸪✺㉳㧗ࡉ㐪࠸࡟࠾ࡅࡿ㌴㍈ࢆண ྍ

⬟࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

ࡲ࡜ࡵ

ᮏ◊✲࡛ࡣ㸪ᚤᑠ✺㉳࡟ࡼࡿࢱ࢖ࣖ᣺ືఏ㐩≉ᛶࢆ

᫂ࡽ࠿࡟ࡋࡓୖ࡛㸪1⮬⏤ᗘࢱ࢖ࣖࣔࢹࣝࢆᥦ᱌ࡋ㸪

⡆᫆࡟௵ព᮲௳ୗࡢ㌴㍈᣺ືࢆண ࡍࡿ᪉ἲࢆᥦ᱌ࡋ ࡓ㸬௨ୗ࡟ᚓࡽࢀࡓ▱ぢࢆ♧ࡍ㸬

1. ከ✺㉳஌ࡾ㉺ࡋ᫬ࡢ㌴㍈᣺ືࡀ༢✺㉳஌ࡾ㉺ࡋ᫬

ࡢ㌴㍈᣺ືࡢ㔜ࡡྜࢃࡏ࡛⾲⌧࡛ࡁࡿࡇ࡜ࢆ♧ࡋ㸪 ᚤᑠ✺㉳࡟ࡼࡾບ㉳ࡉࢀࡿ㌴㍈᣺ືࡣ⥺ᙧᛶࢆ᭷

ࡍࡿࡇ࡜ࢆ᫂ࡽ࠿࡟ࡋࡓ㸬

2. ୖୗ㌴㍈᣺ື1ḟ࡟㉳ᅉࡍࡿࢱ࢖ࣖ࿘᪉ྥ1ḟࣔ

࣮ࢻࡀᅇ㌿ຠᯝ㸪᥋ᆅ࡟ࡼࡿቃ⏺᮲௳ࡢᙳ㡪ࢆཷ

ࡅ࡞࠸ࡇ࡜ࢆᇶ࡟㸪㌿ື᫬ࢱ࢖ࣖ1⮬⏤ᗘࣔࢹࣝ

ࢆᵓ⠏ࡋࡓ㸬ࡇࡢࣔࢹࣝࣃ࣓࣮ࣛࢱ࡛࠶ࡿᅛ᭷᣺

ືᩘཬࡧῶ⾶ẚࡣ㌴㍈᣺ື1ḟඹ᣺ࡼࡾྠᐃ࡛ࡁ

ࡿ㸬

3. ᵓ⠏ࡋࡓ1⮬⏤ᗘࣔࢹࣝ࡜ᐇ ㌴㍈᣺ືࡼࡾධຊ

ࢆྠᐃࡋࡓ㸬ྠᐃࡋࡓධຊࢆࡶ࡜࡟㌿ື㏿ᗘ㸪✺

㉳㧗ࡉ㐪࠸࡟࠾ࡅࡿධຊࢆ᥎ᐃࡋ㸪㌴㍈᣺ືࢆண

ࡋࡓ㸬㌴㍈᣺ືࡢᐇ㦂್࡜ண ್ࢆẚ㍑ࡋ㸪ᮏ ᡭἲࡢጇᙜᛶࢆ♧ࡋࡓ㸬

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࡚ㅰពࢆ⾲ࡍ㸬

ཧ⪃ᩥ⊩

1) ᯇᒸஂ⚈㸪͆ᐃᖖἼ㞳ᩓ໬ࢱ࢖ࣖࣔࢹࣝ࡟ࡼࡿࣟ

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2) ᆏ⏣ဴᚰ㸪᳃ᮧᏹ᫂㸪஭ฟ⚽ᖾ㸪࣮͆ࣟࢻࣀ࢖ࢬ

࡟ཬࡰࡍࢱ࢖ࣖ✵Ὕඹ㬆ࡢᙳ㡪࡟ࡘ࠸࡚͇㸪⮬ື

㌴ᢏ⾡఍Ꮫ⾡ㅮ₇఍๓ๅ㞟㸪No.881㸪45-48㸪 (1988)㸬

3) ᰘ⏣ᓫ㸪ᒣෆ♸ྖ㸪㙊⏣៞ᐉ㸪Ⳣཎಇᙪ㸪ᑠ▼ṇ 㝯㸪ụ⏣ಇஅ㸪࣮͆ࣟࢻࣀ࢖ࢬධຊࡢࣔࢹࣝ໬ᡭ ἲࡢᥦ᱌࡜ண ゎᯒ⢭ᗘࡢ᳨ド͇㸪⮬ື㌴ᢏ⾡఍

Ꮫ⾡ㅮ₇๓ๅ㞟㸪No.81-02㸪1-4㸪(2002)㸬

4) ᒣ⏣ⱥྐ㸪▼ᕝಟ㸪⏕஭ἑ῟἞㸪ᑠᕝᏹ㸪࣮͆ࣟ

ࢻࣀ࢖ࢬண ᡭἲࡢ㛤Ⓨ͇㸪⮬ື㌴ᢏ⾡఍Ꮫ⾡ㅮ

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6) ᑠἨᏕஅ㸪㎷ෆఙዲ㸪ᯇཎ┿ᕫ㸪ᯇᒣᖾྖ㸪┦ᕝ ᑗ㝯㸪኱ᓥ⿱Ꮚ㸪͆ᅇ㌿ຠᯝ࡟╔┠ࡋࡓࢱ࢖ࣖ᣺

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8) 㬗ῲኸ㸪ᑠἨᏕஅ㸪㎷ෆఙዲ㸪ᓥ୍㑻㸪͆㌿ື᫬

ࢱ࢖ࣖ᣺ື࡟㛵ࡍࡿ◊✲͇㸪⮬ື㌴ᢏ⾡఍Ꮫ⾡ㅮ

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