〈再録論文〉二輪車の制駆動中の旋回限界特性についての基礎的考察

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ᩥ ⊩

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Transactions of the JSME (in Japanese)

஧

஧㍯㌴ࡢไ㥑ື୰ࡢ᪕ᅇ㝈⏺≉ᛶ࡟ࡘ࠸࡚ࡢᇶ♏ⓗ⪃ᐹ

㓇஭ ⱥᶞ

*1

Fundamental study of cornering limit characteristics of motorcycles during braking and driving

Hideki SAKAI

*1

*1 _{Kindai Univ. Dept. of Robotics Engineering}

1 Umenobe, Takaya, Higashihiroshima-shi, Hiroshima 739-2116 Japan

Abstract

Sport riding performance on racing circuits and other locations is seen as an important element in the marketability of motorcycles. In sport riding, some riders start a turn while braking or start acceleration (driving) while turning. Furthermore, the braking aspect of sport riding performance is also critical to accident avoidance performance since it is similar to that of the braking during cornering performance. Consequently, in this paper a fundamental study was carried out to determine methods for improving the cornering limit performance during driving and braking. In the case of four-wheeled vehicles, the G-G diagram is used as a method to indicate the cornering limit performance. In the G-G diagram the longitudinal driving and lateral driving of the vehicle are set as the two axes. Therefore, the first part of this paper proposes a G-G diagram for motorcycles theoretically. In the latter part of this paper, this paper discusses the braking force distribution ratio of front wheel that would maximize the maximum lateral driving, the influence of the normal load distribution ratio of front wheel on the limit cornering property and the influence of the height of the center of gravity on it. From these result, this paper proposes methods for improving the cornering limit performance while braking.

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ࢧ࣮࢟ࢵࢺ➼࡟࠾ࡅࡿࢫ࣏࣮ࢶ㉮⾜ᛶ⬟ࡣ㸪஧㍯㌴ࡢၟရᛶࡢ୍ࡘ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡲࡓ㸪ࢫ࣏࣮ࢶ㉮⾜ࡢ ࢥ࣮ࢼ࣮㐍ධ᫬࡟࠾ࡇ࡞ࢃࢀࡿࡇ࡜ࡢ࠶ࡿ᪕ᅇไື(Toyohuku et al.㸪1994)ࡢᛶ⬟ࡣ஦ᨾᅇ㑊ᛶ⬟࡜ࡶඹ㏻ࡍࡿࡓ ࡵ㸪≉࡟㔜せ࡞ᛶ⬟࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡑࡇ࡛ᮏㄽᩥࡣ㸪᪕ᅇไືᛶ⬟ࡢࡉࡽ࡞ࡿྥୖࡢࡓࡵࡢ㌴୧ㅖඖࡸ CBS(Combined Brake System)(すᕝ௚㸪2009)ࡢタィ㸪௚ࡢไᚚࢩࢫࢸ࣒ࡢᨵⰋࡸ๰ฟ㸪ࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡࡢ ᭦࡞ࡿྥୖἲࢆ⪃ᐹࡍࡿ㸬ࡑࡢ᪉ἲࡣ㸪ไື୰ࡢ᪕ᅇ㝈⏺ࡢᇶᮏⓗᛶ㉁ࢆㄪ࡭ࡿࡇ࡜࡛࠶ࡿ㸬ࡲࡎᮏㄽᩥࡢ๓༙ 㒊࡛ࡣ㸪᪕ᅇไືࡔࡅ࡛࡞ࡃ㸪㥑ື᪕ᅇࢆࡶໟྵࡋࡓ᪕ᅇ㝈⏺ᛶ⬟ࡢ⾲♧ἲࢆᥦ᱌ࡋ㸪ᚋ༙㒊࡛ࡣࡇࢀࢆ⏝࠸࡚㸪 ᪕ᅇ㝈⏺ᛶ⬟ࡢྥୖἲࢆ⪃ᐹࡍࡿ㸬࡞࠾ᮏㄽᩥ࡛ࡣ㸪ไ㥑ື୰ࡢ᪕ᅇࡢࡇ࡜ࢆ༢࡟᪕ᅇ࡜࿧ࡪ㸬

ࡲࡎ㸪ᮏㄽᩥ๓༙㒊࡟࠾ࡅࡿ᪕ᅇ㝈⏺ࡢ⾲♧ἲ࡟ࡘ࠸࡚㏙࡭ࡿ㸬ᅄ㍯㌴ࡸ஧㍯㌴ࡢ᪕ᅇ㝈⏺ࡢᛶ⬟⾲♧ἲ࡜ࡋ

࡚G-G ⥺ᅗࡀ⏝࠸ࡽࢀࡿࡇ࡜ࡀ࠶ࡿ(Milliken and Milliken,1995)(㛵᰿,1993)(ရᕝ௚㸪2016)㸬G-G ⥺ᅗ࡜ࡣ㸪㌴୧

ࡢ๓ᚋຍ㏿ᗘ࡜ᶓຍ㏿ᗘࡢ2 ㍈ୖ࡟᪕ᅇ㝈⏺ࢆ⾲ࡋࡓࡶࡢ࡛࠶ࡿ㸬ᅄ㍯㌴ࡢ G-G ⥺ᅗࡢィ⟬ἲࡢ୍ࡘ࡜ࡋ࡚㸪᪕ ᅇ㝈⏺ࡢ㧗ࡉ࡜࡜ࡶ࡟㸪๓ᚋ㍯ࡢ࡝ࡕࡽࡀᦶ᧿㝈⏺࡟㐩ࡋ࡚࠸ࡿ࠿ࡢ᝟ሗࡶ⾲ࡍ G-G ⥺ᅗࡀᥦ᱌ࡉࢀ࡚࠸ࡿ(㓇 ஭㸪2016)㸬ࡑࡢ⌮⏤ࡣ㸪ᅄ㍯㌴࡛ࡣ᪕ᅇ㝈⏺࡟࠾࠸࡚๓㍯ࡀ㝈⏺࡟㐩ࡍࡿ࠿ᚋ㍯ࡀ㝈⏺࡟㐩ࡍࡿ࠿࡟ࡼࡗ࡚㸪ࢻ ࣛ࢖ࣂࡢ᧯సࡸไᚚࢩࢫࢸ࣒ࡢసືࡀ␗࡞ࡿ࠿ࡽ࡛࠶ࡿ㸬ࢻࣛ࢖ࣂࡢ᧯సࡣ㸪๓㍯ࡀᦶ᧿㝈⏺࡟㐩ࡋࡓ᫬ࡣ౛࠼ ࡤ࢔ࢡࢭࣝࢆ⦆ࡵࡿࡢ࡟ᑐࡋ㸪ᚋ㍯ࡀᦶ᧿㝈⏺࡟㐩ࡋࡓ࡜ࡁࡣ࢝࢘ࣥࢱ࣮ࢫࢸ࢔ࢆᙜ࡚ࡿ㸦ࢡ࣒ࣝ㸪2012㸧㸬㌴୧ Ᏻᐃ໬ไᚚࢩࢫࢸ࣒ࡢసືἲࡣ㸪๓㍯ࡀᦶ᧿㝈⏺ࡢ࡜ࡁࡣ୺࡟ᚋෆ㍯ࢆไືࡋ㸪ᚋ㍯ࡀᦶ᧿㝈⏺ࡢ࡜ࡁࡣ୺࡟๓

Received: 7 February 2017; Revised: 4 April 2017; Accepted: 23 May 2017

No.17-00043 [DOI:10.1299/transjsme.17-00043], J-STAGE Advance Publication date : 5 June, 2017 *1_{ṇဨ㸪㏆␥኱ᏛᕤᏛ㒊㸦ࠛ739-2116 ᗈᓥ┴ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶ 1㸧}

E-mail of corresponding author: [email protected]

Keywords : Motorcycle, G-G diagram, Limit cornering, Motor sports, Active safety

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Sakai, Transactions of the JSME (in Japanese), Vol.83, No.854 (2017)

[DOI: 10.1299/transjsme.17-00043] ₂ እ㍯࡟ไືࡍࡿ㸦஭ୖ㸪2000㸧㸬஧㍯㌴ࡢሙྜ࡛ࡶ㸪๓㍯ࢆไືࡋࡓሙྜࡣ࣮ࣟࣝ᪉ྥࡢᏳᐃᛶࡀ㸪ᚋ㍯ࢆไືࡋ ࡓሙྜࡣ࣮ࣚ᪉ྥࡢᏳᐃᛶࡀၥ㢟࡟࡞ࡿ࡜ᛮࢃࢀࡿ㸬ࡑࡇ࡛ᮏㄽᩥࡶ㸪๓ᚋ㍯ࡢ࡝ࡕࡽࡀ㝈⏺࡟㐩ࡋ࡚࠸ࡿ࠿ࡢ ᝟ሗࡶ⾲ࡍG-G ⥺ᅗࢆ⏝࠸ࡿ㸬ࡓࡔࡋ㸪ࡇࡢ G-G ⥺ᅗࢆࡑࡢࡲࡲ஧㍯㌴࡟㐺⏝ࡍࡿࡇ࡜ࡣ࡛ࡁ࡞࠸㸬࡞ࡐ࡞ࡽ㸪 ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡀ㸪஧㍯㌴࡜ᅄ㍯㌴࡜࡛ࡣ␗࡞ࡿ࠿ࡽ࡛࠶ࡿ㸬ࡑࡇ࡛㸪஧㍯㌴ࡢ࣮࣮࣓ࣚࣔࣥࢺ ࡢࡘࡾྜ࠸ࢆ㸪ᅄ㍯㌴ࡢࡑࢀ࡟ኚ᥮ࡍࡿࡇ࡜࡟ࡼࡗ࡚㐺⏝ࡍࡿ㸬 ḟ࡟㸪ᮏㄽᩥᚋ༙㒊࡛ࡣ㸪᪕ᅇ୰ࡢไືຊ㓄ศẚࡸ㔜ᚰ㧗㸪๓㍯Ⲵ㔜㓄ศẚࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪ࢆㄪᰝࡋ㸪 ࡑࡢ⤖ᯝ࡟ᇶ࡙࠸࡚㸪᪕ᅇ㝈⏺ᛶ⬟ࢆࡼࡾྥୖࡉࡏࡿࡓࡵࡢ㌴୧ㅖඖࡸไᚚࢩࢫࢸ࣒࣭ࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡ ࢆ⪃ᐹࡍࡿ㸬 ᅄ㍯㌴ࡢ ** ⥺ᅗ ࡇࡢ❶࡛ࡣ㸪஧㍯㌴ࡢG-G ⥺ᅗࢆ⪃ᐹࡍࡿࡓࡵࡢ‽ഛ࡜ࡋ࡚㸪ᦶ᧿㝈⏺࡟㐩ࡍࡿ㍯ࡶ⾲ࡍᅄ㍯㌴ࡢ G-G ⥺ᅗ(㓇 ஭㸪2016)࡟ࡘ࠸࡚㏙࡭ࡿ㸬 ࣭ ᅄ㍯㌴ࡢࣔࢹࣝ ᅗ1 ࡟ᅄ㍯㌴ࡢࣔࢹࣝࢆ♧ࡍ㸬ࡇࡢࣔࢹࣝ࡟ࡣ௨ୗࡢ௬ᐃࡀタࡅࡽࢀ࡚࠸ࡿ㸦஧㍯㌴࡟࡜ࡗ࡚↓ព࿡࡞௬ᐃࡣ ┬␎ࡍࡿ㸧㸬㸦௬ᐃ1㸧㌴యࡢ࣮ࣟࣝゅࡣ↓どࡍࡿ㸬㸦௬ᐃ2㸧㥑ືຊࡣ↓㝈኱࡜ࡍࡿ㸬㸦௬ᐃ3㸧㥑ື⣔ࡢ័ᛶ࣮࣓ࣔࣥࢺ(ᬒᒣ㸪ᬒᒣ㸪2001)ࡣ↓どࡍࡿ㸬 ࡇࡢࣔࢹࣝࡢ┤஺ᗙᶆ⣔࡜ࡋ࡚㸪ཎⅬo ࢆ㌴୧㔜ᚰ࡟ᅛᐃࡋ㸪x ㍈ࢆỈᖹ㠃ෆࡢ㌴୧๓᪉࡟㸪y ㍈ࢆỈᖹ㠃ෆࡢ ㌴୧ᕥ᪉ྥ࡟㸪z ㍈ࢆ㖄┤ୖ᪉࡟࡜ࡿ㸬ᅇ㌿ࡢ➢ྕࡣ㸪ྛ㍈ࡢṇࡢ᪉ྥ࡟ྑࢿࢪࡢ㐍ࡴᅇ㌿᪉ྥࢆṇ࡜ࡍࡿ㸬ࡑ ࡢࡓࡵ㸪ᕥ᪕ᅇ᫬ࡢ➢ྕࡀṇ࡛࠶ࡿ㸬ࡲࡓ㌴୧㉁㔞ࢆm㸪㔜ᚰ㧗ࢆ h㸪࣍࢖࣮࣮ࣝ࣋ࢫࢆ l㸪๓㍯㹼㔜ᚰ㛫㊥㞳ࢆ lf㸪㔜ᚰ㹼ᚋ㍯㛫㊥㞳ࢆlr㸪๓ᚋຍ㏿ᗘࢆax㸪ᶓຍ㏿ᗘࢆay࡜ࡑࢀࡒࢀグࡍ㸬࡞࠾㸪ᮏㄽᩥࡣỈᖹ㠃ෆࡔࡅࡢ㐠ື ࢆᢅ࠸㸪໙㓄࡟࠾ࡅࡿ㐠ືࡣᢅࢃ࡞࠸㸬

Fig.1 Vehicle model

ᅗ1 ࡢࣔࢹࣝ࡟࠾࠸࡚㸪๓㍯ࡢ๓ᚋຊࢆ Fxf㸪ᚋ㍯ࡢ๓ᚋຊࢆFxr࡜グࡍ࡜㸪x ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣ xr xf x F F ma (1) ࡜࡞ࡿ㸬ḟ࡟๓㍯࡜ᚋ㍯ࡢࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆࡑࢀࡒࢀF’yf㸪F’yr࡜グࡍ࡜㸪y ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣ

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yr yf y F F ma ' ' (2) ࡜࡞ࡿ㸬ࡲࡓ㸪z ㍈ࡲࢃࡾࡢࡘࡾྜ࠸㸪ࡍ࡞ࢃࡕ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡣ yr r yf fF l F l ' ' 0 (3) ࡛࠶ࡿ㸬ୖᘧ࡟࠾ࡅࡿlfࡣ㸪ṇ☜࡟ࡣlf࠿ࡽࢽ࣮࣐ࣗࢳࢵࢡࢺ࣮ࣞࣝࢆῶࡌࡓ㔞࡟ࡍ࡭ࡁ࡛࠶ࡿࡀ㸪ᮏㄽᩥࡢ┠ ⓗࡣ⤯ᑐⓗ࡞ᛶ⬟ண ࡛ࡣ࡞ࡃ㸪௙ᵝ㛫ࡢ┦ᑐẚ㍑࡛࠶ࡿࡢ࡛㸪⡆༢໬ࡢࡓࡵ࡟ࢽ࣮࣐ࣗࢳࢵࢡࢺ࣮ࣞࣝࢆ↓ど ࡋ࡚࠶ࡿ㸬ࡇࢀ࡜ྠᵝ࡟lr࡟࠾࠸࡚ࡶࢽ࣮࣐ࣗࢳࢵࢡࢺ࣮ࣞࣝࢆ↓どࡋ࡚࠶ࡿ㸬 ࡲࡓ㸪ไ㥑ື୰࡟ᘧ(3)ࢆ‶ࡓࡍ᪕ᅇࢆ‽ᐃᖖ෇᪕ᅇ(㓇஭㸪2015)࡜࿧ࡪ㸬ᮏㄽᩥ࡛ࡣ㸪‽ᐃᖖ᪕ᅇ࡟࠾࠸࡚ࡲ ࡎaxࢆ㸪ḟ࡟ayࢆつᐃࡋ㸪ࡑࢀࢆᐇ⌧ࡍࡿ᧯⯦ࢆࢻࣛ࢖ࣂࡀ࠾ࡇ࡞࠺ࡶࡢ࡜ࡍࡿ㸬ࡋࡓࡀࡗ࡚᧯⯦࡟ࡼࡗ࡚ ay ࡀỴᐃࡉࢀࡿࡢ࡛ࡣ࡞ࡃ㸪ax࡜ay࠿ࡽ㏫⟬ࡉࢀࡿ᧯⯦ࡀᐇ⌧ࡉࢀࡿࡶࡢ࡜௬ᐃࡍࡿ㸬 ࡞࠾㸪‽ᐃᖖ෇᪕ᅇ୰ࡢ᭱኱ᶓຍ㏿ᗘ࡜㸪ࡑࡢ࡜ࡁᦶ᧿㝈⏺࡟㐩ࡋࡓ㍯ࢆ⥲⛠ࡋ࡚㸪ᮏㄽᩥ࡛ࡣ᪕ᅇ㝈⏺࡜࿧ ࡪ㸬 ࣭ ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡢู⾲⌧ ᐃᖖ෇᪕ᅇ࡛ࡣ㸪㔜ᚰ఩⨨ࡢᶓຍ㏿ᗘࡶ๓㍯఩⨨ࡢᶓຍ㏿ᗘࡶᚋ㍯఩⨨ࡢᶓຍ㏿ᗘࡶ඲࡚➼ࡋ࠸㸬ࡑࡇ࡛㸪ᮏ ⠇࡛ࡣ㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࢆ㸪๓ᚋ㍯ࡢ఩⨨ࡢᶓຍ㏿ᗘࡀ➼ࡋ࠸ࡇ࡜࡟⨨ࡁ᥮࠼ࡿ㸬ࡲࡎᘧ(3)ࡢ୧ ㎶࡟l/(lflrm)ࢆ஌ࡌࡿ࡜ m l l F m l l F f yr r yf ' ' 0 (4) ࡜࡞ࡿ㸬ࡼࡗ࡚㸪 m l l F m l l F f yr r yf ' ' (5) ࡜࡞ࡿ㸬ࡇࡇ࡛㸪 m l l F a r yf yf ' ' { (6) m l l F a f yr yr ' ' { (7) ࡜グࡍ࡜㸪ᘧ(5)ࡣ yr yf a a' ' (8) ᅄ㍯㌴ࡢ ** ⥺ᅗ ᅄ㍯㌴ࡢࣔࢹࣝ

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© 2017 The Japan Society of Mechanical Engineers [DOI: 10.1299/transjsme.17-00043] ࡜᭩ࡅࡿ㸬ࡋࡓࡀࡗ࡚๓㏙ࡢࡼ࠺࡟a’yf࡜a’yr࡜ࡀ୍⮴ࡍࡿ࡜࣮࣮࣓ࣚࣔࣥࢺࡀࡘࡾྜ࠺㸬ࡑࡇ࡛ᘧ(8)ࢆ㸪࣮ࣚ ࣮࣓ࣔࣥࢺࡢࡘࡾྜ࠸᮲௳࡜ࡋ࡚⏝࠸ࡿ㸬ࡶࡕࢁࢇ㸪a’yf㸪a’yrࡢ༢఩ࡣඹ࡟m/s2㸪ࡍ࡞ࢃࡕຍ㏿ᗘ࡛࠶ࡿ㸬ࡲࡓ㸪 ᐃᖖ෇᪕ᅇ࡟࠾࠸࡚(lr/l)m ࡣ๓㍯ࡀ㈇ᢸࡍࡿ㉁㔞ࢆ㸪(lf/l)m ࡣᚋ㍯ࡀ㈇ᢸࡍࡿ㉁㔞ࢆࡑࢀࡒࢀ⾲ࡍ(㓇஭㸪2013)࠿ ࡽ㸪‽ᐃᖖ෇᪕ᅇ࡟࠾࠸࡚a’yfࡣ๓㍯ࡢࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆ๓㍯఩⨨ࡢᶓຍ㏿ᗘ࡜ࡋ࡚㸪a’yrࡣᚋ㍯ࡢࢥ࣮ࢼ ࣜࣥࢢࣇ࢛࣮ࢫࢆᚋ㍯఩⨨ࡢᶓຍ㏿ᗘ࡜ࡋ࡚㸪ࡑࢀࡒࢀ⾲ࡋࡓࡶࡢ࡛࠶ࡿ㸬 ࣭ ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᫬ࡢᶓຍ㏿ᗘ ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳࡛࠶ࡿᘧ(8)ࡀᡂࡾ❧ࡘ࡜ࡁ㸪ᘧ(2)ࡼࡾ yr yf yr yf y F F ma ma ma ' ' ' ' (9) ࡀᡂࡾ❧ࡘ㸬ࡼࡗ࡚㸪ࡇࡢ࡜ࡁ yr yf y a a a ' ' (10) ࡜࡞ࡿ㸬ࡋࡓࡀࡗ࡚㸪࣮࣮࣓ࣚࣔࣥࢺࡀࡘࡾྜ࠺࡜ࡁ㸪a’yfࡸa’yrࡀayࢆ⾲ࡍ㸬 ௨ୖࡢࡼ࠺࡟㸪a’yf࡜a’yr࡜࠿ࡽ㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸࡜ᶓຍ㏿ᗘࡀศ࠿ࡿ㸬 ࣭ ๓ᚋ㍯ࡢ᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫ ๓㍯ࡢᆶ┤Ⲵ㔜ࢆFzf㸪ᚋ㍯ࡢᆶ┤Ⲵ㔜ࢆFzr㸪๓㍯Ⲵ㔜㓄ศẚࢆdf(=lr/l)㸪ᚋ㍯Ⲵ㔜㓄ศẚࢆ dr(=lf/l)࡜グࡍ࡜㸪 ࠶ࡿ๓ᚋຍ㏿ᗘᗘaxࡀつᐃࡉࢀࡓ࡜ࡁࡢFzf࡜Fzrࡣࡑࢀࡒࢀ x f zf _lma h mg d F (11) x r zr ma l h mg d F (12) ࡜࡞ࡿ㸬࡞࠾g ࡣ㔜ຊຍ㏿ᗘ࡛࠶ࡿ㸬 ḟ࡟඲㍯㥑ື㌴࡟ᑐᛂ࡛ࡁࡿࡼ࠺࡟㸪๓㍯㥑ືຊ㓄ศẚࢆTf㸪ᚋ㍯㥑ືຊ㓄ศẚࢆTr࡜グࡍ࡜㸪㥑ືຊࡢྜィ ࡣmaxࡔ࠿ࡽ x f xf Tma F (13) x r xr Tma F (14) ࡜࡞ࡿ㸬ࡇࡇ࡛Tr=1- Tf࡛࠶ࡿ㸬 ୍᪉㸪๓㍯ไືຊ㓄ศẚࢆBf㸪ᚋ㍯㥑ືຊ㓄ศẚࢆBr࡜グࡍ࡜㸪ไື᫬࡟ࡣ x f xf B ma F (15) 4

(5)

x r xr Bma F (16) ࡜࡞ࡿ㸬ࡇࡇ࡛Br=1-Bf࡛࠶ࡿ㸬 ḟ࡟᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆồࡵࡿ㸬ࡑࡢࡓࡵ࡟ḟࡢ௬ᐃࢆタࡅࡿ㸬㸦௬ᐃ 4㸧ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫ࡜ไ㥑ືຊ࡜ࡢ࣋ࢡࢺࣝ࿴ࡣ୍ᐃ㸪ࡍ࡞ࢃࡕᦶ᧿෇࡟ࡼࡗ࡚⾲ࡉࢀࡿ㸦㛵᰿㸪

㛗Ụ㸪1993㸧㸦Milliken and Milliken㸪1995㸧㸬ࡇࡢ௬ᐃ࠿ࡽ㸪๓㍯ࡢᦶ᧿ಀᩘࢆ μf㸪ᚋ㍯ࡢᦶ᧿ಀᩘࢆμr࡜グࡍ࡜㸪

๓㍯ࡢ᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫF’yfmax࡜ᚋ㍯ࡢ᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫF’yrmaxࡣ㸪ࡑࢀࡒࢀ 2 2 max ( ) 'yf fFzf Fxf F P (17) 2 2 max ( ) 'yr rFzr Fxr F P (18)

࡜࡞ࡿ㸬ḟ࡟㸪Fyfmaxࡀ⏕ࡌ࡚࠸ࡿ࡜ࡁࡢa’yfࢆa’yfmax㸪Fyrmaxࡀ⏕ࡌ࡚࠸ࡿ࡜ࡁࡢa’yrࢆa’yrmax࡜ࡑࢀࡒࢀグࡍ㸬

ࡉࡽ࡟㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࢆ‶ࡓࡍ᭱኱ᶓຍ㏿ᗘࢆaymax࡜グࡍ㸬᭱ᚋ࡟㸪 a’yfmax࡜a’yrmaxࢆ࠶ࡽࡺ

ࡿax࡟࠾࠸࡚ィ⟬ࡋ㸪ᅗ♧ࡍࡿ㸬ࡇࢀࡀ๓㏙ࡢᅄ㍯㌴ࡢG-G ⥺ᅗ࡛࠶ࡿ㸬

a’yfmax࡜a’yrmax࡜ࡢ㛵ಀ࡟ࡼࡗ࡚㸪᪕ᅇ㝈⏺ࡢᛶ㉁ࡣḟࡢࡼ࠺࡟ሙྜศࡅࡉࢀࡿ㸬

i)a’yfmax= a’yrmaxࡢ࡜ࡁaymax= a’yfmax= a’yrmax. ࡇࡢ࡜ࡁ๓㍯࡜ᚋ㍯ࡢ୧᪉ࡀྠ᫬࡟㝈⏺࡟㐩ࡍࡿ㸬ࡇࢀࡣ㸪ᅄ㍯㌴࡛

ࡣDrift ࡜࿧ࡤࢀࡿ㸦Milliken et al.㸪1976㸧㸬ᮏㄽᩥ࡛ࡶࡇࢀࢆ஧㍯㌴࡛ࡶ Drift ࡜࿧ࡪ㸬

ii) a’yfmax> a’yrmaxࡢ࡜ࡁaymax = a’yrmax㸬ࡇࡢ࡜ࡁᚋ㍯ࡔࡅࡀ㝈⏺࡟㐩ࡍࡿ㸬ࡇࢀࡣ㸪ᅄ㍯㌴࡛ࡣSpin ࡜࿧ࡤࢀࡿ

㸦Milliken et al.㸪1976㸧㸬ᮏㄽᩥ࡛ࡣࡇࢀࢆ஧㍯㌴࣭ᅄ㍯㌴࡜ࡶ Rear wheel skid ࡜グࡍ㸬

iii) a’yfmax< a’yrmaxࡢ࡜ࡁaymax = a’yfmax㸬ࡇࡢ࡜ࡁ๓㍯ࡔࡅࡀ㝈⏺࡟㐩ࡍࡿ㸬ࡇࢀࡣ㸪ᅄ㍯㌴࡛ࡣPlow ࡜࿧ࡤࢀࡿ

㸦Milliken et al.㸪1976㸧㸬ᮏㄽᩥ࡛ࡣࡇࢀࢆ஧㍯㌴࣭ᅄ㍯㌴࡜ࡶ Front wheel skid ࡜グࡍ㸬

ᚋ㍯㥑ືࡢ஌⏝㌴ࢆ᝿ᐃࡋࡓㅖඖ࡛ィ⟬ࡋࡓG-G ⥺ᅗࢆᅗ 2(A)࡟♧ࡍ㸬ࡇࡢᅗࡣୖ࡟ฝࡢ᭤⥺ࡔࡅ࡛ᵓᡂࡉࢀ

࡚࠸ࡿ㸬௚ㅖඖ࡜ࡢẚ㍑ࡢࡓࡵ㸪ࡇࡢᅗ࠿ࡽaymaxࢆᢳฟࡋࡓࡶࡢࡀᅗ2(B)࡛࠶ࡿ㸬

(A)Cornering limit of front and rear wheels (B)Maximum lateral acceleration

Fig.2 An example of G-G diagram of four wheeled vehicle㸦μf=μr=1, df=0.5,Bf=0.82,Tf=0, h/l=0.55/2.5(=0.22), g=10[m/s2]㸧㸸In fig.

2(A), the horizontal axis shows longitudinal acceleration ax, while the vertical axis shows maximum front wheel lateral

acceleration ayfand maximum rear wheel lateral acceleration ayr. The smaller of these values is considered the maximum

lateral acceleration aymaxshown in fig. 2(B).

࣭ ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᫬ࡢᶓຍ㏿ᗘ

(6)

Spin 㡿ᇦ࡛ࡣ a’yfmax㸪Plow 㡿ᇦ࡛ࡣ a’yrmax࡛‽ᐃᖖ෇᪕ᅇ࡛ࡁ࡞࠸ࡢ࡛㸪ࡇࢀࡽࡣゝࢃࡤᯫ✵ࡢᶓຍ㏿ᗘ࡛࠶

ࡿ㸬ࡋࡓࡀࡗ࡚㸪ᐇ㌴ヨ㦂ࡸ᧯⯦ධຊ࡟ࡼࡿ‽ᐃᖖ෇᪕ᅇࡢ᫬้Ṕᛂ⟅ィ⟬࡟ࡼࡗ࡚㸪ࡇࢀࡽࢆồࡵࡿࡇ࡜ࡣ࡛

ࡁ࡞࠸㸬ࡑࡇ࡛㸪ᐇ㌴ヨ㦂➼࡟ࡼࡗ࡚ࡇࢀࡽࢆồࡵࡿࡓࡵ࡟ࡣ㸪ḟࡢࡼ࠺࡟ࡍࢀࡤⰋ࠸㸬Plow㸦Spin㸧㡿ᇦࡢ a’yrmax

㸦a’yfmax㸧ࢆồࡵࡿ࡟ࡣ㸪μrӑμf㸦μfӑμr㸧࡟タᐃࡋ࡚㸪๓㍯㸦ᚋ㍯㸧ࡀ㝈⏺࡟㐩ࡍࡿ‽ᐃᖖ෇᪕ᅇࢆ࠾ࡇ࡞࠸㸪

ࡑࡢaymaxࢆa’yfmax㸦a’yrmax㸧࡜ࡍࢀࡤࡼ࠸㸬ࡇࡢࡼ࠺࡟㸪࠶ࡿ㍯ࡢ᭱኱ᶓຍ㏿ᗘࢆィ⟬ࡍࡿ࡜ࡁ௚㍯ࡢ㝈⏺ࢆ↓ど

ࡍࡿࡇ࡜ࡀ㸪ࡇࡢG-G ⥺ᅗࡢィ⟬ᡭἲ࡛࠶ࡿ㸬 ஧㍯㌴ࡢ ** ⥺ᅗ ࡇࡢ❶࡛ࡣ㸪๓❶ࡢG-G ⥺ᅗࢆ஧㍯㌴࡟㐺⏝ࡍࡿ㸬ࡋࡓࡀࡗ࡚ᘬࡁ⥆ࡁ‽ᐃᖖ෇᪕ᅇࢆ௬ᐃࡍࡿ࡜࡜ࡶ࡟㸪ࡑ ࡢᶓຍ㏿ᗘࢆつᐃࡋ㸪ࡑࢀࢆᐇ⌧ࡍࡿࡓࡵࡢ᧯⯦࠾ࡼࡧ࣮ࣟࣝࢆࣛ࢖ࢲࡀ࠾ࡇ࡞࠺ࡶࡢ࡜ࡍࡿ㸬ࡼࡗ࡚᧯⯦ࡸࣟ ࣮ࣝ࡟ᑐࡍࡿᶓຍ㏿ᗘࢆồࡵࡿࡢ࡛ࡣ࡞ࡃ㸪ᶓຍ㏿ᗘ࠿ࡽ㏫⟬ࡉࢀࡿ᧯⯦࡜࣮ࣟࣝࡀᐇ⌧ࡉࢀࡿࡶࡢ࡜௬ᐃࡍࡿ㸬 ࣭ ㌴୧ࣔࢹࣝ ᅗ3 ࡟஧㍯㌴ࡢࣔࢹࣝࢆ♧ࡍ㸬ࡇࡢࣔࢹࣝࡣ㸪ᅗ 1 ࡢࣔࢹࣝ࡟࣮ࣟࣝ⮬⏤ᗘࡔࡅࢆຍ࠼ࡓࡶࡢ࡛࠶ࡾ㸪࣮ࣟࣝ ゅࢆI࡜グࡍ㸬ࡇࡢᗙᶆ⣔ࡣ㸪ᅗ1 ࡢࡶࡢ࡜ྠ୍࡜ࡍࡿࡢ࡛㸪Iࡢṇࡢྥࡁࡣ㸪⫼㠃ど᫬ィᅇࡾ࡛࠶ࡿ㸬ࡇࡢᅗࡢ ࣔࢹࣝࡢグྕࡣ㸪ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆ㝖࠸࡚ᅗ1 ࡢࡶࡢࢆ⏝࠸ࡿ㸬࡞࠾㸪ᮏㄽᩥ࡛ࡣ㸪࢟ࣕࣥࣂࢫࣛࢫࢺ࡜ ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆ⥲⛠ࡋ࡚㸪࢟ࣕࣥࣂࢫࣛࢫࢺ࡜࿧ࡪ㸬࡞࠾ᮏㄽᩥࡣ㸪࢘࢖࣮ࣜ࡞࡝∦㍯ࡢ᥋ᆅⲴ㔜ࡀ 0 ࡢ≧ែࡣᢅࢃ࡞࠸㸬

Fig. 3 Motorcycle’s model: Fxfand Fxryield a moment around z axis when φӆ0.

ࡇࡢࣔࢹࣝࡢx ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣᘧ(1)࡜ඹ㏻࡛࠶ࡿ㸬ࡇࡢࣔࢹࣝ࡟࠾ࡅࡿ๓㍯࡜ᚋ㍯ࡢ࢟ࣕࣥࣂࢫࣛࢫࢺ ࢆࡑࢀࡒࢀFyf㸪Fyr࡜グࡍ࡜㸪y ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣ yr yf y F F ma (19) ࡜࡞ࡿ㸬ḟ࡟㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡣ 6

(7)

x yr r yf fF lF h ma l sinI 0 (20) ࡛࠶ࡿ㸬ୖᘧ࡟࠾ࡅࡿlfࡣ㸪ṇ☜࡟ࡣlf࠿ࡽࢽ࣮࣐ࣗࢳࢵࢡࢺ࣮ࣞࣝࡸ࢟ࣕࣥࣂ࣮࣓ࣔࣥࢺࡢ࢔࣮࣒㛗ࢆῶࡌࡓ ್࡛࠶ࡿࡀ㸪ᮏㄽᩥࡢ┠ⓗࡣ⤯ᑐⓗ࡞ᛶ⬟ண ࡛ࡣ࡞ࡃ㸪௙ᵝ㛫ࡢ┦ᑐẚ㍑࡛࠶ࡿࡢ࡛㸪⡆༢໬ࡢࡓࡵ࡟ Sharp(1971)࡟࡞ࡽࡗ࡚ࡇࢀࡽࢆ↓どࡋ࡚࠶ࡿ㸬ࡲࡓ㸪ୖᘧ࡟࠾ࡅࡿྑ㎶➨୕㡯ࡣ㸪๓ᚋຊ max࡜࣮࣓ࣔࣥࢺ࢔࣮ ࣒㛗hsinI࡜ࡢ✚࡛࠶ࡿ㸬࡞࠾㸪IࡣຊᏛⓗ࣮ࣟࣝゅ(ഌ,1965)࡟୍⮴ࡍࡿࡶࡢ࡜௬ᐃࡋ㸪 g ay I tan (21) ࡜ࡍࡿ㸬ᘧ(21)ྑ㎶ศᏊ࡟㈇ྕࡀ௜ຍࡉࢀࡿ⌮⏤ࡣ㸪ayࡀṇࡢ᪕ᅇ㸦ᕥ᪕ᅇ㸧ࡢ࡜ࡁ࡟㸪Iࡣ㈇㸦⫼㠃ど཯᫬ィᅇ ࡾ㸧ࡔ࠿ࡽ࡛࠶ࡿ㸬࡞࠾ g a g a g a y y y 2 1 1 1 tan sin sin ¸¸ ¹ · ¨¨ © § I (22) ࡛࠶ࡿ㸬ᘧ(20)ࡢྑ㎶➨ 3 㡯ࡢ᭷↓ࡀ㸪஧㍯㌴࡜ᅄ㍯㌴ࡢ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡢ㐪࠸࡛࠶ࡿ㸬 ࣭ ᅄ㍯㌴ࡢ ** ⥺ᅗ࡬ࡢኚ᥮ ࡇࡢ⠇࡛ࡣ㸪ᅗ3 ࡢࣔࢹࣝࢆᅗ 1 ࡢࣔࢹࣝ࡟⨨᥮࠼ࡿ㸬ࡑࡇ࡛㸪ᘧ(19)࡜ᘧ(2)ࡢࡑࢀࡒࢀࡢྑ㎶ࡀ࡝࠺ࡋ➼ࡋ ࠸࡜ࡍࡿ࡜㸪 yr yf yr yf F F F F ' ' (23) ࡞ࡿ㛵ಀࢆᚓࡿ㸬ࡲࡓᘧ(20)࡜ᘧ(3)ࡢࡑࢀࡒࢀࡢྑ㎶࡝࠺ࡋࡀ➼ࡋ࠸࡜ࡍࡿ࡜㸪 yr r yf f x yr r yf fF lF h ma l F l F l sinI ' ' (24) ࡞ࡿ㛵ಀࢆᚓࡿ㸬ᘧ(23)㸪(24)ࢆ F’yf࡜F’yr࡟ࡘ࠸࡚ゎࡃ࡜㸪ࡑࢀࡒࢀ x yf yf ma l h F F' sinI (25) x yr yr _l ma h F F' sinI (26) ࡜࡞ࡿ㸬ࡑࡇ࡛㸪a’yf࡜a’yrࡑࢀࡒࢀࡢ௦ࢃࡾ࡟ ஧㍯㌴ࡢ ** ⥺ᅗ ࣭ ㌴୧ࣔࢹࣝ

(8)

(9)

¸¸ ¸ ¸ ¸ ¸ ¹ · ¨¨ ¨ ¨ ¨ ¨ © § ¸¸ ¹ · ¨¨ © § ¸ ¹ · ¨ © § { x yf yf x f x f f f r yf yf a g a g a l h a B a l h g d d m l l F a max 2 max 2 2 2 max max 1 1 1 ' P (35) ¸¸ ¸ ¸ ¸ ¸ ¹ · ¨¨ ¨ ¨ ¨ ¨ © § ¸¸ ¹ · ¨¨ © § ¸ ¹ · ¨ © § { x yr yr x r x r r r f yr yr a g a g a l h a B a l h g d d m l l F a max 2 max 2 2 2 max max 1 1 ) ( 1 ' P (36) ࡇࡇ࡛㸪࠶ࡿ㍯ࡢ᭱኱ᶓຍ㏿ᗘࢆィ⟬ࡍࡿ࡜ࡁ௚㍯ࡢ㝈⏺ࢆ↓どࡍࡿࡓࡵ㸪ᘧ(35)㸪(36)୰ࡢIࡣࡑࢀࡒࢀࡢ㌴㍯ ࡢ᭱኱࢟ࣕࣥࣂࢫࣛࢫࢺ࡟ᛂࡌࡓI࡜ࡋ㸪௚㍯ࡢࡑࢀࡣ⪃៖ࡋ࡞࠸㸬ࡲࡓ㸪sinIࡢኚᙧ࡟㝿ࡋ࡚ᘧ(22)ࡢ㛵ಀࢆ⏝ ࠸ࡓ㸬࡞࠾㸪㥑ືഃ࡛ࡣ㸪BfࡸBrࡢ௦ࢃࡾ࡟TfࡸTrࢆࡑࢀࡒࢀ௦ධࡍࡿࡇ࡜࡜ࡍࡿ㸬 ࣭ ** ⥺ᅗࡢィ⟬౛

ᘧ(35)ࢆ ayfmax࡟ࡘ࠸࡚ゎࡃࡇ࡜࡟ࡼࡗ࡚ayfmaxࡀỴᐃࡉࢀ㸪ᘧ(36)ࢆ ayrmax࡟ࡘ࠸࡚ゎࡃࡇ࡜࡟ࡼࡗ࡚ayrmaxࡀỴ

ᐃࡉࢀࡿ㸬ࡇࡢィ⟬ࢆ࠶ࡽࡺࡿax࡟ࡘ࠸࡚࠾ࡇ࡞࠺ࡇ࡜࡟ࡼࡗ࡚㸪ax࡟ᑐࡍࡿayfmaxࡸayrmaxࢆᅗ♧ࡍࡿࡇ࡜ࡀ࡛ ࡁࡿ㸬ࡇࢀࡀᮏㄽᩥࡢᥦ᱌ࡍࡿ஧㍯㌴ࡢG-G ⥺ᅗ࡛࠶ࡿ㸬 ࡑࡢィ⟬౛ࢆᅗ4(A)࡟♧ࡍ㸬ࡇࡢᅗ࡜ᅗ 2 ࡜ࡢ┦㐪Ⅼࡢ୍ࡘࡣ㸪඲㥑ື㡿ᇦࡀ๓㍯ࡔࡅ࡛Ỵᐃࡉࢀࡓࡇ࡜࡛࠶ ࡿ㸬ࡶ࠺୍ࡘࡢ┦㐪Ⅼࡣ㸪ไືഃࡸ㥑ືഃ࡟ୗ࡟ฝࡢ༊㛫ࡀ࠶ࡿࡇ࡜࡛࠶ࡿ㸬ࡑࡢࡓࡵax=0 ࡢ௜㏆ࡢ aymaxࡢᙧ ≧ࡣ㸪ᅗ4(B)࡟♧ࡉࢀࡿࡼ࠺࡟㸪ᅄ㍯㌴ࡼࡾࡶ஧㍯㌴ࡢ࡯࠺ࡀࡼࡾᑤࡀࡿࡶࡢ࡜ᛮࢃࢀࡿ㸬ࡇࢀࡀࢫ࣏࣮ࢶ㉮⾜ ࡢ᭱㏿ࣛ࢖ࣥྲྀࡾ࡟ཬࡰࡍᙳ㡪ࡣḟࡢࡼ࠺࡟࡞ࡿ㸬ࡍ࡞ࢃࡕ㸪ᅄ㍯㌴ࡢሙྜ㸪ࢥ࣮ࢼ࣮ࣜࣥࢢࡢᡭ㡰ࡣࣇࣝࣈࣞ ࣮࢟ࣥࢢЍ᪕ᅇไືЍ᭱኱ᶓຍ㏿ᗘ᪕ᅇ㸦ax=0㸧Ѝ᪕ᅇ⦆ຍ㏿Ѝ᪕ᅇࣇࣝຍ㏿࡜ᣦ᦬ࡉࢀ࡚࠸ࡿ㸦ࢡ࣒ࣝ㸪2012㸧 ࡀ㸪஧㍯㌴ࡢሙྜࡣ㸪ᅄ㍯㌴ࡼࡾࡶࡼࡾᑤࡗ࡚࠸ࡿࡓࡵ࡟㸪᪕ᅇไືࡸ᪕ᅇ⦆ຍ㏿ࡢ༊㛫ࡀࡼࡾ▷ࡃ࡞ࡾࡀࡕ࡛ ࠶ࡿ࡜ᛮࢃࢀࡿ㸬┤ほⓗ࡟ゝ࠼ࡤ㸪஧㍯㌴ࡢ㉮⾜ࣛ࢖ࣥࡣU Ꮠࡂࡳ㸪ᅄ㍯㌴ࡢࣛ࢖ࣥྲྀࡾࡣ V Ꮠࡂࡳ࡛࠶ࡿ࡜ᛮ ࢃࢀࡿ㸬࡞࠾㸪ᅗ4 ࡢィ⟬ㅖඖࡣ⮬ື㌴ᢏ⾡ࣁࣥࢻࣈࢵࢡ(⮬ື㌴ᢏ⾡ࣁࣥࢻࣈࢵࢡ⦅㞟ጤဨ఍⦅㸪2011)࡟グ㍕ ࡉࢀ࡚࠸ࡿᩘ್౛ࢆ୸ࡵ࡚⏝࠸ࡓ㸬

(A)Cornering limit of front and rear wheels (B) Comparison with fig.2 (B)

(10)

[DOI: 10.1299/transjsme.17-00043] ₁₀ ⪃ ᐹ ࣭ ไ㥑ືຊ࡟ࡼࡿ࣮࣮࣓ࣚࣔࣥࢺࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪 ᮏ⠇࡛ࡣ㸪ไ㥑ືຊ࡟ࡼࡿ࣮࣮࣓ࣚࣔࣥࢺࡢᙳ㡪ࢆ⪃ᐹࡍࡿ㸬ᘧ(35)㸪(36)࡟࠾࠸࡚ sinI=0 ࡜ࡋ࡚㸪ᅗ 4 ࡢㅖ ඖࢆ⏝࠸࡚ィ⟬ࡋࡓG-G ⥺ᅗࢆᅗ 5(A)࡟♧ࡍ㸬ࡇࡢሙྜ࡟࠾࠸࡚ࡶ㸪ᅄ㍯㌴࡜␗࡞ࡾ㸪㥑ືഃࡢ඲㡿ᇦࡣ๓㍯ࡔ ࡅ࡛Ỵᐃࡉࢀࡿ㸬ࡋࡓࡀࡗ࡚㸪ࡇࢀࡣ㸪஧㍯㌴࡜ᅄ㍯㌴࡜ࡢィ⟬ㅖඖࡢ㐪࠸࡟㉳ᅉࡍࡿ㸬ࡲࡓᅗ4 ࡜ࡢẚ㍑࠿ࡽ㸪 ஧㍯㌴ࡢῶ㏿ഃ࡟ୗ࡟ฝࡢ㒊ศࡀ࠶ࡿࡇ࡜ࡣ㸪ࡇࡢ࣮࣮࣓ࣚࣔࣥࢺ࡟㉳ᅉࡍࡿ㸬ࡋࡓࡀࡗ࡚㸪ࡇࡢ࣮࣮࣓ࣚࣔࣥ ࢺࡢᙳ㡪ࡣ᭷ព࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ḟ࡟ᅗ5(A)࡜ᅗ 4(A)࡜ࡢ᭱኱ᶓຍ㏿ᗘࡢẚ㍑ࢆᅗ 5(B)࡟♧ࡍ㸬ᅗ 5(B)࠿ࡽ㸪 ࡇࡢ࣮࣮࣓ࣚࣔࣥࢺ࡟ࡼࡗ࡚᭱኱ᶓຍ㏿ᗘࡣไືഃ࡛ࡶ㥑ືഃ࡛ࡶῶᑡࡍࡿ㸬 ax[m/s2]

(A)Cornering limit of front and rear wheels (φ=0) (B) Comparison with fig.2

Fig.5 The influence of the yaw moment by braking/driving force on the limit cornering property㸦μf=μr=1, df=0.4, Bf=0.4, Tf=0,

h/l=0.6/1.35(=0.444), g=10[m/s2_{]㸧:These figures was calculated under the assumption that roll angle φ equals zero in} eq.(35) and (36). Figure 5(B) implies that the yaw moment decreases maximum lateral acceleration in braking and increases it in driving.

࣭ ᪕ᅇ㝈⏺ࢆ᭱኱໬ࡍࡿࡓࡵࡢ๓㍯ไືຊ㓄ศẚ

ᮏ⠇࡛ࡣ㸪᭱኱ᶓຍ㏿ᗘaymaxࢆ᭱኱໬ࡍࡿࡓࡵࡢBfࢆ⪃ᐹࡍࡿ㸬aymaxࡣ㸪ayfmax࡜ayrmaxࡢ࠺ࡕࡢᑠࡉ࠸࡯࠺࡛

Ỵࡲࡿ࠿ࡽ㸪୧⪅ࡢᕪศࡔࡅ౑ࢃࢀ࡞࠸࢟ࣕࣥࣂࢫࣛࢫࢺࡀ࠶ࡿ㸬ࡇࡢ࢟ࣕࣥࣂࢫࣛࢫࢺࡀᑠࡉ࠸࡯࡝aymaxࡀ኱

ࡁ࠸࠿ࡽ㸪(ayfmax- ayrmax) 2ࢆ᭱ᑠ໬ࡍࡿBfࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡗ࡚㸪aymaxࢆ᭱኱໬࡛ࡁࡿ㸬ࡓࡔࡋ0ӌBfӌ1 ࡜ࡍࡿ

㸦Bf>1 ࡢሙྜࡣᚋ㍯ࡀ㸪Bf <0 ࡢሙྜࡣ๓㍯ࡀ㸪ไື୰࡟ࡶ࠿࠿ࢃࡽࡎ㥑ືࡋ࡚ࡋࡲ࠺ࡓࡵ㸪aymaxࢆ᭱኱໬࡛ࡁ࡞

࠸㸧㸬

ࡇࡢBfࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡗ࡚㸪ᅗ4 ࡢィ⟬ㅖඖ࡟࠾ࡅࡿ aymaxࢆ᭱኱໬ࡋࡓሙྜࡢG-G ⥺ᅗࡢィ⟬౛ࢆᅗ 6(A)

࡟㸪ࡑࡢ࡜ࡁࡢBfࢆᅗ6(B)࡟♧ࡍ㸬ᅗ 6(A)࡟ࡣ㸪aymax =ayfmax = ayrmaxࡢ㡿ᇦࡀ࠶ࡿࡢ࡛㸪aymaxࡢ᭱኱໬ࡀᐇ⌧ࡉ

ࢀ࡚࠸ࡿࡇ࡜ࡀ☜ㄆ࡛ࡁࡿ㸬ᅗ6(A)ࡢ᭱኱ᶓຍ㏿ᗘࢆᅗ 4(A)ࡢࡑࢀ࡜ẚ㍑ࡋࡓ⤖ᯝࢆᅗ 6(C)࡟♧ࡋࡓ㸬 ⌮ㄽୖࡣ㸪ᅗ6(B)ࡢ Bfࢆᐇ⌧ࡍࡿࡼ࠺࡟ࣛ࢖ࢲࡀไືࡋࡓࡾ㸪ไᚚࢩࢫࢸ࣒ࢆᵓ⠏ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪ไືഃ ࡢ᪕ᅇ㝈⏺ࢆྥୖ࡛ࡁࡿࡣࡎ࡛࠶ࡿ㸬୍᪉㸪⌧ᐇ࡟ࡣ⇍⦎ࣛ࢖ࢲࡣ㸪࡯ࡰᚋ㍯ࡔࡅࣟࢵࢡ࡛᪕ᅇไືࡋࡓ(Toyohuku et al.㸪1994)࡜ሗ࿌ࡉࢀ࡚࠸ࡿ㸬ࡇࡢ⌮⏤ࡣ㸪ࣂࣥࢡ᫬ࡢ๓㍯ࡢไືຊ࡟㉳ᅉࡋࡓ᧯⯦㍈ࡲࢃࡾࡢ࣮࣓ࣔࣥࢺ࡟ࡼ ࡿ⯦ゅኚ໬ࢆ㑊ࡅࡿࡓࡵ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡋࡓࡀࡗ࡚㸪ไືഃࡢ᪕ᅇ㝈⏺ࡢࡉࡽ࡞ࡿྥୖἲ࡜ࡋ࡚㸪ࣂࣥࢡ᫬ ࡟๓㍯࡟ไືຊࢆ୚࠼࡚ࡶ㸪᧯⯦㍈ࡲࢃࡾ࡟࣮࣓ࣔࣥࢺࡀ⏕ࡌ࡞࠸ࡼ࠺࡞ᶵᵓࡸ㸪ࡇࡢ࣮࣓ࣔࣥࢺࡀ⏕ࡌ࡚ࡶ㸪 ࡑࢀࢆ࢟ࣕࣥࢭ࣭ࣝపῶࡍࡿࡼ࠺࡞㸦ไᚚ㸧ᶵᵓࡸࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡࡀ⪃࠼ࡽࢀࡿ㸬ࣂࣥࢡ᫬࡟๓㍯࡟ไ ືຊࢆ୚࠼࡚ࡶ᧯⯦㍈ࡲࢃࡾ࡟࣮࣓ࣔࣥࢺࡀ⏕ࡌ࡞࠸ࡼ࠺࡞ᶵᵓࡢ୍౛࡜ࡋ࡚ࡣ㸪Piaggio MP3 ࡢࡼ࠺࡞๓ࢲࣈࣝ ࢱ࢖ࣖࡢ㌴୧࡟࠾࠸࡚㸪ไືຊ࣋ࢡࢺࣝ࡜஺ࢃࡿ௬᝿࢟ࣥࢢࣆࣥ㍈ࢆࡶࡘ᧯⯦⣔ᶵᵓࡀ⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪ࡇࡢ ࣮࣓ࣔࣥࢺࢆ࢟ࣕࣥࢭࣝࡍࡿᶵᵓࡢ୍౛࡜ࡋ࡚ࡣ㸪ࣃ࣮࣡ࢫࢸ࢔ࣜࣥࢢ࡟ࡼࡿ࢔ࢡࢸ࢕ࣈไᚚࡀ⪃࠼ࡽࢀࡿ㸬ࡉ ࡽ࡟㸪ࡇࡢ࣮࣓ࣔࣥࢺࢆపῶࡍࡿᶵᵓࡢ୍౛࡜ࡋ࡚ࡣ㸪ࢫࢸ࢔ࣜࣥࢢࢲࣥࣃࡢ࢔ࢡࢸ࢕ࣈไᚚࡀ⪃࠼ࡽࢀࡿ㸬ࡇ

(11)

ࢀࡽ࡜⤌ྜࡏࡿ᪕ᅇ୰ࡢCBS ไᚚ࡟࠾࠸࡚ࡣ㸪ᅗ 6(B)ࡢ Bf࡟タᐃࡋ࡚࠾ࡃࡇ࡜࡛㸪᪕ᅇ୰࡟ABS ไᚚࡀసືࡍ

ࡿሙྜࡢࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻ㒊࡜ࡋ࡚స⏝ࡋ㸪ABS ไᚚࡢᛂ⟅ࡀࡼࡾ㏿ࡃ࡞ࡿࡇ࡜ࡀᮇᚅࡉࢀࡿ㸬

(A) G-G diagram (Maximized aymax by Bf) (B) Bfto maximize aymax (C) Comparison with fig.4

Fig.6 The influence of front braking force distribution ratio on the limit cornering property㸦μf=μr=1, df=0.4, Tf=0, h/l=0.6/1.35

(=0.444), g=10[m/s2_]㸧:B

f shown in fig. 6 (B) was chosen to maximize aymax at each ax. Figure 6(c) shows that the maximum

lateral acceleration using this Bf is larger than that in case of Bf =0.4.

࣭ ๓㍯Ⲵ㔜㓄ศẚࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪

๓㍯Ⲵ㔜㓄ศẚdfࡢᙳ㡪ࢆ⪃ᐹࡍࡿࡓࡵ࡟㸪dfࢆ0.4 ࠿ࡽ 0.3 ࡟ኚ᭦ࡋࡓ࠺࠼࡛㸪 Bf࡟ࡼࡗ࡚aymaxࢆ᭱኱໬ࡋ

ࡓሙྜࡢG-G ⥺ᅗࡢィ⟬౛ࢆᅗ 7(A)࡟㸪ࡑࡢ Bfࢆᅗ7(B)࡟♧ࡍ㸬ᅗ 7(A)ࡢ᭱኱ᶓຍ㏿ᗘࢆᅗ 6(A)ࡢࡑࢀ࡜ẚ㍑

ࡋࡓࡶࡢࡀᅗ7(C)࡛࠶ࡿ㸬ᅗ 7(C)࡟♧ࡉࢀࡿࡼ࠺࡟㸪dfࢆ0.4 ࠿ࡽ 0.3 ࡟ኚ᭦ࡍࡿ࡜㸪ไືഃࡢ᭱኱ᶓຍ㏿ᗘࡀቑ ຍࡋ㸪ຍ㏿ഃࡢ᭱኱ᶓຍ㏿ᗘࡀῶᑡࡋࡓ㸬ࡋࡓࡀࡗ࡚㸪㥑ື᫬ࡼࡾࡶไື᫬ࡢ᪕ᅇ㝈⏺ࢆࡼࡾ㔜どࡍࡿ㌴୧௻⏬ ࡢሙྜ㸪dfࢆࡼࡾᑠࡉࡃタᐃࡍࡿࡇ࡜ࡀ᭷ຠ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡲࡓࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡ࡜ࡋ࡚ࡣ㸪᪕ᅇไ ື୰ࡣࡼࡾᚋࢁᐤࡾࡢ࣏ࢪࢩࣙࣥࢆ㸪᪕ᅇ㥑ື୰ࡣࡼࡾ๓ᐤࡾࡢ࣏ࢪࢩࣙࣥࢆࣛ࢖ࢲࡀ࡜ࡿࡇ࡜࡛㸪᪕ᅇ㝈⏺ࢆ ࡼࡾྥୖ࡛ࡁࡿࡶࡢ࡜ᛮࢃࢀࡿ㸬࡞࠾㸪᪕ᅇ㥑ື୰ࡢ๓ᐤࡾ࣏ࢪࢩࣙࣥ࡟㛵ࡋ࡚㸪࿴ḷᒣࡣࢫࣟࢵࢺࣝࢆ㛤ࡅࡿ ࡲ࡛࡟㸪㌟యࢆ๓᪉࡬⛣ືࡋ࡚࠾ࡃ࡜ᣦ᦬ࡋ࡚࠸ࡿ㸦1990㸧ࡢ࡛㸪ࡇࡢᣦ᦬ࡣ๓グ⪃ᐹࡢ୍㒊࡜ᩚྜࡍࡿ㸬

(A) G-G diagram (Maximized aymax by Bf) (B) Bf to maximize aymax (C) Comparison with fig.5

Fig.7 The influence of normal force distribution ratio of front wheel on the limit cornering property㸦μf=μr=1, df=0.3, Tf=0,

h/l=0.6/1.35 (=0.444), g=10[m/s2_{]㸧: Figure 7 (B) shows B}

f which maximizes aymax. Figure 7(C) implies that decrease of df

makes maximum lateral acceleration larger in braking and makes it smaller in driving.

⪃ ᐹ

ไ㥑ືຊ࡟ࡼࡿ࣮࣮࣓ࣚࣔࣥࢺࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪

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[DOI: 10.1299/transjsme.17-00043] ₁₂ ࣭ 㔜ᚰ㧗࡜࣍࢖࣮࣮ࣝ࣋ࢫ࡜ࡢẚࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪 ᮏ⠇࡛ࡣh/l ࡢᙳ㡪ࢆ⪃ᐹࡍࡿ㸬4࣭2 ⠇࡛ࡣ h/l ࡣ 0.6/1.35(=0.444)࡛࠶ࡗࡓࡀ㸪ᮏ⠇࡛ࡣࡇࢀࢆ 0.7/1.35(=0.519) ࡟ኚ᭦ࡋࡓ㸬ࡇࡢh/l ࡟࠾࠸࡚㸪Bf࡟ࡼࡗ࡚aymaxࢆ᭱኱໬ࡋࡓG-G ⥺ᅗࢆᅗ 8(A)࡟㸪ࡑࡢ Bfࢆᅗ8(B)࡟♧ࡍ㸬ᅗ 8(A)ࡢ᭱኱ᶓຍ㏿ᗘࢆᅗ 6(A)ࡢࡑࢀ࡜ẚ㍑ࡋࡓࡶࡢࡀᅗ 8(C)࡛࠶ࡿ㸬ᅗ 8(C)࡟♧ࡉࢀࡿࡼ࠺࡟㸪h/l ࢆ 0.6/1.35 ࠿ ࡽ0.7/1.35 ࡟ኚ᭦ࡍࡿ࡜㸪ไືഃࡶ㥑ືഃࡶ᭱኱ᶓຍ㏿ᗘࡀῶᑡࡋࡓ㸬ࡋࡓࡀࡗ࡚㌴୧௻⏬࡜ࡋ࡚ࡣ㸪 h/l ࢆࡼ ࡾᑠࡉࡃタᐃࡍࡿࡇ࡜ࡀ᭷ຠ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡲࡓ㸪ࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡ࡜ࡋ࡚ࡣ㸪㔜ᚰ㧗ࡀࡼࡾపࡃ࡞ ࡿࡼ࠺࡞ጼໃ࡟ࡼࡗ࡚㸪᪕ᅇ㝈⏺ࢆࡼࡾ㧗ࡃ࡛ࡁࡿࡶࡢ࡜ᛮࢃࢀࡿ㸬

(A) G-G diagram (Maximized aymax by Bf) (B) Bfto maximize aymax (C) Comparison with fig.5

Fig.8 The influence of the ratio of the center of gravity height to the wheel base on the limit cornering property㸦μf=μr=1, df=0.4,

Tf=0, h/l=0.7/1.35(=0.519), g=10[m/s2]㸧: This Bf was chosen to maximize aymax. Figure 8(C) implies that decrease of h/l

makes maximum lateral acceleration larger in both braking and driving.

⤖ ゝ ᮏㄽᩥࡢෆᐜࢆࡲ࡜ࡵࡿ࡜ḟࡢࡼ࠺࡟࡞ࡿ㸬 ไ㥑ື୰ࡢ᪕ᅇ㝈⏺ࡢ㧗ࡉࡸ㝈⏺࡟฿㐩ࡋࡓ㍯ࡢ᝟ሗࢆ⾲ࡍ஧㍯㌴ࡢG-G ⥺ᅗࢆᥦ᱌ࡋࡓ㸬ࡇࡢ G-G ⥺ᅗࢆ ⏝࠸ࡿࡇ࡜࡟ࡼࡗ࡚㸪஦ᨾᅇ㑊ᛶ⬟ࡸࢫ࣏࣮ࢶ㉮⾜ᛶ⬟ࡢᛶ⬟タィࡀ㸪ࡼࡾ඘ᐇࡍࡿ࡜ᛮࢃࢀࡿ㸬 ᪕ᅇ୰ࡢไ㥑ືຊ࡟ࡼࡗ࡚⏕ࡌࡿ࣮࣮࣓ࣚࣔࣥࢺࡣ㸪ไືഃ࡛ࡶ㥑ືഃ࡛ࡶ᪕ᅇ㝈⏺ࢆῶᑡࡉࡏࡓ㸬 ไ㥑ື୰ࡢ᪕ᅇ㝈⏺࡟ᙳ㡪ࢆཬࡰࡍタィኚᩘ࡟ࡘ࠸࡚⪃ᐹࢆ࠾ࡇ࡞ࡗࡓ㸬ࡑࡢ⤖ᯝ㸪ไື୰ࡢ᪕ᅇ㝈⏺ࡢࡉࡽ ࡞ࡿྥୖࡢ᪉⟇࡜ࡋ࡚ձ๓㍯ࡢไືຊ࡟ࡼࡿ᧯⯦㍈ࡲࢃࡾࡢ࣮࣓ࣔࣥࢺࢆ⏕ࡌࡉࡏ࡞࠸᧯⯦ᶵᵓࡸղࡇࡢ ࣮࣓ࣔࣥࢺࢆ࢟ࣕࣥࢭࣝࡸపῶࡍࡿ㸦ไᚚ㸧ᶵᵓճࡑࡢ࣮࣓ࣔࣥࢺࡢస⏝ୗ࡛ࡶ㐺ษ࡞᧯⯦ࢆ࠾ࡇ࡞࠺ࣛ࢖ ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡࡢ◊✲մ᪕ᅇ୰ࡢCBS ไᚚࡢไືຊ㓄ศẚࢆᥦ᱌ࡋࡓ㸬 ᮏㄽᩥࡀ㸪᪕ᅇ㝈⏺࡟ࡘ࠸࡚ࡢᛶ⬟タィ࣭ᛶ⬟ண ࡸCBS ไᚚ࣭ABS ไᚚ➼ࡢࡉࡽ࡞ࡿ㧗ရ㉁໬ࡸၟရᛶࡢ ࡉࡽ࡞ࡿྥୖ㸪࠶ࡿ࠸ࡣࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡ࡬ࡢఱࡽ࠿ࡢ♧၀➼࡟ᑡࡋ࡛ࡶ㈉⊩࡛ࡁࢀࡤᖾ࠸࡛࠶ࡿ㸬 ᩥ ⊩ ഌၨὈ, ᐃᖖ᪕ᅇ࡟࠾ࡅࡿ஧㍯㌴ࡢᇶᮏ≉ᛶ, ᪥ᮏᶵᲔᏛ᭳ㄽᩥ㞟, Vol.31, No.229 (1965), pp.1305-1314. ஭ୖ⚽㞝㸪᭱㏆ࡢ㌴୧㐠ືไᚚࡢືྥ࡟ࡘ࠸࡚̿VSC㸪ࣈ࣮ࣞ࢟࢔ࢩࢫࢺ㸪Active-TRC ࡢ㛤Ⓨ̿㸪⮬ື㌴ᢏ⾡ ఍ࢩ࣏ࣥࢪ࣒࢘ࢸ࢟ࢫࢺ(2000), No.01-00, pp.23-32. ⮬ື㌴ᢏ⾡ࣁࣥࢻࣈࢵࢡ⦅㞟ጤဨ఍⦅㸪⮬ື㌴ᢏ⾡ࣁࣥࢻࣈࢵࢡࠑ➨㸯ศ෉ࠒᇶ♏࣭⌮ㄽ⦅㸪⮬ື㌴ᢏ⾡఍(2011), pp.312-313. ᬒᒣඞ୕㸪ᬒᒣ୍㑻㸪⮬ື㌴ຊᏛ (2001), pp.64-97, ⌮ᕤᅗ᭩㸬 ࢡ࣒ࣝ, M., ࣑ࣁ࢚࣭ࣝࢡ࣒ࣝࡢ࣮ࣞࢩࣥࢢࠕ㉸ࠖ㐠㌿⾡(2012), pp.24-27, ᮾ㑥ฟ∧.

Milliken, W., Dell’Amico, F. and Rice, R., The static directional stability and control of the automobile, SAE Technical Pape, No.760712 (1976).

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Milliken, W. and Milliken, D., Race car vehicle dynamics (1995), pp.345-366, SAE.

㓇஭ⱥᶞ㸪⮬ື㌴ࡢᖹ㠃㐠ື࡟࠾ࡅࡿ࣮ࣚゅ㏿ᗘ㐍ࡳ᫬ᐃᩘ࡟ࡘ࠸࡚ࡢຊᏛⓗ⪃ᐹ㸪᪥ᮏᶵᲔᏛ఍ㄽᩥ㞟 C ⦅㸪 Vol.79, No.801 (2013), pp.1681-1693.

㓇஭ⱥᶞ㸪⮬ື㌴㐠ືຊᏛ(2015), p.100㸪᳃໭ฟ∧㸬

㓇஭ⱥᶞ㸪ไ㥑ື୰ࡢ᪕ᅇ㝈⏺≉ᛶ࡟ࡘ࠸࡚ࡢᇶ♏ⓗ⪃ᐹ㸪᪥ᮏᶵᲔᏛ఍ㄽᩥ㞟㸪Vol.82, No.839 (2016), DOI: 10.1299/transjsme.16-00019.

㛵᰿ኴ㑻㸪㛗ỤၨὈ㸪᪕ᅇไື᫬ࡢ㌴୧ᣲືࡢゎᯒ㸪⮬ື㌴ᢏ⾡఍ㄽᩥ㞟㸪Vol.24, No.4 (1993), pp.76-81㸬 ရᕝ᫭ᚨ㸪㔝⃝ஂᖾ㸪ෆᒣ⿱ኴ㑻㸪඲᪥ᮏࢡࣟࢫ࢝ࣥࢺ࣮ࣜ㑅ᡭᶒ࡟࠾ࡅࡿ࢜ࣇ࣮ࣟࢻ஧㍯㌴ࡢ㉮⾜ࢹ࣮ࢱゎᯒ㸪

᪥ᮏᶵᲔᏛ఍➨ 25 ᅇ஺㏻࣭≀ὶ㒊㛛኱఍(2016), No.1126.

Sharp, R., The stability and control of motorcycles, Journal Mechanical Engineering science, Vol.13, No.5 (1971), pp.316-329. Toyohuku, Y., Matsushima, K., Irie, Y., Yonezawa, H. and Mizuno, K., Study on effects of motorcycle

anti-lock-braking-system for skilled and less-skilled riders : regarding braking in a turn, JSAE Review, Vol.15, No.3 (1994), pp.223-228.

࿴ḷᒣ฼ᏹ㸪ࣛ࢖ࢹ࢕ࣥࢢࡢ⛉Ꮫ (1990), p.142ࢢࣛࣥࣉࣜฟ∧

5HIHUHQFHV

Ho, K., Teijyousennkai ni okeru nirinnsha no kihonntokusei, Transactions of the Japan Society of Mechanical Engineers, Vol.31, No.229 (1965), pp.1305-1314 (in Japanese).

Inoue, H., Advanced vehicle dynamics control technology for active safety - Development of VSC, brake assist, active traction control -, JSAE Symposium proceedings (2000), No.00-01, pp.23-32.

Jidousha gijyutsu handobukku henshuuiinnkai, Jidousha gijyutsu handobukku (No.1) Kiso riron hen (2011), pp.312-313 (in Japanese).

Kageyama, K. and Kageyama, I., Jidousha rikigaku (2001), pp.64-67, Rikoh Tosho (in Japanese). Krumm, M., Driving on the edge (2012), pp.24-27, Toho publishing (in Japanese).

Milliken, W., Dell’Amico, F. and Rice, R., The static directional stability and control of the automobile, SAE Technical Pape, No.760712 (1976).

Milliken, W. and Milliken, D., Race car vehicle dynamics (1995), pp.345-366, SAE.

Nishikawa, Y., Minamisato, T., Takenouchi, K., Tani, K., Takayanagi, S., and Hukatani S., Development of ABS for super sports motorcycles using a brake-by-wire system, Proceedings of JSAE Congress, No.5-09 (2009), pp.15-18.

Sakai, H., A physical interpretation of lead time constant of yaw angular velocity in planar motion of automobile, Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.79, No.801 (2013), pp.1681-1693 (in Japanese).

Sakai, H., Automotive vehicle dynamics (2015), p.100, Morikita Publishing Co., Ltd. (in Japanese).

Sakai, H., Fundamental study of cornering limit characteristics during braking and driving, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016), DOI: 10.1299/transjsme.16-00019.

Sekine, T. and Nagae, H., Cornering behavior analysis of passenger car under braking situations, Transactions of Society of Automotive Engineers of Japan, Vol.24, No.4 (1993), pp.76–81 (in Japanese).

Shinagawa, A., Nozawa, H., and Uchiyama Y., Data analysis of off-road motorcycle in Japan national cross-country, JSME Transportation and logistics 2016 (2016), No.1126 (in Japanese).

Sharp, R., The stability and control of motorcycles, Journal Mechanical Engineering science, Vol.13, No.5 (1971), pp.316-329. Toyohuku, Y., Matsushima, K., Irie, Y., Yonezawa, H. and Mizuno, K., Study on effects of motorcycle

anti-lock-braking-system for skilled and less-skilled riders : regarding braking in a turn, JSAE Review, Vol.15, No.3 (1994), pp.223-228.

Wakayama, T., Raideingu no kagaku (1990), p.142, Grand prix book publishing.

すᕝ㇏㸪༡㔛Ṋᙪ㸪➉அෆ࿴ஓ㸪㇂୍ᙪ㸪㧗ᰗ┾஧㸪῝㇂ಟ୍㸪ࣈ࣮ࣞ࢟ࣂ࢖࣡࢖ࣖࢩࢫࢸ࣒ࢆ⏝࠸ࡓࢫ࣮ࣃࢫ࣏࣮ ࢶ஧㍯㌴⏝ ABS ࡢ㛤Ⓨ㸪Ꮫ⾡ㅮ₇఍๓ๅ㞟㸪No.5-09 (2009), pp.15-18.

㔜ᚰ㧗࡜࣍࢖࣮࣮ࣝ࣋ࢫ࡜ࡢẚࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪

⤖ ゝ