Bulletin of the JSME᪥ᮏᶵᲔᏛ఍ㄽᩥ㞟

Vol.83, No.854, 2017

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

Received: 7 February 2017; Revised: 4 April 2017; Accepted: 23 May 2017
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, theG-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 wheelthat would maximize the maximum lateral driving, the influence of the normal load distribution ratio of front wheel on thelimit 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.

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

ゝ

ࢧ࣮࢟ࢵࢺ➼࡟࠾ࡅࡿࢫ࣏࣮ࢶ㉮⾜ᛶ⬟ࡣ㸪஧㍯㌴ࡢၟရᛶࡢ୍ࡘ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡲࡓ㸪ࢫ࣏࣮ࢶ㉮⾜ࡢࢥ࣮ࢼ࣮㐍ධ᫬࡟࠾ࡇ࡞ࢃࢀࡿࡇ࡜ࡢ࠶ࡿ᪕ᅇไື(Toyohuku et al.㸪1994)ࡢᛶ⬟ࡣ஦ᨾᅇ㑊ᛶ⬟࡜ࡶඹ㏻ࡍࡿࡓࡵ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࡜ࡋ࡚ 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㏿ᗘࡢ 2 ㍈ୖ࡟᪕ᅇ㝈⏺ࢆ⾲ࡋࡓࡶࡢ࡛࠶ࡿ㸬ᅄ㍯㌴ࡢ G-G ⥺ᅗࡢィ⟬ἲࡢ୍ࡘ࡜ࡋ࡚㸪᪕ᅇ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ࢻࣛ࢖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୧Ᏻᐃ໬ไᚚࢩࢫࢸ࣒ࡢసືἲࡣ㸪๓㍯ࡀᦶ᧿㝈⏺ࡢ࡜ࡁࡣ୺࡟ᚋෆ㍯ࢆไືࡋ㸪ᚋ㍯ࡀᦶ᧿㝈⏺ࡢ࡜ࡁࡣ୺࡟๓
No.17-00043 [DOI:10.1299/transjsme.17-00043], J-STAGE Advance Publication date : 5 June, 2017ᮏㄽᩥࡣ㸪➨25ᅇ஺㏻࣭≀ὶ㒊㛛኱఍ ㅮ₇ㄽᩥ㞟(2016), No.1128ࡢᥖ㍕ෆᐜ࡟ᇶ࡙࠸ࡓㄽᩥ࡛࠶ࡿ㸬*1ṇဨ㸪㏆␥኱ᏛᕤᏛ㒊㸦ࠛ739-2116 ᗈᓥ┴ᮾᗈᓥᕷ㧗ᒇ࠺ࡵࡢ㎶ 1㸧
E-mail of corresponding author: sakai@hiro.kindai.ac.jp[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 97 －

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Sakai, Transactions of the JSME (in Japanese), Vol.83, No.854 (2017)
እ㍯࡟ไືࡍࡿ㸦஭ୖ㸪2000㸧
㸬஧㍯㌴ࡢሙྜ࡛ࡶ㸪๓㍯ࢆไືࡋࡓሙྜࡣ࣮ࣟࣝ᪉ྥࡢᏳᐃᛶࡀ㸪ᚋ㍯ࢆไືࡋࡓሙྜࡣ࣮ࣚ᪉ྥࡢᏳᐃᛶࡀၥ㢟࡟࡞ࡿ࡜ᛮࢃࢀࡿ㸬ࡑࡇ࡛ᮏㄽᩥࡶ㸪๓ᚋ㍯ࡢ࡝ࡕࡽࡀ㝈⏺࡟㐩ࡋ࡚࠸ࡿ࠿ࡢ
᝟ሗࡶ⾲ࡍ G-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 ** ⥺ᅗࡇࡢ❶࡛ࡣ㸪஧㍯㌴ࡢ G-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
ᅗ 1 ࡟ᅄ㍯㌴ࡢࣔࢹࣝࢆ♧ࡍ㸬ࡇࡢࣔࢹࣝ࡟ࡣ௨ୗࡢ௬ᐃࡀタࡅࡽࢀ࡚࠸ࡿ㸦஧㍯㌴࡟࡜ࡗ࡚↓ព࿡࡞௬ᐃࡣ┬␎ࡍࡿ㸧㸬㸦௬ᐃ 1㸧㌴యࡢ࣮ࣟࣝゅࡣ↓どࡍࡿ㸬㸦௬ᐃ 2㸧㥑ືຊࡣ↓㝈኱࡜ࡍࡿ㸬㸦௬ᐃ 3㸧㥑ື⣔ࡢ័ᛶ࣮࣓ࣔࣥࢺ(ᬒᒣ㸪ᬒᒣ㸪2001)ࡣ↓どࡍࡿ㸬ࡇࡢࣔࢹࣝࡢ┤஺ᗙᶆ⣔࡜ࡋ࡚㸪ཎⅬ o 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ࡑࡢࡓࡵ㸪ᕥ᪕ᅇ᫬ࡢ➢ྕࡀṇ࡛࠶ࡿ㸬ࡲࡓ㌴୧㉁㔞ࢆ m㸪㔜ᚰ㧗ࢆ h㸪࣍࢖࣮࣮ࣝ࣋ࢫࢆ l㸪๓㍯㹼㔜ᚰ㛫㊥㞳ࢆlf㸪㔜ᚰ㹼ᚋ㍯㛫㊥㞳ࢆ lr㸪๓ᚋຍ㏿ᗘࢆ ax㸪ᶓຍ㏿ᗘࢆ ay ࡜ࡑࢀࡒࢀグࡍ㸬࡞࠾㸪ᮏㄽᩥࡣỈᖹ㠃ෆࡔࡅࡢ㐠ືࢆᢅ࠸㸪໙㓄࡟࠾ࡅࡿ㐠ືࡣᢅࢃ࡞࠸㸬Fig.1 Vehicle modelᅗ 1 ࡢࣔࢹࣝ࡟࠾࠸࡚㸪๓㍯ࡢ๓ᚋຊࢆ Fxf㸪ᚋ㍯ࡢ๓ᚋຊࢆ Fxr ࡜グࡍ࡜㸪x ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣmax

Fxf  Fxr(1)

࡜࡞ࡿ㸬ḟ࡟๓㍯࡜ᚋ㍯ࡢࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆࡑࢀࡒࢀ F’yf㸪F’yr ࡜グࡍ࡜㸪y ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣ
[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 98 －

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

ma y

(2)

F ' yf  F ' yr࡜࡞ࡿ㸬ࡲࡓ㸪z ㍈ࡲࢃࡾࡢࡘࡾྜ࠸㸪ࡍ࡞ࢃࡕ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡣ

(3)l f F ' yf lr F ' yr0࡛࠶ࡿ㸬ୖᘧ࡟࠾ࡅࡿ lf ࡣ㸪ṇ☜࡟ࡣ lf ࠿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
ࡎ ax ࢆ㸪ḟ࡟ ay ࢆつᐃࡋ㸪ࡑࢀࢆᐇ⌧ࡍࡿ᧯⯦ࢆࢻࣛ࢖ࣂࡀ࠾ࡇ࡞࠺ࡶࡢ࡜ࡍࡿ㸬ࡋࡓࡀࡗ࡚᧯⯦࡟ࡼࡗ࡚ ayࡀỴᐃࡉࢀࡿࡢ࡛ࡣ࡞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࡜

0F ' yf F ' yr

lr
lf
m
m
l
l

(4)

࡜࡞ࡿ㸬ࡼࡗ࡚㸪F ' yflrml

F ' yrlfml(5)

࡜࡞ࡿ㸬ࡇࡇ࡛㸪a' yf {

a ' yr {F ' yflrml(6)

F ' yrlfml(7)

࡜グࡍ࡜㸪ᘧ(5)ࡣ

a' yf

(8)

a' yr

[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 99 －

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Sakai, Transactions of the JSME (in Japanese), Vol.83, No.854 (2017)࡜᭩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’yr ࡢ༢఩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’yf ࡣ๓㍯ࡢࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆ๓㍯఩⨨ࡢᶓຍ㏿ᗘ࡜ࡋ࡚㸪a’yr ࡣᚋ㍯ࡢࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆᚋ㍯఩⨨ࡢᶓຍ㏿ᗘ࡜ࡋ࡚㸪ࡑࢀࡒࢀ⾲ࡋࡓࡶࡢ࡛࠶ࡿ㸬࣭ ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᫬ࡢᶓຍ㏿ᗘ࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳࡛࠶ࡿᘧ(8)ࡀᡂࡾ❧ࡘ࡜ࡁ㸪ᘧ(2)ࡼࡾ

may

F ' yf  F ' yr

ma' yf(9)

ma' yrࡀᡂࡾ❧ࡘ㸬ࡼࡗ࡚㸪ࡇࡢ࡜ࡁ

ay

a' yf

(10)

a' yr

࡜࡞ࡿ㸬ࡋࡓࡀࡗ࡚㸪࣮࣮࣓ࣚࣔࣥࢺࡀࡘࡾྜ࠺࡜ࡁ㸪a’yf ࡸ a’yr ࡀ ay ࢆ⾲ࡍ㸬௨ୖࡢࡼ࠺࡟㸪a’yf ࡜ a’yr ࡜࠿ࡽ㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸࡜ᶓຍ㏿ᗘࡀศ࠿ࡿ㸬࣭ ๓ᚋ㍯ࡢ᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫ
 ๓㍯ࡢᆶ┤Ⲵ㔜ࢆ Fzf㸪ᚋ㍯ࡢᆶ┤Ⲵ㔜ࢆ Fzr㸪๓㍯Ⲵ㔜㓄ศẚࢆ df (=lr/l)㸪ᚋ㍯Ⲵ㔜㓄ศẚࢆ dr (=lf/l)࡜グࡍ࡜㸪࠶ࡿ๓ᚋຍ㏿ᗘᗘ ax ࡀつᐃࡉࢀࡓ࡜ࡁࡢ Fzf ࡜ Fzr ࡣࡑࢀࡒࢀ

Fzf

hd f mg  max
l

(11)

Fzr

h
d r mg  maxl(12)࡜࡞ࡿ㸬࡞࠾ g ࡣ㔜ຊຍ㏿ᗘ࡛࠶ࡿ㸬ḟ࡟඲㍯㥑ື㌴࡟ᑐᛂ࡛ࡁࡿࡼ࠺࡟㸪๓㍯㥑ືຊ㓄ศẚࢆ Tf㸪ᚋ㍯㥑ືຊ㓄ศẚࢆ Tr ࡜グࡍ࡜㸪㥑ືຊࡢྜィࡣ max ࡔ࠿ࡽFxf

T f max(13)

Fxr

Tr max(14)࡜࡞ࡿ㸬ࡇࡇ࡛ Tr =1- Tf ࡛࠶ࡿ㸬୍᪉㸪๓㍯ไືຊ㓄ศẚࢆ Bf㸪ᚋ㍯㥑ືຊ㓄ศẚࢆ Br ࡜グࡍ࡜㸪ไື᫬࡟ࡣ

Fxf

(15)

B f max[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 100 －

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Fxr

(16)

Br max࡜࡞ࡿ㸬ࡇࡇ࡛ Br =1-Bf ࡛࠶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᧿ಀᩘࢆ μr ࡜グࡍ࡜㸪
๓㍯ࡢ᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫ F’yfmax ࡜ᚋ㍯ࡢ᭱኱ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫ F’yrmax ࡣ㸪ࡑࢀࡒࢀF ' yf max( P f Fzf ) 2  Fxf

2

(17)

F ' yr max(Pr Fzr ) 2  Fxr

2

(18)

࡜࡞ࡿ㸬ḟ࡟㸪Fyfmax ࡀ⏕ࡌ࡚࠸ࡿ࡜ࡁࡢ a’yf ࢆ a’yfmax㸪Fyrmax ࡀ⏕ࡌ࡚࠸ࡿ࡜ࡁࡢ a’yr ࢆ a’yrmax ࡜ࡑࢀࡒࢀグࡍ㸬ࡉࡽ࡟㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࢆ‶ࡓࡍ᭱኱ᶓຍ㏿ᗘࢆ aymax ࡜グࡍ㸬᭱ᚋ࡟㸪 a’yfmax ࡜ a’yrmax ࢆ࠶ࡽࡺࡿ ax ࡟࠾࠸࡚ィ⟬ࡋ㸪ᅗ♧ࡍࡿ㸬ࡇࢀࡀ๓㏙ࡢᅄ㍯㌴ࡢ G-G ⥺ᅗ࡛࠶ࡿ㸬a’yfmax ࡜ a’yrmax ࡜ࡢ㛵ಀ࡟ࡼࡗ࡚㸪᪕ᅇ㝈⏺ࡢᛶ㉁ࡣḟࡢࡼ࠺࡟ሙྜศࡅࡉࢀࡿ㸬i)a’yfmax = a’yrmax ࡢ࡜ࡁ aymax = a’yfmax = a’yrmax. ࡇࡢ࡜ࡁ๓㍯࡜ᚋ㍯ࡢ୧᪉ࡀྠ᫬࡟㝈⏺࡟㐩ࡍࡿ㸬ࡇࢀࡣ㸪ᅄ㍯㌴࡛
ࡣ Drift ࡜࿧ࡤࢀࡿ㸦Milliken et al.㸪1976㸧
㸬ᮏㄽᩥ࡛ࡶࡇࢀࢆ஧㍯㌴࡛ࡶ Drift ࡜࿧ࡪ㸬ii) a’yfmax > a’yrmax ࡢ࡜ࡁ aymax = a’yrmax㸬ࡇࡢ࡜ࡁᚋ㍯ࡔࡅࡀ㝈⏺࡟㐩ࡍࡿ㸬ࡇࢀࡣ㸪ᅄ㍯㌴࡛ࡣ Spin ࡜࿧ࡤࢀࡿ㸦Milliken et al.㸪1976㸧
㸬ᮏㄽᩥ࡛ࡣࡇࢀࢆ஧㍯㌴࣭ᅄ㍯㌴࡜ࡶ Rear wheel skid ࡜グࡍ㸬iii) a’yfmax< a’yrmax ࡢ࡜ࡁ aymax = a’yfmax㸬ࡇࡢ࡜ࡁ๓㍯ࡔࡅࡀ㝈⏺࡟㐩ࡍࡿ㸬ࡇࢀࡣ㸪ᅄ㍯㌴࡛ࡣ Plow ࡜࿧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⟬ࡋࡓ G-G ⥺ᅗࢆᅗ 2(A)࡟♧ࡍ㸬ࡇࡢᅗࡣୖ࡟ฝࡢ᭤⥺ࡔࡅ࡛ᵓᡂࡉࢀ
࡚࠸ࡿ㸬௚ㅖඖ࡜ࡢẚ㍑ࡢࡓࡵ㸪ࡇࡢᅗ࠿ࡽ aymax ࢆᢳฟࡋࡓࡶࡢࡀᅗ 2(B)࡛࠶ࡿ㸬(A)Cornering limit of front and rear wheels(B)Maximum lateral acceleration

㸸In fig.
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
2(A), the horizontal axis shows longitudinal acceleration ax, while the vertical axis shows maximum front wheel lateral
acceleration ayf and maximum rear wheel lateral acceleration ayr. The smaller of these values is considered the maximum
lateral acceleration aymax shown in fig. 2(B).

[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 101 －

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Spin 㡿ᇦ࡛ࡣ a’yfmax㸪Plow 㡿ᇦ࡛ࡣ a’yrmax ࡛‽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ࡑࡢ aymax ࢆ a’yfmax㸦a’yrmax㸧࡜ࡍࢀࡤࡼ࠸㸬ࡇࡢࡼ࠺࡟㸪࠶ࡿ㍯ࡢ᭱኱ᶓຍ㏿ᗘࢆィ⟬ࡍࡿ࡜ࡁ௚㍯ࡢ㝈⏺ࢆ↓どࡍࡿࡇ࡜ࡀ㸪ࡇࡢ G-G ⥺ᅗࡢィ⟬ᡭἲ࡛࠶ࡿ㸬 ஧㍯㌴ࡢ ** ⥺ᅗࡇࡢ❶࡛ࡣ㸪๓❶ࡢ G-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᧯⯦ࡸ࣮ࣟࣝ࡟ᑐࡍࡿᶓຍ㏿ᗘࢆồࡵࡿࡢ࡛ࡣ࡞ࡃ㸪ᶓຍ㏿ᗘ࠿ࡽ㏫⟬ࡉࢀࡿ᧯⯦࡜࣮ࣟࣝࡀᐇ⌧ࡉࢀࡿࡶࡢ࡜௬ᐃࡍࡿ㸬࣭ ㌴୧ࣔࢹࣝ
ᅗ 3 ࡟஧㍯㌴ࡢࣔࢹࣝࢆ♧ࡍ㸬ࡇࡢࣔࢹࣝࡣ㸪ᅗ 1 ࡢࣔࢹࣝ࡟࣮ࣟࣝ⮬⏤ᗘࡔࡅࢆຍ࠼ࡓࡶࡢ࡛࠶ࡾ㸪࣮ࣟࣝ
ゅࢆI࡜グࡍ㸬ࡇࡢᗙᶆ⣔ࡣ㸪ᅗ 1 ࡢࡶࡢ࡜ྠ୍࡜ࡍࡿࡢ࡛㸪Iࡢṇࡢྥࡁࡣ㸪⫼㠃ど᫬ィᅇࡾ࡛࠶ࡿ㸬ࡇࡢᅗࡢࣔࢹࣝࡢグྕࡣ㸪ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆ㝖࠸࡚ᅗ 1 ࡢࡶࡢࢆ⏝࠸ࡿ㸬࡞࠾㸪ᮏㄽᩥ࡛ࡣ㸪࢟ࣕࣥࣂࢫࣛࢫࢺ࡜
ࢥ࣮ࢼࣜࣥࢢࣇ࢛࣮ࢫࢆ⥲⛠ࡋ࡚㸪࢟ࣕࣥࣂࢫࣛࢫࢺ࡜࿧ࡪ㸬࡞࠾ᮏㄽᩥࡣ㸪࢘࢖࣮ࣜ࡞࡝∦㍯ࡢ᥋ᆅⲴ㔜ࡀ 0ࡢ≧ែࡣᢅࢃ࡞࠸㸬

Fig. 3 Motorcycle’s model: Fxf and Fxr yield a moment around z axis when φӆ0.

ࡇࡢࣔࢹࣝࡢ x ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣᘧ(1)࡜ඹ㏻࡛࠶ࡿ㸬ࡇࡢࣔࢹࣝ࡟࠾ࡅࡿ๓㍯࡜ᚋ㍯ࡢ࢟ࣕࣥࣂࢫࣛࢫࢺ
ࢆࡑࢀࡒࢀ Fyf㸪Fyr ࡜グࡍ࡜㸪y ㍈᪉ྥࡢ㐠ື᪉⛬ᘧࡣ

ma y

(19)

Fyf  Fyr࡜࡞ࡿ㸬ḟ࡟㸪࣮࣮࣓ࣚࣔࣥࢺࡢࡘࡾྜ࠸᮲௳ࡣ

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0

(20)

l f Fyf  lr Fyr  h sin Imax࡛࠶ࡿ㸬ୖᘧ࡟࠾ࡅࡿ lf ࡣ㸪ṇ☜࡟ࡣ lf ࠿ࡽࢽ࣮࣐ࣗࢳࢵࢡࢺ࣮ࣞࣝࡸ࢟ࣕࣥࣂ࣮࣓ࣔࣥࢺࡢ࢔࣮࣒㛗ࢆῶࡌࡓ್࡛࠶ࡿࡀ㸪ᮏㄽᩥࡢ┠ⓗࡣ⤯ᑐⓗ࡞ᛶ⬟ண࡛ࡣ࡞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
tan I

 ay

(21)

g

࡜ࡍࡿ㸬ᘧ(21)ྑ㎶ศᏊ࡟㈇ྕࡀ௜ຍࡉࢀࡿ⌮⏤ࡣ㸪ay ࡀṇࡢ᪕ᅇ㸦ᕥ᪕ᅇ㸧ࡢ࡜ࡁ࡟㸪Iࡣ㈇㸦⫼㠃ど཯᫬ィᅇࡾ㸧ࡔ࠿ࡽ࡛࠶ࡿ㸬࡞࠾

sin I

sin tan 1

 ay
g



§a ·
1  ¨¨ y ¸¸
© g ¹

(22)

ay

1
2

g

࡛࠶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ᅗ 3 ࡢࣔࢹࣝࢆᅗ 1 ࡢࣔࢹࣝ࡟⨨᥮࠼ࡿ㸬ࡑࡇ࡛㸪ᘧ(19)࡜ᘧ(2)ࡢࡑࢀࡒࢀࡢྑ㎶ࡀ࡝࠺ࡋ➼ࡋ࠸࡜ࡍࡿ࡜㸪

Fyf  Fyr(23)

F ' yf  F ' yr࡞ࡿ㛵ಀࢆᚓࡿ㸬ࡲࡓᘧ(20)࡜ᘧ(3)ࡢࡑࢀࡒࢀࡢྑ㎶࡝࠺ࡋࡀ➼ࡋ࠸࡜ࡍࡿ࡜㸪l f Fyf  lr Fyr  h sin Imax

(24)

l f F ' yf lr F ' yr࡞ࡿ㛵ಀࢆᚓࡿ㸬ᘧ(23)㸪(24)ࢆ F’yf ࡜ F’yr ࡟ࡘ࠸࡚ゎࡃ࡜㸪ࡑࢀࡒࢀF ' yfhFyf  sin Imaxl(25)

F ' yrh
Fyr  sin Imaxl(26)࡜࡞ࡿ㸬ࡑࡇ࡛㸪a’yf ࡜ a’yr ࡑࢀࡒࢀࡢ௦ࢃࡾ࡟

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－ 104 －Sakai, Transactions of the JSME (in Japanese), Vol.83, No.854 (2017)a yf max {a yr max {F ' yf max
lrml

F ' yr max
lf
m
l

·
§
¸
¨
2
a yf max ¸
1 ¨
1
h
h ·
2§
2
¨ P f ¨ d f g  ax ¸  B f ax 
ax ¸
2
g
l
l ¹
df ¨
¸
©
§ a yf max ·¸¨¸¸
1  ¨¨
¸
¨
© g ¹
¹
©

§
·
¨
¸
2
¸
¨
a
1
1
h
h
yr max¨ Pr 2 §¨ d r g  ax ·¸  ( Br ax ) 2 
ax ¸
2
g
dr ¨
l ¹
l
¸
©
§a
·
¨
¸
1  ¨¨ yr max ¸¸
¨
¸
© g ¹
©
¹

(35)

(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Bf ࡸ Br ࡢ௦ࢃࡾ࡟ Tf ࡸ Tr ࢆࡑࢀࡒࢀ௦ධࡍࡿࡇ࡜࡜ࡍࡿ㸬࣭ ** ⥺ᅗࡢィ⟬౛ ᘧ(35)ࢆ ayfmax ࡟ࡘ࠸࡚ゎࡃࡇ࡜࡟ࡼࡗ࡚ ayfmax ࡀỴᐃࡉࢀ㸪ᘧ(36)ࢆ ayrmax ࡟ࡘ࠸࡚ゎࡃࡇ࡜࡟ࡼࡗ࡚ ayrmax ࡀỴᐃࡉࢀࡿ㸬ࡇࡢィ⟬ࢆ࠶ࡽࡺࡿ ax ࡟ࡘ࠸࡚࠾ࡇ࡞࠺ࡇ࡜࡟ࡼࡗ࡚㸪ax ࡟ᑐࡍࡿ ayfmax ࡸ ayrmax ࢆᅗ♧ࡍࡿࡇ࡜ࡀ࡛
ࡁࡿ㸬ࡇࢀࡀᮏㄽᩥࡢᥦ᱌ࡍࡿ஧㍯㌴ࡢ G-G ⥺ᅗ࡛࠶ࡿ㸬ࡑࡢィ⟬౛ࢆᅗ 4(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ࡑࡢࡓࡵ ax =0 ࡢ௜㏆ࡢ aymax ࡢᙧ≧ࡣ㸪ᅗ 4(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㉮⾜ࣛ࢖ࣥࡣ U Ꮠࡂࡳ㸪ᅄ㍯㌴ࡢࣛ࢖ࣥྲྀࡾࡣ V Ꮠࡂࡳ࡛࠶ࡿ࡜ᛮ
ࢃࢀࡿ㸬࡞࠾㸪ᅗ 4 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)Fig.4 An example of G-G diagram of motorcycle㸦μf=μr=1, df=0.4,Bf=0.4,Tf=0, h/l=0.6/1.35, g=10[m/s2]㸧

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

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 ࡢㅖඖࢆ⏝࠸࡚ィ⟬ࡋࡓ G-G ⥺ᅗࢆᅗ 5(A)࡟♧ࡍ㸬ࡇࡢሙྜ࡟࠾࠸࡚ࡶ㸪ᅄ㍯㌴࡜␗࡞ࡾ㸪㥑ືഃࡢ඲㡿ᇦࡣ๓㍯ࡔࡅ࡛Ỵᐃࡉࢀࡿ㸬ࡋࡓࡀࡗ࡚㸪ࡇࢀࡣ㸪஧㍯㌴࡜ᅄ㍯㌴࡜ࡢィ⟬ㅖඖࡢ㐪࠸࡟㉳ᅉࡍࡿ㸬ࡲࡓᅗ 4 ࡜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࡟ᅗ 5(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 ineq.(35) and (36). Figure 5(B) implies that the yaw moment decreases maximum lateral acceleration in braking andincreases it in driving.

࣭ ᪕ᅇ㝈⏺ࢆ᭱኱໬ࡍࡿࡓࡵࡢ๓㍯ไືຊ㓄ศẚᮏ⠇࡛ࡣ㸪᭱኱ᶓຍ㏿ᗘ aymax ࢆ᭱኱໬ࡍࡿࡓࡵࡢ Bf ࢆ⪃ᐹࡍࡿ㸬aymax ࡣ㸪ayfmax ࡜ ayrmax ࡢ࠺ࡕࡢᑠࡉ࠸࡯࠺࡛
Ỵࡲࡿ࠿ࡽ㸪୧⪅ࡢᕪศࡔࡅ౑ࢃࢀ࡞࠸࢟ࣕࣥࣂࢫࣛࢫࢺࡀ࠶ࡿ㸬ࡇࡢ࢟ࣕࣥࣂࢫࣛࢫࢺࡀᑠࡉ࠸࡯࡝ aymax ࡀ኱ࡁ࠸࠿ࡽ㸪(ayfmax- ayrmax) 2 ࢆ᭱ᑠ໬ࡍࡿ Bf ࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡗ࡚㸪aymax ࢆ᭱኱໬࡛ࡁࡿ㸬ࡓࡔࡋ 0ӌBfӌ1 ࡜ࡍࡿ㸦Bf>1 ࡢሙྜࡣᚋ㍯ࡀ㸪Bf <0 ࡢሙྜࡣ๓㍯ࡀ㸪ไື୰࡟ࡶ࠿࠿ࢃࡽࡎ㥑ືࡋ࡚ࡋࡲ࠺ࡓࡵ㸪aymax ࢆ᭱኱໬࡛ࡁ࡞
࠸㸧㸬ࡇࡢ Bf ࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡗ࡚㸪ᅗ 4 ࡢィ⟬ㅖඖ࡟࠾ࡅࡿ aymax ࢆ᭱኱໬ࡋࡓሙྜࡢ G-G ⥺ᅗࡢィ⟬౛ࢆᅗ 6(A)࡟㸪ࡑࡢ࡜ࡁࡢ Bf ࢆᅗ 6(B)࡟♧ࡍ㸬ᅗ 6(A)࡟ࡣ㸪aymax =ayfmax = ayrmax ࡢ㡿ᇦࡀ࠶ࡿࡢ࡛㸪aymax ࡢ᭱኱໬ࡀᐇ⌧ࡉࢀ࡚࠸ࡿࡇ࡜ࡀ☜ㄆ࡛ࡁࡿ㸬ᅗ 6(A)ࡢ᭱኱ᶓຍ㏿ᗘࢆᅗ 4(A)ࡢࡑࢀ࡜ẚ㍑ࡋࡓ⤖ᯝࢆᅗ 6(C)࡟♧ࡋࡓ㸬⌮ㄽୖࡣ㸪ᅗ 6(B)ࡢ Bf ࢆᐇ⌧ࡍࡿࡼ࠺࡟ࣛ࢖ࢲࡀไືࡋࡓࡾ㸪ไᚚࢩࢫࢸ࣒ࢆᵓ⠏ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪ไືഃࡢ᪕ᅇ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ࡇࡢ࣮࣓ࣔࣥࢺࢆ࢟ࣕࣥࢭࣝࡍࡿᶵᵓࡢ୍౛࡜ࡋ࡚ࡣ㸪ࣃ࣮࣡ࢫࢸ࢔ࣜࣥࢢ࡟ࡼࡿ࢔ࢡࢸ࢕ࣈไᚚࡀ⪃࠼ࡽࢀࡿ㸬ࡉࡽ࡟㸪ࡇࡢ࣮࣓ࣔࣥࢺࢆపῶࡍࡿᶵᵓࡢ୍౛࡜ࡋ࡚ࡣ㸪ࢫࢸ࢔ࣜࣥࢢࢲࣥࣃࡢ࢔ࢡࢸ࢕ࣈไᚚࡀ⪃࠼ࡽࢀࡿ㸬ࡇ
[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 106 －

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Sakai, Transactions of the JSME (in Japanese), Vol.83, No.854 (2017)ࢀࡽ࡜⤌ྜࡏࡿ᪕ᅇ୰ࡢ CBS 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) Bf to 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: Bf 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ศẚ df ࡢᙳ㡪ࢆ⪃ᐹࡍࡿࡓࡵ࡟㸪df ࢆ 0.4 ࠿ࡽ 0.3 ࡟ኚ᭦ࡋࡓ࠺࠼࡛㸪 Bf ࡟ࡼࡗ࡚ aymax ࢆ᭱኱໬ࡋ
ࡓሙྜࡢ G-G ⥺ᅗࡢィ⟬౛ࢆᅗ 7(A)࡟㸪ࡑࡢ Bf ࢆᅗ 7(B)࡟♧ࡍ㸬ᅗ 7(A)ࡢ᭱኱ᶓຍ㏿ᗘࢆᅗ 6(A)ࡢࡑࢀ࡜ẚ㍑
ࡋࡓࡶࡢࡀᅗ 7(C)࡛࠶ࡿ㸬ᅗ 7(C)࡟♧ࡉࢀࡿࡼ࠺࡟㸪df ࢆ 0.4 ࠿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df ࢆࡼࡾᑠࡉࡃタᐃࡍࡿࡇ࡜ࡀ᭷ຠ࡛࠶ࡿ࡜ᛮࢃࢀࡿ㸬ࡲࡓࣛ࢖ࢹ࢕ࣥࢢࢸࢡࢽࢵࢡ࡜ࡋ࡚ࡣ㸪᪕ᅇไື୰ࡣࡼࡾᚋࢁᐤࡾࡢ࣏ࢪࢩࣙࣥࢆ㸪᪕ᅇ㥑ື୰ࡣࡼࡾ๓ᐤࡾࡢ࣏ࢪࢩࣙࣥࢆࣛ࢖ࢲࡀ࡜ࡿࡇ࡜࡛㸪᪕ᅇ㝈⏺ࢆࡼࡾྥୖ࡛ࡁࡿࡶࡢ࡜ᛮࢃࢀࡿ㸬࡞࠾㸪᪕ᅇ㥑ື୰ࡢ๓ᐤࡾ࣏ࢪࢩࣙࣥ࡟㛵ࡋ࡚㸪࿴ḷᒣࡣࢫࣟࢵࢺࣝࢆ㛤ࡅࡿࡲ࡛࡟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 Bf which maximizes aymax. Figure 7(C) implies that decrease of df
makes maximum lateral acceleration larger in braking and makes it smaller in driving.

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Sakai, Transactions of the JSME (in Japanese), Vol.83, No.854 (2017)࣭ 㔜ᚰ㧗࡜࣍࢖࣮࣮ࣝ࣋ࢫ࡜ࡢẚࡀ᪕ᅇ㝈⏺࡟ཬࡰࡍᙳ㡪ᮏ⠇࡛ࡣ h/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ࡇࡢ h/l ࡟࠾࠸࡚㸪Bf ࡟ࡼࡗ࡚ aymax ࢆ᭱኱໬ࡋࡓ G-G ⥺ᅗࢆᅗ 8(A)࡟㸪ࡑࡢ Bf ࢆᅗ 8(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 ࠿ࡽ 0.7/1.35 ࡟ኚ᭦ࡍࡿ࡜㸪ไືഃࡶ㥑ືഃࡶ᭱኱ᶓຍ㏿ᗘࡀῶᑡࡋࡓ㸬ࡋࡓࡀࡗ࡚㌴୧௻⏬࡜ࡋ࡚ࡣ㸪 h/l ࢆࡼࡾᑠࡉࡃ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) Bf to 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ࡢ G-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୰ࡢ CBS ไᚚࡢไືຊ㓄ศẚࢆᥦ᱌ࡋࡓ㸬ᮏㄽᩥࡀ㸪᪕ᅇ㝈⏺࡟ࡘ࠸࡚ࡢᛶ⬟タィ࣭ᛶ⬟ண ࡸ CBS 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).
[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 108 －

12

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

Milliken, W. and Milliken, D., Race car vehicle dynamics (1995), pp.345-366, SAE.
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.
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.142ࢢࣛࣥࣉࣜฟ∧

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 (inJapanese).
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 supersports 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 (inJapanese), 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 ofAutomotive 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.

[DOI: 10.1299/transjsme.17-00043]© 2017 The Japan Society of Mechanical Engineers－ 109 －

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