〈再録論文〉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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(1)Vol.82, No.839, 2016. Bulletin of the JSME. Transactions of the JSME (in Japanese). *1. Fundamental study of cornering limit characteristics during braking and driving Hideki SAKAI *1 *1. Kindai Univ. Dept. of Robotics Engineering 1 Umenobe, Takaya, Higashihiroshima-shi, Hiroshima 739-2116, Japan. Received 15 January 2016 Abstract The G-G diagram is one way of expressing the cornering limit during braking or driving. When limit driving data is plotted on a graph with the 2 axes representing longitudinal acceleration and lateral acceleration, the shape of the graph indicates the cornering limit. Although the theoretical outline with a one-wheel model is a circle, the shape on the braking side of a G-G diagram which uses actual measured data is similar to a pentagon. As a result, the basic shape of the diagram is unknown. Therefore this paper proposes a graphical method which uses a two-wheel model to explicitly describe the mechanism that determines the G-G diagram shape. This graphical method is as follows. First, the provisional cornering limit line for the front wheel is plotted in the G-G diagram, ignoring the rear wheel cornering limit. Second, the provisional rear wheel cornering limit is plotted in the G-G diagram, ignoring the front wheel cornering limit. Third, the lower of the two cornering limit lines becomes the shape of the G-G diagram. The reason that the braking-side shape of actual measured data looks like a pentagon is due to the fact that these lines cross each other at two points. Furthermore, this paper describes the vehicle behavior when the diagram shape is the front wheel cornering limit line as plow , and the behavior when the shape is the rear wheel line as. . Finally, this paper explains that the cornering limit increases in the order of rear-engine rear-wheel. drive (RR), front-engine rear-wheel drive (FR), and front-engine front-wheel drive (FF) vehicles due to the effects of the engine position and position of the drive wheels. Key words : Automobile, Vehicle dynamics, Kinematics, Cornering limit, Sports driving, Sports car. . 1999. No.16-00019 [DOI:10.1299/transjsme.16-00019], J-STAGE Advance Publication date : 20 June, 2016 *1 739-2116 1 E-mail of corresponding author: [email protected] [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 99 －. 1.

(2) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). 2013 G-G. Milliken and Milliken 1995. G-G. 2 G-G. 1. G-G. 1. Milliken and Milliken 1995. 1. 1. 2. 1. G-G G-G. . . G-G. 2 1 2 Sakai 1997 3. 4 5. 2001 1 x. o. y. l. z lf. m lr. G-G. ax 3. h ay. 4. 7. 4. 1993 1. 2001 1. 4. 2. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 100 －. 2.

(3) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). G-G 2. Fzrf z m oo. y. Fzf. lr lf. l. Fig.1 Vehicle model. 1. Fxf. max. Fxf. Fxr. x. (1). Fxr. Fyf Fyr. ma y. Fyf. y. Fyr. (2). lr Fyr. (3). z. 0 l f Fyf. (1) (3). 2012 ay (3). V (3). ay. ay. ayu. ays ayu. ayu ays Sakai 1997. ays. Fzf ax. Fzr Fzf. df (=lr/l). dr (=lf/l). Fzr. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 101 －. 3.

(4) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). Fzf. d f mg. h max l. (4). Fzr. dr mg. h max l. (5). Tf. Tr. max. Fxf. T f max. (6). Fxr. Tr max. (7). Tr =1- Tf. 6 Bf. Br. Fxf. B f max. (8). Fxr. Br max. (9). Br =1-Bf. (1) (6) (7). 7 1993. Milliken and Milliken 1995 f. r. Fyfmax. Fyf max. f. Fzf ) 2. Fxf. 2. (10). ( r Fzr ) 2. Fxr. 2. (11). (. Fyr max. (3). Fyrmax. f. 2. r. Sakai. 1997 Fyfmax. Fyrmax. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 102 －. 4.

(5) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016) Fyf max. a yf. (12). dfm. Fyr max dr m. a yr. ayf. (13). ayr. a yf. ays l l f Fyf max l f lr m. a yr. (3). (14). lr Fyr max. ay. ayf. ayr. ays. ays. plow spin. Milliken et al. 1976. ayf < ayr. plow ayf - ayr. l f lr m l. a yf. spin. plow. ayf. ayr. ayr < ayf. ayf - ayr. spin. spin. lflrm/l. a yr. l f Fyf max. (15). lr Fyr max. lfFyf-lyrFyr. Milliken. lfFyf-lyrFyr. residual yaw moment. (1976). ayf - ayr ayf. ayr. ays ays. spin/plow. ayr < ayf. ayf - ayr ayf < ayr. ay=ays 0 ayr < ayf. 0 ayu. a yu. Fyf max. (4) (13). ayf < ayr. 0. (2). Fyr max. (16). m. (16). ax. G-G. 4. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 103 －. 5.

(6) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016) . . f= r. =0.8. df= 0.5. 4. 2001 Tf=Bf=Fzf /(mg) 2(A) ayf. ay. Fzf ayr. ayf. ayr. ay. 2. ay. ax. ayf. ayf=ayr=0. ayr. ays. G-G spin. plow. 2(A)(C). spin. 2(B). ax=0. ayf - ayr. 2(C). plow. 2(A). (B) (C). spin plow 2. 1988. 10. 10. 5. -10. -5. 5. 5. Spin. Plow. 0 ax [m/s2]. 5. 10-10. -5. 0 ax [m/s2]. 5. 10 -10. -5. 0 -5. (A) G-G diagram with residual. (B) Maximum lateral acceleration. yaw moment. of quasi steady state turning. 5. 10. ax [m/s2]. -10. (C) Residual yaw moment. Fig.2 Example of G-G diagrams. This figure was calculated using specifications that simulate a four-wheel drive vehicle. The braking/drive force distribution on the front and rear wheels is equal to the distribution of normal load on the front and rear wheels. In Fig.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 for quasi-constant radius turning, and is indicated in Fig.2 (B). ayf-ayr in Fig.2 (C) indicates the magnitude of the spin tendency when turning at the maximum lateral acceleration. When ayf-ayr > 0, the resulting vehicle behavior is spin, when ayf-ayr < 0, the result is plow. ( f= r=0.8[-], df=0.5[-], Tf=Bf=Fzf /(mg) l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). 2 3. 2 3 4. Tf. Tf Tf. 2. 0 3. [DOI: 10.1299/transjsme.16-00019]. 1 4 4. 2. © 2016 The Japan Society of Mechanical Engineers. － 104 －. 6.

(7) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). 10. 10 plow Spin -10. -5. 5. 5. 5 Plow 0 ax [m/s2]. 10-10. 5. -5. 0 ax [m/s2]. 5. 10 -10. -5. 0. 5 4WD ax [m/s2]. 10. -5. -10. (C) Residual yaw moment. (B) Maximum lateral acceleration. (A) G-G diagram with residual. of quasi steady state turning yaw moment Fig.3 Cornering limit characteristics of a front-wheel drive vehicle; Front-wheel drive vehicles (FWD) demonstrate plow behavior on the driving side. ( f= r=0.8[-], df=0.5[-], Tf=1(FWD), Tf=Fzf /(mg) (4WD), Bf=Fzf /(mg), l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). 15. 10. 10. 5. 5. Spin -10. 0. ax. 5. Spin. Plow. -5. 10. 10 -10. 5. [m/s2]. -5. 0 ax [m/s2]. 5. 10. -10. -5. 0. 5 4WD ax [m/s2]. 10. -5. (A) G-G diagram with residual. (C) Residual yaw moment. (B) Maximum lateral acceleration. yaw moment of quasi steady state turning Fig.4 Cornering limit characteristics of a rear-wheel drive vehicle; Rear-wheel drive vehicles (RWD) have both a plow area and a spin area on the driving side. ( f= r=0.8[-], df=0.5[-], Tf=0(RWD), Tf=Fzf /(mg) (4WD), Bf=Fzf /(mg), l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). 3. ax. ayf =0. ax. ays =ayf ax 4. 3. ays. plow. ax. ayr =0 4. 2. ax. plow 2. ayf> ax >0. 2. ayr> ax >0. spin ax. 2 ays. df df =0.673 df. 0.05. 1993 3. df. [DOI: 10.1299/transjsme.16-00019]. 0.65. 1993 5. © 2016 The Japan Society of Mechanical Engineers. － 105 －. df. 7.

(8) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016) 3. 3. 5. df. ays df. df =0.353 2005. 911. 2005. 0.35. df 6. 0.05. 4. df. df. ays. df. 4. 4. spin. 6. plow. 10. 10. 5. 5. 5. df=0.65 df=0.5. -10. -5. 0 ax [m/s2]. 10 -10. 5. -5. 0 ax [m/s2]. 5. 10 -10. -5. 0. 5. ax [m/s2]. 10. -5. (A) G-G diagram with residual. -10. (B) Maximum lateral acceleration. (C) Residual yaw moment. yaw moment of quasi steady state turning Fig.5 Effects of front normal load distribution in a front-wheel drive vehicle (FWD); The maximum lateral acceleration is higher on the driving side and lower on the braking side with a front normal load distribution ratio df = 0.65 compared to a ratio of df = 0.5. ( f= r=0.8[-], df=0.65[-]or 0.5[-], Tf=1, Bf=Fzf /(mg), l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). 15. 10. 10. 5. 5. 10. df=0.35. 5. df=0.5. -10. -5. 0 ax [m/s2]. 5. 10 -10. -5. 0 ax [m/s2]. 10 -10. 5. -5. 0. 5 a [m/s2] 10 x. -5. (A) G-G diagram with residual. (B) Maximum lateral acceleration. yaw moment. of quasi steady state turning. (C) Residual yaw moment. Fig.6 Effects of front normal load distribution in a rear-wheel drive vehicle (RWD). ( f= r=0.8[-], df=0.35[-] or 0.5[-], Tf=0, Bf=Fzf/(mg), l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). 2 2. Bf G-G. spin. 0.66 Bf =0.75 plow. Bf Bf =0.66. 3. Bf. Bf =1,. Bf Bf. [DOI: 10.1299/transjsme.16-00019]. 7. Bf 2 Bf =1. Bf spin. © 2016 The Japan Society of Mechanical Engineers. － 106 －. 8.

(9) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). 10. 10. 5 Spin. 5. 10. 10. Plow. 5. 5. Plow Spin. 5 Bf = ideal. Spin. 0.66 -10. -5. 0 -10. 0 -10. -5 ax [m/s2]. ax [m/s2]. axD. -5 ax [m/s2]. 0. -10. -5. 0 -10. 0. -5. ax [m/s2] -5 ax [m/s2]. (D) Maximum lateral. -10 (E) Residual yaw. with residual yaw. acceleration of quasi. moment. moment ( Bf=0.66[-]). steady state turning. (A). (B) Bf=0.750[-]. G-G diagram. (C) Bf=1[-]. Fig.7 Effects of the front wheel braking force ratio Bf; when Bf is higher, the plow area is larger, the cornering limit in the plow area is lower, and the cornering limit in the spin area is higher. ( f= r=0.8[-], df=0.5[-], Bf=0.75, Tf= Fzf /(mg), l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). Bf =1. spin. Bf=1. ayf= ayr. ax. f= r=. ax. h l. 2. 1. 1 2. 1 2. l h. 2. 1 2. df. (17). df>1/2. Bf=1. df<1/2. (17) spin. h/l. spin. df. spin df =0.5. ax. 2. h l. spin. ax h/l. df. (17). 2. (18). 7(E). Bf=0.66. ayf- ayr. ax. ax -5 Bf=0.75. 2. ax -3[m/s ] ax. -3~-4[m/s2]. 1991. ax ax=-3~-4[m/s2]. (4) (13) ayf - ayr. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 107 －. 9.

(10) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016) Sakai 1997 0 plow. r r. f. 2. f. r - f =0.2. r. 0.8. r. 1.0. 8. G-G. f. ax=0. ax=0 ax=0. 8. plow. ax. plow. r. f. spin. r. ays. 10. 10. 5. -10. -5. 5. 5. 0 ax [m/s2]. 10 -10. 5. -5. f= r=0.8. 0 ax [m/s2]. 5. 10 -10. -5. 0. 5 ax [m/s2]. -5. (A) G-G diagram with residual. (B) Maximum lateral acceleration. 10. (C) Residual yaw moment. yaw moment of quasi steady state turning Fig.8 Effects of the rear wheel coefficient of friction r; when r is higher, ays on the braking side is larger and the residual spin moment is smaller. ( f=0.8, r=1.0[-], df=0.5[-], Tf=Bf=Fzf / (mg), l=2.6[m], m=1500[kg], h=0.55[m], g=10[m/s2]). FF. FR. RR. df. Tf. Bf df. r. f=0.8. f. r=0.85. Sakai. 1997 9(A). FF. 9(B). FR. 9(C). RR. FF. FF. 1993. df =0.65. FR. FR 1993. 2005. 1993. 968 df =0.511(6MT) df =0.486(4AT) 1993. df =0. 5. RR. 3.3. 911. RR 2005. df =0.35 9(D) (E). FF. FR. 9(D) FR. 3.3. FR FF. RR FR. RR 2015 ayr FR. RR. RR. [DOI: 10.1299/transjsme.16-00019]. FR. © 2016 The Japan Society of Mechanical Engineers. － 108 －. 10.

(11) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). 10. 10. 10. 5. 5. 5. -5 0 5 -10 -5 0 5 0 5 -10 ax [m/s2] ax [m/s2] ax [m/s2] Fig.9(A) Cornering limit performance Fig.9(B) Cornering limit performance Fig.9(C) Cornering limit performance. -10. -5. of a front-engine front-wheel drive. of a front-engine rear-wheel drive. of a rear-engine rear-wheel drive (RR). (FF). r=0.85[-],. (FR) vehicle. ( f=0.8,. r=0.85[-],. vehicle. ( f=0.8, r=0.85[-], df=0.35[-],. l=2.6[m],. df=0.50[-], Tf=0, Bf=0.66. l=2.6[m],. Tf=0, Bf=0.56 l=2.6[m], m=1500[kg],. vehicle.. ( f=0.8,. df=0.65[-], Tf=1, Bf=0.81. 2. m=1500[kg], h=0.55[m], g=10[m/s ]). 2. m=1500[kg], h=0.55[m], g=10[m/s ]). h=0.55[m], g=10[m/s2]). 10. 5. 5 f= r=0.8. -10. -5. 0 ax [m/s2]. 5. -10. 10. -5. 0. 5. 10. ax [m/s2]. -5. Fig.9(D) Comparison of the cornering limit levels. Fig.9(E) Comparison of the residual yaw moments for. for FF, FR, and RR vehicles.. FF, FR, and RR vehicles. spin plow. G-G. G-G. FF. FR. RR. RR. FR. FF. G-G. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 109 －. 11.

(12) Sakai, Transactions of the JSME (in Japanese), Vol.82, No.839 (2016). :. (2012), p.207 (2001), pp.64-97. C Vo. 65 No.633(1999), pp.1960-1965 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. 4 Vol.40 No.9(1988) pp.965-971 (2015) p.40 . 1993 (1993) pp.1412-1431 2005 (2005) Sakai, H., Theoretical consideration of relation of rear-wheel skid to steering inputs, SAE Transactions, Vol. 106 No.970378(1997), pp.504-524 Vol.67 No.4(2013) pp.27-32 Vol.24 No.4(1993) pp.76-81 Vol.45 No.3(1991) pp. 55-60..

(13) Abe, M., Automotive vehicle dynamics: Theory and applications (2012), p.207, Tokyo Denki University Press (in Japanese). Kageyama, K. and Kageyama, I., Jidousha rikigaku (2001), pp.64-67, Rikoh Tosho (in Japanese). Kitahama, K. and Sakai, H., Identification Method of Automobile Response to Steering Input Using Normalized Cornering Stiffness, Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.65, No.633 (1999), pp.1960 1965 (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. Mitamura, R. Jyouyousha no yorinkasseika gijyutu no tenbou Science of machine Vol.40 No.9(1988) pp.965-971(in Japanese). Nagata, G., Sokuhou! Shingata Roadster(2015), p.40, San-Ei shobo (in Japanese). Road Transport Bureau of Ministry of Transport, Jidousha shogen hyo 1993(1993), Society of Automotive Engineers of Japan, pp.1412-1431 (in Japanese). Road Transport Bureau of Ministry of Land, Infrastructure, Transport and Tourism, Jidousha shogen hyo 2005 kensakuban (2005), Society of Automotive Engineers of Japan (in Japanese). Sakai, H., Theoretical consideration of relation of rear-wheel skid to steering inputs, SAE Transactions, Vol. 106 No.970378(1997), pp.504-524. Sakai, H., Relationship between tire properties and stability and control, Journal of Society of Automotive Engineers of Japan, Vol.67, No.4(2013), pp.27-32 (in Japanese). 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). Yamaguchi, H., Matsumoto, S., Inoue, S. and Hano, S., Improving Vehicle Stability at Braking in a Turn, Journal of Society of Automotive Engineers of Japan, Vol.45, No.3 (1991), pp.55-60 (in Japanese).. [DOI: 10.1299/transjsme.16-00019]. © 2016 The Japan Society of Mechanical Engineers. － 110 －. 12.

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