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Numerical expression of tyre characteristics for the calculation of vehicle motions
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ABSTRACTS operation of a vehicle with differential and locking inter-axle drives on both asphah and dirt roads. The graphs reveal that, with a locking inter-axle drive, the tractive effort (wheel slip) at the rear axle increases with growth of the steered-wheel angle of turn, and tile tractive effort (wheel slip) at the front-axle declines and, beyond a certain steered-wheel angle of turn, becomes negative. This latter leads to a sharp rise in side force at the front axle, particularly on an asphalt road. The side forces obtained with steered-wheel angles of turn of 20 and 30 deg are shown to increase the radius of vehicle turn by 12 and 32 per cent respectively, although test data indicate that growth of the actual vehicle radius of turn is 14 per cent with a steered-wheel angle of 20 deg. Better stability in turns is provided with a differential inter-axle drive. With a locking inter-axle drive, the tractive effort at the front axle becomes negative on an asphalt road at a steered-wheel angle of turn equal to or greater than 7 deg, the corresponding value on a dirt road being 25 deg. The use of a freewheel in the inter-axle drive to disconnect one of the driving axles, and limited-slip differentials is considered, and it is shown that shift of the vehicle centre of turn during cornering is in quadratic relation to speed and the vehicle design parameters. (M.I.R.A.)
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P. Lugner (Tech. Univ., Vienna). Numerical expression of tyre characteristics for the calculation of vehicle motions. A . T . Z . 74 (1), 17-23. (January 1972) It is shown that tyre characteristics can be expressed by mathematical approximation, which is derived partly analytically and partly through interpolation. Tyre side-force is expressed as a function of tyre slip-angle, tyre contact-force and circumferential force. Forces and moments at the tyre are considered, and the various parameters describing tyre and road effects are introduced. Those values which are essential for the description of vehicle handling are discussed in more detail. The study is confined to an examination of the relationship between side force and the following: angular velocity about the vertical axis (co), angular velocity about the wheel axis (u), velocity of the wheel centre (vo), tyre slip-angle (u), camber angle (~,), tyre contact-force (P), tangential force (T), tyre design and material (b,), tread depth (h) and pattern (F), tyre pressure (P,) and tyre slip and adhesion (~t~).The results of laboratory and road tests which have examined the relation between side force and the various parameters mentioned above are discussed. It is stated that the relationships have not yet been satisfactorily investigated in all cases. Typical tyre characteristics are presented for traditional cross-ply tyres, side force being shown as a function of slip angle, circumferential force and contact force. Tyre design affects the shape of the characteristic curves. Since available tyre characteristics for side force as a function of circumferential force and slip angle have been experimentally determined only for certain values of the tyre contact-force, these curves must be developed analytically to permit use of this information for other values of the contact force. An approximation function is presented of the form S = G (P, ~). F(P, T, a). In this formula, the function G(P, ~) describes, for a given tyre and a given road surface, the dependence of side force S on tyre contact force and slip angle for circumferential force T = O. Function Fexpresses the change in side 2orce due to T. For function F, the condition F(c~, P , T = 0) = 1 must be fulfilled, so that G(P, a) can be equalled to S' (P, ct). With this formula, the measured tyre characteristics are replaced by distorted ellipsoid curves whose centres are displaced relative to the origin of co-ordinates (parameters kl, U), whose axes are inclined relative to the co-ordinate axes (parameter k2) and whose minor axes are fitted to the measured data according to a and P. The calculation procedure including the determination of k~ and k~, is set out. Calculated tyre characteristics are shown for various tyre contact-forces and slip angles. The form of approximation offered is thought to be justifiable in view of the relatively wide variation in measured side forces, even for tyres of the same production series. The method of interpolation is well suited for computer calculation. With a maximum value for ct = 12 deg and for P twice the static tyre load, this method of representing tyre characteristics is able to describe car handling up to the limits of normal driving. ( M . I . R . A . )
14.
B. I. Morozov et. al. (Moscow Automech. Inst.). On the method of investigating and evaluating vehicle handling. Avtom. Prom. No. 11, 12 14 (November 1971) Although vehicle-handling should be evaluated, from the point of view of greatest accuracy, in terms of the vehicle-environment- driver, it is well known that the individual changes the structure and numerical values of his characteristics according to the circumstances surrounding the driving function. As a result, the structure and parameters of the description of driver behaviour are defined by a non-steady-state function, which materially complicates direct calculation of the motion of a vehicle system including the driver. A way out of this situation (since the requisite
ABSTRACTS operation of a vehicle with differential and locking inter-axle drives on both asphah and dirt roads. The graphs reveal that, with a locking inter-axle drive, the tractive effort (wheel slip) at the rear axle increases with growth of the steered-wheel angle of turn, and tile tractive effort (wheel slip) at the front-axle declines and, beyond a certain steered-wheel angle of turn, becomes negative. This latter leads to a sharp rise in side force at the front axle, particularly on an asphalt road. The side forces obtained with steered-wheel angles of turn of 20 and 30 deg are shown to increase the radius of vehicle turn by 12 and 32 per cent respectively, although test data indicate that growth of the actual vehicle radius of turn is 14 per cent with a steered-wheel angle of 20 deg. Better stability in turns is provided with a differential inter-axle drive. With a locking inter-axle drive, the tractive effort at the front axle becomes negative on an asphalt road at a steered-wheel angle of turn equal to or greater than 7 deg, the corresponding value on a dirt road being 25 deg. The use of a freewheel in the inter-axle drive to disconnect one of the driving axles, and limited-slip differentials is considered, and it is shown that shift of the vehicle centre of turn during cornering is in quadratic relation to speed and the vehicle design parameters. (M.I.R.A.)
13.
P. Lugner (Tech. Univ., Vienna). Numerical expression of tyre characteristics for the calculation of vehicle motions. A . T . Z . 74 (1), 17-23. (January 1972) It is shown that tyre characteristics can be expressed by mathematical approximation, which is derived partly analytically and partly through interpolation. Tyre side-force is expressed as a function of tyre slip-angle, tyre contact-force and circumferential force. Forces and moments at the tyre are considered, and the various parameters describing tyre and road effects are introduced. Those values which are essential for the description of vehicle handling are discussed in more detail. The study is confined to an examination of the relationship between side force and the following: angular velocity about the vertical axis (co), angular velocity about the wheel axis (u), velocity of the wheel centre (vo), tyre slip-angle (u), camber angle (~,), tyre contact-force (P), tangential force (T), tyre design and material (b,), tread depth (h) and pattern (F), tyre pressure (P,) and tyre slip and adhesion (~t~).The results of laboratory and road tests which have examined the relation between side force and the various parameters mentioned above are discussed. It is stated that the relationships have not yet been satisfactorily investigated in all cases. Typical tyre characteristics are presented for traditional cross-ply tyres, side force being shown as a function of slip angle, circumferential force and contact force. Tyre design affects the shape of the characteristic curves. Since available tyre characteristics for side force as a function of circumferential force and slip angle have been experimentally determined only for certain values of the tyre contact-force, these curves must be developed analytically to permit use of this information for other values of the contact force. An approximation function is presented of the form S = G (P, ~). F(P, T, a). In this formula, the function G(P, ~) describes, for a given tyre and a given road surface, the dependence of side force S on tyre contact force and slip angle for circumferential force T = O. Function Fexpresses the change in side 2orce due to T. For function F, the condition F(c~, P , T = 0) = 1 must be fulfilled, so that G(P, a) can be equalled to S' (P, ct). With this formula, the measured tyre characteristics are replaced by distorted ellipsoid curves whose centres are displaced relative to the origin of co-ordinates (parameters kl, U), whose axes are inclined relative to the co-ordinate axes (parameter k2) and whose minor axes are fitted to the measured data according to a and P. The calculation procedure including the determination of k~ and k~, is set out. Calculated tyre characteristics are shown for various tyre contact-forces and slip angles. The form of approximation offered is thought to be justifiable in view of the relatively wide variation in measured side forces, even for tyres of the same production series. The method of interpolation is well suited for computer calculation. With a maximum value for ct = 12 deg and for P twice the static tyre load, this method of representing tyre characteristics is able to describe car handling up to the limits of normal driving. ( M . I . R . A . )
14.
B. I. Morozov et. al. (Moscow Automech. Inst.). On the method of investigating and evaluating vehicle handling. Avtom. Prom. No. 11, 12 14 (November 1971) Although vehicle-handling should be evaluated, from the point of view of greatest accuracy, in terms of the vehicle-environment- driver, it is well known that the individual changes the structure and numerical values of his characteristics according to the circumstances surrounding the driving function. As a result, the structure and parameters of the description of driver behaviour are defined by a non-steady-state function, which materially complicates direct calculation of the motion of a vehicle system including the driver. A way out of this situation (since the requisite