Self-steering gradient

With the help of the self-steering gradient , the stationary self-steering behavior of two-lane motor vehicles is given quantitatively. It essentially determines the driving stability at high driving speeds.

Under self-steering behavior is defined as the property of vehicles z. B. To reduce disruptions without the driver having to do anything ( understeer ) or to increase them ( oversteer ). During normal cornering, it influences the steering wheel angle requirement.

definition

Stationary circular travel on a constant radius.

The basis for the definition of the self-steering gradient is the relationship between the steering angle and lateral acceleration during stationary circular travel. This relationship can be determined by driving tests with appropriate measuring equipment or simulations.

According to DIN  70000 or ISO 8855, the self-steering gradient is defined as the difference between the gradient of the steering angle and the Ackermann angle with respect to the lateral acceleration : ${\displaystyle \delta }$ ${\displaystyle \delta _{A}}$  ${\displaystyle a_{y}}$

${\displaystyle EG={\frac {d\delta }{da_{y}}}-{\frac {d\delta _{A}}{da_{y}}}}$

• the steering angle is calculated at a constant total steering Translation  i _S as the quotient of the steering wheel angle (index H for hand ) and total steering ratio: ${\displaystyle \delta _{H}}$

${\displaystyle \delta ={\frac {\delta _{H}}{i_{S}}}}$

• the Ackermann angle is the angle that is enclosed by the polar rays from the instantaneous pole to the front axle and to the rear axle. Approximately is:

${\displaystyle \delta _{A}\approx {\frac {l}{R}}}$

With

• ${\displaystyle l}$ wheelbase
• ${\displaystyle R}$ Curve radius .

Therefore, one can also write the equation for the self-steering gradient as:

${\displaystyle \Leftrightarrow EG={\frac {1}{i_{S}}}\cdot {\frac {d\delta _{H}}{da_{y}}}-{\frac {d\delta _{A}}{da_{y}}}}$

According to the sign of the EG:

• ${\displaystyle EG>0}$: The vehicle is understeering
• ${\displaystyle EG=0}$: Vehicle behaves neutrally
• ${\displaystyle EG<0}$: The vehicle is oversteering.

The self-steering gradient is typically specified for that transverse acceleration range in which the relationship between the steering angle and transverse acceleration can still be described as linear . In the case of cars on dry roads, this is roughly the range between 1 m / s ² and 4 m / s ² .

In the linear range, the self-steering gradient describes the part of the steering angle that is dependent on the lateral acceleration:

${\displaystyle {\begin{aligned}\delta &\approx {\frac {l}{R}}+EG\cdot a_{y}\\\Rightarrow \delta _{H}&\approx i_{S}\cdot \left({\frac {l}{R}}+EG\cdot a_{y}\right)\end{aligned}}}$

All today's cars are designed to understeer in the linear range for reasons of driving safety (see single-track model ), i. H. the self-steering gradient is always positive here. Statements such as “the vehicle behaves largely neutrally” are not applicable in the sense of the definition.

If the self-steering gradient is shown as a function of the transverse acceleration, statements about self-steering behavior in the limit area are also possible. Examples are vehicles with a rear-engine concept, which can understeer in the linear range, but oversteer in the limit range.

Measurement method

In principle, three methods can be used to determine the self-steering gradient:

• Circular travel with constant radius

${\displaystyle {\frac {d\delta _{A}}{da_{y}}}=0}$

• Circular travel at constant speed

${\displaystyle {\frac {d\delta _{A}}{da_{y}}}={\frac {l}{v^{2}}}}$

• Circle travel with constant steering wheel angle

Stationary circular travel on a constant radius is most often used. The main reason is likely to be the relatively small space requirement on the test site. More information on the test procedure is specified in ISO 4138 internationally.

Influencing variables

The main influencing variables on the self-steering gradient are axle load distribution, alternating spring rates, instantaneous center heights, tires and self-steering behavior of the axles. This is to be understood as the changes in the toe angle due to forces and moments or mutual suspension. The latter property is also known as roll steering, since the axis generates steering angles based on a roll angle.

literature

• Adam Zomotor: Driving behavior In: Jörnsen Reimpell (Hrsg.): Fahrwerktechnik . Vogel, Würzburg 1991, ISBN 3-8023-0774-7

Individual evidence

1. ↑ Dieter Schramm, Benjamin Hesse, Niko Maas, Michael Unterreiner: Vehicle technology: Technical principles of current and future motor vehicles . DE GRUYTER OLDENBOURG, 2017, ISBN 978-3-486-71620-7 , p. 87 . ( limited preview in Google Book search)
2. ^ Karl-Ludwig Haken: Fundamentals of automotive engineering . 4th edition. Hanser, 2015, ISBN 978-3-446-44216-0 , pp. 252 . ( limited preview in Google Book search)