Now, study the suspension at rear axle in Figure 3-28. When the axle is propelled, will push the axle in under the body. This means that this design reduces the rear from squatting (transiently). The design concept for rear axle suspension to place the pivot point ahead of axle and above ground is therefore called “anti-squat”.
3.4.7.3 Anti-dive and Anti-Squat Designs
With Anti-dive front and Anti-squat rear, we avoid front lowering at braking and rear lowering at ac- celeration, respectively. But how will the designs influence the parallel tendencies: that rear tend to lift at braking and front then to lift at propulsion? Well, they will luckily counteract also these: Braking at rear axle will stretch the rear axle rearwards and upwards relative to the body. When propelling the front axle, the propulsion force will stretch the front axle forwards and upwards relative to the body. (If one brakes at one axle and propels at the other, the reasoning is not valid. This mode can be desired for a hybrid vehicle with ICE on front axle and electric motor on rear axle, if one would like to charge batteries “via the road”.)
In summary: Anti-dive and anti-squat refer to the front diving when braking and the rear squatting when acceleration. Anti-dive and anti-squat can be measured in fractions: Anti-dive for =𝑒 or = (𝑒 − ) and Anti-squat=𝑒 or = (𝑒 − ) . Normal values are typically 0.05..0.15.
3.4.8 Acceleration and Deceleration
Acceleration performance like, typically, 0-100 km/h over 5..10 s, was addressed in 3.3.6. In present Section we address the similar functionality but include larger transients, such as when wheel longitu- dinal wheel force is changed more rapidly, typically changing ± ⁄2 during 0.2-0.5 s.
3.4.8.1 Deceleration Performance *
Function definition: See 3.4.2.2.
Deceleration performance can now be predicted, including the suspension mechanisms. It is a very im- portant function, and every decimetre counts when measuring braking distance in standard tests like braking from 100 to 0 km/h. The active control of the brake torques (ABS function) is then very im- portant, and this is so fast dynamics that the suspension mechanisms of Anti-lift and Anti-dive influ- ences. The position of the load in the vehicle will influence, since it influences the load transfer. We will now set up a mathematical model, see Equation [3.29], which shows how the normal forces change during a braking event. It is based on the physical model in Figure 3-28. Driving resistance con- tributes normally with a large part of the deceleration, but we will neglect this for simplicity, just to show how the suspension mechanism works. The equations in the model are presented in the dynamic modelling standardized format “Modelica”, and are hence more or less identical to Equation [3.23] to
Ffx = if 1 < time and time < 3 then -0.4*m*g else 0; Frx = if 3 < time and time < 7 then -0.4*m*g else 0; Tsf/Rw = 0;
Tsr/Rw = if 5 < time and time < 7 then -0.4*m*g else 0; // Motion equations:
der(z) = vz; der(py) = wy;
// Constitutive equations for the springs: der(Fsf) = -cf*vfz;
der(Fsr) = -cr*vrz;
// Constitutive equations for the dampers: Fdf = -df*vfz;
Fdr = -dr*vrz;
//(Dynamic) Equilibrium equations: -m*(der(vx)-vz*wy) + Ffx + Frx = 0;
-m*(der(vz)-vx*wy) - m*g + Ffz + Frz = 0;
-Jy*der(wy) + Frz*lr - Ffz*lf - (Ffx + Frx)*h = 0; (Frz - Fsr - Fdr)*gr - Frx*er + Tsr = 0; (Fsf + Fdf - Ffz)*gf - Ffx*ef + Tsf = 0; //Compatibility: zf = z - lf*py; zr = z + lr*py; vfz = vz - lf*wy; vrz = vz + lr*wy; [3.29]
The simulation results are shown in Figure 3-29. It shows a constant deceleration, but it is changed how the decelerating force is generated. At time=3 s, there is a shift from braking solely on front axle to solely on rear axle. The braking is, so far, only done with friction brakes, i.e. generating torque by taking reaction torque in the axle itself. At time=5 s, there is a shift from braking with friction brakes to braking with shaft torque. It should be noted that if we shift axle or shift way to take reaction torque, gives transients even if the deceleration remains constant.
One can also see, at time=1 s, that the normal load under the braked axle first changes in a step. This is the effect of the Anti-dive geometry. Similar happens when braking at rear axle, due to the Anti-squat geometry. Since brake performance is much about controlling the pressure rapidly, the transients are relevant, and the plots should make it credible that it is a control challenge to reach a high braking effi- ciency.
3.4.8.2 Acceleration Performance *
Function definition: See 3.3.6.1.
The model presented in Equation [3.29] can also be used to predict acceleration performance in a more accurate way compared to 3.3.6. Especially, the more accurate model is needed when propelling or braking on the limit of tyre to road adhesion, since the normal load of each tyre then is essential. It is a challenge to control the propulsion and brake wheel torques to utilize the varying normal loads under each axle.
3.4.9 Other Functions
There are many more longitudinal functions, originating from the attribute Driving dynamics, which could have fitted in 3.4. Examples of such:
• Off-road accessibility: Ability to pass obstacles of different kind, such as uneven ground, ex- treme up- and down-hills, mud depth, snow depth, etc.
• Shift quality: Quick and smooth automatic/automated gear shifts
0 1 2 3 4 5 6 7 8 9 0 50 w ithCentrifugalForce.vx 0 1 2 3 4 5 6 7 8 9 -0.02 -0.01 0.00 0.01 0.02 0.03
w ithCentrifugalForce.z [m] w ithCentrifugalForce.py [rad] w ithCentrifugalForce.zf [m] w ithCentrifugalForce.zr [m] w ithoutCentrifugalForce.z [m] w ithoutCentrifugalForce.py [rad] w ithoutCentrifugalForce.zf [m] w ithoutCentrifugalForce.zr [m] trivial_w ithCentrifugalForce.z [m] trivial_w ithCentrifugalForce.py [rad] trivial_w ithCentrifugalForce.zf [m] trivial_w ithCentrifugalForce.zr [m]
0 1 2 3 4 5 6 7 8 9 4.0E3 6.0E3 8.0E3 1.0E4 1.2E4 1.4E4
w ithCentrifugalForce.Fzf w ithCentrifugalForce.Fzr w ithoutCentrifugalForce.Fzf w ithoutCentrifugalForce.Fzr trivial_w ithCentrifugalForce.Fzf trivial_w ithCentrifugalForce.Fzr
Braking on front axle with friction brakes
Braking on rear axle with friction brakes
Braking on rear axle with shaft torque
Different displacements, both transiently and steady state
[ ]
[ ]
[ ]
py=
𝑦 [𝑟 ]Same steady state vertical forces, but transiently different
Figure 3-29: Deceleration sequence with constant vehicle deceleration but changing between different ways of actuation. (With the centripetal term 𝑦 (solid) and without (dashed). Dotted shows without anti-
dive/-squat geometry, i.e. = = . The term 𝑦 makes no visible difference.)
3.5 Control Functions
Some control functions will be described. First, some general aspects on control are given.
3.5.1 Longitudinal Control
Some of the most important sensors available in production vehicles and used mainly for longitudinal control are listed below. (Sensors for instrumented vehicles for testing can be many more.)
• Wheel Speed Sensors, WSS. For vehicle control design, one can often assume that “sensor- close” software also can supply information about longitudinal vehicle speed.
• Vehicle body inertial sensors. There is generally a yaw velocity gyro and a lateral accelerome- ter available, but sometimes also a longitudinal accelerometer. The longitudinal accelerometer is useful for longitudinal control and longitudinal velocity estimation.
• Pedal sensors. Accelerator pedal normally has a position sensor and brake pedal force can be sensed via brake system main pressure sensor. Heavy vehicles often have both a brake pedal po- sition and brake pressure sensors.
• Today’s vehicles have environment sensors (camera, radar, GPS with electronic map, etc.) that can give information (relative distance and speed, etc.) about objects ahead of subject vehicle. It can be both fixed objects (road edges, curves, hills, …) and moving objects (other road users, ani- mals, …). See also 2.7 Environment Sensing System.
• Information about what actuation that is actually applied at each time instant is available, but it should be underlined that the confidence in that information often is questionable. Infor- mation about axle propulsion torque is generally present, but normally relies on imprecise mod- els of the whole combustion process and torque transmission, based on injected amount of fuel and gear stick position. (Electric motors can typically give better confidence in estimation, espe- cially if motor is close to the wheel without too much transmission in between.) Wheel individ- ual friction brake torque is available, but normally rely on imprecise models of the brake sys- tems hydraulic/pneumatic valves and disc friction coefficient, based on brake main cylinder pressure.
• Information about what actuation levels that are possible upon request (availability or capa- bility) is generally not so common. It is difficult to agree of general definitions of such infor- mation, because different functions have so different needs, e.g. variations in accepted time de- lay for actuation.
• Sometime wheel/axle forces can be sensed. One case is when pneumatic suspension. More ex- treme variants are under development, such as sensors in the wheel bearings which can sense forces (3 forces and roll and yaw moment) and sensors in shafts.