# A Concept for Using Road Wetness Information in an All-Wheel-Drive Control

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. State of the Art—Estimation of Tyre-Road Conditions

#### 1.2. State of the Art—Adaptation of Chassis Control Systems to Tyre-Road Sonditions

#### 1.3. Concept of This Work

## 2. Topology of the All-Wheel-Drive with Torque-on-Demand Transfer Case

#### Schematic Overview—Kinematics and Torques

## 3. Driving Dynamics Targets for All-Wheel-Drive Control in Wet Conditions

- stability:
- −
- increase in vehicle stability and avoidance of oversteer situations by influencing the vehicle balance with combined dynamics;
- −
- implementation of a suitable basic torque distribution in pull operation with partial throttle actuation and higher accelerator pedal positions; and

- traction:
- −
- increasing the longitudinal acceleration capability of the vehicle.

- agility:
- −
- maintaining lateral acceleration, especially below the driving dynamic limit of the vehicle; and

- power loss (especially for the torque-on-demand transfer case):
- −
- request of only as much all-wheel-drive torque as necessary to keep the power loss low and and to protect the component from thermal stress.

## 4. Control Strategy in Dry and Wet Conditions

#### 4.1. Control Strategy without Specific Implementation of Wetness Information

#### 4.1.1. Maximum Global Friction Limit ${\mu}_{max}$

#### 4.1.2. Wheel Loads ${F}_{z,ij}$

#### 4.1.3. Wheel Sideforces ${F}_{y,ij}$

#### 4.1.4. Used Friction Potential ${\mu}_{used}$

#### 4.1.5. Remaining Friction Potential ${\mu}_{x,pot}$ and Available Traction Force ${F}_{x,pot}$ on Front Axle

#### 4.1.6. Calculation of the Front and Rear Axle Drive Force

#### 4.2. Implementation of a Wetness Information into the Control Strategy

#### 4.2.1. Overview—Wetness Coordination Unit

#### 4.2.2. Modification of the Remaining Friction Potential ${\mu}_{x,pot}$ on the Front Axle

#### 4.2.3. Special Function—Friction Coefficient Transfer in the Event of Excess Torque

#### 4.2.4. AWD Distribution Key

## 5. Assessment Criteria and Test Manoeuvers

^{®}(Release 2010b). A comprehensive non-linear full vehicle model with 14 degrees of freedom will be used for the assessment (see Figure 8).

^{2}, the accelerator pedal is suddenly actuated up to a defined value. The maneuver is repeated twelve times for different accelerator pedal positions, which are listed in Table 4.

## 6. Simulation Results

#### 6.1. Simulation Results on Dry Conditions

#### 6.2. Simulation Results on Wet Conditions

#### 6.2.1. Drive Torque Distribution (DTD)

#### 6.2.2. Stability and Agility

#### 6.2.3. Insight into the Transient Vehicle Response

## 7. Summary

- ${f}_{y,mod}$: modification of the remaining friction potential on the front axle ${\mu}_{x,pot}$;
- ${f}_{\epsilon ,mod}$: shaping of a self-map function, called modified distribution key; and
- ${\mu}_{deficit}$: calculation of a friction deficit on the rear axle in the event of excess torque.

## 8. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ABS | anti-lock braking system |

ADAS | advanced driver assistance systems |

AFS | active front steering system |

AWD | all-wheel-drive |

DTD | drive torque distribution |

ESP | electronic stability program |

FA | front axle |

FL | front left |

FR | front right |

GO | gearbox output |

PON | power-on-cornering maneuver |

RA | rear axle |

RL | rear left |

RR | rear right |

adapt | adaptive |

eng | engine |

est | estimated |

i | placeholder for F (front axle), R (rear axle) |

j | placeholder for L (left tyre), R (right tyre) |

max | maximum |

mod | modified |

over | overshoot, excess |

pot | potential |

ref | reference |

## Appendix A. Nomenclature

Dimensionless Properties | Description | |

${\mu}_{max}$ | [-] | global friction coefficient |

${\mu}_{used}$ | [-] | used friction potential |

${\mu}_{x,pot}$ | [-] | remaining friction potential for traction |

${\mu}_{deficit}$ | [-] | friction deficit on the rear axle |

${\mu}_{transfer}$ | [-] | traction potential transferred in the event of excess |

${c}_{\mu}$ | [-] | parameter for degression of friction coefficient |

${\epsilon}_{0}$ | [-] | distribution key for the AWD torque |

${f}_{\epsilon ,mod}$ | [-] | first calibration parameter (self-map) |

${f}_{y,mod}$ | [-] | second calibration parameter |

${i}_{D,FA}$, ${i}_{D,RA}$ | [-] | front, rear axle differential ratio |

${i}_{L}$ | [-] | steering ratio |

$\tau $ | [%] | accelerator pedal actuation |

Distances | Unit | Description |

${h}_{COG}$ | [m] | center of gravity height |

${l}_{f},{l}_{r}$ | [m] | front, rear semi-wheelbase |

${r}_{dyn,FA}$, ${r}_{dyn,RA}$ | [m] | front, rear axle dynamic rolling radius |

$\rho $ | [m] | curvature radius of the vehicle trajectory |

${R}_{0}$ | [m] | initial radius (steady-state cornering) |

Torques | Unit | Description |

${T}_{FA}$, ${T}_{RA}$ | [Nm] | front, rear axle drive torque |

${T}_{outRA}$ | [Nm] | main driveshaft torque |

${T}_{GO}$ | [Nm] | gearbox output torque |

${T}_{Eng}$ | [Nm] | engine-sided driveshaft torque |

${T}_{AWD}$ | [Nm] | AWD torque (clutch) |

Forces | Unit | Description |

${F}_{x}$, ${F}_{y}$, ${F}_{z}$ | [N] | longitudinal, lateral, vertical tyre force |

${F}_{x,FA}$, ${F}_{x,RA}$ | [N] | front, rear axle traction force (sum of both tyres) |

${F}_{x,pot,FA}$, ${F}_{x,pot,RA}$ | [N] | front, rear axle potential traction force |

${F}_{x,over}$ | [N] | drive force excess |

${F}_{z,nom}$ | [N] | nominal wheel load |

Angles and Angular Velocities | Unit | Description |

${\delta}_{L}$ | [rad] | steering wheel angle |

$\beta $ | [rad] | sideslip angle |

$\dot{\psi}$ | [rad/s] | yaw velocity |

${\omega}_{FA}$, ${\omega}_{RA}$ | [rad/s] | front, rear axle rotational speed |

${\omega}_{outFA}$, ${\omega}_{outRA}$ | [rad/s] | front, rear axle rotational speed |

${\omega}_{GO}$ | [rad/s] | gearbox output rotational speed |

${\omega}_{Eng}$ | [rad/s] | engine speed |

Miscellaneous properties | Unit | Description |

g | [${\mathrm{m}/\mathrm{s}}^{2}$] | gravitational field strength |

${a}_{x}$, ${a}_{y}$ | [${\mathrm{m}/\mathrm{s}}^{2}$] | longitudinal, lateral acceleration |

m | [kg] | vehicle mass |

${P}_{loss}$ | [W] | power loss (torque-on-demand transfer case) |

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**Figure 1.**Driving mode selection in the Porsche 959 (1986–1988). Operated manually by the driver. [Source: Porsche AG].

**Figure 2.**(

**a**) Torque and (

**b**) rotational speed in the powertrain of an all-wheel-drive vehicle with torque-on-demand transfer case.

**Figure 3.**Used friction potential at PON-maneuver: (

**a**) Schematic representation on the quasi-static twin-track model. (

**b**) Used friction potential ${\mu}_{used}$ and remaining friction potential ${\mu}_{pot}$ on the outside wheel of the front axle and (

**c**) on the outside wheel of the rear axle.

**Figure 4.**Overview of the overall concept of the extended all-wheel-drive control with superordinate wetness coordination unit. Newly created parameters allow a specific calibration for wetness.

**Figure 5.**Concept idea—variable consideration of the required lateral friction potential of the front axle tyres depending on the assumed degree of wetness.

**Figure 6.**Concept idea—calculation of an excess torque and of a friction deficit ${\mu}_{deficit}$ on the rear axle when approaching full throttle.

**Figure 9.**“Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}$ = 6 m/s

^{2}) on dry road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1.0$): (

**a**) drive torque distribution (DTD) after 1s; (

**b**) normalised AWD clutch torque after 1s.

**Figure 10.**“Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}/\mathrm{s}}^{2}$) on dry road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}1.0$): (

**a**) sideslip angle difference after 1s; (

**b**) yaw rate difference after 1s.

**Figure 11.**“Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}/\mathrm{s}}^{2}$) on wet road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}0.6$): (

**a**) drive torque distribution (DTD) after 1s; (

**b**) normalised AWD clutch torque after 1s.

**Figure 12.**“Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}/\mathrm{s}}^{2}$) on wet road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}0.6$): (

**a**) sideslip angle difference after 1s; (

**b**) Yaw rate difference after 1s.

**Figure 13.**“Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}/\mathrm{s}}^{2}$) on wet road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}0.6$): (

**a**) maximum to steady-state sideslip angle; (

**b**) maximum to steady-state yaw rate.

**Figure 14.**Internal controller parameters during “Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}/\mathrm{s}}^{2}$) on wet road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}0.6$): (

**a**) distribution key ${\epsilon}_{0}$; (

**b**) modified distribution key ${f}_{mod}\left({\epsilon}_{0}\right)$; (

**c**) drive torque distribution; (

**d**) AWD clutch torque.

**Figure 15.**Vehicle motion during “Power On Cornering“ maneuver ($R\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\phantom{\rule{4.pt}{0ex}},\phantom{\rule{0.166667em}{0ex}}{a}_{y0}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}6\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}/\mathrm{s}}^{2}$) on wet road (${\mu}_{max}\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}0.6$): (

**a**) vehicle velocity; (

**b**) sideslip angle; (

**c**) yaw rate; (

**d**) curvature of the trajectory.

**Table 1.**Overview and calculation of the rotational speeds and torques in an all-wheel-drive vehicle with torque-on-demand transfer case.

Subsystem | Symbol | Equation |
---|---|---|

Rotational speeds: | ||

gearbox output | ${\omega}_{GO}$ | ${\omega}_{GO}$$={i}_{G}\phantom{\rule{0.166667em}{0ex}}{\omega}_{Eng}$ |

main drive shaft | ${\omega}_{outRA}$ | ${\omega}_{outRA}$$={i}_{k}\phantom{\rule{0.166667em}{0ex}}{\omega}_{GO}$ |

rear axle differential | ${\omega}_{outRA}$ | $({\omega}_{RL}+{\omega}_{RR})$$=2\phantom{\rule{0.166667em}{0ex}}{i}_{{D}_{RA}}\phantom{\rule{0.166667em}{0ex}}{\omega}_{outRA}$ |

front axle differential | ${\omega}_{outFA}$ | $({\omega}_{FL}+{\omega}_{FR})$$=2\phantom{\rule{0.166667em}{0ex}}{i}_{{D}_{FA}}\phantom{\rule{0.166667em}{0ex}}{\omega}_{outFA}$ |

Torques: | ||

gearbox output | ${T}_{GO}$ | ${T}_{GO}$$={i}_{G}\phantom{\rule{0.166667em}{0ex}}{T}_{Eng}$ |

main drive shaft | ${T}_{outRA}$ | ${T}_{outRA}$$={i}_{k}\phantom{\rule{0.166667em}{0ex}}{T}_{GO}-{T}_{AWD}$ |

rear axle differential | ${T}_{RA}$ | ${T}_{RA}$$=2\phantom{\rule{0.166667em}{0ex}}{i}_{{D}_{RA}}\phantom{\rule{0.166667em}{0ex}}{\omega}_{outRA}$ |

front axle differential | ${T}_{FA}$ | ${T}_{FA}$$=2\phantom{\rule{0.166667em}{0ex}}{i}_{{D}_{FA}}\phantom{\rule{0.166667em}{0ex}}{\omega}_{outFA}$ |

Power loss: | ||

AWD clutch | ${P}_{loss,AWD}$ | ${P}_{loss,AWD}$$={T}_{AWD}\phantom{\rule{0.166667em}{0ex}}\Delta {\omega}_{AWD}$ |

Calculation Module | Equation |
---|---|

Friction coefficient: | |

Friction coefficient (load dependend) | ${\mu}_{max,ij}$$={\mu}_{max,0,ij}\phantom{\rule{0.166667em}{0ex}}(1+{c}_{\mu}\phantom{\rule{0.166667em}{0ex}}d{f}_{z,ij})$ |

Tyre forces: | |

wheel loads | ${F}_{z,ij}$$={F}_{z0,ij}+{C}_{q,j}\phantom{\rule{0.166667em}{0ex}}{a}_{y}+{C}_{l,i}\phantom{\rule{0.166667em}{0ex}}{a}_{x}$ |

axle sideforces | ${F}_{y,i}$$=m\phantom{\rule{0.166667em}{0ex}}{a}_{y}\phantom{\rule{0.166667em}{0ex}}(1-{l}_{i}/l)$ |

wheel sideforces | ${F}_{y,FL}$$={F}_{y,FA}\phantom{\rule{0.166667em}{0ex}}{\left(1+{\displaystyle \frac{{\mu}_{iR}}{{\mu}_{iL}}}{\displaystyle \frac{{F}_{z,iR}}{{F}_{z,iL}}}\right)}^{-1}$ |

Used friction potential: | |

used friction potential (longitudinal) | ${\mu}_{x,used,ij}$$={\mu}_{x,ij}/{\mu}_{max,ij}$ |

used friction potential (lateral) | ${\mu}_{y,used,ij}$$={\mu}_{y,ij}/{\mu}_{max,ij}$ |

used friction potential (global) | ${\mu}_{used,ij}$$=\sqrt{{\mu}_{x,used,ij}^{2}+{\mu}_{y,used,ij}^{2}}$ |

Remaining friction potential: | |

remaining friction potential (longitud.) FA | ${\mu}_{x,pot,Fi}$$=1-{\mu}_{y,used,Fi}$ |

remaining friction potential (longitud.) RA | ${\mu}_{x,pot,Ri}$$=1-{\mu}_{used,Ri}$ |

Characteristics | Unit | Description |
---|---|---|

$\Delta {\dot{\psi}}_{1s}$ | [rad/s] | yaw rate deviation after 1s |

$\Delta {\beta}_{1s}$ | [deg] | sideslip angle deviation after 1s |

$\Delta {\beta}_{max}$ | [deg] | maximum sideslip angle deviation |

$max\left(\dot{\psi}\right)/{\dot{\psi}}_{steady-state}$ | [-] | max. yaw rate deviation (as ratio to reference yaw rate) |

${T}_{FA}/{T}_{RA}$ | [%] | Drive Torque Distribution after 1s |

${T}_{AWD}$ | [Nm] | AWD clutch torque after 1s |

${\mathit{\tau}}_{1}$ | ${\mathit{\tau}}_{2}$ | ${\mathit{\tau}}_{3}$ | ${\mathit{\tau}}_{4}$ | ${\mathit{\tau}}_{5}$ | ${\mathit{\tau}}_{6}$ | ${\mathit{\tau}}_{7}$ | ${\mathit{\tau}}_{8}$ | ${\mathit{\tau}}_{9}$ | ${\mathit{\tau}}_{10}$ | ${\mathit{\tau}}_{11}$ | ${\mathit{\tau}}_{12}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

$20\%$ | $30\%$ | $40\%$ | $50\%$ | $60\%$ | $70\%$ | $75\%$ | $80\%$ | $85\%$ | $90\%$ | $95\%$ | $100\%$ |

**Table 5.**Overview of the vehicle configurations and constraints for the investigation of the driving dynamics on dry pavement.

Naming | Maneuver Params | Controller Parameters | |||||
---|---|---|---|---|---|---|---|

Setup | ${\mathit{R}}_{0}$ | $\mathit{\mu}$ | AWD | ${\mathit{\mu}}_{\mathit{max}}$ | ${\mathit{f}}_{\mathit{y},\mathit{mod}}$ | ${\mathit{f}}_{\mathit{\epsilon},\mathit{mod}}$ | ${\mathit{a}}_{1}$ |

fixed DTD | 60 m | $1.0$ | $0\%\phantom{\rule{0.166667em}{0ex}}{T}_{FA}$ | - | - | - | - |

fixed DTD | 60 m | $1.0$ | $25\%\phantom{\rule{0.166667em}{0ex}}{T}_{FA}$ | - | - | - | - |

Adapt. N0 | 60 m | $1.0$ | adaptive | $1.0$ | 0 | ${f}_{\epsilon ,offset}$ | 70% |

**Table 6.**Overview of the vehicle configurations and constraints for the investigation of the driving dynamics on wet pavement.

Naming | Maneuver Params. | Controller Parameters | |||||
---|---|---|---|---|---|---|---|

Setup | ${\mathit{R}}_{0}$ | $\mathit{\mu}$ | AWD | ${\mathit{\mu}}_{\mathit{max}}$ | ${\mathit{f}}_{\mathit{y},\mathit{mod}}$ | ${\mathit{f}}_{\mathit{\epsilon},\mathit{mod}}$ | ${\mathit{a}}_{1}$ |

Adapt. N0 | $60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ | $0.6$ | adaptive | $0.6$ | 1 | ${f}_{\epsilon ,offset}$ | 70% |

Adapt. N1 | $60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ | $0.6$ | adaptive | $0.6$ | $0.5$ | ${f}_{\epsilon ,offset}$ | 70% |

Adapt. N2 | $60\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ | $0.6$ | adaptive | $0.6$ | 0 | ${f}_{\epsilon ,offset}$ | 70% |

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**MDPI and ACS Style**

Warth, G.; Sieberg, P.; Unterreiner, M.; Schramm, D. A Concept for Using Road Wetness Information in an All-Wheel-Drive Control. *Energies* **2022**, *15*, 1284.
https://doi.org/10.3390/en15041284

**AMA Style**

Warth G, Sieberg P, Unterreiner M, Schramm D. A Concept for Using Road Wetness Information in an All-Wheel-Drive Control. *Energies*. 2022; 15(4):1284.
https://doi.org/10.3390/en15041284

**Chicago/Turabian Style**

Warth, Georg, Philipp Sieberg, Michael Unterreiner, and Dieter Schramm. 2022. "A Concept for Using Road Wetness Information in an All-Wheel-Drive Control" *Energies* 15, no. 4: 1284.
https://doi.org/10.3390/en15041284