# Study on the Road Friction Database for Automated Driving: Fundamental Consideration of the Measuring Device for the Road Friction Database

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## Abstract

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## Featured Application

**The magic formula (MF) is used to estimate the road friction characteristics.**

## Abstract

## 1. Introduction

## 2. Characteristics of Road Friction

## 3. Road Friction Estimation Method

_{B}, the following Equation (4) is introduced:

## 4. Identification Result of Road Friction Characteristics

_{P}at which the peak μ occurs is concentrated at about 5% to 10% in the wet surface conditions and around 8% to 18% in the dry surface conditions. Since most vehicles in Japan are equipped with an ABS system, the operating range when emergency braking is required is mainly near this peak μ. In order to improve the estimation accuracy of peak μ as much as possible, it is necessary to concentrate around the slip ratio s

_{P}for the identification. Therefore, the slip ratios for measurement are set to 3, 10, and 17% for the equipment designed in this paper. Therefore, the results of estimating the μ-s characteristics using the characteristics of these three points are shown for the characteristics of the three different characteristics as shown in Figure 12. Figure 12 shows the result of the identification in consideration of the above-mentioned parameter setting region, and the three points in Figure 12 are the values used for identification, and the blue line shows the experimental results and the red line shows the identification results using MF. It can be seen that K

_{B}, μ-max, s

_{P}, etc. are well represented. Therefore, regarding the experimental results conducted in the past, the comparison between the results obtained by identification and the experimental results is shown in Figure 13. These characteristics of road friction are very important factors for traffic safety, such as vehicle behavior and motion control, and so on. Focusing on these identification results, it can be seen that the correlation with the experimental results is very high (each correlation coefficient is more than 0.97) and can be an important index for traffic safety. Therefore, next, we examine a system that simultaneously measures these three points.

## 5. Consideration of the Measurement Device

_{1}= R

_{2}), the sprocket radii (r

_{1}, r

_{2}) are changed, and the slip ratios of each tire are calculated as s

_{1}and s

_{2}from the vehicle speed v and the respective speeds ω

_{1}and ω

_{2}. Here, it is assumed that the rolling resistance is small, and that the μ-s characteristics of each tire are the same. In this case, the slip ratio of the measured tire to the main tire is represented below as Equation (8) using the mechanical connection condition:

_{1}<< 1), the longitudinal force of tire 1 can be approximated as follows:

_{s}of the sensing tire is the same:

## 6. Flow of Supply for Research Results

- The tire characteristic measurement system discussed in Chapter 5 will be constructed, and the continuous characteristics of three sets of μ and s will be measured using this system.
- Using these data sets, the parameters a, b, and c at each measuring point are identified using the steepest descent method according to the recording timing. The basic idea of this is shown in Section 3.In this convergence calculation, the zones a, b, and c shown in Figure 11 are used, but in consideration of expandability, the convergence calculation is performed in the region ± 1.5 times these values.
- Using each of the obtained parameters, the braking stiffness, the peak μ values, its slip ratios, and the lock μ at each point are calculated. The basic image of the database to be constructed is shown in Figure 9.
- A database of these will be created for each road, and will be provided to autopilot vehicles or vehicles using ADAS.

## 7. Conclusion Remarks

- The equipment that measures road friction characteristics were examined, especially continuously measurement for μ-s characteristics, and it was shown that sufficient information cannot be obtained with the current equipment.
- It was shown that identification using three sets of continuous measurement results of μ-s characteristics using MF can provide identification results that can sufficiently contribute to traffic safety.
- Finally, the outline of the trailer-type measuring device using the method was shown.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- Onoda. Skid Resistance on Road Surfaces. Asphalt
**2003**, 46, 3–10. [Google Scholar] - Zaid, N.B.M.; Hainin, M.R.; Idham, M.K.; Warid, M.N.M.; Naqibah, S.N. Evaluation of Skid Resistance Performance Using British Pendulum and Grip Tester. Earth Environ. Sci.
**2019**, 220, 012016. [Google Scholar] [CrossRef] - Holzschuher, C.; Choubane, B.; Lee, H.S.; Jackson, N.M. Measuring Friction of Patterned and Textured Pavements: A Comparative Study. Transp. Res. Rec.
**2010**, 2155, 91–98. [Google Scholar] [CrossRef] - Kageyama, I.; Kobayashi, Y.; Haraguchi, T.; Asai, M.; Matsumoto, G. Study on Measurement for Friction Characteristics on Actual Road Surface. Trans. JSAE
**2020**, 51, 924–930. [Google Scholar] - Pacejka, H.B.; Bakker, E. The magic formula tire model. Supplement to Vehicle System. Dynamics
**1992**, 21, 1–18. [Google Scholar]

**Figure 1.**Sliding friction coefficient and road surface condition [1].

**Figure 9.**Image of μ-s characteristics on actual roads and of the various measurement system data [4].

**Figure 10.**Comparison between the experiment and identification results [4].

**Figure 11.**MF parameters identified from experimental data. (

**a**) Relation between μ

_{max}and parameter a. (

**b**) Relation between parameter b and c.

**Figure 12.**Identification results of μ-s characteristics by three different points (s = 3, 10, 17%).

**Figure 13.**Identification results. (

**a**) Identification result for K

_{B}. (

**b**) Identification result for μ

_{max}. (

**c**) Identification result for s

_{P}.

Peak μ | Lock μ | μ-s Characteristics | Continuity | Velocity Dependence | |
---|---|---|---|---|---|

Trailer tester Bus tester | ○ | ○ | ○ | × | ○ |

Grip tester | △ | × | × | ○ | ○ |

BP tester | × | ○ | × | × | × |

DF tester | × | ○ | × | × | ○ |

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**MDPI and ACS Style**

Kageyama, I.; Kuriyagawa, Y.; Haraguchi, T.; Kaneko, T.; Asai, M.; Matsumoto, G.
Study on the Road Friction Database for Automated Driving: Fundamental Consideration of the Measuring Device for the Road Friction Database. *Appl. Sci.* **2022**, *12*, 18.
https://doi.org/10.3390/app12010018

**AMA Style**

Kageyama I, Kuriyagawa Y, Haraguchi T, Kaneko T, Asai M, Matsumoto G.
Study on the Road Friction Database for Automated Driving: Fundamental Consideration of the Measuring Device for the Road Friction Database. *Applied Sciences*. 2022; 12(1):18.
https://doi.org/10.3390/app12010018

**Chicago/Turabian Style**

Kageyama, Ichiro, Yukiyo Kuriyagawa, Tetsunori Haraguchi, Tetsuya Kaneko, Motohiro Asai, and Gaku Matsumoto.
2022. "Study on the Road Friction Database for Automated Driving: Fundamental Consideration of the Measuring Device for the Road Friction Database" *Applied Sciences* 12, no. 1: 18.
https://doi.org/10.3390/app12010018