# Addressed Fiber Bragg Structures in Load-Sensing Wheel Hub Bearings

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## Abstract

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## 1. Introduction

## 2. Load-Sensing Bearings in Automotive Applications

_{x}is the longitudinal velocity of the vehicle, ω

_{w}is the angular velocity of the wheel, and r

_{w}is the wheel dynamic radius.

_{r}is the radial load applied to the inner ring of the bearing).

## 3. AFBS Interrogation Principle

_{i}and B

_{i}are the amplitudes of the AFBS spectral components, ω

_{i}is the frequency of the left spectral component of the i-th AFBS, Ω

_{i}is the address frequency, and φ

_{Ai}and φ

_{Bi}are the phases. It must be noted that the proposed mathematical representation of the AFBS spectrum does not take into account the spectral shape of the transparency windows, which can be described using the Gaussian (in case of 2λ-FBG [31]) or Lorentz (in case of 2π-FBG [27]) functions.

_{i}is proportional to the amplitudes of the AFBS optical spectral components A

_{i}and B

_{i}. The amplitudes A

_{i}and B

_{i}are defined by the parameters u and v of the linear function describing the frequency response of the optical filter with inclined frequency response ((3) in Figure 3):

_{0}is the amplitude of the optical spectral component of the AFBS prior to entering the filter with inclined linear frequency response. By measuring the amplitude of the photodetector output signal at the address frequency Ω

_{i}, it is possible to define the central frequency shift (or the frequency of the left spectral component ω

_{i}) of the AFBS. However, due to the appearance of the additional frequency components in the last sum of Expression (4), the filtering of the signal at the address frequencies is required.

## 4. Modeling of Vehicle Dynamics

_{L}= 0.2, and the friction of the right side was μ

_{R}= 0.5, which imitates the possible road conditions at low temperatures. The maneuver included braking from the initial velocity of 65 km/h to a standstill with the constant pressure of 15 MPa applied to the brake master cylinder. The ABS was activated during the test in order to eliminate skidding. The profiles of the vehicle longitudinal velocity and steering wheel angle are presented in Figure 4b. As can be seen, the virtual driver applied a certain steering input in order to compensate for the yaw moment generated due to the inequality of left and right wheel forces.

## 5. Modeling of Bearing Outer Ring Deformation

_{r}is the radial load applied to the inner ring of the bearing, x is the position of the sensor (i.e., the point at which the strain is estimated), and a and b are the load positions relative to the left end and the right end of the beam, respectively.

_{x}is the tangential strain at ‘x’ distance from the left end of a beam; E is Young’s modulus; I is the area moment of inertia of a cross-section of the beam; y is distance from the neutral axis, where the strain is calculated (i.e., half of the outer ring thickness); and L = a + b is the beam length (i.e., half of the perimeter of the outer ring circumference).

## 6. Modeling of AFBS Interrogation

_{P}is the shift of the central frequency due to the deformation, Δf

_{T}is the shift of the central frequency due to temperature exposure, and c

_{i,j}are calibration coefficients.

_{i}are calibration coefficients. Applying Equation (11) to the simulation and taking into account a typical gauge factor of FBGs equal to 1.2 pm of wavelength shift per microstrain applied to the fiber [40], the central frequency of the AFBS is calculated for five cases: without strain, at t = 6.35 s from the beginning of the maneuver for both front left and front right bearings, and at t = 6.8 s for both front left and front right bearings. The diagram showing the relative positions of the AFBS spectra and the filter with an inclined frequency response for the abovementioned cases is presented in Figure 10a.

## 7. Experimental Results

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Pretagostini, F.; Ferranti, L.; Berardo, G.; Ivanov, V.; Shyrokau, B. Survey on Wheel Slip Control Design Strategies, Evaluation and Application to Antilock Braking Systems. IEEE Access
**2020**, 8, 10951–10970. [Google Scholar] [CrossRef] - Aksjonov, A.; Augsburg, K.; Vodovozov, V. Design and Simulation of the Robust ABS and ESP Fuzzy Logic Controller on the Complex Braking Maneuvers. Appl. Sci.
**2016**, 6, 382. [Google Scholar] [CrossRef] - Viehweger, M.; Vaseur, C.; Van Aalst, S.; Acosta, M.; Regolin, E.; Alatorre, A.; Desmet, W.; Naets, F.; Ivanov, V.; Ferrara, A.; et al. Vehicle State and Tyre Force Estimation: Demonstrations and Gudelines. Veh. Syst. Dyn.
**2020**, 232, 1883–1930. [Google Scholar] [CrossRef] - Canudas-de-Wit, C.; Tsiotras, P.; Efstathios, V.; Michel, B.; Gissinger, G.L. Dynamic Friction Models for Road/Tire Longitudinal Interaction. Veh. Syst. Dyn.
**2003**, 39, 189–226. [Google Scholar] [CrossRef] - Jousimaa, O.J.; Xiong, Y.; Niskanen, A.J.; Tuononen, A.J. Energy harvesting system for intelligent tyre sensors. In Proceedings of the 2016 IEEE Intelligent Vehicles Symposium (IV), Gothenburg, Sweden, 19–22 June 2016. [Google Scholar] [CrossRef]
- Hopping, K.; Augsburg, K.; Buchner, F. Extending the HSRI tyre model for large inflation pressure changes. In Proceedings of the Engineering for a Changing World: 59th IWK, Technische Universität Ilmenau, Ilmenau, Germany, 11–15 September 2017. [Google Scholar]
- Vehicle Dynamics, Durability and Tire Testing. Kistler Group (2020). Available online: https://www.kistler.com/en/applications/automotive-research-test/vehicle-dynamics-durability/tire-testing/ (accessed on 24 August 2020).
- Coppo, F.; Pepe, G.; Roveri, N.; Carcaterra, A. A Multisensing Setup for the Intelligent Tire Monitoring. Sensors
**2017**, 17, 00576. [Google Scholar] [CrossRef] [PubMed] - Carcaterra, A.; Roveri, N.; Gianluca, P. OPTYRE—A new technology for tire monitoring: Evidence of contact patch phenomena. Mech. Syst. Signal Process
**2015**, 66–67, 793–810. [Google Scholar] [CrossRef] - Roveri, N.; Pepe, G.; Mezzani, F.; Carcaterra, A.; Culla, A.; Milana, S. OPTYRE—Real Time Estimation of Rolling Resistance for Intelligent Tyres. Sensors
**2019**, 19, 5119. [Google Scholar] [CrossRef][Green Version] - Xiong, Y.; Juhani, A. A multi-laser sensor system to measure rolling deformation for truck tyres. Veh. Perform.
**2017**, 3, 115–126. [Google Scholar] [CrossRef] - Xiong, Y.; Juhani, A. Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach. J. Terramechanics
**2015**, 61, 33–42. [Google Scholar] [CrossRef] - Matsuzaki, R.; Hiraoka, N.; Todoroki, A.; Mizutani, Y. Strain Monitoring and Applied Load Estimation for the Development of Intelligent Tires Using a Single Wireless CCD Camera. J. Solid Mech. Mater. Eng.
**2012**, 6, 935–949. [Google Scholar] [CrossRef][Green Version] - Mendoza-Petit, M.F.; Garcia-Pozuelo, D.; Olatunbosun, O.A. A Strain-Based Method to Estimate Tire Parameters for Intelligent Tires under Complex Maneuvering Operations. Sensors
**2019**, 19, 2973. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mendoza-Petit, M.F.; Garcia-Pozuelo, D.; Díaz, V.; Olatunbosun, O.A. A Strain-Based Intelligent Tire to Detect Contact Patch Features for Complex Maneuvers. Sensors
**2020**, 20, 1750. [Google Scholar] [CrossRef] [PubMed] - Singh, K.B.; Taheri, S. Accelerometer Based Method for Tire Load and Slip Angle Estimation. Vibration
**2019**, 2, 11. [Google Scholar] [CrossRef][Green Version] - Suzuki, M.; Nakano, K.; Miyoshi, A.; Katagiri, A.; Kunii, M. Method for Sensing Tire Force in Three Directional Components and Vehicle Control Using This Method. SAE Tech. Paper 2007-01-0830 2007
**2007**. [Google Scholar] [CrossRef] - Ohkubo, N.; Horiuchi, T.; Yamamoto, O.; Inagaki, H. Brake Torque Sensing for Enhancement of Vehicle Dynamics Control Systems. SAE Tech. Paper 2007-01-0867
**2007**. [Google Scholar] [CrossRef] - Den Engelse, J. Estimation of the Lateral Force, Acting at the Tire Contact Patch of a Vehicle Wheel, Using a Hub Bearing Unit Instrumented with Strain Gauges and Eddy-current Sensors. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2013. [Google Scholar]
- Kerst, S.; Shyrokau, B.; Holweg, E. Reconstruction of Wheel Forces Using an Intelligent Bearing. SAE Int. J. Passeng. Cars–Mech. Syst.
**2016**, 9, 196–203. [Google Scholar] [CrossRef] - Nishikawa, K. Hub Bearing with Integrated Multi-axis Load Sensor. Tech. Rev.
**2011**, 79, 58–63. [Google Scholar] - Kerst, S.; Shyrokau, B.; Holweg, E. A model-based approach for the estimation of bearing forces and moments using outer-ring deformation. IEEE Trans. Ind. Electron.
**2019**, 67, 461–470. [Google Scholar] [CrossRef] - Gandhi, N. Load Estimation and Uncertainty Analysis Based on Strain Measurement: With Application to Load Sensing Bearing. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2013. [Google Scholar]
- Sakhabutdinov., A.Z.; Agliullin, T.A.; Gubaidullin, R.R.; Morozov, O.G.; Ivanov, V.; Sakhabutdinov, A.Z.; Agliullin, T.A.; Gubaidullin, R.R.; Morozov, O.G.; Ivanov, V. Numerical Modeling of Microwave-Photonic Sensor System for Load Sensing Bearings. In Proceedings of the 2020 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF), Saint-Petersburg, Russia, 1–5 June 2020. [Google Scholar] [CrossRef]
- Dincmen, E.; Güvenç, B.A.; Acarman, T. Extremum-Seeking Control of ABS Braking in Road Vehicles with Lateral Force Improvement. IEEE Trans. Control Syst. Technol.
**2014**, 22, 230–237. [Google Scholar] [CrossRef] - Pacejka, H. Tire and Vehicle Dynamics, 3rd ed.; Butterworth-Heinemann: Oxford, UK, 2012; pp. 87–147. [Google Scholar]
- Sahabutdinov, A.Z.; Morozov, O.G.; Agliullin, T.A.; Gubaidullin, R.R.; Ivanov, V. Modeling of Spectrum Response of Addressed FBG-Structures in Load Sensing Bearings. In Proceedings of the 2020 Systems of Signals Generating and Processing in the Field of on Board Communications, Moscow, Russia, 19–20 March 2020. [Google Scholar] [CrossRef]
- Sakhabutdinov, A.Z.; Morozov, O.G.; Morozov, G.A. Universal Microwave Photonics Approach to Frequency-Coded Quantum Key Distribution. In Advanced Technologies of Quantum Key Distribution; Gnatyuk, S., Ed.; IntechOpen: London, UK, 2018. [Google Scholar] [CrossRef][Green Version]
- Morozov, O.; Sakhabutdinov, A.; Anfinogentov, V.; Misbakhov, R.; Kuznetsov, A.; Agliullin, T. Multi-Addressed Fiber Bragg Structures for Microwave-Photonic Sensor Systems. Sensors
**2020**, 20, 2693. [Google Scholar] [CrossRef] - Gubaidullin, R.R.; Sahabutdinov, A.Z.; Agliullin, T.A.; Morozov, O.G.; Ivanov, V. Application of Addressed Fiber Bragg Structures for Measuring Tire Deformation. In Proceedings of the 2019 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO), Yaroslavl, Russia, 1–3 July 2019. [Google Scholar] [CrossRef]
- Gubaidullin, R.R.; Agliullin, T.A.; Nureev, I.I.; Sahabutdinov, A.Z.; Ivanov, V. Application of Gaussian Function for Modeling Two-Frequency Radiation from Addressed FBG. In Proceedings of the 2020 Systems of Signals Generating and Processing in the Field of on Board Communications, Moscow, Russia, 19–20 March 2020. [Google Scholar] [CrossRef]
- Agliullin, T.A.; Gubaidullin, R.R.; Ivanov, V.; Morozov, O.G.; Sakhabutdinov, A.Z. Addressed FBG-structures for tire strain measurement. In Proceedings of the SPIE 11146, Optical Technologies for Telecommunications 2018, Ufa, Russian Federation, 20–22 November 2018; p. 111461. [Google Scholar] [CrossRef]
- Morozov, O.G.; Sakhabutdinov, A.J. Addressed fiber Bragg structures in quasidistributed microwave-photonic sensor systems. Comput. Opt.
**2019**, 43, 535–543. [Google Scholar] [CrossRef] - Morozov, O.G.; Sakhabutdinov, A.Z.; Nureev, I.I.; Misbakhov, R.S. Modelling and record technologies of address fibre Bragg structures based on gratings with two symmetrical pi-phase shifts. J. Phys. Conf. Ser.
**2019**, 1368, 022048. [Google Scholar] [CrossRef] - Gubaidullin, R.R.; Agliullin, T.A.; Morozov, O.G.; Sahabutdinov, A.Z.; Ivanov, V. Microwave-Photonic Sensory Tire Control System Based on FBG. In Proceedings of the 2019 Systems of Signals Generating and Processing in the Field of on Board Communications, Moscow, Russia, 20–21 March 2019. [Google Scholar] [CrossRef]
- Oswald, F.B.; Zaretsky, E.V.; Poplawski, J.V. Effect of Internal Clearance on Load Distribution and Life of Radially Loaded Ball and Roller Bearings. Tribol. Trans.
**2012**, 55, 245–265. [Google Scholar] [CrossRef] - Sakhabutdinov, A.Z.; Nureev, I.I.; Morozov, O.G.; Kuznetsov, A.A.; Faskhutdinov, L.M.; Petrov, A.V.; Kuchev, S.M. Calibration of combined pressure and temperature sensors. Int. J. Appl. Eng. Res.
**2015**, 10, 44948–44957. [Google Scholar] - Gupta, P.K.; Taketa, J.I.; Price, C.M. Thermal interactions in rolling bearings. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2019**, 234, 1233–1253. [Google Scholar] [CrossRef] - Kumaran, S.S.; Velmurugan, P.; Tilahun, S. Effect on stress and thermal analysis of tapered roller bearings. J. Crit. Rev.
**2020**, 7, 492–501. [Google Scholar] [CrossRef] - Fajkus, M.; Nedoma, J.; Martinek, R.; Vasinek, V.; Nazeran, H.; Siska, P. A Non-Invasive Multichannel Hybrid Fiber-Optic Sensor System for Vital Sign Monitoring. Sensors
**2017**, 17, 111. [Google Scholar] [CrossRef] - Lai, M.; Karalekas, D.; Botsis, J. On the Effects of the Lateral Strains on the Fiber Bragg Grating Response. Sensors
**2013**, 13, 2631–2644. [Google Scholar] [CrossRef]

**Figure 1.**Dependence of longitudinal wheel force on the wheel slip ratio for different conditions of the road surface [25].

**Figure 2.**Sensor position relative to the rolling elements at maximum and minimum of measured strain.

**Figure 3.**Structure of the interrogation system for two addressed fiber Bragg structure (AFBS)-based sensors: (1) wideband light source, (2.1, 2.2) AFBS sensors, (3) optical filter with a linear inclined frequency response, (4) photodetector of the measuring channel, (5) analog-to-digital converter (ADC) of measuring channel, (6,9) fiber-optic splitters, (7) photodetector of the reference channel, (8) ADC of the reference channel, (10) fiber-optic coupler, (a) spectrum of the wideband light source, (b,c) are the spectra of light propagated through the AFBS sensors, (d) spectra of AFBS sensors at the output of the optical filter, (e) spectra of AFBSs in the reference channel; blue connection lines denote optical fibers, black connection lines represent electrical wires.

**Figure 4.**(

**a**) Visualization of the split-mu braking test. (

**b**) Vehicle longitudinal velocity (blue line) and steering wheel angle (orange line) during the split-mu braking test.

**Figure 5.**Longitudinal force of the front left wheel (blue line) and front right wheel (red line) during the split-mu braking test.

**Figure 6.**Beam model for a single-load case for estimation of the bearing outer ring deformation [23]: P is the load transmitted by a ball, P

_{r}is the load applied to the inner ring of the bearing, x is the sensor position, and a and b are the load positions relative to the left end and the right end of the beam, respectively.

**Figure 7.**Strain simulated for the front left wheel hub bearing (blue line) and front right wheel hub bearing (red line): (

**a**) for the whole duration of the split-mu braking test; (

**b**) for t = [6, 6.8] s.

**Figure 8.**Assessment of the force estimation accuracy by solving the inverse problem: (

**a**) strain simulated for the front right hub bearing (red line) and its upper envelope (blue line) shown for a short time interval; (

**b**) longitudinal wheel force obtained from the simulation (red line) and estimated force (blue line) for the whole duration of the maneuver; (

**c**) force estimation error.

**Figure 10.**(

**a**) AFBS spectra and the optical filter frequency response for five cases of applied strain: AFBS without strain (green line), front right bearing at t = 6.35 s (red solid line), front right bearing at t = 6.8 s (red dashed line), front left bearing at t = 6.35 s (blue solid line), and front left bearing at t = 6.8 s (blue dashed line); (

**b**) Corresponding spectra of electrical signal at the photodetector.

**Figure 11.**Static load test: (

**a**) prototype load-sensing bearing with AFBS sensor; (

**b**) experimental setup with a mechanical press for static load test; (

**c**) relative amplitude of the resulting beating signal at the photodetector during the static load test.

**Figure 12.**Tangential strain of the bearing measured by AFBS sensor for the whole duration of the dynamic testing procedure.

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**MDPI and ACS Style**

Agliullin, T.; Gubaidullin, R.; Sakhabutdinov, A.; Morozov, O.; Kuznetsov, A.; Ivanov, V. Addressed Fiber Bragg Structures in Load-Sensing Wheel Hub Bearings. *Sensors* **2020**, *20*, 6191.
https://doi.org/10.3390/s20216191

**AMA Style**

Agliullin T, Gubaidullin R, Sakhabutdinov A, Morozov O, Kuznetsov A, Ivanov V. Addressed Fiber Bragg Structures in Load-Sensing Wheel Hub Bearings. *Sensors*. 2020; 20(21):6191.
https://doi.org/10.3390/s20216191

**Chicago/Turabian Style**

Agliullin, Timur, Robert Gubaidullin, Airat Sakhabutdinov, Oleg Morozov, Artem Kuznetsov, and Valentin Ivanov. 2020. "Addressed Fiber Bragg Structures in Load-Sensing Wheel Hub Bearings" *Sensors* 20, no. 21: 6191.
https://doi.org/10.3390/s20216191