# The Bearing Stiffness Effect on In-Wheel Motors

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Bearing Function in IWM

_{X-Y}, which acts via pneumatic tire’s effective rolling radius and rim, as shown in Figure 4. F

_{Y}is shown as an example for left cornering shown as F

_{Y-L}in Figure 3.

_{X-Z}is much smaller since it is resulting from the vertical force and the small distance from the tire center to the point of rotational deflection. As identified, the most critical loads are severe braking, cornering and driving over a road pothole/obstacle causing an impact load. M

_{X-Z}from vertical impacts or M

_{X-Y}from severe cornering can reach values that result in large deflection angles and should be anticipated during the design stage. Hub bearing deflection is less problematic for conventional vehicle corners, where the deflection acts on the movement of disc brake towards braking pads inside the caliper (Figure 5). The objective of every brake manufacturer is to design a braking assembly, which will be functional and not affect wheel rotation during severe cornering.

## 3. Understanding the Mechanism of Bearing Deflection

_{1}and F

_{2}being the applied forces and δ

_{1}, δ

_{2}the resulting deformations in nodes 1 and 2, respectively [23]. Stiffness matrix of a double row angular contact ball bearing is obviously more complex; however, many publications exist that differ in mathematical models and geometry of analyzed bearing layouts. Figure 10 schematically represents the existing approaches for the definition of the stiffness matrix for a double row ball bearing.

_{j}represents the resulting normal load on a single rolling element at position j, K

_{n}is a stiffness constant accounting for geometry and material (also known as Hertzian stiffness constant or load-deflection factor), and n is a value (exponent) defining the nature of the contact; for point contacts (i.e., ball bearings) n = 1.5 [18]. By adding the contribution from each rolling element, (3) can be translated into a complex relationship between the bearing load vector (${f}_{\mathrm{b}}$) and the bearing deflection vector $\left({q}_{\mathrm{b}}\right)$ [25]. Bearing stiffness matrix can then be obtained by applying the mathematical definition of stiffness and taking partial derivatives of each load term against each deflection term.

## 4. Loads on IWM

_{X}being the bending moment in longitudinal direction, F

_{Y}force in the axial direction, R

_{w}the tire radius, F

_{Z}the vertical force on the tire and a, the axial distance between the middle of the contact patch and the middle of both ball raceways of the bearing, M

_{Z}the vertical bending moment and F

_{X}the longitudinal force. The distances R

_{W}and a are not fixed. During cornering the extra weight on outer wheels compress the tires so much that M

_{X-Y}decreases (–4% of M

_{X}) and due to the axial deformation on the tire M

_{X-Z}increases (+8% of M

_{X}).

## 5. Determination of Stiffness

## 6. Validation of Hub Bearing Stiffness on Test Rig

**Load Case 1**with the use of only one hydraulic cylinder generating F

_{k2}, resulting in 7.2 kN of compressive axial force and 4500 Nm of bending moment acting on the bearing.

**Load Case 2**with the use of both hydraulic cylinders generating F

_{k1}and F

_{k2}, each applying a force up to 3.6 kN resulting in 4500 Nm of pure bending moment acting on the bearing.

**Load Case 3**with the use of only one hydraulic cylinder generating F

_{k1}, resulting in 7.2 kN of tensile axial force and 4500 Nm of bending moment acting on the bearing. Figure 22 shows measurements for load case 2, which results in the highest deformations from all three scenarios.

## 7. Validation of IWM Stiffness

_{X-Mag}can be integrated over all magnets, presuming a pure bending of the rotor by:

_{Yi}is the axial force of i-th magnet, and Z

_{i}is the vertical position of i-th magnet. After integration the results show that this counter moment of force is of the order of magnitude of 1% of the bending moment resulting from the road; thus, the stiffness contribution from magnets is small and can be neglected.

## 8. Results

## 9. Conclusions

## 10. Patents

- WO2012138303A2; Electromagnetic design: Compact multiphase wave winding of a high specific torque electric machine.
- WO2018124971A1; 23465; Electromagentic design of in-wheel motors: Arrangement for determining maximum allowable torque.
- CT/EP2017/081085; WO/2012/138303/A2; Electric machine with a cooling system and a method for cooling an electric machine.
- SI23465; WO/2013/180663; Electrical gear for electric vehicles with direct drive.
- SI23406; Electric machine with reduced holding torque, with torque vibration and unchanged torque constant.
- PCT/EP2017/079793; WO/2018/095868; Integrated electric gear and charger system for battery powered electric vehicles.
- EP3340439; USA: 20180183292 and EPO: 3340439; Voltage balanced winding pattern for an electric machine with a minimal number of connections and method for assembly of such winding.
- PCT/SI2016/000030; WO/2018/124971; Arrangement for determining maximum allowable torque.
- WO/2019/098949; Method and apparatus for compact insertion of multiphase pseudo helical wave winding into electrical machine.
- WO/2019/139545; In-wheel electric motor maintenance integration.
- WO/2019/151956; Integrated gap retention element for electric motor.
- WO/2020/00966; Electric vehicle energy balance crediting and debiting system and a method thereof.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Elaphe Propulsion Technologies, Ltd. Internal archive (formats: .pdf, .cae, .odb, .sldprt, .sldasm, .stp, .sat); Elaphe Propulsion Technologies, Ltd.: Ljubljana, Slovenia, 2017. [Google Scholar]
- Vallance, A. Advanced In-Wheel Electric Propulsion Technology. Protean Electric, The Centre For Sustainable Design. 2010. Available online: https://cfsd.org.uk/pdf/March%202010%20General%20Presentation%20-%20CFSD%20lecture%204.pdf (accessed on 15 June 2019).
- Perovic, D.K. Making the Impossible, Possible–Overcoming the Design Challenges of in Wheel Motors. World Electr. Veh. J.
**2016**, 5, 514–519. [Google Scholar] [CrossRef][Green Version] - Ifedi, C.J.; Mecrow, B.C.; Brockway, S.T.M.; Boast, G.S.; Atkinson, G.J.; Kostic-Perovic, D. Fault tolerant in-wheel motor topologies for high performance electric vehicles. In Proceedings of the 2011 IEEE International Electric Machines Drives Conference, Niagara Falls, ON, Canada, 14–17 May 2010; pp. 1310–1315. [Google Scholar]
- Cakir, K. In-Wheel Motor Design for Electric Vehicles. Ph.D. Thesis, Sabanci Unversity, Tuzla, Turkey, 2004. [Google Scholar]
- Gruber, W.; Back, W.; Amrhein, W.; Bäck, W. Design and implementation of a wheel hub motor for an electric scooter. In Proceedings of the 2011 IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, 6–9 September 2011; pp. 1–6. [Google Scholar]
- Pérez, S.R. Analysis of a Light Permanent Magnet In-Wheel Motor for an Electric Vehicle with Autonomous Corner Modules; Royal Institute of Technology (KTH): Stockholm, Sweden, 2011. [Google Scholar]
- Heim, R.; Hanselka, V.; El Dsoki, C. Technical potential of in-wheel motors. ATZ
**2012**, 114, 4–9. [Google Scholar] - Wang, R.; Wang, J. Fault-Tolerant Control with Active Fault Diagnosis for Four-Wheel Independently Driven Electric Ground Vehicles. IEEE Trans. Veh. Technol.
**2011**, 60, 4276–4287. [Google Scholar] [CrossRef] - Vos, R. Influence of In-Wheel Motors on the Ride Comfort of Electric Vehicles; Eindhoven University of Technology: Eindhoven, The Netherlands, 2010. [Google Scholar]
- Fraser, A. In-Wheel Electric Motors. In Proceedings of the 10th International CTI Symposium, Novi, MI, USA, 9–12 May 2016. [Google Scholar]
- Nagaya, G. Development of an in-wheel drive with advanced dynamic-damper mechanism. JSAE Rev.
**2003**, 24, 477–481. [Google Scholar] [CrossRef] - Biček, M.; Gotovac, G.; Miljavec, D.; Zupan, S. Mechanical Failure Mode Causes of In-Wheel Motors. Strojniški Vestnik J. Mech. Eng.
**2015**, 61, 74–85. [Google Scholar] [CrossRef][Green Version] - Ziehl-Abegg Automotive GmbH. ZAwheel—Movement by perfection, ZAwheel In-Wheel Hub Motor. 2014. Available online: http://www.ziehl-abegg.com/gb/en/product-range/automotive/ (accessed on 30 July 2019).
- Wong, J.Y. Theory of Ground Vehicle, 3rd ed.; John Wiley & SONS, Inc.: New York, NY, USA, 2001. [Google Scholar]
- Shevket, C. Asymmetric Hub Assembly. U.S. Patent 10964013, 13 October 2004. [Google Scholar]
- NTN. Hub Bearings—CAT. No. 4601/E, CAT. No. 4601/E. 2014. Available online: http://www.ntnamericas.com/en/website/documents/brochures-and-literature/catalogs/hub_bearings_4601.pdf (accessed on 15 June 2019).
- Harris, T.A.; Kotzalas, M.N. Essential Concepts of Bearing Technology, 5th ed.; Taylor & Francis: Boca Raton, FL, USA, 2007. [Google Scholar]
- Yang, M. A Study on the Lateral Stiffness of the Passenger Car Suspension. In Proceedings of the 2012 SIMULIA Customer Conference, Providence, RI, USA, 15–17 May 2012; pp. 1–21. [Google Scholar]
- Koyama, T. Applying FEM to the Design of Automotive Bearings. Motion Control
**1997**, 2, 23–30. [Google Scholar] - Kajihara, K. Improvement of Simulation Technology for Analysis of Hub Unit Bearing. KOYO Eng. J. Engl. Ed.
**2005**, 167, 35–39. [Google Scholar] - Lee, I.; Cho, Y.; Cho, Y.; Kim, M.; Jang, C.; Lee, Y.; Lee, S. Development of Stiffness Analysis Program for Automotive Wheel Bearing. In Proceedings of the 2012 SIMULIA Customer Conference, Providence, RI, USA, 15–17 May 2012. [Google Scholar]
- Rothbart, H.; Brown, T.H. Mechanical Design Handbook, 2nd ed.; McGraw-Hill: New York, NY, USA, 2006. [Google Scholar]
- Gunduz, T.H.; Singh, R. Stiffness matrix formulation for double row angular contact ball bearings: Analytical development and validation. J. Sound Vib.
**2013**, 332, 5898–5916. [Google Scholar] [CrossRef] - ISO. ISO 4138:2012—Passenger Cars—Steady-State Circular Driving Behavior—Open-Loop Test Methods; ISO: Geneva, Switzerland, 2012. [Google Scholar]
- ISO. ISO 16750-3:2007(E)—Road Vehicles—Environmental Conditions and Testing for Electrical and Electronic Equipment—Part 3: Mechanical Loads; ISO: Geneva, Switzerland, 2007. [Google Scholar]
- Frajnkovic, M.; Omerovic, S.; Rozic, U.; Kern, J.; Connes, R.; Rener, K.; Biček, M. Structural Integrity of In-Wheel Motors. In Proceedings of the International Powertrains, Fuels & Lubricants Meeting, Heidelberg, Germany, 18 September 2018; Volume 1, p. 11. [Google Scholar]
- Gunduz, A.; Dreyer, J.T.; Singh, R. Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly: Experiments on double row angular contact ball bearings. Mech. Syst. Signal Process.
**2012**, 31, 176–195. [Google Scholar] [CrossRef] - Gerhard, F.; Grubisić, V.; Fischer, G.; Grubisić, V.; Grubišić, V. Biaxial Wheel/Hub Test Facility; Report No. TB-221; Fraunhofer Institute for Structural Durability and System Reliability LBF Darmstadt: Darmstadt, Germany, 2001. [Google Scholar]
- SAE International. SAE International J328/2005-2—Wheels; Passenger Car and Light Truck Performance Requirements and Test Procedures; SAE International: Warrendale, PA, USA, 2009. [Google Scholar]
- Biček, M. Modelling and Optimization of In-Wheel Motor Mechanical Design. Ph.D. Thesis, University of Ljubljana, Ljubljana, Slovenia, 2019. [Google Scholar]

**Figure 1.**Internal Combustion Engines (ICE) drivetrain with an all-wheel drive with obvious complexity [1].

**Figure 2.**In-Wheel Motor (IWM) propulsion platform with Elaphe M700 all-wheel drive showing simplicity [1].

**Figure 5.**Conventional suspension with components in display. Hub bearing deflection angle β is limited by braking pads inside the caliper and can be larger in comparison to when integrated inside an IWM.

**Figure 6.**Elaphe M700 IWM with central hub bearing layout in section cut and air gap in schematic circumference.

**Figure 8.**Hub bearing section cut with schematically applied bending moment M

_{X}resulting in deflection angle β of rotational part in relation to static part.

**Figure 9.**Radial tolerance stack (TS) path of an IWM with integrated drum brake in section cut. X markings are presenting press fits without effect on TS.

**Figure 10.**(

**a**) Schematic view of an assembled double row bearing [24]; (

**b**) model with two stiffness matrices; (

**c**) model with one stiffness matrix. (

**b**) and (

**c**) with multi-dimensional non-linear springs (no torsional stiffness).

**Figure 12.**Lateral force linked with weight transfer on front wheels depending on the lateral acceleration.

**Figure 13.**Photo from one of the test sessions, where accelerations were measured for severe cornering.

**Figure 14.**Simulated version for severe cornering shown in Figure 12.

**Figure 16.**Input data for standard BMW X6 front bearing in the analytical bearing design/analysis tool.

**Figure 17.**Analytically calculated bearing deflection without including the elastic deformation of bearing housing.

**Figure 19.**Visualization of results for a numerical simulation of BMW X6 M front bearing Y-plane deformation in [mm] with maximum bending moment applied around Y axis.

**Figure 20.**BMW X6 front bearing on the deflection test rig at the University of Ljubljana (UL), Faculty of Mechanical Engineering (FME) [27].

**Figure 22.**Bearing deflection measurement results for different hub bearings, original in specified vehicles and pure bending load case [1].

**Figure 23.**IWM in Wheel Accelerated Life test (WALT) for endurance testing at Fraunhofer LBF [1].

**Figure 24.**Measurements of the deflection for analyzed IWM with BMW X6 hub bearing before and after the endurance sequence [1].

**Figure 25.**Temperature measurements with timestep 1 ms on the hub bearing, directly above ball (green) and 15 mm away (blue) during the first characterization and cornering sequences as shown on Figure 8.

**Figure 26.**Thermal pictures of the motor when the radial endurance sequence starts (from 0 to 15 min) [1].

**Table 1.**Obtainable research on hub bearing deflection angle done for conventional vehicles, used load cases and concluding deflections.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Biček, M.; Connes, R.; Omerović, S.; Gündüz, A.; Kunc, R.; Zupan, S. The Bearing Stiffness Effect on In-Wheel Motors. *Sustainability* **2020**, *12*, 4070.
https://doi.org/10.3390/su12104070

**AMA Style**

Biček M, Connes R, Omerović S, Gündüz A, Kunc R, Zupan S. The Bearing Stiffness Effect on In-Wheel Motors. *Sustainability*. 2020; 12(10):4070.
https://doi.org/10.3390/su12104070

**Chicago/Turabian Style**

Biček, Matej, Raphaël Connes, Senad Omerović, Aydin Gündüz, Robert Kunc, and Samo Zupan. 2020. "The Bearing Stiffness Effect on In-Wheel Motors" *Sustainability* 12, no. 10: 4070.
https://doi.org/10.3390/su12104070