The University of Nottingham, Ningbo, China, 199 Taikang East Road, Ningbo, , China

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1 Increasing the road safety of e-bike: Design of protecting shell based on stability criteria during severe road accidents Lele ZHANG 1,a, Alexander KONYUKHOV 2,b,*, Edwin MOK 1,c, Hui Leng CHOO 1,d 1 The University of Nottingham, Ningbo, China, 199 Taikang East Road, Ningbo, , China 2 Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131, Karlsruhe, Germany a , Lele.ZHANG@nottingham.edu.cn, b Alexander.Konyukhov@kit.edu c Edwin Mok Hui Leng Choo, d huileng.choo@nottingham.edu.cn *Corresponding author, Alexander Konyukhov Contact Phone Number, Keywords: Passive road safety, E-bike, stability criteria during falling incident, design criteria for safety shell. Abstract. Electric bike in China has experienced enormous increase in the last decade. Traffic safety for e-bike riders becomes an issue of extensively attracting public attention because of the rapid increasing of the number of death and injuries. For the sake of reduce accidents attribute to e-bike, necessary measures, which focus on security of electric bicycle, have been taken by researchers and government. One of the standard approaches in Europe (ISO 26262) [1] and USA (FMVSS 108) [2] is to increase the passive road safety of the vehicle. The current work is proposing to employ the stability criteria based on principles of the passive road safety applied to the E-bike. This stability criteria is formulated for the case of severe road accidents during the side falling of e-bike. A safety shell protecting the driver during side falling can be designed based on this criteria. The full sequence of the proposed safety design approach includes the following steps: 1) CAD model of E-Bike prototype; 2) FEM model of various complexity; 3) formulation of Roly-Poly stability criteria; 4) FEM simulation of the road accident; 5) designing the safety shell. Roly-Poly stability criteria Stable side rolling. The motivation starts from the famous property of the Roly-Poly toy [3]. The toy rights itself when pushed over. Let us consider a general statement of problems in terms of stability of the equilibrium. The rigid body for simplicity taken in 2D - is shaped from below with a curve y (x). The body has a mass m. The center of mass is a point G is situated at height y (x) for the equilibrium situation. A geometrically exact formulation of contact conditions is necessary to describe the rolling [4]. Now consider situation of rolling contact for the profile O'P' the profile is rolled into the line OP. A center of mass is moved into a new point. One can see, that the point with coordinates (0,0) is stable during the rolling motion if during rolling to the right (left) the gravity force vectormg remains from the left (right) side from the normal reaction vectorn. This stability criteria can be formulated geometrically asy A0 h, see Fig. 1. Some knowledge from the differential geometry of curves should be involved to formulate this criteria in the form of ordinary differential equations. The profile O P is given in 2D Cartesian system asρ = { x y(x) }. The unit tangent vector to this profile is τ = dρ dρ

2 dρ 1 = { dy} with dρ = { 1 dy}and length of a vector. This allows us to write an equation for the unit normal vector based on the condition of orthogonalityas ν = { y 1 } (y ) 2 An equation of the line P'A0 is then written as y x r = ρ + ν = { x y(x) } + { y 1 } (y ) = 1 + (y ) 2 2 y(x) + { 1 + (y ) 2 } Figure 1. Rolling contact of the profile O'P'. The distanceisfound by setting (r ) x = 0. After some transformation we can find the coordinate of the point A as (r ) y = y A0 = y(x) (y ) 2 = y(x) + x 1 + (y ) 2 y 1 + (y ) 2 = y(x) + x y The last equation gives us the following differential equation for the limit case curve: y(x) + x y h The solution of this ordinary differential equation is (y h) 2 + x 2 2c = R 2

3 which is describing a circle as the limit case curve which gives us stable rolling. All smooth curves laying below this curve gives us the profile rolling on which will cause stable vibrations with the equilibrium point (0,0) in the given coordinate system, see Fig. 2. Figure 2. The limit case stability curve a circle. All smooth curves below are leading to stable rolling. Design criteria for the protecting shell no overturning during side falling. Now design criteria can be formulated as follows: All smooth curves laying below the limit circle are delivering a stable rolling vibration at zero point. However, we do not require that E-bike should be totally stable during the side rolling moreover it would lead to extremely large shell. We require that the side falling should be without turnover. In this case the curve is not starting at zero point of contact, but a certain point of possible side contact. Exact position of the limit case is regulated now by constant cand the exact shape is satisfying then equation: (y h) 2 + x 2 2c = R 2. This design criteria can be applied to each E- bike prototype in order to build the protecting shell. A road accident should be then investigated during computer simulation. The following steps are applied in order to design the protecting shell: CAD model of E-bikeprototype; Sequence of FEM models; Design of the safety shell; Finite Element Simulation of side falling road accident; Improvement of the design. Development of the safety shell

4 The proposed steps are illustrated on E-Scooter Zu Ma. We start with CAD model which will be basis for further finite element model as well as the basis to finalize the shape of the protecting shell. During this step the CAD model is simplified taking into account only 1) essential parts responsible for transmitting all loads namely all frames; 2) essential parts for contact during side falling wheels, handle and side frames, see Fig. 3. Figure 3. Simplified CAD model consists of frames, front fork, shock absorber, axles, tires, and some connectors. Pro-Engineer CAD-software. The sequence of the following Finite ElementModels can be constructed by 1. Direct import into CAD package and meshing 2. Simplified modeling in FEM package. Though, the first approach seems to be straightforward it is required, nevertheless, to model separately all connections carefully with regards to specific Finite Element. The simplest approach is then direct modeling in FEM package. In this case, various types of finite elements can be used to create the model with the most important mechanical properties. The following finite elements are provided by ANSYS used in the current finite element model: beam, pipe, shell, combine, springdamper, mass, solid, link elements. The frame is modeled using pipe elements combined with beam element; some connectors are modeled depending on geometry by shell or by solid finite elements. Combination of link, damper and combine finite elements are used in order to include shock absorber and other kinematical pairs. Finally, shell elements are used to model tires attached to the shafts by beam finite element, see Figure 4. This type of the finite element model requires specification of the total mass of the E-Bike and the driver. Though, both masses can be modelled by supplied MASS element in ANSYS, it is required to know position of the center of mass. The experimental plumb method is involved in order to determine the geometrical position of the center of gravity. Several physical pendulum tests are used to measure eigen frequency of free vibration of suspended E-Bike. This information is necessary in order to calculate the set of corresponding second moment of inertia. The mass properties of the driver can be implemented using the standard dummy model widely used in crash test modeling [5]. Both mass elements are connected to the frame using link elements.

5 Figure 4. Finite Element Model of E-Scooter. Now, the minimal model is created and can be used to add the safety shell in order to protect the driver during the side falling road accident. The strategy is as follows: selecting a typical boundary point on the side structure we can define the limit case stability curve using criteria proved above, then geometry of the shell is adjusted to the current structure, however, all the time satisfying the criteria smooth surface below the limit stability curve. In this case, the side falling will not lead to overturning. Conclusion The article presents the development of the strategy to increase the road safety by designing a special shell protecting the driver during the side falling road accident. The design criteria is based on Roly- Poly stability criteria for stable rolling vibration. It is shown that in this case, the rolling profile should satisfy the corresponding differential equation. In the simplest 2D case, it is proved that all smooth curves laying below the limit stability curve (a circle) are leading to the stable rolling vibration profiles. The proposed design strategy is based on the sequential CAD and FEM models with the simulation of side falling in order to construct the optimal geometry of the protecting shell satisfying the rolling stability criteria. References 1. ISO Road vehicles Functional safety European Standards ISO Norms, 2. FMVSS-108. Federal Motor Vehicle Safety Standard and Regulations. USA Norms 3. Roly-Poly Toy. Wikipedia Article 4. Konyukhov A. and Schweizerhof K., Computational Contact Mechanics- Geometrically Exact Theory for Arbitrary Shaped Bodes. Springer, Dummy Models