# Optimizing the Honeycomb Spoke Structure of a Non-Pneumatic Wheel to Reduce Rolling Resistance
## 1 Introduction  
As one of the most important components of a vehicle, tyres are closely related to all aspects of vehicle performance, such as dynamics, fuel economy, braking, handling stability, smoothness, and so on [1]. Pneumatic tyres have been widely used in a variety of moving vehicles due to their better vibration damping, load carrying capacity, grip performance, comfort, and other comprehensive performance aspects [2]. However, pneumatic tyres have a number of disadvantages, such as the risk of flat tyres, complex manufacturing processes, low recycling rates, and so on [3]. According to statistics, the proportion of traffic accidents caused by flat tyres reaches 40%, and the mortality rate of traffic accidents caused by flat tyres at high speeds is close to 100% [4]. In contrast, a non-pneumatic tyre (NPT) does not require air for support, which avoids disadvantages such as flat tyres and air leaks, and at the same time has the advantages of being environmentally friendly, highly recyclable, simple to manufacture, and so on [5, 6, 7]. Well-known tyre companies such as Michelin, Goodyear, and Bridgestone have launched corresponding airless tyres, with Michelin's Uptis range of NPIs already in use. A non-pneumatic tyre usually consists of a rim, elastic spokes, reinforcements, shear bands, and tread, and tyre performance is largely determined by the elastic spokes [8]. The main considerations in the design of NPIs are tyre mass, stiffness, ground pressure, and rolling resistance [9]. Some spokes derived from bionic designs are able to combinethese properties, such as honeycomb spokes, petal spokes, and so on [10]. Honeycomb structures have a low mass in addition to high elasticity and stiffness [11]. Therefore, the selection of honeycomb structures as spokes for non-pneumatic types is appropriate. Many scholars have done a lot of research in these areas. [PERSON] et al. proposed a cellular structure design method based on the tangent method; built hexagonal and circular cellular structures; and investigated the displacement, radial stiffness, and ground pressure patterns of cellular structures with different densities. This laid a foundation for the study of contact performance analysis of non-pneumatic types under complex working conditions [12]. Based on honeycomb non-pneumatic tyres, [PERSON] et al. investigated the static and dynamic mechanical properties of tyres in good condition and in local damage condition and found that spoke damage has an effect on tyre performance [13]. [PERSON] et al. optimized spokes with honeycomb porous structure by the design of experiments and finite element method with the objective of minimum rolling resistance and assessed the sensitivity of the design variables by analysis of variance (ANOVA) [14]. Different spoke configurations' effects on tyre contact pressure were compared by [PERSON] et al. The findings from the study showed that the honeycomb spoke structure reduces the contact pressure and the stress on the spokes of the tyre [15]. In general, if a material has a high stiffness, it has a low elastic strain limit. [PERSON] et al. designed the spokes of NPT with both stiffness and resilience by using an auxiliary honeycomb structure with negative Poisson's ratio [16]. An in-depth study of the honeycomb structure is more helpful in improving the performance of NPT. The regular honeycomb structure is generally a positive hexagonal cell with some energy absorption. It has been shown that irregular structures absorb the energy of load impacts better, resulting in better vibration damping and longer service life [17; 18; 19]. The gradient honeycomb structure is an irrational hexagonal structure, which refers to the loss of periodicity in a certain direction. [PERSON] et al. investigated the anisotropic gradient honeycomb structure and analyzed its energy absorption capacity by 3D printing prepared samples for static and cyclic compression tests in the in-plane direction, which showed the highest damping capacity with mixed gradient results [20]. [PERSON] et al.