As the leading cause for mechanical vehicle failures, flat tires pose a serious threat to the safety of a driver. At speeds greater than 160 km/h, flat tires have a 100% mortality rate because the stability of the vehicle is impossible to maintain beyond these speeds. Multiple solutions have been proposed to reduce the frequency of tire blowouts, such as run-flat tires, but these solutions do not address the problem completely or sacrifice other important criteria for tire design. Graphene, a strong and lightweight material, has great potential for use in run-flat tires as an alternative to synthetic rubber nanocomposites. By simulating its properties in run-flat tires, its potential as an alternative to traditional tire rubbers can be assessed. Using the CAD (Computer-aided Design) Software Solidworks, multiple run-flat tires of different dimensions were drawn. Next, a stress analysis was run with the given run-flat tire and the application of linear forces. Material constraints that align with Graphene-Rubber properties were applied and then the stress analysis found the deformation of the tire at any specific location along its surface. With this data, the stress analysis helped assess graphene’s efficacy in reducing the stiffness and maintaining the durability of the tire. The applicability of these tests can be justified by examining the properties of a graphene composite constructed with the specific rubbers used in tires today. By examining the utilization of graphene-nanocomposites in run-flat tires, an ideal tire can be designed that can save thousands of lives.
Keywords: Run-Flat Tire, Stress Analysis, Graphene
The objective of this project is to find the optimal design of a run-flat tire based on a graphene/rubber nano-composite, which balances both durability and versatility.
As the amount of graphene mixed in with the styrene-butadiene rubber composite increases, the flexural strength of the rubber will also increase while simultaneously maintaining high levels of durability.
Flat tires have a serious impact on the stability of a vehicle (Liu et al., 2014), and can jeopardize the safety of a driver. Reportedly, 70 percent of all highway accidents are caused by deflated tires (Liu et al., 2021). The tires of a vehicle are the sole support between the body of the vehicle and the ground. In the case that a tire blows out, one of these four supports are compromised, and the vehicle tilts due to a lack of stability. Consequently, due to great speeds of vehicles on freeways, it is difficult to maintain a proper path of travel in the event of a tire blowout. There have been numerous solutions to this problem, such as the advent of run-flat tires, a tire designed with a reinforced sidewall (Hasegawa et al., 2021).
The main design aspect of a run-flat tire is its sidewall insert rubber. Insert rubber is usually constructed with a dense rubber such as polymerized-butadiene rubber (Won et al., 2016). These rubbers are fabricated so that they are resistant to deformation in ordinary driving conditions, therefore ensuring the rigidity of the tire in the case of a flat tire (Yang et al., 2016). By maintaining its rigidity, sidewall insert rubbers can properly reinforce the sidewalls until the issue with the tire is properly diagnosed. Unfortunately, this property hinders other important mechanical properties in the tire, which are directly related to the durability and longevity of the tire. Additionally, the rigidity of the sidewall insert contributes to increased energy loss due to greater friction. Therefore, through the utilization of industry-standard rubbers such as polymerized-butadiene, run-flat tires are not able to fulfill energy loss requirements and cannot attain the high specific performance required for a device of its kind (Yang et al., 2016). This is due to the density of the materials used in traditional tire compositions which is why other types of materials must be considered.
One of the materials that can fix this design flaw is graphene, a two-dimensional sheet of carbon atoms that are organized in a hexagonal lattice (Giem & Novoselov, 2007). Due to its atomic structure, graphene has many unique mechanical properties and has been sought after for its potential in numerous applications, including rubber tires (Thomas et al., 2019). As a stand-alone material, graphene exhibits high intrinsic strength and thermal conductivity (Abuoudah et al., 2021). For this reason, graphene compositions such as carbon nanotubes (shown in Figure 2), which have numerous applications in medical and engineering fields, exhibit high levels of durability as well as flexibility. Examples of these applications range from nanotubes to electric batteries to polymer compositions. By mixing graphene into polymer compositions, it can potentially emulate the balance between flexibility and durability experienced by other graphene-based materials (Giem & Novoselov, 2007).
This project was computationally based, and it utilized various design applications and material data. Computation technology used for this project include a 13-inch MacBook Pro (2020) with a 2 GHz Quad-Core Intel Core i5 Chip, and the Worcester Polytechnic Institute-administered remote desktops located at arc-teach-01.wpi.edu and elabs.wpi.edu. CAD models of run-flat tires were drawn using the web-based CAD software Onshape, and simulations were conducted using Solidworks 2021 with the Nonlinear Simulation extension. Material data was extracted from the research articles published by Xing et al., and graph data was interpreted using PlotDigitizer. Data analysis was conducted using RStudio.
The initial stage of this project involved generating the final tire model to be utilized in testing. Onshape was used for this stage due to its accessibility as a web-based software, and its compatibility with Solidworks 2021, which would be used later in the project. Four practice iterations were drawn, each of which continued to refine a specific aspect of the tire design. The first iteration of the tire depicted a U-shaped tire with exaggerated sidewalls. This iteration did not account for the curvature of the sidewalls, or the geometry of the outer edge of the tire. These design aspects were addressed in the second and third iterations of the tire design, which further refined the sidewall design, and curvature of the tire’s outer edge.
Despite the accurate shape of the tire, the second and third iterations of the tire design were not dimensionally accurate to a run-flat tire. This was addressed in the fourth iteration of the tire design, which was made dimensionally accurate to a 195 / 55 R 16 sized run-flat tire. This meant drawing a run-flat tire with an outer shell width of 195 mm, 55% aspect ratio (ratio of width to sidewall height), and a wheel radius of 16 inches.
The outer shell of the run-flat tire designed in the fourth iteration was applied in the final assembly, where it was then put together with a model of the two sidewall rubber inserts. These sidewall rubber inserts were sketched to mesh with the constructed outer layer of the tire. The parts were linked using two fastened mates, which ensured that the parts would act as one solid object during simulations instead of being split apart.
To run an accurate simulation, it is critical to apply relevant material data to the designed model. In this case, it is necessary that the run-flat tires being tested upon are calibrated with material data that aligns with Styrene-Butadiene Rubber (SBR), the most commonly used rubber in such tires.
The required parameters for a simulation with rubber are Poisson’s Ratio, Mass Density, and Tensile Strength. Additionally, for nonlinear simulations, it is necessary for the rubber data to include a stress-strain plot, so that the simulation can take the material’s responsiveness to external forces into consideration.
Due to a lack of available data, SBR could not be used in the simulations. As a substitute, Natural Rubber was used due to better availability of data, and its similarity to the mechanical properties of SBR. Clean Natural Rubber has a Poisson’s Ratio of 0.45, a Mass Density of 960 (kg/m3), and a Tensile Strength of 20 MPa. Additionally, the stress-strain curve of Natural Rubber was obtained from a research article published by Xing et al., which was converted into a CSV (Comma Separated Values) file of points using PlotDigitizer.
The clean Natural Rubber was designated as the control group, and four other experimental groups were developed, with 0.1, 0.5, 1, and 2 PHR (parts per hundred rubber) of Graphene respectively. Different stress strain data was used for each of the different concentrations of graphene, obtained from the aforementioned research article. Due to a lack of available data, the Poisson’s Ratio, Mass Density, and Tensile Strength were kept constant among the five groups. In reality, these values would differ between groups.
Nonlinear simulations were used for this project in order to properly emulate the behavior of rubber objects. Since rubber responds to forces differently from other rigid solids, it is important to take its behavior into consider. The obtained rubber data was applied to five different iterations of the designated run-flat tire design. In each of the simulations, a normal force of 15,000 Newtons was applied equally across the outer shell of the tire, and the inside rims of the tires were designated as fixed geometries. This ensured that parts of the tire closer to the wheel rims would remain stationary while forces were applied to the outer edges, just as a physical tire would. The models were then meshed as per the default Solidworks settings, as anything finer than set would be redundant.
Each of the nonlinear simulations were run for 15 steps, which equates to approximately 0.03 seconds of real-time simulation. From 15 steps, three plots were generated which contained stress, displacement, and strain data respectively. These plots were then saved, and data from each of the plots was collected as a CSV file to be used in further analysis. Two different data frames were collected for each of the simulations, one for the outer shell of the tire, and one for the sidewall rubber inserts.
The collected CSV files were aggregated into three data frames, each of which contained data for stress, displacement, and strain respectively. Since the data does not follow an equation or definite set of rules, it can be considered non-parametric. For this reason, the Kruskal-Wallis test was selected to analyze the data, which is run by collecting multiple samples of data and using the medians and sample sizes to calculate if the distribution of the samples is similar.
As shown by the visual inspection of the tire simulations, the tire fabricated with 0.1 PHR GE/NR most effectively optimizes the displacement of the tire for a given value of stress. The same conclusions can be drawn from the strain data, where the tire constructed with 0.1 PHR GE/NR outperforms the rest of the tires.
Although this simulation finds the most optimal solution between a number of Natural Rubber compositions, this data cannot be applied to Styrene-Butadiene Rubber, as the interactions between SBR and GE slightly vary from that between Natural Rubber and GE. Additionally, due to the computing power with which the simulations were conducted with, the data collected is not consistent on the basis of time. Since captured data reflects different durations of tire simulation, there are additional discrepancies in the results that should be acknowledged.
The exploratory data analysis mirrors the results found in the visual inspection, demonstrating that the tire made with 0.1 PHR GE/NR is the most optimized of the five tires. The box and whisker plots show the smallest range of displacement and strain values for the tire constructed with 0.1 PHR GE/NR, and additionally shows the largest range of displacement and strain values for the sidewall of the same tire. This shows that the sidewall is most effective in this tire specifically, as the greatest proportion of displacement and strain occurs in the sidewalls, allowing the tire itself to more effectively maintain its structural integrity.
In order to determine which of the five tires were statistically significant, a Kruskal Wallis statistical test was conducted. The p values obtained show that at least one of the tires in all six different simulations are statistically significant. Although the Kruskal-Wallis test effectively assesses the distribution of the data, the discrepancies in data collection prevent conclusive results from being drawn from the test. Since the data collected was over varying time intervals, the levels of simulation data, especially stress, showed great variation. For this reason, it cannot be conclusively said that the statistically significant tire is more effective than the others.
To find the most statistically significant tire, a post-hoc Dunn test was conducted, which showed that the tire conducted with 0.1 PHR GE/NR was the most statistically significant. This aligned with the conclusions drawn from the EDA as well as the visual inspection. Due to the simplicity of the Dunn Test, it is generally considered a conservative post-hoc test, as it simplifies the process of comparing the distribution of sample data. It has been decided that the results of the Dunn test adequately address the research question, although a more robust post-hoc test such as a Mann Whitney-U test could have yielded more accurate results.
The results drawn from experimentation would more accurately represent a physical model of the tire had there been more accurate rubber data to test with. If SBR rubber was used in testing as opposed to the Natural Rubber substitute, the results drawn from the simulation would more closely mirror an industry-standard run flat tire. Additionally, if more levels of GE were tested with variations in run-flat tire structure, the data gathered would be more robust. Moreover, a more accurate simulation conducted with more powerful computing software would deliver more accurate data, strengthening the validity of the claims made by this project.
In conclusion, graphene in small concentrations present in Natural Rubber helps reinforce the strength of the tire, allowing it to experience less deformation in the presence of stress. The data shows that a tire constructed with 0.1 PHR GE/NR, as opposed to four other material compositions varying from 0-2 PHR, was the most effective. The resulting data could be applied to a more complex simulation of run-flat tires, or used in a mechanical evaluation with physically fabricated rubber compounds.