NFX|汽车轮辋仿真分析
ABSTRACT:
The oil crises in early 1970’s draw the attention of researchers to explore alternate option to reduce the dependence on fossil fuels for transportation. This trend derived the possibility of electric vehicles (EVs) powered by batteries. The two main challenges, currently, these EVs are facing are long charging time to charge the batteries and limited range. This work deals with the solution of reducing weight to address the above mentioned two challenges. A carbon reinforced composite (CRC) is used to replace the usual alloy material in the fabrication of vehicle wheels. Finite Element Analysis (FEA) has been used to study the structural properties under usual loading conditions. The results proved that the use of CRC for wheel rim can reduce the weight of unsprung mass of the vehicle and also rotational inertia of the wheel assembly. This reduction in weight can help improve the life of battery installed on the EV. Thus, improving the endurance and range of EV.
KEYWORDS:
Electric vehicles; Weight reduction; Carbon reinforced composite; Finite element analysis
1.Introduction
Global warming has been posed as a serious problem causing changes in climate by many nations. Many reports revealed the cause for this negative impact on climate is majorly driven by human activities. The dependency on fossil fuel for energy generation to meet the needs of industries and humans has increased air pollution [1]. With the growing civilization the need to transport goods, humans, etc. also growing and the emissions by these transport vehicles cannot be ignored. Vehicle emissions, namely, carbon dioxide(
), carbon monoxide (CO), Nitrogen Oxides (NOx) and inhalable particulate matters (PM2.5 and PM10), are the main causes to the effect of greenhouse gases and led the increased risk of different forms of cancers and other serious lung diseases [2-3]. According to the European Union (EU) report 2011, 28% of the total emissions are coming from the transport sector and road transport is accounted for 70% of these emissions[4]. Hence, government authorities of many countries are encouraging EVs by giving tax incentives, purchase aids, free public parking, or free use of paid highways etc. to reduce air pollutants concentration and emission of greenhouse gases.
Engine elements of EV’s are less (no gear shift, elements reducing noise, no cooling circuit, clutch) ensuring cheaper maintenance [5]. No inherent wear and tear by engine vibrations, explosions or fuel corrosion [6] in the EVs. Thereby, reduced vibrations and engine noise ensures comfortable traveling in EVs. A recent study by OECD, concluded that replacing traditional vehicles with EV’s did not improve air quality situation by reducing particulate matter (PM) emissions [7]. The challenges EV’s face these days are, driving range - usual range of EV’s these days restricting to 200-350 km with full charge. For example, Nissan leaf has a range of 364 km and Tesla model S has a range of 500 km. Charging time of usually, 4-8 hours is required to fully charge all the batteries. Even using fast charge takes 30 mins to charge up to 80% capacity. Large battery packs are expensive and they are required to be installed on the vehicles, hence, occupies space and adds to the weight of the vehicle [8-9]. Typically, around 200 kg weight for batteries to be allotted. The number may even go higher depending on the capacity of the battery. This tends to look for alternate solutions for reduction of weight in other components of EV.
Ding et al [10] reviewed the existing EVs and the importance of weight reduction for better performance and future developments of EVs. Stefan et al [11] compared the mechanical properties and studied the stresses generated in aluminium alloy and CFRP wheels under radial loading conditions. They used 6.8kg CFRP wheel and compared with 8.1kg weight aluminium wheel. Dynamic cornering fatigue test has been carried out on both the wheels and the results are compared and also considered bending loading. The present work deals with the design and alternate solution to a wheel rim of outer diameter 0.33m. Detailed study on the wheel rim design is carried out using finite element analysis approach. Aluminium alloy (Al6061-T6) and Carbon Fibre Reinforced Plastic (CFRP) materials are considered on two different designs (design 1 with 5 spokes, design 2 with 6 spokes).
2.Vehicle dynamics
2.1.Theory
Any ground vehicle to stay controlled, the tire must maintain a considerable amount of force to have constant contact with the ground. In other words, vehicle’s suspension system must be capable of following the road ignoring all imperfections. The response time of the suspension system is characterized by the natural frequency. A simple mathematical model of the suspension system deduces the sprung mass to be fixed, the un-sprung mass and tire rigidity to oscillate freely ignoring damping. This system is characterized by,
Where,
is the natural frequency,
is wheel rate or wheel stiffness and
is the un-sprung mass. Eqn. (1) describes the relation between natural frequency and un-sprung mass as inversely proportional. With decrease in un-sprung mass natural frequency increases and the response time will reduce. This implies that the ideal un-sprung mass is to be ‘0’. This allows the suspension system to respond quickly to any external disturbances and wheel can follow the road without detaching from it even on rough terrains. Eqn. (1) can be simplified as,
Where 𝛿=𝜎𝑙/𝐸 is deformation, g is acceleration due to gravity (m/s²), 𝜎 is normal stresses (MPa), 𝑙 is the length of cross section (m), E is Young’s modulus (MPa).
The equations of motion for a 2- DoF (Degree of Freedom) system is,
Where,
is suspension stiffness,
is sprung mass, 𝑥 is position of suspension and 𝑦 is position of chassis. Rearranging the terms in Eqns. (2) and (3), to estimate accelerations,
From the Eqns. (4) and (5), it is evident that 𝑥̈ increases with decrease in
this results in suspension keeping constant contact with the road. Similarly, 𝑦̈ decreases with increase in ensuring the position of chassis relatively constant. In other words, the ratio of sprung mass to un-sprung mass (/) increases with increase in suspension response and decrease in chassis displacement. This ensures comfortable and smooth driving for the driver while enhances the manoeuvring of the vehicle
2.2.Loading conditions
-radial, bending and impact
Radial, bending and impact loads are usually considered for the structural analysis of the wheel rim. Radial loading condition is when constant load is applied in the radial direction by the drum on the wheel either towards or away from the center of the wheel. The wheel structure is fully rested on a mounting disk and bolt hole. A cosine function of radial load is applied on the rims. In this work, a tire pressure of 3 bar has been used to exert an inflation pressure on the entire outer rim. Bending and impact load analysis have also been considered. The radial load applied on the rim is,
is the maximum vertical static load on the wheel as specified by the manufacturer, K is the reinforcement test coefficient. The cosine load as mentioned above is,
is the maximum vertical static load on the wheel specified by the wheel or the automobile manufacturer or the rated load of the wheel. The impact test is a transient response kinetic problem. In this work, we have considered the usual case of impact load condition. To simplify the problem and solve it as a static problem than dynamic, we considered the dynamic load (punch) while falling from certain height into static load and applied it on the wheel rim. The geometry of the wheel for design 1 is shown in Fig.1. A finite element mesh of the rim is shown in Fig.2 along with its loads and boundary conditions in Fig.3.
3.Numerical implementation
The geometry of the wheel is created using commercial software Solidworks. Commercially available FE analysis software midas NFX has been chosen to carry out the analysis and post processing of results. The geometry from Solidworks has been imported to midas NFX software for further meshing and analysis. 9-noded tetrahedral mesh elements of uniform size are generated by the mesh generator within the midas NFX software on the geometry. 2 models of wheels with different materials are generated, meshed and the results have been compared. Approximately, 208517 elements with 49073 nodes are generated on design 1 and design 2. Aluminium and CFRP have been chosen as the material for the simulation. The detailed properties list of the material, geometry and loading conditions used are listed in Table 1. At the supports, all 6 DoF are constrained. The wheel’s rim is fixed at only one location (i.e., bolt hole) and the modal frequency analysis has been carried out for both materials and both designs
Upon simulating the models with all the required boundary conditions and properties, the file is imported to the solver. As mentioned above midas NFX solver is used for simulation. The grid independence study for design 1 with 5 spokes has been carried out to justify the grid dependency of the current grid. Al6061-T6 material and radial load conditions are used. Initially, approximately 25000 nodes and 12564 mesh elements were used and then after the number of mesh elements were increased by 
times for every simulation and the results are reported in Table 2. It is evident from the table that the grid with nearly 75000 elements yields the saturated values for maximum stresses. In this work, 208517 nodes with 118965 elements are used.
Nodal displacements and respective contours on the wheel rim for radial loading condition are presented in Fig. 4.
It can be clearly seen that wheel made with CFRP is outperforming Al-6061-T6 in terms of factor of safety, deformation for both design 1 and 2. The maximum nodal displacement on the rim is reported as 0.09mm and 0.041mm for design 1 with Al-6061-T6 and CFRP respectively. Similarly, the maximum nodal displacements on the rim for design 2 are 0.081mm and 0.032mm for Al6061-T6 and CFRP respectively. Contours of von Mises stresses on both designs with Al 6061-T6 and CFRP are reported in Fig. 5
and their respective strain contours are reported in Fig. 6.
The maximum von mises stress of 25.6MPa has been reported in the case of design 1 with Al6061-T6 material. In all other cases it is less than 25 MPa. Design 2 with CFRP material is outperforming all other variants in the radial load condition. Under radial load condition it is the rim on which the maximum stresses are identified which are very less when compared with the yield strength of both the materials used resulting in a factor of safety more than 10 [11]. The percentage reduction of maximum stresses in comparison with design 1 made of aluminium alloy are 21%, 7.8% and 30.8% for design 1 with CFRP, design 2 with Al6061-T6 and CFRP respectively. The same results are reported in Table 3, D1 - design 1 and D2 - design 2. The maximum stress is within the yield strength limit of the material. It is also reported that the maximum von mises stresses are observed near the midline of the width of the wheel for the radial loading condition [11].
Fig. 7 depicts the von mises stress contours on the wheel rim for bending and impact loading. A summary of the simulations are listed in Table 4 and Table 5. The maximum stress value reported is 107.6 MPA for design 1 with CFRP and is located on the center of the spoke. The maximum nodal displacement value is reported as 0.81 mm for the same design. It is understood that from the results Al alloy is performing marginally better than CFRP under bending load condition. This may be due to the poor resistance between the layers of CFRP rim. Design 2 with Al alloy is marginally better performing under bending. Similar trend is observed under impact load condition. With a reduced weight of nearly 18% and enhanced properties under all types of loading conditions (radial, bending and impact) design 2 with CFRP material is outperforming all other designs. Modal analysis is a very important characteristic to evaluate the natural frequency of the wheel as the suspension system of the vehicle relies on the natural frequency. Along with natural frequencies in Table 6, the first 6 mode shapes of the CFRP rim are presented for both the designs in Fig. 8. Similar trends were observed in the rest of the modes.
5.Conclusion
A detailed structural analysis under radial, bending and impact loading conditions of an automobile wheel has been studied. CFRP and aluminium alloy Al-6061-T6 materials are considered. Finite Element analysis is carried out using midas NFX. The results show that there is a reduction of weight when CFRP is used by around 16% with improved factor of safety by 12.5%. Modal frequency analysis on both the design is also carried out to find the mode shapes along with the natural frequency. It is concluded that Design 2 with CFRP is outperforming all other designs considered
REFERENCES:
[1]J.H. Wee. 2010. Contribution of fuel cell systems to CO2 emission reduction in their application fields, Renewable and Sustainable Energy Reviews, 14(2), 735-744. https://doi.org/10.1016/j.rser.2009.10.013.
[2]J. Fenton and R. Hodkinson. 2001. Lightweight Electric/ Hybrid Vehicle Design, Elsevier. https://doi.org/10.1016/B978-075065092-2/50009-2.
[3]P. Fajri and B. Asaei. 2008. Plug-in hybrid conversion of a series hybrid electric vehicle and simulation comparison, Proc. 11th Int. Conf. Optimization of Electrical and Electronic Equipment, 287-292, Brasov, Romania.
https://doi.org/10.1109/OPTIM.2008.4602422.
[4]European Commission. 2011. Transport in Figures-Statistical Pocketbook, EU Pub.
[5]C.C. Chan. 2007. The state of the art of electric, hybrid, and fuel cell vehicles, Proc. IEEE Explorer, 95, 704-718.
https://doi.org/10.1109/JPROC.2007.892489.
[6]A. Albatayneh, M.N. Assaf, D. Alterman and M. Jaradat. 2020. Comparison of the overall energy efficiency for internal combustion engine vehicles and electric vehicles, Environ. Clim. Tech., 24, 669-680.
https://doi.org/10.2478/rtuect-2020-0041.
[7]OECD iLibrary. 2020. Non-Exhaust Particulate Emissions from Road Transport: An Ignored Environmental Policy Challenge, Technical Report, OECD Pub., Paris, France.
[8]M. Rajasekaran, V. Hariram and M. Subramanian. 2016. Multi-objective optimization of material layout for body-in-white using design of experiments, Int. J. Vehicle Structures and Systems, 8(1), 17-22.
https://doi.org/10.4273/ijvss.8.1.04.
[9]J.B. Lidoy and J.M.M. Moreno. 2010. Energy efficiency in the automotive industry, the electric vehicle, A present challenge, Econ. Ind., 377, 76-85.
[10]N. Ding, K. Prasad and T.T. Lie. 2017. The electric vehicle: A review, Int. J. Electric and Hybrid Vehicles, 9(1), 49-66.
https://doi.org/10.1504/IJEHV.2017.082816.
[11]S. Czypionka and F. Kienhöfer. 2019. Weight reduction of a carbon fibre composite wheel, Sci. and Engg. of Composite Materials, 26(1), 338-346.
https://doi.org/10.1515/secm-2019-0018.
