designing space frame race car chassis structure …
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Research Paper
DESIGNING SPACE FRAME RACE CAR CHASSIS STRUCTURE USING NATURAL FREQUENCIES DATA FROM ANSYS MODE SHAPE ANALYSIS
Mohammad Al Bukhari Marzuki Mechanical Engineering Department
Sultan Azlan Shah Polytechnic Behrang Stesyen, 35950 Behrang
Mohd Arzo Abu Bakar Mechanical Engineering Department
Sultan Azlan Shah Polytechnic Behrang Stesyen, 35950 Behrang
Mohammad Firdaus Mohammed Azmi Mechanical Engineering Department
Sultan Azlan Shah Polytechnic Behrang Stesyen, 35950 Behrang
Abstract Designing and fabricating space frame chassis structure requires a certain set of knowledge especially in design, material selection and metal joining and fabrication which will result in rigid, sturdy and competitive chassis design. The outcome of the design will reflect the success of chassis especially if the chassis design is used for racing competition. This study focuses on the analysing the initial chassis design using mode shape analysis and the mode shape frequencies and characteristic produced from the analysis are studied. The modelling and the finite element model of the chassis structure are carried out using coordinate system in ANSYS Design Modeller and ANSYS APDL Version 13 respectively. The main objective of this analysis is to establish the natural frequency and mode shape characteristic corresponds to the natural frequency from the chassis structure to ensure that the ride comfort is beyond the unhealthy frequency range. Result from the study can be used to study the dynamic behaviour and to improvise the overall dynamic response of the chassis structure.
Key Terms: Mode shape, vibration, natural frequency, space frame, ANSYS
International Journal of Information System and Engineering
www.ftms.edu.my/journals/index.php/journals/ijise
Vol. 3 (No.1), April, 2015 ISSN: 2289-7615 DOI: 10.24924/ijise/2015.11/v3.iss1/54.63
This work is licensed under a Creative Commons Attribution 4.0 International License.
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1. Introduction Car racing competition usually involved in racing driver race each other, either competing who gets the fastest time or who complete the course first. Car racing comes in several category which include opened-wheel Formula Series, production car Rally Series, highly modified production car Japan GT Series and a few other car-based racing competition which being held locally and internationally. In opened-wheel car racing competition divided into a number of levels, this may include entry level kart racing and highly advance Formula 1 Championship. There are also racing competition tailored made for university or college student can participate. Among the well-known university level race car competition are Formula SAE, organised by the Society of Automotive Engineers and Formula Student, organised by the Institute of Mechanical Engineers UK. Locally, there are also a number of competitions for the local universities student can take part, the majority of the competition are organised by a university and also car manufacturers in Malaysia, i.e. PROTON and PERODUA. Most of the local racing competition loosely based on the Formula SAE standard and the regulation are modified to suit local competition requirements. The chassis structure specification for this study is based on regulation of UniMAP-MODENAS Racing Challenge specification which only allowed the participant to construct a space frame race car platform. The advantages of using space frame chassis construction are the mass of the structure is lesser and cost effective than other types of chassis but due to complicated manufacturing process, space frame chassis platform is only used for high performance and niche market cars. The main chassis structure is divided into several segments, which are the Main Hoop, Front Hoop, Side Impact Protection and Crush Zone. The Main and Front Hoop is tasked to protect the driver in the event if the car rolls over. The Main Hoop protects the upper part of the driver’s body while the Front Hoop protects the drivers arm and hand if rollover occurs. As for the Side Impact Protection section, this section is created to protect the driver from side in the event of any collision from the either side of the car. As part of the chassis, the Crush Zone is located at foremost section of the chassis. This section is specially made to absorb energy in case of a head-on collision. The main sections of the chassis are illustrated in Figure 1.
Figure 1: An example of space frame race car chassis structure based on Formula SAE specification
The dynamic behaviour is one of the important aspects in designing a car. Dynamic characteristic of a structure can be analysed either through modal or harmonic analysis which can be carried out from experiment or simulation. In reference to He et al. (2001), the car chassis is tested experimentally by suspending the chassis structure with springs to simulate free-free boundary condition and the chassis is excited using a shaker so that the mode shape of the chassis can be derived. Experimental modal analysis studied by Wenlin et al. (2010) utilised Land-Wind X6 chassis to study the dynamic behaviour through modal analysis. The tests are conducted using data acquisition system and an input hammer which generated eleven mode
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shapes with the frequency below 150Hz and later verified with Modal Assurance Criteria (MAC) method for data validation. Another notable experimental modal analysis is conducted by Naveen et al. (2014). The result illustrated from two wheeler chassis derived from Operation Deflection Shape (ODS) analysis produced 6 experimental mode shapes, which includes torsion, lateral bending and vertical bending in different modes. The result from Naveen et al (2014) later can be used for further strengthening the chassis to minimise the deflection caused by natural frequencies. Finite element method is a computational technique to extract mode shapes of a structure where the rigidity of the structure can be analysed and the resonance vibration could be avoided. There are several software that can be used to analyse dynamic characteristic, computer-based finite element analyses ANSYS APDL is one of the commercial computational aided engineering software that extract mode shapes from chassis structure. Dynamic characteristic response can be obtained using variety of vibration and structural design analyses method accessible in the software as explained by N. Lin et al. (2012) and Wang et al. (2010). A further study by Riley (2002) utilising computational method, a tubular frame car chassis produced four different mode shapes which are all below 15Hz and the displacement of every mode shape is recorded for chassis improvement purposes. Modal analysis also can be used to determine the human response against structure vibration. A research conducted by Nissar (2003), presented a result from motorcycle chassis mode shape analysis showed that large displacement at handlebar position could cause the rider discomfort and the first two frequencies obtained lies in the human discomfort region (0-100 Hz). Thus, Nissar (2003) conclude that further study and improvement is needed to bring the motorcycle chassis vibration within the human comfort zone. In the ISO 2631-1 state that the frequency range consideration for health and comfort is between 0.5 Hz to 80 Hz which in relation to human health and comfort, the probability of vibration perception and the incidence of motion sickness as stated in a study lead by Agostoni (2009). Although there are various studies on car chassis structure vibration analysis both in experimentation and simulation, but most of the research are not fully address modal analysis specifically on space frame race car chassis for student’s race competition. Apart from that, the ride and comfort of the race car driver usually is not being take care of and winning the competition or race is the only motivation for any particular racing team. Therefore, the purpose of this study is to design a space frame race car chassis structure based on the natural frequencies and shape characteristic obtained from the mode shape analysis simulated using ANSYS software package. The study is performed as a first step to improve vibrational characteristics of the initial chassis structure design and to ensure that the natural frequencies are beyond the human unhealthy and discomfort frequency range. 2. Finite Element Model The race car chassis is designed and fabricated according to the Formula SAE design criteria as stated in the UniMAP-MODENAS Racing Challenge 2014 Regulation. There are three types of tube frame specification is used in the chassis, with all the different specification are intended for the specific purposes of the chassis structure. A 27 mm diameter tube with wall thickness of 2 mm is used for both hoops construction. Other tube frame construction such as the side beam and front beam is constructed by using a 25 mm with 1.6 mm wall thickness tube as shown in Figure 2. The thicker tube is selected for both hoops sections since it withstand any rolling impact in case the car rolls over. The wishbone which is assumed as not part of the chassis construction since it is not permanently fixed to the chassis structure. The entire tube specifications and thicknesses are entered to the section geometry data (SECDATA) option in the ANSYS APDL.
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Figure 2: The complete fabricated race car chassis structure complete with wishbones
The material selected for the chassis construction is based on the rules and regulations required by the race organiser. In the regulation, there is a single type of material that can be used for constructing the car chassis, which is ferrous material. For the analysis purposes, steel is selected with the material properties include material density of 7860 kg/m2, a Poisson’s Ratio of 0.3, and Young’s Modulus of 200 GPa. The finite element model in ANSYS APDL is assumed to be made from tube frame in which PIPE288 element is selected to represent the chassis structure. PIPE288 element is chosen because the element is suitable for analysing short pipe structures which based on the Timoshenko beam theory with shear deformation effect are included (ANSYS, 2010). PIPE288 is a 3-D linear, quadratic two-noded pipe element which has six degrees of freedom, making the element suited for linear, large rotation and strain nonlinear application (ANSYS, 2010) as shown in Figure X (element pic). Key point is created by using the dimension according to the actual chassis construction and then the key points created are connected using lines option and the lines are meshed using mesh tool in ANSYS APDL. The model is meshed using mapped element with equivalent mesh size on every line. A total of 5875 nodes and 5900 elements are created. The total number of nodes and elements created are sufficient to produce an acceptable result, the simplified finite element meshed model is illustrated in Figure 3 - 6.
Figure 3: Isometric view of the simplified race car chassis model in ANSYS APDL interface
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Figure 4: The main hoop, protects the driver during roll over
Figure 5: Front section of the chassis
Figure 6: Rear section, housing the engine and transmission of the race car
There are no weight is carried by the chassis, therefore there are no loads are applied in ANSYS vibration analysis with all degree of freedom are free to evaluate the natural response of the chassis structure. For the analysis purposes, damping coefficient is ignored for modal analysis. 3. Finite Element Mode Shape Analysis Frequency Response Function utilises measurement techniques of Fast Fourier Transform (FFT), which is widely used in analysing structural dynamic especially in automotive design and engineering field to establish vibration characteristic i.e. mode shape, natural frequencies of vehicle model (Mehdi et al., 2014). The equation of motion for undamped system is formulated from;
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(1)
Where m, q and k is the constant which describe the mass, displacement and stiffness of the system and Equation (1) equal to zero if there is no force applied to the system. q is displacement for a linear system, which in harmonic form will be;
(2)
Where is the amplitude of mode shape of the ith natural frequency ωi , therefore;
(3)
The solution from Equation (3) gives Eigen values, which is the square root of the natural frequencies and the Eigen vectors are the amplitude of the corresponding natural frequencies. The natural frequencies gathered from the modal analysis can be used to provide information on critical mounting points for vibration sourced component i.e. engine, transmission, suspension system, electric motors and etc. Block Lanczos method is selected to analyse the mode shape from the structure. Block Lanczos method has been widely used in studies for extracting mode shapes and natural frequencies in a structure (Wang Hai-fei et al. 2014, Rao et al. 2014, Samrudhi et al. 2014). Five mode shapes is selected in the mode shape extraction option in ANSYS. Five mode shapes is assumed to be adequate since the most important result from modal analysis is the first-five mode shapes as it represents the lower range of natural frequencies of the race car chassis. End frequency of the analysis is selected at a maximum of 1000Hz where these options enable ANSYS APDL to search the mode shape of the car chassis from 0Hz to 1000Hz and will stop searching beyond the stipulated range. A simple single axis support is applied at the 4 point where the bracket holding the both right and left, front and rear wishbone to simulate the chassis’s actual resting position. 4. Finite Element Mode Shape Result This study utilises Modal Analysis to generate the natural frequencies and mode shapes of the space frame chassis structure. Result from Modal Analysis is important as it can predict the response of structural parameters under dynamic loading condition. Mode shapes simulated from Modal Analysis can provide the information of how the chassis structure will naturally displace. ANSYS APDL Mechanical is used as pre-processor, solver and post-processor for the modal analysis. Utilising Block Lanczos method, 5 mode shapes are obtained between 0 - 1000 Hz range. Table 1 illustrates the first five natural frequencies for the corresponding mode shape which are important to the study. Mode shapes frequencies and characteristic are tabulated in Table 2.
First mode shape – 150.39 Hz
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Second mode shape – 203.15 Hz
Third mode shape – 389.10Hz
Fourth mode shape – 515.66Hz
Fifth mode shape – 759.38Hz
Table 1: Mode shape
Table 1 outlines the first natural frequency for the chassis is at approximately 150.39 Hz. The mode shape of the race car structure is critical because resonance usually occurs in these frequencies. The second modal frequency is vibrated at 203.15 Hz, the third modal frequency vibrated at 389.10 Hz, fourth modal frequency at 515.66 Hz and the last modal frequency within 0 - 1000 Hz range vibrated at 759.38 Hz.
Mode Shape Frequency (Hz) Mode Shape Characteristics
1 150.39 Rear section downward bending along Y-axis
2 203.15 Torsional in middle section
3 389.10 Bending in middle and rear section
4 515.66 Torsional in front section
5 759.38 Torsional at rear and bending at front section
Table 2: List of mode shape frequencies and characteristic
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The 5 mode shapes are produced by ANSYS illustrates different modal frequency
characteristic. The first mode shape generated a bending behaviour, occurred at the rear section of the chassis. If the bending behaviour is animated in ANSYS, it produced a flapping-like animation resembling a bird flapping its wing, as called by Wenlin et al. (2010). The result from ANSYS solver shows large deformation caused by the modal frequencies and can be magnified, that in so doing, any small or large deformation can be seen in the result. 5. Race Car Chassis Structure Improvement The mode shapes produced from the modal analysis illustrates that different frequency on each mode shape produced different reaction behaviour. The reaction characteristics include torsional, bending and combination of torsional and bending. It is important to identify the mode shape characteristic and the displacement caused by the natural frequencies. It is known that if vibration caused by external excitation is similar to that of the natural frequencies, this will result in deflection in the chassis structure. The highest deflection recorded by the Modal Analysis is located in the third mode shape, with a displacement of 0.375 mm. The response of the race car chassis structure in the third mode shape is bending behaviour in both middle and rear section. The highest displacement of the race car chassis structure is located at the side impact protection sub-frame as shown in Figure 12.
The side impact protection sub-frame displaced 0.375 mm from its original position which is the highest shape deformation recorded from the mode shape analysis. High deformation located at the side impact protection sub-frame is due to lack of support between the front-end and back-end joint of the frame. This can be improved by mounting a cross member frame at the side impact sub-frame to minimise the displacement at the specified area as illustrated in Figure 12. 6. Conclusion
The Modal Analysis generates 5 mode shapes, extracted from Block Lanczos method with the simulated natural frequencies ranging from 150 Hz to 1000 Hz. The first mode shape recorded the lowest frequency at 150 Hz, which is considered as safe and comfortable for human application as explained by Nissar (2003). The natural frequencies generated from the Modal Analysis also are far-off from any critical external source of excitation which is ranging from 0 Hz to 100 Hz. At this frequency range, the race car chassis structure is likely to be force exited from external source of vibration i.e. road surfaces, engine unbalance cycle and transmission vibration. The highest frequency produce by the chassis structure is in fifth mode shape, vibrated at 759.39 Hz. The fifth mode shape is located at higher frequency range and will not affected by external nor other source of vibration likely in a car.
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The natural frequency in the third mode shape is recorded at 389.10 Hz and a displacement of 0.375 mm. This frequency caused the highest displacement to the race car chassis structure. This phenomenon is known as resonance and at this frequency it is likely the chassis structure will experience excessive displacement and leading to failure. Due to resonance frequency is vibrated at higher frequency range, therefore it is unlikely that any external forced vibrational excitation ranging from 0 Hz to 100 Hz could caused resonance frequency to the chassis structure. To deal with the displacement caused by the frequency, improvement can be made by mounting a cross member frame on the both side of the chassis sub-frame, although, the amount of the displacement is considered small. The overall dynamic characteristic produced is considered safe for human application and adequate to be used in racing circuits based on the analysis. In general, the result produced from Modal Analysis is vital in finding the dynamic response of the race car chassis structure. The findings can be utilised as an initial data before it can be validated from Harmonic Analysis and experimentally. Reference Agostoni, S., Barbera, A., Leo, E., Pezzola, M., Vanali, M., (2009). Investigation on Motorvehicle
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