The response of simple dynamic structures which include plates, shells that are cylindrical and beams which are uniform, could be obtained through equation solving of their motion, however, several circumstances of practical either the properties of material vary geometrical or the boundaries’ shape cannot be in known functions of mathematical terms be described.

This challenge is solved by seeking some solutions that are in numerical form and methods of finite element. The industry of automotive is one the greatest users of modal analysis technology, however, the behaviour of the modal of truck chassis is the most important part of information for the dynamic behaviour of the truck for inspection. In this article the truck’s chassis modal analysis has been researched on as a truck runs on the road there is the excitement of the truck chassis caused by forces which are dynamically induced by the roughness of the road, transmission and the engine.

Literature review

The vibrational features of a vehicle that are global is in relation to both its distribution of mass and stiffness, the torsional modes and global bending of vibration frequencies are used commonly as examples in structural performance of vehicles while, the stiffness of torsion and bending influences the behaviour of the structure vibration in regards to the first natural frequency. The truck’s chassis shape modes are very important at a certain point of natural frequency in determining the point of mounting of components which include suspension, engine and transmission among others hence, to include the effect of dynamic is very important in the chassis designing.

(Henry, 2017)and (Khanna, 2017)made a research on 3530 FORD chassis for optimization of thickness and main criteria to develop chassis got to be safety and reliability usually so as for reliability to increase, the membranes of the chassis has to be increased which adds much cost to
the truck’s chassis. A study to find out the thickness that is optimum for the chassis was conducted, analysis of linear static was also conducted for 3 kinds of chassis thickness such as 4mm, 6mm and 5mm with a 16-ton load constant distributed. The study indicated the thickness in the 4mm can in the place cross member chassis of 6mm be replaced without the safety being affected.

(Kashem, et al., 2017)made a research on truck chassis of 4.5 tones comprising of C 2 side rail sections and 5 numbers of cross member compared to excitations and roughness of the road. The fixed components vibration to the chassis is as a result of the roughness of the road and excitation were researched and an examination on the response of the chassis by the distribution of stress and displacement. The locations that area suitable for engines and system of the suspension was determined the findings of the shape of the mode and outcome of the analysis showed that the main chassis disturbance is as a result of excitation of the road.

(China, 2015)Studied chassis alternative materials such as Epoxy or Carbon, Epoxy or S-glass and Epoxy or E-glass were applied as chassis materials in a variety of three cross-sections as Box-section, I-section, and C-section. Chassis TATA 2515 EX was analysed.  Finite element analysis and 3D modelling analysis were conducted in ANSYS and Pro-E software in a respective manner. The study showed that the Epoxy or Carbon section I-type has mechanical properties that are much better such as weight stiffness and stiffness than other cross-sections and materials.

(Dorst, 2015)Researched on the impact of cyclic loading in Gross Vehicle Weight of 36 tones cargo truck. A chassis of 2.45m in width and 12.35m in length measurements was analysed and load as a result of cargo was used as a load that is distributed uniformly that is divided equally to the body of the cargo’s contact surfaces with chassis. The method of sub-modelling of Finite element method was applied to acquire results that are accurate at regions with high stress.  Information from accelerometer was as forces converted that has been used as cyclic loading in components of sub-structure of the chassis. The results indicated that the static load of the cargo leads more stresses than the cyclic load produced by the roughness of the road.

Methodology

Many studies have been conducted on the chassis by a number of researchers (Gokhale, 2008)dynamically analysed a truck additionally in his method of truck simulation with ANSYS Finite element package making sure that the vibrational structure modes are in a suitable range, the vibrational ability was analysed.

(Khennane, 2013)Compared than the natural frequencies of chassis ladder with Finite element and methods of experimental. (Heißing & Ersoy, 2010)Study into modal analysis and dynamic of a space chassis that is, the complex chassis of dimension3 and transient response analysed by use of superposition principle.

This article works on truck chassis of 6 tones which has mode shapes and natural frequencies, it has been shortened by companies that are related for applying municipal service hereby, facing the question it raises and also the challenge as to whether the natural frequencies of the chassis with modification are in an appropriate range. In the researched model as compared to the original model, bolts and rivets have been completely modelled and the shell element also applied for analysis (Sheng, 2012). This element has a meshing that is more disciplined and better as compared to various elements with the potential of attaining results that are accurate with the meshing consisting of the dimensional 3 elements. It is valid to mention that the results have proven by the results being compared from a model that is similar to the proposed model by (Genta & Morello, 2008)

In this paper, a truck chassis of 6 tonnes has been researched on and it is longitudinal and a ladder chassis and the sections cross connecting are channel-shaped. The view of the automotive with dimensions and the dimensional plan has been shown in figures 1, 2 and table 1. The material of chassis is JIS-SAPH41 with 520MPa strength of the yield, 7800kg/m density, and 590MPa strength of the tensile (Madenci & Guven, 2015).

Finite Element Model

With the use of the 4-node shell element, the truck chassis is developed with ANSYS. This study makes use of a 4-node element with 6 degrees of freedom which is proper for nonlinear and linear alterations together with big deflections. There exist an approximate 70000 elements found in modelling which have proven to be suitable for comparison with various cases (Smith, 2016). Every case has an error that is less than 1 percent. In the figures 4 and 5, the model of the chassis is displayed with the appropriate accuracies together with the consideration of rivet and bolt joints effect simulation. Constraints and measurements have been displayed in fig 5.

The set boundary conditions are different in every analysis. In the analysis performed in normal mode, the used free-free boundary conditions are to be set to the model truck chassis with a lack of constraint being set to this chassis model. The choice of using a free-free boundary condition is due to its simpler experimental tests in the set conditions (Ehsani, et al., 2009).

Results and Discussion

Modal analysis was performed after the creation of the finite element chassis meshing and model in the free-free state with lack of constraints results were obtained with a calculation of the first 30 modes of the frequency with an indication of the importance of road simulation being erratic for the chassis of the truck. This analysation makes uses the ANSYS subspace methodology.

Since the chassis lacks constraints, the 6 modes of frequency get vanished. 3 set modes have a relation to the chassis displacement in the x, y and z directions with the other three nodes relating to the chassis rotation in the x, y and z-axes. The figure below makes a display of the related natural frequencies as well as the shapes of the mode for the chassis having a maximum displacement in the y-direction in all the modes.

The second, first and sixth modes consist of the global vibrations, of which the modes that remain should be the local vibrations. The beginning of the local vibrations is from the third mode that has 29.6 Hz. An existence of the dominant mode should be the proof of the torsion that occurs at 7.219 Hz in a maximum experienced translation by both chassis ends. The 2^nd mode is composed of the vertical bending existing at 17.153 Hz. In this mode, the beginning of maximum translation is at the chassis’ front section. The fourth and third modes have their localized bends existing at 33.517 Hz and 29.612 Hz. The greatest translation can be noticed using the top hat cross member. This member is exposed to huge translations at the 5^th mode that has a localized torsion. The top hat cross member has to be mounted to the truck’s gearbox. The sixth torsion mode is at the 38.475 Hz frequency whose maximum translation exists in the ends of the chassis.

The noticed natural frequencies from the modal analysis of the chassis of the truck can be used in determining the suitable situations for the parts of the truck that is in working conditions. Fig 6 displays the twisting mode that is found in the 7.219 Hz frequency that is a prevailing mode. The results from the first 30 modes that were analysed for the chassis are in table 2 below;

Since this is a free-free state analysis, the first 6 modes which exhibit zero frequency will not be considered and the 7 - 12 mode numbers in table 2 are a representation of the first 6 frequency mode.

It would be necessary to take notice that usually the first 6 frequency modes shone in the table from 7 to 12, play important roles in the dynamic behaviour of the chassis together with their higher frequency effects. This is due to their increased noise effects with their limited motor energy in the generation of such frequencies being ignored.

Generally, the natural frequency can be obtained by the use of the equation 1 shown below;

In the above equation, K represents the stiffness while m represent the mass.

Diesel engines are known to have the speed of operation varying from 8 to 33 revolutions in a second. In lesser idling speed conditions, the range of speed is about 8 to 10 rps. This is a translation of the frequency excitation that varies from 24 – 30 Hz. The low speeds compose of the main excitation. This is when the truck has been put in its first gear. In gear speeds that are higher, the chassis excitation is much lesser.

The truck chassis’ natural frequencies are not to coincide with the range of frequencies present in the axle, because it could lead to resonance which may sprout higher stresses and deflections hence a poor ride comfort. Road excitation exhibits a major influence to the chassis of the truck when the truck cruises along the roads. Practically, road excitation possesses known values that vary from 0 – 100 Hz. In higher cruising speeds, the excitation ranges from 3000 rpm – 50 Hz.

Vibration components mounting in the truck’s chassis nodal point as one of the methods of vibration attenuation for the reduction of the vibration along the chassis. The location of mounting the engine as well as the transmission system would be along the chassis’ symmetrical axis first mode of torsion where the influence of the first mode would be less.

The installed truck service equipment would raise the mass of the chassis hence leading to a decrease in the natural frequencies. Which regards to the previous discussions on the speed of the diesel engine, one could conclude the natural frequencies to be set in the critical range. Therefore, a decrease of the length of the chassis, the stiffness of the chassis increases. Also, the natural frequencies increase and are placed in an appropriate range.

Conclusion

This article has looked at the changes in the dynamic chassis behaviour due to change in the use of finite element method. The first 6 modes of frequencies in the modified chassis determine the dynamic behaviours are less than 40 Hz and shift from 7.22 – 38.475 Hz. The first 2 and 6 modes made the truck chassis experience global vibration the truck’s global vibration on the chassis include the vertical and torsion bending with two nodal points.

Since there is an increase in the mass of the chassis due to equipment installed, the natural frequencies would be far from the natural range that has a compensation with the increased stiffness of the chassis. The use of this method is able to prevent resonance phenomenon as well as unusual vibration of the chassis and place the natural frequencies in the natural range.

References

Barton, D. & Fieldhouse, J., 2018. Automotive Chassis Engineering. 1 ed. Broken Hill: Springer. https://books.google.co.ke/books?id=ZGJRDwAAQBAJ&pg=PA327&dq=Barton,+D.+%26+Fieldhouse,+J.,+2018.+Automotive+Chassis+Engineering.&hl=en&sa=X&ved=0ahUKEwja6ZDWrpbbAhVD1xQKHQiTBvEQ6AEIJzAA#v=onepage&q=Barton%2C%20D.%20%26%20Fieldhouse%2C%20J.%2C%202018.%20Automotive%20Chassis%20Engineering.&f=false

China, S. o. A. E. o., 2015. Proceedings of SAE-China Congress 2015: Selected Papers. illustrated ed. Nelson Bay: Springer. https://books.google.co.ke/books?id=M_kUCwAAQBAJ&printsec=frontcover&dq=Proceedings+of+SAEChina+Congress+2015:+Selected+Papers.&hl=en&sa=X&ved=0ahUKEwjLiYT_-4_bAhVCFMAKHV-XD2IQ6AEILDAB

Dai, L. & Jazar, R., 2018. Nonlinear Approaches in Engineering Applications: Energy, Vibrations, and Modern Applications. 1 ed. Devonport: Springer. https://books.google.co.ke/books?id=ONBJDwAAQBAJ&printsec=frontcover&dq=Nonlinear+Approaches+in+Engineering+Applications:+Energy,+Vibrations,+and+Modern+Applications.&hl=en&sa=X&ved=0ahUKEwi5zOKe-4_bAhViK8AKHYogCy0Q6AEIJzAA

Dorst, K., 2015. Frame Innovation: Create New Thinking by Design. illustrated, reprint ed. Nelson Bay: MIT Press. https://books.google.co.ke/books?id=UBt8BwAAQBAJ&printsec=frontcover&dq=Frame+Innovation:+Create+New+Thinking+by+Design&hl=en&sa=X&ved=0ahUKEwjZz-Ck_I_bAhWnKcAKHfAQCaMQ6AEIJzAA

Ehsani, M., Gao, Y. & Emadi, A., 2009. Modern Electric, Hybrid Electric, and Fuel Cell Vehicles: Fundamentals, Theory, and Design, Second Edition. 2, revised ed. Bathurst: CRC Press. https://books.google.co.ke/books?id=Rue_FhZsV40C&printsec=frontcover&dq=Modern+Electric,+Hybrid+Electric,+and+Fuel+Cell+Vehicles:+Fundamentals,+Theory,+and+Design&hl=en&sa=X&ved=0ahUKEwjrwNXK_I_bAhUpDsAKHdMpAycQ6AEIJzAA

Genta, G. & Morello, L., 2009. The Automotive Chassis: Volume 1: Components Design. illustrated ed. Portland: Springer Science & Business Media. https://books.google.co.ke/books?id=ZBrg8iwcRfsC&printsec=frontcover&dq=Genta,+G.+%26+Morello,+L.,+2009.+The+Automotive+Chassis:+Volume+1&hl=en&sa=X&ved=0ahUKEwjN5ydr5bbAhUJUhQKHVDoBoYQ6AEIJzAA#v=onepage&q=Genta%2C%20G.%20%26%20Morello%2C%20L.%2C%202009.%20The%20Automotive%20Chassis%3A%20Volume%201&f=false

Gokhale, S., 2008. Practical Finite Element Analysis. 1 ed. Nelson Bay: Finite To Infinite. https://books.google.co.ke/books?id=yKTObdhQ66YC&printsec=frontcover&dq=Practical+Finite+Element+Analysis&hl=en&sa=X&ved=0ahUKEwiy5oiT_Y_bAhVMKcAKHbXlBuEQ6AEIJzAA

Heißing, B. & Ersoy, M., 2010. Chassis Handbook: Fundamentals, Driving Dynamics, Components, Mechatronics, Perspectives. illustrated ed. Taree: Springer Science & Business Media. https://books.google.co.ke/books?id=NSlSJtEy-NIC&printsec=frontcover&dq=Chassis+Handbook:+Fundamentals,+Driving+Dynamics,+Components,+Mechatronics,+Perspectives&hl=en&sa=X&ved=0ahUKEwieoMyq_Y_bAhUpLMAKHa5qBVkQ6AEIJzAA

Henry, C., 2017. Kar-Kraft: Race Cars, Prototypes and Muscle Cars of Ford's Specialty Vehicle Activity Program. illustrated ed. Port Lincoln: CarTech Inc. https://books.google.co.ke/books?id=tPEoDwAAQBAJ&printsec=frontcover&dq=Race+Cars,+Prototypes+and+Muscle+Cars+of+Ford%27s+Specialty+Vehicle+Activity+Program.&hl=en&sa=X&ved=0ahUKEwj01qjF_Y_bAhXlJsAKHezdCjkQ6AEIJzAA

Kashem, S., Nagarajah, R. & Ektesabi, M., 2017. Vehicle Suspension Systems and Electromagnetic Dampers. 1 ed. Alice Springs: Springer. https://books.google.co.ke/books?id=bBo0DwAAQBAJ&printsec=frontcover&dq=Vehicle+Suspension+Systems+and+Electromagnetic+Dampers&hl=en&sa=X&ved=0ahUKEwiE8Pje_Y_bAhWMRMAKHRLtAscQ6AEIJzAA

Khanna, V., 2017. Extreme-temperature and Harsh-environment Electronics: Physics, Technology and Applications. 1 ed. Lismore: Iop Publishing Limited. https://books.google.co.ke/books?id=qq3inAAACAAJ&dq=Extreme-temperature+and+Harsh-environment+Electronics:+Physics,+Technology+and+Applications&hl=en&sa=X&ved=0ahUKEwi6x8T6_Y_bAhXMJcAKHQ3CC5UQ6AEIJzAA

Khennane, A., 2013. Introduction to Finite Element Analysis Using MATLAB® and Abaqus. illustrated ed. Taree: CRC Press. https://books.google.co.ke/books?id=IHXfSNYXRD8C&printsec=frontcover&dq=Introduction+to+Finite+Element+Analysis+Using+MATLAB%C2%AE+and+Abaqus.&hl=en&sa=X&ved=0ahUKEwjvwKSf_o_bAhVIJ8AKHWV7Bz0Q6AEIJzAA

Madenci, E. & Guven, I., 2015. The Finite Element Method and Applications in Engineering Using ANSYS®. 2, illustrated ed. Alice Springs: Springer. https://books.google.co.ke/books?id=aJKeBgAAQBAJ&printsec=frontcover&dq=The+Finite+Element+Method+and+Applications+in+Engineering+Using+ANSYS%C2%AE&hl=en&sa=X&ved=0ahUKEwiw0b_e_o_bAhWMCcAKHahjDREQ6AEIJzAA

Sheng, G., 2012. Vehicle Noise, Vibration, and Sound Quality. illustrated ed. Bathurst: SAE International. https://books.google.co.ke/books?id=D-OapwAACAAJ&dq=Vehicle+Noise,+Vibration,+and+Sound+Quality&hl=en&sa=X&ved=0ahUKEwj00_H4_o_bAhVMFMAKHf17DaUQ6AEIJzAA

Smith, C., 2016. The Car Hacker's Handbook: A Guide for the Penetration Tester. 1 ed. Bathurst: No Starch Press. https://books.google.co.ke/books?id=Ao_QCwAAQBAJ&printsec=frontcover&dq=The+Car+Hacker%27s+Handbook:+A+Guide+for+the+Penetration+Tester&hl=en&sa=X&ved=0ahUKEwjZ4tSU_4_bAhUHK8AKHSQ_CsYQ6AEIJzAA