# Design of a Car Suspension System - Mathematical Modelling, the Cut-Off Frequency Related to the Natural Frequency – Math Problem Example

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The paper “ Design of a Car Suspension System - Mathematical Modelling, the Cut-Off Frequency Related to the Natural Frequency”   is an engrossing variant of a math problem on mathematics. The design of car suspension considered a car that weighs 2 tons and only damping coefficient and spring stiffness was adjusted to determine their impact. The Matlab was used to generate results and the results show that when stiffness is increased the oscillation reduces while damping coefficient changes produce similar results. This is the due occurrence of an error due to the spring constant changes.

This means that changing the damping constant of the suspension system and springs constant the response of the car suspense system. IntroductionThe car suspension system is interconnected parts of a car that hard in the car motion as well as reduces passenger discomfort caused by various barriers on the road. These parts include shock absorbers, stabilizers, springs, tires, and air tires. When designing a car suspension system, one considers a simple shock absorber which is an important device in a car. The shock absorber or a suspension system will help in preventing socks that result from barriers such as drag forces irregular road sections, vibrations from engines and wheels, and other factors.

In designing suspension systems these factors should be taken into consideration to improve the convertibility of drivers and passengers of vehicles. The car suspension system designed relay on a signal to estimate the impact of road barriers on the motion of the car and the comfort of vehicle use. This is because the car suspension system produces signals which are as a result of the oscillation of the chassis system.

Once there is contact between the road and the car suspension system, signals are produced which can be analyzed to produce output signals. In this case, Matlab has been used to design the vehicle suspension system. The initial stiffness constant is taken as 3000 N/m(K), the damping constant of the suspension system as 30 N. m/s, and weight of the car as 2 ton. The relationship is that when there changes in the damping coefficient, there are corresponding changes in the force. Kind of filter to be usedWhen designing the car suspension system, a low pass filter is used because of its ability to identify irregular signals within an image thus eliminating necessary features from the analysis.

Low pass filters allow high-frequency filters to pass through. The following is an example of an original image that is filtered using a low pass filter to produce a filtered image. The image brightness has been reduced and its quality improved without shadows. There are differences between a low pass filter and a high pass filter that is a high pass filter allows some sections of the image to be pronouncedMathematical modelingIn this case, a simple suspension system is been designed in consideration of the effect of dumper the impact of the mass between the motioned barriers and the impact of the mass when it collided with the barriers.

In modeling, one considers a simple case of a damper system with stiffness k, damping coefficient, C and mass M as shown in the diagram below From the consideration above there is two motion of the wheel and road that is (/2) and collision motion that is (/2).

References

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Hsu, K, Soong, R, Chen, K & Lan, T, (2013). A Computerized Approach to the Design of Automobile Suspension System

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Likaj, R., Shala, A., Bruqi, M. & Bajrami, XH (2014). Optimal design and analysis of vehicle suspension system, DAAAM International scientific book.

Proulx, T. (2011). Rotating Machinery, Structural Health Monitoring, Shock and Vibration: Proceedings of the 29th Imac, a Conference on Structural Dynamics, Springer, 2011. London: Print.

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Sun Lu, 2002. Optimum design of “road-friendly” vehicle suspension systems subjected to rough pavement surfaces. Applied Mathematical Modelling, Volume 26, issue 2002

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