Design of a Car Suspension System - Assignment Example

Running Head: Design of a car suspension system Design of a car suspension system [Student Name] [Course Title] [Instructor Name] [Date] Table of Contents Introduction 3 1 Filter 3 2. Mathematical modelling 4 3). Changing parameters 6 4. New component to suspension 6 5. The design criteria for the car suspension system 10 6. The optimum parameters for the car suspension system 13 7 Summarizing your findings 13 References 14 Introduction All cars have car suspension system which helps in shock absorption due to vibrations caused by road roughness. The shock absorption system is a system of the car where there is a wheel, a spring, stabilizers, tires, and many others. The car suspension system is an important component of the vehicle since it makes the passengers comfortable or uncomfortable. The car suspension system is studied under the signals and systems because it converts vibrations caused by road roughness and filters them using a low pass filters to change them to small amplitude response frequency. This paper aims at covering variation of damping ratio as well as other parameters to see how the signals change. Therefore it can be said that there is a relationship between a car suspension system and signals. These signals are produced due to oscillation of the chassis of a car. These signals are taken as input signals to be analyzed by designers of cars in order to come up with a car that has reduced response frequency. Matlab has been used to design optimum parameters for the car suspension system. 1 Filter The car suspension system should act has a low pass filter because of its ability to reduce vibrations of the car due to road roughness to small amplitude. The low pass filter allows only low frequency vibrations. This means it has the ability to indentify high frequency signals and filter it. The following images show the original image and a filtered image using a low filter. Low pass filter is commonly used for noise reduction while a high pass filter may be used separate signals. 2. Mathematical modelling The following diagram has details of the coordinate of the suspension system, the mass of the car and the motion of the car. It has the length of the spring as Lo with a spring constant of K which complies with Hooke’s law of elasticity. The forces acting on the mass i.e the car is the force of spring and gravity. 2a. differencial equation governing the motion of the chassis. As mentioned in the first statement above the differential equation governing the motion of the chassis, Hooke’s law is used and the first equation is. Ma=k Whereby F is the magnitude of the force used on the spring, while is the distance of the spring that is stretched or compressed, k is the spring constant. The spring constant is the stiffness of the spring therefore the following are differential equations governing the movement of chassis. This equation is farther analyzed and reduced as follows; The laws of physics that are applied in this case is Hooke’s law of elasticity and Newton’s law of motion. 2b) The frequency response The frequency response of this LTI system is derived linear constant-coefficient differential equation is shown below; 2c). In minimizing the amplitude of the up and the down motion of the car suspension system we develop an equation which contains natural frequency. It has been noted that the car amplitude depended on shock absorbers as compared to frequency that means barriers such as bumps, played an important role in determining the signs of the amplitude. However the spring constant does not do the same job in terms of regulating frequency, thus the equation for the same is shown below; 3). Changing parameters From the previous result, the road roughness increases the amplitude of the frequency thus increasing the discomfort in the car. The discomfort in the car is as a result of the vibration of the car as it tries to negotiate with the roughness. This will lead the customers to complain about the discomfort in the car. The aim is to determine as to whether changing the parameters will reduce the discomfort. Looking at the equation below; From the equation above which represent natural frequency that determines the comfort or discomfort of the passenger’s shows that change of k or M will lead to change in natural frequency. This means that since mass is constant therefore changing in k will change comfort. Therefore not all parameters will be changed to bring difference in comfort. The shortest wavelength corresponds to the highest frequency. The highest frequency is produced when the electron’s is kinetic energy is given up in the emission of a single photon. 4. New component to suspension Introducing a new component in the name of a shock absorber will change the parameters and the modeling that will be used in solving the problem. 4a)the new component will change linear constant-coefficient differential equation-by introducing coefficient C which will have dimensions relating to the level of car motion on the ground level. The equation will be as follows; kx(t) = + ky(t) + c ( Where c ( is part of the new component. The equation has be integrated to be in uniform with other equations. 4b) the new frequency response after introducing the new component, it will be as follows; In the case above the new frequency have been calculated and incorporated in the final equation. 4c) weight of a car to turn frequency response with varying wn and zeta values 4d). varying wn and zeta values wn = 10; zeta = .1; 5. The design criteria for the car suspension system a). The cut‐off frequency related to the natural frequency The car response is at maximum amplitude when the cut off frequency is equal to the natural frequency. This means that, the road is very bumpy and the system is sluggish. Natural frequency is attained when resonance occurs or there is high amplitude due to barriers in the road. When the natural frequency is greater than or lower than the cutoff frequency the ride is smooth as well as the car’s response is low. It should be noted that when the cutoff frequency is lower than the natural frequency it is said to have a soft ride and a sluggish while when the cutoff frequency is greater than the natural frequency it is said to have a soft ride and rapid system. This shows that the natural frequency and the cutoff frequency have similar effects. b). The effects of varying the damping ratio looking at the effect of changing the damping ratio, it will be noted that increase in damping ratio will lead to declined oscillation as shown in the Matlab output below; It shows that the relationship between damping coefficient and the stiffness of the spring is inverse that is an increase in damping coefficient will lead to a decrease in the number of oscillation that are experienced by the passengers. When decreasing the damping ratio there will be reduced uncomfortable oscillatory response leading to increased comfort. It shows that the relationship between damping coefficient and the stiffness of the spring is inverse that is an increase in damping coefficient will lead to a decrease in the number of oscillation that are experienced by the passengers. 6. The optimum parameters for the car suspension system The analysis of the car suspension system which has a mass of 2 tons shows that the optimum parameters based on the criteria is that wn=20,zeta=2 and a situation where the cut off frequency is not equal to natural frequency. At the point where the cut off frequency and natural frequency are equal the passengers are uncomfortable due to road barriers. It should be noted that natural frequency is responsible for structural damage due to its large vibration which causes large amplitude. Therefore there is need for replacement of shock absorbers once they are defective due to there ability to reduce the amplitude of car suspension. 7 Summarizing your findings The findings of this design process indicated that car suspension system is a low pass filter and it involves small amplitude changes as a result of changes of road surface due to road topography. This is because it filters rapid variations to small amplitudes making the vehicle comfortable. The result also indicated that when the cut off frequency is equal to natural frequency the road is bumpy and the passengers are uncomfortable. It was noted that changing damping ratio was responsible for changes in frequency of a car. The assignment as played a very important role in enhancing my understanding of the topic signals and systems. This is because it gave me an opportunity to model differential equations governing the motion of the chassis and learner constant-coefficient differential equation. Through this assignment I was able to learn how to vary frequencies as well as how to use Matlab program in signals and system. Therefore it has achieved the objectives of the study. References Eisner, H. (2008). Essentials of Project and Systems Engineering Management. Hoboken, N.J.: John Wiley & Sons. Hsu, K, Soong, R, Chen, K & Lan, T, (2013). A Computerized Approach to the Design of Automobile Suspension System Jadlovska, A., Katalinic, B.; Hrubina, K., & Wessely, E. (2013). On Stability of Nonlinear Systems and Application to Apm Modeling, DAAAM International Scientific Book., 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. Robichaud, J. M. (2010). Reference Standards for Vibration Monitoring and Analysis. Saint John, NB Canada. n.d. Sun Lu, 2002. Optimum design of “road-friendly” vehicle suspension systems subjected to rough pavement surfaces. Applied Mathematical Modelling, Volume 26, issue 2002 Read More