Design and Analyze the Car Suspension System - Term Paper Example

Running Head: Design of a car suspension system Design of a car suspension system [Student Name] [Course Title] [Instructor Name] [Date] Abstract The main purpose was to design and analyze the car suspension system with intention of understanding the effects of damping ratio and natural frequency on the passenger comfort. In designing and simulation of result, Matlab has been utilized. The results indicate that changing damping ration had effects on the amplitude of the frequency as compared to changing natural frequency. This was shown by both step response and frequency response. It was also noted that when the cu-off frequency was equal to natural frequency the amplitude was low while it was high when it was higher than or less than. Table of Contents Abstract 2 Introduction 5 1.Kind of filter to be used 5 2.Mathematical modelling 7 2b) The frequency response 8 3). Changing parameters 9 4. New component to suspension 9 5. The design criteria for the car suspension system 14 Car suspension system 18 7 Summarizing your findings 18 References 19 Introduction The Car suspension system is an important part as it provides a means of separating vibrations which will cause discomfort among passengers. This is done because it has shock absorbers and springs that act as a damper. In this assignment we have designed a chassis whereby we have analyzed the impact of 1. Kind of filter to be used A car chassis acts a low pass filter as it separates irregular signals caused by road roughness to create a comfort in the car. The two diagram below shows effects of a low pass filter on original image as well as the frequency graph shows how, the images frequency was smoothened. Figure 1: original and filtered image plus the frequency for filtering(www.cs.unm.edu , 2015). It can be seen that the images brightness has been eliminated and from the frequency graphs, the original input has irregular amplitude while the filtered amplitude using low pass filter is regular. 2. Mathematical modelling The following is a version of the suspended mass of the chassis system of the car to be modeled. Figure 2: car suspension model and Road roughness The following presents parameters that will be used in modeling It can be noted that there are two motions that needs to be considered which inlude (/2) for the wheel and road as well as /2) which is a collission motion. a) Whe begun by forming equations that will guide the analysis of the car suspension system. The first equations is differential equation governing the motion of the chassis assuming the it obeys Hooke’s law of elasticity which is force exerted by spring F = k whereby F is the resultant force on the car attached to the spring, Lo is the displacement of the car and k is spring constant. It should be said that resultant force can be also calculated as F=Ma , Where a is acceleration, M is mass of the car, k is spring constant and Lo is the displacement of the car This equation can changed to differential equation by introducing factor of time in the acceleration M = Where is acceleration, M is mass of the car, k is spring constant and Lo is the displacement of the car This equation is futher calculated as follows M = where is This further simplified as follows Thus kh(t) = ky(t) + 2b) The frequency response In calculating frequency response for linear constant-coefficient differential equation, frequency is calculated below; kh(t) = ky(t) + ------------------------------------- (1) h(t) = --------------------------------------- (2) y(t) = f (j) ----------------------------------------- (3) = ------------------------------- (4) Combining and replacing y(t) and h(t) k (= k ( + M ------------------ (5) then let us replace . Then the new equation becomes k (= k ( + --------- (6) this can be simplified to k = k ( + ------------------------ (7) it is further simplified as k = (k --------------------------- (8) then frequency is expressed as --------------------------------- (9) 2c). The comfort of a passenger depended on the car suspension system. If this system does not have shock absorber then there is a problem for users of the car. This is minimized by designing system that minimizes natural frequency. This is an upward and downward of frequency. The following equation is utilized in this case. where is natural frequency, k is damping ratio and M is the mass of the car which is 2 ton in this case 3). Changing parameters The main purpose of changing parameters during simulation is to determine which parameters are relevant in reducing the amplitude of the roughness of the road. In this case we have three parameters in mind that is the weight of the car that is M, the damping coefficient, k and the natural frequency. The mass of the car remains the same as we are design a chassis for a specific car. This means the parameters to be considered are the damping coefficient, k and the natural frequency. Since the car suspension system acts as a low pass filter to attenuate high amplitudes then changing parameters relating to amplitude of the suspense will help. This will be analysed to determine which of the parameter has impact on the aplitude. 4. New component to suspension 4a) this section deals with introducing a new component to the chassis that is a shock absorber. Let consider the changes in linear constant-coefficient differential equation due to introduction of a shock absorber. this is done as shown below , Where a is acceleration, M is mass of the car, k is spring constant and Lo is the displacement of the car This equation can changed to differential equation by introducing factor of time in the acceleration M = Where is acceleration, M is mass of the car, k is spring constant and Lo is the displacement of the car This equation is futher calculated as follows M = where is This further simplified as follows Thus kh(t) = ky(t) + then here a component is introduced c ( and new equation becomes kh(t) = ky(t) + + c ( 4b) the frequency response was and k = while c = 2 Thus they are substituted as shown below; h(t) = + y(t) + 2( This is further simplified as 2 4c) the main aim is to investigate the impact of natural frequency and damping ratio for a car with a weight of a car is 2 ton. This is done by use of Matlab in making frequency response plots. Changing natural frequency has no impact on the amplitude as shown below. Figure 3: changing natural frequency From the above observation it appears changing the natural frequency has no impact on the amplitude Now let us change the damping ratio of the same equation Figure 4: changing damping ratio Changing damping ration appears to change in amplitude of the frequency 4d). this is when we use Step command to plot graphs with varying wn and zeta values The following matlab code has been used Figure 5: Changing damping ratio Figure 6: Changing natural frequency The amplitude is not affected by changing natural frequency but it is affected by changing damping ratio. 5. The design criteria for the car suspension system The cut‐off frequency related to the natural frequency Cut-off frequency is the frequency at corner frequency and always is -3 db frequencies. Let consider the following plots and consider their natural and cut‐off frequency. The matlab code used to make this graphs is shown below; Figure 7: original amplitude and cut-off frequency Figure 8: Zeta= 2, wn= 0.1 and cut-off frequency Figure 9: zeta=0.1, wn=0.707 In this case we were finding out the relationship between cut of frequency and the natural frequency and the component that controls the cut off frequency. It has been noted that the cut off frequency is controlled by the shock absorber. When decreasing the cut off frequency there is a smooth ride while of the cut off frequency is equal to the natural frequency the ride is bumpy and sluggish. The result obtained above indicates that there is no conflict requirement in designing a soft suspension system. A soft suspension system is where the ride is comfortable to the users. The effects of varying the damping ratio The code for varieng the damping ratio in matlab was determined and the graphs bellow were produced. From the graphs it will be noted that changing the damping ratio led to change in amplitude of the frequency. A reduction in damping ratio led to increased frequency while increase in damping ratio led to reduced amplitude. This is a clear indication that damping ratio is responsible for creating comfort in a car. Figure 10: zeta =0.1, wn=1 Figure 11: zeta =0.1, wn=1 Figure 12: Increase damping ratio Car suspension system The optimum parameters that should be selected from the criteria mentioned above is where the natural frequency is greater than the cut off frequency and the damping ratio should be greater than 0.77. 7 Summarizing your findings This assignment has been helpful in helping me understand how to design a car suspension system thus increasing my knowledge in the subject. I have learned how to design the suspension system by known that the damping ratio was important in changing the frequency amplitude of road roughness. I have also learned that there is a relationship between a natural frequency and the cut off frequency. The relationship between the natural and the cut off frequency is inverse. References Hsu, K, Soong, R, Chen, K & Lan, T, (2013). A Computerized Approach to the Design of Automobile Suspension System Likaj, R., Shala, A., Bruqi, M. & Bajrami, XH (2014). Optimal design and analysis of vehicle suspension system, DAAAM International scientific book. Sun Lu, 2002. Optimum design of “road-friendly” vehicle suspension systems subjected to rough pavement surfaces. Applied Mathematical Modelling, Volume 26, issue 2002. www.cs.unm.edu (2015). Introduction to Fourier Transforms For Image Processing Read More