Simplified Suspension System - Research Paper Example

Simplified Car Suspension System (Students Name) (Institution) (Date) Introduction Many people who contemplate about the performance of motor vehicles normally think about horsepower, high acceleration and torque power. However, the entire energy generated by the piston engine serves no purpose if the car has poor control. This explains the reasons regarding the intense concentration on the suspension system following the invention of the four-stroke combustion engine. Suspension usually acts as interconnectors for various parts of a vehicle. They suspend most crucial parts such as shock absorbers, wheels, stabilisers as well as springs. Primarily, these parts offer the motion to a vehicle since they are interconnected o the wheel. Essentially, the suspension system offers comfort to the passengers who use the car and further aids in a safety of the car from bumpy and irregular roads (Gaid et al., 2006). The mechanics behind the suspension system is to ensure that the car is devoid of shocks and discomfort to the passengers. They produce signals which come out of kinematic excitation. The oscillation is normally caused by the pumps on the roads and the objects which a car passes. The existing barriers and objects on the roads lead to the production of input and output signals for the restoration of comfort and safety of the car. The interactions which exist between the car and the road produce the input, and the vibrations which are produced by the interaction are referred to as output. One characteristic of the car suspension system is their mode of operation which tends to follow more harmonic patterns. Several models have been used to relate to the movement of the suspension system such as Fourier Analysis, Wavelets and Correlation Techniques (Bastow et a., 2004). These models have been used to explain the interactions between the various input and output signals. A close relationship exists between the suspension system and the signals produced. The relationship is premised on the fact that the car suspension system produces parameters such as specified torque, vibration, speeds and both necessary and unnecessary noise. This paper aims at using the technique of Signal Analysis to explore the frequencies produced and the signals of the signal parameters produced by the suspension. Low Pass Filter Every waveform consists of sine waves which normally occur at different frequencies. The rates normally exist in the categories of lower and higher frequencies. Therefore, the primary role of Low Pass Filter is to filter out signals with high frequencies. It only permits low-frequency signals to pass through. Essentially, the low pass filter is used to identify periodic components existing in a particular image. This is aided by filtering the high and low-frequency components in a given image. Therefore, the process of filtering ensures that the image is not affected regarding saturation, colour, opacity and inversion. The filtering process normally depends on the strength of every frequency (Gaid et al., 2006). The low frequencies are regarded as a different classification which stores and keep most of its strength. On the other hand, the high frequencies are normally reduced and not stored. This aids in the filtering process at a particular frequency referred to as f3db. The following diagram represents a typical low pass filter and the mode of operation as presented in the caricature. In the diagram above, the high frequencies normally pass from the cap and straight to the ground through the resistor and the capacitor. They are normally not sieved out at any point. On the other hand, signals with low frequencies pass through the resistor and are flittered out through the Signal Out section. They do not pass through the Capacitor to the ground or to the final intended destination. This, therefore, explain why the low filtering frequencies are easily sieved out from the general frequencies whole the signal with high frequencies are allowed to pass through. Signals such as noise are filtered out due to their low frequencies by the use of suspension systems (Kim & Ro, 2000). The following pictures portray the effects of the low pass filter categorized as the original picture and the aftermath of low pass filter; The picture set below shows the original image and that produced from the effects of exposure to low pass filter. The original image is outstanding, bright, clear and highly visible. On the other hand, the second image is relatively blurred, less bright and appears faded. Also, the spots on the second image have significantly changed from the first image. The low pass filter has considerably reduced the brightness of the second image. Suppose the image had some shadows, the low pass filter would have substantially improved the entire image. The high pass filters normally make an image or an effect more pronounced and amplified. On the other hand, low pass filter reduces the intensity and pronouncement of a frequency or an image. It seeks to reduce the effects and lowers the intensity of the general frequency (Bastow et a., 2004). The car suspension performs a similar role with that of the low pass filter. It normally seeks to reduce the intensity of shocks, noise and discomfort caused by the contact of the car and the road. It, therefore, aims at reducing the consequences of the vibrations caused by the contact of the tire and the road. Likewise, the low pass filters work towards reducing the intensity of the waves and the effects on an image or item. Scholars, therefore, considers the suspension system to be a perfect example of a low-pass filter so as to ensure comfort to the passengers and reduction of vibration effects on the car. In summary, the low pass filter technique explains the role of the suspension system by the use of differences in the frequencies of vibrations. The existence of both high and low frequencies generated by an array of vibrations aids in the use of low pass filter technique in assessing the role of the suspension system (Gaid et al., 2006). The process of filtering out any noise, discomfort or any vibration caused between the contact of the car and the road aids the suspension system in ensuring comfort for the passengers. It relies on filtering out all unnecessary disturbances between the car and the road so as to generate the required comfort. Hooke’s Law Hooke’s Law states that the force (F) of restoring spring is directly proportional to a small displacement of the spring. When the force is applied in the spring, the stretch is referred to as the extension. Therefore, this law stipulates that the extension (e) caused by the spring is directly proportional to the force (F) in the spring. The force is normally measured in Newton’s while the extension is measured in centimetres or meters. Hooke’s Law can be measured using the following formula; F= K x E Where: F is the force in Newton’s, N k is the 'spring constant' in Newton’s per meter, N/m e is the extension in meters, m It can also be described as; F = maf = k Where; F is the magnitude of the force exerted on each end of the spring L is the distance that the spring is stretched or compressed from its relaxed length, K is the spring constant of particular spring The spring constant used in the determination of this law is the degree of how hard or easy it is to succeed in stretching or compressing a spring. This is normally possible due to the differences in the nature and components of springs. Scholars argue that a hard or stiffer spring exhibits a relatively larger spring constant (Kim & Ro, 2000). On the other hand, a soft spring shows a narrower spring constant due to the little force required to compress or stretch the spring. This can be explained using the following model; m = m = Let h(t) = x(t) kx(t) = ky(t) + The essence of application of the suspension system is to ensure that the springs act as absorbers of any frequencies possible of causing discomfort for the passengers. The various effects of the contact between the vehicle and the road lead to an exertion of force. The force usually has little o much effect on the car. Therefore, the extent of the force has an implication on determining the extent of stretch or compression of the spring. The rule of the thumb applicable in this situation is to ensure that the cars have little disturbance or noise as a result of the force exerted by the road objects such as bumps. Therefore, Hooke’s law aims at ensuring that the relationship existing between force and the spring extension determine the result of the effect of suspension on cars (Bastow et a., 2004). Frequency Response of Hooke’s Law Frequency Response Transformation refers to the time, frequency and frequency signals which form the frequency domain. The constituents of the frequency domain normally hold the amplitude of cosine and sine waves. Therefore, the role of frequency response is to determine the performance if the suspension system using two major criteria. The first one regards the concept of changing time and the second one relates to the concept of damping ratio. These two concepts normally determine the extent to which the suspensions systems achieve their role of enhancing comfort be reducing the effects of shocks and disturbances in the car. The essential underlying idea is the relevance of Hooke’s Law in determining the exact role of spring system as part of the suspension system (Gaid et al., 2006). The frequency domain determines the functionality of the suspension system of any motor vehicle. Normally, the particular contents of the frequency domain which includes time-frequency and damping ratio determine the extent to which the suspension system achieves its intended objectives. Different signals are normally sent to the frequency domain depending on the particular cause such as objects or bumps on the road. These signals enter into the suspension system on a singular and differentiated model. However, the efficiency of this system requires a combined and harmonic synthesis of the signals (In Liu et al., 2013). Therefore, the synthesising of the frequency domain which makes it shift from single separate signals into a harmonic signal requires three important loops. The concentric loops aid the suspension system to diffuse the different single signals into a combined domain. These loops can be explored as shown in the below mathematical procedure; kx(t) = ky(t) + x(t) = y(t) = H (j) = k (= k ( + m k (= k ( + k = k ( + k = (k - Whenever a typical vehicle is in motion, the springs normally aid in the up and down movement pattern. The up and down movements are as a result of frequency responses. The differences in the amplitudes lead to the differences in the actions of the springs in controlling the effects of signals out of motion. The springs are normally less efficient in responding to all frequencies developing out of the movement of a car. This is explained from the errors which are likely to exist from the amplitudes of frequency display. The springs may have different effects in terms of extensions, nature and responds to the signals causing a less significance in responding to various frequencies. The consequence of this scenario leads to possible obscuring of small peak frequencies which tend to appear very close to large peak frequencies (Gaid et al., 2006). This spectral leakage is the main cause of irregularities witnessed in the use of suspension systems with different spring characteristics. The best way to manage these glaring anomalies is through the assessment and developing the resonant frequency. This can be using the following formula; k - Changing System parameters The role of suspension system depends less significantly on the nature or the parameters of the system. Instead, it depends much on the kind of force or frequency exerted which ultimately instigates a response on the springs used as components of the entire system. In fact, changing the system parameters (k or m) will be less significantly since they have no effect on changes in the amplitude. The vibrations which occur in any vehicle is not determined by changes in mass or even stiffness of the springs. It majorly depends on the extent of force and pressure from which further generates the vibrations (Bastow et a., 2004). The essence of this analogy rests on the premise that changes in weight lead to the corresponding change in force. This implies that it’s possible to use force response function as a tool for estimating mass response function. This is possible since both of them are correspondingly determined by changes in on parameter. Relevance of Hooke’s law in Suspension system Hooke’s law describes the behaviour of springs as illustrated in the previous sections of this paper. It assesses the relationship between forces, extension and constant that exists in sprigs. Therefore, this law is instrumental in determining the role of springs in the suspension system. The suspension system acts as the comfort provider in the engineering of a car (Kim & Ro, 2000). This is achieved when the springs respond by absorbing unnecessary shock, noise and stress caused when the car is in motion. The following graph illustrates the essence of relationship which exists between the models in Hooke’s law The graph illustrates the relationship which exists between Force, extension and the constant. Suppose the elastic limit is not passed, the gradient shows a straight line as depicted in the graph. The gradient illustrates the constant K which defines the stiffness or the softness of the spring. The greater the value of k, the stiffer the springs therefore, engineers aim at ensuring that the modeling of the suspension system integrates the extent to which the spring responds to force. A smaller value of k implies desirability of the spring since it will cause slight movement of the car while in constant with an object (Bastow et a., 2004). Suspension System with Damping The introduction of damping is a show of improvement on the suspension systems. The introduction of the new component introduces a new constant C into the entire equation. This is achieved by introducing the new dimensions of the new components (shock absorber) into the general equation (Kim & Ro, 2000). The following equation best summarizes the effect of the introduction of the shock absorber into the system; kx(t) = + ky(t) + c ( The inclusion of the shock absorber causes an addition drag force top the vehicle. The drag force, however proportional to the speed of the vehicle as depicted in the equation above. Frequency Response with Damping The introduction of damping effect leads to the creation of small and numerous frequency responses. These responses can be explained using the following equation; k = c = 2 x(t) = + y(t) + 2 ( 2 Frequency response Graphs with varying and values: The following are the various frequency response graphs with varying and values = 5, =0.2: =10, = 1: =5 , = 0.1: Step command Graphs with varying and values: = 20, =0.2 (Sport Suspension): =80, =2 (Sport suspension): =10, = 0.1 (Comfort Suspension): =10, =0.09 (Comfort Car): Relationship between Cut-Off Frequency and Natural Frequency There exist a close relationship between Cut-Off Frequency and Natural Frequency. The relationship is that Cut-Off Frequency causes an influence on natural frequency. Therefore, when Cut-Off Frequency occurs, then there will be a corresponding occurrence of natural frequency within the setup. The following are the three possible scenarios which explain the relationship between these two frequencies; i. When Cut-Off Frequency is EQUAL to natural frequency; the response of the car will be MAXIMUM. This implies that the car will be having a very bumpy ride and a relatively sluggish system. ii. When the Cut-Off Frequency is LESS than the natural frequency; the response of the car will be relatively LOW. This implies that the car will be moving smoothly, sluggish system and experience a relatively soft ride. iii. When the Cut-Off Frequency is greater than the natural frequency; then the response of the car will be relatively LOW. This further implies that there will be a very smooth ride of the car, rapid system and a relatively very soft ride The result of the relationship between these two frequencies is that the design of the cars will aim at having the Cut-Off Frequency as greater than the natural frequency. The engineering function on every car aims at ensuring that the cars have absolute comfort and very smooth and soft ride. This is intended towards giving customers a satisfactory product which also meets their comfort demands (Kim & Ro, 2000). The Effects of Varying the Damping Ratio: The damping ratio normally determines the level of comfort achieved for any particular vehicle using the system. The ratio determines the extent of oscillation changes witnessed when the car is in motion. Essentially, the introduction of the damping effect aims at ensuring that the car is at its comfort for use by the customers (Bastow et a., 2004). When the damping ratio is increased, there will be a corresponding decrease on the comfort achieved in the vehicle. This occurs due to the increase in the vibration changes causing ultimate changes in the frequencies. A decrease of the damping ratio will lead to a corresponding increase in the comfort of the vehicle. This is achieved through reduced uncomfortable vibrations or oscillatory response that further enhances the levels of comfort. This Illustration shows an inverse relationship between the damping coefficient and the stiffness of the spring. The increase in the damping coefficient leads to decrease in the vibrations or number of oscillations that determine the comfort of passengers. Also, the effect of the damping ratio changes on the time-domain of a system. This further determines the extent of the comfort of a vehicle. The design of a vehicle integrates the concept of damping coefficients and the stiffness of spring as a means of achieving comfort of a vehicle. The rule of the thumb requires the increase in damping coefficients so as to reduce the extent of vibrations witnessed in a car (In Liu et al., 2013). The Optimum Parameters for the Car Suspension System: The car suspension system integrates the use of Optimum Parameters as means aiding in the achievement of comfort. They aim at increasing the damping coefficients which are essentially responsible for the determination reduced the number of oscillations. Whenever spring stiffness is increased, the number of vibrations is correspondingly reduced. Also, the change in the damping constant leads to the possible occurrence of errors (Kim & Ro, 2000). The spring damper is normally improved trough changing the damping constant and the spring constant. However, the trade-off exists between enhancement of passenger comfort and the road safety for the vehicle. This implies that maximum comfort desired can possibly lead to easy accidents for the vehicle. Having a higher sporty effect on the vehicle also implies a supreme stability effect. Therefore, the process of designing the suspension system needs to integrate the elements of the comfort of the customers and the general safety of the vehicle. Scholars advise that the design of the suspension system needs to consider the small cars as opposed to the large automotive such as Lorries or motorbikes (In Liu et al., 2013). Summary The paper has exclusively determined the aspect of the suspension system and the exploration of various parameters that defines the engineering and the physics behind the system. It explored the effect of low filter pass in the determination of the suspension system. Also, it explored the essence of Hooke’s law in explaining and determining the application of spring and force in the designing of the system (Kim & Ro, 2000). The paper equally integrates the introduction of damping components which equally determine the effect of the suspension system in achieving comfort. The use of various equations made me understand the necessary concepts regarding the use of suspension system and the body of knowledge behind the establishment of the entire system. References Bastow, D., Howard, G., & Whitehead, J. P. (2004). Car suspension and handling (p. 29). Warrendale: SAE international. Gaid, M. M. B., Cela, A., & Hamam, Y. (2006). Optimal integrated control and scheduling of networked control systems with communication constraints: application to a car suspension system. IEEE Transactions on Control Systems Technology, 14(4), 776-787. In Liu, H., In Gao, H., In Li, P., & Institution of Engineering and Technology. (2013). Handbook of vehicle suspension control systems. Kim, C., & Ro, P. I. (2000). Reduced-order modelling and parameter estimation for a quarter-car suspension system. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 214(8), 851-864. Read More