Design of a Simplified Car Suspension System - Assignment Example

Signal And System Institution Affiliation Student’s Name Date Design of a (Simplified) Car Suspension System TASK 1 The car suspension system is basically analog type of filter since it utilizes physical components. Since it produces a scaled signal it can be classified as a linear time invariant filter. The purpose of this system is to reject rapid input there it qualifies to be a low pass type of a filter. TASK 2 I. DETERMINATION OFF THE SYSTEM OF DIFFERENTIAL EQUATION GORVENING THE MOTION. This task can be accomplished using various approaches. This approach includes, using Newton’s second law of motion, using Alembert’s principle or law of conversation of energy. Using the Newton’s second law of motion is the rate of change of momentum is equal to the force causing it; At equilibrium (when travelling on a smooth surface), the spring is slightly compressed. At this state slight compression can be assumed to be.At this state the upward spring force exactly balance the downward gravitation force i.e. When the car moves on a rough surface the wheel moves from the equilibrium position upwards through a distance h. This motion causes the chassis to move upwards through a distance y from its equilibrium position. Due to this movement the spring is compressed by the length . Applying the Newton’s second law of motion i.e Mg If we assume the roughness profile is assumed simple harmonic then where H is the maximum displacement of the wheel then the differential equation changes to Mg II. THE FREQUENCY RESPONSE From this equation; Substituting in this in the in differential equation in Cancelling on both side of the equation III. The magnitude of the frequency response represents the scalar multiple of the input amplitude. This scalar is a function of the frequency therefore the amplitude of the chassis is a function of the frequency. Yes there is frequency that causes a lot of concern in the design of car suspension system. This frequency is known as the nature frequency which is the frequency that the system oscillates at freely without any excitation. If the frequency of the excitation equals this frequency then the system resonant. This frequency can be expressed as IV. This kind of the system the output amplitude varies directly to the input amplitude. Therefore an increase in the roughness will causes a proportional increase in the amplitude of the chassis. Changing the system parameters will result short time solution such that regular adjustment will be required. In addition changing the system parameter is a costly process therefore the best is to resolve a better system that will be self-adjusting depending on the surface changes. TASK 4 a) Due to addition of shock absorber a third force acting upwards is introduced such that a third additional term is introduced in the previous LCCD and the new equations will be, This additional term result from shear force of the fluid moving between the fixed component and the moving component of the shock absorber. The shearing force is proportional to the velocity of the system as follows. The Newton’s law of viscous fluid state that Applying the newton second law of motion and assuming a simple harmonic excitation We have b) The frequency response will be calculated as follows Input y(t)= From this equation the derivatives will be | , , We have to find the complex form of by first dividing by H and we square the denominator we have Then we take the components in the denominator By multiplying by all over we have Taking the square root of -1 we have Substituting we have c) d) for a unit response for different values damping ratio b) For different value of natural frequency c) TASK 5 a) The cut-off frequency is a point the magnitude is equal to this point is related to the natural frequency as follows. The cut off frequency is controlled by the damping constant and the spring constant .This is because the spring constant determines the natural frequency of the system while the damping constant determines the damping factor. The cut-off frequency is a corner frequency where amplitude having higher frequency than the input frequencies is reduced toward -. Due to this the ride feels bumpy. To reduce the cut-off frequency one has to reduce the either the natural frequency or the damping factor therefore .doing this makes the step response rapid this can be seen the step response graph which indicates that low values of natural frequency and lower values makes the system assume stability rapidly . A hard suspension system very low cut-off frequency such that the time response of unit step input gives a rapid respond. While a soft system has high cutoff frequency which makes the response sluggish. b) Reducing the cut of frequency decreases the damping factor. This results in decreased value of the frequency response that is the maximum magnitude reached decreases. This makes the ride feels smooth when cut off frequency is decreased. Doing so makes the step response rapid as can be seen from the step response of various damping factors. That is the step input represents amplitude of very high frequency that is the magnitude is accelerated rapidly. The plots achieved agree with this fact. TASK 6 Considering the fact that a smooth ride ids desired and no sharp division of frequencies to be passed and the one to be rejected i would suggest that a system of high values of cutoff frequency. Summary and conclusion From this study it was found that a suspension with a spring element only has the disadvantage of not being self-adjusting.it requires to readjusted when it operates of different condition.to solve this a damper was added in the system. This provided extra parameters that can be varied to achieve the desired output. It also presented a very important parameter (cut off frequency) that helps the designer to select a limit of frequencies to operate at. If the frequencies are more than this point there attenuated back to the comfort level of the system. This makes the system with a damper a self-adjusting system. This makes the system a noble type of filter that will not require the design to adjust the system parameter every time an different surface is met. I found this study quite helpful because it a better understanding of the design of filters as well as their application. Reference Automotive design & production. (2001). Cincinnati, OH: Gardner Publications Chen, C.-T., & Chen, C.-T. (2004). Signals and systems. Oxford: Oxford University Press. Lalanne, C. (2002). Mechanical vibration & shock: Volume 3. London: Hermes Penton Ltd. Moodle.autolab.uni-pannon.hu,. 'Chapter 1.  Introduction'. N.p., 2015. Web. 21 Oct. 2015. . Read More