Design of a Car Suspension System - Assignment Example

Design of a Car Suspension System Institution Affiliation Student’s Name Date Design of a (Simplified) Car Suspension System The car suspension system accepts a sinusoidal input and scales it by varying its amplitude and phase angle giving a sinusoidal output .the output of this system has the same frequency as that of the input .this system does not add additional frequencies that are not present in the input frequency. The main purpose of this system is to attenuate amplitude with high frequencies. For this reason car suspension system is linear time invariant filter of a low pass design 2 On a smooth surface the spring is compressed slightly at a distance from its free length. In this condition the reaction spring force caused by the compression exactly balances with the weight of the chassis therefore; When the wheel rolls over a rough surface it is displace upwards by h from the equilibrium position. This causes the chassis to move upwards by y. Therefore the spring will be compressed by . The weight of the chassis acts downward shown. During this motion the chassis will be accelerating to its final position therefor the is a net forces which causes this motion. Therefore applying the Newton’s second law of motion i.e where is the net force causing the motion Mg Rearranging we have where both the h and y are function of time. a) The frequency response Sinusoidal input linear time invariant gives sinusoidal output as shown below Taking time derivatives Substituting 1,2 and 3 in the LCCD Cancelling b) The frequency response also called transfer function scales the input amplitude to give the output. The magnitude of these scalar is given by which is obviously a function of the frequency. Therefore the amplitude of the chassis is a function of the frequency. looking at this magnitude equation and dividing with the k all over it will found that there is a certain value of the frequency when the magnitude goes to infinity ie when frequency is equal to: This means that the amplitude of the chassis will increase indefinitely .ie resonance. Hence win design of this system this situation should be avoided. This frequency is known as the natural frequency 3) From the analysis above changing the surface roughness changes the output signal proportionally. There if this system was designed to operate at a given point this point has to be adjusted to fit the new condition. Doing so will be a short time solution because it then the surface is changed again then we need to re adjust again. Adjusting the system parameter actually increase the cost since we can only do so by changing the spritherefore a better solution should be found 4 a) Adding a shock absorber changes the linear constant‐coefficient differential equation to The term is the shearing force of the fluid between the fixed cylinder and the moving piston of the shock absorber. This derived from the Newton’s law of viscous fluid where the shear stress in the fluid When the wheel moves on rough surface then it will be displaced upwards setting the chassis in motion. Therefore applying Newton’s second law of motion we have b) The frequency response will be calculated as follows y(t)= Dividing by Factoring Since Fig 1 Fig2 fig 3 c) Fig 4: Plot for different value of natural frequency 5 a) cutoff frequency is point also called the corner frequency were the response(magnitude) is equal to 1.414 and it is related to the natural frequency as follows Hence cut off frequency is controlled by the damping constant and the spring constant and the mass of the system. From this equation it is evident that to decrease the cutoff frequency the natural frequency of the system has to be decreased. Doing so means that the maximum magnitude of the frequency response is decreased and the slope this motion as can be observed from fig2 is also decreased. Therefore the ride feels smooth. For step input the curve is shifted to the left (fig4) which means the final amplitude is reached within a short time there the response is rapid. b) Decreasing the cut of frequency means that we have to decrease the damping factor which makes the frequency response becomes steeper (fig 1) there high values of the frequency response magnitude are reached by a small variation in the frequency of the roughness which means that the ride would feel bumpy. Checking on the step response (fig 3) it can be seen that the response tends to be sluggish. 6. Considering that we need the consumer to enjoy a smooth ride and the one has no steep attenuation of frequency I would consider designing a system with low high values of damping factor but low values of natural frequencies Summary This this exercises was competed by analyzing two of design using a unicycle car. According to the analysis the system failed because it was not self -adjusting that is is could not readjust back to the operating point when the surface design conditions were changed. Therefore it was found not to be the best system to filter out high frequencies. The second system that had a damping component provided the designer an adjusting parameter by which he can select the range of frequencies to be allowed the suspension and any other frequency higher than this range are attenuated. The design was found to fulfill the purpose of the system at a lesser cost. This analysis was found quite resourceful by the end of the exercise I had a clear understanding of the filters design and implementation.in addition to that it provides a clear a powerful approaches of analysis signal system. References Chaparro, L. F. (2014). Signals and systems using MATLAB Paraskevopoulos, P. N. (2002). Modern control engineering. New York: Marcel Dekker. Passenger Car Meeting and Exposition. (1991). Car suspension systems and vehicle dynamics. Warrendale, PA: Society of Automotive Engineers. . Read More