QUESTION 1: 1 DOF Modeling
Create a 1 DOF system approximation of your car and analyse the system using theoretical vibration calculations/ or Matlab scripts and compare with a simulink model:
i. For free vibration
ii. For forced vibration (you will have to estimate the forced vibration that could be expected in your vehicle)
iii. The response of your car to expected road surface roughness and possible road defects.
iv. Include in your Simulink model suitable non-linearity’s, discuss and show how or if these will affect the previous analysis. You may have to generate some extreme road defects to show the operation of the non-linear properties.
v. Damping helps to isolating vibration and reduces transmitted vibration. Based on your analysis write a paragraph on the effect of damping in affecting your car’s performance i.e. Where would be better to use high damping; Where would it be better to use low damping; and how does the damping levels you have chosen in your car affect passenger comfort and the wheel-road contact force.
QUESTION 2: 2 DOF modelling
Improve your car model and include the roll DOF in addition to vertical motion. For this 2DOF system there will be two mode shapes and two natural frequencies to calculate. Demonstrate your competence by:
i. Creating the two (2) equations of motion
ii. Creating the equations of motion in matrix form
iii. Creating/modifying a Matlab script using eigenvalues and eigenvectors or other means to find the natural frequencies and mode shapes.
iv. Discuss what the mode shapes and natural frequencies results refer to and what analysis conclusions you can draw from these.
v. Create a Simulink model to investigate the response of the system to expected road surface roughness and defects, like corrugations, potholes and speedbumps.
vi. Write a conclusion on your overall analysis above, for example: Is the suspension suitable? How could the suspension be changed to improve it? What future analysis or investigation is needed?
QUESTION 3: Vibration Table
A vibration table in Figure 2, includes a hydraulic cylinder, a mass, a sensor and a controller. The table is resisted by a linear spring and viscous damping as shown. It is desired to vibrate the mass in a pure sinusoidal motion at an amplitude of +5mm and at frequencies from 0 to 10Hz. Use m = 100kg, k = 5000N/m, c = 1000 N.s/m.
Develop a suitable model and PID controller for the system and model this in Simulink and analyse its performance.
a. Demonstrate that the controller is able to produce the desired movement and comment on any limitations you may discover.
b. Document how you determined the PID parameters.
c. Discuss any PID values that failed to produce the desired movement.
d. Determine force required from the hydraulic ram and the force on the damper and spring.
e. Determine and discuss the stability of the control system.
f. Demonstrate that your controller is capablable of two following design changes:
a. The mass of the table is increased to 200kg
b. The spring stiffness is doubled for the ranges (+4mm to +5mm) and ( -4mm to -5mm)
g. Determine the new force required from the hydraulic ram and the force on the damper and spring due to the changes in part (f).
QUESTION 4: Cruise Control
Use Simulink to develop a suitable cruise controller for a loaded truck. The controller must be designed to adjust the engine power setting (i.e. fuel control) and provide braking control in over speed circumstances. Choose a truck to determine its mass, engine power, torque etc. Clearly specify the make and model of the truck used.
You will need to consider the effect of grades and propulsion resistance.
• For grades consider that grades up to 1 in 12 are possible on roads.
• For air and rolling resistance use: F = mg x 0.01 + 0.5 * 0.7 * 1.225 *A.V2
where m is in kg; V is speed in m/s, A is frontal area in m2.
a) Demonstrate the robustness of your design with a test road containing both up and down grades as well as flat road
b) Demonstrate the operation of the brake control.
c) Provide a measure of the stability of the cruise control system.
d) Comment on the disadvantages of your controller and possible improvements or investigations
Section C – Other Vibration Applications
QUESTION 5: Rotational and Linear Vibrating System
For the mechanical system in Figure 3:
a) Determine the equation of motion for the system*, calculate the free vibration response, forced vibration, critical damping* and Magnification Factor*. *Express in terms of J, m1, m2, k1, k2, c1, c2 and L. State and explain any assumptions you make.
b) Select some values for the unknowns (clearly state these) and calculate/graph the values listed in part (a) of the question. Briefly comment on and explain what your results mean.
c) Use a Simulink model to verify your results.