Section A - Rail Vehicle Suspension

BACKGROUND

The context for Questions 1 to 2 is a tram, light rail vehicle or a railway freight wagon that contains a spring and damping type suspension, see the images for some ideas. Clearly state the vehicle you are analysing.

The idea is that using this context you should complete various analysis that demonstrates your competence, starting, like we did during the term, looking at very simple modeling approximations and then progressing on to more complex models.

You will need to find, estimate or calculate the mass and suspension data for the vehicle you choose. (they should be reasonable and somewhat justified):
- Masses, 2nd Moments of Inertia
- Stiffness, Damping
- Dimensions
- Centre of gravity

QUESTION 1: 1 DOF Modeling

Approximate your selected vehicle as a single degree of freedom system and analyse the system using theoretical calculations/ or Matlab scripts and compare with a simulink model:
i. For free vibration
ii. For forced vibration
iii. The response of the vehicle to typical track surface roughness and possible track defects.
iv. Include in your Simulink model suitable non-linearity's and write a paragraph and/or show how or if these will affect the previous analysis.
v. Damping has a key role in isolating vibration and transmitting vibration. In relation to your analysis write a paragraph on the effect of damping in affecting your vehicles performance i.e. In which situations would be better to use high damping and where would you use low damping; How does the damping characteristic affect passenger/cargo comfort and the wheel- rail contact force.

QUESTION 2: 2 DOF modelling

Improve your vehicle model to include roll in addition to vertical motion. For this 2DOF system there will be two mode shapes and two natural frequencies that can be calculated. Demonstrate your competence by:
i. Writing the two (2) equations of motion
ii. Writing the equations of motion in matrix form
iii. Using a Matlab script using eigenvalues and eigenvectors or other means, find the natural frequencies and mode shapes.
iv. Explain what the mode shapes and natural frequencies refer to.
v. With a Simulink model investigate the response of the system to track surface roughness and possible track defects.
vi. Draw some conclusions on what implications does this analysis have for the design analysed? What changes do you suggest are made to the specified suspension?

Section B - Control

QUESTION 3: Skyhook Damper

There is a common control technique called the skyhook damper for active suspension control. The damper is connected between the mass and an absolute reference (e.g. ‘the Sky') and vibration characteristics are greatly improved. One small problem - it cannot be built. (see Figure 2). For a practical Skyhook damper a control system is used. The idea is that the absolute velocity of the mass is measured and a control system is used to provide a damping force proportional to the absolute velocity. Absolute velocity can be obtained from an accelerometer - which measures the absolute acceleration. You can set target damping force by multiplying the absolute velocity by a constant (e.g. Cs ) . This then needs to be converted to a force. You need a control system, a valve to control either damper flow or a hydraulic cylinder.

HINT: In Simulink you can just add a constant damper to see how skyhook damping works - This is useful in establishing the ‘ideal case' or ‘design target' - but this is not a practical solution.

a) Start by implementing an ideal skyhook damper (second diagram in Figure 2). This is as simple as adding a damper block in simulink.

b) Implement a practical skyhook damper (third diagram in Figure 2). You may utilise a motor drive system to apply the force or a hydraulic system. You will need to select a suitable controller, test your system in Simulink etc. There are two options, one being to vary the characteristics of a linear damper as shown in the diagram, or add an active force control - the later gives better results.

c) Compare your practical skyhook system with an ideal skyhook damper, i.e. a linear damper fictitiously attached to a fixed point.

d) Examine your systems and discuss implications for stability and performance.

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 specific truck to determine the mass, engine power, torque etc.

You will need to consider the effect of grades and propulsion resistance.
- For grades consider that grades up to 1 in 9 are possible on roads.
- For propulsion resistance use: F = m ( 0.09 + 0.0027*V) + 0.42*A.V² where m is in kg; V is 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 the controller and possible improvements or investigations

Section C - Other Vibration Applications

QUESTION 5: Vibrating Column

For the system in Figure 3:

a) Develop the equation of motion for the system*, determine 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/explain what your results mean.

c) You can use a Simulink model to verify your theoretical results.