Homework 1 Feedback
Konstruktion 7BS
Revised 28.11.05

General comments:

I want you to develop a feel for the relationship between your formal math studies and how all of that is expressed in Simulink.

Use the binoculars on the Scope graphs to scale your outputs properly.  Do not have vast expanses of black or long, straight outputs at the end of the time scale.  They show nothing and are just wasted space.  Change the "Stop time" for the simulation to a shorter time to avoid this.

You cannot just produce a bunch of output and throw it at me without any explanation.  Every page that you turn in should stand alone.  I.e. I should be able to pick any page at random out, look at it, and tell what is going on.  I should be able to ascertain what exercise it belongs with, what model produced it, what the loading conditions are.  Then it should be annotated (neat handwritten notes are okay) to explain important points and points pertinent to the exercise.  For example if I tell you to input an initial deflection of -3 cm, you should point out that the output starts at -0.03.  You need to ask yourself what is important for the exercise and then make that jump out at the reader.

In industrial life, you will be asked (required) to produce concise, to-the-point results that even an idiot (your boss) could understand quickly.  It is not his/her job to dig through your stuff to find all the pertinent parts to answer a questions.  It is not his/her job to complete all the stuff that you left off.

Also to that point, answer all the questions that are asked.  In this homework assignment I asked a number of questions that a number of people just didn't bother to answer.

It is your job to convince me or your boss that you understand the situation and that your results are believable.  You cannot just say, "Now I understand" and nothing else.

Besides being clear, what you turn in needs to be checkable.  I.e. I need to be able to check it.  So all steps need to be shown, including unit calculations.  Everything needs to be written out in detail, so that if someone wants to check your work, it is all laid out for him/her to check.  Do not do unit calculations on a separate piece of paper and then throw that away.  I cannot check that.  Do not hand in Simulink models with the "-K-" shown in the block.  I cannot tell what is in that block.  This type of comprehensive documentation is not just something that I require you to do.  It is what I would do if I were working for an industrial client too.  If something goes awry, I want to be able to troubleshoot it.  When you are creating technical information or results for use in industry, you should be constantly asking the questions, "Is this understandable?  Am I explaining this well enough to a reader, so that he/she can easily understand it?  Will I be able to understand what I'm writing when I come back to it in the distant future?"

Exercise 1

Create a Simulink model with a step input feeding an integration block.  Initially set the step value to 0 and the step time to 1 second.  Plot the result out on a scope.  This is the “do nothing” case and is always the first case you should run.  The input to the integration block is 0, so the output should be 0.  Once you have ascertained that the integration block output is 0 when its input is always 0, change the step value to 5.  Rerun the simulation.  What would you expect to happen?  Does it?  Now install a gain in the system before the integration block.  Give it a value of 2.  Set up a scope between the gain block and the integration block.  Rerun the simulation.  Look at the intermediate output and the final output.  Are they performing as expected?

I need the system output on a scope mostly.  The output from the gain block is useful, but it is not complete.

Many people did not scale this output with the binoculars properly.

Exercise 2

Given a quarter car mass of 500 kg, design the spring rate of the suspension spring to give a natural frequency of 1 Hz.  Assume the damping to be 0 as a start.  Also assume that the suspension spring rate, k_c, is significantly lower than the tire spring constant, k_w.

Once you have calculated the suspension spring rate, build a Simulink model of the car.  Leave a place for a force, but set it to zero.  The first check on your model is the “do nothing” check described above.  Once you have determined that your model will stay still, use the initial conditions on the -to-z integrator to input an initial downward deflection of 3 cm.  Look at the output and see that it looks reasonable.  What is the initial deflection shown?  Between what two values does the car oscillate?  What is the car’s natural frequency of vibration?  What is the initial static deflection of the spring?

Most shock absorbers in use today have damping coefficients of 0.2-0.4.  Copy your model and install a damper in this range into the new model.  Run the new model and compare the result with the undamped case.  Recall that the damped frequency of oscillation is less than the natural frequency ().  Check the %OS and the T_p.  What are they?  Are they what they should be?  Check that after T_s the oscillations are mostly gone.

Use z = 0.22 or 0.25, not 0.30.  I asked for quarter-cycle damping, which we discussed in class.

Answer all questions, including those about the %OS and T_p.

Set the stop time of the simulation long enough to capture the output but not so long that a lot of the time axis on the scope shows just a straight line, i.e. the inactivity of the system after the response takes place.

Exercise 3

Copy the model and then make the road load input possible.  Check the “do nothing” case on the road-load model.  Then have the car run up on a curb that is 8 cm high.  Check the final value of the car location.  Does it make sense?  What is the overshoot?  This is important to observe so that you can design the travel of the suspension.

Change your input somewhat to have the car run over a curb that is 8 cm high and 6 cm wide.  Let the car be traveling at 10 kph.  Hint:  get the loading of z_g worked out before you hook it up to the model.  Look at the final value of z.  Does it make sense?  Can you see the individual up and down excitations in the car displacements?  Why or why not?

Now input a washboard road into the model.  Let the bumps be 2 cm high (amplitude).  Let them be 1 m apart.  Run the car across this road at various speeds.  At what speed would the resulting steady state oscillation amplitude be the greatest?  Confirm that this is so.  Run tests above and below the car’s oscillation frequency.  Check the relative phase of the input ground displacement and the car displacement.  Are these as they should be?

Notice the initial part of the response curve.  Before the curve settles out to the steady state response, there is some additional movement.  This is the transient response of the model.  This is what would happen if you were initially traveling on a smooth road and then ran into an washboard section.  The initial vibration would be a little rougher than the final steady state vibration.

Many people just dumped a bunch of output on me without explaining much, expecting me, I guess, to sort through it all and make sense of it.  That would be extremely time consuming and something your boss certainly would not do in the real world.  Part of your job is to organize and present results concisely.

Some people put input in here as a force.  It is not.  The input is a displacement disturbance, z_g and its derivative.  You cannot add meters and Newtons in any case.  The first summing junction in your model represents a force equation.  You cannot add meters directly in there.  Just as you have to have all the same units in an equation, every summing junction in Simulink needs to have only one type of quantity going into it (force, displacement, velocity, etc.). 

Exercise 4

Let the mass of the wheel assembly be 50 kg.  Let the tire stiffness be 10 times the suspension spring stiffness.  What is the natural frequency of the wheel?  What is the damped frequency of the wheel?  What is z for the wheel?  Once you have calculated these values, build a Simulink hop model and confirm them.

This exercise requires some manual calculations.  These should be shown in enough detail that I can check them.

Exercise 5

Using the wheel hop model developed in Exercise 4, see what happens with the following imbalance:  30 gm at 40 cm eccentricity.  Use a wheel diameter of 90 cm.  Drive the car at various speeds and investigate the amplitude of vibration at these speeds.  Can you find a way to input the car speed in kph as a model input?  Plot vibration amplitude at various speeds.  At what speed is the vibration worst?

The hop model is in the book.

There are two things here that could cause the amplitude of the vibrations to increase.  You should point them out and decide what simulations to run (i.e. what car speeds) to show how they effect the output and which case is worse.  These two effects should be clearly explained and discussed.

Exercise 6

Now build a full two-DOF model of the car and wheel.  Go back through Exercises 2-5 and perform the same experiments on this model.  Compare the results with this model with those given by the simplified single-DOF ride and hop models.  Plot vertical acceleration of the car and wheel over a range of frequencies that spans the ride and wheel hop frequencies.

This comparison should be organized, clearly executed and presented.  Perhaps a table comparing important results should be constructed and given as part of the answer.  That is generally how comparisons such as this are made.