Konstruktion 7BS
Final Homework
Revised 25.01.05

1.    Produce a pitch model of the car in the Suspension Design homework in Simulink.  This is a 2 DOF model, so it will be like the wheel/car 2 DOF model in form, except here we'll have z and q as outputs.  We'll also get z_f and z_r as outputs (they're algebraically related to z and q).  Inputs will be z_Rf and z_Rr, the road obstacles.  To make this model, look at equations 3, 4, and 5 in Lecture 2 of Iannce.  As physical parameters, use:

m_s = 2000 kg
R = 1.1 (COP parameter)
Weight distribution = 50/50
Wheelbase = 3.0 m
c_f = 2906 N/(m/sec)   (one front wheel)
c_r = 3436 N/(m/sec)   (one rear wheel)
k_f = 20,763 N/m   (one front wheel)
k_r = 29,597 N/m   (one rear wheel)

a)    Check the decoupling of the front and rear wheels.  Input a step or 4 cm into z_Rf and see how the rear axle responds.  Then input the same step into z_Rr and see how the front axle responds.  There should be little coupling between the front and rear axles.  Also, when you input a step into the front or rear axle only, what should the steady-state pitch value be?

b)    Check the frequencies for the front axle, the rear axle, the bounce, and the pitch.  They should be 1.0 Hz, 1.2 Hz, 1.0 Hz, and 1.2 Hz, respectively.

c)    Check that we have quarter cycle damping on the front and rear axles, which was part of the specification.  If the results show that the damping is not correct as given, alter it until you do have quarter cycle damping.  Report any new damping coefficients.  Or just report that you needed to make no change.

d)    Finally, run the car up on a curb of 4 cm at 100 kph.  How does the car respond?  Is the response of Figure 3.4, or something corresponding for this case, duplicated by the model?  Print this first part of the response out.

It is your job to convince me that you have answers to these questions.  Provide ANNOTATED graphs where necessary to make your point.

A useful trick sometimes is to use only variable names in your Simulink model.  You can load values for the variables into the variables in the Matlab session that is running under Simulink.  The most convenient way to do this is to create an m file called something like initial.m.  In this file will be the assignment statements that load the variables.  If you do this, make sure to print out a copy of this m file and turn it in with the assignment.

2.     A car has a mass of 2000 kg with a 55/45 front/rear weight distribution.  The wheelbase is 2.5 m.  The tires have the cornering stiffness values given in the table below.

Find the following cornering properties for the vehicle:

a)     Ackerman steer angles for 150 m, 60 m, 30 m, and 15 m turn radii

b)    Understeer gradient

c)    Characteristic speed

d)    Lateral acceleration gain at 100 kph

e)    Yaw velocity gain at 100 kph

f)    Sideslip angle at center of mass in a 250 m radius turn at 100 kph

g)    Static margin