p2 - passive suspension system
TRANSCRIPT
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CMPSC 200 & 201 – SP13
Project #1Passive Suspension System
Date Due: Monday – April 1, 2013Upload to Angel by 10 am
Hard copy to Mrs. Ford at the beginning of class.
Objective:
Write a program that will calculate the maximum velocity and displacement for the wheel and thecar for different vehicles in the data file. You will be given specific values and then you need tosolve a series of equations to determine those maximum values.
Problem:
The passive suspension system of an automobile is illustrated in Figure 1.
Figure 1. The passive suspension system [Franklin, 2004, Fig 2-3].
A quarter of the suspension system of the automobile can be modeled by mass, spring and dash-potas described below.
Figure 2. The quarter-car model [Franklin, 2004, Fig 2-4].
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Where r is the displacement of road surface relative to the sea level; m1 is the mass of the wheel,m2 is the mass of the quarter car, kw is the spring constant of the tire, ks is the spring constant of the spring, b is the damping constant of the dash-pot. Assume the model is for a car with a mass of 1580 kg including the four wheels, which have a mass of 20 kg each. K s=130,000N/m, K w =1,000,000N/m. The damping coefficient is b = 9800 N/(m/s). Figure 3 shows the free body diagram of eachmass.
Figure 3. Free Body Diagram of the quarter-car. [Franklin, 2004, Fig 2.5]
The equations to describe the masses in this system are listed below:
This system can further be described by four first differential equations listed below:
4
2
3
2
2
2
1
2
4
43
1
4
1
3
1
2
1
1
1
2
21
)(
xm
b x
m
k x
m
b x
m
k x
x x
r m
k x
m
b x
m
k x
m
b x
m
k k x
x x
s s
w s sw
Where x 1 is the displacement of the wheel, x 2 is the velocity of the wheel, x 3 is the displacement of the car, and x 4 is the velocity of the car.
Taking the integration of the four equations we get:
n x
t
n xn x
211 1
nr
m
k n x
m
bn x
m
k n x
m
bn x
m
k k
t
n xn xw s sw
1
4
1
3
1
2
1
1
1
22 1
n x
t
n xn x
433 1
n x
m
bn x
m
k n x
m
bn x
m
k
t
n xn x s s
4
2
3
2
2
2
1
2
44 1
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Suppose now this automobile is ridding on a rugged road, and the function to describe the shape of the surface with the given car speed is:
)2sin(*2.0)( t t r (meters)
Calculate the acceleration, the velocity, and displacement of the car over the time. It is knownthat the smaller the acceleration of the car, the more comfortable the passenger feels.
Input:
The data file will be giving you the following values and in this order: (File format: EOF)
Name of the car
Spring constant of the tire
Spring constant of the spring
Damping constant of the dash-pot
Mass of the wheel
Mass of the whole car
Start and end value of time
Increment value for time
Specifications:
Each formula will be its own function.
All decimal values will be formatted to either 4 or 5 decimal places.
CMSPC 201: The only global variable you are allowed is PI.
CMPSC 201: Your input file MUST BE located and named: P:\Private\ProjData.txt. If not inthat location or named that file, your program will be graded as incomplete.
CMPSC 200: Your input file MUST BE named ProjData.txt. If not named this then yourprogram will be graded as incomplete.
Turn in a hard copy and upload your source code (with the proper name) to Angel.
If you neglect to either upload or turn in your hard copy you will receive a zero on this
assignment.
Output:
Be sure all output is clearly labeled. I am not as concerned with units but you can include them if you wish. Echo the output of all input variables as well as the maximum displacement and velocityof the car and the wheel for each vehicle in the data file. Decimal places should be formatted.
Hints:
Solve for the first set of x values. We assume the all of the cars starts from a stopped position sothe first round of x (1-4) [x(n)] values will all be 0.000. Use the previous x values to solve for thenext set of x (1-4) [x(n+1)] values.
Remember that you are trying to find the maximum displacement of the car and wheel as well asthe maximum velocity of the car and wheel.