Mech Engin Lab Research

Dynamics of a Single DOF Mechanical System (Transient Response) Lab Reserch
OBJECTIVE
To:
• explore the transient response of a 2nd-order mechanical system,
• estimate model parameters from the measured response, and
• compare with theory.
BACKGROUND
• Setup videos
EQUIPMENT
• PAScar Dynamics System (the track should not be moved, as it has been carefully
leveled)
• PASCO CAPSTONE software
PROCEDURE
Setup:
1. Use the balance to find the cart’s mass and record this value in your lab book.
2. Select any two springs from the spring set at your station. Nominal stiffness values are
3.4 N/M and 6.8 N/M. Let your GTA know which springs you selected.
3. Set the cart on the track and attach the two springs to the two sides by inserting the end
of each spring onto the hook provided on the cart. Extend the fixed end on the right such
that both springs are in tension.
4. Power on the cart by pressing the start icon on the cart and then start the CAPSTONE
software by opening the Single Cart Position experiment file. Click on the Hardware
Setup and find your cart by its serial number. Click on your cart to connect it to your
experiment and close the Hardware Setup by clicking on it. Next, select a sampling
frequency (based on system dynamics bandwidth), start recording the cart motion (by
clicking on “Record”), then displace and release the cart to capture its transient
response.
Note:
• Start recording when the cart is at steady-state, then displace it for the computer to
establish the x = 0 position.
• The springs must have a small pre-stretch for a linear operation and do not stretch the
short/long springs over 30/50 cm in length, respectively. Finally, if you are satisfied with
the retuned plot, you can start the transient and frequency response tests.
TRANSIENT RESPONSE (initial conditions)
1. Displace the cart from equilibrium a specific distance and release. Collect the data of
your cart motion time history through the CAPSTONE software (using File|Export Data).
Estimate the natural frequency and damping ratio from the collected data (red response
data into Matlab and use class M-files). After saving each file, verify that the correct data
is saved by plotting in Excel.
2. Repeat this process at four other initial displacements.
3. Add a known mass to your cart and repeat the test at one of the initial conditions used
above.
Data obtained (Check the attachment):
Using a 3.4N/M springs at both side
[Test machine]——-[Spring]——[Cart]——[Spring]——[Fixed point]
Initial point is at 50cm, the cart weight is 246g, stretch the cart to left at
1. 36cm
2. 33cm
3. 37cm
4. 30cm
5. 30cm +250g weight
6. 38.5cm
Answer the following questions:
In this assignment, your objective is to compare the theoretical initial condition response of the
single-cart system to the measured response in the lab. Your work should include the following:
1. Theory: viscous friction and dry friction models (final differential equations are sufficient
with all variables defined).
2. Parameter estimation: damped natural frequency, natural frequency, viscous friction
coefficient, and dry friction force. Include all relevant plots showing your work.
3. Comment on the agreement between theory (using estimated parameters) with
experimental results.
You do not need to include the Simulink model and M file unless you use different ones from
mine.