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Hands on session:
Analyse a car-body resting on coil-springs   

This example consists of a car-body named car_1 supported by four springs kmcb11r, kmcb11l, kmcb12r and kmcb12l and four dampers cmcb11r, cmcb11l, cmcb12r and cmcb12l. The body has a weight of 50e3 [kg]. The coil-springs have a vertical stiffness of 500e3 [N/m] The dampers have a damping coefficient of 30e3 [Ns/m] in vertical direction. Eigen value for the vertical bounce mode can be calculated as:

Relative damping for the vertical bounce mode can be calculated as:

In current example the vertical bounce mode was found to have an eigen frequency of 1.01 [Hz] with a relative damping of 19.0 %.

TSIM

Make a time-domain simulation with a vertical excitation of 1[mm] at a frequency of 0.97 [Hz].

1. Open the gensys file manager window by: clicking the -icon on the desktop.
   
   
2. Create a work space by writing the UNIX-command mkdir my_car_body.
   
   
3. Goto the newly created directory.
   
   
4. Under the pulldown menu Help press Examples Html.
   
   
5. Scroll down and click on program TSIM.
   
   
6. In the page "Input data examples for Program TSIM", press on the link car_body.
   
   
7. Press Copy in the popup-widows, in order to accept the files to be copied the to your directory.
   
   
8. Execute file runf/car_body_tsim.tsimf
   
   
9. Execute file mplotf/tsim.mplotf

A copy of the resulting plot:


If we look at the phase between excitation and responce we can see that there is a phase shift of about 90 degrees, which indicates that the excitation is very close to the natural eigen frequency.

In the plot, measure the amplitude of the car-body.
Please use the mouse buttons: zoom with btn_1, move with btn_3 and measure with btn_2.

MODAL

Make a modal analysis of the car-body model

1. Stay on the directory my_car_body created under TSIM above.
   
   
2. Under the pulldown menu Help press Examples Html.
   
   
3. Scroll down and click on program MODAL.
   
   
4. In the page "Input data examples for Program MODAL", press on the link car_body.
   
   
5. Press Copy in the popup-widows, in order to accept the files to be copied the to your directory.
   
   
6. Execute file runf/car_body_modal.modalf
   
   
7. Animate the modal analysis in GPLOT by:
   1. Double click file runf/car_body_modal.modalf
   2. Press the Gplot button
   3. In GPLOT press File->read_GPdat and select gp/car_body_modal.gp
   4. Press the Fwd button in order to start the animation
   5. Press the Next button in order to change eigen mode.
   6. Zooming in the model can be made with mouse button 1
   7. Rotation of the model can be made with mouse button 2
   8. Translation of the model can be made with mouse button 3
      
      
8. Execute file mplotf/modal.mplotf

Write down the frequencies and damping ratios for all eigen modes. Also give names to the modes.

In the MPLOT diagram it can be seen that the real part of all eigen values are negative. What will happen if an eigen value had a positive real part?
(If you need help look at Eigen_Freq_Deduce.html)

FRESP

Make a frequency-responce analysis of the car-body model

1. Stay on the directory my_car_body created under TSIM above.
   
   
2. Under the pulldown menu Help press Examples Html.
   
   
3. Scroll down and click on program FRESP.
   
   
4. In the page "Input data examples for Program FRESP", press on the link car_body.
   
   
5. Press Copy in the popup-widows, in order to accept the files to be copied the to your directory.
   
   
6. Execute file runf/car_body_fresp.frespf
   
   
7. Execute file mplotf/fresp.mplotf

A copy of the resulting plot:

In the plot, measure the amplitude and frequency of the car-body at maximum response. Compare the results found under TSIM above.

Find out the asymptotic phase angle between excitation and response for high frequencies.
(If you need help look at Fresp_Deduce.html)

QUASI

Make a quasi-static analysis of the car-body model.

1. Stay on the directory my_car_body created under TSIM above.
   
   
2. Under the pulldown menu Help press Examples Html.
   
   
3. Scroll down and click on program QUASI.
   
   
4. In the page "Input data examples for Program QUASI", press on the link car_body.
   
   
5. Press Copy in the popup-widows, in order to accept the files to be copied the to your directory.
   
   
6. Execute file runf/car_body_quasi.quasif
   
   
7. Inspect the results in file gp/car_body_quasi.gp by, marking the file with your mouse and select open->run in the window background menu.
   
   
8. In the results we can see that the model is not the same as in TSIM above. If we had used the same model as under TSIM all positions would have been equal to 0.(zero).
   
   
9. Apply a roll angle of 1[mRad] to the ground and make a new quasi-static analysis.

Calculate the vertical displacement by hand and check with the results from QUASI.

Calculate the roll coefficient of the car-body.
(You can find the definition of roll coefficient in analyse_roll.html)

If time permits:

In TSIM run more simulations at other frequencies and compare with the results found in FRESP.

Compare file runf/car_body_tsim.tsimf with the other files found under the runf directory.
Please use Unix->Compare from the PullDown-Menu.