Vehicle Crash Test Bee Thao Me 270 October 30, 2007

1. Vehicle Crash Test Bee Thao Me 270 October 30, 2007

2. First Step BOND GRAPH

3. Hand Work

4. Second Step • Put bond graph into CAMP-G • Interface to Matlab • Results: Four Files • campgmod.m, campgequ.m, campgnum.m, campgsym.m

5. Step Three • Edit campgequ.m to define: • STEP • EFFORTS • TIME • FLOWS

6. Step Four • Edit campgmod.m file • Input parameters: • Initially displacement is zero • Initially momentum is mass x velocity • M= 1500 Kg, k1= 1 x 104 N/m, b1=500 N-s/m • m= 100 kg, k2= 3 x 105 N/m, b2=8 x 104 N-s/m

7. Step Five • Run campgmod.m file to get displacement and force plots

8. Six Step • Change velocity values to see from plot if displacement of dummy is less than 1 meter and the force is less than 6670 Newtons for one seatbelt • Change velocity values to see from plot if displacement of dummy is less than 1 meter and the force is less than 13340 Newtons for two seatbelt

9. Seven Step • Check hand differential equations • Check state space form matrices • Use simulink to check

10. Final Step • Design by changing bumper or seatbelt values for k2,b2 and k1,b1 • Use loops to iterate for values, get max velocity, and other factors you want Note: See Report File for graphs and Matlab files for iterations for values

11. Report • The problem states that a dummy is driving his new VW‑Rabbit into a wall! The question is to find out if his shock-absorbing bumper (k2, b2) and his seat belts (k1, b1) will prevent him from hitting the windshield without breaking his collarbone? • DATA ON INJURIES (SAE Handbook) • Seat belts must be tested to 3000 lbs. (1.334 x 104) N • Chest can sustain a force of 1500 lbs. distributed over 30 in2. • Seat belt effective area = 30 in2 • Shoulder strap-seat belt combination = 60 in2 • Design Criteria: • The design for the 25 mph and 55 mph that stops the dummy from hitting the windshield is a seatbelt with the parameters of k1= 20000 N/m, b1=800 N-s/m and a bumper with the parameters of k2=100000 N/m, b2=10000 N-s/m. • The force that is exerted on the dummy at 25 mph for one seatbelt is 4368.6 N so he is not injured internally by the seatbelt. At 55 mph the force he experiences is 9617.5 N and this is greater than the limit of 6670 N so he is crushed by the seatbelt. With the design criteria, the force at 25 mph is 2938 N and 6479.4 N at 55 mph which is below the limit of 6670 N so injuries occur. Furthermore, the force that is exerted on the dummy at 25 mph for two seatbelt is 7454.2 N so he is not injured internally by the seatbelt because the limit now is 13340 N. At 55 mph the force he experiences is 16411 N and this is greater than the limit of 13340 N so he is crushed by the seatbelt. With the design criteria, the force at 25 mph is 3701.6 N and 8171.8 N at 55 mph which is below the limit of 13340 N so injuries occur. • The maximum velocity was determined to be 30 mph for the original parameters that allowed the dummy to be safe from the crash. • It takes 0.1033 seconds for the dummy to hit the windshield with no seatbelts at 25 mph, 0.0714 seconds at 40 mph, and 0.0566 seconds at 55 mph. The force that is on him during the impact is zero for all the speeds. • In conclusion the best design that allowed the dummy to be safe was a seatbelt with factors k1= 20000 N/m, b1=800 N-s/m and a bumper with the parameters of k2=100000 N/m, b2=10000 N-s/m. Below is the simulink comparison which verifies the solution. PHYSICAL PARAMETERS M= 1500 Kg, k1= 1 x 104 N/m, b1=500 N-s/m m= 100 kg, k2= 3 x 105 N/m, b2=8 x 104 N-s/m

12. Simulink simulink graphs matlab graphs

13. One Seatbelt

14. Design for One Seatbelt

15. Two Seatbelt

16. Design for Two Seatbelt

17. Max Velocity Velocity of 30 mph

18. No Seatbelts

19. Excel Numbers