First Step BOND GRAPH

Hand Work

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

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

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

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

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 Newtons for two seatbelt

Seven Step  Check hand differential equations  Check state space form matrices  Use simulink to check

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

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 in 2. Seat belt effective area = 30 in 2 Shoulder strap-seat belt combination = 60 in 2 Design Criteria: 1.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= N/m, b1=800 N-s/m and a bumper with the parameters of k2= N/m, b2=10000 N-s/m. 2.The force that is exerted on the dummy at 25 mph for one seatbelt is N so he is not injured internally by the seatbelt. At 55 mph the force he experiences is 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 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 N so he is not injured internally by the seatbelt because the limit now is N. At 55 mph the force he experiences is N and this is greater than the limit of N so he is crushed by the seatbelt. With the design criteria, the force at 25 mph is N and N at 55 mph which is below the limit of N so injuries occur. 3.The maximum velocity was determined to be 30 mph for the original parameters that allowed the dummy to be safe from the crash. 4.It takes seconds for the dummy to hit the windshield with no seatbelts at 25 mph, seconds at 40 mph, and 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= N/m, b1=800 N- s/m and a bumper with the parameters of k2= N/m, b2=10000 N-s/m. Below is the simulink comparison which verifies the solution. Report 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

Simulink simulinkgraphs matlabgraphs

One Seatbelt

Design for One Seatbelt

Two Seatbelt

Design for Two Seatbelt

Max Velocity Velocity of 30 mph

No Seatbelts

Excel Numbers