Simulink - Vehicle Acceleration 2
All assumptions are as in the previous model except that first gear is assumed to have an overall reduction of 10:1 and second gear an overall reduction of 7:1.
3. Building the Model
To incorporate the gear change the model is build a little differently to the previous one.
For the signal source, the step final value is set to 170 (the engine torque in Nm). For convenience the Step time is set to zero.
The output engine torque is then directed into two paths, in the lower one the first gain (Gain 2) is set to 10 (the overall first gear ratio) and in the upper path the first gain is set to 7 (the overall second gear ratio).
A gain block in each of these paths (Gain 7 and 8) is set = 1 / wheel radius to give the total forward driving force.
Each of these pathways then has a summing point to enable the negative effect of the force of the air resistance to be fed back. Each path then goes through a gain block with a gain equal to 1/equivalent inertia of the car at the wheels, (Gain 3 and 4) the output from these is the the vehicle acceleration.
The equivalent inertia (mass) of the vehicle is:
where I is the moment of inertia of each wheel, m the mass of each wheel, r the wheel radius and M the mass of the vehicle less the wheels.
= 4[(0.4/0.32) + 10] +1000 = 1057.8 kg
The output signal from the switch then goes through an integrator block (to give velocity)
A loop from the velocity line is fed back to the switch middle input (port 2) for comparison
with the threshold.
Two other loops are taken back from the velocity line and then fed into the dot product block to give the v2 value which is fed into the gain block (Gain 1) near the bottom of the diagram which contains the value of
The (velocity) output from the first integrator is fed through a second integrator (Integrator 1) to give the distance travelled.
Running this simulation (using only 2 gears) gives the time to cover 1000m as 25 s and the time to reach 60 mph as just over 6 seconds. These are reasonable considering the model limitations.
David J Grieve, 2 November 2004.