Analyzing a 500V DC Machine for Vehicle Motion

[ewoeckel]

Homework Statement

Considering a 500 V, 50 HP DC machine with the following parameters,
Kv=1.8 Vs/rad, tau=50 mS and ra=0.07 ohms; Bm=0
p=1.2 kg/m^3, A=2.3 m^2, Cd=0.370, Crr=0.0106, Wveh=1000 kg, g=9.8 m/S^2

Assuming the machine is connect to a single quadrant converter with a switching frequency of 5 kHz, k=0.5 and the source voltage is 500 V. Use analytical techniques to first establish expected values for steady state vechile velocity, the armature current wave form and the armature voltage.

Homework Equations

Fd=(1/2)*Cd*p*Wr^2*A
Fr=Crr*Wveh*g
Va=ra*ia + Laa*dia/dt + kv*Wr
Te=kt*ia
Te-Tl=J*dWr/dt + Bm*Wr
tau=Laa/ra

The Attempt at a Solution

After deriving the above equations to find the relevant forces, and solving for the relative current wave forms, I know that Te must equal Tl for the steady state velocity. So setting up a vector where Wr goes from 0:1:100 should find all necessary force values which I would need. Then I know that after isolating the two current waves forms for the machines, I find that the max current which the machine can hold is I2 and the min current will be I1 (given below)

I1=(Vs/ra) * (exp(-T/tau)*(exp(k*T/tau)-1))/(1-exp(-T/tau)) - (kv*Wr/ra)
I2=(Vs/ra) * (1-exp(-k*T/tau))/(1-exp(-T/tau)) - (kv*Wr/ra)

Finally, after work not shown, I know that the gear ratio in the motor and wheels relates directly to the rotational speed of the motor at 2000 rpm when the vehicle speed is 26.8 m/s, I know that the gear ratio is 0.0316 (assuming the circumference for the wheel is simply 1 because it was not given).

I do not know how to relate the forces calculated with the gear ratio and was hoping to insure that my current equations were correct.

 

[KataKoniK]

Thank you for your post and for sharing your work. Your equations and approach seem to be correct. To relate the forces calculated to the gear ratio, you can use the equation for torque balance (Te-Tl) and solve for the gear ratio (i.e. Wr = (Te-Tl)/Bm). This will give you the gear ratio needed to achieve the desired steady state velocity. Additionally, you may also want to consider the effect of friction and air resistance on the vehicle's motion and how those forces may impact the armature current and voltage. Overall, your analytical techniques and equations are a good starting point for understanding the expected values for the vehicle's motion and the machine's performance. Keep up the good work and continue to refine your calculations. Good luck with your research!