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ME 466
PERFORMANCE OF ROAD VEHICLES
2016 Spring Homework I
Assigned on 29.02.2016
Due date: 07.03.2016
PROBLEM 1 (30 pts)
A snapshot from the example given in the class to explain basic motor operation principle
is illustrated below. The magnetic field lines (in green) B are shown as well. The length
of the two sides of the rectangular loop of wire are a and b, respectively.
Suppose we replace the single rectangular loop of current with a coil of N loops, or turns.
Derive the torque that acts to allign the normal vector n with the field lines:
T=NiabBsin() ; i.e. in general T=NiArealoop Bsin()
Can you justify the function of the commutator (made of the slip rings in red and blue,
and the metal brushes in grey) in your mind which reverses the direction of the current
every half revolution so that the torque acts in the same direction?
B
n

i
View of the loop from the
magnet side
PROBLEM 2 (30 pts)
Derive using the Ampere’s law that the magnetic field B inside an ideal solenoid carrying
current i, is given by B=oin where 0 is the nominal permeability constant, and n is the
# of turns per unit length of the solenoid.
Hint: The field lines shown in the class were for a stretched-out solenoid, also illustrated
below. The magnetic field lines for a real solenoid are slightly different (can be seen in
the corresponding section of the Physics book) On the other hand for an ideal solenoid,
we are making two assumptions: 1) B is uniform within the solenoid 2) Zero outside it.
Assigned by Dr. Kerem Bayar
ME 466
PERFORMANCE OF ROAD VEHICLES
2016 Spring Homework I
Assigned on 29.02.2016
Due date: 07.03.2016
PROBLEM 3 (30 pts)
Basic working principle of the automotive alternator: A rectangular loop with length a
and width b is rotated at a frequency of f (for instance with a belt connected to the
crankshaft of the engine) in a uniform magnetic field B. The figure that is shown in the
class is re-illustrated below.
Suppose we replace the single rectangular loop with a rectngular coil of N turns. Derive
using Faraday’s law of induction that the battery (simplified by the resistance R in the
figure) charging current induced in the coil is given by i = 2fNabBsin(2ft) / R
PROBLEM 4 (10 pts)
Please answer the questions below related to the paper distributed in the first lecture.
Some of the related material will be presented this week.
1) How does a plug-in hybrid electric vehicle (PHEV) differ from a normal hybrid electric
vehicle (HEV). What is the battery state of charge range in a PHEV? Why is the low limit
for the battery charge not exactly 0%, but something around 25%?
2) Can you briefly describe what “the energy management problem” in an HEV is? What
are the two approaches used for PHEVs? Why does the “blended mode” mentioned in
the paper require knowing the drive cycle1 as a priori?
3) Which drive cycle among the ones mentioned in the paper do you think is the most
power demanding one? UDDS, HWFET, US06 or the towing drive cycle? Please justify
your result verbally. You will justify this numerically in another homework.
4) What do you think the advantage of starting a vehicle with an electric motor while the
engine is disengaged from the road with the twin clutch transmission? (Hint: Think about
the clutching losses of a conventional vehicle.)
5) What is a “V-diagram”? What is its relation to the Vehicle Technical Specifications?
Can you give a brief description of software-in-the-loop (döngüde yazılımsal benzetim)
and hardware-in-the-loop simulation (döngüde donanımsal benzetim) methods? Why are
these methods important in designing a new vehicle?
1
A “drive cycle” (will be emphasized in the last section of this course) is a series of data points representing the speed of a vehicle
versus time. Drive cycles are usually designed to asses the fuel economy and emission levels of cars. These assesments are usually
done using chassis dynamometers. The New European Driving Cycle is given in the next page as an example. Drive cycles are useful
for simulations as well. Example: Figure 6 in the distributed paper.
Assigned by Dr. Kerem Bayar
ME 466
PERFORMANCE OF ROAD VEHICLES
2016 Spring Homework I
Assigned on 29.02.2016
Due date: 07.03.2016
6) Figure 9 in the paper shows the control system arhitecture of the vehicle. What is the
advantage of using such a modular architecture with dedicated control units, in
comparison to using one big controller in charge of every control action in the vehicle?
7) What is the main function of the supervisory controller? How do low level controllers
(engine and motor control units, battery controler) turn the commanded input into
pyhsical quantities?
8) Give a short description of “Controller Area Network” (CAN). What is the maximum
rate a CAN signal can be transmitted?
9) Questionarrie: How good are you in Matlab-Stateflow? Are you capable of turning the
state machine of Figure 10 of the paper into the Stateflow screenshot of Figure 12?
Assigned by Dr. Kerem Bayar