30-10-2014, 04:02 PM
Optimizing Flywheel Design for use as a
Kinetic Energy Recovery System for a Bicycle
1408158628-2013KevinLudlumThesis.pdf (Size: 663.03 KB / Downloads: 169)
Introduction
A flywheel is an energy storage device that uses its significant moment of inertia to store
energy by rotating. Flywheels have long been used to generate or maintain power and are most
identified with the industrial age and the steam engine. In one sense it can be thought of as a
rechargeable battery that store energy in the form of mechanical energy instead of
electrochemical. Flywheels have been gaining popularity as a possible replacement for chemical
batteries in vehicles, but until last year there was no record of a flywheels being used to increase
the efficiency of a bicycle.
Motivation
In 2011, Maxwell von Stein, a student at Cooper Union, added a flywheel and a
continuously variable transmission to his bike for his senior project.1 He used a car flywheel he
found that weighs 15 pounds. His idea won him the Nicholas Stefano Prize, which is Cooper
Union’s award for superior mechanical engineering design. He also gained quite a bit of
notoriety on various biking websites and was featured in NPR’s weekly segment, “Science
Friday.”2
This idea of adding a flywheel to a bicycle is very appealing because it can increase the
efficiency of what is already considered a very efficient machine. The only concern with Mr. von
Stein’s design is that his flywheel is very heavy. It was made for a car, so an extra 15 pounds
would hardly be significant in such a heavy vehicle. However, when 15 pounds are added to a
bike it makes a significant difference in the additional work it takes to accelerate the bike. Mr.
von Stein estimated that the additional weight adds about ten percent more weight to the system,
and he also estimated the peak efficiency gain from his flywheel is ten percent. This means at its
peak, the flywheel is only making up for the efficiency lost by its additional weight. If the
flywheel was optimized for the different design requirements of a bike, it could increase the
efficiency of a bike in more significantly.
Flywheel Background
Rotating wheels have been used to store and deliver energy since prehistoric times. The
potter’s wheel is perhaps the first invention to resemble a flywheel and it has existed for 4,000
years. The first instance of the word flywheel occurred in 1784 during the industrial revolution.3
At this time flywheels were used on steam engine boats and trains and were often used as energy
accumulators in factories. Flywheels became more popular with steep drops in the cost of cast
iron and cast steel. In the industrial revolution, flywheels were very large and heavy so that they
could store significant energy at low rotational speeds. The first use of flywheels in road vehicles
was in the gyrobuses in Switzerland during the 1950’s. The flywheels used on the buses were
1500kg and had a diameter of 1.626 meters. When they were fully charged they could store
3.3*107
Joules.3
Flywheels are now found in many road vehicles as well as space, sea, and air
vehicles. Flywheels are also used for energy storage in power plants and as voltage controllers.
Newly raised concerns about the environment have increased interest in flywheels. This along
with the developments in carbon fiber are making flywheels a viable technology despite the
developments in battery technology. Flywheels now are smaller, can spin faster, are safer, and
output more energy than ever before. In fact a group at the University of Texas in Austin has
developed a flywheel that stores and outputs enough energy to take a train from a full stop to
cruising speed.4
Though flywheels are most identified with the large spinning wheels of the
industrial age, the technology may currently be finding new life in a environmentally conscious
world with major developments in materials science.
The distinctive feature of the flywheel is its high power density. Especially with the
development of carbon fiber, small, light flywheels can store very high amounts of energy safely.
They also can be charged very quickly and can deliver high amounts of power, as shown by their
use in nuclear fission plants. Flywheels are also a zero pollution method of storing energy. In
short bursts flywheels are near one hundred percent efficient. Though efficiency drops depending
on how long the flywheel has to stay charged, the decay in efficiency depends greatly on the
system the flywheel is placed in and whether or not it has any type of housing. The main limit for
flywheel performance will be the efficiency of the transmission connected to the flywheel. Such
ratings can cut the power transfer in half or by even more. Transmission design also often puts an
upper limit on the speed at which the flywheel can spin, in some cases effectively putting an
upper limit on its energy capacity. Since it is a mechanical system that stores energy, there are
concerns about fatigue and wear from vibration and repeated use, as well as safety concerns.
With modern advanced flywheels, they are usually designed to break so that there would be no
large pieces, and would be contained in a housing which will prevent injury of anyone nearby.
In road vehicles, as well as other applications, flywheels are being considered as a
replacement for electrochemical batteries.3
Flywheels have high energy per kilogram, low
charging times, are lightweight, and have a longer lifetime than batteries. Batteries need to be
replaced during the life of a hybrid vehicle, which can be costly and hazardous to the
environment. The main limit on flywheels in vehicles is the design and rating of the
transmission. It is already clear how to create electrical energy from braking, but there aren’t
designs for a purely mechanical kinetic energy recovery system in cars. Flywheels do not yet
have an economic advantage over batteries since flywheel technology in small road vehicles is
not well developed, but there is a promising future in flywheel hybrid cars.
Flywheel use in cars
Flywheels have been used in cars for a very long time, but they haven’t been used as
kinetic energy restoration systems until recently. The flywheel’s main use in cars is to convert
the power from the engine and transfer it to the clutch plate.5 An internal combustion engine
generates its power by firing pistons. Only one in four of these strokes actually drive the vehicle.
This means that the output power of the engine is not steady. This problem is less severe the
more cylinders a car has, since the pistons will be firing at different times to make up for the long
gaps. Regardless of how many cylinders are present a flywheel is still needed to maintain a
steady power supply. All of the pistons firing drive the flywheel to create a smooth power output.
The flywheel can then transfer its power by being pushed into the clutch plate. When the
flywheel and the clutch plate are pushed together, the clutch plate starts spinning which engages
the transmission. A typical set up for a flywheel in a car is shown below in figure 2.The flywheel
is therefore a key part in delivering the power from the engine. Overall it serves three purposes;
as energy storage for the engine, as a surface for the clutch plate and as the drive gear for the
starter.
Cars now have flywheels not just used to transfer power from the engine to the
transmission, but as kinetic energy recovery systems. Formula One changed its rules in 2009 to
allow kinetic energy recovery systems in racing cars.6
These systems could either be electric or
mechanically based. Some teams chose to develop flywheel based recovery systems. One such
system that is becoming popular in racing cars is the Williams Hybrid Power flywheel system,
shown in figure 3.
7
This system converts braking energy into electrical energy which is used to
spin a carbon fiber flywheel. This flywheel can get up to speeds of 60,000 rpm, which on its
outer rim is approximately twice the speed of sound. For this reason the flywheel is stored in a
vacuum sealed chamber and suspended with magnetic bearings. This prevents any significant air
resistance and the flywheel is thus very efficient. The system weighs approximately 300 pounds,
which is fairly heavy for most cars, but the system can also be fitted to buses or subways, for
which the weight gain would be much less significant.
Car manufacturers are also starting to make flywheel based recovery systems for
commercial vehicles. Both Volvo and Jaguar are developing prototype hybrid cars that use
flywheel technology.8
Instead of driving the car for long distances, these systems will be used to
give the car a boost when needed. A Jaguar representative admitted that the system would only
be able to go about a half a mile on its own power. The power output in boost will still be
significant though. Volvo, which expects its flywheel hybrid car to hit markets in 2015, claims that its kinetic energy recovery system will be able to give the car an 80 horsepower boost when
engaged. With this kind of power there will be significant fuel savings.
Transmissions
Every mechanical system that needs to control the power it outputs requires a
transmission. The transmission accepts the power input to the system and outputs it in whatever
fashion is necessary for the system. In the case of the bicycle chains and sprockets are used to
deliver the power from the crank to the back wheel. The relative size of the sprockets will
determine how quickly the wheels spin relative to the crank. Chain drive is also used to transmit
power between the flywheel and the bicycle. In Mr. von Stein’s flywheel bicycle, he used a
continuously variable transmission to connect the crank.1 A continuously variable transmission is
a device that changes the radius the chain rests on to continuously change the gear ratio. This
allows the rider to shift the transmission from allowing the crank to spin quickly to allowing the
flywheel to spin quickly. The mathematics of the gear ratio will be discussed in the next section.
A variable transmission would suffice for the purposes of the flywheel. This would mean the
flywheel has a fixed number of gear ratios it can switch between, much like bicycles that have
more than one speed. The premise for a variable transmission is still the same as it is for the
continuously variable; the gear ratio will switch between the crank spinning quickly and the
flywheel spinning quickly. The design of the transmission is the limiting factor for the speed of
the flywheel, and will largely determine how efficient the flywheel system is. Inefficiencies in
the transmission as well as speed and torque limitations caused by the transmission will by and
large outweigh any theoretical limitations of the flywheel.
Statics of clutch design
The clutch that will be used for the flywheel will use a caliper to engage and disengage
the two gears, which will shift the gear ratio. This mechanism will be explained more in the
following chapter. A similar example problem exists in Shigley’s Mechanical Engineering
Design.
13
Though the example problem does not involve rotating velocities, it is similar enough
to the clutch design in the bike that it is worth reproducing below.
The problem we are analyzing is shown in figure 4. The analysis of all friction clutches
and brakes uses the same general procedure:
1. Assume or determine the distribution of pressure on the frictional surfaces.
2. Find a relation between the maximum pressure and the pressure at any point.
3. Apply conditions of static equilibrium to find (a) the actuating force, (b) the torque, and © the
support reactions.
We will now apply these steps to our problem. Figure 4 shows a short shoe hinge at A
having an actuating force F, a normal force N pushing the surfaces together, and a frictional
force fN, f being the coefficient of friction. The shoe is stationary and the surface it is contacting
is moving to the right. The pressure at any given point is designated as p and the maximum
pressure is designated as pa. The area of the shoe is A.
Clutch and Shifting Mechanism
The clutch is the most complicated and troublesome aspect of the flywheel system
design. Mr. von Stein’s implementation used a continuously variable transmission. This is a
device that can seamless change its shape to create an infinite number of gears ratios. The device
is simple to implement but is very complicated to make, so it is not within the limits of this
project. A normal multi-speed bike has devices such as derailers to switch between its sprockets,
but the shift in sprocket size is considerably smaller than what the clutch for the flywheel will switch between. The flywheel’s clutch will shift between a gear much smaller than the crank
sprocket to a gear much larger than the crank sprocket. This is too difficult of a task to physically
move the chain from one sprocket to the other. A disc or caliper braking system might be thought
of as a simple, off the shelf clutch, but what they have in their simplicity they suffer in the
difficulty of implementation. All bike braking systems of those types use a hydraulic cable to
actuate the brakes. This cable is usually fixed to the bike frame since the brakes of a bike simply
try to make the wheels stop, or in the view of a clutch they lock the bike wheel in with the same
radial velocity of the frame, which is to say zero. The problem in the flywheel system is that both
objects the brake would be trying to connect are rotating, so the cable would get twisted and
bound and become unusable.
With these problems on the table, the clutch design required a bit of ingenuity. Rather
than having a hydraulic cable to push the caliper onto its new surface, a hollow axle will be used
to allow a line to pull the surface onto the caliper. The line will be a brake cable for a simple
friction caliper brake. This means that the mechanism for the shifting is an off the shelf part,
though the clutch itself will require custom parts. The brake line, when pulled, will pull the large
gear into contact with the small gear and thus will shift the ge
Conclusion
The design displayed above is a fairly simple implementation of a kinetic energy
recovery system with a non-negligible increase in the efficiency of a bicycle. Though there are
quite a few parts, many of them are off the shelf and none of the custom parts require highly
developed shop skills, such as computer programmed cuts. Also, the installation of the system
would not be very complicated outside of actuating the gear shift mechanism, which would
mostly involve measuring the correct distance for the line along with some trial and error.
Compared to Mr. von Stein’s design, it is significantly simpler and lighter. However, the use of a
continuously variable transmission allows for the flywheel to spin much faster and is more
elegant in its gear shifting mechanism and long term use. The design shown above makes up for
its lack of an elegantly design clutch by placing the flywheel in a more optimal spot on the bike
and by weighing less. It is impossible for me to use the same measurement of efficiency increase
for Mr. von Stein’s design because I do not know the rotational speed of the flywheel in his
design and I don’t know the total weight added to the bike by the flywheel system. But, by his
own estimation his kinetic energy recovery system adds ten percent efficiency to the system, and
with a fifteen pound flywheel on top of the additional crank, chains, and transmission, it is
reasonable to assume that the flywheel system will add approximately ten percent of weight to
the bike and its rider, thus canceling out the increased efficiency from stored braking energy.
This means despite the design above being simple and unclean in some ways, it promises to be
more efficient overall than Mr. von Stein’s design. This, however, is contingent on the measured
efficiency of the transmission
Modifications can be made to the design above to make it hypothetically more efficient.
Though it would hurt the simplicity of the design, the use of a continuously variable transmission
would make the flywheel system better by almost every measure. The flywheel would spin faster
and the gear shift mechanism would be more standard. It would be difficult to find a place for the
transmission, but this could be overcome by modifying the frame of the bike. Again, this is
difficult to implement but is an improvement in the design. Also, the flywheel itself could be
heavier to store more energy. This would mean it is harder to accelerate initially, but would give
greater boosts to the rider during the trip. When more is known about the measured output of the
flywheel, including its energy stored and the efficiency of the transmission, an optimal weight
could be selected for maximum efficiency. But this doesn’t mean that a person wouldn’t want to
have additional weight on the flywheel to make it less efficient but more fit to the specific rider’s
desires.
Flywheel technology is on the rise across many kinds of technology and rightly so. It is a
pollution free method of storing energy that has many current and potential applications. In the
case of road vehicles there is much to be desired in terms of energy efficiency, especially when
considering pollution per unit of energy. Any system of brake regeneration can help that, but
flywheels have the potential to increase the efficiency of road vehicles without direct or indirect
negative effects on the environment. The batteries used in hybrids do not last the cars lifetime
and can have costly environmental effects. A flywheel has environmental impact only at its time
of production, and has the potential to heavily outweigh those costs through its use. Bikes do not
have the pollution problems cars and other modes of transportation have, but they can serve as a
good analogy for how a kinetic energy recovery system can increase the efficiency of a vehicle.