However, several engineering challenges that prevent the FES from being used in production cars still exist. First of all, the flywheel’s reliability is related to how fast it is being spun. Engineers have to determine the safe range of which it can spin without tearing itself apart. The stress and fatigue that a rapidly spinning flywheel can experience over time is so great, that any inconsistency in the manufacturing of the material of the flywheel could lead to a failure. Secondly, the little but still significant amount of friction still exists in the assembly, especially in a vehicle, because magnetic bearings would have to take the task of dealing with the bumps and shocks that the car transfers to the flywheel during driving. Also, friction can cause the flywheel to lose energy over time, even when it is not in use. Thirdly, rapidly spinning objects such as the flywheel system could subject the car to many forces when the car is in motion. This effect, also known as the gyroscopic effect, is an effect that will cause the flywheel to turn in a different direction when an external torque is exerted on the system (see Appendix 1). The car may experience handling problems that can severely hamper the safety of the car.
My research question
Since there are still existing problems and uncertainties in the appliance of the FES on cars, this essay will attempt to locate the problems that FES engineers face, and possible solutions. First of all, I will analyze the conditions of the maximum rotational speed that the flywheel can spin in safely, and also, I will consider the reliability problems that arise from the speed of rotation will be discussed. Secondly, the leakage of energy stored in the FES will be investigated. I will locate the sources of these leakages, and possible solutions that can minimize them. As a part of this research, a brief account of the workings of magnetic bearings will be included. Lastly, I will investigate the origin of the gyroscope effect, and possible danger that this effect poses on a mobile vehicle.
Maximizing the energy stored in the flywheel – in theory
Why, in a flywheel, it is desirable to have a high angular velocity instead of a very large moment of inertia
The maximum energy that a flywheel could store depends on the amount of rotational kinetic energy that it could possess. A simple equation of kinematics show that the amount of energy a flywheel has is
Where KEr is the rotational kinetic energy of the spinning flywheel, I is the moment of inertia of the flywheel, and is the rotational velocity of the flywheel. If the flywheel is to be applied to a vehicle, it would be to the benefit of the car’s handling if it could be kept as light weight as possible. But on the other hand, a flywheel with a larger moment of inertia would be beneficial to its rotational stability. The moment of inertia increases proportionally with mass, and when there is a larger moment of inertia it is more difficult to change the angular velocity of a body rotating about a particular axis. This could lead to a more consistent rotational speed, being less prone to shock and bumps that the flywheel assembly might experience. Here, we have a trade off in determining the optimum moment of inertia – the larger the moment of inertia, the more consistently spinning the flywheel will be; but the trade off is the increased mass of the whole assembly, hence causing the car to consume more energy to move and more difficult to maneuver. This optimum value will be based on the size limitations of the car and the type of car it is powering. It is beyond the scope of my abilities to determine this value- some values and dimensions of the car have to be known.
To determine the maximum energy that a flywheel can store, we refer to equation 1. Here, it is shown that doubling the moment of inertia of the flywheel would double the amount of energy stored in the flywheel. However, doubling the rotating velocity of the flywheel would increase the energy stored, by four times. A good, high capacity flywheel would be one that can spin the fastest. The question remains, however; how fast can it spin?
The maximum angular velocity of the flywheel
In theory, high speeds are desirable for flywheels in order to avoid using wheels that are unnecessarily large and heavy. This way, the flywheel will have a large energy stored per weight ratio. However, as the rotational speed of the wheel increases, the centripetal force required to hold the individual particles in the spinning wheel increases by the equation
Where Fc is the centripetal force, and is the angular velocity of the spinning object. The stress on the particles of the flywheel increases directly with the flywheel’s spinning velocity. Therefore, when a certain speed is reached, the tensile stress on the flywheel would exceed the tensile breaking stress of the material, and consequently, the flywheel particles would fly off in a straight path, tangential to its intended circular path (because it is no longer held by the forces of the particles in the flywheel). Hence, there is a limit to the safe working velocity.
Consider Figure 2.1, a flywheel’s rim section abcd, where r is the mean radius of the rim. If A is the cross-sectional area of the rim, the volume of the segment is given by
And if is the density of the flywheel material, the mass of the section is
The centripetal force, P, which is mv2/r, would become
The tangential component of the force, F, is responsible for the tensile stress on the radial sections such as ad and bc. The magnitude of F can be found by considering the vector diagrams of Figure 2.2.
Figure 2.2(i) shows the direction of the forces involved, and Figure 2.2(ii) shows P resolved into two equal components F. The angle between these two force vectors is and so we have
Substituting in equation 2 we have
The stress produced by this force is
In terms of angular velocity (v = r) the stress is
Now we have an equation that defines the stress that the rim of the flywheel experiences at a given radius, rotational speed, and density. The maximum tensile breaking stress that the flywheel can tolerate depends on the molecular properties of the material which it is built from. If Sb is the tensile breaking stress of the material, then the maximum velocity that the flywheel can spin without tearing apart is given by
From this equation, we can see that if the flywheel material strength is strong, the maximum safe velocity that the flywheel can spin is increased. Density, in this case, is the attribute that lowers the maximum velocity of the wheel. Therefore, to extract the most speed out of a flywheel, the tensile breaking stress have to be maximized, and the radius and the density of the material minimized. In simpler terms, we have to maximize the strength to density ratio.
The maximum energy stored
However, it might seem like equation 1 does not justify the fact that we have to maximize the strength to density ratio. Since KE = ½I2, it seems that increasing the density would also increase the moment of inertia (since = m / V). But that is not the case. The maximum KE for a flywheel (assuming its moment of inertia is ½MR2) is given as follows
Substituting equation 3 we have
Thus, the maximum allowable energy storage in a flywheel of any size depends only on the strongest and lightest materials we can make.
Fatigue at the flywheel
Besides exceeding the breaking velocity of the flywheel, fatigue could dominate the life of a flywheel. The forces generated in the flywheel are so great, the materials of the flywheel often expand, or stretch to a larger diameter circle. Even if there’s no contact present, the expansion and contraction of the flywheel could reduce the number the cycles that the flywheel could sustain before it fails.
However, fatigue failure of materials is a random phenomenon; there have not yet been a way of accurately estimating the fatigue behavior of a particular material. It is not an easy problem to handle theoretically or experimentally, since the process commences within the concept of atomic structure of the material and develops from the first few cycles of stress, and extending to thousands or millions of cycles - until failure. Fatigue happens in two phases, initiation of a crack (fig 3.1a) and the propagation of this crack (Fig 3.1b) to final rupture of the material.
Eventually, after a specific number of cycles, the material will lose its structural integrity and break apart.
The reasons that fatigue occur is still widely debated. According to a textbook by P.P Benham and R.J. Crawford, fatigue is initiated by the movement of dislocations. A dislocation is a hole, fault, or misplacement in the atomic lattice of the metal. Microscopic deformation allows dislocations to move through and fill vacancies of the lattice, and it is believed that these movements initiate the beginnings of a crack.
There are others, who argue that fatigue might be caused by intrinsic defects in the material, that different materials have different fatigue characteristics. Whichever theory holds, fatigue is a phenomenon that depends on the geometry of the component, the material, the type of stressing, and the environment.
What materials would be feasible in this application
From the analysis of the maximum speed and above, we arrive at the conclusion that the optimum high energy storing material that the flywheel could be made of is a high strength, stiff, but light material. Also, to solve the problem of fatigue, the flywheel material might have the high-energy attributes as well as fatigue- resisting characteristics that could withstand fatigue and high speed for a long period of time. From an article by Iannotta, a lot of flywheel research labs have already determined to use fiber-reinforced composites such as carbon fiber and Kevlar. For these composites the base material is usually metal or plastic and the fibers used could be carbon, aramid (for Kevlar), and boron.
Also, since the stretching and deforming of the flywheel cannot be prevented, it must be controlled. This means that any deformation must occur symmetrically around the flywheel’s axis of rotation. If there are any holes, or slots in the materials, the process of deforming would force the fibers to move throughout the dislocations. These movements would not only accelerate the process of fatigue, if the dislocations are relatively big, it could affect the centers of mass of the flywheel, causing vibrations that send the wheel spinning out of control.
Several flywheel researchers apparently know how to prevent this happening, but it is still kept as a trade secret. All that is publicly known is that during the process of making the flywheel, when the fiber lines are wound around the flywheel (this is part of a flywheel manufacturing process. Fiber materials are make as strings and wound around a flywheel’s axis), there must be constant tension in every part of the string in the finished flywheel, in order to keep inconsistencies from forming.
The leakage of energy stored
The leakage of energy from the FES system is an important element to consider. The total leakage from the FES can be categorized into two types: electrical loss, and mechanical loss. Mechanical losses, such as friction caused by flywheel sediments or friction at the bearings, could pose a serious problem if the energy stored in the FES needs to be available even if it is not used for a longer period of time. In an effort to reduce mechanical losses, researchers have developed ways of eliminating friction, most successfully the active magnetic bearing system. However, this poses more design challenges, and also introduces more electrical losses within the FES.
How friction prevents flywheels from being efficient
For a flywheel to work at its peak efficiency, friction must be kept to a minimum to minimize the decrease of speed of the flywheel. This includes the need to reduce air friction inside the flywheel containment vessel, residual friction, and friction at the bearings. The reduction of air friction in the flywheel has already been done by using a vacuum pump which creates a vacuum inside the flywheel assembly, eliminating air friction. Residual friction is friction that occurs when particles from the flywheel had broken out of the flywheel disc, hitting the flywheel disc at random inside the containment vessel(see Fig 4.1). These particles had broke free from the flywheel disc as result of the fatigue of the wheel, after it has been used for a substantial amount of cycles. However, the effect of this is relatively small to be considered, only costing the flywheel 0.03% of the total energy over a 24 hour period. This amount can be kept very low due to the high quality manufacturing of the flywheels, and it can be ignored.
Friction at the bearings, however, brings up a new challenge for flywheel research firms. The invention of the magnetic bearings works for flywheel that sits on a stationary place. But for FESs in vehicles –the frequently encountered bumps and movements – poses a problem for these magnetic bearings.
Magnetic bearing – and its workings
The flywheel is supported by magnetic bearings, enabling it to float in the containment vessel of the FES. There will be virtually no friction and no lubricant needed, because the flywheel does not come into contact with any material.
Figure 4.2
The ends of the hub of the flywheel contain a stationary disk inside the ring on the flywheel. The bearing parts of the containment vessel contain a ring of magnet also. They are both of identical polarity, so repulsive forces keep the flywheel assembly away from touching any parts of the bearing, like a top. But when there are shock, jerks, or rapid movements on the containment vessel, if the magnetic bearing does not provide enough repulsive forcers to keep the flywheel floating, the spinning flywheel will not move with these shock, jerks, or rapid movements relative to the position of the car. Therefore the bearings could possibly come into contact with the flywheel hub. In a flywheel-equipped EV travelling on a rough road, the flywheel’s axle might touch down every few seconds, hence quickly rub to a halt.
In active magnetic bearings, electronics calculate the gaps between the rotating and the non-rotating parts of the FES. Active bearing control can be applied by running a current through the electromagnets that attract a steel ring on the flywheel, in order to adjust clearances. They respond to road shocks by boosting the amount of power to electromagnets – a few thousandths of an inch from the spinning axle – just in time to prevent touchdown. Active bearings need fast electronics, since sensors should check the axle’s position several times per rotation. They must therefore work faster then the flywheel turns. A processor must then evaluate this information faster then the sensors sending it, and compute how to jiggle the bearings’ electronic system. However, a processor that could handle this tremendous amount of data flow is not yet available. Therefore, there is still a possibility that a flywheel will suffer from friction at touchdown. Moreover, the spinning flywheel must provide the amount of electricity needed to keep the active bearings in work - some efficiency is lost here.
The actual bearings, however, incorporate ball bearings, for “catcher” or start-up support. The “catcher” bearing supports the rotor at rest and during start-up. In the event of a loss of active bearing control power, the “catcher” bearing must be true to its name, and accept and control the spinning rotor after a short stop.
In summary, the active magnetic bearings system had to be improved in terms of efficiency, and reliability in its prevention of the flywheel from touching down.
The gyroscopic effect
The gyroscopic effect of the flywheel
The rapidly spinning flywheel of the FES produces large gyroscopic forces. These gyroscopic forces are the principles behind gyrocompasses, and toy gyroscopes (the gyrocompass is based on the effect of a flywheel which is free to rate about two perpendicular axes. It tends to orient its spin axis parallel to the axis of rotation of the system, therefore able to point in a fixed direction). A rotating wheel would tend to have the flywheel axis pointing to a fixed position in space. And if a force is applied to move this axis’ direction, the flywheel will move in a different direction than the applied force. With an extremely high spin velocity, it will cause a huge amount of external movements and forces to the vehicle if the car moves about on curves, slopes, etc. Please consult appendix 1 for information of the vector nature of angular momentum to see how a spinning wheel produces gyroscopic forces.
In particular, the angular momentum of a flywheel will be
With direction along the flywheel axis. Also, since
We see that an external force applied to the flywheel will cause a change in the angular momentum perpendicular to the force. This could cause handling problems for the car that it is attached to – because the flywheel’s behavior on external torque can disturb the handling of the car (external torque meaning any torque acting from the outside of the FES).
For example, consider a car going up a slope. If the flywheel is mounted horizontally, and turning in a direction indicated by the arrow below
when the car approaches a slope, the torque that the car has on the flywheel will create a change of momentum ΔL, in addition to the original angular momentum of the flywheel. The sum of these momentum vectors would force the car, which is rigidly connected to the flywheel, to turn right (relative to the car’s motion). If the car can adhere to the road and not move to the right, this gyroscopic force could severely overload the magnetic bearings (because of its unwillingness to turn) and lead to failure of the flywheel.
Even if the flywheel were mounted vertically
as in Figure 5.2, it would still pose danger, because when the car makes a turn, it would tend to lift the vehicle upwards, overloading the bearings. Also, this upward force could also lessen the weight of the car on the wheels, hence increasing the possibility of a vehicle skid.
What could be used to eliminate them
However, there is a way to eliminate or compensate for the gyroscopic effect. There are two ways: one of them is to mount two flywheels on one shaft and have them counter-rotating to compensate for each other’s angular momentum. Another way is to employ complicated gimbaled bearings to allow the flywheel to be isolated from the rotational motions of the vehicle. The former solution is a method that could work theoretically but poses more problems and doubts on its application.
Since the equation for angular momentum L applies to the entire rigid system
therefore, if two flywheels are connected by a rigid shaft, the sum angular momentum of the system will then be zero, allowing us to turn it easily. However, in order to keep the angular momentum to be zero constantly, the wheels need to be spun down and up simultaneously in order to avoid getting a non-zero net angular momentum. If one flywheel fails to match the rotation speed of the other, the gyroscopic forces will be in effect. In addition, the actual viability of this method depends on the shear strength of the connecting shaft, which must be able to transfer the torque without snapping or bending. The single axle supporting those two flywheels is stationary, so magnetic bearings has to be embedded in the wheels themselves, at the hub – a potential source of flaws, where different materials would join.
The second method, employing gimbals to isolate the rotating parts of the flywheel from the car, involves a complicated set of bearings to allow the flywheel to move in the x, y, and z axis. A simple version of the configuration of the gimbals is drawn below
Figure 6.1
Conclusion
The development of the flywheel has evolved greatly from a simple concept to a complicated, precise piece of machinery capable of being a feasible battery. Flywheel could be made from high strength and low density composite materials such as carbon fiber, and Kevlar, and can store great amount of energy without difficulty. Some problems still exists, however, such as the reliability of the flywheel from fatigue failure, the unpredictability of the deformations of flywheel material is still uncertain, and any doubts in the longevity of a flywheel must be dealt with before it is marketed into mass produced EVs. Friction is a problem that is partly solved, and somewhat questionable. The development of the air vacuum and magnetic bearings has made the flywheel nearly friction-free, but could it really cradle the flywheel assembly without contact and danger? Also, the introduction of the active magnetic bearings has introduced yet more electrical energy loss in the operation of the flywheel. A way to reinforce magnetic bearings must be found. The gyroscope effect of the flywheel exists, and a way to use gimbals to separate flywheel motion from the vehicle must be perfected.
However, please take note that since this essay is based on information that is about a year or more before today, recent discoveries and innovations might have already resolved the problems that I outlined. Also, there is a lot more physics is in engineering materials of the flywheel, as well as the gyroscope effect of the flywheel, but it is beyond the scope of my understanding and therefore not included.
The potential of the flywheel is still waiting to be exploited. With numerous innovations being discovered everyday, a perfected flywheel system could very likely be powering your family car by the year 2000.
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Appendix 1
Vector nature of angular momentum (the gyroscope effect)
Just as Newton’s Second Law is a vector equation, the rotational equivalent of it is vector based as well. In all the particles in a rotating body, the only direction that they all commonly possess is along the axis of rotation. Since there is still an ambiguity (there is two separate directions which they can point to), physicists have defined a common convention, known as the right hand rule.
Figure A 1.1
The direction of the vector is towards an observer who sees the rotation as being counterclockwise. Or put it another way, when the fingers of the right hand curled around the rotation axis and point in the direction of the rotation, the thumb points in the direction of the vector.
This fact poses a large and interesting problem to flywheel design. Since flywheels rotate with a very high angular velocity, they possess a momentum vector which can produce very noticeable forces when the flywheels is moved, in reference to space.
Let us consider a rapidly spinning wheel in Figure A 1.2.
The spinning of the wheel produces an angular momentum that points to the right side of the diagram. Now, when a person holding on to the axle of the wheel and tries to tilt up, changing its plane, the spinning wheel will not go up – instead, it moves to the right. To explain this effect, we need to consider the vectors at work here. When the person try to tilt the flywheel, it changes its plane – and the wheel is given a torque about an axis through the person’s wrist. Therefore, there is now two different angular momentum on the wheel here – the momentum of the spinning cylinder, and the momentum exerted by the person about an axis through his wrist, from the equation
The change in L results from the torque exerted. Thus, the new total angular momentum on the spinning wheel is L + ΔL, as shown in Figure A 1.3.
The original L points in the y direction, but when it is added to ΔL, which points to the x-axis, the resultant angular momentum now points somewhere else. This is why the wheel would swerve to the right instead of going upwards. This property of spinning objects would affect flywheels the same way.
This phenomenon is what makes a child’s spinning top, also known as a gyroscope, precesses around a point on a table.
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