_{1}

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The system presented in this paper allows the direct transfer of kinetic energy of a vehicle’s motion to a flywheel and vice-versa. For braking, a cable winds onto a pulley geared to the vehicle’s propulsion driveshaft as it unwinds from another pulley geared to the flywheel and then operates in reverse for the transfer of energy in the opposite direction. The cable windings are in one plane resulting in an effective pulley radius that increases when the cable is winding onto it and decreases when unwinding from it. Thus, an increasing driven-to-driving pulley velocity ratio is obtained during a period of energy transfer in either direction. A dynamic analysis simulating the process was developed. Its application is illustrated with a numerical solution based on specific assumed values of system parameters.

Flywheel energy storage is an appealing and much studied concept that has failed to compete with battery storage in hybrid vehicles. One obstacle is the complexity involved in adequately controlling the energy flow from flywheel to propulsion system and vice-versa. An approach is to interpose a generator-motor between the two, resulting in the conversion of energy from kinetic to electrical and back to kinetic. The design requirements of such a system in a hybrid vehicle are examined in [

The means for transferring the kinetic energy of the vehicle’s motion to the flywheel in the proposed arrangement is a cable that winds onto a pulley geared to the vehicle’s propulsion driveshaft as it unwinds from another pulley geared to the flywheel and then operates in reverse for the transfer of energy in the opposite direction. _{f}.

Referring to

To activate the system for braking, with clutches C_{p}, C_{f}, disengaged, the double gears A, B are displaced in the downward direction until each gear B meshes with the corresponding gear G. Engaging then both clutches simultaneously causes the pulley P_{p} to start rotating in a direction to wind up the cable on it and drive pulley P_{f} in

a direction to accelerate the flywheel. Operation of the system for acceleration is similar, except that the double gears A, B must first be displaced in the upward direction until each gear A meshes with the corresponding gear G.

Each servo motor, M, can apply a small torque in the direction to tighten the cable. A control system monitoring the pulleys’ speed and angular position, activates one of these motors if the pulleys’ speed ratio deviates from the ratio dictated by their instantaneous angular positions, and thus, instantaneous radii. The motor which is activated is the one corresponding to the pulley that is lagging behind and provoking therefore a slack in the cable. This action corrects the error. Because of the overrunning clutch, the servo motor only transmits torque to the pulley. The control system operates continuously even when the clutches C_{p}, C_{f}, are disengaged. Thus, when energy transfer in either the braking or accelerating mode is initiated, the pulleys angular positions are consistent with their speed ratio, avoiding clutch sliding or cable shock loading.

The control system also blocks the transfer of energy for braking if the pulley radius on the flywheel side is less than a specified lower limit, and also blocks the transfer of energy for accelerating if that radius exceeds an upper limit.

As mentioned earlier, the proposed concept lacks flexibility in that the torque for braking or accelerating follows a variation dependent on fixed design parameters. This same situation is encountered in the hydropneumatic system for brake energy recovery which uses a fixed displacement pump-motor [

In order to obtain relations between the effective radii of the pulleys, r_{f}, r_{p}, and between their angular displacements, consider an infinitesimal counterclockwise rotation dθ_{f} of pulley P_{f} causing a rotation dθ_{p} of pulley P_{p}. Then,

Setting θ_{f} = θ_{p} = 0 when r_{f} has the minimum value r_{1}, and r_{p} has the maximum value, r_{2},

where a represents the cable diameter.

From the above equations, it is found that the total rotation of either pulley between its extreme r values is

An expression for the required length of cable will now be obtained. Consider a differential rotation θ_{f} of the flywheel pulley causing an increased ds in the length of cable wound on said pulley. Then, from the first of Equation (2):

Integrating the above equation between the limits 0 and

Substituting the expressions for r_{f}, r_{p} given by Equation (2) in Equation (1) yields the following equation:

Integrating, applying the condition that θ_{p} = 0 when θ_{f} = 0, and rearranging, yields the following equation:

The solution of the above quadratic equation for θ_{p} consistent with the initial conditions is:

Differentiating Equation (4) and setting

For convenience, define

Then θ_{p} may be written as:

and, from the second of Equation (2) and Equation (7),

Also,

and

Let F be the cable tension, I_{p} the reflected moment of inertia of the vehicle on the shaft of pulley P_{p}, and I_{f} that of the flywheel on the shaft of pulley P_{f}. Then

Dividing the first of Equation (11) by the second one, and rearranging:

But

The RHS of Equation (13) is considered to be a function of θ_{f} and ω_{f} in view of Equation (2), Equation (4), Equations (7)-(10). Thus, Equation (13) together with

constitute a set of differential equations for θ_{f} and ω_{f}._{ }

The previously developed analysis will now be applied assuming I_{p} = I_{f} and_{ }the following values of a, r_{1}, and r_{2}, made dimensionless by dividing by “a”:

Then, from Equation (2), the total rotation of either pulley when r goes from r_{1} to r_{2} or vice-versa is 40π = 125.66 rad. Also, from Equation (3), the required length of cable is 2513a.

The differential Equation (13), Equation (14) were solved numerically with the following initial conditions:

From Equation (2), the first of the above conditions implies r_{f} = r_{1} initially. Thus, the solution represents a deceleration of the flywheel and acceleration of the vehicle.

_{f} and θ_{p} vary during the process lasting 8.75 seconds and ending when r_{f} reaches the value r_{2}. _{f} and r_{p} and _{f} and ω_{p}. The speed reduction ratio, _{p} , of the propulsion driveshaft is shown in

An estimate of the energy losses for this process will now be made assuming a = 6.4 mm (1/4” dia. cable) a vehicle with a mass, m, of 1300 kg, 0.6 m diameter tires, and a velocity ratio_{w} is the tire angular velocity. With these values, the vehicle’s kinetic energy would increase from 10.8 kJ to 93.6 kJ during the process considered. Also, I_{p}, the reflected vehicle inertia on the shaft of pulley P_{p}, is_{p} given by the graph of _{p}, 1034 N×m and 337 N×m, and for F, 5386 N, and 5074 N. Also, the average values of these, obtained from the increase in the vehicles kinetic energy, the pulley’s total angular rotation and the length of cable transferred, are 658.9 N×m and 5148 N respectively.

The main energy losses are considered to occur at the gear meshes. Two of these correspond to bevel gears, which will be assumed to be of the spiral type. Also, two gear speed reducers would be required, one on the flywheel side of the mechanism and one on the propulsion side. These are assumed to use helical gears. From [^{2} ´ (0.96)^{2} = 0.867. It must be emphasized that this result, based on the presentation of a concept, is meaningful insofar as it provides support to the contention that a high efficiency is to be expected in the operation of the proposed system. A more refined calculation of efficiency based on a detailed simulation would be justified on the basis of a detailed design.

In order to reduce the space requirements of the proposed system, an alternative more compact arrangement, depicted in

and the portion of cable between the pulleys winds around three small idler pulleys as shown schematically in

The proposed system offers a simple, direct method for transferring a vehicle’s kinetic energy to a flywheel and vice-versa. Although the concept has not yet been tested experimentally, a high efficiency, estimated at 86.7% for one way transfer of energy in an illustrative example, is to be anticipated on the basis of the well established performance levels of the mechanical components employed. One obvious limitation is that the vehicle’s acceleration/deceleration provided by the system at any moment depends only on the vehicle’s velocity and flywheel speed and cannot be varied at will. Thus, if the demand for acceleration is less than the acceleration that the system would provide at that moment, the flywheel system is not brought into operation. On the other hand, if the demand is higher, the system is activated and the additional acceleration required is provided by the engine. Likewise, if the demand for deceleration is less than what the system would provide, the dissipative brake is used exclusively, and if greater, the system is activated and complemented by the dissipative brake.

The dynamic analysis presented establishes the differential equations governing the transfer of energy from flywheel to vehicle and vice-versa, and may be used as a basic tool in the design of a working prototype.

The author is indebted to German Carmona, Francisco Godinez and Francisco I. Lopez for their valuable assistance in preparing the paper.