Proceedings of the ASME 2014 International Design Engineering Technical Conferences &Computers and Information in Engineering Conference

IDETC/CIE 2014August 17-20, 2014, Buffalo, New York, USA

DETC2014-34413

A NOVEL, ELASTICALLY-BASED, REGENERATIVE BRAKE AND LAUNCH ASSISTMECHANISM

Joshua E. Nieman David H. Myszka∗ Andrew P. MurrayDesign of Innovative Machines Laboratory

Dept. of Mechanical and Aerospace EngineeringUniversity of Dayton

Dayton, Ohio 45469-0210Email: dmyszka@udayton.edu

ABSTRACTThis paper presents the development of a regenerative brake

and launch assist (RBLA) mechanism that stores energy in anelastic medium. Automotive regenerative braking systems har-ness kinetic energy while a vehicle decelerates, and subsequentlyuses that stored energy to assist propulsion. Commerciallyavailable hybrid vehicles use generators, batteries, and motorsto electrically implement regenerative braking and increaseoverall vehicle efficiency. With the intent to apply regenerativebraking technology to conventional automobiles equipped withonly an internal combustion engine, a spring-based mechanicaldevice is proposed. This RBLA concept implements clutches,gears, a ratchet and a spring. The mechanism captures energyfrom, and releases energy to, an additional shaft allowing theaxle to continually rotate. Governing equations were formulatedand validated by a dynamic simulation. In creating the detaileddesign, an optimization determined ideal spring and mechanismdimensions. A physical prototype was designed and fabricatedto demonstrate the concept. A model of the proposed spring-based RBLA shows an increase in the urban fuel efficiency foran average sedan.

1 INTRODUCTIONWith increasing fuel prices and an emphasis on sustainabil-

ity, automotive manufacturers are placing substantial effort on

∗Address all correspondence to this author

making their vehicles more fuel efficient. The rise of hybrid andelectric vehicles is directed at improving fuel efficiency [1]. Evenso, hybrid and electric vehicles only make up approximately 3%of the market [2]. The vast majority of vehicles on the road arestill powered by conventional internal combustion (IC) engines.An increased focus on improving the fuel efficiency in conven-tional IC vehicles fostered recent developments including the useof alternative fuels [3], reduced friction within engines [4], andefficient continuously variable transmissions [5]. Regenerativebraking has long been considered as an energy-saving strategy,dating back to an electric car in 1906 [6].

Regenerative braking is the harnessing of kinetic energytypically lost due to braking and converting it to a another formof energy to be used later [7]. While regenerative braking isproposed for various devices, such as actuators in motion controlsystems, it has become most widely known from current hybridelectric vehicles. Hybrids use a regenerative brake and launchassist (RBLA) system that employs electric motors to convertthe kinetic energy of the vehicle into electricity when the caris braking. This energy is stored in the batteries and used topropel the vehicle later. Without propulsion motors, hybrid-styleRBLA technology is not directly applicable to a conventionalvehicle. However, a mechanical RBLA may allow conventionalautomobiles to benefit from this technology.

Various mechanical methods for both harnessing and storingthe energy have been used, as mechanical versions of regenera-tive braking do not suffer from energy-mode conversion losses.

1 Copyright c© 2014 by ASME

Flywheel storage, such as the Kinetic Energy Recovery System(KERS), utilizes regenerative braking and stores the energy in aflywheel rotating at speeds up to 65,000 rpm [8]. A HydraulicLaunch Assist (HLA) uses a pump/motor to convert the kineticenergy to pressurize fluid for refuse trucks and buses withfrequent start-stop operation [9].

This paper explores the potential for a spring-based RBLAsystem to allow conventional consumer vehicles regenerativebraking ability. Elastic strain (spring) energy is one of themost basic forms of energy storage. Springs have been usedas a source of energy storage for centuries in clocks, bows, andanimal traps, and more recently in garage doors and automotivehoods. The simplicity, low cost, and minimal environmentaleffects of springs make them a viable candidate. At approxi-mately 0.3 kJ/kg (100 ft-lb/lb) [10], the specific energy densityof a steel spring is much less than the 100 kJ/kg (35,000 ft-lb/lb)for batteries used in hybrids [11]. Accordingly, springs are notcommonly considered as a viable option for wide-spread, highenergy storage. Despite having a low energy density, however,springs are able to rapidly release their stored energy. This“power density” can make a spring an attractive alternative forlaunch assist applications. Additionally, springs are environmen-tally friendly alternative to batteries and their well-known designmethods increase their durability and reliability. Hyperelasticsprings, such as rubber, have much a larger energy density of 12kJ/kg (4,000 ft-lb/lb) [10], but further research studies must becompleted to find the fatigue life of these materials at high strain.Ongoing research by Hill et al. involves constructing springsfrom carbon nano-tubes, having an energy density of 800 kJ/kg(270,000 ft-lb/lb) greatly exceeding the capacity of batteries[12]. Commercialization of this technology greatly enhances theattractiveness of an elastically-based RBLA system.

The remainder of the paper is organized as follows. Section2 describes the general RBLA concept. The equations governingthe design details and vehicle response is developed in Section 3.Section 4 presents a dynamic simulation preformed to confirmthe design equations. To have the greatest effect on a vehicle,an optimization to determine ideal design values is presented inSection 5. The development of a benchtop prototype to validatethis RBLA concept is described in Section 6.

2 DESCRIPTION OF CONCEPTThere are three modes for this elastically-based, RBLA

mechanism: charge or regenerative braking (RB), discharge orlaunch assist (LA), and idle. When the RBLA is in chargingmode, the spring deforms as it stores energy. The springdeformation reduces as the RBLA is discharged and energy isreleased. In strain-based storage devices, this deformation andrelaxation cycle involves a reversal of directions. Thus, theRBLA mechanism must account for these reversals as the deviceis intended to function only when the vehicle is moving forward.

Additionally, an idle mode retains any charge in the springand deactivates the RBLA, allowing the vehicle to function asnormal.

A sketch of the mechanical RBLA concept is shown inFig. 1.

Wheel

Ratchet and Pawl

Drum

Spring

LA ClutchRB Clutch

Idler Shaft

Countershaft

Axle

LA Gear Train

RB Gear Train

Strap

FIGURE 1. CONCEPT SKETCH OF THE RBLA DEVICE.

The four major components of the RBLA are identifiedbelow.

I The storage spring is attached to a countershaft that runsparallel to the vehicle’s non-driven axle. A variety of typesof strain-based storage devices could be implemented in thisdesign. For example, a torsional spring could attach directlyto the countershaft. In the proposed design, an extensionspring attaches to a strap that winds onto a drum mountedon the countershaft, as seen in Fig. 1.

II Two gear trains transmit the spring torque to/from the axle.Each gear train is used separately, depending on whetherthe device is in RB or LA mode. The LA gear train containsan idler to account for the storage and release directions ofspring energy. For the gears that mount to the axle, bearingsare pressed into their bores, permitting independent rotationof the gears and axle.

III Two clutches are used to engage the gears mounted on theaxle with the axle itself. One side of each clutch is rigidlyfixed onto the axle and the other side is rigidly attachedto the corresponding gear. Only one clutch is engaged at

2 Copyright c© 2014 by ASME

a time, depending on whether the device is in RB or LAmode. Engaging the RB clutch allows the transmission oftorque from the axle to the countershaft, slowing the vehicle.Engaging the LA clutch allows the transmission of torquefrom the countershaft to the axle, accelerating the vehicle.The clutches are selected to allow the RBLA and axle tosmoothly achieve the same speed in a short period. Clutchesare a commonly used and reliable automotive componentwith well known performance characteristics.

IV A pawl and ratchet are used on the countershaft for idlemode to lock the charged spring in place.

The configurations of each component for each operational modeare given in Table 1.

TABLE 1. COMPONENT CONFIGURATION FOR THE RBLAMODES OF OPERATION

Idle Charge (RB) Discharge (LA)

Pawl Engaged Overridden Disengaged

RB Clutch Disengaged Engaged Disengaged

LA Clutch Disengaged Disengaged Engaged

Spring Static Charging Discharging

When the RBLA is idle, the pawl is engaged and the springwill not discharge until the pawl is released, retaining any storedenergy. Both clutches are disengaged and the RBLA will notbe in motion since the gears are not coupled to the axle. Theperformance of the vehicle will be minimally affected by theRBLA when it is idle, attributed only to the drag from twobearings and clutch discs.

During the energy storage mode, the RB clutch is engagedwhich rotates the countershaft in the direction that overrunsthe pawl. The spring is charged by stretching in length. Theresistance torque on the wheels, caused by the spring force,decelerates the vehicle until either the spring reaches full ca-pacity or the vehicle stops decelerating. Regenerative brakingwill be activated when the brake pedal is applied and the springis not fully charged. Conventional friction brakes may be usedsimultaneously if a higher rate of deceleration is desired.

During the energy discharge mode, the LA clutch is engagedand the pawl is simultaneously released. The spring dischargesenergy, propelling the vehicle forward until the spring is nolonger deformed or the vehicle acceleration is no longer desired.Launch assist is activated when the gas pedal is depressed. Thismode may be used simultaneously with the engine when higheraccelerations are required. If the pawl is released before the

clutch is engaged, some spring energy may be lost. If the clutchengages before the pawl is released the clutch will slip or thepawl failsafe will activate. This failsafe is designed to release thepawl when a designated force, which is higher than the maximumspring force, is applied.

The initial RBLA concept is designed to be installed onto thenon-driven shaft of a two-wheel drive vehicle. This will lessenthe necessary controls of the system. Sensors must be used tomonitor the level of spring charge. While charging or discharg-ing, the spring deformation will be continually changing, thusthe torque affecting the speed of the vehicle will also change.Hence, the RBLA is not designed to be the sole means to propelor stop the vehicle. For example, during launch assist the springis releasing torque to the non-drive wheels. If the user desiresa higher acceleration, they will press the gas pedal harder andthe engine will apply torque to the drive wheels. With differingamounts of torque applied to the wheels, the drive wheels willdictate the speed the car moves, while the RBLA will lessenthe torque required. Regenerative braking is a similar scenario,where the brakes aid the spring. The peak acceleration of theRB and LA cycles are limited to standards of comfort, thus itis assumed that the RBLA will aid required accelerations, notdefine them. Each mode will have the least effect on vehiclespeed when the spring is closest to discharged, and the greatesteffect when the spring is closest to fully charged.

3 DESIGN EQUATIONSIn this section, the equations used to assess the effect of

design parameters are formulated.

Vehicle response to the RBLAA free body diagram of an automobile of mass mc being

propelled by the RBLA is shown in Fig. 2. The principlevehicle forces include drag FD, the weight W = mc g, the normalforces on the tires N, and the thrust FT from the launch assist.The vehicle motion coordinate xc is also defined in Fig. 2 withvelocity xc and acceleration xc. Note that FT can be either withor against motion xc, depending on whether the mechanism is inLA or RB mode.

Summing the forces along the direction of motion,

FT −FD−W sinψ = mcxc. (1)

The drag force of the vehicle is dependent on the referencefrontal area S, the coefficient of drag CD, the air density ρa andthe speed of the air with respect to the vehicle, which is assumedto be the speed of the vehicle xc,

FD =12

CD S ρaxc2. (2)

3 Copyright c© 2014 by ASME

 

FD

FT

W

N1

N2 , ,

FIGURE 2. FREE BODY DIAGRAM OF THE VEHICLE BEINGPROPELLED BY THE RBLA

The RBLA has a velocity ratio between the countershaft andthe axle of Rv, which may be different for RB and LA. The springdrum has a radius rd and the tire has a radius rw. The energystorage spring has a constant of k and is stretched an amountxs. With an initial stretch of xs0 , the relationship between thedisplacement of the car and the spring stretch is

xc =

(rw

Rvrd

)(xs0 − xs

). (3)

A spring force of kxs produces a torque on the shaft carryingthe spring drum of rd k xs. Transferring that torque to the wheelaxle gives Rv rd k xs. Summing torques on the axle,

Rv rd k xs−FT rw = J θw, (4)

where θw is the acceleration of the axle and J is the effectiverotational inertia of the RBLA system along with the wheels.Note that θw = xc/rw. Substituting into Eq. 3, the thrust forceproduced by the spring is

FT =Rv rd k xs

rw− J

r2w

xc. (5)

Substituting Eqs. (5) and (2) into Eq. (1),

Rv rd

rwk xs−

Jr2

wxc−

CDSρa

2xc

2−W sinψ = mcxc. (6)

Further substitution of Eq. (3) into Eq. (6) produces the equationof motion for a vehicle launching or braking, when the spring has

an initial stretch of xs0 ,

(mc +

Jr2

w

)xc +

CD S ρa

2xc

2 +R2

v r2d

r2w

k xc

=Rv rd

rwk xs0 −W sinψ. (7)

Equation (7) represents a single degree-of-freedom dynamicsystem and can be used to model both the regenerative brakeas well as the launch assist phase of operation. Focusing on alaunch, the relatively low speed will allow FD to be neglected.The solution to Eq. (7), the vehicle response, when releasing thespring of initial stretch xs0 is

xc = Acos(ω t +φ)−rw xs0

Rv rd+

r2wW sinψ

R2v r2

d, (8)

where the system natural frequency is

ω =

√StiffnessInertia

=

√R2

v r2d k

r2w mc + J

. (9)

Control of the clutches will prohibit the vehicle response beyondthe time where xs = 0. If the vehicle is propelled from rest, φ =π . Substituting xc = 0 at (ω t) = 0 into Eq. (8),

A =rw xs0

Rv rd− r2

wW sinψ

R2v r2

d. (10)

The time derivatives of Eq. (8) are

xc = A ω sin(ω t−π), (11)xc = A ω

2 cos(ω t−π). (12)

The vehicle will reach its top speed xcmax at time ts. Observedfrom Eq. (11) is that xc is a maximum when ωts = π/2. Thus,

ts =π

2

√r2

w mc + JR2

v r2d k

. (13)

Also from Eq. (11), the maximum vehicle speed and accelerationobtained by the spring stretch of xs0 is

xcmax = Aω, (14)xcmax = Aω

2. (15)

4 Copyright c© 2014 by ASME

Substituting Eq. (9) into Eq. (14),

xcmax =

(rw xs0 −

r2wW sinψ

Rv rd

)√k

r2w mc + J

, (16)

and Eq. (9) into Eq. (15),

xcmax =(Rv rd rw xs0 − r2

wW sinψ) k

r2w mc + J

. (17)

Equations (8), (16), and (17) are used to determine the effectof the RBLA on vehicle performance. Both the regenerativephase as well as the launch assist phase can be modeled withthese design equations by using the appropriate value of the gearratio. From the eight variables in the above equations, only twoare prescribed vehicle parameters (mc and rw), the rest are designvariables (Rv, rd , J, k, xs0 ). Note that mc and J will slightlychange with the selection of RBLA components.

Extension Spring EquationsFor the feasibility study, a steel helical extension spring was

selected because of its widespread use for storing energy. For anextension spring, the spring constant is [15]

k =d4G

64D3Na(18)

where d is the spring wire diameter, G is the shear modulus ofelasticity of the spring material, D is the mean coil diameter, andNa is the number of active coils. The maximum torsional stressin the spring wire is

τ =Ki G d xsmax

8 π D2 Na(19)

where xsmax is the maximum allowable spring extension, Ki is astress concentration factor,

Ki =4C−14C−4

+0.615

C, (20)

and C = D/d is the spring index.

4 SIMULATIONTo validate the design equations, a multibody dynamic

motion simulation was performed using SolidWorks, a CAD

software package. This software has the ability to simulate mo-tions and interaction forces between components. The geometricand mass properties of each component were specified. TheRBLA system dynamic model contains only the moving partsof the device (wheel, gears, spring, shafts, and drum) and isshown in Fig. 3. All other aspects of the design were assumedto be a portion of the vehicle mass and lumped into a singleinput parameter. The values used in the model were based onan average consumer sedan, using its wheel diameter (31 cm)and vehicle mass (900 kg). The vehicle was constrained to moveparallel to the ground, eliminating the need to model the vehiclecenter of gravity. This neglects any change in vehicle pitchduring acceleration.

FIGURE 3. RBLA DYNAMIC SIMULATION MODEL

A launch assist was simulated with the vehicle starting fromrest (xc=0), expelling spring energy until the spring returns to itsundeformed length (xs=0). The simulations were conducted onflat pavement (ψ=0) and did not include frictional losses. Ad-ditionally, since the maximum launch speed is low, drag forceswere not included. For each simulation case, a spring constantk and stretched length xs0 were specified. The simulation resultsfor one case are shown in Fig. 4

Multiple configurations were run in the motion study tovalidate the design equation formulation. The gear sizes, gearratio, drum diameter, and spring parameters were changed toensure the formulation was valid. After each configuration wassimulated, the vehicle position, velocity, and acceleration werecompared to Eqs. (8), (14) and (15), respectively. The simulationresults were within 2% of the design equations. Attributing thediscrepancy to differences between mass properties of the truegeometry and the cylindrical representation, the design equationswere validated.

5 Copyright c© 2014 by ASME

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (sec)

xc(m)

_xc(ms)

Bxc(ms2 )

FIGURE 4. VEHICLE RESPONSE TO A SPRING POWEREDLAUNCH ASSIST

5 OPTIMIZATIONTo ideally select the RBLA mechanism design variables

(xcmax , xcmax , dLA1 , RV , rd , xsmax , Na , ds , Ds , and k),an optimization was preformed using MATLAB’s fmincon com-mand. This command minimizes a user-defined multivariableobjective function subject to constraints. The ultimate goal ofthe RBLA device is to improve the fuel efficiency of a vehicle.Accordingly, the fuel efficiency was used as the objective. Tocreate a standard, vehicle-independent measure of RBLA benefit,the Environmental Protection Agency (EPA) City Driving Cyclewas used.

EPA City CycleThe EPA City Cycle [13] is a standardized sequence of

driving events used to evaluate vehicle fuel consumption. Itspecifies vehicle speed xr for each second in time over a 22.8minute course, simulating urban traffic with many accelerationsand decelerations. These driving events include 18 stops, anaverage speed of 32 km/h (20 mph), a top speed of 90 km/h (56mph), encompassing 12.0 km (7.45 mi). This EPA City Cyclespeed profile is shown in Fig. 5 where the vehicle velocity xri isspecified at each of the i = 0, . . . ,1369 seconds in the profile.

Each positive slope (xri+1 > xri ) in the driving cycle rep-resents vehicle acceleration, where energy must be supplied toincrease the kinetic energy of the vehicle. With a flat terrain andnegligible drag forces, the energy required to complete the courseis

Ea =12

mc

1369

∑i=2

[(xri)

2−(xri−1

)2]

iff xri > xri−1 . (21)

0 200 400 600 800 1000 1200 14000

20

40

60

80

100

Test Time (sec)

Veh

icle

Sp

ee

d (

km

/h)

FIGURE 5. EPA CITY CYCLE REPRESENTED BY A VEHICLEVELOCITY PROFILE

Conversely, each negative slope (xri+1 < xri ) in the drivingcycle represents vehicle deceleration and the kinetic energyis dissipated to the environment through brakes and, with noregenerative braking, is wasted. This energy dissipated throughthe course is

Eb =12

mc

1369

∑i=2

[(xri)

2−(xri−1

)2]

iff xri < xri−1 . (22)

The maximum percentage of energy reduction with a regenera-tive brake system is

η fmax = 1− Ea−Eb

Ea, 0≤ η fmax ≤ 1. (23)

With the frequent starts and stops, an RBLA installed on avehicle in this urban setting is expected to have the greatestimpact.

RBLA Objective FunctionThe energy stored and subsequently released by the RBLA

on the EPA City Cycle is affected by the RBLA design param-eters. Each time the vehicle decelerates, energy will be storedin the spring, until the spring is at its maximum deformation,xs = xsmax . Likewise, as the vehicle accelerates, energy will be re-leased from the spring until the spring is at its free length, xs = 0.Additionally, each acceleration (or deceleration) event may notsolely be accomplished by the spring and would require the aid ofthe engine (or brakes). For each acceleration/deceleration periodin the EPA cycle, Eq. (17) provides the vehicle acceleration xci

that can be obtained by the spring with an initial deformation ofxs0 .

At each time increment, the acceleration (or deceleration)

6 Copyright c© 2014 by ASME

prescribed from the EPA Cycle, xri , is calculated,

xri =xri − xri−1

ti− ti−1. (24)

The previous spring deflection level xsi−1 and xri determineswhich mode should be implemented.

RB Mode: For any interval when the prescribed vehiclemotion involves acceleration (xri < 0) and the spring is notcurrently at its maximum stretched length (xsi−1 < xsmax ), theregenerative brake clutch will be activated. The spring deflectionxsi is determined by rewriting Eq. (3) and substituting the vehiclemotion xc =

(xri + xri−1

)(ti− ti−1)/2 ,

xsi = xsi−1 +RVRB rd

rw

[xri + xri−1

2(ti− ti−1)

]. (25)

The deceleration attributed to the spring is determined by rewrit-ing Eq. (7),

xci =−RVRB rw rd k xsi

JRB +mc r2w

. (26)

If the magnitude of the prescribed deceleration is greater than thedeceleration that can be generated by the spring (|xci |< |xri |), theremaining deceleration must be provided by the vehicle brakes.Alternatively, if |xci | > |xri |, the RB will be deactivated beforethe interval is complete in order to achieve xri+1 . In this case, thespring deflection is determined from Eq. (3),

xsi = xsi−1 +xri(JRB +mc r2

w)

RVRB k rd rw. (27)

If the spring stretch is greater than maximum deformation (xsi ≥xsmax ) in either Eq. (25) or Eq. (27), then xsi is set to xsmax .

LA Mode: For any interval when the prescribed vehiclemotion involves acceleration (xri > 0) and the spring is notcurrently at its minimum deformation (xsi−1 > 0), the launchassist clutch is activated. The spring deformation is determinedin a similar manner as Eq. (25),

xsi = xsi−1 +RVLA rd

rw

[xri + xri−1

2(ti− ti−1)

], (28)

providing an acceleration produced from the spring as deter-mined from Eq. (7),

xci =RVLA rw rd k xsi

JLA +mc r2w

. (29)

As before, if the prescribed vehicle acceleration is greater thanthe spring can provide (xci < xri ), the additional acceleration mustbe provided by the engine. Also, if xci > xri , the RBLA willbe deactivated before the interval is complete. In this case, thespring deflection is determined from Eq. (3),

xsi = xsi−1 −xri(JLA +mc r2

w)

RVLA k rd rw. (30)

If the spring stretch is below the minimum deformation (xsi ≤ 0)in either Eq. (28) or Eq. (30), then xsi will be set to 0. The vehiclevelocity attributed to the spring is

xc =

(rw

Rvrd

)(xsi−1 − xsi

ti− ti−1

). (31)

Idle Mode: If neither RB or LA modes are activated, thespring deflection remains unchanged. That is, xsi = xsi−1 andxci = xci−1 .

Once the spring length throughout the EPA City Cycle isdetermined, the total spring energy regenerated from the RBLAto create vehicle acceleration is ELA.

ELA =12

k1368

∑i=2

[(xci)

2−(xri−1

)2]

iff xri > xri−1 . (32)

An example of this exchange of kinetic to spring energy withinspring capacity limits is shown in Fig. 6.

Energy released from the RBLA corresponds to an amountof gasoline saved, since the engine does not need to producethat energy. The increase in fuel efficiency of the RBLA isapproximated as

η f = η f0

(1+

ELA

Ea

), (33)

where η f0 is the fuel efficiency of the vehicle operating withoutan RBLA.

While increasing the fuel efficiency, the RBLA has a penaltyof increasing the mass of the vehicle, which can be modeledas extra payload. Reynolds and Kandlikar [14] quantified a

7 Copyright c© 2014 by ASME

0 200 400 600 800 1000 1200 14000

2000

4000

6000

8000

10000

Test Time (sec)

Ene

rgy p

er

unit m

ass (

J/k

g)

Vehicle Kinetic Energy

RBLA Strain Energy

FIGURE 6. RBLA ACTIVITY DURING THE EPA CITY CYCLE

correlation between weight and fuel efficiency for conventionalvehicle of approximately 0.7 L/100 km for each additional 100kg of vehicle mass (0.0018-.0040 mpg/lb). This fuel efficiencypenalty ε is multiplied by the mass of the RBLA, mRBLA, whichis estimated assuming all gears, shafts, and springs are made ofsteel and approximated as (potentially hollow) cylinders. Addingthis to Eq. (33), the estimate for fuel efficiency with an installedRBLA is

η fob j =−[

η f0

(1+

ELA

Ea

)− ε mRBLA

]. (34)

Equation (34) represents the objective of the optimization andis minimized to determine the ideally sized components for theelastically-based RBLA.

ConstraintsThe optimization includes multiple constraining functions.

Four equality constraints are used, three ensure the design willpropel the vehicle as intended, as represented in Eqs. (8), (16),and (17). The final equality ensures the spring will meet thedesired stiffness, given in Eq. (18).

An inequality constraint is implemented for reliability. Thespring will encounter cyclical stress loading as given in Eq. (19).This will be limited to acceptable endurance stress limits forspring steel, τmax ≤ 500 MPa (75 ksi). To facilitate manufac-turing, the spring index C is constrained to

4≤C ≤ 12. (35)

An inequality constraint is implemented to prevent interfer-ence. The center distance between the axle and countershaft is(dLA2 +dLA1)/2. To ensure that the drum and axle have at least

a clearance of dg,

12(dLA1 +dLA2)− rax− rd ≥ dg, (36)

where rax is the radius of the axle and the LA input and outputgears have diameters of dLA1 , and dLA2 , respectively.

Throughout the optimization, the size of each rotating com-ponent in the RBLA is sized and selected, influencing theeffective rotational inertia J of the vehicle drivetrain. The drumhas a width of wd and all gears are considered to have a width ofwg. The RB input and output gears have diameters of dRB1 , anddRB2 . Additionally, the clutches have inertia of Jcl and the axleand wheels of Jax. Combining each component, the effectiverotational inertia is

J =π

32ρwg

[d4

LA1+d4

RB2+

d4RB1

+d4LA2

R2V

]+

πρwdr4d

2R2V

+2(Jax + Jcl). (37)

In addition to the constraints, bounds are placed on eachdesign variable as shown in Table 2. Each variable was assignedupper and lower bounds constraining it due to practicality, safety,or manufacturability. For example, the acceleration had anupper bound of 0.2 g since this is the maximum comfortableacceleration for a passenger [16]. Spring variables are limitedto practicality and manufacturability. For example, the totallength of the spring is limited proportionally by the length ofthe vehicle. The completed optimization function will outputall design variables as well as the size all of the primary RBLAcomponents.

Optimization ResultsThe component design parameters for an elastically-based

RBLA, optimally designed for the EPA City Driving Cycle, aregiven in Table 2. With modeling assumptions of no vehicledrag, traveling on a flat terrain, and perfect mechanism efficiency,the conventional sedan exhibited an 8.4% increase in the fuelefficiency, increasing 27 city mpg (8.7 L/100 km) to over 29 mpg(8.0 L/100 km).

6 BENCHTOP PROTOTYPEThe optimization was repeated for a much smaller applica-

tion and resulting values were used to design a benchtop proto-type. The design CAD model is shown in Fig. 7. This prototypeuses a 230 mm (9 inch) long spring with k = 61.8N/mm (17.9lb/in), rd = 152 mm (6 in) and Rv =1.25 to propel a car brakerotor, acting as a flywheel, to over 400 rpm. Electromagnetic,air conditioner clutches were used for their size and ease ofactuation.

8 Copyright c© 2014 by ASME

TABLE 2. RBLA DESIGN OPTIMIZATION PARAMETERS

xcmax dLA RVLA dRB RVRB rd xsmax ls ds Ds k

Units m/s2 cm - cm - cm cm cm cm cm kg/cm

Lower Bound 1.3 5.08 0.10 5.08 0.10 2.54 7.6 12.7 0.08 0.12 5.8

Upper Bound 2.4 15.24 10.00 15.24 10.00 15.24 330.2 431.8 2.03 9.60 230.4

Sedan 2.4 9.29 0.16 5.08 0.28 2.54 127.4 223.8 2.03 8.13 192.2

FIGURE 7. RENDERED IMAGE OF THE RBLA BENCHTOPPROTOTYPE

TestingThe prototype was constructed and is shown in Fig. 8.

Testing will assess the efficiency of the spring as well as thelosses of the system. In the initial test, the spring will be stretchedto its maximum length. Then the launch assist clutch will beengaged and the spring released. Encoders will monitor thespeeds of both shafts to monitor the slipping of the clutches.Once the spring reaches its free length and the flywheel hasreached its maximum speed, the regenerative braking clutch willbe actuated. The flywheel will slow and the spring will extend.The stored energy in the spring will then be noted to find theloss from the system. Then the prototype will be cycled betweenlaunch assist and regenerative braking multiple times. This testestimates the losses due to spring storage, clutch slip, and theefficiency of the entire system.

DiscussionThe air-conditioner clutch is assumed to have similar losses

to the full sized RBLA clutch. The clutch in the RBLA isdesigned to be fully engaged or fully disengaged. Clutch lossesoccur when it is engaging during regenerative braking. Since

the two shafts are spinning at different speeds the clutch willslip until both shafts reach the same speed. The clutch is sizedbased on the spring used in the system, thus it will not slip duringlaunch assist since the output of the spring will not surpass therated torque of the clutch. The prototype spring is expected topropel the axle to over 400 rpm, similar to a vehicle moving 50-65 km/h (30-40 mph) depending on the tire size. This is a greaterspeed than the RBLA should experience.

The initial models used steel coiled extension springs. Theoptimization function, since it finds the optimal energy to weightratio of the spring, outputs springs with thick wire (approx. 2 cm(0.8 in.), and maximizes the length of the spring extension. Thiswire diameter is similar that used for shock absorber springs inconsumer trucks. The total extended spring length limit has ahigh effect on the performance of the RBLA. Further researchwill be implemented to find the longest spring that will fit inan existing vehicle, which will increase the performance ofthe RBLA. Possible devices will contain cables and pulleys toincrease the total possible stretched distance.

FIGURE 8. PHYSICAL RBLA BENCHTOP PROTOTYPE

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7 CONCLUSIONThis paper presented the conceptual design and development

of an elastically-based RBLA. Governing design equations wereformulated and verified with commercial dynamic modelingsoftware. To provide the greatest effect on a vehicle, thedesign equations were posed as an optimization problem. Withmodeling assumptions that include neglecting vehicle drag andmechanism inefficiencies, the optimization results produced adesign that is projected to increase the fuel efficiency of aconsumer sedan by 8.4%. A benchtop version of the prototypewas designed and constructed for feasibility testing purposes.

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