P a g e | 1

1.0 Introduction

In recent years, the push for more fuel efficient cars has become more prominent, as

influence from many sectors drives car manufacturers to update and look to the future. The U.S.

government has placed CAFE, or Corporate Average Fuel Economy, standards on the automobile

industry, mandating an increase in the average fuel economy of each car manufacturer’s fleets to

35.5 miles per gallon by 2016, continuing to a goal of 54.5 miles per gallon in 2025 [1].

Consumers are also demanding smaller, more fuel efficient cars as gas prices soar. Behind all of

this is the idea of peak oil, and a need for the reduction in the carbon footprint of humans. Peak

oil is the point at which the oil production of the world can no longer match the oil consumption

of the world, leading to rising oil prices and a highly stressed global economy, as seen in Figure 1

by the simplified graph [2]. The carbon footprint issue is more wholesome in nature, referring to

the earth as a complex, interconnected system that humans are helping to force into an imbalance

through the continued use of fossil fuels. More efficient vehicles, and therefore a smaller carbon

footprint, will help alleviate the climate issues that we are facing.

Figure 1. Simplified graph of diverging production and consumption lines due to “peak oil”. [3]

Many different measures have been attempted that aim to increase the fuel efficiency of

vehicles, including enhanced aerodynamics of small cars and regenerative braking in hybrid

vehicles [4]. These measures attempt to reduce the power needed to move a car, or capture

wasted energy for reuse. This thesis proposes an idea for a spring-based energy storage device

that can be used to start a vehicle’s engine in a more efficient manner. The project was initiated

DEMAND Continues

PRODUCTION Peaks

P a g e | 2

by General Motors (GM) under a broader ongoing project invested in the development of

mechanical energy devices for automobiles that can capture, store, and utilize the energy

associated with vehicles in a more efficient manner. While the team at the University of Dayton

is focusing on elastically-based devices, other universities are focusing on compressed air and

flywheel devices to perform similar tasks.

The proposed design enables the engine starting system to have a reduced size and

weight, while decreasing the use of more valuable and environmentally harmful heavy metals,

such as the lead in the large batteries. The reduction in size and weight also allows car engines to

be smaller and more fuel efficient, saving oil and reducing the carbon footprint of humans. The

reduction in hazardous materials used has the potential to reduce the harmful effects, other than

those caused by carbon emissions, that humans are having on the planet.

In addition to reducing the size and weight of the starting system and reducing the

amount of hazardous materials, a device utilizing mechanical energy has the potential to be more

efficient than one utilizing electrical energy. In an electrical starter system, chemical energy in

the battery is converted into electrical energy in a high power energy dump, and then into

mechanical energy in a highly variable power transfer. This variation results in the motor being

under various partial loads for a significant period of time. When a motor is run under a load

other than its optimal load, the efficiency decreases [5]. A mechanical starter, however, would

utilize a much smaller electric motor, and the load would be very stable and constant. This would

allow the motor to run closer to its optimal load, lending to much higher efficiency in the

chemical to electrical to mechanical energy transfers. The final energy transfer would be from

the spring to the engine, both of which are mechanical devices, resulting in a highly efficient

transfer of energy. Therefore, a mechanical spring starter would have the potential to be a more

efficient system than an electrical starter, as well as being lighter, smaller, and less

environmentally hazardous.

A vehicle engine starter using a spring to store and release the energy has potential to be

successful in specific automotive applications. Size and weight reductions show promise for

many vehicles, but may only be truly effective in applications where the user will accept a

possibility of reduced convenience. Such applications include large commercial freight trucks

and vehicles in developing nations. Users in developed nations tend to require a higher level of

convenience, one that a spring-based starter may not be able to provide.

P a g e | 3

In commercial freight trucks, a bulky system is necessary for starting the engine. These

systems require two large lead-acid batteries and a large electric starter motor in order to supply

the power to start the large diesel engine [6]. Additionally, these trucks travel the majority of the

time on the highway, meaning that the starting system is only used minimally. Thus, having a

large and heavy starting system produces a disproportionate situation where a large system is

used for a small percentage of the time. Furthermore, diesel engines do not necessarily require

electricity to start, but an electric starter system does. Therefore, an emergency loss of electricity

produces a situation where the vehicle cannot start, even though the engine itself has the potential

to start. These issues can be solved by implementing a spring-based starter in large commercial

freight vehicles. A spring starter, with its inherent efficiencies, has the potential to be smaller and

lighter, increasing fuel and space economy. Additionally, a spring starter can be designed to have

a manual charging mode. This means that even in the event of a failed electrical system, the

starter can be manually loaded to start the diesel engine, requiring no electricity to start. These

advantages give a spring starter system a great deal of promise in the trucking industry.

Small personal vehicles can also utilize a spring starter in a similar manner, with the only

major difference being the frequency of starting the engine. This increased frequency means that

users may be forced to wait more often for the spring to reload in the event that the spring starter

fails to start the engine on the first attempt. The frequency of starting may result in an increase in

the number of failed starts, resulting in a greater decrease in convenience than in the

implementation in a large truck. In developing nations, where the convenience of having a car

that starts every time on the first try is less important than having a car in the first place, this wait

time is less of an issue.

With these potential applications in mind, this research will focus on the design,

prototyping, and analysis of a vehicle engine starter that utilizes a spring to store and release the

energy necessary to start an engine. Section 2 covers the history of the automotive engine starter

from its origins to the current day, as well as instances of spring-based starters. Section 3

discusses the initial considerations pertaining to the type of spring that was chosen for the design.

Section 4 presents the process of designing, modeling, and building the prototype of the spring

starter concept. Section 5 illustrates the testing and analysis performed on the prototype, as well

as the key results of the process. Section 6 presents the conclusions drawn from the project,

contributions made, and recommendations for the team to move forward with.

P a g e | 4

2.0 History

Standard gasoline or diesel vehicle engines, known as internal combustion (IC) engines,

must be cranked by an outside force in order to start. Today, electric motors are used to do this,

but this was not always the case. Early vehicle engines were started with hand cranks, which

proved to be difficult and dangerous for the operator. Because of the nature of IC engines, if the

engine is cranked with too little force, or was at a position of the engine cycle that made it

resistant to starting, it could backfire and cause injury to the hand crank operator [7]. This was an

issue, especially once cars started to get larger and heavier, thereby requiring larger and more

powerful engines and subsequently more cranking power. Charles Kettering invented a device

that solved these issues.

The electric self-starter, as it was called, was invented and patented in 1915 in Dayton,

Ohio by Charles Kettering, and was a huge step forward in the development of automobiles [8].

The power and convenience provided by electric starters established the dominance of IC engine

powered automobiles, as seen to this day. Electric starters also allowed vehicles to get more

advanced and more powerful than ever before. Still, these starters have changed very little from

the time they were first implemented into automobiles. An image of Charles Kettering next to his

self-starter invention is seen in Figure 2.

Figure 2. Charles Kettering and his self-starter invention. [9]

P a g e | 5

Although electric starters seemed to solve all the problems associated with starting

engines, issues in specific applications became apparent, such as a dead battery or otherwise

failed electrical system. Spring-powered engine starters have been developed to overcome these

issues, which are usually emergency-related. Many spring-powered starters are designated as

back-up starters for stationary engines [10]. These starters require hand cranking to operate, and

are only used when the standard electrical system has failed. Thus, they are often incorporated

into the engine in addition to the traditional starter, resulting in no opportunity for reduced size,

weight, or environmental impact. Still, the size of the starter in relation to the engine is

impressively small, warranting the use of spring starters. The extra weight an additional spring

starter is not an issue for stationary applications, but in automotive applications, this is a strong

constraint that has kept spring starters from application in the automotive industry.

The objective of this project is to demonstrate the concept of a spring starter through a

working prototype. Specific experiments and analyses of this prototype will determine the

properties of the spring, including the spring constant, the energy storage, and the power

delivered by the spring. These values will then be extrapolated to demonstrate the potential of a

spring starter in an automotive application with the goal of reducing the size, weight, and

environmental impact of the engine starting system.

P a g e | 6

3.0 Energy Storage Medium

A spring stores energy in the form of elastic potential energy as a result of applying a

tensile or compressive force to the material that the spring is made of, whether it is the fibers in a

polymer or the molecular bonds in a metal. A common example is a steel spring, in which the

steel wire is shaped in such a way to allow the steel to bend or twist, thereby either tensioning the

outer fibers of the wire and compressing the inner fibers, or twisting the wire along its axis,

subsequently storing energy. As seen in Figure 3, when a force is applied, the outer fibers, shown

as the links on the top of the structure, are longer than normal, and the inner fibers, shown as the

links on the bottom, are shorter than normal. The shape also prevents the material from bending

so far as to permanently deform the wire. This shape is commonly a spiral, whether in a tension,

compression, or torsion spring. There are numerous applications for which each of these types is

best suited. For the engine starter concept, it was determined that a torsion spring would best

meet the requirements and constraints.

Figure 3. Diagram demonstrating tension and compression due to bending. [11]

Both torsion and tension spring styles were considered for the engine starter, each having

advantages and disadvantages. A tension spring offers very simple attachment, but requires a

P a g e | 7

large devoted section of the device to allow it to change overall length. The device would have to

be as long as the spring would be under full load. This made tension springs impractical for a

device that needed to fit in a compact, rigid space. A torsion spring, on the other hand, maintains

approximately the same dimensions whether it is loaded or unloaded. This allows it to be

packaged in a smaller space, and means that the device utilizes the entire space throughout

operation, increasing its space effectiveness. The compact nature of a torsion spring made it the

ideal choice for the engine starter concept.

Rubber was also considered for use as the elastic member to store the energy in the

starter. Much effort went into determining the strength, energy density, durability and overall

suitability for the concept. Rubber seemed promising for its high energy density, but after some

testing and research, there were many issues the hindered the feasibility of rubber [12]. Attaching

the ends of the rubber element looked to be extremely difficult, and the low durability, relative to

steel, furthered the implausibility of its use in the harsh environment of automobile use. The

plausibility of rubber could be supported with further research into high performance elastomer

materials, but for this research, steel was chosen as the ideal material because of its durability and

its widespread use as spring material in the industrial world. Steel does have some disadvantages,

namely its relatively low energy density that necessitates a heavy spring. However, this

disadvantage is outweighed by its advantages over other materials, such as rubber, making steel

the material of choice.

P a g e | 8

4.0 Prototype

4.1 Initial Concept

The operation of the spring starter was first conceptualized to utilize a small motor and

battery to turn a worm gear, which would then wind up an elastic entity. The elastic entity would

store the energy required to start the engine until the operator releases the energy of the elastic

entity into the engine through a gear train, by way of turning the ignition key. This concept of

operation has remained unchanged throughout the design of the spring starter. The major

components to be designed are therefore the elastic entity, the worm gear, and the gear train.

These components were critical to the design of the prototype, and will again be critical to the

future optimization of a spring-based engine starter.

The concept of the spring-based engine starter was originally developed as a device

designed to assist the traditional electric starter. This concept was referred to as a “Dual-Start

Option” in which the spring-powered device would attempt to start the engine, and the electric

motor would assist it or take over if the spring failed to start the engine. This concept provided

some solutions, as well as some issues, prompting further development of the device and its

implementation.

By augmenting the spring starter with the traditional electric starter, the system was sure

to start, even if the spring was incapable of starting the engine alone. The Dual-Start Option

concept, with the 3-dimensional component of the spring starter overlaid on an image of the

cross-section of a traditional electric starter, is shown in Figure 4. However, the complexity of

the system led to increased weight and size, leaving the concept with few advantages. Leaving

the original starter system intact meant that the spring system only added weight and size,

because no components were replaced or redesigned. Also, the incorporation of both spring and

electric systems required more solenoids to control the function of the starter, increasing the

control system requirements. These issues could never be overcome if the electric starter were to

remain in the system. Removing the electric starter opened up many possibilities for the concept.

P a g e | 9

Figure 4. Daul-Start Option concept adding spring starter to existing electric starter.

A stand-alone spring starter was potentially capable of reducing the weight of the large

electric motor and lead battery, as well as decreasing the overall size of the system. The

elimination of the electric starter system allowed the spring starter system to have a much simpler

design, easing prototyping and optimization. The visual of this stand-alone concept is essentially

what is shown in Figure 4 with the electric starter portion removed and the spring starter mated

directly to the engine and flywheel. Still, this concept had design issues, such as starting

reliability and energy density of the spring. These issues could be solved through clever design

and appropriate design constraints, but a prototype was to be built first in order to prove the

concept and provide direction for further developments.

4.2 Design and Modeling

Once the spring starter was conceptualized, the theoretical system and components had to

be interpreted and conceived as readily available parts that could be assembled into a working

prototype. These components had to be approximately sized in order to handle the expected

loads, and had to fit together with minimal fabrication. It was determined that the spring and

worm gear components would be the most difficult to find and size correctly, so these

components were the first to be purchased and were the basis for the sizing of the remaining

components.

A garage door spring was determined to be the most readily available and appropriate

type of torsion spring for the prototype. The function of assisting in lifting garage doors made a

garage door spring seem like an appropriate strength for the anticipated size of the prototype. A

worm gear was acquired at Mendelson’s Liquidation Outlet that was of appropriate size and

strength for the prototype [13]. This worm gear had a 15:1 gear ratio, making it appropriately

P a g e | 10

sized for hand cranking. Figure 5 shows the garage door spring and the worm gear in the

approximate orientation in which they are assembled.

Figure 5. Purchased garage door spring and worm gear components.

In addition to determining the spring and worm gear components, a component had to be

designed to simulate the loads of starting an engine. A standard internal combustion engine has a

varying load during starting due to the friction and compression in the cylinders. It was

determined that a barbell weight should be used to simulate the load in a more consistent and

predictable manner, facilitating simpler testing and analysis. The inertia of the weight would

provide a reverse torque that the spring starter would need to overcome. Unloading the potential

energy of the spring into the kinetic energy of the barbell weight, shown in Figure 6, would

provide a proof of concept for unloading the potential energy of the spring to overcome the

friction and compression of an engine. The barbell would also need an overrunning clutch system

in order for it to be powered by the spring in one direction and left to spin under its own

momentum once the spring released all of its energy. This simulates the point at which the

engine starts running under its own power. A one-way bearing was chosen for this function, and

is shown in Figure 6 in the center of the barbell weight.

Input from Worm Gear

Output to Gears

P a g e | 11

Figure 6. A barbell weight was used to simulate the engine load.

The design of the prototype needed to accommodate the three components that were

already acquired due to their uniqueness. The garage door spring determined the majority of the

length of the device, as well as the size of the shaft driving the motion of the device, hereon

referred to as the drive shaft. The worm gear determined the height of the drive shaft and the

components aligned with it. The barbell weight determined the size of the bearings and shaft that

it would ride on, or the output shaft. The various sizes and constraints of each of these

components called for some limited fabrication and other unique component selections.

The remaining components, including pillow block bearings and coupling and adapter

components, were sized to fit the shaft sizes and positions of the predetermined parts. The

components were placed in space relative to each other such that all the shafts lined up, the gears

meshed, and there was adequate spacing between components. The frame was then designed to

fit the various intricacies of the components and their positioning. The various center distances

and component sizes forced the frame to take a specific shape, seen in Figure 7. The various

constraints that determined the size and shape of the frame are discussed below.

P a g e | 12

Figure 7. CAD model of prototype frame after accommodation of all components.

The size of the garage door spring, as well as the number of bearings and gears,

determined the length of the drive shaft. The drive shaft had to extend from the worm gear shaft

to the bearing at the other end of the frame. It was also determined that a ¾ inch shaft would be

the best size, based on the availability of certain components, namely the spur gears, which only

came with ¾ inch bores in the appropriate sizes. With the bore of the garage door spring end

caps being ⅞ inch, shaft spacers had to be purchased to fit the components snugly together.

Additionally, a ball bearing had to be fit into the end of the garage door spring nearest to the

worm gear in order to balance the bending force on the drive shaft. This is shown in Figure 8.

Figure 8. Cross-section of the drive shaft and spring, with the worm gear positioned on the right.

The height of the worm gear output shaft meant that the pillow block bearing on the other

end of the drive shaft would have to be raised a certain distance above the frame. However, since

the worm gear would have to sit on a plate to be attached to the frame, it was determined that the

frame would be built with a taller base under the bearings, requiring that the worm gear instead

Worm Gear

on this end

Pillow block

bearings and

barbell weight

on this end

Ball Bearing

Shaft Spacers

Spur Gear

P a g e | 13

would have to be raised a certain distance above the frame. Figure 9 shows the worm gear raised

on aluminum plates to align with the drive shaft. This height was determined by the height of the

center of the pillow block bearings located on the left of the image.

Figure 9. Side view showing tall base under bearings on left and raised worm gear on right.

The size of the spur gears also determined the shape of the frame by requiring the pillow

block bearings to overlap. This was due to the fact that the distance between the shafts was less

than the distance between the bores of the pillow blocks when placed side-by-side. Figure 10

shows a top view of the prototype, highlighting the staggering of the bearing to accommodate the

spur gears. This positioning of the bearings also allows for the gears to be switched out with

gears of different ratios, with the bearings being able to slide sideways to accommodate them,

thereby simulating different angular loads and speeds.

Figure 10. Staggering of pillow block bearings to achieve smaller center distance of spur gears.

Staggered Bearings

Spur Gears

P a g e | 14

The barbell weight had an inner diameter of approximately two inches. However, the

one-way bearing necessary for the overriding clutch system of the starter could only be found

measured in metric units. The outer diameter of the one-way bearing was 52 mm and the inner

diameter was 25 mm. The large tolerance of the barbell weight allowed for the one-way bearing

to fit in the barbell weight, even though the nominal diameter of the one-way bearing was larger

than the nominal diameter of the barbell weight bore. The discrepancy between the inner

diameter of the one-way bearing and the output shaft, however, was a larger issue. In order to fit

the driven gear, the shaft had to be ¾ inch at one end, and one inch at the other end in order to

have a diameter approximately equal to the internal diameter of the one-way bearing. McMaster-

Carr was able to supply a dual-diameter shaft to these specifications, but the one inch diameter

portion was slightly too large for the one-way bearing, as this bearing was metric [14].

Machining of the dual-diameter shaft was necessary to fit the one-way bearing, as well as to

create a keyway to prevent the one-way bearing from slipping on the shaft. The output shaft and

one-way bearing are shown in Figure 11, highlighting the location on the shaft where the

machining occurred. The sizing of the one-way bearing, output shaft, and barbell weight led to

the determination that one pillow block bearing needed to have a one inch diameter, while the

remaining pillow block bearings needed to have ¾ inch diameters. The barbell weight also had to

have a keyway machined into it in order to lock onto the outside of the one-way bearing. Two

standard bearings with the same dimensions as the one-way bearing were place on either side of

the one-way bearing in order to stabilize the barbell weight. Finally, shaft collars were placed on

the outsides of the standard bearings to keep the barbell assembly from slipping off the shaft.

Figure 11. Cross-section of output shaft showing the need for reducing the diameter to 25 mm.

One-way bearing

requiring 25mm shaft

25mm 1 in.

Standard bearing

Shaft collar

P a g e | 15

The final subsystem was the stopping mechanism. This mechanism held the output end

of the spring in place while the worm gear turned the input end of the spring. The stopping

mechanism also had to be able to release the spring once the winding operation was completed,

thus releasing the energy of the spring into the barbell weight through the gears. This was

accomplished by hinging a bar on the frame that could swing a stopping pin into the teeth of a

flange on the drive shaft. In order to refrain from accidentally releasing the spring, the stopping

mechanism was angled such that it positively engaged the toothed flange to hold the end of the

spring in place. This meant that as the spring torque applied force on the stopping mechanism,

the toothed flange tended to pull the mechanism in towards the shaft, opposite to the direction of

disengaging the stopping mechanism. This allowed the spring starter to be safely operated, even

at high torque loads. A side view of the stopping mechanism is shown in Figure 12 in its engaged

state, showing that the mechanism cannot release on its own. This system especially went

through many iterations of design review before arriving at the final design.

Figure 12. Left: Stopping mechanism engaged. Right: Mechanism released.

The only remaining component to design was the adapter plate that mated the worm gear

shaft to the input end of the garage door spring. This adapter plate was fabricated from 1/16 inch

aluminum plate and was fitted to the end cap of the garage door spring and to a flange mount

piece on the worm gear shaft, joining the two components. The plate also secured the ball

bearing inside the spring end cap and allowed the drive shaft and the worm gear shaft to rotate

smoothly in relation to one another, enabling smooth functioning of the prototype. The plate is

shown in Figure 13 in relation to its neighboring components, and as a highlighted component to

show the shape and bolt holes.

P a g e | 16

Figure 13. Left: Adapter plate with neighboring components. Right: Highlighted adapter plate.

Once all the components were designed and drawn in the Autodesk Inventor software,

and approved by project advisors, acquisition of the components began. The completed computer

model of the prototype is seen in Figure 14.

Figure 14. Completed model of prototype.

4.3 Assembly

Multiple orders were placed to acquire the more unique components, such as the one-way

bearing, but the majority of the components were purchased from McMaster-Carr. Orders were

only placed once the embodiment design was completed in the Autodesk Inventor software and

all sizing and design issues were resolved.

The aluminum frame was purchased from Alufab, a Cincinnati based company that

supplies the structural aluminum extrusions called for by the embodiment design. This aluminum

P a g e | 17

framing material is designed to be extremely easy to assemble in an infinite number of ways. The

length and width of the aluminum extrusion is designated by the customer, as well as the number

and type of joint connection pieces. The extruded aluminum is then sized and cut by the

aluminum company, and the order is shipped with all the necessary parts and hardware. An

example of the parts that are prepared and sold by Alufab is shown in Figure 15.

Figure 15. Example aluminum extrusion products from Alufab. [15]

Once the frame was completed, the components were able to be assembled onto the

frame. Certain components, such as the aluminum platform for the worm gear or the stopping

mechanism, had to be cut, drilled, or welded in order to be ready to assemble. Once all the pieces

were ready, the components were simply bolted to each other and to the frame. The completed

prototype is shown in Figure 16.

Figure 16. Completed prototype.

P a g e | 18

5.0 Testing and Analysis

5.1 Testing

Two tests were performed on the prototype in order to determine properties of the spring

and the system as a whole. Properties of the spring were determined by a torque test, and the

properties of the system were determined by a kinematic motion test.

Tests were performed to measure the torque that the spring produced at certain angular

positions. The goal of this testing was to determine the spring constant for the garage door

spring. The spring constant is a measure of how much force is required to make a spring travel a

unit of displacement, or in this case, angular displacement. A torque arm was attached to the

output end of the garage door spring in order to test the torque produced for every turn of the

worm gear shaft at the input end of the spring. A spring scale was attached to the end of the

torque arm at a measured distance from the center of the drive shaft and held stationary with

respect to the frame of the prototype. The worm gear handle was then rotated the appropriate

number of turns to cause the worm gear shaft to turn one half rotation. The force measured in the

spring scale was recorded as a force for one half turn of the garage door spring. The worm gear

shaft was advanced one half turn at a time, and the force was recorded each time. An image of

the setup is shown in Figure 17.

Figure 17. Testing setup for determining the spring torque at various angular positions.

Spring Scale

Torque Arm

P a g e | 19

The testing for the kinematic motion of the barbell weight required tracking the position

of the weight with respect to time over time intervals of approximately 0.02 seconds. A video

camera and strobe light provided images of a quality suitable for data collection. The barbell was

marked at 45 degree increments to facilitate measuring the angular position of the weight in the

videos. The video camera was set to capture video at 60 frames per second, fast enough to

precisely collect data as the barbell weight accelerated from rest to relatively high angular

velocities. The strobe light was utilized to eliminate blurring of the video frames by matching the

frame rate of the video camera, thereby only lighting up the prototype for a fraction of the time

that the frame was being captured. The strobe light had to be programmed to flash at the same

frequency of the video camera such that one flash occurred during each frame. The result was a

video that consisted of clear frames that could be individually viewed in order to collect angular

measurements off of the barbell weight. An image of one frame from a single test is shown in

Figure 18. Approximations were made between the markings on the barbell weight by overlaying

lines on the video image using video editing software. These overlaid lines provided a reference

point from which to measure the angular position of the barbell weight.

Figure 18. One frame from a video taken during the acceleration testing showing 90° and 135°.

Overlaid Line

P a g e | 20

5.2 Analysis

The results from the torque testing were compiled using Microsoft Excel, and the force

measurements were converted to torque by multiplying the force by the torque arm, or the

distance from the center of the drive shaft to the spring scale.

� = � × �(1) Equation 1 gives the torque (τ) of the garage door spring as a function of the force (F)

measured in the spring scale and the torque arm (d). By comparing the torque values to the

number of turns of the worm gear shaft corresponding to each value, data points were produced.

The resulting graph of the calculated data points is shown in Figure 19.

Figure 19. Torque of the garage door spring versus angular position.

The slope of the line of best fit through the data points gives the spring constant of the

garage door spring used in the prototype. The spring constant is measured in Newton-meters per

radian and is equal to 0.4287 Nm/rad. This spring constant is a function of the thickness of the

spring wire, the diameter of the spring coils, the number of active coils, and the elastic modulus

of the spring material. By varying these factors, a spring could potentially be designed to suit any

application, including a spring starter in a vehicle.

The videos from the kinematic motion testing were analyzed frame-by-frame, and the

angular position of the barbell weight relative to a stationary mark on the screen was recorded at

y = 0.4287x

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

To

rqu

e (

N-m

)

Spring Position (rad)

Spring Constant

P a g e | 21

each frame. These data were input into an Excel spreadsheet for further analysis. The frame

number was converted into seconds based on the frame rate of 60 frames per second, with time

zero marking the start of motion of the barbell. The angular position of the barbell was converted

from degrees to radians, for ease of future calculations. A plot of the position data and the

corresponding best-fit line, as determined by the Microsoft Excel software, is shown in Figure 20.

The motion of the spring was also noted in the videos to determine the time at which the spring

stopped turning, shown by the red line in the plots.

Figure 20. Plot of angular position data and best fit line.

These data points were used to determine the angular velocity of the barbell by utilizing a

simple three-point estimation of the slope of the angular position data curve.

�(�) = (� − ℎ) + (� + ℎ)2ℎ (2)

This method finds the slope between the point before each data point, located at x – h,

and the point after each data point, located at x + h. This makes the resulting curve smoother

than if a more simple two-point estimation was used. The line of best fit from the position data

-10.000

0.000

10.000

20.000

30.000

40.000

50.000

0.00 0.50 1.00 1.50 2.00 2.50

An

gu

lar

Po

siti

on

(ra

d)

Time (s)

Experimental and Theoretical Position

after Four Rotations of the Spring

P a g e | 22

was also theoretically differentiated using standard differentiation techniques in order to

determine the curve that the data should follow. The line of best fit for the position data was

determined to be a cubic function, making the velocity curve equation quadratic and the

acceleration linear, as shown in the next two figures. A plot of the calculated velocity data points,

as well as the theoretically differentiated curve, is shown in Figure 21.

Figure 21. Plot of numerically differentiated velocity data and theoretical curve.

The same formulas and methods were used to determine the experimental acceleration

and theoretical acceleration of the barbell. The successive manipulation of the data resulted in

increased error with each differentiation of the data, but the general trends of each set can still be

seen clearly. A plot of the angular acceleration data points and the theoretical line the points

should follow are shown in Figure 22.

-10.000

0.000

10.000

20.000

30.000

40.000

50.000

0.00 0.50 1.00 1.50 2.00 2.50

An

gu

lar

Ve

loci

ty (

rad

/s)

Time (s)

Experimental and Theoretical Velocity

after Four Rotations of the Spring

P a g e | 23

Figure 22. Plot of numerically differentiated acceleration data and theoretical curve.

For each set of data points, the theoretical lines fit very well to the general trend of the

data. This allows the experimental data to be checked for accuracy. The close fit of each

theoretical line to its respective experimental data verifies the accuracy of the original data, and

its ability to accurately describe the physics of the prototype. This verification allowed any

further analysis to be performed on the theoretical curves, reducing the error and noise in the

curves for successive data manipulations, including energy and power.

By further analyzing the torque and velocity data, the energy and power transferred from

the spring to the barbell were calculated. The formula for determining the energy transferred to

the barbell is calculated by determining the kinetic energy in the barbell as a function of its

angular velocity.

� = 12 × � × ��(3)

In this formula, E is the energy in the barbell, I is the moment of inertia of the barbell,

and ω is the angular velocity of the barbell. The moment of inertia was determined by accurately

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

0.00 0.50 1.00 1.50 2.00 2.50

An

gu

lar

Acc

ele

rati

on

(ra

d/s

2)

Time (s)

Experimental and Theoretical Acceleration

after Four Rotations of the Spring

P a g e | 24

modeling the barbell weight in Autodesk Inventor software, and utilizing the software to calculate

the moment of inertia around the appropriate axis. This value was determined to be 0.316 N-m2.

The angular velocity was taken directly from the theoretical data in order to maintain a smooth

curve.

The power (P) delivered from the spring was also derived from the theoretical motion

data. This was calculated by multiplying the torque (τ), found using equation 1, by the velocity

(ω) of the barbell, found using equation 2.

� = � × �(4) This calculation also utilized the theoretical values of both the torque and the angular

velocity in order to produce a smooth curve. Both of these data sets were manipulated using

numerical differentiation and integration to produce the power transferred to the barbell and the

energy stored in the spring. The power transferred to the barbell was determined by the same

three-point estimation of the derivative as was used to determine the experimental velocity and

acceleration of the barbell. The energy stored in the spring was determined by a numerical

integration method known as the trapezoidal rule. The resulting energy curves were plotted

against time in Figure 23, and the power curves were plotted in Figure 24

� (�)��

�� ≈ (� − �) (�) + (�)2 (5)

P a g e | 25

Figure 23. Graph of the energy of the spring and barbell as a function of time.

Figure 24. Graph of the power of the spring and barbell as a function of time.

-20.000

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 0.5 1 1.5 2 2.5

En

erg

y

(J)

Time (s)

Energy in Spring and Barbell

Energy From Spring

Energy in Barbell

-40.000

-20.000

0.000

20.000

40.000

60.000

80.000

100.000

120.000

0 0.5 1 1.5 2 2.5

Po

we

r (W

)

Time (s)

Power in Spring and Barbell

Power from Spring

Power to Barbell

P a g e | 26

The gap between the two energy curves and the two power curves represents the

efficiency of the spur gears and bearings in transferring energy and power from the spring to the

barbell weight. For this prototype, efficiency loss is significant, as the data and calculations are

based on a machine that was constructed and aligned by hand, making the bearing alignment and

spur gear meshing highly inaccurate. A commercially manufactured product would have much

higher tolerances and would be constructed with much higher accuracy. This would minimize the

efficiency losses and allow the extremely high efficiencies of a mechanical system to be realized.

The discrepancy between the points at which the power curves reach zero is due to in accuracy of

the data collection method, compounded by theoretical calculation assumptions and numerical

differentiation techniques. Theoretically, these two points should be the same, but one is the

curve of an equation based directly on the theoretical velocity, whereas the other is the curve of a

numerical differentiation of an equation based on the theoretical velocity. This extra

differentiation step to reach the power curve of the barbell, versus the single step to reach the

power curve of the spring, introduced error that is evident in the plots of the data.

The motion and characteristics of this spring starter system are useful in determining the

necessary characteristics of a spring designed to start an automotive engine. A major constraint

on the spring design is the weight of the spring. Based on various sources for automotive

components, the allowable mass of the spring in the spring starter can be determined. A current

electric starter system, based on specific products sold by specific companies, weighs

approximately 25 kg (55 lbs). This is made up of the lead-acid battery, which weighs about 20

kg, and the electric motor, which weighs about 5 kg [16],[17]. The spring starter system requires

a torsion spring, housing and gears, a small battery and a small electric motor. A small battery,

such as one found in a motorcycle, weighs approximately 5 kg, and a small motor weighs

approximately 2 kg [16],[18]. The housing around the spring and the other essential components,

such as the gears, could be designed with the goal of minimizing size and weight, and could

potentially weigh just 2 kg. This leaves 16 kg (35 lbs) of the starter system’s weight to be

devoted to a torsion spring.

If an engine requires a certain amount of torque (τengine) and a certain number of turns in

order to start, a spring can be designed to provide this energy by utilizing the formulas for the

mass of a coil spring (mspring), the angular deflection of a coil spring (φspring), and the bending

stress (σ) in a material.

P a g e | 27

� !"#$% = &' × �(#")�4 * × (' × +,-#. ×/) × 0 1)). (6)

3 !"#$% = 2 × +,-#. × / × ' × 4� × �(#") , 6ℎ7873 !"#$% = 3)$%#$)/:7�88�;<=(7)

4 = 32 × � !"#$%' × �(#")? , 6ℎ787� !"#$% = �)$%#$) × :7�88�;<=(8)

Using equations 6, 7, and 8 as a series of equations, various properties of the spring can

be determined based on sufficient information about the rest of the spring properties, including

the diameter of the wire and coils (dwire Dcoil), the number of coils (N), and the density (ρsteel) and

modulus of elasticity (E) of the material. Taking the mass of the spring to be 16 kg and assuming

a value for the diameter of the wire, the gear ratio of the engine to the spring starter and the stress

in the wire can be determined. The wire diameter and gear ratio can then be optimized to

determine the design of the spring with the best utilization of the spring material’s strength, as

well as the best size and shape utilization. For instance, based on an engine that requires 100 Nm

(74 ft-lbs) of starting torque and must be turned 4 times, and assuming a wire diameter of

approximately 5 mm (0.2 in), the gear ratio must be about 8.3:1. This produces a stress of

approximately 980 MPa (140 ksi). Based on the graph in Figure 23, a wire with a 5 mm diameter

should have a tensile strength of at least 190 ksi, or 1,309 MPa.

P a g e | 28

Figure 23. Tensile strength of various wire materials as a function of diameter. [19]

According to the calculations for a specific method of spring design, a good fatigue life

of a spring should be expected when 75% of the tensile strength is utilized. Therefore, a value of

approximately 982 MPa should be used for a comparison with the previous calculations [20].

This gives a value approximately equal to the 980 MPa that was calculated as the maximum stress

in the torsion spring that could deliver the required amount of torque. Table 1 shows several

materials from the chart in Figure 23, and uses the calculations from above to determine the mass

of a spring that utilizes each of the materials. The masses show the weight savings that can be

realized with the use of high quality spring steel.

Table 1. Minimum mass of springs based on tensile strength and 0.2 in. diameter.

Material Tensile Strength, MPa (ksi) Mass of Spring, kg (lbs)

Hard Drawn ASTM – A227 1309 (190) 16.0 (35.2)

Oil Tempered ASTM – A229 1344 (195) 15.2 (33.4)

Alloy Steel ASTM – A232 1516 (220) 11.9 (26.2)

Music Wire ASTM – A228 1654 (240) 10.0 (22.0)

P a g e | 29

By using high quality spring material, approximate weight savings of up to 6 kg (13 lbs.)

is viable. This weight savings enforces the plausibility of the implementation of a steel spring-

based starter into automobiles.

P a g e | 30

6.0 Conclusions, Contributions, and Recommendations

The research and calculations concluded that the utilization of a torsion spring for starting

automotive engines is a feasible application and should be continued to be developed by the GM-

sponsored team. The concept for the spring starter was explored from an experimental

standpoint, and further analyzed using material properties and theoretical calculations. The

original idea was taken from the conceptual stage through the prototype and analysis stage

throughout the duration of this thesis project. By constructing a working prototype, torque and

motion data was able to be collected through experimental testing. This data was manipulated

and combined with material properties and various formulas to determine whether a steel spring

could store enough energy to start an engine while having a lower weight than a traditional

electric starter system. Therefore, a spring starter could be design to sufficiently start an engine

while having less weight than the conventional system. The argument for spring starters is

further strengthened by the fact that a proposed spring starter system will incorporate

significantly less hazardous materials, namely in the lead-acid battery, than the conventional

starter system, making a spring starter more environmentally friendly.

In order to determine the feasibility of the concept for a torsion spring-driven engine starter, a

prototype was constructed to showcase the capabilities of a steel spring. Taking a concept and

creating a working prototype required interpretation of the specific components of the concept

and the location of readily available items that could accurately demonstrate the concept. The

key components, including the torsion spring, worm gear, and barbell weight, used to simulate the

forces in an engine, all had to be purchased and then drawn in Autodesk Inventor, a three-

dimensional computer modeling software. These drawings were used as a reference for the

design of the remaining components, including the bearings, spur gears, and adapter plates. Once

all the components were designed and fitted together in the computer modeling software, the

remaining components were purchased. Having acquired all the pieces, assembly of the

prototype took place, requiring some machining of components as necessitated by the computer

model. The final assembly of the prototype was capable of accelerating the barbell weight from a

stopped position to a high rate of rotation under the power of the torsion spring. This motion was

recorded as angular position data and, along with the torque capabilities of the spring, was used to

mathematically represent the energy and power in the spring system. This information was used

to determine the feasibility and size of spring necessary for starting a small automotive engine.

P a g e | 31

By concluding that a spring starter is a feasible concept, the team should continue to

develop the concept, as long as the GM sponsorship continues. The next step in the development

of the spring starter is to replace the barbell weight, which simulates an engine, with a real

engine, possibly from a motorcycle. An analysis of this development will provide data more

consistent with real-world use, as the varying loads of an IC engine are difficult to simulate

except with an actual IC engine. The continued development of this concept may allow the team

to see this design through to implementation into GM’s future vehicles.

P a g e | 32

Bibliography

[1] Del-Colle, Andrew. “Obama Announces 54.5 mpg CAFÉ Standard by 2025.” Popular Mechanics. 29 Jul. 2011. Web. 14 Mar. 2012. <http://www.popularmechanics.com/cars/news/fuel-economy/obama-announces-54-6-mpg-cafe-standard-by-2025>.

[2] Vega, Rocky. “Germany’s Peak Oil Strategy Leaks: 7 Dire Consequences Considered.” The Daily

Reckoning. 17 Sep. 2010. Web. 8 Mar. 2012. <http://dailyreckoning.com/germanys-peak-oil-strategy-leaks-7-dire-consequences-considered/>.

[3] Angelantoni, André. “Peak Oil Primer.” Post Peak Living. Oil Scarcity, Growth, and Global Imbalances, May 2010. Web. 16 Mar. 2012. <http://www.postpeakliving.com/peak-oil-primer>.

[4] “Tires and Passenger Vehicle Fuel Economy.” Transportation Research Board Special Report 286. National Academy of Sciences. Washington, D.C. 2006. Web. 20 Mar. 2011. <http://onlinepubs.trb.org/onlinepubs/sr/sr286.pdf>.

[5] “Determining Electric Motor Load and Efficiency.” Motor Challenge. U.S. Department of Energy. Web. 6 Mar. 2012. <http://www1.eere.energy.gov/manufacturing/tech_deployment/pdfs/10097517.pdf>.

[6] “Diesel Engine Starting Fundamentals.” Cantec Systems Ltd. Web. 5 Mar. 2012. <http://www.cantecsystems.com/ccrdocs/Supercapacitor-Engine-Cranking-fundamentals.pdf>.

[7] Ingram, Antony. “The Electric Self-Starter Turns 100.” High Gear Media. Fox News.com. 15, Feb. 2012. Web. 25 Feb. 2012. <http://www.foxnews.com/leisure/2012/02/15/electric-starter-turns-100/>.

[8] “Charles Kettering Receives Patent for Electric Self-Starter.” This Day in History. History.com. 17 Aug. Web. 25 Feb. 2012. <http://www.history.com/this-day-in-history/charles-kettering-receives-patent-for-electric-self-starter>.

[9] Jackson, David D. “The History of the Delco-Remy Division of General Motors.” Delco-Remy, 1896-1994. Web. 27 Mar. 2012. <http://www.delcoremyhistory.com/Products/startingmotors.htm>.

[10] “How Spring Starting Works.” Spring Starter. Kineteco, 2012. Web. 23 Feb. 2012. <http://springstarter.com/spring_starting.asp>.

[11] “Why Guitar Strings Break.” Graph Tech’s Blog. Graph Tech, 2010. Web. 6 Mar. 2012. <http://graphtechsblog.com/?p=108>.

[12] Direnzi, Nick. “The Use of Elastically-Based Mechanical Energy Storage in Motor Vehicles.” Honors Thesis. University of Dayton. 2011.

[13] Mendelson’s Liquidation Outlet. 340 East First Street, Dayton, OH.

[14] McMaster-Carr. McMaster-Carr ®. <www.mcmaster.com>.

[15] Alufab. Alufab. Infitech. 2002-2007. Web. 18 Oct. 2011. <http://www.alufab.cc/>.

[16] Batteries Plus. Batteries Plus LLC. 2011. Web. 13 Mar. 2012. <http://www.batteriesplus.com/>.

[17] “JEGS Mini Starters.” JEGS High Performance. Web. 12 Mar. 2012. <http://www.jegs.com/p/JEGS/JEGS-Mini-Starters/751068/10002/-1>

[18] Electric Motor Warehouse. Winans Inc. 1999-2012. Web. 13 Mar. 2012. <http://www.electricmotorwarehouse.com/>.

[19] “Spring Steel Types Used in Spring Making.” Spring-Makers-Resource.net. Web. 4 Mar. 2012. <http://www.spring-makers-resource.net/spring-steel.html>.

[20] “Torsion Spring Design Techniques: Logic Diagram and Example.” Spring-Makers-Resource.net. Web. 4 Mar. 2012. <http://www.spring-makers-resource.net/torsion-spring-design.html>.