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Optimization and analysis of a hybrid continuously variable power split transmission

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Title:
Optimization and analysis of a hybrid continuously variable power split transmission
Creator:
Ozdemir, Serhan, 1968-
Publication Date:
Language:
English
Physical Description:
vi, 94 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Acceleration ( jstor )
Block and tackle ( jstor )
Engine transmissions ( jstor )
Engines ( jstor )
Gears ( jstor )
Hydrostatics ( jstor )
Mechanical transmission ( jstor )
Recreational vehicles ( jstor )
Speed ( jstor )
Torque ( jstor )
Dissertations, Academic -- Mechanical Engineering -- UF ( lcsh )
Mechanical Engineering thesis, Ph. D ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 92-93).
General Note:
Printout.
General Note:
Vita.
Statement of Responsibility:
by Serhan Ozdemir.

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University of Florida
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The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact the RDS coordinator (ufdissertations@uflib.ufl.edu) with any additional information they can provide.
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43757191 ( OCLC )

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OPTIMIZATION AND ANALYSIS OF A HYBRID
CONTINUOUSLY VARIABLE POWER SPLIT TRANSMISSION












By

SERHAN OZDEMIR


A DISSERTATION PRESENTED TO THE GRADUATE SCHOO OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1999















ACKNOWLEDGMENTS



The author would like to express his gratitude to Dr. John K. Schueller for his

encouragement, guidance, and patience, to Dr. Ali Seireg, who provided some of the vital material, and also to Dr. Kim Reisinger, Dr. Carl Crane and Dr. Roger Tran-Son-Tay. The author is also indebted to Izmir Institute of Technology, which provided the scholarship and support.














TABLE OF CONTENTS

Page

ACKN OW LED GEM ENTS .......................................................................................... ii

KEY TO SYM BOLS ..................................................................................................... v

ABSTRA CT ..................................................................................................................... vi

CHAPTERS

1 INTROD UCTION ...................................................................................................... 1

2 CVTs ........................................................................................................................... 3

CVT Types ........................................................................................................... 5
Electronic Controls and Integrated Power Train Management .............................. 12
M odern-D ay CVTs and M etal Belt Drives ............................................................ 16
Electronic Control Strategies ................................................................................. 20

3 CVTs vs CVPSTs ................................................................................................. 22

Evolution of CVTs ................................................................................................. 22

4 D Y NAM ICS OF CVTs .......................................................................................... 27

Basics ........................................................................................................................ 27
Four Possible Configurations with a Planetary Gear Train ................................... 29
Sum m ary of the Possible Configurations .............................................................. 35
Power Recirculation Configurations ..................................................................... 38
Power Split (PS) vs Power Recirculation (PR) ..................................................... 40
Proposed Design ................................................................................................... 42
Dynam ics of the Proposed Design ......................................................................... 45
Special Cases ........................................................................................................ 51
Crossovers ........................................... : ................................................................ 52
Torque Relations .................................................................................................. 53
Torque Ratios and Diagram s ................................................................................ 57









5 OPTIMIZATION AND ANALYSIS OF RECIRCULATING POWER ............. 66

W ith Reverse Gear ................................................................................................. 66
N o Reverse Gear ................................................................................................... 77


6 THE MODELING OF THE PROPOSED TRANSMISSION ............................ 78

M odeling ................................................................................................................... 79

7 CON CLUSIONS ................................................................................................... 90

REFERENCES .............................................................................................................. 92

BIOG RAPHICAL SKETCH ....................................................................................... 94














TABLE OF VARIABLES




D Damping, K : Structural Stiffness, r : Radius of a Gear, Rr: Recirculation Composite Ratio, (r7 / rg) (r9 I r,1), Rpr: Recirculation Planet Ratio, r5 / r4, Rr : Recirculation Rim Ratio, r3 / r4, R, : First CVU ratio, r, / r2, Rps: Split Planet Ratio, R, : Split Rim Ratio, r16 / r13. Rs: Split (Second) CVU Ratio, r18 / r17 0) : Angular Velocity, V : Linear Velocity.


Subcripts

a: Arm,

p: Planet,

r: Rim,

s: Sun.














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosoph OPTIMIZATION AND ANALYSIS OF A HYBRID
CONTINUOUSLY VARIABLE POWER SPLIT TRANSMISSION By

Serhan Ozdemir

December 1999


Chairman: John Schueller
Major Department: Mechanical Engineering Department

Automotive transmissions match the speed and torque of the power source to the speed and torque requirements of the load. Properly designed continuously variable transmissions (CVTs) have shown promise to improve efficiency and performance. This work analyzes some existing CVTs and proposes a new hybrid continuously variable power split transmission (CVPST).

The speed and torque relationships are analyzed in power split and power

recirculation mechanisms. The problem of geared neutral phenomenon with recirculating transmissions are identified. A new CVPST transmission incorporating power split and power recirculation is proposed and analyzed. Optimization of the transmission to minimize the circulating power is performed.













CHAPTER 1
INTRODUCTION



An automotive transmission is any device that is capable of matching the torque and speed of the input to the torque and speed requirements of the output member which drives the load. Transmissions have come a long way since their introduction into automobiles in the late 19th century. They have evolved, yielding to the demands of more powerful and more efficient engines. By itself, it is impossible to design a transmission, for it is a mechanism and is a vital member of a piece of machinery, in this case the automobile. Transmission and engine designs are intertwined.

Contemporary transmissions are comprised of either mechanical, hydrostatic, or torque converter components, or a combination thereof. Mechanical transmission forms the basis of this work. Being the most efficient transmission makes it indispensable in cars and other machinery. In this work, a newly popular mechanism will be analyzed using various calculations. The first set of formulae, the dynamics of epicyclic gears, are specialized relations for any possible combination. Instead of using one generalized formula for epicyclic gears which is given as a ratio of differences in the gear speeds, and deriving new ones from the definition, the author preferred to derive relations in advance, ready to be used and compared, which simplifies the work to a degree.

It has been shown that CVTs can be successfully used in small and medium cars. It has also been shown that a CVT mechanism may be improved when the transmission contains multiple power flow paths, which are optimized for a given range of vehicle







2

speeds. The author hopes to enhance the performance of CVTs using power split methods.

When a power split mechanism is combined with a CVT transmission, the new

power split CVT has been proved to be not only a viable alternative to an ordinary CVT but also an improved version in performance (6, 16).

The author believes that a combination of a power recirculation, power split, and a regular CVT mechanism in a transmission box would refine the acceleration characteristics of a vehicle and enable a car to move at creeping speeds, even zero vehicle speed with an inherent clutch, characteristic to a recirculation design.

The objectives of the following work could be summarized as follows:

1. Analysis of speed and torque in power split (PS), power recirculation (PR)
mechanisms.

2. Proposal and analysis of a new transmission to incorporate PS and PR.

3. Optimization of this hybrid transmission to minimize the circulating power.















CHAPTER 2
CVTs


A continuously variable transmission (CVT) may allow an engine to run over a range of speeds and loads independent of the speed and torque requirements placed on the wheels by the vehicle and the driver. An engine can produce a broad range of torque at any speed demanded or a broad range of engine speeds for any given torque demand. For any given power demand, however, there is only a very narrow operating speed and torque window at which the engine is most efficient or where the trade-off between emissions and fuel consumption may be optimized. Because the CVT allows an engine to run at this most efficient point virtually independent of vehicle speed, a CVTequipped vehicle may yield substantial fuel economy benefits when compared to a conventional transmission offering only a limited number of input/output ratios.

Acceleration performance of a CVT-equipped vehicle may likewise be optimized. The CVT can allow an engine to run at its maximum torque condition almost regardless of drive wheel speed. Because full engine torque may be produced all the time, the acceleration may be maximized. Alternatively, a vehicle equipped with a given engine and a CVT may achieve the same acceleration as an identical vehicle equipped with a higher output engine and a conventional transmission.

A CVT is cost-effective not so much for its ability to improve the fuel econom

and performance of a given vehicle, but in its ability to optimize the fuel economy of a







4

range of vehicles using the same transmission. It is shown (1) by computer simulation that there are potentially few if any differences in fuel economy between continuousl variable and an optimized, conventional fixed ratio, stepped transmission of equivalent ratio ranges. This conclusion assumes that the comparison is between transmissions of equal efficiency and that the gear ratios for each transmission are optimized such that the

0 to 60 mph acceleration performance of the vehicles with either transmission is optimized and identical. Further it assumes that emissions performance of both vehicles can be made identical with no impact on fuel economy. Practically speaking, these assumptions likely make the analysis insensitive to the differences between stepped ratio and continuously variable transmissions. Simulations by others have shown that CVTs may in fact result in fuel economy improvements in cases where stepped ratio transmissions provide little or no fuel consumption advantages.

The manufacturing and cost advantage of the CVT lies in the fact that its shift

schedule and ratios can be much more easily optimized for a variety of vehicles than a conventional stepped transmission with fixed gear ratios. The real promise (4) of the CVT, then, is that a manufacturer's fleet may be optimized for performance and fuel economy with only a few models of CVT transmissions to handle different torque ranges or drive wheel location. This may be contrasted with the use of a large number of stepped ratio gearboxes where, at one extreme, it would potentially require one custom-tailored model of a fixed ratio stepped transmission for each engine/vehicle combination offered if a vehicle manufacturer were to optimize-every vehicle produced. The introduction of CVTs, thus, offers new and invaluable features and various advantages.







5

We may summarize these advantages as follows:

1. Improved driveability and passenger comfort due to the lack of shifting and
consequent uneven vehicle acceleration,

2. Improved vehicle performance (acceleration) and fuel economy.

3. Minimum manufacturing cost for a drive train.

As engine and drivetrain controls evolve, the potential benefits of the CVT ma increase when compared to conventional fixed ratio, stepped transmissions. Electronic engine controls will allow variable engine emissions, fuel consumption and output characteristics such as those afforded by variable valve timing and air/fuel ratio control. Engine and transmission controls will become integrated such that the engine and transmission are treated as a single prime mover system. When this occurs, only a CVT can provide the precise, independent coupling of engine speed and torque output with drive wheel requirements which allow an optimized combination of performance, fuel comsumption, and emissions.


CVT TYPES


There are five basic concepts on which extensive modem-day continuousl variable transmission developments have been or are currently based.

1. Belt Drive (5, 6, 7, 8),

2. Hydrostatic Pump/ Motor Combinations (11),

3. Friction /Traction Drive (3),

4. Variable Stroke (4),

5. Gear Type (2).







6

Other concepts which have proved (4) not as popular such as engine/generator

motor sets, hydrokinetic converters, magnetic, hydraulic, or mechanical drag have been examined through the years. Many of those which achieved some level of production in passenger cars have been the forerunners of modem CVTs. Others have continued to be developed and have found new applications in industrial drives. Still others have been developed for and/or are used in many types of wheeled vehicles from simple to complex machinery.

Almost all of the CVT concepts have not found acceptance by modem passenger car manufacturers due to a variety of factors. When compared with conventional or other alternative transmissions, these concepts have fallen short in one or more of the following areas:

1. Noise

2. Efficiency

3. Excessive weight

4. Cost

5. Drivability 6. Durability

7. Ease of control

It is fair to say, however, that as new materials and analytical techniques are developed, some of these thus unsuccessful concepts may yet find passenger car applications. Indeed, passenger car manufacturers (1, 4, 15, 16) worldwide are examining a variety of CVT technologies.








Belt Drives


Belt drive transmissions have come a long way from the belt change gear or

variable cone pulley transmissions. Belt drive CVTs are used as low-power industrial drives and light-duty vehicular applications such as snowmobiles, go-karts, and all-terrain vehicles. In recent low-power units, the belts are fabric-reinforced rubber running on steel pulleys. One half of each pulley is normally fixed to its shaft, while the other half slides axially on a spline. The input/output ratio is determined by the width of the pulleys. With a fixed-length belt, the pulley width determines the effective diameter of the pulley.

A simple force balance control mechanism is used in many drives, including those for snowmobiles and other recreational vehicles. Normally held apart by a spring, the two halves of the driving pulley are forced together by a centrifugal mechanism as engine speeds increase. A corresponding spring in the driven pulley keeps its two halves closel spaced, resulting in a high input/output speed reduction and torque multiplication. As the rotating speed of the entire system increases, and the forces decrease, the mechanism in the driving pulley forces the two halves together. This causes the belt to ride radiall outward at an increased diameter, effectively increasing the working diameter of the driving pulley. Tension decreases in the belt as a result of the increased driving pulle diameter. The greater belt tension works against the spring and allowing the belt to move radially inward, effectively, reducing the working diameter of the driven pulley and the input/output torque ratio while increasing the speed ratio.

Belt drives have their own shortcomings which must be overcome. The maximum torque which can be transmitted is limited by the strength of the belt and the coefficient of friction between the belt and the pulleys. Increasing the belt size in order to handle







8

greater engine power also increases its mass. Heavier belts must use a portion of their tensile strength to overcome centrifugal force while generating adequate friction forces between the belt and its pulleys. Greater power levels may also be handled by splitting the torque between a number of sets of pulleys and belts. Hydrostatic Pump/Motor


A hydrostatic transmission consists of a hydraulic pump connected to a hydraulic motor. As it is inefficient to throttle the hydraulic pressure in order to govern input and output characteristics, mechanical features are usually varied in order to change input/output torque. For hydrostatic units with variable displacement, input/output torque multiplication is determined b the ratio of pump to motor displacements. Speed ratio changes are accomplished by varying the displacement of the pump or motor.

Hydrostatic transmissions have enjoyed a broad range of automotive and industrial applications. Successful automotive uses include agricultural and off-highway equipment where their durability, infinite variability, and smooth power-flow control afford the equipment operator excellent vehicle control. Despite all of the advantages of hydrostatic transmissions, their noise, cost, and efficiency have so far kept them from production passenger cars.

Efficiency and packaging improvements can be obtained if a hydrostatic

transmission is coupled with a mechanical gear set. Splitting the torque between the hydraulic and the mechanical units reduces the power carried by the hydrostatic module, and hence, the overall mechanical efficiency because the hydraulic power losses as a







9

percentage of the total system power are reduced. Such a combination is called a hydromechanical transmission.

In one version (4) of hydromechanical transmission, input power is mechanicall coupled to one side of a differential. Power input to the other side of the differential comes from a hydrostatic module which derives its power from the input shaft as well. The output of the transmission is taken from the center of the differential.

In such an arrangement, the transmission output shaft speed is the average of the input shaft speed and the hydrostatic shaft speed as long as the hydrostatic CVT is transmitting some of the input power. If the output shaft of the hydrostatic unit is allowed to freewheel such that it can rotate backward and transmit no torque, the transmission output speed will be zero, with output torque due only to the parasitic drag of the hydrostatic system.


Traction Drive


Like the friction drive units used, modem traction drive transmissions transmit power through rolling contact. In some cases, modem traction drive development programs have copied the functional principles if not the precise configuration of the pioneer units.

Traction drive transmissions (3, 4) have been used in the machine tool industry for a number of years. However, their potential to withstand high power outputs and the torque impulses typical of automotive drivetrains has been enhanced by advances in lubricant technology and the ability to use computer analysis to better understand the stresses on traction elements, thereby improving their design.







10

Instead of relying on the dry friction between driving and driven members, the

force is transmitted through the viscous shear of a thin film of special lubricant between the rolling contact surfaces. Unlike many lubricants, traction fluids greatly increase their viscosity under pressure, becoming almost glass-like under the high pressures present between the rolling elements of modem traction drive units. The tangential force which can be transmitted between the driving and the driven elements is greatly improved by the traction fluid, which also acts as a coolant and provides some protection against wear of the working surfaces.

Traction drives offer the ability to continuously adjust input/output ratio with

simple, highly efficient mechanisms. This ability is due to the fact that no teeth or other engagement devices are required to lock the driving and the driven elements together. As seen around the turn of the century, any mechanical configuration which will allow two different rotating members to adjust their effective working diameters may be considered as a potential traction transmission configuration.

They can operate at very high surface speeds, thereby providing high input/output ratios with essentially no noise because of the continuous, smooth contact surfaces. In vehicular applications, where high-speed power sources such as gas turbines or inertial storage flywheels are being considered, this feature makes them very attractive primar speed reducers between the engine and a conventional automatic transmission. Their potential in such applications is further enhanced by the relatively low forces encountered at high speeds to transmit a relatively large amount of power.































Figure 2.1. Conventional Traction Drive (3).


Figure 2.2. Hydrostatic Transmission with Shiftable Gearbox (11).







12

Electronic Controls and Integrated Power Train Management


For effective use of CVTs in automobiles, electronic control of the transmission is necessary. The application of electronics to transmission control offers advantages in three areas. The advantages of an electronically-controlled CVT are reduced complexity, more precise and accurate control independent of operating conditions, and integration of engine and transmission system control, including adaptive control.


Reduced Complexity


The numbers of different control system parts required to match a given

transmission to an engine and vehicle combination can be eliminated. Whereas several different valve bodies or control component parts may have been used for each different power team, a single valve body may be used. The differences in control parameters can be programmed into memory chips for each vehicle. A multiplicity of mechanical parts is thus reduced to a single microchip for each make, model, and engine combination in which a given transmission is used.


More Precise and Accurate Control


Precision and accuracy are two distinct characteristics of control. A precise control is very repeatable. That is, it does the same thing every time. An accurate control is not only precise, but it does the correct thing every time.

Mechanical and hydraulic transmission controls have been neither precise nor accurate. Variations from one mechanical part to another are inevitable. When mechanical devices are used as a computer, careful selective fitting of parts and final







13

calibration of the assembly is required in order to achieve accurate operation. In highvolume production, such care is not cost-effective, and so variations in control parameters due to part-to-part variations have been tolerated in the past. To make matters worse, changes in operating conditions, particularly temperature, affect the dimensions of mechanical control systems and the viscosity of the control medium, the oil. These changes reduce the precision of the transmission, causing changes in performance and drivability as the vehicle warms up.

Wear also has a similar effect. As a vehicle ages, mechanical controls become less accurate, and unless recalibrated, do not produce the same results as when first produced. Mechanical transmission controls will slowly allow a change in vehicle-to-engine speed and torque relationships as the control system components wear.

Control precision and accuracy was not so important before fuel economy, emissions, and performance trade-offs became vital. Large variations in engine and transmission control parameters were tolerated and, to a large extent, went unnoticed b all but the most discerning drivers.

As both fuel economy and emissions became more stringently regulated and as the public has demanded increased performance, more accurate control systems have been needed. Good fuel economy, high power output, and low emissions are sometimes mutually exclusive, and there is a fine operating line which must be followed to maximize all three. In addition, every vehicle produced must perform within acceptable regulatory limits throughout its life. Adaptive electronic controls with feedback loops compare the desired operation with the actual situation and make corrections in order to







14

stay on target, thus assuring both precise and accurate power train performance during the vehicle's lifetime.


Integration of Engine and Transmission Control


Only recently has the integration of transmission and engine control functions been considered. For a long time, the engine has been more or less a slave to the transmission and the driver. This slave has been limited in the way it could satisfy vehicle and driver requirements.

With manual transmissions, engines at any given moment provided power at a

fixed speed and torque, determined as a function of vehicle speed, throttle position, and transmission ratio. A demand for more power in any given gear could only be satisfied by increasing torque, because the engine speed was constrained by the gearbox.

The torque converter in an automatic transmission provided some measure of

increased flexibility, allowing both engine torque and speed to change in response to the driver's demand for more power. Still, however, the engine's ability to produce the required power was constrained somewhat by the fixed relationships of the gearsets and characteristics of the torque converter.

Electronic controls combined with an appropriately flexible transmission allow the decoupling of engine speed from the torque delivered to the vehicle. When the engine may be allowed to provide the required torque at any speed, and vice versa, engine and transmission designers are free to optimize the response of the power train to demands of the driver and the vehicle operating conditions. Ultimately, this will be accomplished b removing any direct mechanical control link between the driver and the engine and/or







15

transmission using so-called "fly-by-wire" systems. Perhaps the most exciting benefit of integrated power train control is the improvement in vehicle responsiveness to driver inputs. The response of the throttle and/or engine speed as a function of accelerator position can offer straight line, progressive, or degressive relationships. These relationships can be changed under predetermined conditions, by driver selection, or automatically by the sensing of road conditions, vehicle load, etc.

On the production line, critical conditions which exist in one model but not in the next can be selectively programmed out with the same hardware. In the same vehicle, lugging conditions present when the vehicle is heavily loaded can be avoided, while that operating speed and load regime may be used under light-load conditions.

The performance or economy settings now available on some transmissions can be expanded to include a continuum of settings between these extremes as a function of traction, vehicle payload, driver preference, driver type, etc. The differences which can be programmed into various settings may include the shift feel as well as the shift schedule.

Transmission and engine controllers can be used to tailor an engine's output such that the life of a transmission may be increased. This would be the case when, for example, a particular transmission is to be used behind an engine with a maximum torque which exceeds that for which the transmission, under an ordinary control environment, would be capable of reliably handling. This is possible if the engine and transmission management system work together to avoid offering the transmission more torque than it can handle.









Two factors make this possible:

1. The engine's maximum torque is produced under certain, well-defined
conditions.

2. The torque capacity of the transmission and torque converter system at an
given moment is a function of torque converter slip and transmission gear ratio.


Modern Day CVTs and Metal Belt Drives


Transmissions are one of the most expensive and important components of

vehicles. Among the transmission types, CVTs offer an optimal way to change the gear ratio between a car engine and the wheels. But CVTs' appearance in today's transmissions is not by chance. New environmental mandates and (15) improved designs may help CVTs be an integral part of the new generation gear boxes.

A continuously variable transmission is a stepless gearbox with an unlimited number of gear ratios. It is as old as the automobiles, and surprisingly, the first automobile was fitted with a rubber belt CVT. From then on, countless attempts have been made to equip cars with these automatic gear-change units. Their geared counterparts, however, whether manual or automatic, have taken over almost entirely the task of transmitting power and torque from the power source to the means of traction.

Last century, repeated attempts were made (4) to refine conventional gearbox

designs while automakers investing huge sums of money in the plants needed to massproduce them. Despite the undisputed ascendancy of the gearbox, CVTs are still around, and it is believed by some that CVTs will-make a modest return to the machine with which it made its world debut.







17

There are a couple of reasons that may make CVTs desirable. The fuel econom and the driving performance provided by the latest CVTs are in close proximity to today's complex and costly gearboxes, which in turn are believed to be at their practical and economical limits. Another factor is that the increasingly stringent governmental regulations regarding fuel comsumption and exhaust emissions are forcing auto engineers to consider the use of high-efficiency steady state engines designed to run in a limited engine speed, a perfect match for CVTs. In the long run, these environmental mandates are expected to force the development of hybrid drive vehicles using singlespeed power plants of various types, another highly suitable application for CVTs.

A modem CVT consists of a multi-segment steel push belt that runs between a pair of variable-width pulleys, whose facing surfaces form shallow cones. The belt, which comprises hundreds of thin steel plates or elements held together by spring steel bands, rides in the V-grooves formed by the facing cone sides. Each pulley clamps down on the belt elements as they make their way around the circuit. The crankshaft-driven input pulley essentially pushes the stack of elements, which are loaded in compression, to the output pulley, causing it to turn. This push-belt configuration can transmit torques that could tear a conventional traction or "pull" belt to pieces. When a gear-ratio change is needed, the pulley cones are pushed together hydraulically, forcing the belt to ride farther out from the shaft, effectively increasing the pulley diameter. The result is a smooth gear-ratio change, an "infinite" number of "gears," and potentially a larger range of mechanical advantage.







18

In spite of its relative obscurity, there are several indications that CVT technolog is growing in popularity. Today, there are more than a million Japanese and Europeanbuilt compact cars, using a technology licensed from a Dutch company (VDT).

The key issue is fuel economy. Current cars are basically vehicles with small

engine volume. These cars are meant to be convenient for the city and comfortable on the highway. Meanwhile, more advanced CVTs for larger automobiles are being developed by VDT and by German manufacturers. Two Chrysler Voyager minivans equipped with a new CVT design boasted (1) a 10 % fuel economy and improved acceleration performance in road tests. Perhaps the most impressive new application for these stepless transmissions is the CVT-driven Renault Formula One race car, which is powered by a 800-HP Renault V-10 engine.

In the mid- I 960s, Dutch automotive researchers (1) investigated the development of more compact CVTs that could be coupled to higher-powered engines. After analysis, it was concluded that a metal belt CVT could attain higher power density values than traction drives could. In addition, when metal-push V-belts were compared to metal Vchains, the former came out on top. In the early 1970s, VDT formed a design and test engineering group to develop CVT technology that could operate with larger engines, which meant developing a better drive belt, critical component of a CVT.

Interestingly, the steel push belt was discovered by accident. The early design was composed of thin steel bands, which were so highly loaded by the pulleys that these steel bands eventually buckled. Later, steel bands were supported by movable blocks. These movable blocks, in turn, acted to transmit torque by pushing one another around the pulleys.







19

The resulting push-block V-belt consisted of several thin, flat-tension bands of

steel that connected the V-blocks. The sets of bands had a very narrow mutual tolerance to avoid friction. The blocks, which were from 3 to 6 mm thick, could move freely over the bands and pushed each other forward, thus transmitting torque. The bands were locked in the block elements with pins. Unfortunately, the high machining accuracies required for the contact surfaces made the push-block system expensive.

The new V-element belt is an endless train of thin, trapezoid-shaped, metal plates, which are clamped in place with the axial force produced by hydraulic pressure on the pulley sheaves. The sum of the friction forces causes a pushing load in the stack of elements, which transmits the torque from the driving to the driven pulley. In the driven pulley, the pushing load is transformed into the output torque. The advantage of this is that it allows a very small pitch on the elements, which results in low noise.

In the production of the belt, sheets of high fatigue strength steel are rolled into tubes and cut into loops in a slitting operation. The small loops are then stetched to size by rolling, whereupon the bands are annealed, closely calibrated, hardened to relieve internal stress, and then nitrided to harden the surface. Final measurement follows and the bands are combined into matched sets.

The high tolerance elements are fabricated using techniques similar to those used to manufacture high-velocity gears or roller bearings. First the gear-steel elements are fineblanked to produce dimensional accuracies on the order of microns. Afterwards, they are hardened, deburred, and profile-shot blasted. At this point, they undergo a complicated sorting and selection process to match similarly dimensioned elements.







20

The critical dimension is the height of the support where the bands run over. The inside surface is ground down because it is important to have a smooth surface for friction properties. All the elements must support the bands at the same time load distribution rate, or there will be local overloading.

CVT control systems manipulate engine speed. The more independent relation between engine speed and vehicle speed in CVTs, compared with other transmission types, will make it possible to run the engine at more constant conditions or to follow the optimal path through changing driving conditions. The freedom to choose different relations between throttle position and engine speed provides the possibility of optimizing fuel consumption, emission levels, performance, and driving comfort.


Electronic Control Strategies


Modern control of the continuously variable transmissions require electronic

control with sophisticated hardware and software engineering. CVTs offer a great deal of flexibility to the control engineer.

The wide range of the shift map between the two extreme ratios could be used to correct tuning of the optimal control management. Therefore, CVTs also considerabl improve fuel economy in gasoline and diesel engines. Furthermore, higher-order electronic management provides even more possibilities for improvement.

The general idea (1, 4) behind new electronic controls is to combine all subsystems influencing fuel consumption, and to activate them by the driver's desire for a particular degree of acceleration or deceleration. The system detects this desire from the movement and position of the accelerator pedal, both of which are converted into electrical signals.







21

Using this data, the electronic control unit and appropriate software calculates the engine power and the best gear ratio required for the maneuver. Thanks to fuzzy logic control, the system can adapt the selection of gear ratios to a driver's style as well as current traffic and driving conditions. a














CHAPTER 3
CVTs vs CVPSTs


The modem day CVT concept is one of the latest attempts to improve a vehicle's performance. It also represents an optimum path among other transmission designs when many stipulations are imposed upon them such as fuel economy and acceleration performance. CVTs have been around for a long time but the implementation, understandably, has taken a couple of decades to ensure the further evolution of the idea. The next idea to follow CVTs has been the CVPSTs, or continuously variable power split transmissions.


Evolution of CVTs


Similar to CVTs, CVPSTs (continuously variable power split transmissions) are the next logical step further. CVPSTs have not only all the advantages of CVTs but also have the added capabilities. Unlike the regular CVTs, where power has only one route to follow, CVPSTs generally have two paths for the power flow. Dividing the power and running it through two separate lines allows the designer to acquire the optimum operating conditions at all speeds by changing the amount of power through each path.

For example, torque splitting between the hydrostatic and the planetary gearsets

significantly improves efficiency over a purely hydrostatic transmission. The ratio ranges of each module within the transmission were chosen so that under cruise conditions onl







23

moderate torque multiplication by the hydrostatic modules was required. Most of the power was transmitted through the planetary gearset. Only when ratio changes need to be rapidly executed does the hydrostatic module transmit a significant fraction of the total power.

Some of the CVTs are intended to be used as an overdrive gear applied to the conventional automatic. Within the limits of acceptable driveability and the fuel consumption characteristics of the engine, the CVT will allow engine speeds to be modulated under cruise conditions to achieve maximum fuel economy. By continuousl and smoothly changing the ratio, the CVT will maintain engine operation at the minimum fuel consumption point for any reasonable cruise or light-load condition. When low vehicle speeds or high rates of acceleration or steep hill-climbing capability is required, the conventional transmission will down-shift as usual to the required lower gear as the CVT changes to a 1:1 ratio.

Since the intention of this chapter is to provide a basic introduction to both CVTs and CVPSTs, further characteristics will be shown in the following pages. The detailed torque and velocity analysis will be made in Chapter 4, along with the modeling in Chapter 6. In Figure 3.1, a basic schematic is given regarding the differences of both systems. In Figure 3.2 and 3.3, two split path designs are shown.











Transmission


Differential


Transmission


Transmission


Figure 3.1. Schematics of a (a) CVT, a (b) Split and a (c) Recirculation Design















Continuously Variable Power-Split
Transmission Single Stage


Figure 3.2. Power Split Mechanism (7).
















Continuously Variable Transmission Power
Recirculation With Gear Neutral


Figure 3.3. Power Recirculation Mechanism (7).














CHAPTER 4
THE DYNAMICS OF CVTS


Basics


A basic system of planetary gears consisting of a sun (central) gear, a rim (ring) gear, and an arm to which planet gears are connected. A planetary gear set is a two degree of freedom mechanism, and requires two inputs at any of its two members for the other to be determined. Planetary gear dynamics could be analyzed using traditional formulae based on the ratio of the velocity differences, or as later to be shown in this chapter, a new and simple way may be utilized.


Rim (ring) gear


Planet


Sun


n i

Figure 4.1. A Planetary Gear Set, Side View.







28

A rim gear can be internal, and a planet gear acts as an intermediate element

between the sun and the rim gears. In Figures 4.1 and 4.2, two views of a planetary set are shown, and the legend regarding the radii are indicated. As can be seen from Figure 4.2, all the radii are related. The angular speed and all the torque relationships are based on the combinations of ratios of these radii.


Figure 4.2. Planetary Gear Set, Front View The geometrical relationship among the gears can be expressed as follows: ra = Arm radius, rr = ring gear radius, rp = planet radius, r, = sun radius. For the arm,
ra = r, + rp


and for the rim,


rr = r, + 2rp.


(4.1) (4.2)







29

Four Possible Configurations with a Planetary Gear Train


Characteristic to planetary gears, two input speeds always have to be specified.

When two of its members are used to input motion, either of the two remaining elements may be used as an output gear. With this, we come up with four distinct possibilities, or configurations. Configuration 1


Input: Sun and rim gears Output: Arm


Planet Gear


Vr = . rr


Vs= -: . r,


Figure 4.3.a. Velocity Profile, Configuration 1.







30

The velocity profile of configuration I is shown in figures 4.3.a and 4.3.b. In figure

4.3.a velocities are drawn on the planet gear itself, and the interaction of the inputs b the sun and the rim gears become obvious. When the circumferantial velocity vector on the rim gear and the velocity vector on the sun are drawn on the planet, Figure 4.3.b, the circumferantial speed of the arm can be found by a ruler or an expression below.


b.- Vr


(


I

b) //
I
VI a


(a)
I
I,


Figure 4.3.b. Velocity Profile.


Va= (Vr + V,)/2


o% = (o .r, + o -.rr) / 2ra




whereas,


Vr - Vs Or �rr cos . rs

2 rp 2 rp


(4.3) (4.4)









(4.5)







31

In the velocity profile above, Figure 4.3.b, the rectangular section (a) represents the translational motion of the planet gear. The triangular (b) section, on the other hand, corresponds to the rotational motion of the planet gear. Configuration 2


Input : Arm and sun gear Output : Rim gear


I VW Figure 4.4.a. Velocity Profile.


Where


V, = (Vr + V, )/2 or,


Vr = 2 V., -V


(4.6)


(4.7)












V
.. .........

V


V"
I I I I/
I

Vs


Figure 4.4.b. Velocity Profile







2 Wja. ra - .r

Wr,
rr



and,



(Q~ . ra - Os. r


(4.8)


(4.9)


Velocity profiles regarding configuration 2 can be seen in Figures 4.4a and 4.4b. It should be noticed that in the velocity profile, the direction of the angular velocities of both arm and sun are taken positive (cw).


........................... ........... ........... -............ i...............









Configuration 3


Input: Arm and rim gear Output: Sun gear


Vr
I
iI ii:~V


- j
I I/
I,
I/V


Figure 4.5. Velocity Profile.







2 o .r - .rr

rs





o .rr - .ra

rp




It should be noted that, as in configuration 2, the output speed is given as the difference of two input speeds. Figure 4.5 shows a detailed velocity profile.


(4.10)


(4.11)









Configuration 4


This configuration is about an unlikely case where motion is input through arm and planet gear, and output through either of the two remaining gears.





b- V p
Va













Wa ~ ~ - -+ r
I
I,
-I


Figure 4.6. Velocity Profile as the Summation of Two Cases






As was the case before, inputs speeds maybe divided into its components. The

input through the arm represents a uniform translational motion, whereas the planet gear assumes a pure rotational motion. This is depicted in figure 4.6. Here, the output speeds could be formulated similar to previous derivations.




Oa.ra + ODp.rp
(o = (4.12)
rr




. - .,. rp
(Ls =(4.13)







35

Summary of the Possible Configurations


With the cases given on the previous pages, the possible configurations can be

viewed summarily below in table 4.1. The column on the left designates the entry of an two members, whereas the top line shows the output members. For example, when the sun and the arm are taken to be input elements, we immediately dismiss sun and arm as output members since the "s" and "a" columns contain "N" which states that for this combination, sun and arm are not available for output. One of the remaining rim and planet might be used to transfer power.



Table 4.1. Configuration Chart. S=Sun Gear, A=Arm, R=Rim Gear, P=Planet, N=Not.
O U T P U T I S A R P N S N

p A N

U R N T P N




Power Split Configurations


As briefly mentioned in chapter 3, the proposed design has combined a split and a recirculation mechanism together. In a split gear set, the power is split in two, and while part of the power runs through the CVU unit, the other part carries it along the gear-togear path, i.e. through the sun gear. A split and a recirculation mechanisms are originall







36

the same, except an idler gear, whose sole function is to transmit power. In the presence of an idler gear, the sun and rim gears turn in the same direction, which is shown in Figure 4.7a. The sun and the rim gears turning in the same direction in the configuration below ensures that there is no circulating power and the power is split in a straightforward manner.

The clutch seen between the back of the rim and the counter gear allows the controller to transmit power on demand.




Clutch


I
CVU:
Continuously
............................. V ariable U nit,
Belt Drive


Idler Geari


Figure 4.7a. A Power Split Gear Set.









The formula without the idler:



rs - (.Or .rr

2 ra



The idler gear changes the direction of the rim gear thus, -(-wr)




o,.rs + 0Dr. rr

2 ra













Output "T'l Input


Figure 4.7b. Another Power Split Configuration.


(4.14)


(4.15)







38

This configuration could have been a recirculation system with an idler. The lack of an idler gear causes the arm to turn opposite in direction to sun, thus





2 c% . ra + , .r
Wr =(4.16)
rr



Power Recirculation Configurations


The examples of power recirculation configurations are the same as split design except the existence of an idler gear. The lack of an idler gear causes the rim gear to turn opposite in direction to the sun gear, thus creating an equation of


Figure 4. 8a. Power Recirculation Configuration.






39

subtraction rather than addition as in the split design. Figure 4.8 shows a recirculation mechanism where power is fed into the system along the sun and the rim gears, and the output is taken from the arm. The arm angular velocity is given by:




r - - . rr
,= (4.17)
2 ra



In a different design below, this time the existence of an idler causes an equation of subtraction. The reason for this is that the configuration shown in figure 4.8.b. has an inherent minus sign imbedded in the equation of output speed. Thus the existence of an idler gear ensures that the sun and the arm both have the same direction of rotation.









Input

Output flm


Figure 4.8b. Power Recirculation Configuration.







40

The output speed could be formulated as follows:



20a. - .r
(4.18)




Power Split (PS) vs Power Recirculation (PR)


Table 4.2, the advantages and the disadvantages of both mechanisms are

summarized. Unfortunately, none of the systems is well-suited by itself for automobile applications. The recirculation mode offers multiple good features for better control and efficiency. For example, with the recirculation feature, it is possible to hold the car stationary simply by changing the ratios, or to achieve reverse and forward gears.

Recirculation mode allows zero or near zero speeds. However, as will be shown in later chapters, the zero speed condition is called geared neutral and requires an accurate control CVU ratio. It is also known as the nervous state, since small variations in CVU ratio causes great changes in torque values that are imposed on the gears.

Calculations have shown that at points close to this nervous state, internal torques may reach values that are many times the input torque.

Split mode offers alternative ways of improving the vehicle handling. Even though it is not possible to achieve zero speeds with this mode, it is possible to acquire high speeds, a characteristic of the split design.














Table 4.2. Comparison of Two Systems.


POWER SPLIT POWER RECIRCULA TION FEATURES


WELL SUITED TO START-UP AND OVERCOMING INERTIAL FORCES HAS A BUILT-IN CLUTCH (GEARED NEUTRAL)



REVERSE GEAR POSSIBLE COMPARATIVELY HIGH SPEED SLOWER FORWARD GEARS LIMITED RANGE OF SPEED


GEARS GET OVERLOADED


YES


YES


YES


YES


NO


YES


YES


YES







42

Proposed Design


The following hybrid PS-PR gearbox has been intended to contain the advantages of both modes of power split mechanisms. It has four distinguishable gears, one being the reverse gear. The reverse and the drive I are governed by power recirculation equations. In this mode, the vehicle can back up, achieve the so-called "geared neutral" phenomenon, and set the vehicle in forward motion.

At a designated speed, which might be called first-crossover, the motor vehicle switches to drive 2, or split mode. This mode allows the driver to achieve quicker acceleration, and to acquire relatively higher speeds. In this mode, all of the power is carried through system's two belt units. The lessening of torques at high speeds permit the running of torques along continuously variable units. This feature is the key to rapid acceleration.

Further down the road, at even higher speeds, a third drive has been provided. At a second designated speed, another switch occurs. This shift from drive 2 to drive 3 might be called the second-crossover. In this mode, to take advantage of ever-smaller torques, and to eliminate the inertia of masses of rotating gears, the path is now a single line, and no power split is needed.

The proposed design, as shown in Figure 4.9, is the combination of a recirculation and a split design. The power is input into the system from the right lower corner of the picture and output from the upper left corner. The design contains two CVUs or two belts, and is composed of three stages. In each stage, the power follows a different path, in accordance with the control and the vehicle speed. The caption explains the symbols in the figure.




















11 OUT


CVU


3 C6


U - CVU

Figure 4.9. The Proposed Design. C .C7 : Clutches;
CVU: Continuously Variable Units;1, 2, 17, 18: Variable Pulleys; 3, 4..15, 16 : Gears







44

General Layout Table


The Table 4.3. shows the management of the transmission, and which clutches to be activated to switch to a certain mode. As it is clear from the table below, the reverse and the drive I have both the same clutch configuration. This is to say that at lower speeds, the reverse and the drive I use the same clutch group, whereas the split (drive 2), and the high speed gear (drive 3 ) use different paths and different clutch logic.


Table 4.3. General Layout Table


Cl C2 C3 C4 C5 C6 C7 Reverse ON ON Drive I ON ON Drive 2 ON ON ON Drive 3 ON ON ON Neutral







45

Dynamics of the Proposed Design Velocity Analysis


This section establishes a kinematic relationship between the various elements of the proposed transmission. Recirculation Mode, Reverse and Drive 1

In Figure 4.10, power flow path has been shown with a thicker line to emphasize and demonstrate the path. The angular speed calculations are facilitated by the prederived equations earlier this chapter.

In this mode, the angular velocity of the gear 7 may be defined as follows:




c0.r5 - o)4 . r4
1)7 = (4.19)
2 r7



where



r7 = (r5 + r4 ) /2 (4.20)



(Lis= a . . Rv, (4.21)



where


Rv = r, / r2


(4.22)


















CVU

H17


3 C6 Ia"WH1


CvU


Figure 4.10. Recirculation Mode Power Flow Path.


11 OUT









(0)4 = )n. Rr, where Rr = r3 / r4


=)out 0. (r7 / r8) (r9 / r I)


(Rv. Rpr - Rr)
(A)7 =n
(1 + Rpr)




Rpr = r5 / r4, and with


where,


R -, = (r7 / r8 ) . ( r9 / r, ), the output speed can be written as oout = (f. Rcr. ( Rv. Rpr- Rr) / (1 + Rpr)


0.5 0.7 0.9 1.1 1.3 1.5 First (R,) CVU Ratio
Figure 4.11. Ratio of Output to Input Angular Speed.
Rcr = 1, Rpr = 0.6, Rr = .347


(4.23) (4.24) (4.25)


(4.26)


(4.27) (4.28)


(4.29)







48

Figure 4.11 depicts for a given set of variables the change of input and output

speeds with respect to each other. It should be noted that at lower CVU ratios, the output speed gets smaller compared to the input speed. Split (Drive 2) Mode

In this case, the output speed can be stated as follows:


(1014 . r14 + (013 . r13 2outr
2 r1l


where,


(4.30) (4.31)


r, = ( r13+ r14) / 2


(013= "3. Rs, where R, =(r6/ r13)


O14 = (04 . R, where


()4 = &oin. R, where


(4.32), (4.33) (4.34), (4.35a)


Rvs= ( r18 / r17 )


Rrs = ( ra / rsa )


(4.35b)


%n . R, . Rvs. r14 + Q0n . Rv. Rs . r13 (2[ru+ =
2 .[(r13 + r14 V/2]


(1 . ( Rrs. Rvs. RPS + R, . R,)

(I + RPS)


" = (oin . R,


(4.36)


(4.37)



















cVU

H17


3 C6 I a ,,UI


cVU


Figure 4.12. Drive 2 Power Flow Diagram.


II

OUT




















cVU


3 C6


Figure 4.13. Drive 3 Power Flow Diagram.


Drive 3


11 OUT


.......


cVU







51

In the last drive, as depicted in Figure 4.13 the power flows through the two existing belt drives.

Here, the output speed is simply two CVU ratios times the input speed, namely


Wout= n. Rv . Rs, (4.38) where


R,=(r1/r2), and Rs r17 / r18 )(4.39)


Special Cases


It should be noted from the recirculation formulae that at certain speeds, some ratios become critical. To determine those critical speeds and conditions, a further analysis is needed.


Recirculation Mode


Reverse Gear:

R,. Rpr Rr > 0 (4.40a)

Geared Neutral:

R,. Rpr - Rr = 0 (4.40b)

Drive 1


R,. Rpr - Rr < 0


(4.40c)







52

Crossovers


Crossovers represent the passage from one mode to the other. Since there are no synchronizers to equilize the speeds at various points of contact, a careful control of speeds prove essential.


First Crossover


First crossover is the transition from recirculation mode to split mode. At this

point, for a smooth passage, the output speed of the transmission has to be the same at the end of the recirculation mode and at the start of the split mode. =ut-rec = ut-spit, or (4.41)



0but-rec = On. Rcr. (Rv. Rpr - Rr) I (+ Rpr) (4.42)



%On � (Rr. Rs. RPS + Rv. R,)
0,out-split = (4.43) ( 1 + RPS)


Second Crossover


Second crossover occurs when it is switched from drive 2 to drive 3, in a similar way utilized above.



O� ( R,.. ps + Rv. Rs)
(Oout-split - = out= n - R . Rvs. (4.44) (I + Rps )







53

Torque Relations


In the derivation of the following torque relations, three classes of equations are needed. The speed ratio ( o / co ) of the pair, which is clearly defined for each and any possible case above. There are various design methods, and one can be seen in (14).

Input - output power relations (9, 12), as


Ti.ou + Tj .o + Tk.Ok = 0


(4.45)


Figure 4.14. Three Element Diagram.



This equation holds in the absence of losses, and is nothing more than the preservation of energy. In all of the calculations, Figure 4.14 is used.

And finally,


T, + Tj + Tk = 0.


(4.46)


The above equation holds when the links are at rest, or when rotating at uniform speed. After some algebraic manipulations through the equations 4.45 and 4.46, the equations presented below can be obtained.









Recirculation Mode


( O)ut / o n) Rcr. (Rv. Rpr -Rr) / ( + Rpr) ( Tin / Tout) Rcr. (Rv. Rp - Rr) / (1 + Rpr) ( Tgear / Tin) R, / ,. Rpr - Rr )



A positive ratio would indicate that the vehicle is in reverse gear. ( Tc,/ Tin ) = Rv. Rpr / ( Rv. Rpr - Rr) ( Tgear/ Tout ) Rr/ (I + Rpr ) ( Tcvu/ Tout ) = Rv. Rpr / ( + Rpr) ( Tgear/ ) = Rr/ (Rv. Rpr ) Split Mode


(toout/ ojn) (Rs. Rvs.Rps + R,,.R)/ (I + Rps) ( Tin/Tout)= (Rs.RS. Rps + Rv.Rs)/ (1 + Rps


( T,:,o/Tin ) = ( R,. Rs ) / ( Rr. R,,. Rps + Rv. Rs )


(4.47a)


(4.47b)


(4.47c)


(4.47d)


(4.47e)


(4.47f)


(4.48a)


(4.48b)








(4.48c)


( Tvuj2/T ) = ( Rrs ,,. Rps ) / ( Rrs. Rv. Rps + R,. R, ) (Tvul /Tout ) = ( R,. R, (1 + Rps) ( Tcvu2 / Tout ) = ( R.. .v. R, ) / (1 + Rps) ( T,:vu / Tu2 ) = ( R, . Rs ) / (R-, . R,. Rps ).


(4.48d)


(4.48e)


(4.480


Wout Win















19 1.8 2.1 2.4 2.7


Second CVU

Figure 4.15. Split Mode. Rs = 0.347
(+) First, ( . ) Second, and (x) Third Variations.


1.6

1.4 1.2

1

0.8 0.6 0.4 0.2

0







56

In Figure 4.15, different control strategies have been implemented. In Figure 4.15, the ratio of the first belt is kept constant(+), as for the second variation ( . ), the first CVU ratio is determined as the square root of the ratio of the second CVU. In the third variation (x), ratios have been kept equal.

It is clear from these figures that the output speeds get progressively larger from the first variation towards the third. The third variation may be taken as an overdrive at around a CVU ratio of 2.1.

First variation, allows a faster output speed with respect to any specified input speed.


Drive 3


A similar method could be utilized to determine the response of the system when different control strategies are imposed.



1.6 out /Win
1 .6

1.4 1.2
1
0.8 0.6
0.4 0.2
0
2.1 2.3 2.5 2.7 2.9 3.1 Second (R,,) CVU Ratio Figure 4.16. Drive Three.
Rv (First CVU) = .5







57

In Figure 4.16 again similar to the control strategy done in split mode, the first CVU ratio is kept constant. In the second variation, varied as the square root of the second CVU ratio, and finally, in the third variation, CVU ratios are made equal. However second and third variations have shown that these two are not practical. In these regimes, output speed reached many times the input speed, thus are not drawn.

The above diagrams were drawn using the first equation below. ( 0 / o. ) = R,. R.


( Ti. / Tout ) = Rv. Rvs


(4.49)


Torque Ratios and Diagzrams


Recirculation Mode


0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 F4rst (R,) CVU Ratio

Figure 4.17a. Output Torque with Respect to Input Torque.
Rr = .347, Rpr = .6












2


1.5


1


0.5


0
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (R,) CVU Ratio Figure 4.17b. Gear Torque with Respect to Input Torque.







3Tcvu / Tin


2.5

2

1.5

1

0.5

0
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (R,) CVU Ratio Figure 4.17c. The CVU Torque with Respect to Input Torque.














0.25 Tgear / T out

0.2

0.15

0.1

0.05

0
0.9 1.05 1.2 1.5 1.8 2.1 2.4 2.7 3
First (R,) CVU Ratio
Figure 4.17d. Gear Torque with Respect to Output Torque.




Figure 4.17a shows a linear relationship of input and output torques with respect to CVU ratio. In the next one, Figure 4.17b, it is seen that the torque carried by the gear is getting smaller with respect to the input torque. The CVU load also depicts a similar trend in Figure 4. 17c. One thing should be clear that at a given CVU ratio, for this configuration, the load carried by the CVU is larger than the gear load.

Figure 4.1 7d, the gear load remains constant throughout the range of the CVU, in Figure 4.17e, the load of the CVU linearly changes with respect to the output torque.

The Figure 4.17f shows a rather desired effect where as the vehicle speeds up and from low CVU ratios gear to CVU ratio gets smaller. However, the fact that the ratio is less than unity at slower speeds is not a desired effect, due to the fact that this would mean a larger load on the belt drive than on the gear.













T / To.t
1.2 r


1.2 1.5 1.8 2.1 2.4 2.7 First (R,) CVU Ratio

Figure 4.17e. CVU Torque with Respect to Output Torque.


1.1 1.3 1.5 1.7 1.9 2.1 First (R,) CVU Ratio

Figure 4.1 7f. Gear Torque with Respect to CVU Torque.


0
0.9










Split Mode


Here, in the same way as in finding the charts for angular speed ratios, to find torque relations, again the first CVU ratio is modified in three different cases called variations. In Figure 4.18a, when it is switched to split mode, at the moment of switch, if it is 0.9 for example, then the output torque is approximately twice the input torque. And the relationship varies linearly as CVU ratio increases. For this variation, the first CVU ratio is kept constant.

As for the second variation where first CVU ratio is the square root of the second. In the third variation where ratios are held equal, the torque ratio takes on at approximately the same range to well over 0.8, in this case 1.1. This sudden increase of output torque, given the sufficent engine power, might give a relatively good acceleration. Since the graphs of variations on the speeds are the same as on torques, and are given in Figure 4.15, they are not repeated here once again.

The next one, Figure 4.18b, puts on a gradual decrease of the ratio of CVU torque to the input torque, towards the end of the range of the CVU. The second CVU, Figure

4.18c, however, presents a tendency to increase from well below 0.3 to slightly over 0.5. Second belt, thus, assumes more and more load as the vehicle speeds up.

Figure 4.18d shows that there is no mathematical relationship between the output load and the load on the first CVU. For the data used to chart the graphs, the ratio remains slightly above 0.3. The Figures 4.18e and 4.18f demonstrate the torque ratios of second belt drive with respect to output and first belt torques.











To. / Tout


9 1.2 1.5 1.8 2.1 2.4 2.7 Second (R ,) CVU Ratio

Figure 4.18a. Split Mode.
Rv = 0.9


Tcvu 1 / Ti,


0.9


1.2 1.5 1.8 2.1 2.4 2 First (R,) CVU Ratio Figure 4.18b. Split Mode, Tc,u-vs-T,.


n I


. I


. I









T~u 2 / Tn














).9 1.2 1.5 1.8 2.1 2.4 2.7 Second (Rv,) CVU Ratio


Figure 4.18c. Split Mode, Tcvu2-vs-Tin.


T,, 1 / Tout


1.2 1.5 1.8 2.1 2.4 2.7
First (R,) CVU Ratio

Figure 4.18d. Split Mode, Tcvul-vs-Tout.


0.35 0.3 0.25 0.2 0.15 0.1 0.05

0
0.9









0.5Tvu 2 / Tout


0.4 0.3 0.2 0.1


0
0.9 1 .












Tv 1 / Tc,


3

2.5

2

1.5

1

0.5

0
0.9 1


1.5 1.8 2.1 2.4 2.7 Second (Rs) CVU Ratio Figure 4.18e. Split Mode, Tc,.2-vs-Tout.


.1 1.3 1.5 1.7 1.9
Second (R,,) CVU Ratio

Figure 4.18f. Split Mode, Tvuj-vs-Tcv.2.









Drive 3

Control strategies represent various options of accelerations. For the first variation, only the second belt drive ratio is varied. For such a condition, in Figure 4.19, the input torque remains large at all times. Since this mode is used solely for high speeds, this is only to be expected. The relationship between these two torque values change in a linear fashion.





1.6 1.4 1.2
1

0.8 0.6

0.4 0.2
0
2.1 2.3 2.5 2.7 2.9 3.1 Second (R,) CVU Ratio Figure 4.19. Drive Three.
Rv = 0.5.














CHAPTER 5
OPTIMIZATION AND ANALYSIS OF RECIRCULATING POWER


In this chapter, the effects of the recirculating power will be discussed. Since reverse gear is the byproduct of recirculation mode, it is also logical to discard this mode altogether if all the excessive torques and accurate control are to be avoided. Thus, the first section deals with the option of having the reverse gear, and a related analysis, and the last section discusses effects if the reverse gear is desired to be avoided.



With Reverse Gear


The geared neutral point can be found from



R, .Rpr-Rr = 0,

or,

Rr = R,. Rpr.



If Rvgn is the value that R, assumes at geared neutral, then




R,gn = Rr /Rpr. (5.1)






67

The ratio of torque through gear to CVT was given in Chapter 4 as


Tg / T," = Rr / (R,. Rpr).


(5.2)


At slower speeds, Tg is expected to be larger than T,., and gradually, Tc, should increase while the vehicle is speeding up.


Tg / Tvt = RT,


RT> 1 when R, is small


RT < 1 when R, is large.


Substituting (5.1) in (5.2), at the start,


Tg / Tcvu = RT > 1 or,


RT= ( Rg / Rstrt) > 1


Rvgn = RT. Rvstart


(5.3)


If, initially, we want the torque running through the gear twice the torque through the CVT, then,










Rvg, = 2 . Rvw. (5.4)


What (4) says can be depicted by a diagram:




Gear

Forward - G.N. -- Reverse



Low High Rv Figure 5.1. The Location of the GN Point.



In words, the geared neutral has to take place at higher CVT ratios, and further down the reverse gear can be attained.

A typical (Tg / Tin) or (T, / Tin) curve has two parts.


60T9 / Tj,
60 40

20

0

-20 -40 -60
0.7 0.75 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 1.2 1.25 1.3
CVU Ratio Geared Neutral at 1
Figure 5.2. Excessive Torques Near Point GN.






69

First part of the curve can be seen to go asymptoticly to infinity having x = Rn whereas the other portion of the curve goes to infinity in the other direction. In the example below, geared neutral is reached when R, attains the value of 1.

When CVU ratio reaches the 75-80 % of GN value, the torque ratio demonstrates a sudden jump, which must be avoided. The reverse gear ratio, similarly, should be placed as far away from GN as possible.


The Effects of the Position of the Geared Neutral Point


The idea that initially a large portion of the power should be carried through the gear mandates that the location of the geared neutral point be placed at a larger CVU ratio. However, this positioning comes at a price. An analysis would be helpful to disclose the characteristics of two possible cases.

1. Geared neutral (GN) placed at a lower CVU ratio

2. GN placed at a larger CVU ratio



1)RT < I



The above expression reveals that the reverse gear should be deployed at the

lowest CVU ratio, then the GN point and finally forward regime. The characteristic curve is:














50

40

30 2D 10 0
0.7 0.75 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 1.20 1.25 1.3
Rrt R(,) CW Fio Gewed NxIY at 1
Figure 5.3. Effects of the Location of GN.



Since the parameters given above has influence on Tg/ Ti,, T,, / Ti, and Tg/ T,,, it would be easy to see the effects by drawing these diagrams with numerical values.


0
0.9


1.1 1.3 1.5 1.7 1.9
First (R,) CVU Ratio Figure 5.4. GN on the Left.







71

The Tg / Ti, diagram shows that at first the gear load is almost twice the input torque. However, the next diagram depicts a down side to case 1. CVT torque assumes even a larger percentage at a given CVU ratio, which is clear in the last chart, where Tg Tcvt never comes close to 1, or even above.

Throughout the figures given in this chapter, it is clear that close to the geared

neutral point, internal torques reach many times either in or output torques. In Figure 5.2, close to the geared neutral point, the gear load becomes 60 to infinity times the input load. This should mean that after a certain point at the loading, a break would occur.

Even at a safe distance, at a CVU ratio of 0.9, Figure 5.4, the gear load descends from around 2.0, and below.






3 T,, / Tin
3


2.5

2

1.5

1

0.5

0
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (R,) CVU Ratio Figure 5.5. Tcvu-vs-Tin.










0.7 gear TCVu

0.6

0.5 0.4 0.3

0.2 0.1

0
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 First (R,) CVU Ratio Figure 5.6. Tg-vs-Tcvu.



2) RT > I

Here, the reverse gear is to be placed at the largest CVU value, and the vehicle ma start at the lowest speed possible.


0.5 0.6 0.7 0.8 0.9- 0.98 1.02 1.1 1.2 1.3 1.4 1.5 1.6
First (Rv) CVU Ratio Geared Neutral at 1


Figure 5.7. Tg-vs-Tin.










25 20 15 10

5

n


Tg/ Tin


0.5 0.7 0.9 Geared Neutral at 2.4


1.1 1.3 1.5 1.7
First (R,) CVU Ratio Figure 5.8.Tg-vs-Tin.


1.9 2.1 2.3


v./ Tin


0.7 0.9 1.1 1.3 1.5 1.7 First (R,) CVU Ratio neutral at 2.4
Figure 5.9. Tcu-vs-Tin.


1.9 2.1 2.3


25 20 15 10


5

0
0


.5


Geared N












4 3 2 1


0
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (R,) CVU Ratio
Geared Neutral at 2.4

Figure 5.10. Tg-vs-Tcvu.



Figure 5.6 shows that when RT < 1, gear to CVU ratio starts at around 0.65. When this value is above the unity, the vehicle can start at the lowest speed possible. In Figure 5.8, the ratio of gear load to input torque displays a tendency to increase. In this dramatic increase, gear load jumps from twice the value of input torque to 25 times of it.

Figure 5.9, also shows a similar rise, this time for the CVU. Figure 5.10 shows that the gear loads decreases with respect to CVU load as the CVU ratio increases.

Tort/ Tin was expected to go up with respect to CVU ratio, and it does. But

Tg/ Tin goes up with the ratio, which we would not like it to happen. In both diagrams, it is clear that for a given numerical set of values, after the CVU ratio of 1.5, torque ratios become already too high.








The Direction of the Power Flow

The following discussion and figures explain the power recirculation phenomena in the transmission. The direction of power could simply be determined by an algebraic equation:

R,.R ,- R, > 0



A B Out 4 In




Figure 5.11. Positive Circulation



At point A,

Pcvt = Pout + Pa. At B,

Pcvt = pgw + Pin.



Rv.P- R,<0





A B Out 4 i4 - In


Figure 5.12. Negative Circulation.






76

After crossing the geared neutral point, the inequality changes sign and the major carrier hence becomes the gear itself.


At point A, PgCar = Pout + Pcvl.

At point B, Pgea = Pcvt + Pin.


The Ways of Reducing the Circulating Power


If the CVT is to be taken as the main carrier of torque in forward mode, which means that RT < I , this places the geared neutral point on the left on a Tcvt -Ti diagram. In such a case, Tc, / Tin, Tg / Tin decreases, as CVU ratio increases. But Tg / Tcvt opens up at ratios that are less than or equal to unity.

It is essential to set the operating points away from the vertical G.N. asymptote b a safety margin. For RT < 1 case, a start should be made at least 20 % more than the CVU ratio that G.N. occurs. On the following chart, geared neutral takes place at 1. As can be seen, even at around a CVU ratio of 1.2, which gives us a margin of 20 %, one of the two possible paths could carry multiple times the input torque. However it is clear that such a margin cut should be optimized itself. For every cut would limit the ver precious working range of CVTs.









60 50

40 30

20 10 0
0.5 0.6 0.7 0.8 0.9 0.98 1.02 1.1 1.2 1.3 1.4 1.5 1.6
First (R,) CVU Ratio Figure 5.13. Tg-vs-Tin.


No Reverse Gear


Having a reverse and a forward gear, and the geared neutral case, unfortunately, comes at a price. The necessity to stay away from the neighborhood of geared neutral point loses the transmission some of its operating ranges. It is possible, nevertheless, to skip the reverse gear and to shift the GN further away from the feasible working range of CVT. To achieve reverse gear option, an additional gear and a clutch, or any other auxiliary system will be needed. Two advantages may be obtained with the removal of reverse phase from the recirculation mode:

1. Getting rid of the unstable transition zone,

2. Retrieving the valuable working range otherwise lost.














CHAPTER 6
THE MODELING OF THE PROPOSED TRANSMISSION


A complete understanding of the transmission would only be possible through a

detailed work on the proposed transmission. For the development and implementation of control laws, and the utilization of computer simulation, modeling of the transmission is required.

Optimization of current systems is divided into two major categories:

1. Economy Mode,

2. Performance Mode.

In the economy mode, the vehicle operates in accordance with the least fuel consumption curves. It is possible to create an engine operating map based on the experimental data for the specific engine in question. Since the whole operation range of the vehicle can be roughly divided into two, the economy and the performance modes, it is possible to run the engine at a specified regime, or a default operating system, then switch to the other regime whenever there is a need for the vehicle or the computer to comply with the current state of driver or road needs.

In the performance mode, the major parameter is the differential output torque,

which determines the amount of acceleration with respect to the vehicle mass. As later to be seen, the path to achieve a maximum torque is not always obvious without some indepth analysis. For all the main shafts below, a structural stiffness and a damping have been attributed. A typical shaft is modeled as shown below where the stiffness and






79

damping elements are connected in parallel. Rotational masses have been lumped to point loads and designated by Ii (5).

Ki


Figure 6.1 .A Modeling Unit.



Modelin


Recirculation


By excluding the engine output shaft stiffness, damping and viscous damping, and simply referring transmission input torque as Tin, the CVU input pulle and shaft acceleration is given as a function of the state of the clutch C6:



C6 is slipping


(6.1)


C6 is locked-up


Lxi = (Tin - R, . TD4 - Tp - T4. Rr - D3 � o - Dr.Co)4 . Rr ) / ( I+ 3 - Rr2 )


where,


(6.2)


(xi = ( Tin - Rv . T4 - Tp - Tc6 -D3. o(01) � ( I1/ I )













11I

OUT



p

D8


D6, K6, 12 //" V


2/



IN


%.- v U


D7, K7, 14


Figure 6.2. Modeling of the Recirculation Unit.


Dr
6 LLL/




5 4

/77
D5





/73 C6
/77


n 711


9
C1


/' � 7T T









TD4= ( K4,.04 + D4. (01. R, - o02)) (6.3)



The angular acceleration of the second pulley of the CVU could be described as follows:



oX2 = (To4 - T6 - .D5).(1/I2) (6.4) where,



TD6 = K6.J(o"-".)dt + D6.(0)2-0) (6.5)


Similarly, the angular acceleration of the shaft of the gear 4 depends on the two

possible positions of the clutch 6. When slipping, a partial torque transmittal occurs and this transmittal is in turn a function of the slip.



Slipping of C6


(x4 = (Tc6 / Rr - T4 - Dr. o4) . (1 / 13)


(6.6)


and for the lock-up, = Rr. 1c.


(6.7)


x8= (T7 - TD7).(r7/r8).( 1 / 14 )


(6.8)











To find T7, a simple derivation would be needed: 7= (o..r5 - ot4.r4)/(2r7) where,



(04=0 .Rr/R, thus,


(07 =o(05 (rs - rr . Rr/ R,,) / (rs+rr )


so that,


T7 = TD6. (R,.( Rp + 1)/ (Rv. Rpr - Rr)) Also with



T4 = - TD6/ Rp and,


TD7 = K7 f ((09 - , ) dt + D7 ( ()9 - 08)


c4Uu = (TD7. ( r1I/rg) - Ds. &out).( 1/18)


(6.9)


(6.10)


(6.11)


(6.12)








(6.13)


(6.14)


(6.15)









Split Mode

C6 is slipping al, = ( Tin - R, . TD4 - Tp - Tc6 - D3.1 ) �W 1 I C6 is locked-up oX = (Tin- R, .TD4-Tp-T4.R. - D3.(01-Dr.o4.Rr) /( i+ 3.R R2)



where,

TD4= ( K4.04 + D4.(01.R, - oh)) Slipping of C6 x4= ( Tc6 / R. - TD. Rvs - Dr. 4) ( 1/ 13) and for the lock-up, 4= Rrs. 1


(6.14)


(6.15)


(6.16)


(6.17)


(6.18)


The angular acceleration of the second pulley of the CVU could be described as follows:


ot2 = ( TD4 - TD5 - " . D5 ). ( 1 / 12 ), where


(6.19)

















K1o, D1o

cvU C4 17


117


K9, D9


Dr




K5, D5


L 18ua


cvU


Figure 6.3.Modeling of the Split Unit.


11 OUT


/7777
D8









TD5 = Ks. f(")-0")dt + D.(o-o)


X13 = (TD5.( r3 / r16) - T13)/ ( 13)


(6.21)


To find the torque T13, a similar expression which was carried out in recirculation mode is needed.


0)uut = (c014- r14 + 0)13. r13 ) / ( 2 rout )


(014 = (.In . Rrs . Rvs 0)13 = On Rv� Rs


=014 = )13 . Rrvs


(6.22)


(6.23) (6.24)


(6.23)


where



R,-= R,-. Rws / Rv .Rs


(6.24)


,ut = ( (0)13 . Rrvs. r4 + (013 . r13) 2 rout rout= ( r13+r14 )/2


(6.26)


4ut = (13 (Rrvs. Rps + 1 )/(Rps + 1)


(6.25)


(6.20)


(6.27)









T13 = Tout(R S.RpS + 1)I(Rp, + 1) With the above expression, out- (TI, - - out.D8 /I8 X17 (TD9 - D1I �(017 - TDo)/I17 where



TDIO = K1o. f ( o17 - (o14 ) dt + DIo. (o17 - (O14) When clutches C2 and C4 are fully locked,


(X17 = (X14


and,


oJWout = (14 ( Rs. Rps + 1)/Rvs .(Rps + 1)


T14 = Tout (Rrvs. Rps + I )/Rr. (Rps + 1)


(6.28)


(6.29)


(6.30)


(6.31)


(6.32)


(6.33)


(6.34)









Drive 3


Drive 3 differs in that it does not have a split path. All the power is channelled along the successive belt drives. The angular acceleration on the first sheave is:


(6.35)


(xi = (Ti. - R, .TD - Tp ) / ( I )


where,


(6.36)


TD= ( K4.04 + D4.(01.R, - "))) The acceleration of the second sheave : (X2 = (TN - ".D5 - TD9. R,).(1/II8) where


(6.37)


(6.38)


TD9 = K9.09 + D9.(0)2.Rs-017)


(X17 = (TD9 - (017. DI - TDIO)/ 17 where


(6.39)


TD9 = K9 f ( " - co17 )dt + D9 ( (02 - 0)17 )


(6.40)


















cvU 17 C2, C4.1
I


K9, D9


18


118





2

_ IK, D4


cvU


Figure 6.4. Modeling of Drive 3.


1

OUT


p
/7777
D8













TDIO = KIo f ( (017 - O.ut ) dt + D, ( o017 - owt) Provided that clutches C2 and C4 are on. Finally, oh1ut = (TDIO - D8. cout ) / 8


(6.41)


(6.42)















CHAPTER 7
CONCLUSIONS


This dissertation first described CVTs and then provided a general overview of CVTs. CVTs have been compared and their compatibility has been discussed. The incentive behind the CVT concept was dealt with, and the reasons were explained.

In chapter 4, first, a new way of calculation of planetary gears were presented, and with the introduction of recirculation and split designs, the speed and torque entities were given.

This dissertation proffered a possible way of improving the CVT performance in the form of a new CVPST design. This new design was proven to be a better design than the conventional CVTs in load carrying capacity. However, the new improved design has also brought a few setbacks such as added complexity and weight.

The proposed design consisted of three distinct paths for the power to flow. Each path was designed to optimize the vehicle performance at various phases of the motion. The recirculation mechanism had the ability to reach a very specific ratio characteristic to the system, when the vehicle could remain stationar even though the tires of the vehicle are tightly connected to the engine. This mode has considerable virtues that might not be ignored for automobiles. The salient features of the recirculation mode were the possibility of attaining the reverse, forward and neutral gears as well as slow speeds that would allow a car to help overcome the inertial loads.







91

The split mode offered top speeds while the system had two paths to ease torques that were run through the belt drive. In the final mode, however, the power was run through the two successive belt drives. Two belts showed that a faster acceleration was possible.

In this work, it was shown that, theoretically, it is possible to incorporate the three separate modes, recirculation, split and a plain CVT, into one single transmission unit, and prove by the speed formulae that, by computer control for example, it is also possible to shift from one mode to another seamlessly at designated switching points.

Unfortunately, the greatest obstacle proved to be the power recirculation in the

recirculation mode. Since this power build-up is characteristic to the recirculation mode, it seems that it is not possible to eliminate it completely. However, as shown in chapter 5, by truncation of the working range of CVTs, this power build-up was considerably reduced, further away from the geared neutral (G.N.) point.

Understanding and designing such a system will require a working model of the

transmission at a scale, to observe whether the formulae presented in this dissertation can predict exact failing points of gears, or even whether they will hold at all.

Future of a CVPST will be dictated by various factors, such as how well this

transmission can be optimized in weight, performance and recirculating power and the trend of consumer demand for acceleration, price and economy of a vehicle equipped with a CVPST.














REFERENCES


I. Ashley, S. "Is CVT the car Transmission of the Future?", Mechanical Engineering,
pp 64-68, Nov. 1994.

2. Dooner, D., Yoon, H-D., Seireg, A. "Kinematic Consideration for Reducing the
Circulating Power Effects in Gear-Type CVTs", Proc. Instn. Mech. Engrs.,
vol.212, pp 463-478, part D, 1998.

3. Fel, L. "Development of the Ball Toroidal Continuously Variable Transmission",
1998 Earthmoving Industry Conference and Exposition, Peoria, IL April
1998.

4. Gott, P. "Changing of Gears", SAE Historical Series, Warrandale PA, 1991.

5. Hanachi, S. "A Study of the Dynamics of a Split Torque, Geared Neutral
Transmission", Journal of Mechanical Design, vol. 112, pp 261-270,
Sept. 1990.

6. Mucino, V.H. "A Continuously Variable Power Split Transmission for Automobile
Applications", SAE Paper No 970687, pp 75-80, 1997.

7. Mucino, V.H. "A Double Planetary Gear Train CVT Transmission with Multiple
Applications", SAE Paper No 950094, pp 1-10, 1995.

8. Mucino, V.H. "Parametric Modeling and Analysis of a Planetary Gear-CVT
Mechanism", SAE Paper No 940519, pp 113-123, 1994.

9. Pennestri, E. "A systematic Approach to Power-Flow and Static-Force Analysis in
Epicyclic Spur-Gear Trains", Journal of Mechanical Design, vol. 115,
pp 639-644, 1993.

10. Pennestri, E. "The Mechanical Efficiency of Epicyclic Gear Trains", Journal of
Mechanical Design, vol. 115, pp 645-651, 1993.

11. Rydberg, K. "Hydrostatic Drives in Heavy Mobile Machinery", lOP Congress and
Exposition, Milwaukee, WI, Sept. 1998.








12. Saggere, L. "A simplified Approach for Force and Power-Flow Analysis of
Compund Epicyclic Spur-Gears Trains", Advances in Design Automation,
vol.2, pp 83-89, 1992.

13. Takiyama, T. "Simultaneous Control for Optimization of Fuel Consumption",
Transactions of the Japan Society of Mechanical Engineers, pp 386-391,
Jan 1996.

14. Tian, L. "Matrix System for the Analysis of Planetary Transmissions", Journal of
Mechanical Design, vol 119, pp 333-337, 1997.

15. Wu, G. "Optimal Control of the Vehicular Powertrain with a CVT", SAE Paper
No 973281. pp 47-51, 1997.

16. Vahapzadeh, H., Linzell, M. "Modeling, Simulation, and Control Implementation for
a Split-Torque, Geared Neutral, Infinitely Variable Transmission",
SAE Paper No 910409, pp 21-32, 1991.














BIOGRAPHICAL SKETCH


The author was born in Ankara, Turkey, on December 23, 1968. He earned a

degree in mechanical engineering from the Dokuz Eylul University at Izmir. He worked before and after graduation as an assistant engineer on elevator maintenance and the control of plastic injection machines at an engineering workshop. In 1993, he won a scholarship in United States for graduate studies. After two years, he earned a master of engineering degree at Illinois Institute of Technology, in Chicago. The author plans to return to his homeland and continue his work at a university starting as a research assistant.




Full Text

PAGE 1

OPTIMIZATION AND ANALYSIS OF A HYBRID CONTINUOUSLY VAIUABLE POWER SPLIT TRANSMISSION By SERHAN OZDEMIR A DISSERTATION PRESENTED TO THE GRADUATE SCHOO OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1999

PAGE 2

ACKNOWLEDGMENTS The author would like to express his gratitude to Dr. John K. Schueller for his encouragement, guidance, and patience, to Dr. Ali Seireg, who provided some of the vital material, and also to Dr. Kim Reisinger, Dr. Carl Crane and Dr. Roger Tran-Son-Tay. The author is also indebted to Izmir Institute of Technology, which provided the scholarship and support. ii

PAGE 3

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii KEY TO SYMBOLS v ABSTRACT vi CHAPTERS 1 INTRODUCTION 1 2 CVTs 3 CVT Types 5 Electronic Controls and Integrated Power Train Management 12 Modern-Day CVTs and Metal Belt Drives 16 Electronic Control Strategies 20 3 CVTs vs CVPSTs 22 Evolution of CVTs 22 4 DYNAMICS OF CVTs 27 Basics 27 Four Possible Configurations with a Planetary Gear Train 29 Summary of the Possible Configurations 35 Power Recirculation Configurations 38 Power Split (PS) vs Power Recirculation (PR) 40 Proposed Design 42 Dynamics of the Proposed Design 45 Special Cases 51 Crossovers : 52 Torque Relations 53 Torque Ratios and Diagrams 57 iii

PAGE 4

5 OPTIMIZATION AND ANALYSIS OF RECIRCULATING POWER 66 With Reverse Gear 66 No Reverse Gear 77 6 THE MODELING OF THE PROPOSED TRANSMISSION 78 Modeling 79 7 CONCLUSIONS 90 REFERENCES 92 BIOGRAPHICAL SKETCH 94 iv

PAGE 5

TABLE OF VARIABLES D : Damping, K : Structural Stiffness, r : Radius of a Gear, Rcr : Recirculation Composite Ratio, (T^ I x%) (rg / rn), Rpr : Recirculation Planet Ratio, rs / r4, Rf : Recirculation Rim Ratio, rs / r4, Rv : First CVU ratio, ri/r2. Rps : Split Planet Ratio, Rs : Split Rim Ratio, rie / r^, Rvs: Split (Second) CVU Ratio, rig/rp, 0) : Angular Velocity, V : Linear Velocity. Subcripts a : Arm, p: Planet, r: Rim, s: Sun.

PAGE 6

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosoph OPTIMIZATION AND ANALYSIS OF A HYBRID CONTINUOUSLY VARIABLE POWER SPLIT TRANSMISSION By Serhan Ozdemir December 1999 Chairman: John Schueller Major Department: Mechanical Engineering Department Automotive transmissions match the speed and torque of the power source to the speed and torque requirements of the load. Properly designed continuously variable transmissions (CVTs) have shown promise to improve efficiency and performance. This work analyzes some existing CVTs and proposes a new hybrid continuously variable power split transmission (CVPST). The speed and torque relationships are analyzed in power split and power recirculation mechanisms. The problem of geared neutral phenomenon with recirculating transmissions are identified. A new CVPST transmission incorporating power split and power recirculation is proposed and analyzed. Optimization of the transmission to minimize the circulating power is performed. vi

PAGE 7

CHAPTER 1 INTRODUCTION An automotive transmission is any device that is capable of matcliing the torque and speed of the input to the torque and speed requirements of the output member which drives the load. Transmissions have come a long way since their introduction into automobiles in the late 19th century. They have evolved, yielding to the demands of more powerful and more efficient engines. By itself, it is impossible to design a transmission, for it is a mechanism and is a vital member of a piece of machinery, in this case the automobile. Transmission and engine designs are intertwined. Contemporary transmissions are comprised of either mechanical, hydrostatic, or torque converter components, or a combination thereof. Mechanical transmission forms the basis of this work. Being the most efficient transmission makes it indispensable in cars and other machinery. In this work, a newly popular mechanism will be analyzed using various calculations. The first set of formulae, the dynamics of epicyclic gears, are specialized relations for any possible combination. Instead of using one generalized formula for epicyclic gears which is given as a ratio of differences in the gear speeds, and deriving new ones from the definition, the author preferred to derive relations in advance, ready to be used and compared, which simplifies the work to a degree. It has been shown that CVTs can be successfully used in small and medium cars. It has also been shown that a CVT mechanism may be improved when the transmission contains multiple power flow paths, which are optimized for a given range of vehicle 1 1

PAGE 8

2 speeds. The author hopes to enhance the performance of CVTs using power split methods. When a power spHt mechanism is combined with a CVT transmission, the new power split CVT has been proved to be not only a viable alternative to an ordinary CVT but also an improved version in performance (6, 16). The author believes that a combination of a power recirculation, power split, and a regular CVT mechanism in a transmission box would refine the acceleration characteristics of a vehicle and enable a car to move at creeping speeds, even zero vehicle speed with an inherent clutch, characteristic to a recirculation design. The objectives of the following work could be summarized as follows: 1 . Analysis of speed and torque in power split (PS), power recirculation (PR) mechanisms. 2. Proposal and analysis of a new transmission to incorporate PS and PR. 3. Optimization of this hybrid transmission to minimize the circulating power.

PAGE 9

CHAPTER 2 CVTs A continuously variable transmission (CVT) may allow an engine to run over a range of speeds and loads independent of the speed and torque requirements placed on the wheels by the vehicle and the driver. An engine can produce a broad range of torque at any speed demanded or a broad range of engine speeds for any given torque demand. For any given power demand, however, there is only a very narrow operating speed and torque window at which the engine is most efficient or where the trade-off between emissions and fuel consumption may be optimized. Because the CVT allows an engine to run at this most efficient point virtually independent of vehicle speed, a CVTequipped vehicle may yield substantial fuel economy benefits when compared to a conventional transmission offering only a limited number of input/output ratios. Acceleration performance of a CVT-equipped vehicle may likewise be optimized. The CVT can allow an engine to run at its maximum torque condition almost regardless of drive wheel speed. Because full engine torque may be produced all the time, the acceleration may be maximized. Alternatively, a vehicle equipped with a given engine and a CVT may achieve the same acceleration as an identical vehicle equipped with a higher output engine and a conventional transmission. A CVT is cost-effective not so much for its ability to improve the fiiel econom and performance of a given vehicle, but in its ability to optimize the fuel economy of a 3

PAGE 10

4 range of vehicles using the same transmission. It is shown (1) by computer simulation that there are potentially few if any differences in fuel economy between continuousl variable and an optimized, conventional fixed ratio, stepped transmission of equivalent ratio ranges. This conclusion assumes that the comparison is between transmissions of equal efficiency and that the gear ratios for each transmission are optimized such that the 0 to 60 mph acceleration performance of the vehicles with either transmission is optimized and identical. Further it assumes that emissions performance of both vehicles can be made identical with no impact on fuel economy. Practically speaking, these assumptions likely make the analysis insensitive to the differences between stepped ratio and continuously variable transmissions. Simulations by others have shown that CVTs may in fact result in fuel economy improvements in cases where stepped ratio transmissions provide little or no fuel consumption advantages. The manufacturing and cost advantage of the CVT lies in the fact that its shift schedule and ratios can be much more easily optimized for a variety of vehicles than a conventional stepped transmission with fixed gear ratios. The real promise (4) of the CVT, then, is that a manufacturer's fleet may be optimized for performance and fuel economy with only a few models of CVT transmissions to handle different torque ranges or drive wheel location. This may be contrasted with the use of a large number of stepped ratio gearboxes where, at one extreme, it would potentially require one custom-tailored model of a fixed ratio stepped transmission for each engine/vehicle combination offered if a vehicle manufacturer were to optimizeevery vehicle produced. The introduction of CVTs, thus, offers new and invaluable features and various advantages.

PAGE 11

5 We may summarize these advantages as follows: 1 . Improved driveability and passenger comfort due to the lack of shifting and consequent uneven vehicle acceleration, 2. Improved vehicle performance (acceleration) and fuel economy. 3. Minimum manufacturing cost for a drive train. As engine and drivetrain controls evolve, the potential benefits of the CVT ma increase when compared to conventional fixed ratio, stepped transmissions. Electronic engine controls will allow variable engine emissions, fuel consumption and output characteristics such as those afforded by variable valve timing and air/fuel ratio control. Engine and transmission controls will become integrated such that the engine and transmission are treated as a single prime mover system. When this occurs, only a CVT can provide the precise, independent coupling of engine speed and torque output with drive wheel requirements which allow an optimized combination of performance, fuel comsumption, and emissions. CVT TYPES There are five basic concepts on which extensive modem-day continuousl variable transmission developments have been or are currently based . 1. Belt Drive (5, 6, 7, 8), 2. Hydrostatic Pump/ Motor Combinations (II), 3. Friction /Traction Drive (3), 4. Variable Stroke (4), 5. Gear Type (2).

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6 Other concepts which have proved (4) not as popular such as engine/generator motor sets, hydrokinetic converters, magnetic, hydrauHc, or mechanical drag have been examined through the years. Many of those which achieved some level of production in passenger cars have been the forerunners of modern CVTs. Others have continued to be developed and have found new applications in industrial drives. Still others have been developed for and/or are used in many types of wheeled vehicles from simple to complex machinery. Almost all of the CVT concepts have not found acceptance by modem passenger car manufacturers due to a variety of factors. When compared with conventional or other alternative transmissions, these concepts have fallen short in one or more of the following areas: 1 . Noise 2. Efficiency 3. Excessive weight 4. Cost 5. Drivability 6. Durability 7. Ease of control It is fair to say, however, that as new materials and analytical techniques are developed, some of these thus unsuccessful concepts may yet find passenger car applications. Indeed, passenger car manufacturers (1,4, 15, 16) worldwide are examining a variety of CVT technologies.

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Belt Drives 7 Belt drive transmissions have come a long way from the belt change gear or variable cone pulley transmissions. Belt drive CVTs are used as low-power industrial drives and light-duty vehicular applications such as snowmobiles, go-karts, and all-terrain vehicles. In recent low-power units, the belts are fabric-reinforced rubber running on steel pulleys. One half of each pulley is normally fixed to its shaft, while the other half slides axially on a spline. The input/output ratio is determined by the width of the pulleys. With a fixed-length belt, the pulley width determines the effective diameter of the pulley. A simple force balance control mechanism is used in many drives, including those for snowmobiles and other recreational vehicles. Normally held apart by a spring, the two halves of the driving pulley are forced together by a centrifugal mechanism as engine speeds increase. A corresponding spring in the driven pulley keeps its two halves closel spaced, resulting in a high input/output speed reduction and torque multiplication. As the rotating speed of the entire system increases, and the forces decrease, the mechanism in the driving pulley forces the two halves together. This causes the belt to ride radiall outward at an increased diameter, effectively increasing the working diameter of the driving pulley. Tension decreases in the belt as a result of the increased driving pulle diameter. The greater belt tension works against the spring and allowing the belt to move radially inward, effectively, reducing the working diameter of the driven pulley and the input/output torque ratio while increasing the speed ratio. Belt drives have their own shortcomings which must be overcome. The maximum torque which can be transmitted is limited by the strength of the belt and the coefficient of friction between the belt and the pulleys. Increasing the belt size in order to handle

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8 greater engine power also increases its mass. Heavier belts must use a portion of their tensile strength to overcome centrifugal force while generating adequate friction forces between the belt and its pulleys. Greater power levels may also be handled by splitting the torque between a number of sets of pulleys and belts. Hydrostatic Pump/Motor A hydrostatic transmission consists of a hydraulic pump connected to a hydraulic motor. As it is inefficient to throttle the hydraulic pressure in order to govern input and output characteristics, mechanical features are usually varied in order to change input/output torque. For hydrostatic units with variable displacement, input/output torque multiplication is determined b the ratio of pump to motor displacements. Speed ratio changes are accomplished by varying the displacement of the pump or motor. Hydrostatic transmissions have enjoyed a broad range of automotive and industrial applications. Successful automotive uses include agricultural and off-highway equipment where their durability, infinite variability, and smooth power-flow control afford the equipment operator excellent vehicle control. Despite all of the advantages of hydrostatic transmissions, their noise, cost, and efficiency have so far kept them from production passenger cars. Efficiency and packaging improvements can be obtained if a hydrostatic transmission is coupled with a mechanical gear set. Splitting the torque between the hydraulic and the mechanical units reduces the power carried by the hydrostatic module, and hence, the overall mechanical efficiency because the hydraulic power losses as a

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9 percentage of the total system power are reduced. Such a combination is called a hydromechanical transmission. In one version (4) of hydromechanical transmission, input power is mechanicall coupled to one side of a differential. Power input to the other side of the differential comes from a hydrostatic module which derives its power from the input shaft as well. The output of the transmission is taken from the center of the differential. In such an arrangement, the transmission output shaft speed is the average of the input shaft speed and the hydrostatic shaft speed as long as the hydrostatic CVT is transmitting some of the input power. If the output shaft of the hydrostatic unit is allowed to freewheel such that it can rotate backward and transmit no torque, the transmission output speed will be zero, with output torque due only to the parasitic drag of the hydrostatic system. Traction Drive Like the friction drive units used, modem traction drive transmissions transmit power through rolling contact. In some cases, modem traction drive development programs have copied the functional principles if not the precise configuration of the pioneer units. Traction drive transmissions (3, 4) have been used in the machine tool industry for a number of years. However, their potential to withstand high power outputs and the torque impulses typical of automotive drivetrains has been enhanced by advances in lubricant technology and the ability to use computer analysis to better understand the stresses on traction elements, thereby improving their design.

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10 Instead of relying on the dry friction between driving and driven members, the force is transmitted through the viscous shear of a thin film of special lubricant between the rolling contact surfaces. Unlike many lubricants, traction fluids greatly increase their viscosity under pressure, becoming almost glass-like under the high pressures present between the rolling elements of modem traction drive units. The tangential force which can be transmitted between the driving and the driven elements is greatly improved by the traction fluid, which also acts as a coolant and provides some protection against wear of the working surfaces. Traction drives offer the ability to continuously adjust input/output ratio with simple, highly efficient mechanisms. This ability is due to the fact that no teeth or other engagement devices are required to lock the driving and the driven elements together. As seen around the turn of the century, any mechanical configuration which will allow two different rotating members to adjust their effective working diameters may be considered as a potential traction transmission configuration. They can operate at very high surface speeds, thereby providing high input/output ratios with essentially no noise because of the continuous, smooth contact surfaces. In vehicular applications, where high-speed power sources such as gas turbines or inertial storage flywheels are being considered, this feature makes them very attractive primar speed reducers between the engine and a conventional automatic transmission. Their potential in such applications is further enhanced by the relatively low forces encountered at high speeds to transmit a relatively large amount of power.

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11 Figure 2.1. Conventional Traction Drive (3).

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12 Electronic Controls and Integrated Power Train Management For effective use of CVTs in auton:iobiles, electronic control of the transmission is necessary. The application of electronics to transmission control offers advantages in three areas. The advantages of an electronically-controlled CVT are reduced complexity, more precise and accurate control independent of operating conditions, and integration of engine and transmission system control, including adaptive control. Reduced Complexity The numbers of different control system parts required to match a given transmission to an engine and vehicle combination can be eliminated. Whereas several different valve bodies or control component parts may have been used fa each different power team, a single valve body may be used. The differences in control parameters can be programmed into memory chips for each vehicle. A multiplicity of mechanical parts is thus reduced to a single microchip for each make, model, and engine combination in which a given transmission is used. More Precise and Accurate Control Precision and accuracy are two distinct characteristics of control. A precise control is very repeatable. That is, it does the same thing every time. An accurate control is not only precise, but it does the correct thing every time. Mechanical and hydraulic transmission controls have been neither precise nor accurate. Variations from one mechanical part to another are inevitable. When mechanical devices are used as a computer, careful selective fitting of parts and final

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13 calibration of the assembly is required in order to achieve accurate operation. In highvolume production, such care is not cost-effective, and so variations in control parameters due to part-to-part variations have been tolerated in the past. To make matters worse, changes in operating conditions, particularly temperature, affect the dimensions of mechanical control systems and the viscosity of the control medium, the oil. These changes reduce the precision of the transmission, causing changes in performance and drivability as the vehicle warms up. Wear also has a similar effect. As a vehicle ages, mechanical controls become less accurate, and unless recalibrated, do not produce the same results as when first produced. Mechanical transmission controls will slowly allow a change in vehicle-to-engine speed and torque relationships as the control system components wear. Control precision and accuracy was not so important before fuel economy, emissions, and performance trade-offs became vital. Large variations in engine and transmission control parameters were tolerated and, to a large extent, went unnoticed b all but the most discerning drivers. As both fuel economy and emissions became more stringently regulated and as the public has demanded increased performance, more accurate control systems have been needed. Good fuel economy, high power output, and low emissions are sometimes mutually exclusive, and there is a fine operating line which must be followed to maximize all three. In addition, every vehicle produced must perform within acceptable regulatory limits throughout its life. Adaptive electronic controls with feedback loops compare the desired operation with the actual situation and make corrections in order to

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14 Stay on target, thus assuring both precise and accurate power train performance during the vehicle's lifetime. Integration of Engine and Transmission Control Only recently has the integration of transmission and engine control functions been considered. For a long time, the engine has been more or less a slave to the transmission and the driver. This slave has been limited in the way it could satisfy vehicle and driver requirements. With manual transmissions, engines at any given moment provided power at a fixed speed and torque, determined as a function of vehicle speed, throttle position, and transmission ratio. A demand for more power in any given gear could only be satisfied by increasing torque, because the engine speed was constrained by the gearbox. The torque converter in an automatic transmission provided some measure of increased flexibility, allowing both engine torque and speed to change in response to the driver's demand for more power. Still, however, the engine's ability to produce the required power was constrained somewhat by the fixed relationships of the gearsets and characteristics of the torque converter. Electronic controls combined with an appropriately flexible transmission allow the decoupling of engine speed from the torque delivered to the vehicle. When the engine may be allowed to provide the required torque at any speed, and vice versa, engine and transmission designers are free to optimize the response of the power train to demands of the driver and the vehicle operating conditions. Ultimately, this will be accomplished b removing any direct mechanical control link between the driver and the engine and/or

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15 transmission using so-called "fly-by-wire" systems. Perhaps the most exciting benefit of integrated power train control is the improvement in vehicle responsiveness to driver inputs. The response of the throttle and/or engine speed as a function of accelerator position can offer straight line, progressive, or degressive relationships. These relationships can be changed under predetermined conditions, by driver selection, or automatically by the sensing of road conditions, vehicle load, etc. On the production line, critical conditions which exist in one model but not in the next can be selectively programmed out with the same hardware. In the same vehicle, lugging conditions present when the vehicle is heavily loaded can be avoided, while that operating speed and load regime may be used under light-load conditions. The performance or economy settings now available on some transmissions can be expanded to include a continuum of settings between these extremes as a function of traction, vehicle payload, driver preference, driver type, etc. The differences which can be programmed into various settings may include the shift feel as well as the shift schedule. Transmission and engine controllers can be used to tailor an engine's output such that the life of a transmission may be increased. This would be the case when, for example, a particular transmission is to be used behind an engine with a maximum torque which exceeds that for which the transmission, under an ordinary control environment, would be capable of reliably handling. This is possible if the engine and transmission management system work together to avoid offering the transmission more torque than it can handle.

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16 Two factors make this possible: 1 . Tiie engine's maximum torque is produced under certain, well-defined conditions. 2. The torque capacity of the transmission and torque converter system at an given moment is a function of torque converter slip and transmission gear ratio. Modern Day CVTs and Metal Belt Drives Transmissions are one of the most expensive and important components of vehicles. Among the transmission types, CVTs offer an optimal way to change the gear ratio between a car engine and the wheels. But CVTs' appearance in today's transmissions is not by chance. New environmental mandates and (15) improved designs may help CVTs be an integral part of the new generation gear boxes. A continuously variable transmission is a stepless gearbox with an unlimited number of gear ratios. It is as old as the automobiles, and surprisingly, the first automobile was fitted with a rubber belt CVT. From then on, countless attempts have been made to equip cars with these automatic gear-change units. Their geared counterparts, however, whether manual or automatic, have taken over almost entirely the task of transmitting power and torque from the power source to the means of traction. Last century, repeated attempts were made (4) to refine conventional gearbox designs while automakers investing huge sums of money in the plants needed to massproduce them. Despite the undisputed ascendancy of the gearbox, CVTs are still around, and it is believed by some that CVTs will make a modest return to the machine with which it made its world debut.

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17 There are a couple of reasons that may make CVTs desirable. The fuel econom and the driving performance provided by the latest CVTs are in close proximity to today's complex and costly gearboxes, which in turn are believed to be at their practical and economical limits. Another factor is that the increasingly stringent governmental regulations regarding fuel comsumption and exhaust emissions are forcing auto engineers to consider the use of high-efficiency steady state engines designed to run in a limited engine speed, a perfect match for CVTs. In the long run, these environmental mandates are expected to force the development of hybrid drive vehicles using singlespeed power plants of various types, another highly suitable application for CVTs. A modern CVT consists of a multi-segment steel push belt that runs between a pair of variable-width pulleys, whose facing surfaces form shallow cones. The belt, which comprises hundreds of thin steel plates or elements held together by spring steel bands, rides in the V-grooves formed by the facing cone sides. Each pulley clamps down on the belt elements as they make their way around the circuit. The crankshaft-driven input pulley essentially pushes the stack of elements, which are loaded in compression, to the output pulley, causing it to turn. This push-belt configuration can transmit torques that could tear a conventional traction or "pull" belt to pieces. When a gear-ratio change is needed, the pulley cones are pushed together hydraulically, forcing the belt to ride farther out from the shaft, effectively increasing the pulley diameter. The result is a smooth gear-ratio change, an "infinite" number of "gears," and potentially a larger range of mechanical advantage.

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18 In spite of its relative obscurity, there are several indications that CVT technolog is growing in popularity. Today, there are more than a million Japanese and Europeanbuilt compact cars, using a technology licensed from a Dutch company (VDT). The key issue is fuel economy. Current cars are basically vehicles with small engine volume. These cars are meant to be convenient for the city and comfortable on the highway. Meanwhile, more advanced CVTs for larger automobiles are being developed by VDT and by German manufacturers. Two Chrysler Voyager minivans equipped with a new CVT design boasted (1) a 10 % fuel economy and improved acceleration performance in road tests. Perhaps the most impressive new application for these stepless transmissions is the CVT-driven Renault Formula One race car, which is powered by a 800-HP Renault V10 engine. In the mid-1960s, Dutch automotive researchers (1) investigated the development of more compact CVTs that could be coupled to higher-powered engines. After analysis, it was concluded that a metal belt CVT could attain higher power density values than traction drives could. In addition, when metal-push V-belts were compared to metal Vchains, the former came out on top. In the early 1 970s, VDT formed a design and test engineering group to develop CVT technology that could operate with larger engines, which meant developing a better drive belt, critical component of a CVT. Interestingly, the steel push belt was discovered by accident. The early design was composed of thin steel bands, which were so highly loaded by the pulleys that these steel bands eventually buckled. Later, steel bands were supported by movable blocks. These movable blocks, in turn, acted to transmit torque by pushing one another around the pulleys.

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19 The resulting push-block V-belt consisted of several thin, flat-tension bands of steel that connected the V-blocks. The sets of bands had a very narrow mutual tolerance to avoid friction. The blocks, which were from 3 to 6 mm thick, could move freely over the bands and pushed each other forward, thus transmitting torque. The bands were locked in the block elements with pins. Unfortunately, the high machining accuracies required for the contact surfaces made the push-block system expensive. The new V-element belt is an endless train of thin, trapezoid-shaped, metal plates, which are clamped in place with the axial force produced by hydraulic pressure on the pulley sheaves. The sum of the friction forces causes a pushing load in the stack of elements, which transmits the torque from the driving to the driven pulley. In the driven pulley, the pushing load is transformed into the output torque. The advantage of this is that it allows a very small pitch on the elements, which results in low noise. In the production of the belt, sheets of high fatigue strength steel are rolled into tubes and cut into loops in a slitting operation. The small loops are then stetched to size by rolling, whereupon the bands are annealed, closely calibrated, hardened to relieve internal stress, and then nitrided to harden the surface. Final measurement follows and the bands are combined into matched sets. The high tolerance elements are fabricated using techniques similar to those used to manufacture high-velocity gears or roller bearings. First the gear-steel elements are fineblanked to produce dimensional accuracies on the order of microns. Afterwards, they are hardened, deburred, and profile-shot blasted. At this point, they undergo a complicated sorting and selection process to match similarly dimensioned elements.

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20 The critical dimension is the height of the support where the bands run over. The inside surface is ground down because it is important to have a smooth surface for friction properties. All the elements must support the bands at the same time load distribution rate, or there will be local overloading. CVT control systems manipulate engine speed. The more independent relation between engine speed and vehicle speed in CVTs, compared with other transmission types, will make it possible to run the engine at more constant conditions or to follow the optimal path through changing driving conditions. The freedom to choose different relations between throttle position and engine speed provides the possibility of optimizing fuel consumption, emission levels, performance, and driving comfort. Electronic Control Strategies Modern control of the continuously variable transmissions require electronic control with sophisticated hardware and software engineering. CVTs offer a great deal of flexibility to the control engineer. The wide range of the shift map between the two extreme ratios could be used to correct tuning of the optimal control management. Therefore, CVTs also considerabl improve fuel economy in gasoline and diesel engines. Furthermore, higher-order electronic management provides even more possibilities for improvement. The general idea (1, 4) behind new electronic controls is to combine all subsystems influencing fuel consumption, and to activate them by the driver's desire for a particular degree of acceleration or deceleration. The system detects this desire from the movement and position of the accelerator pedal, both of which are converted into electrical signals.

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21 Using this data, the electronic control unit and appropriate software calculates the engine power and the best gear ratio required for the maneuver. Thanks to fuzzy logic control, the system can adapt the selection of gear ratios to a driver's style as well as current traffic and driving conditions. •

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CHAPTER 3 CVTs vs CVPSTs The modem day CVT concept is one of the latest attempts to improve a vehicle's performance. It also represents an optimum path among other transmission designs when many stipulations are imposed upon them such as fuel economy and acceleration performance. CVTs have been around for a long time but the implementation, understandably, has taken a couple of decades to ensure the further evolution of the idea. The next idea to follow CVTs has been the CVPSTs, or continuously variable power split transmissions. Evolution of CVTs Similar to CVTs, CVPSTs (continuously variable power split transmissions) are the next logical step further. CVPSTs have not only all the advantages of CVTs but also have the added capabilities. Unlike the regular CVTs, where power has only one route to follow, CVPSTs generally have two paths for the power flow. Dividing the power and running it through two separate lines allows the designer to acquire the optimum operating conditions at all speeds by changing the amount of power through each path. For example, torque splitting between the hydrostatic and the planetary gearsets significandy improves efficiency over a purely hydrostatic transmission. The ratio ranges of each module within the transmission were chosen so that under cruise conditions onl 22

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23 moderate torque multiplication by the hydrostatic modules was required. Most of the power was transmitted through the planetary gearset. Only when ratio changes need to be rapidly executed does the hydrostatic module transmit a significant fraction of the total power. Some of the CVTs are intended to be used as an overdrive gear applied to the conventional automatic. Within the limits of acceptable driveability and the fuel consumption characteristics of the engine, the CVT will allow engine speeds to be modulated under cruise conditions to achieve maximum fuel economy. By continuousl and smoothly changing the ratio, the CVT will maintain engine operation at the minimum fuel consumption point for any reasonable cruise or light-load condition. When low vehicle speeds or high rates of acceleration or steep hill-climbing capability is required, the conventional transmission will down-shift as usual to the required lower gear as the CVT changes to a 1:1 ratio. Since the intention of this chapter is to provide a basic introduction to both CVTs and CVPSTs, further characteristics will be shown in the following pages. The detailed torque and velocity analysis will be made in Chapter 4, along with the modeling in Chapter 6. In Figure 3. 1, a basic schematic is given regarding the differences of both systems. In Figure 3.2 and 3.3, two split path designs are shown.

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Transmission Differential < Engine < ^ (a) Transmission Differential 4 < < Engine < (b) Transmission Differential < < Engine ^ (c) Figure 3.1. Schematics of a (a) CVT, a (b) Split and a (c) Recirculation Design

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25 Continuously Variable Power-Split Transmission Single Stage Wheel Ring gear Sun gear Diff. Planet gear i-rClutch u Control gear Driving pulley Idler" ~t Wheel Countershaft gear Belt Driven pulley Engine Figure 3.2. Power Split Mechanism (7).

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26 Continuously Variable Transmission Power Recirculation With Gear Neuti^l Wheel EagnK Figure 3.3. Power Recirculation Mechanism (7).

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CHAPTER 4 THE DYNAMICS OF CVTS Basics A basic system of planetary gears consisting of a sun (central) gear, a rim (ring) gear, and an arm to which planet gears are connected. A planetary gear set is a two degree of freedom mechanism, and requires two inputs at any of its two members for the other to be determined. Planetary gear dynamics could be analyzed using traditional formulae based on the ratio of the velocity differences, or as later to be shown in this chapter, a new and simple way may be utilized. Rim (ring) gear Planet Arm Sun Figure 4.1. A Planetary Gear Set, Side View. 27

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28 A rim gear can be internal, and a planet gear acts as an intermediate element between the sun and the rim gears. In Figures 4. 1 and 4.2, two views of a planetary set are shown, and the legend regarding the radii are indicated. As can be seen from Figure 4.2, all the radii are related. The angular speed and all the torque relationships are based on the combinations of ratios of these radii. Figure 4.2. Planetary Gear Set, Front View The geometrical relationship among the gears can be expressed as follows: ra = Arm radius, = ring gear radius, rp = planet radius, rs = sun radius. For the arm, and for the rim. Ta = + Tp fr = Ts + 2r, P(4.1) (4.2)

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29 Four Possible Configurations with a Planetary Gear Train Characteristic to planetary gears, two input speeds always have to be specified. When two of its members are used to input motion, either of the two remaining elements may be used as an output gear. With this, we come up with four distinct possibilities, or configurations. Configuration 1 Input: Sun and rim gears Output: Arm Figure 4. 3. a. Velocity Profile, Configuration 1.

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30 The velocity profile of configuration 1 is shown in figures 4.3.a and 4.3. b. In figure 4.3. a velocities are drawn on the planet gear itself, and the interaction of the inputs b the sun and the rim gears become obvious. When the circumferantial velocity vector on the rim gear and the velocity vector on the sun are drawn on the planet, Figure 4.3.b, the circumferantial speed of the arm can be found by a ruler or an expression below. Figure 4.3.b. Velocity Profile. Va= (Vr + V,)/2 COa = (COs . fs + COr . rr ) / 2 ra (4.3) (4.4) whereas. Vr Vs (Or . Tr CDs . Ts (Op= = . (4.5) 2 rp 2 rp

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31 In the velocity profile above, Figure 4.3.b, the rectangular section (a) represents the translational motion of the planet gear. The triangular (b) section, on the other hand, corresponds to the rotational motion of the planet gear. Configuration 2 Input : Arm and sun gear Output : Rim gear Figure 4.4.a. Velocity Profile. Where Va = ( V, + V, ) / 2 (4.6) or. Vr = 2 V, V, (4.7)

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32 Figure 4.4.b. Velocity Profile (Or = and. (Da . Ta (Oi . Ts (Or = (4.8) (4.9) Velocity profiles regarding configuration 2 can be seen in Figures 4.4a and 4.4b. It should be noticed that in the velocity profile, the direction of the angular velocities of both arm and sun are taken positive (cw).

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33 Configuration 3 Input: Arm and rim gear Output: Sun gear Figure 4.5. Velocity Profile. 2 (Oa Ta COr . rr COs = (4.10) C0p= (4.11) •"p It should be noted that, as in configuration 2, the output speed is given as the difference of two input speeds . Figure 4.5 shows a detailed velocity profile.

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34 Configuration 4 This configuration is about an unlikely case where motion is input through arm and planet gear, and output through either of the two remaining gears. ^ Vp Figure 4.6. Velocity Profile as the Summation of Two Cases As was the case before, inputs speeds maybe divided into its components. The input through the arm represents a uniform translational motion, whereas the planet gear assumes a pure rotational motion. This is depicted in figure 4.6. Here, the output speeds could be formulated similar to previous derivations. (Oa . Ta + (Op . rp (Or = (4.12) Wa . ra (Op . rp (Os = (4.13)

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35 Summary of the Possible Configurations With the cases given on the previous pages, the possible configurations can be viewed summarily below in table 4.1. The column on the left designates the entry of an two members, whereas the top line shows the output members. For example, when the sun and the arm are taken to be input elements, we immediately dismiss sun and arm as output members since the "s" and "a" columns contain "N" which states that for this combination, sun and arm are not available for output. One of the remaining rim and planet might be used to transfer power. Table 4. 1 . Configuration Chart. S=Sun Gear, A=Arm, R=Rim Gear, P=Planet, N=Not. o U T P U T I S A R P N s N P A N U R N T P N Power Split Configurations As briefly mentioned in chapter 3, the proposed design has combined a split and a recirculation mechanism together. In a split gear set, the power is split in two, and while part of the power runs through the CVU unit, the other part carries it along the gear-togear path, i.e. through the sun gear. A split and a recirculation mechanisms are originall

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36 the same, except an idler gear, whose sole function is to transmit power. In the presence of an idler gear, the sun and rim gears turn in the same direction, which is shown in Figure 4.7a. The sun and the rim gears turning in the same direction in the configuration below ensures that there is no circulating power and the power is split in a straightforward manner. The clutch seen between the back of the rim and the counter gear allows the controller to transmit power on demand. Clutch CVU : Continuously Variable Unit, Belt Drive Idler Gear Figure 4.7a. A Power Split Gear Set.

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37 The formula without the idler: (l>a = CDs . Ts COr . Tr 2r. The idler gear changes the direction of the rim gear thus, -(-cor) (Os . + (Or . rr 2r. (4.14) (4.15) Output Input Figure 4.7b. Another Power Split Configuration.

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38 This configuration could have been a recirculation system with an idler. The lack of an idler gear causes the arm to turn opposite in direction to sun, thus 2 (Oa . Ta + (Os . rs (Or = (4.16) Power Recirculation Configurations The examples of power recirculation configurations are the same as split design except the existence of an idler gear. The lack of an idler gear causes the rim gear to turn opposite in direction to the sun gear, thus creating an equation of [ 1_ Figure 4. 8a. Power Recirculation Configuration.

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39 subtraction rather than addition as in the split design. Figure 4.8 shows a recirculation mechanism where power is fed into the system along the sun and the rim gears, and the output is taken from the arm. The arm angular velocity is given by: cOs . rs dir. Tr 2ra (4.17) In a different design below, this time the existence of an idler causes an equation of subtraction. The reason for this is that the configuration shown in figure 4.8.b. has an inherent minus sign imbedded in the equation of output speed. Thus the existence of an idler gear ensures that the sun and the arm both have the same direction of rotation. ^ Output Input n Figure 4.8b. Power Recirculation Configuration.

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40 The output speed could be formulated as follows: 2 (Oa . Ta CDs . Ts (4.18) Power Split (PS) vs Power Recirculation (PR) Table 4.2, the advantages and the disadvantages of both mechanisms are summarized. Unfortunately, none of the systems is well-suited by itself for automobile applications. The recirculation mode offers multiple good features for better control and efficiency. For example, with the recirculation feature, it is possible to hold the car stationary simply by changing the ratios, or to achieve reverse and forward gears. Recirculation mode allows zero or near zero speeds. However, as will be shown in later chapters, the zero speed condition is called geared neutral and requires an accurate control CVU ratio. It is also known as the nervous state, since small variations in CVU ratio causes great changes in torque values that are imposed on the gears. Calculations have shown that at points close to this nervous state, internal torques may reach values that are many times the input torque. Split mode offers alternative ways of improving the vehicle handling. Even though it is not possible to achieve zero speeds with this mode, it is possible to acquire high speeds, a characteristic of the split design.

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41 Table 4.2. Comparison of Two Systems. FEATURES POWER SPUT POWER RECIRCULATION WELL SUITED TO START-UP AND OVERCOMING INERTL\L FORCES NO YES HAS A BUE.T-IN CLUTCH (GEARED NEUTRAL) NO YES REVERSE GEAR POSSIBLE NO YES COMPARATIVELY HIGH SPEED YES NO SLOWER FORWARD GEARS NO YES LIMITED RANGE OF SPEED YES NO GEARS GET OVERLOADED NO YES

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42 Proposed Design The following hybrid PS-PR gearbox has been intended to contain the advantages of both modes of power split mechanisms. It has four distinguishable gears, one being the reverse gear. The reverse and the drive 1 are governed by power recirculation equations. In this mode, the vehicle can back up, achieve the so-called "geared neutral" phenomenon, and set the vehicle in forward motion. At a designated speed, which might be called first-crossover, the motor vehicle switches to drive 2, or split mode. This mode allows the driver to achieve quicker acceleration, and to acquire relatively higher speeds. In this mode, all of the power is carried through system's two belt units. The lessening of torques at high speeds permit the running of torques along continuously variable units. This feature is the key to rapid acceleration. Further down the road, at even higher speeds, a third drive has been provided. At a second designated speed, another switch occurs. This shift from drive 2 to drive 3 might be called the second-crossover. In this mode, to take advantage of ever-smaller torques, and to eliminate the inertia of masses of rotating gears, the path is now a single line, and no power split is needed. The proposed design, as shown in Figure 4.9, is the combination of a recirculation and a split design. The power is input into the system from the right lower corner of the picture and output from the upper left corner. The design contains two CVUs or two belts, and is composed of three stages. In each stage, the power follows a different path, in accordance with the control and the vehicle speed. The caption explains the symbols in the figure.

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43 13 1 1 OUT C2 HI12 14 CVU C4 17 18a 15 HH C3 10 16 CI C5 18 C7 IN 3 C6 la CVU Figure 4.9. The Proposed Design. CI..C7 : Clutches; CVU: Continuously Variable Units;!, 2, 17, 18: Variable Pulleys; 3, 4.. 15, 16 : Gears

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44 General Layout Table The Table 4.3. shows the management of the transmission, and which clutches to be activated to switch to a certain mode. As it is clear from the table below, the reverse and the drive 1 have both the same clutch configuration. This is to say that at lower speeds, the reverse and the drive 1 use the same clutch group, whereas the split (drive 2), and the high speed gear (drive 3 ) use different paths and different clutch logic. Table 4.3. General Layout Table CI C2 C3 C4 C5 C6 C7 Reverse ON ON Drive 1 ON ON Drive 2 ON ON ON Drive 3 ON ON ON Neutral

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45 Dynamics of the Proposed Design Velocity Analysis This section establishes a kinematic relationship between the various elements of the proposed transmission. Recirculation Mode. Reverse and Driye 1 In Figure 4. 10, power flow path has been shown with a thicker line to emphasize and demonstrate the path. The angular speed calculations are facilitated by the prederived equations earlier this chapter. In this mode, the angular velocity of the gear 7 may be defined as follows: (1)5 . rs (1)4 . r4 CO7 = (4.19) where T-! = (r.s + r4 ) / 2 (4.20) 0>s = Win . R. •v> (4.21) where Rv = ri / T2 (4.22)

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46 11 OUT C2 13 12 14 cvu C4 17 15 18a HH U C3 10 16 CI C5 18 HH C7 IN 3 C6 la CVU Figure 4.10. Recirculation Mode Power Flow Path.

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47 0)4 = (Oin Rr, where Rr = r;, / r4 cOou, = ci>7 . (r7 / rs ) . (r9 / rn) (4.23) (4.24) (4.25) (Rv . Rpr Rr ) 0>7 = (An (1 + Rpr) where, (4.26) Rpr = r
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48 Figure 4. 1 1 depicts for a given set of variables the change of input and output speeds with respect to each other. It should be noted that at lower CVU ratios, the output speed gets smaller compared to the input speed. Split (Drive 2) Mode In this case, the output speed can be stated as follows : CDu . ri4 + C0|3 . ri3 (Oout= where, (4.30) 2rn rii = ( ri3 + ri4)/2 (4.31) C0i3 = CO5 . R, where =(ri6/ ri3 ) (4.32), (4.33) C0i4 = 0)4 . Rvs, where Rvs = ( ris / rp ) (4.34), (4.35a) 0)5 = coin . Rv, CO4 = coin . Rrs , where Rrs = ( ria/ riga ) (4.35b) (Din . Rrs • Rvs • r|4 + COjp • Ry Rs • fis Wout = or. (4.36) 2.[(r,3 + r,4)/2] 0)in • ( Rrs • Rvs • Rps + Rv Rs ) COoul = (4.37) ( 1 + Rps )

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49 p-i 13 OUT C2 12 14 15 C4 4f cvu 17 18a HH C3 10 16 9 CI C5 i 18 NH 3 C6 la IN cvu Figure 4. 12. Drive 2 Power Flow Diagram. t

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50 Drive 3 rn 13 11 OUT C2 12 14 cvu C4 4f 17 15 HH C3 10 16 18a CI C5 18 IN 3 C6 la CVU Figure 4.13. Drive 3 Power Flow Diagram.

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51 In the last drive, as depicted in Figure 4. 1 3 the power flows through the two existing belt drives. Here, the output speed is simply two CVU ratios times the input speed, namely (Oout = COin . Rv • Rvs, (4.38) where Rv = ( ri / r2 ), and Rvs= (rn/r.s) (4.39) Special Cases It should be noted from the recirculation formulae that at certain speeds, some ratios become critical. To determine those critical speeds and conditions, a further analysis is needed. Recirculation Mode Reverse Gear: Rv . Rpr Rr > 0 (4.40a) Geared Neutral: Rv . Rpr Rr = 0 (4.40b) Drive 1 Rv . Rpr Rr < 0 (4.40c)

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52 Crossovers Crossovers represent the passage from one mode to the other. Since there are no synchronizers to equilize the speeds at various points of contact, a careful control of speeds prove essential. First Crossover First crossover is the transition from recirculation mode to split mode. At this point, for a smooth passage, the output speed of the transmission has to be the same at the end of the recirculation mode and at the start of the split mode. c«>out-rec = cObut-split, or (4.41) CObut-rec = (Din . Rcr . ( Rv Rpr Rr ) / ( 1 + Rpr ) (4-42) COin . ( Rr • Rvs • Rps + Rv • Rs ) CObul-split = (4.43) ( 1 + Rps ) Second Crossover Second crossover occurs when it is switched from drive 2 to drive 3, in a similar way utilized above. COin • ( Rr • Rvs • Rps + Rv Rs ) tOout-split = = COout = COin • Rv • Rvs(4.44) (1 + Rps )

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53 Torque Relations In the derivation of the following torque relations, three classes of equations are needed. The speed ratio ( (1)2 / coi ) of the pair, which is clearly defined for each and any possible case above. There are various design methods, and one can be seen in (14). Input output power relations (9, 12), as T, . 0)i + Tj . 0^ + Tk . cok = 0 (4.45) Figure 4. 14. Three Element Diagram. This equation holds in the absence of losses, and is nothing more than the preservation of energy. In all of the calculations. Figure 4.14 is used. And finally, T + Tj + Tk = 0. (4.46) The above equation holds when the links are at rest, or when rotating at uniform speed. After some algebraic manipulations through the equations 4.45 and 4.46, the equations presented below can be obtained.

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54 Recirculation Mode (CObut/ COin)= Rcr.(Rv.Rpr-Rr) / (1 + Rpr ) ( Ti„/Tou,)= Rcr.(Rv.Rpr-Rr) / ( 1 + Rpr ) (4.47a) ( Tgear / T,„ ) = R^ / ( Rv • Rpr " Rr ) (4.47b) A positive ratio would indicate that the vehicle is in reverse gear. ( Tcvu / Tin ) = Rv . Rpr / ( Rv . Rpr Rr ) (4.47c) ( Tgear/ Tou, ) = Rr/ (1 + Rpr) (4.47d) ( Tcvu / Tou, ) = Rv . Rpr / ( 1 + Rpr ) (4.47e) ( Tgear/ Tcvu ) = Rr / (Rv. Rpr) (4.47f) Split Mode ( COcut / CCn ) = ( Rrs . Rvs Rps + Rv • Rs ) / ( 1 + Rps ) ( T,n / To„, ) = ( R„ . Rvs . Rps + Rv . Rs ) / ( 1 + Rps ) (4.48a) ( Tcvul/ Tn ) = ( Rv . Rs ) / ( Rr. . Rvs . Rps + Rv . Rs ) (4.48b)

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55 ( Tcvu2 / Tin ) = ( Rrs • Rvs • Rps ) / ( Rfs • Rvs • Rps + Rv • Rs ) (4.48c) (Tcvul/Tou,) = (Rv.Rs)/ (1+Rps) (4.48d) ( Tcvu2 / Tout ) ( Rrs • Rvs • Rps ) / ( 1 + Rps ) (4.48e) ( Tcvul / Tcvu2 ) ( Rv • Rs ) / (Rrs • Rvs • Rps )• (4.48f) Wout / W 0.9 1.2 1.5 1.8 Second CVU 2.1 Figure 4. 15. Split Mode. Rrs = 0.347 (+) First, ( . ) Second, and (x) Third Variations.

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56 In Figure 4.15, different control strategies have been implemented. In Figure 4.15, the ratio of the first belt is kept constant(+), as for the second variation ( . ), the first CVU ratio is determined as the square root of the ratio of the second CVU. In the third variation (x), ratios have been kept equal. It is clear from these figures that the output speeds get progressively larger from the first variation towards the third. The third variation may be taken as an overdrive at around a CVU ratio of 2. 1 . First variation, allows a faster output speed with respect to any specified input speed. Drive 3 A similar method could be utilized to determine the response of the system when different control strategies are imposed. Figure 4. 16. Drive Three. Rv (First CVU) = .5

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57 In Figure 4. 1 6 again similar to the control strategy done in split mode, the first CVU ratio is kept constant. In the second variation, varied as the square root of the second CVU ratio, and finally, in the third variation, CVU ratios are made equal. However second and third variations have shown that these two are not practical. In these regimes, output speed reached many times the input speed, thus are not drawn. The above diagrams were drawn using the first equation below. ( (Oout / (0,n ) = Rv . Rvs ( T,n/Tou,)= Rv.Rvs (4.49) Torque Ratios and Diagrams Recirculation Mode Figure 4. 17a. Output Torque with Respect to Input Torque. R, = .347, Rpr = .6

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58 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (Rv) CVU Ratio Figure 4.17b. Gear Torque with Respect to Input Torque. 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (Rv) CVU Ratio Figure 4. 17c. The CVU Torque with Respect to Input Torque.

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59 Q 25 Tgear / Tput 0.2 0.15 0.1 0.05 0 0.9 1.05 1.2 1.5 1.8 2.1 2.4 2.7 First (Rv) CVU Ratio Figure 4 Aid. Gear Torque with Respect to Output Torque. Figure 4.17a shows a Hnear relationship of input and output torques with respect to CVU ratio. In the next one, Figure 4. 1 7b, it is seen that the torque carried by the gear is getting smaller with respect to the input torque. The CVU load also depicts a similar trend in Figure 4. 17c. One thing should be clear that at a given CVU ratio, for this configuration, the load carried by the CVU is larger than the gear load. Figure 4.17d, the gear load remains constant throughout the range of the CVU, in Figure 4.17e, the load of the CVU linearly changes with respect to the output torque. The Figure 4. 17f shows a rather desired effect where as the vehicle speeds up and from low CVU ratios gear to CVU ratio gets smaller. However, the fact that the ratio is less than unity at slower speeds is not a desired effect, due to the fact that this would mean a larger load on the belt drive than on the gear.

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60 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 First (Rv) CVU Ratio Figure 4.17e. CVU Torque with Respect to Output Torque. gear ' > cvu 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (Rv) CVU Ratio Figure 4. 17f. Gear Torque with Respect to CVU Torque.

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61 Split Mode Here, in the same way as in finding the charts for angular speed ratios, to find torque relations, again the first CVU ratio is modified in three different cases called variations. In Figure 4.18a, when it is switched to split mode, at the moment of switch, if it is 0.9 for example, then the output torque is approximately twice the input torque. And the relationship varies linearly as CVU ratio increases. For this variation, the first CVU ratio is kept constant. As for the second variation where first CVU ratio is the square root of the second. In the third variation where ratios are held equal, the torque ratio takes on at approximately the same range to well over 0.8, in this case 1.1. This sudden increase of output torque, given the sufficent engine power, might give a relatively good acceleration. Since the graphs of variations on the speeds are the same as on torques, and are given in Figure 4.15, they are not repeated here once again. The next one, Figure 4. 1 8b, puts on a gradual decrease of the ratio of CVU torque to the input torque, towards the end of the range of the CVU. The second CVU, Figure 4. 1 8c, however, presents a tendency to increase from well below 0.3 to slightly over 0.5. Second belt, thus, assumes more and more load as the vehicle speeds up. Figure 4. 18d shows that there is no mathematical relationship between the output load and the load on the first CVU. For the data used to chart the graphs, the ratio remains slightly above 0.3. The Figures 4. ISe and 4. 18f demonstrate the torque ratios of second belt drive with respect to output and first belt torques.

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62 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Second (Rvs) CVU Ratio Figure 4.18a. Split Mode. Rv = 0.9

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63 _ „ _ Tcvu 1 / Tout 0.35 0.9 1.2 1.5 1.8 2.1 2.4 2.7 First (Rv) CVU Ratio Figure 4. 1 8d. Split Mode, Tcvui-vs-Tom -

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64 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Second (Rvs) CVU Ratio Figure 4.18e. Split Mode, Tcvu2-vs-Tout. 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 Second (Rvs) CVU Ratio Figure 4. 18f. Split Mode, Tcvui-vs-Tcvu2-

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65 Drive 3 Control strategies represent various options of accelerations. For the first variation, only the second belt drive ratio is varied. For such a condition, in Figure 4.19, the input torque remains large at all times. Since this mode is used solely for high speeds, this is only to be expected. The relationship between these two torque values change in a linear fashion. 2.1 2.3 2.5 2.7 2.9 3.1 Second (R^s) CVU Ratio Figure 4.19. Drive Three. Rv = 0.5.

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CHAPTER 5 OPTIMIZATION AND ANALYSIS OF RECIRCULATING POWER In this chapter, the effects of the recirculating power will be discussed. Since reverse gear is the byproduct of recirculation mode, it is also logical to discard this mode altogether if all the excessive torques and accurate control are to be avoided. Thus, the first section deals with the option of having the reverse gear, and a related analysis, and the last section discusses effects if the reverse gear is desired to be avoided. With Reverse Gear The geared neutral point can be found from 0, or. If Rvgn is the value that Rv assumes at geared neutral, then pr • (5.1) 66

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67 The ratio of torque through gear to CVT was given in Chapter 4 as Tg / Tev, = Rr / (Rv. Rpr). (5-2) At slower speeds, Tg is expected to be larger than Tcvu, and gradually, Tcvu should increase while the vehicle is speeding up. Tg / Tcvt = Rt. Rt > 1 when Rv is small Rt < 1 when Ry is large. Substituting (5.1) in (5.2), at the start, Tg / Tcvu = Rt > 1 or, Rt = ( Rvgn / Rvstart ) > 1 or, Rvgn = Rt • Rvstart (5.3) If, initially, we want the torque running through the gear twice the torque through the CVT, then.

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68 = 2 . Rysiart . What (4) says can be depicted by a diagram : (5.4) Gear Forward -> G.N. Reverse Low High Rv Figure 5.1. The Location of the GN Point. In words, the geared neutral has to take place at higher CVT ratios, and further the reverse gear can be attained. A typical (Tg / Tin) or (Tcvu / Tin) curve has two parts. 0.7 0.75 0.8 0.85 0.9 0.95 1.00 1.05 1.1 1.15 1.2 1.25 1.3 CVU Ratio Geared Neutral at 1 Figure 5.2. Excessive Torques Near Point GN.

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69 First part of the curve can be seen to go asymptoticly to infinity having x = Rvgn , whereas the other portion of the curve goes to infinity in the other direction. In the example below, geared neutral is reached when Rv attains the value of 1. When CVU ratio reaches the 75-80 % of GN value, the torque ratio demonstrates a sudden jump, which must be avoided. The reverse gear ratio, similarly, should be placed as far away from GN as possible. The Effects of the Position of the Geared Neutral Point The idea that initially a large portion of the power should be carried through the gear mandates that the location of the geared neutral point be placed at a larger CVU ratio. However, this positioning comes at a price. An analysis would be helpful to disclose the characteristics of two possible cases. 1 . Geared neutral (GN) placed at a lower CVU ratio 2. GN placed at a larger CVU ratio 1)Rt < 1 The above expression reveals that the reverse gear should be deployed at the lowest CVU ratio, then the GN point and finally forward regime. The characteristic curve is:

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70 0.7 0.75 as aas 0.9 0.95' 1.00 1.05 1.1 1.15 1.20 125 1.3 Rtst(R,)C\/UFfetio Geared ^fe(iral at 1 Figure 5.3. Effects of the Location of GN. Since the parameters given above has influence on Tg/ Tin, Tcvu / T,n and Tg/ Tcvu, it would be easy to see the effects by drawing these diagrams with numerical values. 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (Rv) CVU Ratio Figure 5.4. GN on the Left.

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71 The Tg / Tin diagram shows that at first the gear load is almost twice the input torque. However, the next diagram depicts a down side to case 1 . CVT torque assumes even a larger percentage at a given CVU ratio, which is clear in the last chart, where Tg / Tcvt never comes close to 1, or even above. Throughout the figures given in this chapter, it is clear that close to the geared neutral point, internal torques reach many times either in or output torques. In Figure 5.2, close to the geared neutral point, the gear load becomes 60 to infinity times the input load. This should mean that after a certain point at the loading, a break would occur. Even at a safe distance, at a CVU ratio of 0.9, Figure 5.4, the gear load descends from around 2.0, and below.

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72 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 First (Rv) CVU Ratio Figure 5.6. Tg-vs-Tcvu2) Rt > 1 Here, the reverse gear is to be placed at the largest CVU value, and the vehicle ma start at the lowest speed possible. Tg/Tin 0.5 0.6 0.7 0.8 0.90.98 1.02 1.1 1.2 1.3 1.4 1.5 1.6 First (Rv) CVU Ratio Geared Neutral at 1 Figure 5.7. Tg-vs-Ti,

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73 First (Rv) CVU Ratio Geared Neutral at 2.4 Figure 5.8.Tg-vs-Ti 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (Rv) CVU Ratio Geared Neutral at 2.4 Figure 5.9. Tcvu-vs-Tin.

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74 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 First (Rv) CVU Ratio Geared Neutral at 2.4 Figure 5.10. Tg-vs-T cvuFigure 5.6 shows that when Rt < 1, gear to CVU ratio starts at around 0.65. When this value is above the unity, the vehicle can start at the lowest speed possible. In Figure 5.8, the ratio of gear load to input torque displays a tendency to increase. In this dramatic increase, gear load jumps from twice the value of input torque to 25 times of it. Figure 5.9, also shows a similar rise, this time for the CVU. Figure 5.10 shows that the gear loads decreases with respect to CVU load as the CVU ratio increases. Tcvt/ Tin was expected to go up with respect to CVU ratio, and it does. But Tg/ Tin goes up with the ratio, which we would not like it to happen. In both diagrams, it is clear that for a given numerical set of values, after the CVU ratio of 1 .5, torque ratios become already too high.

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75 The Direction of the Power Flow The following discussion and figures explain the power recirculation phenomena in the transmission. The direction of power could simply be determined by an algebraic equation: Rv . Rpr Rr > 0 A B Figure 5. 11. Positive Circulation At point A, P, cvt gear • AtB, P, cvt = p, gear + Pin. Rv . Rp, Rr < 0 A B Out —4 In Figure 5.12. Negative Circulation.

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76 After crossing the geared neutral point, the inequality changes sign and the major carrier hence becomes the gear itself. At point A, Pgear = Pout + Pcvt At point B, Pgear = Pcvt + Pin • The Ways of Reducing the Circulating Power If the CVT is to be taken as the main carrier of torque in forward mode, which means that Rt < 1 , this places the geared neutral point on the left on a Tcvt Tjn diagram. In such a case, Tcvt / Tin, Tg / Tin decreases, as CVU ratio increases. But Tg / Tcvt opens up at ratios that are less than or equal to unity. It is essential to set the operating points away from the vertical G.N. asymptote b a safety margin. For Rj < 1 case, a start should be made at least 20 % more than the CVU ratio that G.N. occurs. On the following chart , geared neutral takes place at 1 . As can be seen, even at around a CVU ratio of 1 .2, which gives us a margin of 20 %, one of the two possible paths could carry multiple times the input torque. However it is clear that such a margin cut should be optimized itself. For every cut would limit the ver precious working range of CVTs.

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77 60 50 40 30 20 10 0.5 0.6 0.7 0.8 0.9 0.98 1.02 1.1 1.2 1.3 1.4 1.5 1.6 First (Rv) CVU Ratio Figure 5.13. Tg-vs-Tjn . No Reverse Gear Having a reverse and a forward gear, and the geared neutral case, unfortunately, comes at a price. The necessity to stay away from the neighborhood of geared neutral point loses the transmission some of its operating ranges. It is possible, nevertheless, to skip the reverse gear and to shift the GN further away from the feasible working range of CVT. To achieve reverse gear option, an additional gear and a clutch, or any other auxiliary system will be needed. Two advantages may be obtained with the removal of reverse phase from the recirculation mode: 1 . Getting rid of the unstable transition zone, 2. Retrieving the valuable working range otherwise lost.

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CHAPTER 6 THE MODELING OF THE PROPOSED TRANSMISSION A complete understanding of the transmission would only be possible through a detailed work on the proposed transmission. For the development and implementation of control laws, and the utilization of computer simulation, modeling of the transmission is required. Optimization of current systems is divided into two major categories: 1 . Economy Mode, 2. Performance Mode. In the economy mode, the vehicle operates in accordance with the least fuel consumption curves. It is possible to create an engine operating map based on the experimental data for the specific engine in question. Since the whole operation range of the vehicle can be roughly divided into two, the economy and the performance modes, it is possible to run the engine at a specified regime, or a default operating system, then switch to the other regime whenever there is a need for the vehicle or the computer to comply with the current state of driver or road needs. In the performance mode, the major parameter is the differential output torque, which determines the amount of acceleration with respect to the vehicle mass. As later to be seen, the path to achieve a maximum torque is not always obvious without some indepth analysis. For all the main shafts below, a structural stiffness and a damping have been attributed. A typical shaft is modeled as shown below where the stiffness and 78

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79 damping elements are connected in parallel. Rotational masses have been lumped to point loads and designated by Ij (5). K, Di Figure 6. 1 .A Modeling Unit. Modelin Recirculation By excluding the engine output shaft stiffness, damping and viscous damping, and simply referring transmission input torque as Tin , the CVU input puUe and shaft acceleration is given as a function of the state of the clutch C6: C6 is slipping a, = ( T,n Rv . Td4 Tp Tc6 D3 . co, ) . ( 1 / 1 ) (6.1) C6 is locked-up a, = (T,n Rv . Td4 Tp T4 . Rr D3 . CO, D, .(O4 . Rr ) / ( 1 + 3 • Rr ) (6.2) where,

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80 Figure 6.2. Modeling of the Recirculation Unit.

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81 Td4 = ( K4 . 04 + D4 . ( 0), . Rv Oh ) ) (6-3) The angular acceleration of the second pulley of the CVU could be described as follows: a. = ( Td4 Td6 CO2 . D5 ) . ( 1 / 12 ) (^-'^^ where, Td6 = K6 . I ( o>2 o>; ) dt + D6 . ( 0)2 CDs ) (6-5) Similarly, the angular acceleration of the shaft of the gear 4 depends on the two possible positions of the clutch 6. When slipping, a partial torque transmittal occurs and this transmittal is in turn a function of the slip. Slipping of C6 04= (Tc6/Rr T4 -Dr.o)4).( I/I3) (6-6) and for the lock-up, 04 = Rr . tti (6.7) ag = ( T7 Td7 ) .( r7 / rg ) . (1 / 14 ) (6.8)

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82 To find T7, a simple derivation would be needed: a>7 = { 0)5 . rs (1)4 . r4 ) / ( 2 ) where. (O4 = CO5 . Rr / Rv thus, 0>7 = 0)5 ( fs fr . Rr / Rv ) / ( Ts + Tr ) SO that. T7 = Td6 . ( Rv . ( Rpr + 1 ) / ( Rv . Rpr Rr ) ) Also with T4 = Td6 / Rpr and. Td7 = K7 J ( CO9 0)8 ) dt + D7 ( 0)9 0)8 ) cx„ut = ( Td7 • ( ri 1 / ) Ds . O)out ) • ( 1 / Is )

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83 Split Mode C6 is slipping = ( T,n Rv . Td4 Tp Tc6 D3 . CO, ) . ( 1 / 1 ) (6.14) C6 is locked-up tti = (TinRv .TD4-Tp-T4.Rrs D3.CO, -Dr.CO4.Rrs) /( '+ 3 • ^rsM (6-15) where, Td4 = ( K4 . 04 + D4 . ( CO, . Rv CO2 ) ) (6.16) Slipping of C6 CX4 = ( Tc6 / Rrs Td9 . Rvs Dr . con ) . ( 1 / I3 ) (6-17) and for the lock-up, 0(4 = Rrs.ai (618) The angular acceleration of the second pulley of the CVU could be described as follows: CX2 = ( To4 Td5 CO2 . D5 ) . ( 1 / 12 ), where (6.19)

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84 Is 11 OUT 4/7777 D8 II, 12 14 ll3 15 HH C3 16 K,o,D 10 C4 Dr CVU 18a 17 tl7 K9,D9 IB . 18 C7 la 2 '^Ds K4,D4 IN CVU Figure 6.3.Modeling of the Split Unit.

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85 Td5 = Ks . J ( 0)2 0)5 ) dt + D5 . ( 0)2 0)5 ) (6.20) a,3 = (TD5.(r,3/r,6) T^)/ ( 13) (^-^l) To find the torque T,3, a similar expression which was carried out in recirculation mode is needed. ax,ui = ( 0)i4 . ri4 + 0)13 • ri3 ) / (2 rout ) (^-^^^ 0)14 = 0)in . Rrs • Rvs ^^'^^^ 0)13 = o)in Rv . Rs or, (6.24) 0)14 = 0)13 . Rrvs (^-^^^ where R,vs = Rrs . Rvs / Rv .Rs (6-24) cOou, = ( 0)13 • Rrvs • ri4 + 0)13 • ) / 2 rou, (6.25) rou. = ( ri3 + r,4 ) / 2 (6.26) 0)but = 0)13 ( Rrvs • Rps + 1 ) / (Rps + 1 ) or, (6.27)

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86 T,3 = Tou, ( Rrvs . Rps + 1 ) / (Rps + 1 ) With the above expression, ocoui = (Tii Tout cooui . Dg ) / Is 0Ci7 = ( Td9 Dii . 0)17 Tdio ) / In where Tdio = Kio . J ( 0)17 0)14 ) dt + Dio . ( 0)17 0)|4 ) When clutches C2 and C4 are fully locked, ai7 = ai4 and, O)oui = 0)14 ( Rrvs • Rps + 1 ) / Rrvs -(Rps + 1 ) Or, T|4 = Tout ( Rrvs • Rps + 1 ) / Rrvs • (Rps + 1)

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87 Drive 3 Drive 3 differs in that it does not have a split path. All the power is channelled along the successive belt drives. The angular acceleration on the first sheave is: a, = (TinRv .Td4-Tp) /( I ) where, (6.35) Td4 = ( K4 . 04 + D4 . ( 0), . Rv 0)2 ) ) (6-36) The acceleration of the second sheave : OC2 = ( Td4 tth • D5 Td9 • Rvs).(l/Ii8) (6-37) where Td9 = K9 . 09 + D9 . ( 0)2 . Rs 0)17 ) (6-38) ai7 = (TD9 0)i7.D,, Tdio)/ n (6-39) where Td9 = K9 J ( 0)2 0)i7 ) dt + D9 ( 0)2 0)i7 ) (6.40)

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88 11 /7777 Dg cvu 17 C2, C4 K9, D9 I Hi Dn I18 D5 J 1 18 K4. D4 1 . IN CVU Figure 6.4. Modeling of Drive 3.

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89 and Tdio = K,o J ( (On C0but)dt + DgCcop cObut ) (6-41) Provided that clutches C2 and C4 are on. Finally, Oorn = ( Tdio Dg . cObu, ) / 8 (6.42)

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CHAPTER 7 CONCLUSIONS This dissertation first described CVTs and then provided a general overview of CVTs. CVTs have been compared and their compatibility has been discussed. The incentive behind the CVT concept was dealt with, and the reasons were explained. In chapter 4, first, a new way of calculation of planetary gears were presented, and with the introduction of recirculation and split designs, the speed and torque entities were given. This dissertation proffered a possible way of improving the CVT performance in the form of a new CVPST design. This new design was proven to be a better design than the conventional CVTs in load carrying capacity. However, the new improved design has also brought a few setbacks such as added complexity and weight. The proposed design consisted of three distinct paths for the power to flow. Each path was designed to optimize the vehicle performance at various phases of the motion. The recirculation mechanism had the ability to reach a very specific ratio characteristic to the system, when the vehicle could remain stationar even though the tires of the vehicle are tightly connected to the engine. This mode has considerable virtues that might not be ignored for automobiles. The salient features of the recirculation mode were the possibility of attaining the reverse, forward and neutral gears as well as slow speeds that would allow a car to help overcome the inertial loads. 90

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91 The split mode offered top speeds while the system had two paths to ease torques that were run through the belt drive. In the final mode, however, the power was run through the two successive belt drives. Two belts showed that a faster acceleration was possible. In this work, it was shown that, theoretically, it is possible to incorporate the three separate modes, recirculation, split and a plain CVT, into one single transmission unit, and prove by the speed formulae that, by computer control for example, it is also possible to shift from one mode to another seamlessly at designated switching points. Unfortunately, the greatest obstacle proved to be the power recirculation in the recirculation mode. Since this power build-up is characteristic to the recirculation mode, it seems that it is not possible to eliminate it completely. However, as shown in chapter 5, by truncation of the working range of CVTs, this power build-up was considerably reduced, further away from the geared neutral (G.N.) point. Understanding and designing such a system will require a working model of the transmission at a scale, to observe whether the formulae presented in this dissertation can predict exact failing points of gears, or even whether they will hold at all. Future of a CVPST will be dictated by various factors, such as how well this transmission can be optimized in weight, performance and recirculating power and the trend of consumer demand for acceleration, price and economy of a vehicle equipped with a CVPST.

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REFERENCES 1 . Ashley, S. "Is CVT the car Transmission of the Future?", Mechanical Engineering, pp 64-68, Nov. 1994. 2. Dooner, D., Yoon, H-D., Seireg, A. "Kinematic Consideration for Reducing the Circulating Power Effects in Gear-Type CVTs", Proc. Instn. Mech. Engrs., vol.212, pp 463-478, part D, 1998. 3. Fel, L. "Development of the Ball Toroidal Continuously Variable Transmission", 1 998 Earthmoving Industry Conference and Exposition, Peoria, IL April 1998. 4. Gott, P. "Changing of Gears", SAE Historical Series, Warrandale PA, 1 99 1 . 5. Hanachi. S. "A Study of the Dynamics of a Split Torque, Geared Neutral Transmission", Journal of Mechanical Design, vol.1 12, pp 261-270, Sept. 1990. 6 Mucino, V.H. "A Continuously Variable Power Split Transmission for Automobile Applications", SAE Paper No 970687, pp 75-80, 1997. 7. Mucino, V.H. "A Double Planetary Gear Train CVT Transmission with Multiple Applications", SAE Paper No 950094, pp 1-10, 1995. 8. Mucino, V.H. "Parametric Modeling and Analysis of a Planetary Gear-CVT Mechanism", SAE Paper No 940519, pp 1 13-123, 1994. 9. Pennestri, E. "A systematic Approach to Power-Flow and Static-Force Analysis in Epicyclic Spur-Gear Trains", Journal of Mechanical Design, vol.1 15, pp 639-644, 1993. 10. Pennestri, E. "The Mechanical Efficiency of Epicyclic Gear Trains", Journal of Mechanical Design, vol.1 15, pp 645-651, 1993. 11. Rydberg, K. "Hydrostatic Drives in Heavy Mobile Machinery", lOP Congress and Exposition, Milwaukee, WI, Sept. 1998. 92

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93 12. Saggere, L. "A simplified Approach for Force and Power-Flow Analysis of Compund Epicyclic Spur-Gears Trains", Advances in Design Automation, vol.2, pp 83-89, 1992. 13. Takiyama, T. "Simultaneous Control for Optimization of Fuel Consumption", Transactions of the Japan Society of Mechanical Engineers, pp 386-391, Jan 1996. 14. Tian, L. "Matrix System for the Analysis of Planetary Transmissions", Journal of Mechanical Design, vol 1 19, pp 333-337, 1997. 15. Wu, G. "Optimal Control of the Vehicular Powertrain with a CVT", SAE Paper No 973281, pp 47-51, 1997. 16. Vahapzadeh, H.. Linzell, M. "Modeling, Simulation, and Control Implenientation for a Split-Torque, Geared Neutral, Infinitely Variable Transmission", SAE Paper No 910409, pp 21-32, 1991.

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BIOGRAPHICAL SKETCH The author was born in Ankara, Turkey, on December 23, 1968. He earned a degree in mechanical engineering from the Dokuz Eylul University at Izmir. He worked before and after graduation as an assistant engineer on elevator maintenance and the control of plastic injection machines at an engineering workshop. In 1993, he won a scholarship in United States for graduate studies. After two years, he earned a master of engineering degree at Illinois Institute of Technology, in Chicago. The author plans to return to his homeland and continue his work at a university starting as a research assistant. 94

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is folly adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. John K. Schueller, Chairman Associate Professor of Mechanical Engineering I certify that I have read this sfody and that in my opinion it conforms to acceptable standards of scholarly presentation and is folly adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Carl D. Crane III, Professor of Mechanical Engineering 1 certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is folly adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Kim D. Reisinger, Assistant Professor of Mechanical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is folly adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ali Seireg Professor of Mechanical Engineering

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Roger Tran-Son-Tay Professor of Aerospace Epgmeenng, Mechanics and Engineering Science This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 1999 M. J. Ohanian Dean, College of Engineering Winfi-ed M. Phillips Dean, Graduate School