23-03-2011, 03:09 PM
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INTRODUCTION
The primary function of a transmission is to transmit mechanical power from a
power source to some form of useful output device. Since the invention of the internal
combustion engine, it has been the goal of transmission designers to develop more
efficient methods of coupling the output of an engine to a load while allowing the engine
to operate in its most efficient or highest power range. Conventional transmissions allow
for the selection of discrete gear ratios, thus limiting the engine to providing maximum
power or efficiency for limited ranges of output speed. Because the engine is forced to
modulate its speed to provide continuously variable output from the transmission to the
load, it operates much of the time in low power and low efficiency regimes. A
continuously variable transmission (CVT) is a type of transmission, however, that allows
an infinitely variable ratio change within a finite range, thereby allowing the engine to
continuously operate in its most efficient or highest performance range, while the
transmission provides a continuously variable output to the load.
The development of modern CVTs has generally focused on friction driven
devices, such as those commonly used in off-road recreational vehicles, and recently in
some automobiles. While these devices allow for the selection of a continuous range of
transmission ratios, they are inherently inefficient. The reliance on friction to transmit
power from the power source to the load is a source of power loss because some slipping
is possible. This slipping is also a major contributor to wear, which occurs in these
devices.
To overcome the limitations inherent in the current CVT embodiments employing
friction, a conceptual, continuously variable, positive engagement embodiment has been
proposed for investigation at Brigham Young University. This concept proposes utilizing
constantly engaged gears which transmit power without relying on friction. Because the
proposed embodiment is new, no engineering analysis has yet been performed to
determine its kinematic and meshing characteristics, an understanding of which are
necessary to validate the proposed concept as a viable embodiment. This research will
investigate both the kinematic and meshing characteristics of this and related concepts.
The objective of this research is also to analyze the family of positive engagement
CVTs. Although the CVT embodiment that has been proposed for investigation is new,
other embodiments belonging to this family have been developed and published. The
embodiments in this family do not rely on friction based power transmission. All
embodiments in this family, however, have been based on overcoming a distinct problem
which manifests itself seemingly regardless of the embodiment and will hereafter be
referred to as the non-integer tooth problem. This research describes the nature of the
non-integer tooth problem and details the occurrence of the problem in the proposed
concept, as well as three published embodiments, and details solutions to the non-integer
tooth problem as embodied in the three published embodiments. The presentation of
some published solutions to the non-integer tooth problem clarifies the nature of the noninteger
tooth problem, as well as aids in the development of characteristics of a general
solution to the non-integer tooth problem applying to all members of the positive
engagement CVT family.
BACKGROUND
Continuously variable transmissions have been in use for many years. Near the
beginning of the twentieth century, cars like the Sturtevant, Cartercar, and Lambert
featured friction dependent CVTs (Puttré, 1991). These friction drive CVTs were
common in automotive use until engines capable of producing higher torques became
common and necessitated the move to geared, fixed-ratio transmissions capable of high
torque transfer and having better wear characteristics than friction dependent CVTs.
Only in the past few years, with the advent of advanced materials and technology, have
friction dependent CVTs returned to commercial application in the automotive industry.
To provide a foundation and motivation for the research presented, this chapter
first presents a definition of a continuously variable transmission. For background
purposes, a review of the current literature on CVTs is included. The families in which
various embodiments can be classified are presented, along with a description of the
operating principles in each family. A new family of embodiments of the positive
engagement classification is also presented, along with the principles governing this new
classification. This research focuses most heavily on embodiments in the final
classification.
DEFINITION AND TERMINOLOGY
A transmission is a device which allows the transmission of power from a rotating
power source to a rotating load. Conventional transmissions allow for the selection of
discrete gear ratios, thus limiting the engine to providing maximum power or efficiency
for limited ranges of transmission output speed. A continuously variable transmission,
however, is a type of transmission that allows an infinitely variable ratio change within a
finite range, thereby allowing the engine to continuously operate in its most efficient or
highest performance range.
Beachley and Frank, 1979, present a sub-classification of the continuously
variable transmission called the infinitely variable transmission (IVT). While the two
terms are often used interchangeably, there is a distinct difference between them. While
a CVT allows an infinitely variable ratio change within a finite range, an IVT must be
capable of producing an output speed of zero for any input speed, thus giving an infinite
speed ratio.
CVT CLASSIFICATIONS
There are several classifications of CVTs. The following five are most relevant to
the current research: hydrostatic, friction, traction, variable geometry, and electric.
HYDROSTATIC
Hydrostatic transmissions are commonly used in off-road vehicles and
agricultural machinery. Many commercial riding lawn mowers commonly employ
hydrostatic transmissions in their drivetrains. These transmissions use high-pressure oil,
commonly at pressures up to 5000 psi, to transmit power. They are composed of a
hydraulic pump and hydraulic motor (see Figure 2.1), which are connected by hydraulic
lines (not labeled in Figure 2.1). The hydraulic pump, which is generally driven by the
engine, provides power to the hydraulic motor, in the form of high-pressure fluid. The
hydraulic motor, in turn, converts the hydraulic power into mechanical power, which is
transferred to a load.
The continuously variable nature of this transmission comes in the ability of the
hydraulic pump to adjust the pressure and flow of hydraulic fluid that it supplies to the
hydraulic motor by changing its displacement. Hydrostatic transmissions will almost
always have a ratio range of infinity, i.e., be IVT’s. This is accomplished because the
stroke of the pump can be varied from zero to its maximum. Also, because the stroke of
the pump can generally be reversed, the hydraulic motor can have both positive and
negative rotation, thus providing forward and reverse rotations of the output.
An advantage of the hydrostatic transmission is the ability that it has to transmit
high torque from the input to the output, which allows for its application in a wide range
of devices. This is enhanced by the ability hydrostatic transmissions have for precise
speed control. One major disadvantage of hydrostatic CVTs is their moderate efficiency
(between 60 and 80%), which offsets the efficiency gains of allowing the engine to
operate in its most efficient regime.
FRICTION
The friction CVT is one of the most common forms of CVTs in use today. These
CVTs are characterized by the use of friction to transmit power. Traction drives use a
form of friction to transmit power, but are classified separately and will be discussed
later. In the friction CVT family, there are several different embodiments. These include
rubber V-belts, metallic V-belts, flat rubber belts and chain drives.
The common characteristic of the V-belt drives is the use of a drive and driven
sheave, each with variable diameters. The effective diameter of the sheave is adjusted by
varying the distance between the two halves of the sheave (see Figure 2.2). Each sheave
consists of one mobile and one stationary half, and the two sheaves are positioned at a
fixed center distance. As the halves of the sheave move together, the belt is forced up to
a larger diameter on the sheave. As the halves of the sheave move apart, the belt returns
to a smaller diameter. The ability to continuously vary the diameter of the drive and
driven sheaves allows for a continuously varying transmission ratio.
The sheave diameters can be varied in several ways, depending on the type of
control desired and the ratio range needed. Figure 2.3 shows a common CVT used in
snowmobile and ATV applications. It consists of two sheaves, referred to as the driver or
primary clutch, and the driven or secondary clutch, and a composite v-belt. In this
application, the control of the CVT is automatic. The primary clutch is actuated by
engine rotation, using centrifugal force on flyweights that produce an axial force on the
mobile half of the sheave, causing it to move toward the stationary half of the sheave.
The secondary sheave is referred to as a torque sensing sheave, and is spring loaded to
maintain proper belt tension.
Rubber V-belt CVTs are also commonly used in machine tools. The control in
this case, however, is a mechanical system that determines the spacing of the two halves
of one of the sheaves. Because the belt length remains constant, the second pulley must
be spring loaded, allowing it to adjust automatically.
It is common for slipping to occur in both rubber V-belt CVT applications
presented. This is because the driving force is transmitted through friction between the
sides of the V-belt and the inside surfaces of the sheaves. While this negatively affects
efficiency, it can have a positive safety effect in machine tools, especially when the
machine becomes overloaded.
An advantage of the rubber v-belt CVT is the high ratio range that it can provide,
as well as the ability for automatic speed control, which is what makes it so desirable for
use in ATVs where an expensive control system is not desirable. Some disadvantages of
this type of CVT are its low torque capability and the significant wear that develops due
to belt slipping. This wear inhibits the ability of the CVT to shift ratios properly. Belt
slipping also contributes to the moderate efficiency of the device, which is usually
between 70% and 80%.
Another common belt-type CVT is the metal push belt CVT. This belt driven
CVT is different from the previously mentioned rubber belt versions in that power is
transmitted through the belt by way of compression. The first company to commercially
develop this concept was Van Doorne Transmisse. This metal push belt CVT can
transmit more force, and therefore is better suited to the automotive industry. Figure 2.4
shows the XTRONIC CVT, developed by Nissan, which employs a metal push belt.
The construction of the metal push belt is shown in Figure 2.5. The belt consists
of thin, high-strength, segmented steel blocks that are held together by stacked bands of
steel. The bands are stacked into slots on both sides of the blocks, and help maintain the
shape of the belt as it passes through the sheaves. Kluger and Fussner, 1997, stated that
the load path is dependent on the complex interaction and friction between the bands and
block slots, the adjacent blocks, and the block sidewalls and the faces of the sheaves.
The advantage of the metal push belt over the rubber v-belt is its ability to
transmit higher torque, usually up to 350 N-m, which, as stated previously, makes it more
useful in higher torque situations, like in automobiles. It is also more efficient - between
80% and 90% - than the rubber v-belt, due to the reduced amount of slipping that it
allows. A disadvantage of the metal push belt CVT is the high contact stresses in the
sheaves, which requires special materials and special controls to minimize belt slip,
which would otherwise rapidly wear the sheaves.
A third type of friction CVT is the flat belt CVT. Kluger and Fussner, 1997, state
that flat belts are more efficient for transmitting power because more of the allowable belt
tension can be used for transmitting power rather than producing belt to sheave forces.
Developed originally by Kumm Industries, the flat belt CVT is composed of a flat
elastomer belt and two pulleys. The two pulleys are composed of two guideway discs on
each side. These guideway discs have logarithmic spiral guideway slots which support
the ends of the belt drive elements. The set of guideways in one disc have clockwise
curvature and the slots in the opposing disc have counterclockwise curvature
Actuation and control of the flat belt CVT is accomplished by means of a
hydraulic actuator in each of the two pulleys. This actuator rotates the inner set of discs
of each pulley relative to the outer set of discs. This causes the belt drive elements to be
positioned at a desired diameter (see Figure 2.7). Pressure is set in the hydraulic actuator
to generate the required belt tension at the desired speed ratio.
INTRODUCTION
The primary function of a transmission is to transmit mechanical power from a
power source to some form of useful output device. Since the invention of the internal
combustion engine, it has been the goal of transmission designers to develop more
efficient methods of coupling the output of an engine to a load while allowing the engine
to operate in its most efficient or highest power range. Conventional transmissions allow
for the selection of discrete gear ratios, thus limiting the engine to providing maximum
power or efficiency for limited ranges of output speed. Because the engine is forced to
modulate its speed to provide continuously variable output from the transmission to the
load, it operates much of the time in low power and low efficiency regimes. A
continuously variable transmission (CVT) is a type of transmission, however, that allows
an infinitely variable ratio change within a finite range, thereby allowing the engine to
continuously operate in its most efficient or highest performance range, while the
transmission provides a continuously variable output to the load.
The development of modern CVTs has generally focused on friction driven
devices, such as those commonly used in off-road recreational vehicles, and recently in
some automobiles. While these devices allow for the selection of a continuous range of
transmission ratios, they are inherently inefficient. The reliance on friction to transmit
power from the power source to the load is a source of power loss because some slipping
is possible. This slipping is also a major contributor to wear, which occurs in these
devices.
To overcome the limitations inherent in the current CVT embodiments employing
friction, a conceptual, continuously variable, positive engagement embodiment has been
proposed for investigation at Brigham Young University. This concept proposes utilizing
constantly engaged gears which transmit power without relying on friction. Because the
proposed embodiment is new, no engineering analysis has yet been performed to
determine its kinematic and meshing characteristics, an understanding of which are
necessary to validate the proposed concept as a viable embodiment. This research will
investigate both the kinematic and meshing characteristics of this and related concepts.
The objective of this research is also to analyze the family of positive engagement
CVTs. Although the CVT embodiment that has been proposed for investigation is new,
other embodiments belonging to this family have been developed and published. The
embodiments in this family do not rely on friction based power transmission. All
embodiments in this family, however, have been based on overcoming a distinct problem
which manifests itself seemingly regardless of the embodiment and will hereafter be
referred to as the non-integer tooth problem. This research describes the nature of the
non-integer tooth problem and details the occurrence of the problem in the proposed
concept, as well as three published embodiments, and details solutions to the non-integer
tooth problem as embodied in the three published embodiments. The presentation of
some published solutions to the non-integer tooth problem clarifies the nature of the noninteger
tooth problem, as well as aids in the development of characteristics of a general
solution to the non-integer tooth problem applying to all members of the positive
engagement CVT family.
BACKGROUND
Continuously variable transmissions have been in use for many years. Near the
beginning of the twentieth century, cars like the Sturtevant, Cartercar, and Lambert
featured friction dependent CVTs (Puttré, 1991). These friction drive CVTs were
common in automotive use until engines capable of producing higher torques became
common and necessitated the move to geared, fixed-ratio transmissions capable of high
torque transfer and having better wear characteristics than friction dependent CVTs.
Only in the past few years, with the advent of advanced materials and technology, have
friction dependent CVTs returned to commercial application in the automotive industry.
To provide a foundation and motivation for the research presented, this chapter
first presents a definition of a continuously variable transmission. For background
purposes, a review of the current literature on CVTs is included. The families in which
various embodiments can be classified are presented, along with a description of the
operating principles in each family. A new family of embodiments of the positive
engagement classification is also presented, along with the principles governing this new
classification. This research focuses most heavily on embodiments in the final
classification.
DEFINITION AND TERMINOLOGY
A transmission is a device which allows the transmission of power from a rotating
power source to a rotating load. Conventional transmissions allow for the selection of
discrete gear ratios, thus limiting the engine to providing maximum power or efficiency
for limited ranges of transmission output speed. A continuously variable transmission,
however, is a type of transmission that allows an infinitely variable ratio change within a
finite range, thereby allowing the engine to continuously operate in its most efficient or
highest performance range.
Beachley and Frank, 1979, present a sub-classification of the continuously
variable transmission called the infinitely variable transmission (IVT). While the two
terms are often used interchangeably, there is a distinct difference between them. While
a CVT allows an infinitely variable ratio change within a finite range, an IVT must be
capable of producing an output speed of zero for any input speed, thus giving an infinite
speed ratio.
CVT CLASSIFICATIONS
There are several classifications of CVTs. The following five are most relevant to
the current research: hydrostatic, friction, traction, variable geometry, and electric.
HYDROSTATIC
Hydrostatic transmissions are commonly used in off-road vehicles and
agricultural machinery. Many commercial riding lawn mowers commonly employ
hydrostatic transmissions in their drivetrains. These transmissions use high-pressure oil,
commonly at pressures up to 5000 psi, to transmit power. They are composed of a
hydraulic pump and hydraulic motor (see Figure 2.1), which are connected by hydraulic
lines (not labeled in Figure 2.1). The hydraulic pump, which is generally driven by the
engine, provides power to the hydraulic motor, in the form of high-pressure fluid. The
hydraulic motor, in turn, converts the hydraulic power into mechanical power, which is
transferred to a load.
The continuously variable nature of this transmission comes in the ability of the
hydraulic pump to adjust the pressure and flow of hydraulic fluid that it supplies to the
hydraulic motor by changing its displacement. Hydrostatic transmissions will almost
always have a ratio range of infinity, i.e., be IVT’s. This is accomplished because the
stroke of the pump can be varied from zero to its maximum. Also, because the stroke of
the pump can generally be reversed, the hydraulic motor can have both positive and
negative rotation, thus providing forward and reverse rotations of the output.
An advantage of the hydrostatic transmission is the ability that it has to transmit
high torque from the input to the output, which allows for its application in a wide range
of devices. This is enhanced by the ability hydrostatic transmissions have for precise
speed control. One major disadvantage of hydrostatic CVTs is their moderate efficiency
(between 60 and 80%), which offsets the efficiency gains of allowing the engine to
operate in its most efficient regime.
FRICTION
The friction CVT is one of the most common forms of CVTs in use today. These
CVTs are characterized by the use of friction to transmit power. Traction drives use a
form of friction to transmit power, but are classified separately and will be discussed
later. In the friction CVT family, there are several different embodiments. These include
rubber V-belts, metallic V-belts, flat rubber belts and chain drives.
The common characteristic of the V-belt drives is the use of a drive and driven
sheave, each with variable diameters. The effective diameter of the sheave is adjusted by
varying the distance between the two halves of the sheave (see Figure 2.2). Each sheave
consists of one mobile and one stationary half, and the two sheaves are positioned at a
fixed center distance. As the halves of the sheave move together, the belt is forced up to
a larger diameter on the sheave. As the halves of the sheave move apart, the belt returns
to a smaller diameter. The ability to continuously vary the diameter of the drive and
driven sheaves allows for a continuously varying transmission ratio.
The sheave diameters can be varied in several ways, depending on the type of
control desired and the ratio range needed. Figure 2.3 shows a common CVT used in
snowmobile and ATV applications. It consists of two sheaves, referred to as the driver or
primary clutch, and the driven or secondary clutch, and a composite v-belt. In this
application, the control of the CVT is automatic. The primary clutch is actuated by
engine rotation, using centrifugal force on flyweights that produce an axial force on the
mobile half of the sheave, causing it to move toward the stationary half of the sheave.
The secondary sheave is referred to as a torque sensing sheave, and is spring loaded to
maintain proper belt tension.
Rubber V-belt CVTs are also commonly used in machine tools. The control in
this case, however, is a mechanical system that determines the spacing of the two halves
of one of the sheaves. Because the belt length remains constant, the second pulley must
be spring loaded, allowing it to adjust automatically.
It is common for slipping to occur in both rubber V-belt CVT applications
presented. This is because the driving force is transmitted through friction between the
sides of the V-belt and the inside surfaces of the sheaves. While this negatively affects
efficiency, it can have a positive safety effect in machine tools, especially when the
machine becomes overloaded.
An advantage of the rubber v-belt CVT is the high ratio range that it can provide,
as well as the ability for automatic speed control, which is what makes it so desirable for
use in ATVs where an expensive control system is not desirable. Some disadvantages of
this type of CVT are its low torque capability and the significant wear that develops due
to belt slipping. This wear inhibits the ability of the CVT to shift ratios properly. Belt
slipping also contributes to the moderate efficiency of the device, which is usually
between 70% and 80%.
Another common belt-type CVT is the metal push belt CVT. This belt driven
CVT is different from the previously mentioned rubber belt versions in that power is
transmitted through the belt by way of compression. The first company to commercially
develop this concept was Van Doorne Transmisse. This metal push belt CVT can
transmit more force, and therefore is better suited to the automotive industry. Figure 2.4
shows the XTRONIC CVT, developed by Nissan, which employs a metal push belt.
The construction of the metal push belt is shown in Figure 2.5. The belt consists
of thin, high-strength, segmented steel blocks that are held together by stacked bands of
steel. The bands are stacked into slots on both sides of the blocks, and help maintain the
shape of the belt as it passes through the sheaves. Kluger and Fussner, 1997, stated that
the load path is dependent on the complex interaction and friction between the bands and
block slots, the adjacent blocks, and the block sidewalls and the faces of the sheaves.
The advantage of the metal push belt over the rubber v-belt is its ability to
transmit higher torque, usually up to 350 N-m, which, as stated previously, makes it more
useful in higher torque situations, like in automobiles. It is also more efficient - between
80% and 90% - than the rubber v-belt, due to the reduced amount of slipping that it
allows. A disadvantage of the metal push belt CVT is the high contact stresses in the
sheaves, which requires special materials and special controls to minimize belt slip,
which would otherwise rapidly wear the sheaves.
A third type of friction CVT is the flat belt CVT. Kluger and Fussner, 1997, state
that flat belts are more efficient for transmitting power because more of the allowable belt
tension can be used for transmitting power rather than producing belt to sheave forces.
Developed originally by Kumm Industries, the flat belt CVT is composed of a flat
elastomer belt and two pulleys. The two pulleys are composed of two guideway discs on
each side. These guideway discs have logarithmic spiral guideway slots which support
the ends of the belt drive elements. The set of guideways in one disc have clockwise
curvature and the slots in the opposing disc have counterclockwise curvature
Actuation and control of the flat belt CVT is accomplished by means of a
hydraulic actuator in each of the two pulleys. This actuator rotates the inner set of discs
of each pulley relative to the outer set of discs. This causes the belt drive elements to be
positioned at a desired diameter (see Figure 2.7). Pressure is set in the hydraulic actuator
to generate the required belt tension at the desired speed ratio.
